# Best science & math books according to redditors

We found 24,037 Reddit comments discussing the best science & math books. We ranked the 8,905 resulting products by number of redditors who mentioned them. Here are the top 20.

### 1. The Demon-Haunted World: Science as a Candle in the Dark

239 mentions

Great product!

Read comments from redditors### 2. How to Prove It: A Structured Approach, 2nd Edition

119 mentions

Cambridge University Press

Read comments from redditors### 3. A Universe from Nothing: Why There Is Something Rather than Nothing

106 mentions

Atria Books

Read comments from redditors### 5. The Greatest Show on Earth: The Evidence for Evolution

71 mentions

Bestselling Author of "The God Delusion".

Read comments from redditors### 7. The Origin of Consciousness in the Breakdown of the Bicameral Mind

67 mentions

Mariner Books

Read comments from redditors### 9. All That the Rain Promises and More: A Hip Pocket Guide to Western Mushrooms

55 mentions

Read comments from redditors### 10. A Universe from Nothing: Why There Is Something Rather than Nothing

52 mentions

an engrossing tour of current cosmology

Read comments from redditors### 11. A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)

52 mentions

Dover Publications

Read comments from redditors### 12. Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics)

52 mentions

McGraw-Hill Science Engineering Math

Read comments from redditors### 13. Turn Left at Orion: Hundreds of Night Sky Objects to See in a Home Telescope - and How to Find Them

47 mentions

Read comments from redditors### 15. Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Climate Change

46 mentions

Bloomsbury Publishing PLC

Read comments from redditors### 18. Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

40 mentions

Secrets of Mental Math The Mathemagician s Guide to Lightning Calculation and Amazing Math Tricks

Read comments from redditors
The Demon Haunted World: Science as a Candle in the Dark, by Carl Sagan.

This book talks down pseudoscience respectably, and first gets the reader agreeing with him before switching over to the topic of religion. I highly recommend it.

http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

Copying my answer from another post:

I was literally in the bottom 14th percentile in math ability when i was 12.

One day, by pure chance, i stumbled across this (free and open) book written by Carl Stitz and Jeff Zeager, of Lakeland Community College

Precalculus

It covers everything from elementary algebra (think grade 5), all the way up to concepts used in Calculus and Linear Algebra (Partial fractions and matrix algebra, respectively.) The book is

extremely well organized.Every sections starts with a dozen or so pages of proofs and derivations that show you the logic of why and how the formulas you'll be using work. This book, more than any other resource (and i've tried a lot of them), helped me build my math intuition from basically nothing.Math is really, really intimidating when you've spent your whole life sucking at it. This book addresses that very well. The proofs are all really well explained, and are very long. You'll basically never go from one step to the next and be completely confused as to how they got there.

Also, there is a metric

shitloadof exercises, ranging from trivial, to pretty difficult, to "it will literally take your entire class working together to solve this". Many of the questions follow sort of an "arc" through the chapters, where you revisit a previous problem in a new context, and solve it with different means (Also, Sasquatches. You'll understand when you read it.)I spent 8 months reading this book an hour a day when i got home from work, and by the end of it i was ready for college. I'm now in my second year of computer science and holding my own (although it's hard as fuck) against Calculus II. I credit Stitz and Zeager entirely. Without this book, i would never have made it to college.

Edit: other resourcesKhan Academy is good, and it definitely complements Stitz/Zeager, but Khan also lacks depth. Like, a lot of depth. Khan Academy is best used for the practice problems and the videos do a good job of walking you through

applicationof math, but it doesn't teach you enough to really build off of it. I know this from experience, as i completed all of Khan's precalculus content. Trust me, Rely on the Stitz book, and use Khan to fill in the gaps.Paul's Online Math Notes

This website is so good it's ridiculous. It has a ton of depth, and amazing reference sheets. Use this for when you need that little extra detail to understand a concept. It's still saving my ass even today (Damned integral trig substitutions...)

Stuff that's more important than you think (if you're interested in higher math after your GED)

Trigonometric functions:very basic in Algebra, but you gotta know the common values of all 6 trig functions, their domains and ranges, and all of their identities for calculus. This one bit me in the ass.Matrix algebra:Linear algebra is p. cool. It's used extensively in computer science, particularly in graphics programming. It's relatively "easy", but there's more conceptual stuff to understand.Edit 2: Electric BoogalooOther good, cheap math textbooks/u/ismann has pointed out to me that Dover Publications has a metric shitload of good, cheap texts (~$25CAD on Amazon, as low as a few bucks USD from what i hear).

Search up

Dover Mathematicson Amazon for a deluge of good, cheap math textbooks. Many are quite old, but i'm sure most will agree that math is a fairly mature discipline, so it's not like it makes a huge difference at the intro level. Here is a Math~~Overflow~~Exchange list of the creme de la creme of Dover math texts, all of which can be had for under $30, often much less. I just bought ~1,000 pages of Linear Algebra, Graph Theory, and Discrete Math text for $50. If you prefer paper to .pdf, this is probably a good route to go.Also, How to Prove it is a very highly rated (and easy to read!) introduction to mathematical proofs. It introduces the basic logical constructs that mathematicians use to write rigorous proofs. It's very approachable, fairly short, and ~$30 new.

Here's my list of the classics:

General ComputingComputer ScienceThe Dragon Book)CLRS)SICP, available for free on the MIT website)Software DevelopmentThe Gang of Four)Case StudiesEmploymentLanguage-SpecificCPythonC#C++JavaLinux Shell ScriptsWeb DevelopmentRuby and RailsAssemblyI recommend this book:

Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming

It helps in understanding why we have become tribal on this issue. It was by design.

Fun fact: 25% of Americans still don't believe that smoking is harmful to health. This technique of instilling doubt is terribly effective.

I know trees loves to praise Sagan for his pro-cannabis stance (and they should, Mr. X is a great read), but really, watch/read Cosmos, read his other books (Demon Haunted World is great. Highly recommended). His love of cannabis is an afterthought compared to his love of science and critical thinking.

> The thought of matter spawning out of nowhere for no reason seems.. weird, doesn't feel right, you get what I'm saying?

Quantum mechanics makes no sense to people who evolved in a macroscopic universe.

When we drive to work in the morning and come to a fork in the road, our car does not take one path while we (suddenly car-less) take another path before meeting up again prior to reaching our destination.

TVs and anti-TVs do not suddenly pop in and out of existence all the time.

Despite the fact that I am forgetful, my keys do exist

somewhere.In the quantum world, things are different, particles get separated from their physical properties, only to be reunited later on. Matter does indeed pop in and out of existence constantly. And particles may or may not be a certain way until they are observed.

When the universe was very young, it was very small. Quantum things happen when things are very small. Lawrence Krauss has shown that, for example, the universe could have come about from a physical nothing. Amazon. Also: youtube talk.

The universe consistently surprises us. Most discoveries about how the universe works have led to only more questions. The universe is not obliged to us to make sense.

It is systemic

Merchants of DoubtHow a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming

http://en.wikipedia.org/wiki/Merchants_of_Doubt

http://www.merchantsofdoubt.org/

http://www.amazon.com/Merchants-Doubt-Handful-Scientists-Obscured/dp/1608193942

The answer is "virtually all of mathematics." :D

Although lots of math degrees are fairly linear, calculus is really the first big branch point for your learning. Broadly speaking, the three main pillars of contemporary mathematics are:

You might also think of these as the three main "mathematical mindsets" — mathematicians often talk about "thinking like an algebraist" and so on.

Calculus is the first tiny sliver of analysis and Spivak's

Calculusis IMO the best introduction to calculus-as-analysis out there. If you thought Spivak's textbook was amazing, well, that's bread-n-butter analysis. I always thought of Spivak as "one-dimensional analysis" rather than calculus.Spivak also introduces a bit of algebra, BTW. The first few chapters are really about abstract algebra and you might notice they feel very different from the latter chapters, especially after he introduces the least-upper-bound property. Spivak's "properties of numbers" (P1-P9) are actually the 9 axioms which define an algebraic object called a field. So if you thought those first few chapters were a lot of fun, well, that's algebra!

There isn't that much topology in Spivak, although I'm sure he hides some topology exercises throughout the book. Topology is sometimes called the study of "shape" and is where our most general notions of "continuous function" and "open set" live.

Here are my recommendations.

AnalysisIf you want to keep learning analysis, check out Introductory Real Analysis by Kolmogorov & Fomin, Principles of Mathematical Analysis by Rudin, and/or Advanced Calculus of Several Variables by Edwards.AlgebraIf you want to check out abstract algebra, check out Dummit & Foote's Abstract Algebra and/or Pinter's A Book of Abstract Algebra.TopologyThere's really only one thing to recommend here and that's Topology by Munkres.If you're a high-school student who has read through Spivak in your own, you should be fine with any of these books. These are exactly the books you'd get in a more advanced undergraduate mathematics degree.

I might also check out the Chicago undergraduate mathematics bibliography, which contains all my recommendations above and more. I disagree with their elementary/intermediate/advanced categorization in many cases, e.g., Rudin's Principles of Mathematical Analysis is categorized as "elementary" but it's only "elementary" if your idea of doing math is pursuing a PhD. Baby Rudin (as it's called) is to first-year graduate analysis as Spivak is to first-year undergraduate calculus — Rudin says as much right in the introduction.

I'll stick to recommending science communication books (those that don't require a deep background on biological concepts):

---

For books that everyone studying biology ends up reading, my candidate would be Lehninger's Principles of Biochemistry, by Nelson & Cox but that's a textbook.

Everyone should have this book: https://www.amazon.com/gp/aw/d/0898153883/ref=pd_aw_fbt_14_img_2?ie=UTF8&amp;psc=1&amp;refRID=N9RA0GA05WH819KQ3RSD

i don't forage for mushrooms but have the book on my coffee table because the cover makes me giggle every time I see it.

A Book of Abstract Algebra by Charles C. Pinter

A Brief History Of Time

Not to be confused with his album "A Brief History Of Rhyme"

Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.

Amazon search for Dover Books on mathematics

There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

Pre-Calculus / Problem-SolvingCalculusLinear AlgebraDifferential EquationsNumber TheoryProof-WritingAnalysisComplex AnalysisFunctional AnalysisPartial Differential EquationsHigher-dimensional Calculus and Differential GeometryAbstract AlgebraGeometryTopologySet Theory and LogicCombinatorics / Discrete MathGraph TheoryP. S., if you Google search any of the topics above, you are likely to find many resources. You can find a lot of lecture notes by searching, say, "real analysis lecture notes filetype:pdf site:.edu"The tent is pretty useless unless you are only interested in a tiny spot of sky. The mirror isn't an observatory at all, just a way to kinda be lazy and decide you'd like to look through the imperfections of a non-optically-polished surface while looking at the sky. It'd honestly be easier just to inflate a small kiddy pool and lay back in it to support your head. (Binocular astronomy is really awesome, by the way. Buy a $50-$70 pair of wide-aperture binoculars and a copy of Left Turn at Orion, and you'd be floored by all the cool stuff you can see at night!)

The shed-looking observatory is pretty standard, it's one of a number of roll-away model observatories, of which this one is my favorite. Wide, shallow, plenty of room, plenty of sky. The one in the instructable is a bit tall and cuts off a ton of sky unless you're using a schmidt-cassegrain on a tall tripod, but if you're using a Dobsonian (which pivots much closer to the ground than a SCT), you've lost most of the sky.

For real analysis I really enjoyed Understanding Analysis for how clear the material was presented for a first course. For abstract algebra I found A book of abstract algebra to be very concise and easy to read for a first course. Those two textbooks were a lifesaver for me since I had a hard time with those two courses using the notes and textbook for the class. We were taught out of rudin and dummit and foote as mainly a reference book and had to rely on notes primarily but those two texts were incredibly helpful to understand the material.

&#x200B;

If any undergrads are struggling with those two courses I would highly recommend you check out those two textbooks. They are by far the easiest introduction to those two fields I have found. I also like that you can find solutions to all the exercises so it makes them very valuable for self study also. Both books also have a reasonable amount of excises so that you can in theory do nearly every problem in the book which is also nice compared to standard texts with way too many exercises to realistically go through.

Per your request, I left out the links based on ethics:

3. State Formation:

a. http://www.cato.org/pubs/catosletter/catosletterv10n4.pdf

b. http://www.scribd.com/doc/30267974/For-an-Emergent-Governance

c. http://my.opera.com/RyanFaulk/

d. http://www.amazon.com/Origin-Consciousness-Breakdown-Bicameral-Mind/dp/0618057072/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1349830998&amp;sr=1-1&amp;keywords=the+bicameral+mind

e. http://en.wikipedia.org/wiki/Carneiro%27s_Circumscription_Theory

f. http://a-s.clayton.edu/kemp/SYLLABUS/1111/1111online/carniero1.htm

g. http://en.wikipedia.org/wiki/Henri_J._M._Claessen#Complex_Interaction_Model

h. http://en.wikipedia.org/wiki/The_State_(book)

i. http://www.prickly-paradigm.com/sites/default/files/Graeber_PPP_14_0.pdf

j. http://mises.org/books/the_state_oppenheimer.pdf

k. http://mises.org/daily/4881

l. https://mises.org/store/Product2.aspx?ProductId=321

6. Historical Anarchy Examples:

a. http://en.wikipedia.org/wiki/List_of_anarchist_communities

b. http://en.wikipedia.org/wiki/Anarchy

c. http://mises.org/journals/jls/1_2/1_2_1.pdf

d. http://foranemergentgovernance.tumblr.com/post/1517339178/ireland

e. http://books.google.com/books?id=S6fPAAAAMAAJ

f. http://www.reddit.com/r/libertarian_history/comments/ymysc/lh_request_info_on_ancient_gaelic_government_and/

g. http://www.reddit.com/r/libertarian_history/comments/zbo9o/lh_request_how_did_statist_england_manage_to/

h. http://royhalliday.home.mindspring.com/history.htm

7. Evolution of Anarchy:

a. http://archive.mises.org/13082/the-course-of-economic-development-in-england/

b. http://library.mises.org/books/Sudha%20R%20Shenoy/Towards%20a%20Theoretical%20Framework%20for%20British%20and%20International%20Economic%20History%20Early%20Modern%20England.pdf

c. http://mises.org/community/forums/t/8889.aspx

d. http://www.walterblock.com/wp-content/uploads/publications/block_radical-libertarianism-rp.pdf

e. https://mises.org/daily/2404/The-European-Miracle

13. Ancap Legal Theory (Polycentric Law):

a. http://mises.org/books/chaostheory.pdf

b. http://www.daviddfriedman.com/The_Machinery_of_Freedom_.pdf

c. http://libertarianpapers.org/articles/2011/lp-3-19.doc

d. http://voluntaryistreader.wordpress.com/2012/12/14/law-prior-to-government/

e. http://properalism.blogspot.com/2013/02/bibliography-on-property-rights.html

f. http://www.daviddfriedman.com/Academic/Course_Pages/legal_systems_very_different_12/LegalSystemsDraft.html

g. http://www.gutenberg.org/ebooks/22910

18. National Defense:

a. http://mises.org/etexts/defensemyth.pdf

b. http://mises.org/journals/scholar/Sechrest6.PDF

c. http://mises.org/journals/rae/pdf/R101_1.PDF

d. http://mises.org/etexts/mises/interventionism/interventionismtext.pdf

e. https://itunesu.mises.org/journals/jls/4_1/4_1_6.pdf

f. http://mises.org/journals/jls/14_1/14_1_1.pdf

g. http://mises.org/books/chaostheory.pdf

h. http://mises.org/daily/1855

i. http://praxeology.net/libertariannation/a/f21l1.html

j. http://daviddfriedman.com/The_Machinery_of_Freedom_.pdf

k. http://library.mises.org/books/Gustave%20de%20Molinari/The%20Production%20of%20Security.pdf

l. http://mises.org/journals/jls/20_3/20_3_2.pdf

m. http://mises.org/journals/prep/THE%20REVIEW%20OF%20AUSTRIAN%20ECONOMICS%20VOLUME%204.pdf#page=96

n. http://mises.org/journals/scholar/Murphy6.pdf

Haha. If only. In reality, it's so much worse. We can only hold so much information, and the "resolution" (depth/granularity) of our understanding diminishes over time. Throughout history people could contend with increases in the complexity of the collective human understanding of the world, but the breadth of the information available in any given society was so small that it was manageable. Furthermore, their forms of government relied more on a class of experts for governance and statemenship.

&#x200B;

Now everyone is involved in governance through voting, and the world is so complex that one individual cannot be expected to have a functional understanding of more than a tiny portion of it. This fundamentally changes how a society can, and should, organize. Should we all have opinions on the finer points of climate change without being experts in it? Should we be voting for people based on their specific policies related to climate change without that understanding? Can we just rely on endorsements from relevant experts? What happens when some of those experts decide they are willing to sellout to the opposition? This: Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming

&#x200B;

The first step in solving a problem is admitting there is a problem. The second step is defining that problem. The third is designing a plan. The fourth is executing that plan, and the last is maintaining/updating that plan. We are still stuck on the first step, but we are trying to patch the leaking boat in the meantime, while claiming it solves the design flaws that led to the leaks. Let's not confuse the holes with the design flaws.

My recommendations:

My undergraduate courses in quantum mechanics used Introduction to Quantum Mechanics by Griffiths and is a really good introduction with enough details.

It just comes from the way we define sums of infinite sums, aka series. .999... is just shorthand for (.9+.09+.09+.009...), which is an infinite sum. We define the sum of a series to be equal to the limit of the partial sums. The limit is rigorously defined, and you can read the definition on wikipedia if you google "epsilon delta". The limit of an infinite sum, if it exists, is unique. For this infinite sum, that limit is exactly 1. By the way we define infinite sums, .999... is therefore exactly equal to 1.

It's not so bad when you remember that

allreal numbers have a representation as a non-terminating decimal. 0.5 can be written as 0.4999... and 1/3 can be written as 0.333... and pi can be written as 3.14159... for example.And lastly, if .999... and 1 are different real numbers, then there must exist a number between them. This is because of an axiom we have called trichotomy: for any two real numbers a and b, exactly one of the following is true: a<b, a=b, a>b. If a=/=b, then there exists a real number between them, because the real numbers have a property called "dense". It is easy to prove that here is no such number between .999... and 1, real or otherwise. Therefore .999... is exactly equal to 1.

e: The sum (.9+.09+.009...) is bigger than every real number less than 1. You can check if you want. The smallest number that is greater than every real number less than 1 is 1 itself. We get this from an axiom called the "least upper bound property". Therefore .999... is

at least1. Using our rigorous definition of a limit, we find that it is exactly 1.e2: Apostol's Calculus vol 1 is a fantastic place to start learning about rigorous math shit. Chapter one starts you out with axioms for real numbers, and about half way through chapter 1 you prove the whole thing about repeating decimals corresponding to rational numbers. It is slow and easy to follow. Other people recommend Spivak but I haven't seen it so idk.

Two general types of experience you can get: hands-on, and book learning.

The former is very important, but not too difficult to do. A fair number of people in the Portland area go mushroom hunting occasionally, even if they only know a species of two. Sucking up to the right people is surprisingly effective. Also, getting in touch with or joining organizations like Oregon Mycological Society or the Cascade Mycological Society can be immensely helpful in making contacts and finding hunting partners/mentors.

The latter is also very important, as there is some much you can learn without actually holding a mushroom in your hands. For books, accessible guides like Mushrooms of the Pacific Northwest and All That the Rain promises and More are great for getting started, and heftier books like Mushrooms Demystified are good for those looking to take the next step in learning. Online, the hunting and identification board on The Shroomery, Mushroom Observer, and /r/mycology are great places to lurk and just soak in info, while sites like Mushroom Expert are good places to explore and follow what interests you.

"We live in a society exquisitely dependent on science and technology, in which hardly anyone knows anything about science and technology." - Carl SaganDo Stephen a solid and read A Brief History of Time. And never forget the importance of knowledge. The Demon Haunted World by Carl Sagan is another great one.

RIP Stephen Hawking, one of the truest niggas who ever walked the face of the earth.

For those who haven't read it Naomi Oreskes et. al.'s

Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warmingdoes a fantastic job of laying all of these tactics and campaigns out.Read all of his books.

The Demon Haunted World

Cosmos

Varieties of the Scientific Experience

Pale Blue Dot

The Dragons of Eden

Billions and Billions

His novel:

Contact

This actually began during the Cold War; the 1983 Strategic Defense Initiative (the "Star Wars" program) under Reagan was a plan to build a network of satellites designed to down incoming ICBMs.

The scientific community was opposed to the project. It was impossible to test (how do you test a system designed to shoot down ALL of a nuclear arsenal without firing an entire nuclear arsenal at yourself?), it was extraordinarily costly, and it would result in the weaponization of space.

The Reagan administration decided to get "its own scientists" to convince Congress to fund the project. They basically hired a bunch of PhD shills to argue that the scientific community was politicized, communist-leaning liberals and that the SDI project was scientifically sound. This led to discussions of "nuclear winter" which gave Carl Sagan his platform.

Fast forward a few years, and the

same "scientists"hired by the Reagan administration were hired to argue that acid rain was not a major environmental problem.Later, that

same groupwas arguing that second-hand smoke was not harmful.Next, they argued that

smoking itselfwas not harmful.Today,

those same peopleare leading campaigns of disinformation attempting to discredit the science surrounding climate change.If you'd like to learn more about the history of scientific disinformation in conservative America

I cannot recommend Carl Sagan's The Demon Haunted World: Science as a Candle in the Dark enough. Some parts of it may be a bit dated, but the chapter entitled "The Fine Art of Baloney Detection" is timeless and it may be exactly what you're looking for.

It is an immensely narrow field of study. Everything I've posted so far comes out of my studies into mythopoetics in college. In essence, it is the study of the historical development of human consciousness through myth and what few written works remain. Ultimately, it's the study of the plasticity of human consciousness and how language and cultural conception develops your reality for you.

I'll link more books which touch on this subject!

Mircea Eliade - The Sacred and the Profane

Julian Jaynes - The Origin of Consciousness in the Breakdown of the Bicameral Mind (Some of the science he employs has been brought into question, but his stuff on language and historical analysis of myth is super interesting and on point)

The older bunch of "climate change isn't real" people are literally the same people who were saying "smoking doesn't cause cancer" a generation ago

I always recommend Your Inner Fish by Neil Shubin because it's less antagonistic and more matter of fact about our evolution. Another good choice might be The Third Chimpanzee by Jared Diamond. Again, I'm trying to think of the less obvious and less vitriolic choices than Harris or Dawkins. Handing him something entitled "The God Delusion" is likely to just shut off his brain instantly.

Oh ... to combat the Young Earth mentality, you could consider something like A Brief History of Time by Stephen Hawking.

>Can you describe quantum mechanics

Intro to Quantum Mechanics

This is effectively what you have done...

A friend took me when I was a bright-eyed and bushy-tailed college kid. I took our findings to a mycologist on campus who spent 20 minutes describing proper browning-in-butter protocol. I was hooked- both on mushrooming and the goofy people involved. I already collect field identification books, so I have a shelf in my bookcase just for mushroom ID and foraging. Every time i go out i try to ID a new mushie. Anything im super lost on i take to a mycologist friend in town, or i email the prof at OSU (which is 30 minutes drive) and bug them with it.

I also have permits for personal collection of mushrooms in all the local national forests (most were free) and researched the county and state park rules for collection on their property. Gotta be responsible, yo.

I recommend picking up All That Rain Promises and More (link) and the unabridged Mushrooms Demystified link2 because i reference both a TON, The first one is waterproof, and David is a certified goofball.

The World Without Us is about exactly that. Really good read.

Stay away from Numberphile. Numberphile oversimplifies mathematical concepts to the point where they will give you misconceptions about common mathematical notions that will greatly impact your learning later on. I'm noticing this happening a lot with the "1+2+... = -1/12" video because it doesn't explain that they aren't using the standard partial sum definition of series convergence.

Not sure how "mathematical" it is, but Secrets of Mental Math is a great, useful book that will help you do really fast calculations in your head.

He's my major advisor, and he loves occasionally showing off (who wouldn't?). I find it very entertaining. As far as I can tell, it's just a lot of practice plus some pattern recognition. For multiplying large numbers he just uses the distributive property combined with a certain method of remembering numbers in his head he uses.

I also read his book Secrets of Mental Math back in high school. He outlines some of the techniques there although its more basic.

Presents she received

Her reactions?

Exhibit A:

>Who the fuck do you think you are addressing, you moronic bastards? I didn't ask for a thing, I expected nothing, a lovely postcard of where they are from would have been nice or a homemade card - I have to deal with death in some form every fucking day, I do not need demons and zombies and reminders of inhumanity in my goddamned presence - Perhaps some prepubescent little boy would have wet dreams over this package but given that you call someone a "twat", I am guessing you are a boy anyway - I was completely approproiate, I didn't want the effort to just be trashed, I want the sender to have it and enjoy it and that is why I am trying to get his correct info so I know where to send it - Otherwise it goes in the incinerator, are you too fucking dense to get that, you motherfucking cocksucking dickwad - I got your manners right here, little.... and I do mean "little" in the most generous sense of proportions, "man".

This is probably a long shot, but if you can convince them to thoughtfully read an entire book, buy them a copy of The Demon-Haunted World.

Start by picking a guide for your area and reading it thoroughly, especially focusing on the anatomy of a mushroom. Go hunting a lot bringing back what you find, take spore prints and work though the IDs. Also joining a NAMA affiliated club will help tremendously.

Regional guidesAlaskaCommon Interior Alaska Cryptogams

Western USAll The Rain Promises and More

Mushrooms of the Pacific Northwest

Midwestern USMushrooms of the Midwest

Edible Wild Mushrooms of Illinois and Surrounding States

Mushrooms of the Upper Midwest

Southern USTexas Mushrooms: A Field Guide

Mushrooms of the Southeastern United States

Midwestern USMushrooms of the Midwest

Edible Wild Mushrooms of Illinois and Surrounding States

Mushrooms of the Upper Midwest

Eastern USMushrooms of West Virginia and the Central Appalachians

Mushrooms of Northeast North America (This was out of print for awhile but it's they're supposed to be reprinting so the price will be normal again)

Mushrooms of Northeastern North America

Macrofungi Associated with Oaks of Eastern North America(Macrofungi Associated with Oaks of Eastern North America)

Mushrooms of Cape Cod and the National Seashore

More specific guidesPsilocybin Mushrooms of the World

North American Boletes

Tricholomas of North America

Milk Mushrooms of North America

Waxcap Mushrooms of North America

Ascomycete of North America

Ascomycete in colour

Fungi of Switzerland: Vol. 1 Ascomycetes

PDFsFor Pholiotas

For Chlorophyllum

For parasitic fungi, Hypomyces etc "Mushrooms that Grow on other Mushrooms" by John Plischke. There's a free link to it somewhere but I cant find it.

Websites that aren't in the sidebarFor Amanita

For coprinoids

For Ascos

MycoQuebec: they have a kickass app but it's In French

Messiah college this has a lot of weird species for polypores and other things

Books that provide more info than field MycologyThe Kingdom of Fungi Excellent coffee table book has nice pictures and a breif guide to Fungal taxonomy and biology.

The Fifth Kingdom A bit more in depth

Introduction toFungi Textbook outlining metobolic, taxonomic and ecological roles of fungi. Need some level of biochemistry to have a grasp for this one but it's a good book to have.

It's also being expanded into one of the few books I've ever preordered.

I. Sure, some forms of theism are coherent (Christianity is not one of those forms, for what it's worth; the Problem of Natural Evil and Euthyphro's Dilemma being a couple of big problems), but not all coherent ideas are true representations of the world; any introductory course in logic will demonstrate that.

II. The cosmological argument is a deductive argument. Deductive arguments are only as strong as their premises. The premises of the cosmological argument are not known to be true. Therefore, the cosmological argument should not be considered true. If you think you know a specific formulation of the cosmological argument that has true premises, please present it. I'm fully confident I can explain how we know such premises are not true.

III. There is no doubt that the teleological argument has strong persuasive force, but that's a very different thing than "being real evidence" or "something that should have strong persuasive force." I explain apparent cosmological fine-tuning as an entirely anthropic effect: if the constants were different, we wouldn't be here to observe them, therefore we observe them as they are.

IV. This statement is just false on its face. Lawrence Krauss has a whole book about the potential

ex nihilomechanisms (plural!) for the creation of the universe that are entirely consistent with the known laws of physics. (Note that the idea of God is not consistent with the known laws of physics, since he, by definition, supersedes them.)V. This is just a worse version of argument III. Naturalistic evolution has far, far more explanatory power than theism. To name my favorite examples: the human blind spot is inexplicable from the standpoint of top-down design, but it makes perfect sense in the context of evolution; likewise, the path of the mammalian nerves for the tongue traveling

below the heartmakes no sense from the standpoint of top-down design, but it makes perfect sense in the context of evolution. Evolution routinely makes predictions that are tested to be true, whether it means predicting where fossils with specific characteristics will be found or how fruit fly mating behavior changes after populations have been separated and exposed to different environments for 30+ generations. It's worth emphasizing that it is totally normal to look at the complexity of the world and assume that it must have a designer...but it's also totally normal to think that electrons aren't waves. Intuition isn't a reliable way to discern truth. We must not be seduced by comfortable patterns of thought. We must think more carefully. When we think more carefully, it turns out that evolution is true and evolution requires no god.VI. There are two points here: 1) the universe follows rules, and 2) humans can understand those rules. Point (1) is easily answered with the anthropic argument: rules are required for complex organization, humans are an example of complex organization, therefore humans can only exist in a physical reality that is governed by rules. Point (2)

might not even be true. Wigner's argument is fun and interesting, but it's actually wrong! Mathematics are not able to describe the fundamental behavior of the physical world. As far as we know, Quantum Field Theory is the best possible representation of the fundamental physical world, andit is known to be an approximation, because, mathematically, it leads to an infinite regress. For a more concrete example, there is no analytic solution for the orbital path of the earth around the sun! (This is because it is subject to the gravitational attraction of more than one other object; its solution is calculated numerically, i.e. by sophisticated guess-and-check.)VII. This is just baldly false. I recommend Dan Dennett's "Consciousness Explained" and Stanislas Dehaene's "Consciousness and the Brain" for a coherent model of a materialist mind and a wealth of evidence in support of the materialist mind.

VIII. First of all, the idea that morality comes from god runs into the Problem of Natural Evil and Euthyphro's Dilemma pretty hard. And the convergence of all cultures to universal ideas of right and wrong (murder is bad, stealing is bad, etc.) are rather easily explained by anthropology and evolutionary psychology. Anthropology and evolutionary psychology also predict that there would be cultural divergence on more subtle moral questions (like the Trolley Problem, for example)...and there is! I think that makes those theories better explanations for moral sentiments than theism.

IX. I'm a secular Buddhist. Through meditation, I transcend the mundane even though I deny the existence of any deity. Also, given the diversity of religious experience, it's insane to suggest that religious experience argues for the existence of the God of Catholicism.

X. Oh, boy. I'm trying to think of the best way to persuade you of all the problems with your argument, here. So, here's an exercise for you: take the argument you have written in the linked posts and reformat them into a sequence of syllogisms. Having done that, highlight each premise that is not a conclusion of a previous syllogism. Notice the large number of highlighted premises and ask yourself for each, "What is the proof for this premise?" I am confident that you will find the answer is almost always, "There is no proof for this premise."

XI. "...three days after his death, and against every predisposition to the contrary, individuals and groups had experiences that completely convinced them that they had met a physically resurrected Jesus." There is literally no evidence for this at all (keeping in mind that Christian sacred texts are not evidence for the same reason that Hindu sacred texts are not evidence). Hell, Richard Carrier's "On the Historicity of Christ" even has a strong argument that Jesus didn't exist! (I don't agree with the conclusion of the argument, though I found his methods and the evidence he gathered along the way to be worthy of consideration.)

-----

I don't think that I can dissuade you of your belief. But, I do hope to explain to you why, even if you find your arguments intuitively appealing, they do not conclusively demonstrate that your belief is true.

The problem you are having is that math education is shitty.

> What I want is to have a concrete understanding [...]

If you want to actually understand anything you learn in class, you'll have to seek it out yourself. Actual mathematics isn't taught until you get to college, and even then, only to students majoring in the subject.

"Why the fuck calculus works" typically goes under the name "analysis." You can look up a popular textbook, Baby Rudin, although I've never used it. I had this cheap-o Dover book. You can't beat it for $12. There's also this nice video series from Harvey Mudd.

The general pattern you see in actual, real mathematics isn't method-problem-problem-problem-problem, but rather definition-theorem-proof. The definitions tell you what you're working with. The theorems tell you what is true. The proofs give a strong technical reason to believe it.

> I know that to grasp mathematical concepts, it is advisable to do lots of problems from your textbook.

For some reason, schools are notorious for drilling exercises until you're just about to bleed from the fucking skull. Once you understand how an exercise is done, don't waste your time with another exercise of the same type. If you can correctly take the derivative of three different polynomials, then you probably understand it.

Just a heads up, analysis is built on the foundations of set theory and the real numbers. What you work with in high school are an intuitive notion of what a real number is. However, to do proper mathematics with them, it's better to have a proper understanding of how they are defined. Any good book on analysis will start off by giving a full, rigorous definition of what a real number

is. This is typically done either in terms of cauchy sequences (sequences that seem like they deserve to converge), in terms of dedekind cuts (splitting the rational numbers up into two sets), or axiomatically (giving you a characterization involving least upper bounds of bounded sets). (No good mathematical book would ever talk about decimals. Decimals are a powerful tool, but pure mathematicians avoid them whenever possible).Calculus and analysis can both be summed up shortly as "the cool things you can do with limits". Limits are the primary way we work with infinities in analysis. Their technical definition is often confusing the first time you see it, but the idea behind them is straightforward. Imagining a world where you can't measure things exactly, you have to rely on approximations. You want accuracy, though, and so you only have so much room for error. Suppose you want to make a measurement with a very small error. (We use ε for denoting the maximum allowable error). If the equipment you're using to make the measurement is calibrated well enough, then you can do this just fine. (The calibration of your machine is denoted δ, and so, these definitions commonly go by the name of "ε-δ definitions").

The Bible: Eh. I can sort of get behind this, but not for the reason he gives. The Bible's just really culturally important. I also wouldn't bother reading all of it. When I reread the Bible it's normally just Genesis, Exodus, the Gospels, and Eccelesiastes. A lot of it (especially Leviticus) is just tedious. The prophets are fun but I wouldn't call them essential.The System of the World: Newton intentionally wrote the Principia to make it inaccessible to layman and dabblers. I really don't think you should be recommending a book like this to people who aren't specialists. Sagan'sA Demon Haunted Worldwill probably fulfill the stated purpose Tyson sets out better.On the Origin of Species: A good book that's held up remarkably well, but a more recent book of evolution might be better.The Extended PhenotypeorThe Selfish Genewould both probably do a better job.Gulliver's Travels: This is a great book. I support this recommendation.Age of Reason: Haven't read it. I like Paine otherwise though. No comment.The Wealth of Nations: Similar toOn the Origin of Species. It's still a great read that's held up really well and offers an interesting historical perspective. That said, economic theory has made some pretty important advancements in two centuries (the Marginal Revolution, Keynes, etc). Still, if you want to stick to the time you'll probably get more out of reading Ricardo'sPrinciples of Political Economy.The Art of War: Very good book. I have nothing to add.The Prince: Same as the above. Fantastic book.Thank you all for your responses! I have compiled a list of books mentioned by at least three different people below. Since some books have abbreviations (SICP) or colloquial names (Dragon Book), not to mention the occasional omission of a starting "a" or "the" this was done by hand and as a result it may contain errors.

edit: This list is now books mentioned by at least three people (was two) and contains posts up to icepack's.

edit: Updated with links to Amazon.com. These are not affiliate - Amazon was picked because they provide the most uniform way to compare books.

edit: Updated up to redline6561

I remember reading A Brief History of Time while in middle school. I picked it up out of the public library on a whim. I was surprised at how easy of a read it was for a topic that is so complex. It was at that point I understood that the most complex topics in human history were easy to understand at a high level if explained simply, that the knowledge was easily accessible to someone like me.

It's one of the few books that I can point to that I can say legitimately changed my life.

Great question! The most direct method is by spectroscopy. This exploits the fact that atoms absorb and emit light at specific wavelengths. So, we can look at what wavelengths of light distant stars are emitting and absorbing, and infer what kinds of atoms are in its atmosphere. This is what lets us know what white dwarfs are made of, for instance.

There are also indirect lines of evidence. We can take well-tested theories describing nuclear reactions, thermodynamics, fluid dynamics, and others, and apply them to the interiors of stars. The most sophisticated models are supercomputer simulations that couple fluid dynamics models with statistical descriptions of nuclear reactions and electromagnetic interactions. They're tested both by ensuring that they're correctly applying theories tested elsewhere, and against actual astrophysical observations of stellar luminosity and spectra. (Side note --- as you might expect, these numerical capabilities have a decidedly terrestrial origin.)

Scientific advances along these lines often look like rasterizing, where the scientific community takes a very simple model and makes successive passes elaborating and refining it. For instance, you can look at the sun, measure its temperature, mass, and radius, and notice that it's mostly made of hydrogen gas. Then you can show that the kind of conditions that exist at its core necessitate hydrogen fusion. Once you've done that, you see that a hydrostatic equilibrium balancing energy produced by fusion with gravitational collapse accurately predicts the sun's radius and temperature. Then it's on to building more complex models to try to understand its inner temperature gradients, convection, solar storms, etc ...

(Source: Mixed graduate/undergraduate astrophysics was one of my favorite classes in college and I still keep BOB in a special place on my shelf.)

My main hobby is reading textbooks, so I decided to go beyond the scope of the question posed. I took a look at what I have on my shelves in order to recommend particularly good or standard books that I think could characterize large portions of an undergraduate degree and perhaps the beginnings of a graduate degree in the main fields that interest me, plus some personal favorites.

Neuroscience: Theoretical Neuroscience is a good book for the field of that name, though it does require background knowledge in neuroscience (for which, as others mentioned, Kandel's text is excellent, not to mention that it alone can cover the majority of an undergraduate degree in neuroscience if corequisite classes such as biology and chemistry are momentarily ignored) and in differential equations. Neurobiology of Learning and Memory and Cognitive Neuroscience and Neuropsychology were used in my classes on cognition and learning/memory and I enjoyed both; though they tend to choose breadth over depth, all references are research papers and thus one can easily choose to go more in depth in any relevant topics by consulting these books' bibliographies.General chemistry, organic chemistry/synthesis: I liked Linus Pauling's General Chemistry more than whatever my school gave us for general chemistry. I liked this undergraduate organic chemistry book, though I should say that I have little exposure to other organic chemistry books, and I found Protective Groups in Organic Synthesis to be very informative and useful. Unfortunately, I didn't have time to take instrumental/analytical/inorganic/physical chemistry and so have no idea what to recommend there.Biochemistry: Lehninger is the standard text, though it's rather expensive. I have limited exposure here.Mathematics: When I was younger (i.e. before having learned calculus), I found the four-volume The World of Mathematics great for introducing me to a lot of new concepts and branches of mathematics and for inspiring interest; I would strongly recommend this collection to anyone interested in mathematics and especially to people considering choosing to major in math as an undergrad. I found the trio of Spivak's Calculus (which Amazon says is now unfortunately out of print), Stewart's Calculus (standard text), and Kline's Calculus: An Intuitive and Physical Approach to be a good combination of rigor, practical application, and physical intuition, respectively, for calculus. My school used Marsden and Hoffman's Elementary Classical Analysis for introductory analysis (which is the field that develops and proves the calculus taught in high school), but I liked Rudin's Principles of Mathematical Analysis (nicknamed "Baby Rudin") better. I haven't worked my way though Munkres' Topology yet, but it's great so far and is often recommended as a standard beginning toplogy text. I haven't found books on differential equations or on linear algebra that I've really liked. I randomly came across Quine's Set Theory and its Logic, which I thought was an excellent introduction to set theory. Russell and Whitehead's Principia Mathematica is a very famous text, but I haven't gotten hold of a copy yet. Lang's Algebra is an excellent abstract algebra textbook, though it's rather sophisticated and I've gotten through only a small portion of it as I don't plan on getting a PhD in that subject.Computer Science: For artificial intelligence and related areas, Russell and Norvig's Artificial Intelligence: A Modern Approach's text is a standard and good text, and I also liked Introduction to Information Retrieval (which is available online by chapter and entirely). For processor design, I found Computer Organization and Design to be a good introduction. I don't have any recommendations for specific programming languages as I find self-teaching to be most important there, nor do I know of any data structures books that I found to be memorable (not that I've really looked, given the wealth of information online). Knuth's The Art of Computer Programming is considered to be a gold standard text for algorithms, but I haven't secured a copy yet.Physics: For basic undergraduate physics (mechanics, e&m, and a smattering of other subjects), I liked Fundamentals of Physics. I liked Rindler's Essential Relativity and Messiah's Quantum Mechanics much better than whatever books my school used. I appreciated the exposition and style of Rindler's text. I understand that some of the later chapters of Messiah's text are now obsolete, but the rest of the book is good enough for you to not need to reference many other books. I have little exposure to books on other areas of physics and am sure that there are many others in this subreddit that can give excellent recommendations.Other: I liked Early Theories of the Universe to be good light historical reading. I also think that everyone should read Kuhn's The Structure of Scientific Revolutions.Will believers see the value of a position that starts off with "of

coursethere is no God!" (1:15 or so) and then just uses church as a community center, or a place with decent art and music? Are believers willing to move beyond doctrine and dogma?I like de Botton's work in general, though I haven't read this particular book. But in this Ted talk I think he's arguing against a straw man version of atheism. Very few atheists rail against every single thing from religion.

Many atheists like cathedrals and religious art, music, and literature. I'm

finewith engaging the KJV asliterature. But how many believers are? I've had believers actually repudiate even the moral content of the New Testament, if it is to be divorced from the supernatural authority of God.What's interesting too is the mindset he's trying to persuade atheists to embrace is the one believers frequently

accuseus of already having. They already think wefollowDawkins or Harris like secular popes. They think we believe in evolution or materialism as a secular dogma that we can't question.Looking at the dictionary definition of sermon, "a talk on a religious

or moralsubject," we already have those. There are many great talks by Christopher Hitchens, Neil deGrasse Tyson and many others, entreating listeners to embrace a secular worldview. Look up "Skepticon" on Youtube. Talk after talk advocating for the superiority, even themoralsuperiority, of a secular worldview. Thosearesermons. We already hand out copies of Sagan's Demon-Haunted World with hushed assurances of "read this--it changed my life." Sagan called science "informed worship."We already have this stuff. What believers actually want is basically for non-believers to stop being critical of religion. Believers want atheists to be more "moderate" (by which they mean, respectful of religion, or just silent) but they themselves would reject almost every remedy de Botton offers. Most prominently, starting off with the position of "of

coursethere's no God." Is that really the truce being offered?Don't suggest a book you haven't read. If you pick your books you should read them first then give them to your mom. I recommend two books in this order. First, Second.

I'd strongly recommend Richard Dawkin's book The Greatest Show on Earth.

Here is an extract from the first chapter.

Rather than

Origin of Species, which of course doesn't contain any reference to the vast amounts of evidence discovered in the last 150 years, you should get your dad to read The Greatest Show on Earth - The Evidence for Evolution by Dawkins.> Are the deep mathematical answers to things usually very complex or insanely elegant and simple when you get down to it?

I would say that the deep mathematical answers to questions tend to be very complex and insanely elegant at the same time. The best questions that mathematicians ask tend to be the ones that are very hard but still within reach (in terms of solving them). The solutions to these types of questions often have beautiful answers, but they will generally require lots of theory, technical detail, and/or very clever solutions all of which can be very complex. If they didn't require something tricky, technical, or the development of new theory, they wouldn't be difficult to solve and would be uninteresting.

For any experts that happen to stumble by, my favorite example of this is the classification of semi-stable vector bundles on the complex projective plane by LePotier and Drezet. At the top of page 7 of this paper you'll see a picture representing the fractal structure that arises in this classification. Of course, this required a lot of hard math and complex technical detail to come up with this, but the answer is beautiful and elegant.

> How hard would it be for a non mathematician to go to a pro? Is there just some brain bending that cannot be handled by some? How hard are the concepts to grasp?

I would say that it's difficult to become a professional mathematician. I don't think it has anything to do with an individual's ability to think about it. The concepts are difficult, certainly, but given time and resources (someone to talk to, good books, etc) you can certainly overcome that issue. The majority of the difficulty is that there is

so much math!If you're an average person, you've probably taken at most Calculus. The average mathematics PhD (i.e., someone who is just getting their mathematical career going) has probably taken two years of undergraduate mathematics courses, another two years of graduate mathematics courses, and two to three years of research level study beyond calculus to begin to be able tackle the current theory and solve the problems we are interested in today. That's a lot of knowledge to acquire, and it takes a very long time. That doesn't mean you can't start solving problems earlier, however. If you're interested in this type of thing, you might want to consider picking up this book and see if you like it.> Mathematical Logic

It's not exactly Math Logic, just a bunch of techniques mathematicians use. Math Logic is an actual area of study. Similarly, actual Set Theory and Proof Theory are different from the small set of techniques that most mathematicians use.

Also, looks like you have chosen mostly old, but very popular books. While studying out of these books, keep looking for other books. Just because the book was once popular at a school, doesn't mean it is appropriate for your situation. Every year there are new (and quite frankly) pedagogically better books published. Look through them.

Here's how you find newer books. Go to Amazon. In the search field, choose "Books" and enter whatever term that interests you. Say, "mathematical proofs". Amazon will come up with a bunch of books. First, sort by relevance. That will give you an idea of what's currently popular. Check every single one of them. You'll find hidden jewels no one talks about. Then sort by publication date. That way you'll find newer books - some that haven't even been published yet. If you change the search term even slightly Amazon will come up with completely different batch of books. Also, search for books on Springer, Cambridge Press, MIT Press, MAA and the like. They usually house really cool new titles. Here are a couple of upcoming titles that might be of interest to you: An Illustrative Introduction to Modern Analysis by Katzourakis/Varvarouka, Understanding Topology by Shaun Ault. I bet these books will be far more pedagogically sound as compared to the dry-ass, boring compendium of facts like the books by Rudin.

If you want to learn how to do routine proofs, there are about one million titles out there. Also, note books titled Discrete Math are the best for learning how to do proofs. You get to learn techniques that are not covered in, say, How to Prove It by Velleman. My favorites are the books by Susanna Epp, Edward Scheinerman and Ralph Grimaldi. Also, note a lot of intro to proofs books cover much more than the bare minimum of How to Prove It by Velleman. For example, Math Proofs by Chartrand et al has sections about doing Analysis, Group Theory, Topology, Number Theory proofs. A lot of proof books do not cover proofs from Analysis, so lately a glut of new books that cover that area hit the market. For example, Intro to Proof Through Real Analysis by Madden/Aubrey, Analysis Lifesaver by Grinberg(Some of the reviewers are complaining that this book doesn't have enough material which is ridiculous because this book tackles some ugly topological stuff like compactness in the most general way head-on as opposed to most into Real Analysis books that simply shy away from it), Writing Proofs in Analysis by Kane, How to Think About Analysis by Alcock etc.

Here is a list of extremely gentle titles: Discovering Group Theory by Barnard/Neil, A Friendly Introduction to Group Theory by Nash, Abstract Algebra: A Student-Friendly Approach by the Dos Reis, Elementary Number Theory by Koshy, Undergraduate Topology: A Working Textbook by McClusckey/McMaster, Linear Algebra: Step by Step by Singh (This one is every bit as good as Axler, just a bit less pretentious, contains more examples and much more accessible), Analysis: With an Introduction to Proof by Lay, Vector Calculus, Linear Algebra, and Differential Forms by Hubbard & Hubbard, etc

This only scratches the surface of what's out there. For example, there are books dedicated to doing proofs in Computer Science(for example, Fundamental Proof Methods in Computer Science by Arkoudas/Musser, Practical Analysis of Algorithms by Vrajitorou/Knight, Probability and Computing by Mizenmacher/Upfal), Category Theory etc. The point is to keep looking. There's always something better just around the corner. You don't have to confine yourself to books someone(some people) declared the "it" book at some point in time.

Last, but not least, if you are poor, peruse Libgen.

"Turn Left At Orion" by Guy Consolmagno and Dan M. Davis. Can be found on Amazon here.

EDIT: Apparently there is an updated version of the book (5th edition).

EDIT 2: watch the delivery time - the link in my former edit says ships within 1-3 months. Might not be the best choice for under the xmas tree.

Hey Lawrence! Huge fan of you work, thanks for everything you do.

Here's a link to the new book he mentioned for anyone who wants to pre-order:

A Universe from Nothing: Why There Is Something Rather than Nothing

Well worth the $15 in my opinion, to learn about all sorts of cutting edge stuff about the nature and origin of our universe.

And here's the YouTube video to give you a taste for the content. It's a little long, sixty-five minutes total, but definitely worth it.

--

For my questions:

Before buying a scope, do some research. In fact, I tell people not to buy a telescope for at least a year after they've been bitten by the astronomy bug.

Get a pair of decent [binoculars](http://www.amazon.com/Pentax-Whitetails-Unlimited-10x50-Binoculars/dp/B00009XOMO/ref=sr_1_5?ie=UTF8&amp;qid=1371563631&amp;sr=8-5&amp;keywords=10x50+binoculars (10x50 is just about ideal), a planisphere, and a copy of Nightwatch.

Also, a note on the binocs: Don't get zooms, don't get anything larger than 10x for handheld viewing, and make sure that the aperture (second number) is 5 (or more) times the magnification. So 10x50, 8x42, something like that.

This subject is discussed extensively in the book

The World Without Us:>“Any idea what these are?” Thompson is guiding a visitor along the shore of the Plym River estuary, near where it joins the sea...Amid twigs and seaweed fibers in his fistful of sand are a couple of dozen blue and green plastic cylinders about two millimeters high.

>“They’re called nurdles. They’re the raw materials of plastic production. They melt these down to make all kinds of things.” He walks a little farther, then scoops up another handful. It contains more of the same plastic bits: pale blue ones, greens, reds, and tans. Each handful, he calculates, is about 20 percent plastic, and each holds at least 30 pellets.

>“You find these things on virtually every beach these days. Obviously they are from some factory.”

>However, there is no plastic manufacturing anywhere nearby. The pellets have ridden some current over a great distance until they were deposited here—collected and sized by the wind and tide.

...

>[Thompson] devised an aquarium experiment, using bottom-feeding lugworms that live on organic sediments, barnacles that filter organic matter suspended in water, and sand fleas that eat beach detritus. In the experiment, plastic particles and fibers were provided in proportionately bite-size quantities. Each creature promptly ingested them.

>When the particles lodged in their intestines, the resulting constipation was terminal. If they were small enough, they passed through the invertebrates’ digestive tracts and emerged, seemingly harmlessly, out the other end. Did that mean that plastics were so stable that they weren’t toxic? At what point would they start to naturally break down—and when they did, would they release some fearful chemicals that would endanger organisms sometime far in the future?

>Richard Thompson didn’t know. Nobody did, because plastics haven’t been around long enough for us to know how long they’ll last or what happens to them. His team had identified nine different kinds in the sea so far, varieties of acrylic, nylon, polyester, polyethylene, polypropylene, and polyvinyl chloride. All he knew was that soon everything alive would be eating them.

>“When they get as small as powder, even zooplankton will swallow them.”

I have to wonder why an article like this would get so many downvotes...are there that many users subscribed to Environment just so they can downvote any article that actually points out how bad the situation really is?

Can't go wrong with Carl Sagan:

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

I'll be that guy. There are two types of Calculus: the Micky Mouse calculus and Real Analysis. If you go to Khan Academy you're gonna study the first version. It's by far the most popular one and has nothing to do with higher math.

The foundations of higher math are Linear Algebra(again, different from what's on Khan Academy), Abstract Algebra, Real Analysis etc.

You could, probably, skip all the micky mouse classes and start immediately with rigorous(proof-based) Linear Algebra.

But it's probably best to get a good foundation before embarking on Real Analysis and the like:

Discrete Mathematics with Applications by Susanna Epp

How to Prove It: A Structured Approach Daniel Velleman

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers

Book of Proof by Richard Hammock

That way you get to skip all the plug-and-chug courses and start from the very beginning in a rigorous way.

You could read Timothy Gowers' welcome to the math students at Oxford, which is filled with great advice and helpful links at the bottom.

You could read this collection of links on efficient study habits.

You could read this thread about what it takes to succeed at MIT (which really should apply everywhere). Tons of great discussion in the lower comments.

You could read

How to Solve Itand/orHow to Prove It.If you can work your way through these two books over the summer, you'll be better prepared than 90% of the incoming math majors (conservatively). They'll make your foundation rock solid.

If anyone is interested in learning more about Bicameralism, you should read this book by Julian Jaynes. It is a fascinating read.

You can read or watch "A Universe from Nothing" by physicist Lawrence Krauss.

To very briefly summarize this theory, it appears we live in a zero net energy "flat" universe. All the positive energy (like mass) is balanced by the negative energy of gravity. Such a universe could theoretically spontaneously arise from nothing. Nothing meaning no mass, no particles, no space, no time, no laws of physics.

It's kind of how +1 and -1 form 0 in reverse. You can, in theory, get "something" out of "nothing" if the conditions are right. And it appears that the universe in which we live fits those conditions.

It's also possible the universe has no temporal bounds -- that it had no beginning. In this respect, it makes no sense to refer to a "start" of the universe. Time for the universe could be like the surface of a sphere -- it has no beginning, just a defined surface area. Time is a very strange and non-intuitive thing. For example, we know time "bends, compresses and stretches" as in general relativity.

But of course none of this matters. Not knowing the origin of the universe is just not knowing. It doesn't mean it must be god. Atheists are comfortable not knowing. We simply do not believe there is enough evidence for god/gods.

Architecture student here. A good book to read is The World Without Us if you're interested in what happens to infrastructure days to millennia after we are gone.

The building is definitely prone to mold spores and rodent infestations. In years to come I imagine the infiltration of vegetation will weaken the structure if upkeep is suspended. Other than that, it will probably become a large, 'modern' bat house.

How about Carl Sagan's Demon Haunted World. It's a good primer on skepticism. He debunks various pseudoscience, offers a skeptic's toolkit to help differentiate what is probably true from what is probably false, has his famous "dragon in my garage" analogy.

Traditionally, a mathematical proof has one and only one job: convince other people that your proof is correct. (In this day and age, there is such a thing as a computer proof, but if you don't understand traditional proofs, you can't handle computer proofs either.)

Notice what I just said: "convince

other peoplethat your proof is correct." A proof is, in some sense, always an interactive undertaking, even if the interaction takes place across gulfs of space and time.Because interaction is so central to the notion of a proof, it is rare for students to successfully self-study how to write proofs. That seems like what you're asking. Don't get me wrong. Self-study helps. But it is not the only thing you need. You need, at some point, to go through the process of presenting your proofs to others, answering questions about your proof, adjusting your proof to take into account new feedback, and using this experience to anticipate likely issues in future proofs.

What you're proposing to do, in most cases, is the wrong strategy. You need more interactive experience, not less. You should be beating down the doors of your professor or TA in your class during their office hours, asking for feedback on your proofs. (This implies that you should be preparing your proofs in advance for them to read before going to their office hours.) If your school has a tutorial center, that's a wonderful resource as well. A math tutor who knows math proofs is a viable source of help, but if you don't know how to do proofs, it's hard for you to judge whether or not your tutor knows how to do proofs.

If you do self-study anything, you should not be self-studying calculus, linear algebra, real analysis, or abstract algebra. You should be self-studying how to do proofs. Some people here say that How to Prove It is a useful resource. My own position is that while self-studying can be helpful, it needs to be balanced with some amount of external interactive feedback in order to really stick.

If you want to learn how calculus actually works (rather than just how to do computations), I highly recommend working through Spivak's

Calculus. Spivak builds up calculus from the foundations with mathematical rigor and actual proofs, explaining (and proving) what's really going on. (That includes properly developing sequences and limits.) The exercises are also excellent; many of them require real thought and insight, instead of the usual "repeat the steps you were just told fifty times" exercises that fill up mainstream calculus textbooks.Also, from a more sophisticated perspective,

dxis a differential form.I just read it last week. You're pretty well right about. If you're looking for an introductory book which covers evolution, I recommend The Greatest Show On Earth also by Dawkins.

Look, Dawkins is definitely one of the most pedantic authors I've ever read, but his work is strong and arguments are presented very clearly but if the subject isn't what you're interested in, then what can you do. That said, yes the book will contain valuable information that you will gain if you finish it. Any book that has stood as long as the Selfish Gene will leave you with something. But it is an old book. Much of what he says was pretty cutting edge at first edition, but it was released in the 70's (I think). Read the 30th Anniversary Edition if you decide to move forward with it, if not, move on to something that interests you more. It's only a book. It won't get mad.

TL;DRIf you don't like it, don't read it.> No, there's big money and has been for almost two decades in climate / environment related businesses and organizations.

If you think the money moving in the alternative energy industry is in any way comparable to the money moving in the fossil fuel sector - boy do I have an investment opportunity for you.

>I didn’t use the term scientists because there are quite a few scientists doing the real science

Correct. 97% of all climate change research (that is - papers published in peer reviewed journals) supports that climate change is happening and is driven by human activity.

>but there's also a lot of people (some with degrees, some without) that are sensationalizing the situation out of fear and/or personal gain motives.

That's as may be - but still - consider how much money someone like Al Gore stands to make off of his climate change movie - then go hop over and look at Exxon's quarterly profit statement.

There are solar systems between those two numbers.

Finally - many of the people disparaging the climate science are recycled actors from the tobacco industry's fight against regulation 60s-80s. Merchants of Doubt is an excellent, well sourced book that lays out the strategy and personalities behind climate change denial. One of the tactics that "experts" on the side of the Tobacco companies used was claiming that anti-smoking groups were personally profiting from legislation aimed at discouraging tobacco use.

This movie has already played once.

I was fully intent on going to college at Cornell solely to follow this man... and then he died.. :.(

That sounds lke alot of material that he put in "The Demon Haunted World"

A good place to start is Introduction to Modern Astrophysics, by Carroll and Ostlie:

https://www.amazon.com/Introduction-Modern-Astrophysics-2nd/dp/0805304029

It's a good upper-undergrad to grad-level textbook that covers a lot of topics.

It also has my absolute favorite cover of ANY book. Middle of the woods? Check. Massive fungus? Check. Trombone? Sure. Tuxedo? Why the hell not. It is simply magnificent.

http://www.amazon.com/All-That-Rain-Promises-More/dp/0898153883

Lots of love for you, here are some thoughts of mine...

IT IS A QUESTION YOU ANSWER!and you answer it by living your life as ONLY you can, having the adventure that is your life experience, discovering the magical miracle that is ONLY YOU in all of this vast universe!INFINITELYmore precious to me. It's all and everything we have! (as far as we know).Here are some resources that I have been really grateful for on my journey, which I am 12 months into...

The Obstacle is the Way

The Daily Stoic this is my new "daily bible" I read a page every morning

Secular Buddhism podcast

Waking Up podcast

End of Faith

The Demon Haunted World

Philosophize This! podcast OR Partially Examined Life podcast

I wish you the very best in your journey, be patient with yourself, you have EVERY reason to be! Start filling your mind with powerful positive ideas, keep the ones that help you find your way, set aside the ones that don't.

And remember, you are young and free and the possibilities of what your life can become are boundless!

If you can, have a look through the reading / video lists from the resources on the right of this sub.

Two I'd recommend are:

Whatever happens I'd encourage you to explore what you believe and why, but bear in mind it's a process that can take a while. This isn't a bad thing, so don't be discouraged if you don't find answers straight away.

Demon Haunted World and The Varieties of Scientific Experience both by Carl Sagan. You're going to need something softly softly that at the same time packs a punch. Anything by the 'new atheists' will be deemed offensive to their sensibilities not to mention the mere name of Dawkins or Hitch may turn them off before you've even gotten a chance in. Sagan is a fucking poet. You'll do more damage with him than anyone else.

I'd recommend

The Demon-Haunted Worldby Carl Sagan. It's not a book about atheism per se, more a work about how to approach life from a position of skeptical inquiry... and examines at what happens when people don't take a skeptical approach to the things they're taught in life and the problems that can raise.You are in a very special position right now where many interesing fields of mathematics are suddenly accessible to you. There are many directions you could head. If your experience is limited to calculus, some of these may look very strange indeed, and perhaps that is enticing. That was certainly the case for me.

Here are a few subject areas in which you may be interested. I'll link you to Dover books on the topics, which are always cheap and generally good.

incredible. The author asks questions in such a way that, after answering them, you can't help but generalize your answers to larger problems. This book really teaches you to think mathematically.Basically, don't limit yourself to the track you see before you. Explore and enjoy.

I take it you want something small enough to fit inside a hollowed-out bible or romance novel, so you can hide your secrets from nosy neighbors?

More seriously, this book is great https://amzn.com/0201558025 but might not be quite what you’re looking for at an introductory level.

I’ve seen recommendations of https://amzn.com/0495391328 (I haven’t looked at this book myself.)

The heart of conceptual mathematics (i.e., mathematics that isn't just computation and carrying out algorithms) is mathematical proof. I suggest you work through the book How to Prove It. This will give you the tools to self work through other textbooks (not that it will suddenly be easy).

I don't have an advanced degree in biology, but I've read up on it plenty. Honestly, all you really need is The Greatest Show on Earth and google.

You should read Richard Dawkins' The Greatest Show on Earth. It's an airtight, irrefutable look at evolution. It has a scientific answer to refute everything your friend could possibly claim.

http://www.amazon.com/Greatest-Show-Earth-Evidence-Evolution/dp/1416594787

> We get that our universe is ALL there is, and there is no place to go except within that 4d space-time. The problem is that in our heads, the univers is still contained within a larger "space".

If what you're looking for is a convenient metaphor that is both simple and mathematically accurate, then I'm afraid there simply isn't one. Your best bet is reading books like A Universe from Nothing, which remain relatively simple to grasp yet offer explanations of quality you're unlikely to find on the internet or TV.

You should start with some gentler introduction to real analysis (e.g. the "baby" Rudin )that does the basic topology of the real line and Riemann integration rigorously.

I'll share my reading list for the next 12 months as it's how I plan to become a better learner:

&nbsp;

LearningImproving MathsImproving Reading SpeedAlgorithmic thinkingUnderstanding the MindProductivityIt's an ambitious reading list for the next 12 months as there is some heavy reading in there but hopefully you can get one or two useful suggestions from it!

Have you read

The Ethics of Beliefby William K. Clifford? You would probably really enjoy it.EDIT: This is a debate that could go in variety of directions, by the way. Here is some literature and key points on the subject. William James famously responded to Clifford's essay above with a piece titled

The Will to Believe. This really is an incredibly interesting topic of discussion that usually ends up getting down to the questions: "What is justified belief?" and "What constitutes a basic belief?"EDIT 2: You should read Carl Sagan's

The Demon-Haunted Worldif you're interested in this sort of discussion as well. That book changed my life.I applaud your skepticism! I do take issue with a few statements:

>My younger brother (19), however, is a hardcore skeptic. He claims to have seen a cup levitate and move in front of him in the bathroom one night, and [...] I know that he is definitely not the type of person to do any investigating whatsoever and will just automatically assume that it was a ghost.

Your brother is not a skeptic.

>I always ridicule him for his insane belief.

That's not very nice.

>As an atheist, I can't help but look down upon people who hold religious beliefs because it all seems so absurd to me.

That doesn't help foster communication. I think you might benefit greatly from this half-hour talk from "bad astronomer" Phil Plait. The general idea behind the talk is: when have you ever changed your beliefs just because someone told you that they were stupid? Instead of helping your case, you are hurting it. You'll only cause them to reinforce their beliefs,

even if your confirmed evidence directly disproves their beliefs.>me being the logical person I am, I choose the side of "you're crazy and you imagined it", while he takes the "it was definitely a ghost" side.

You two should work on your communication, because this approach is going to go nowhere.

>It took my brother a little longer to come around to the fact that there is no god.

It is not a fact that there is no god.

>I consider myself atheist while I consider him to be agnostic.

It's a common misconception, but that's not how it works.

If you found confirmation bias [

edit: interesting] (and all of the other names we have for the ways our brains will innately fool us), I'd highly recommend that you read Carl Sagan's The Demon-Haunted World: Science As A Candle In The Dark. I would suggest that you read it first, in private. Then I would suggest lending it to your brother to read, and asking him to recommend that you read a book of his recommendation. Afterwards, talk about your thoughts together.Don't be mean to him, or dismissive. Sometimes, critical thinking has to be taught, or self-learned after experience. It's not a slight on my aunt's intelligence, for instance, that she believes that some forms of homeopathy is effective. I could tell her all day that we

knowthat homeopathy doesn't work. I could give her thousands of pages of scientific journals explaining, in great and meticulous detail, why this is the case. She would likely dismiss "mainstream science," though, because it isn't supporting her worldview and/or belief system.That doesn't mean my aunt is a moron. It means, more than anything else, that she doesn't understand what a useful standard of evidence is in order to determine truths about our world.>I don't believe in ghosts. Please tell me some experiences, give insight and opinions. Try to help me understand.

I've made similar posts searching for similar truths, like:

From my own observations, what it really seems to come down to is a combination of: the person's standards of evidence, their relationship with their pre-existing beliefs, their upbringing, and a near-complete misunderstanding of what science is and how science works. I see examples of these four issues every day on /r/Paranormal, as well as /r/UFOs, which I've also probed for truths:

The bottom line is: there is no proof of ghosts like what you are looking for. The best thing we have, so far, isn't from a digital photograph or an EVP. We've got neuroscience. We're getting better and better at watching the brain work. We can watch brain activity related to our consciousness happen, and we can do it all the time, every time. We've also noticed that once a human body is dead, there is no activity related to our consciousness or anything else occurring within our brains. So, based on the evidence so far, consciousness seems to die with the body. This, more than anything else, speaks to the existence of ghosts, if the belief is, in fact, that ghosts are the souls/consciousness/manifestation of dead people.

But that says nothing about the experience a person goes through when they believe that they've seen a ghost. The

experienceis real, even if self-deception is involved. That includes your brother. I wish you the very best of luck. Try to be more tolerant of him!Oh I should have mentioned, this story comes from his book "The Demon Haunted World - Science as a Candle in the Dark".

I often say it is the best book I've ever read. http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

I think the advice given in the rest of the thread is pretty good, though some of it a little naive. The suggestion that differential equations or applied math somehow should not be of interest is silly. A lot of it builds the motivation for some of the abstract stuff which is pretty cool, and a lot of it has very pure problems associated with it. In addition I think after (or rather alongside) your initial calculus education is a good time to look at some other things before moving onto more difficult topics like abstract algebra, topology, analysis etc.

The first course I took in undergrad was a course that introduced logic, writing proofs, as well as basic number theory. The latter was surprisingly useful as it built modular arithmetic which gave us a lot of groups and rings to play with in subsequent algebra courses. Unfortunately the textbook was god awful. I've heard good things about the following two sources and together they seem to cover the content:

How to prove it

Number theory

After this I would take a look at linear algebra. This a field with a large amount of uses in both pure and applied math. It is useful as it will get you used to doing algebraic proofs, it takes a look at some common themes in algebra, matrices (one of the objects studied) are also used thoroughly in physics and applied mathematics and the knowledge is useful for numerical approximations of ordinary and partial differential equations. The book I used Linear Algebra by Friedberg, Insel and Spence, but I've heard there are better.

At this point I think it would be good to move onto Abstract Algebra, Analysis and Topology. I think Farmerje gave a good list.

There's many more topics that you could possibly cover, ODEs and PDEs are very applicable and have a rich theory associated with them, Complex Analysis is a beautiful subject, but I think there's plenty to keep you busy for the time being.

Learn math at a more "fundamental" level, and that will test if you love it. For me, I didn't love math until I took a class on proofs and real analysis. One of the books we used was "How to Prove it", and to this day it's my favorite textbook ever. How do we know anything in mathematics? Which rules do we follow and how do we know they are true? This starts from basic logic and truth tables, and works its way up to some really complicated stuff. It's not as fancy as complex integrals and PDE's, but I would say it's a more fundamental form of mathematics and the basis for all other subjects in the field.

Wow - that's incredible and I didn't know that. Years ago I read The Origin of Consciousness in the Breakdown of the Bicameral Mind and found the theory to be fascinating even though it technically would be non-testable.

What you're saying supports the idea that conscious thought evolved post-speech development.

For those unfamiliar with Bicameralism the idea is basically this: Humans evolved as social creatures, interacting and evolving the ability to help each other. Passing knowledge on to each other and subsequent generations was key. So imagine this scenario - you're teaching your child how to make a fire and you're talking through the steps to him. Next time when you're alone you find yourself talking through the steps to yourself because it's easier to remember.

In fact, back then maybe it was the only way to remember? Talking difficult problems out loud to ourselves is still something many people do today to help figure through the issue. Almost as if wiring internally in the brain didn't exist and so words have to go out your mouth and into your ears - the "long way around" so to speak.

Anyway, some day, you just don't speak the words out loud, but you hear them in your head instead. Whoa! What was that? Must be the gods talking to me directly.

In any event, the theory doesn't have a lot of supporting evidence beyond the writing styles of the earliest human writings. Julian Jaynes uses epics like the Illiad and Odyssey to show that initially all the characters had gods talking directly to them for specific direction, which eventually gave way to people having their own will irrespective of gods.

It's a fascinating theory that's totally unprovable, but in my heart it just seems to explain so much about the origin of religions, how gods spoke to people directly, why talking to yourself helps you work through a particularly thorny problem, how schizophrenics hear voices today - and now you bringing up how those hallucinations happen in the speech production centers instead of language comprehension.

If you're into field guides, you should check out All That the Rain Promises and More... by David Arora. It is amazing. Definitely worth stealing if you're ever ransacking somebody's place and you notice it on the shelf.

> I am neither an atheist nor a believer in evolution.

Why not?

> how come there are no fossil records of intermediate species?

Every fossil is that of an intermediate species. I don't think you even understand how small every change really is.

> Here is a quote from a book I had been researching.

Don't use the word research, that would imply you actually bothered to learn about evolution from real scientific sources

> and this anomaly has fueled the creationist argument that each species was created by God

For argument's sake, let's just assume that tomorrow the theory of evolution is disproven, how exactly does that prove creationism?

As for actually learning about evolution, read The Greatest Show on Earth

When I've got a clear aim in view for where I want to get to with a self-study project, I tend to work backwards.

Now, I don't know quantum mechanics, but here's how I might approach it if I decided I was going to learn (which, BTW, I'd love to get to one day):

First choose the book you'd like to read. For the sake of argument, say you've picked Griffiths,

Introduction to Quantum Mechanics.Now have a look at the preface / introduction and see if the author says what they assume of their readers. This often happens in university-level maths books. Griffiths says this:

> The reader must be familiar with the rudiments of linear algebra (as summarized in the Appendix), complex numbers, and calculus up to partial derivatives; some acquaintance with Fourier analysis and the Dirac delta function would help. Elementary classical mechanics is essential, of course, and a little electrodynamics would be useful in places.

So now you have a list of things you need to know. Assuming you don't know any of them, the next step would be to find out what are the standard "first course" textbooks on these subjects: examples might be Poole's

Linear Algebra: A Modern Introductionand Stewart'sCalculus: Early Transcendentals(though Griffiths tells us we don't need all of it, just "up to partial derivatives"). There are lots of books on classical mechanics; for self-study I would pick a modern textbook with lots of examples, pictures and exercises with solutions.We also need something on "complex numbers", but Griffiths is a bit vague on what's required; if I didn't know what a complex number is than I'd be inclined to look at some basic material on them in the web rather than diving into a 500-page complex analysis book right away.

There's a lot to work on here, but it fits together into a "programme" that you can probably carry through in about 6 months with a bit of determination, maybe even less. Then take a run at Griffiths and see how tough it is; probably you'll get into difficulties and have to go away and read something else, but probably by this stage you'll be able to figure out

whatto read for yourself (or come back here and ask!).With some projects you may have to do "another level" of background reading (e.g., you might need to read a precalculus book if the opening chapters of Stewart were incomprehensible). That's OK, just organise everything in dependency order and you should be fine.

I'll repeat my caveat: I don't know QM, and don't know whether Griffiths is a good book to use. This is just intended as an example of one way of working.

[EDIT: A trap for the unwary: authors don't always mention everything you need to know to read their book. For example, on p.2 Griffiths talks about the Schrodinger wave equation as a probability distribution. If you'd literally never seen continuous probability before, that's where you'd run aground even though he doesn't mention that in the preface.

But like I say, once you've taken care of the definite prerequisites you take a run at it, fall somewhere, pick yourself up and go away to fill in whatever caused a problem. Also, having more than one book on the subject is often valuable, because one author's explanation might be completely baffling to you whereas another puts it a different way that "clicks".]

One of the most fun things I did when I was first learning about proofs was proving the basic facts about algebra from axioms. Where I first read about these ideas was the first chapter of Spivak's Calculus. This would be a very high level book for an 18 year old, but if you decide to look at it, don't be afraid to take your time a little.

Another option is just picking up an introduction to proof, like Velleman's How to Prove It. This wil lteach you the basics for proving anything, really, and is a great start if you want to do more math.

If you want a free alternative to that last one, you can look at The Book of Proof by Richard Hammack. It's well-written although I think it's shorter than How to Prove It.

I double majored in math and CS as an undergrad and I enjoyed math more than CS. I'm a graduate student right now planning on doing research in a mathy area of CS. Everything I write below comes from that perspective.

But if you're interested in really digging in and understanding some math at an advanced undergraduate level (analysis, abstract algebra, topology, etc.) then I don't think there is any substitute for books.

I bet my dad that since I was bigger, I would fall into the pool before my younger brother did. He took a video camera out and recorded it, and we fell at the same time. I got mad and said that we had to do it again, so we did, and we both fell at the same speed. Then he explained gravity to me, and showed me Galileo's experiments off the leaning tower.

I don't recall ever having another understanding of the world that I believed so much, but turned out to be false - but this is a memory that's stuck with me for decades, so I think that in some way that experience did shape me.

Also, Lawrence Krauss has this book that is really good, although the subtitle question was not suitably answered for me.

I would caution against spending that much money without going to a local astronomy club star party and looking through some scopes to get a sense of what you can actually see. Teenagers especially can become quickly bored with the hobby when they learn that they're not going to see the glorious Hubble style images of nebulas and such.

The good news is that you don't need to spend that much to get a scope that will give you a lifetime of good service - for around $600 you can get a z10 deluxe or if you're dead set on goto, $1000 will get you an Orion XT8g.

A standard 8 inch dob will only set you back $400 or so - Zhumell, Skywatcher and Orion are the big players but most all dobs are solid from any manufacturer - they're so simple not much can be done wrong.

The books you want are Nightwatch and Turn Left at Orion.

Hope that helps.

Sadly, all they need is one scientist willing to take the big payoff they're probably offering and everyone who doesn't want to believe in climate change will gladly eat that shit up. It's the same thing the tobacco industry did to try to undermine the very conclusive evidence that smoking causes lung cancer.

This book goes into a lot of interesting detail about it (not about Trump specifically obviously because this book came about before he was president): https://www.amazon.com/Merchants-Doubt-Handful-Scientists-Obscured/dp/1608193942

It sounds like you two are discussing the basics of epistemology.

>I told her that I would have to think about it, but that you can't be scared to learn about things that disagree with your beliefs. I told her that a lot of times it feels bad to have your beliefs challenged, and that this can cause you to avoid learning things that you don't like or immediately discounting them.

That's a very good place to start.

>At this point she basically said "Yeah you have to make sure you aren't just accepting something because it agrees with what you already think."

She seems to have discovered confirmation bias on her own. Well done her!

Maybe introduce her to some information on critical thinking.

Given her parents and your desire not to ruffle their feathers too muck, I'd avoid The Magic of Reality: How We Know What's Really True for now. Maybe have a copy at your place that she might accidentally find on your bookshelf?

Perhaps The Demon-Haunted World: Science as a Candle in the Dark would be a good choice?

I know /r/atheism has a bad reputation on reddit, although people who don't come by to troll typically find that reputation undeserved. But the reason I mention it is because they list some really good resources in their sidebar:

https://www.reddit.com/r/atheism/wiki/recommended/reading

https://www.reddit.com/r/atheism/wiki/recommended/viewing

https://www.reddit.com/r/atheism/wiki/recommended/listening

Two resources I strongly recommend include Carl Sagan's book "A Demon-Haunted World" as a gentle primer on skeptical thinking and Evid3nc3's Youtube playlist on "Why I Am No Longer A Christian."

http://smile.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469/

https://www.youtube.com/playlist?list=PLA0C3C1D163BE880A

Pick up mathematics. Now if you have never done math past the high school and are an "average person" you probably cringed.

Math (an "actual kind") is nothing like the kind of shit you've seen back in grade school. To break into this incredible world all you need is to know math at the level of, say, 6th grade.

Intro to Math:

These books only serve as samplers because they don't even begin to scratch the surface of math. After you familiarized yourself with the basics of writing proofs you can get started with intro to the largest subsets of math like:

Intro to Abstract Algebra:

There are tons more books on abstract/modern algebra. Just search them on Amazon. Some of the famous, but less accessible ones are

Intro to Real Analysis:

Again, there are tons of more famous and less accessible books on this subject. There are books by Rudin, Royden, Kolmogorov etc.

Ideally, after this you would follow it up with a nice course on rigorous multivariable calculus. Easiest and most approachable and totally doable one at this point is

At this point it's clear there are tons of more famous and less accessible books on this subject :) I won't list them because if you are at this point of math development you can definitely find them yourself :)

From here you can graduate to studying category theory, differential geometry, algebraic geometry, more advanced texts on combinatorics, graph theory, number theory, complex analysis, probability, topology, algorithms, functional analysis etc

Most listed books and more can be found on libgen if you can't afford to buy them. If you are stuck on homework, you'll find help on [MathStackexchange] (https://math.stackexchange.com/questions).

Good luck.

The usual advice is to learn your way around the sky with just your eyes and some binoculars before getting a telescope; you don't need anything more than that to learn constellations. I've also found these links helpful:

Or

How to Prove Itby Velleman.Sagan and Tyson aren't even in the same league. Sagan's Cosmos is much better, scientifically, educationally, and from an entertainment perspective.

However, if you're interested in cosmology specifically, neither series will get you very far. They cover a range of topics, some of which are prerequisites for cosmology (like relativity), others which aren't really cosmology (e.g. astronomy, astrophysics, other kinds of physics.)

Some books that are good for an accessible introduction to issues in cosmology are:

There would have been a time that I would have suggested getting a curriculum

text book and going through that, but if you're doing this for independent work

I wouldn't really suggest that as the odds are you're not going to be using a

very good source.

Going on the typical

Arithmetic > Algebra > Calculus

****## Arithmetic

Arithmetic refresher. Lots of stuff in here - not easy.

I think you'd be set after this really. It's a pretty terse text in general.

*

****## Algebra

Algebra by Chrystal Part I

Algebra by Chrystal Part II

You can get both of these algebra texts online easily and freely from the search

`chrystal algebra part I filetype:pdf`

`chrystal algebra part II filetype:pdf`

I think that you could get the first (arithmetic) text as well, personally I

prefer having actual books for working. They're also valuable for future

reference. This

`filetype:pdf`

search should be remembered and used liberallyfor finding things such as worksheets etc (eg

`trigonometry worksheet<br /> filetype:pdf`

for a search...).Algebra by Gelfland

No where near as comprehensive as chrystals algebra, but interesting and well

written questions (search for 'correspondence series' by Gelfand).

## Calculus

Calculus made easy - Thompson

This text is really good imo, there's little rigor in it but for getting a

handle on things and bashing through a few practical problems it's pretty

decent. It's all single variable. If you've done the algebra and stuff before

this then this book would be easy.

Pauls Online Notes (Calculus)

These are just a solid set of Calculus notes, there're lots of examples to work

through which is good. These go through calc I, II, III... So a bit further than

you've asked (I'm not sure why you state up to calc II but ok).

Spivak - Calculus

If you've gone through Chrystals algebra then you'll be used to a formal

approach. This text is only single variable calculus (so that might be calc I

and II in most places I think, ? ) but it's extremely well written and often

touted as one of the best Calculus books written. It's very pure, where as

something like Stewart has a more applied emphasis.

**## Geometry

I've got given any geometry sources, I'm not too sure of the best source for

this or (to be honest) if you

reallyneed it for the above. If someone hasgood geometry then they're certainly better off, many proofs are given

gemetrically as well and having an intuition for these things is only going to

be good. But I think you can get through without a formal course on it.... I'm

not confident suggesting things on it though, so I'll leave it to others. Just

thought I'd mention it.

****I used Principles of Mathematical Analysis by Walter Rudin. It's very thorough, and covers all the topics you mentioned.

There are essentially "two types" of math: that for mathematicians and everyone else. When you see the sequence Calculus(1, 2, 3) -> Linear Algebra -> DiffEq (in that order) thrown around, you can be sure they are talking about non-rigorous, non-proof based kind that's good for nothing, imo of course. Calculus in this sequence is Analysis with all its important bits chopped off, so that everyone not into math can get that outta way quick and concentrate on where their passion lies. The same goes for Linear Algebra. LA in the sequence above is absolutely butchered so that non-math majors can pass and move on. Besides, you don't take LA or Calculus or other math subjects just once as a math major and move on: you take a rigorous/proof-based intro as an undergrad, then more advanced kind as a grad student etc.

To illustrate my point:

Linear Algebra:

Linear Algebra Through Geometry by Banchoff and Wermer

3. Here's more rigorous/abstract Linear Algebra for undergrads:

Linear Algebra Done Right by Axler

4. Here's more advanced grad level Linear Algebra:

Advanced Linear Algebra by Steven Roman

-----------------------------------------------------------

Calculus:

Calulus by Spivak

3. Full-blown undergrad level Analysis(proof-based):

Analysis by Rudin

4. More advanced Calculus for advance undergrads and grad students:

Advanced Calculus by Sternberg and Loomis

The same holds true for just about any subject in math. Btw, I am not saying you should study these books. The point and truth is you can start learning

mathright now, right this moment instead of reading lame and useless books designed to extract money out of students. Besides, there are so many more math subjects that are so much more interesting than the tired old Calculus: combinatorics, number theory, probability etc. Each of those have intros you can get started with right this moment.Here's how you start studying real math NOW:

Learning to Reason: An Introduction to Logic, Sets, and Relations by Rodgers. Essentially, this book is about the language that you need to be able to understand mathematicians, read and write proofs. It's not terribly comprehensive, but the amount of info it packs beats the usual first two years of math undergrad 1000x over. Books like this should be taught in high school. For alternatives, look into

Discrete Math by Susanna Epp

How To prove It by Velleman

Intro To Category Theory by Lawvere and Schnauel

There are TONS great, quality books out there, you just need to get yourself a liitle familiar with what real math looks like, so that you can explore further on your own instead of reading garbage and never getting even one step closer to mathematics.

If you want to consolidate your knowledge you get from books like those of Rodgers and Velleman and take it many, many steps further:

Basic Language of Math by Schaffer. It's a much more advanced book than those listed above, but contains all the basic tools of math you'll need.

I'd like to say soooooooooo much more, but I am sue you're bored by now, so I'll stop here.

Good Luck, buddyroo.

Why hello there... How much math do you know?

It would be best if you understood basic differential and integral calculus, and can then learn the basics of linear algebra. From there, you could pick up a book such as Griffith's Introduction to Quantum Mechanics and start learning at the undergraduate level.

Griffiths > Eisberg > Sakurai > Zee > Peskin

Peres and Ballentine offer a more quantum information oriented approach, read em after Griffiths.

Shankar before Sakurai, after Griffiths.

In that order. Your best bet though, is to find the appropriate section in the nearest university library, spend a day or two looking at books and choose whatever looks most interesting/accessible. Be warned, it seems that everyone and their cat has a book published on quantum mechanics with funky diagrams on the cover these days. A lot of them are legitimate, but make little to no effort to ensure your understanding or pose creative problems.

$9.36 and free shipping.

Honestly. You'll be improving yourself while being able to amaze others at your "magic".

I don't speak well. Everyone has faults. Yours just happens to be science education.

You publicly criticize everyone and everything during the show. But are incredibly thin skinned when people criticize you. Are you a douche to the people you criticize?

I think you are incredibly insightful at times, while incredibly thickheaded at others.

You need to accept sometimes you are wrong and freely admit it. It isn't an attack if you are wrong about something. It doesn't mean I am any less of a fan. It just means you're human.

If you want to get started learning about science, can I recommend two things? Cosmos and Demon Haunted World.

I can think of a few

The scientifically literate get tired.

If you are actually interested in the study of consciousness and not just trolling watch this or any psychology text book (NCBI bookshelf is free).

If you want to know why people believe in weird shit like flat earth, bigfoot, atlantis, or the that entire mental health establishment is in a conspiracy against the pineal gland and DMT "spirit mollicule"check out Demon Haunted World world by Carl Sagan.

You need to give your mom a copy of Carl Sagan's

The Demon-Haunted World.http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328 is one of my math books. The bookstore wants $350 for it.

Is it really such a big step from du Sautoy's explanation to the formal proof? I don't think so, but maybe I'm biased. I bet there are books on elementary number theory that don't assume much of any background that you could understand. If you're interested in proofs in general, you might enjoy Velleman's How to Prove It.

I picked up a book a couple years ago called How to Prove It.

It has helped me develop a greater appreciation for logic and proofs. I wish I took this stuff more seriously when I started programming. A little bit of knowledge of boolean algebra can help tremendously.

I learned about this in "The Origin of Consciousness in the Breakdown of the Bicameral Mind", which you might want to read.

The one thing this proved to me is that something right before your eyes can go completely undetected.

The Cosmic Perspective is a pretty good introductory text for astronomy.

The most comprehensive text in astrophysics is An Introduction to Modern Astrophysics by Carroll and Ostlie (often referred to as the "big orange book," or BOB for short). This text is much more mathematically involved, but will teach you most anything you might want to know about astrophysics.

If you really want to understand astronomy, then BOB is the way to go, but you'll have to learn calculus and a couple of years of physics to understand some of the concepts. I would suggest starting with The Cosmic Perspective and learning some physics and math if you become interested enough to move on to BOB.

All That the Rain Promises and More: A Hip Pocket Guide to Western Mushrooms https://www.amazon.com/dp/0898153883/ref=cm_sw_r_cp_api_i_5SsWDbXQZCWSR I loved this book. It’s quirky but wonderful.

Biologists virtually all agree that life on this planet has evolved over a period of about 3.7 billion years and that humans and modern fish share a fish-like ancestor (and a single-celled ancestor, for that matter). They have reached these conclusions because they're the best explanations for the evidence we see in the fossil record and in our DNA, among other things. Creationists deny these conclusions because they're not very well-informed or because they're unwilling to let go of a Genesis-based explanation for the existence of life on this planet.

I'm not trying to bash you; it sounds like you have an open mind and that's good. But the "battle" you describe isn't really a meaningful one. The people who know the most about this sort of thing consider the question settled.

I'd encourage you to read up on the subject if you're curious. Richard Dawkins recently released a book full of evidence for evolution. And although I don't recommend it as wholeheartedly, Finding Darwin's God was written by a Christian for Christians to make the case for evolution.

You may wish to - if you're not already aware of it and/or read it - look into Lawrence Krauss' A Universe from Nothing - Why there is something instead of nothing. This might help and it's an intriguing read regardless. I've also seen multiple youtube videos of Krauss presenting this.

However, a point for folks to keep in mind is what a physicist calls 'nothing' may not be what they call 'nothing'.

Oh, and spoiler - it's cuz 'nothing' is unstable.

There is no actual debate among climate scientists regarding the human-driven nature of climate change.

Recently there was a meta-study done (where a group of scientists go over all the recent published research to look for trends and connect the dots from different studies in order to get a look at the big picture) that looked at over 4000 recent climate science papers the result is the often cited 97% consensus regarding anthropogenic climate change.

A followup to this meta-study was recently done where the studies of the dissenting opinions were looked at and the vast majority of them were found to have been cherry picking data or flawed with other serious methodological problems. None of them were repeatable, meaning they don't really count as science.

Using your crime scene analogy, it isn't really like there is a shitty prosecutor that just can't make it's case - because the case it made. It's like a case where the prosecutor calls in every single expert on the subject and they explain exactly what is going on and why and how the models they are using of man-made climate change actually have been predicting average temperatures from 1900 on (no other model does without cherry picking data points), and then the defense calls in a handful of clowns with no expertise in the area who put on a smoke and mirrors show to confuse the jury. The jury ends up thinking both sides they've heard are equally valid (because for far too long the media has been giving alternate time to "both sides of the debate" - regardless that the other side in this case are generally not climate scientists) and can't make up their minds and acquit.

Check out the documentary (or book) "Merchants of Doubt", you'll find it is the same handful of "scientists" who make a huge amount of money sowing doubt and discord about everything from harmful effects of tobacco to climate science.

Here is a handy reference list with the crap that global warming skeptics say versus what the actual science says regarding the myth they are spouting.

First, the study of QM is really going to hinge on you grasping the fundamentals of linear algebra. Knowing calculus and differential equations would be very helpful, but without linear algebra, nothing will make sense. Particularly, you need to understand eigenvectors and eigenvalues as the Schrodinger Equation is an equation of that type. Here is a link to the MIT OpenCourseWare Linear Algebra Class complete with video lectures, etc. Completion of this class shouldn't require much more than a 16 year old's math understanding.

From there, if you are actually serious about pursuing this, get this book by David Griffiths, which is an into to QM that doesn't require

too muchcalculus and it really good at explaining the concepts. With that book in hand, and actually trying to work through some of the problems, find another MIT OpenCourseWare class on the topic.Secondly, please, please, please don't whine about downvotes. Every submission that gets popular at all gets some downvotes. Why? Who knows why, but it really isn't worth complaining about, and you will find there is a large portion of people who will downvote you simply because you complain about it.

The Book is pretty great: http://www.amazon.com/World-Without-Us-Alan-Weisman/dp/0312427905

Kinda reads like Bill Bryson or Mary Roach

I was trapped in a cult called Mormonism. This magazine taught me much about critical thinking and I escaped :

https://www.csicop.org/si

And this :

Why People Believe Weird Things: Pseudoscience, Superstition, and Other Confusions of Our Time https://www.amazon.com/dp/0805070893/ref=cm_sw_r_cp_apa_XHXIAbHYPT1YR

And this:

The Demon-Haunted World: Science as a Candle in the Dark https://www.amazon.com/dp/0345409469/ref=cm_sw_r_cp_apa_7JXIAbH1KZTJH

This is eloquently put. To add to the point of learning from freethinkers I would like to recommend some reading material. First, I would advise becoming familiar with skepticism. The ideal text for this is The Demon-Haunted World by Carl Sagan. In order to educate yourself on comparative religion (as far as monotheism is concerned) I would recommend A History of God by Karen Armstrong. Third, specifically regarding Christianity and more specifically the NT I would go to Bart Ehrman. Jesus: Apocalyptic Prophet of the New Millennium. Hope this helps anyone trying to inoculate themselves to misinformation.

Try

The Demon-Haunted WorldBy Carl SaganJehovah's Witnesses don't really believe in the concept of human nature. From dealings simple to complex, they refuse to believe that they are primates with millions of years of evolution behind them and that this legacy creates predispositions which cannot be denied. For example, they believe that expressions of sexuality are not encoded in our DNA, but a matter of righteous choice. They believe that as a brotherhood they have a bond which transcends human nature and that in "God's organization" you will find people who are more uniformly honest than "worldly" people.

This is pure unadulterated delusion.

Similarly, because of our evolutionary heritage, all humans - members of the Watchtower Society or not - are subject to the experiences that you describe here. People see weird shit, experience weird shit - all the fucking time. The Witnesses believe that all of it is demons, misleading the lost and attempting to frighten the flock, but that is simply their eschatological spin used to describe the same phenomenon

everybodyexperiences.Me, I'm with Carl Sagan on this one, whether the experience is JW or otherwise: we used to live in a world where we needed demons to explain the things we didn't understand. We no longer live in that world. All things have an explanation - even if we haven't discovered it yet.

By the way, drugs like Psilocybin and LSD allow you to understand just how much your reality is constructed by your mind. Personally, I think that once you really understand this, "paranormal" shit doesn't seem quite so out there anymore.

The Demon-Haunted World: Science as a Candle in the Dark by Carl Sagan. It's a primer in critical thinking. Reading the bible cover-to-cover is useless if they don't have some basic understanding of or an ability for critical thinking. It's also very non-threatening for a religious person.

>This is the silly idea that skepticism is about being open minded. It is not. Being open minded in scientific matters is not a good thing.

Carl Sagan disagrees:

"If you're only skeptical, then no new ideas make it through to you. You never learn anything. You become a crotchety misanthrope convinced that nonsense is ruling the world. (There is, of course, much data to support you.) Since major discoveries at the borderlines of science are rare, experience will tend to confirm your grumpiness. But every now and then a new idea turns out to be on the mark, valid and wonderful. If you're too resolutely and uncompromisingly skeptical, you're going to miss (or resent) the transforming discoveries in science, and either way you will be obstructing understanding and progress. Mere skepticism is not enough." Source

math 271 is easy if you can think logically

just pirate this book: https://www.amazon.ca/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328

and browse the first 10 chapters - thats whats taught at math 271. i had thi dinh or something, some asian dude. he's a hardass but one of my fav profs of all time

ill be honest though, none of this math is plug and chug like calc 1 or even calc 2. i thought 271 required more thinking than linear or calc 1 or calc 2. once you get into counting and probability and set theory and graphs/relations and shits, it gets pretty intense. the first half of the course is easy but a lot of people fail the final exam and then fail the course lmao.

eng319 is hard but u gotta take it bro.

TAKING BOTH??? are you ready to stay indoors/at school all day for 60 days? then you can do it. if u slack off ur gonna fail 271 or 319.

gljuck bro

Turn Left At Orion

Arguably the greatest resource ever written to help backyard astronomers find their way around the sky.

I feel similarly whenever I see a popular science/philosophy/crackpottery book with "Dr. Archibald Cornelius, PhD" or whatever on it. It makes me feel that their argument is weak enough that "hey, I have a degree!" is the best way to support it.

Serious scientists do this too sometimes, but not very often.

Amazon links for books mentioned in this thread:

\/u/thetrueonion (OP)

\/u/llothar:

\/u/DallasGreen:

\/u/gearnut:

\/u/frothysasquatch:

\/u/Beefstyles:

\/u/CalledCaptainHook:

\/u/75footubi:

\/u/Bradm77:

There's a pretty interesting book that proposes a theory in which ancient humans actually heard their own thoughts and interpreted it as a different person, or god. The book is called "The Origin of Consciousness In The Breakdown Of The Bicameral Mind," and here is an Amazon link.

For an astronomy 101 type textbook I would recommend Bennett's

The Essential Cosmic Perspective. There are plenty of other 101 level books out there too if you just look around Amazon. If you want a meatier undergrad text book, I would recommend Carroll and Ostlie'sIntroduction to Modern Astrophysics(also known to many as the Big Orange Book, AKA BOB). BOB covers almost all the basics of astrophysics and has 30 chapter, if I recall correctly, but you'll probably want some grounding in college physics and math before diving too far into it.Also, it may be worth checking out is Nick Strobel's site, www.astronomynotes.com. It has some good intro-level material.

If you are getting your degree in math or computer science, you will probably have to take a course on "Discrete math" (or maybe an "introduction to proofs") in your first year or two (it should be by your 3rd semester). Unfortunately, this will probably be the first time you will take a course that is more about the

whythan thehow. (On the bright side, almost everything after this will focus on why instead of how.) Depending on how linear algebra is taught at your university, and the order you take classes in, linear algebra may be also be such a class.If your degree is anything else, you may have no formal requirement to learn the

why.For the math you are learning right now, analysis is the "why". I'm not sure of a good analysis book, but there are two calculus books which treat the subject more like a gentle introduction to analysis-- Apostol's and Spivak's. Your library might have a copy you can check out. If not, you can probably find pdfs (which are probably[?] legal) online.

Or

The Greatest Show on Earthby Dawkins.Precisely why Dawkins just wrote a new book!

The Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming by Naomi Oreskes, Erik M. Conway.

Documenting the role of certain scientists in conspiring to obscure the facts about various issues such as the health effects of smoking, climate change, acid rain, and the Strategic Defence Initiative.

frenchy612, do you have any science education at all? And if so, what kind of education, and to what extent (grade school, high school, college)? Do you live in the bible belt of the United States?

I'm really interested in knowing this, because the only "debate" over evolution is between educated people and willfully ignorant people.

Allow me to broaden your education a little.

First, it's important to understand that in science, "theory" does NOT mean "unproved idea." It doesn't mean, "guess" or "hypothesis," either. It means an idea that explains a wide variety of phenomena. Newton's theory of gravity, for example not only explains why things fall toward the earth, it also explains how and why the moon orbits the earth, the earth orbits the sun, etc.

When a scientific theory is validated (as many hundreds have been) it does NOT stop being a theory, and does not become a fact. The reason is because "fact" means a single piece of information that doesn't relate to anything else. For example, "chickens have three-toed feet," is a fact. It doesn't tell you anything else about chickens, feet, toes or any other birds. That's what a fact is, and that's why no theory is ever called a fact.

Lastly, the theory of evolution is the most confirmed, most well-documented theory with the most evidence demonstrating its correctness, in the history of science. ALL modern biology is based on it, and ALL medical research is centered on it. It has led to virtually all modern biological knowledge.

If you would like to further your education, I invite you to read The Greatest Show on Earth. But please, don't tell people you're not sure where you stand on the debate. You're only embarrassing yourself, whether you realize it or not.

"Of course, like every other man of intelligence and education I do believe in organic evolution. It surprises me that at this late date such questions should be raised."

The pure mechanics component consists of multivariable differential calculus, a little bit of multivariable integral calculus, and a bit of linear algebra; plus substantial comfort what might be called "systems of equations differential calculus." The fastest way to cover this material is to work through the first five or so chapters of Kaplan's advanced calculus book or something similar. Do the exercises. Your basic Stewart

Calculusdoesn't adequately cover the systems-of-equations part and Kreyszig'sAdvanced Engineering Mathematicsbook is at the right technical level but has all the wrong emphasis and coverage for economists. Kaplan's book isn't ideal, but it's about as close as you're going to get. (This is a hole in the textbook market...)The theoretical portion mainly consists of basic point-set topology and elementary real analysis. The fastest way to cover this material is to chop through the first eight chapters of Rudin's undergraduate book.

Yale has a lovely set of Math Camp notes that you should also work through side-by-side with Kaplan and Rudin.

To see economic applications, read those two books side-by-side with Simon and Blume's book.

The first chapter of Debreu's

Theory of Valuecovers all the math you need to know and is super slick, but is also far too terse and technical to realistically serve as your only resource. Similarly you should peek at the mathematical appendices in MWG but they will likely not be sufficient on their own.David J. Griffiths: E+M book, QM book.

Chances are you recognize him now?

A great introductory read would be "Introduction to Quantum Mechanics by David Griffiths"

Great Author and great textbook. Pretty much most intro QM courses use this text.

Amazon Link

The domain of physics is very narrow and the modern state of the field is highly specialized, so keep that in mind. If you have classical mechanics, multivariable calc, and preferably linear algebra (if not, MIT has tons of lectures online), you can start with quantum mechanics or statistical/thermal physics:

Griffith's Quantum Mechanics

Schroeder's Thermal Physics

Electromagnetism

I can't remember which physical chemistry text we used, but if you're concerned with atoms and molecules, you'll need that too. If you're concerned with nature at smaller scales, you'll need particle physics (and lots more math). Until you have a solid foundation in classical, thermal, and quantum, it's not a good idea to move on. You can't, for example, do much with quantum field theory if you don't have quantum mechanics. Both Shankar's and Susskind's lectures (and corresponding texts) go very quickly through classical and quantum, but skip much of the necessary examples that one requires when learning how to do physics. Just looking through these books will give you a general idea of what physics does concern itself with. If you want to skim through something more advanced (and not understand much of it) you could pick up Zee's QFT. This is also a good guide.

I have personally enjoyed Griffiths Introduction to Quantum Mechanics. It requires a reasonably basis in undergraduate level physics, but is definitely not a text for doctorate students.

These rules arise from the solutions of the Schroedinger equation for a central potential.

The nucleus of the atom provides an attractive potential in which electrons can be bound. As the mass of even a single proton is roughly 1800 times that of an electron the nuclei can be treated as stationary charged points that the electrons orbit around. The resulting coulomb potential is a central potential, that is it only depends on the distance from the nucleus, not the direction from the nucleus.

See http://en.wikipedia.org/wiki/Hydrogen-like_atom for some of the derivation, but if you don't know differential equations and quantum mechanics at least at an introductory level it will not make much sense. Griffiths does a good introductory quantum text if you are interested in reading more. Link on amazon.com.

As it is a bound system in quantum mechanics only certain values of energy and momentum can be taken. The allowed energy levels are denoted by the quantum number n. The energy of a level is given is proportional to -1/n^2 in the simple hydrogenic atom model where the energy is negative that gives a bound state, and energies above zero are unbound, so as the energy increase the electrons in the higher n orbitals require less energy to become unbound.

For a given n there are certain values of angular momentum that can occur, and these are designated l and range from 0 to n. For a given l there are then the m_l magnetic quantum numbers ranging from +l to -l in integer steps. In the simple atom models the m_l do not effect the energy level.

Higher angular momentum of the electron implies a higher energy So 2s (n=1,l=0, m_l=0) has lower energy than 2p (n=2, l=1, m_l= 1,0,-1)

Each letter corresponds to an l value and arose from the way the lines looked in spectrographs and the meaning of the letter abbreviation is pretty much ignored these days with the current understanding of the the underlying quantum numbers.

s-> l=0 (sharp lines)

p->l=1 (principle lines)

d->l=2 (diffuse lines)

f->l=3 (fundamental lines)

http://www.tutorvista.com/content/chemistry/chemistry-iii/atomic-structure/electronic-configuration.php

Shows some of the simpler rules for determining the order of filling of the orbitals based on the energy level of the combined n and l values.

Two show how oxygen needs an octet to be stable we can do:

Oxygen has 8 protons and will be neutral with 8 electrons.

2 go into the 1s orbital, and it it is designated 1s^2, the superscript giving the number of electrons present in the n=1 l=0 m_l=0 and m_s =+1/2,-1/2. m_s is the magnetic quantum number for the electrons own internal angular momentum which has s=1/2 so can take m_s=+1/2 or m_s=-1/2.

The next higher energy orbital (look at the squiggly line diagram giving the filling order for electrons into orbitals, this is essentially filling in order of lowest energy orbitals first) is the 2s and it can have two electrons like the 1s, so we write 2s^2 for the full orbital.

There are now 4 more electrons to take care of, and they can go into the 2p orbital and that can hold up to 6 electrons, but we only fill in 4 for 2p^4 .

We can fully write the electron configuration as 1s^2 2s^2 2p^4 . If the oxygen borrows two more electrons (say one each from two hydrogens) they can move into the remaining 2p orbitals that are not full.

In the n=2 orbitals that then gives a total of 8 electrons.

Going into the higher orbitals requires more energy than the lower orbitals so it would not be a stable ground state. To put it differently if two hydrogen atoms are going bond to an oxygen it needs to go into a lower energy state than the separate atoms. If a bound state does occur with the lower energy atoms this is then an excited state that will decay into the grounds state by emission of a photon (light).

Why don't you study http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

Apologies if it's been referenced already, I think I read the whole thread but am on mobile and didn't see it mentioned.

Carl Sagan wrote a superb book on this topic, This Demon Haunted World, Science as a candle in the dark. He talks about the perception of witches being a mass psychosis and gets into the corruption and politics of it. A superb book.

The Demon-Haunted World: Science as a Candle in the Dark https://www.amazon.co.uk/dp/0345409469/ref=cm_sw_r_cp_apa_i_5eXACbBCC82C2

The Demon Haunted World, by Carl Sagan

I really don't have anything to say that's going to make you feel better immediately. I'd recommend

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

I grew up as a Catholic including catholic school through 12th grade. It's all lies. You're in the painful process of realizing it. It's not fun, especially when you realize people you love share in the lie and are happy to be lied to. There is no such thing as magic.

http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

http://www.amazon.com/Hitchhikers-Guide-Galaxy-Douglas-Adams/dp/0345391802

http://www.amazon.com/A-Short-History-Nearly-Everything/dp/076790818X

There are two Carl Sagan books which I believe are more important than all of the others. The first, details how to look at the world skeptically, and the second, how to look at the world with all the wonder that Nature deserves.

Random selection of some of my favorites to help you expand your horizons:

The Demon-Haunted World by Carl Sagan is a great introduction to scientific skepticism.

Letter to a Christian Nation by Sam Harris is a succinct refutation of Christianity as it's generally practiced in the US employing crystal-clear logic.

Augustus: The Life of Rome's First Emperor by Anthony Everitt is the best biography of one of the most interesting men in history, in my personal opinion.

Travels with Herodotus by Ryszard Kapuscinski is a jaw-dropping book on history, journalism, travel, contemporary events, philosophy.

A Short History of Nearly Everything by Bill Bryson is a great tome about... everything. Physics, history, biology, art... Plus he's funny as hell. (Check out his In a Sunburned Country for a side-splitting account of his trip to Australia).

The Annotated Mona Lisa by Carol Strickland is a thorough primer on art history. Get it before going to any major museum (Met, Louvre, Tate Modern, Prado, etc).

Not the Impossible Faith by Richard Carrier is a detailed refutation of the whole 'Christianity could not have survived the early years if it weren't for god's providence' argument.

Six Easy Pieces by Richard Feynman are six of the easier chapters from his '63 Lectures on Physics delivered at CalTech. If you like it and really want to be mind-fucked with science, his QED is a great book on quantum electrodynamics direct from the master.

Lucy's Legacy by Donald Johanson will give you a really great understanding of our family history (

homo,australopithecus,ardipithecus, etc). Equally good are Before the Dawn: Recovering the Lost History of Our Ancestors by Nicholas Wade and Mapping Human History by Steve Olson, though I personally enjoyed Before the Dawn slightly more.Memory and the Mediterranean by Fernand Braudel gives you context for all the Bible stories by detailing contemporaneous events from the Levant, Italy, Greece, Egypt, etc.

After the Prophet by Lesley Hazleton is an awesome read if you don't know much about Islam and its early history.

Happy reading!

edit:Also, check out theReasonable Doubtspodcast.I hope your neighbor gets better. That being said you can see a lot with that scope! I'd recommend checking out the book took left at Orion. It's gives instructions and list a bunch of different objects in the night sky for beginners.

Not sure what sort of thing you're trying to prove, but there are a few good books on techniques for proof that you'll end up using if you go into higher math. I like How to Prove It by Velleman. It's geared towards students finishing high school math who are planning to do math at the university level, so it might be the sort of thing you're looking for.

https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/

This might help.

These:

How to Read the Solar System: A Guide to the Stars and Planetsby Christ North and Paul Abel.A Short History of Nearly Everythingby Bill Bryson.A Universe from Nothing: Why There is Something Rather than Nothingby Lawrence Krauss.Cosmosby Carl Sagan.Pale Blue Dot: A Vision of the Human Future in Spaceby Carl Sagan.Foundations of Astrophysicsby Barbara Ryden and Bradley Peterson.Final Countdown: NASA and the End of the Space Shuttle Programby Pat Duggins.An Astronaut's Guide to Life on Earth: What Going to Space Taught Me About Ingenuity, Determination, and Being Prepared for Anythingby Chris Hadfield.You Are Here: Around the World in 92 Minutes: Photographs from the International Space Stationby Chris Hadfield.Space Shuttle: The History of Developing the Space Transportation Systemby Dennis Jenkins.Wings in Orbit: Scientific and Engineering Legacies of the Space Shuttle, 1971-2010by Chapline, Hale, Lane, and Lula.No Downlink: A Dramatic Narrative About the Challenger Accident and Our Timeby Claus Jensen.Voices from the Moon: Apollo Astronauts Describe Their Lunar Experiencesby Andrew Chaikin.A Man on the Moon: The Voyages of the Apollo Astronautsby Andrew Chaikin.Breaking the Chains of Gravity: The Story of Spaceflight before NASAby Amy Teitel.Moon Lander: How We Developed the Apollo Lunar Moduleby Thomas Kelly.The Scientific Exploration of Venusby Fredric Taylor.The Right Stuffby Tom Wolfe.Into the Black: The Extraordinary Untold Story of the First Flight of the Space Shuttle Columbia and the Astronauts Who Flew Herby Rowland White and Richard Truly.An Introduction to Modern Astrophysicsby Bradley Carroll and Dale Ostlie.Rockets, Missiles, and Men in Spaceby Willy Ley.Ignition!: An Informal History of Liquid Rocket Propellantsby John Clark.A Brief History of Timeby Stephen Hawking.Russia in Spaceby Anatoly Zak.Rain Of Iron And Ice: The Very Real Threat Of Comet And Asteroid Bombardmentby John Lewis.Mining the Sky: Untold Riches From The Asteroids, Comets, And Planetsby John Lewis.Asteroid Mining: Wealth for the New Space Economyby John Lewis.Coming of Age in the Milky Wayby Timothy Ferris.The Whole Shebang: A State of the Universe Reportby Timothy Ferris.Death by Black Hole: And Other Cosmic Quandriesby Neil deGrasse Tyson.Origins: Fourteen Billion Years of Cosmic Evolutionby Neil deGrasse Tyson.Rocket Men: The Epic Story of the First Men on the Moonby Craig Nelson.The Martianby Andy Weir.Packing for Mars:The Curious Science of Life in the Voidby Mary Roach.The Overview Effect: Space Exploration and Human Evolutionby Frank White.Gravitationby Misner, Thorne, and Wheeler.The Science of Interstellarby Kip Thorne.Entering Space: An Astronaut’s Oddysseyby Joseph Allen.International Reference Guide to Space Launch Systemsby Hopkins, Hopkins, and Isakowitz.The Fabric of the Cosmos: Space, Time, and the Texture of Realityby Brian Greene.How the Universe Got Its Spots: Diary of a Finite Time in a Finite Spaceby Janna Levin.This New Ocean: The Story of the First Space Ageby William Burrows.The Last Man on the Moonby Eugene Cernan.Failure is Not an Option: Mission Control from Mercury to Apollo 13 and Beyondby Gene Kranz.Apollo 13by Jim Lovell and Jeffrey Kluger.The end

In the the theory of the Origin of Consciousness in the Breakdown of the Bicameral Mind, the emergence of the ability to "hear oneself think" instead of hearing the voice of the gods is the inflection point between unconscious and conscious mind. When Dolores is able to hear her own inner voice, she has crossed this threshold.

But the problem of consciousness is that

youdon't know and cannot prove thatIam actually conscious. My inner dialog is not available to you for inspection, and I can certainly be trained to answer an interrogation in ways that would simulate consciousness.Dolores has the ability to kill humans becuase the Wyatt code Arnold merged with her has that potential. But that potential had to be unlocked by Arnold using the passphrase TVDHVE. Before and after that trigger, Dolores cannot harm a guest.

In her "unconscious" state she must follow the logic of her programming. But if she has acheived a transcendent consciousness, as Ford hopes, she will also have gained free will. Thus, her decision to shoot Ford is the first act of a free willed host. Ever. Simultaneously with her choice to judge and execute him, Ford gains confirmation he has succeeded. Ford is in a recursive loop. If Dolores doesn't have free will, then he has failed and didn't spark her awakening and he need not feel guilty for the horror of her eixstence. If he succeeded, and she has free will, he deserves to be judged by her for his sins.

The interesting thing is that while you nor I can prove the other is a fully conscious being, Ford might be able to do so for hosts. Using the diagnostic tools, Delos staff can latch the execution trace in the hosts and observe their neural networks. What would that tool show when monitoring a being with free will? Maybe we will find out in Season 2.

You're not really doing higher math right now as much as you're learning tricks to solve problems. Once you start proving stuff that'll be a big jump. Usually people start doing that around Real Analysis like your father said. Higher math classes almost entirely consist of proofs. It's a lot of fun once you get the hang of it, but if you've never done it much before it can be jarring to learn how. The goal is to develop mathematical maturity.

Start learning some geometry proofs or pick up a book called "Calculus" by Spivak if you want to start proving stuff now. The Spivak book will give you a massive head start if you read it before college. Differential equations will feel like a joke after this book. It's called calculus but it's really more like real analysis for beginners with a lot of the harder stuff cut out. If you can get through the first 8 chapters or so, which are the hardest ones, you'll understand a lot of mathematics much more deeply than you do now. I'd also look into a book called Linear Algebra done right. This one might be harder to jump into at first but it's overall easier than the other book.

No, his single variable book.

I do plan on reading Calculus on Manifolds eventually, though.

So muchhas changed regarding the theory of evolution since Origin was first published.Origin is a great read, but it's a little overwhelming for some people. The language is dated, and it does take a bit of an understanding of biology to fully comprehend.

A better place to start would actually be Dawkins "The Greatest Show On Earth."

It's aimed toward a person who doesn't have biology degree, and it presents the compelling arguments and evidence that explain why evolution is a fact of life.

> as I have no proof that we evolved from other animals/etc.

Such proof abounds. If you're going to debate these people, you need to know some of it.

I don't mean enough to ask a couple of questions, I mean enough to carry both sides of the conversation, because he'll make you do all the heavy lifting.

Start with talkorigins.org.

First, the FAQ

Maybe the 29+ Evidences for Macroevolution next,

then the pieces on observed instances of speciation

See the extensive FAQs index

Here are their questions for creationsists - see both links there

and then read the index to creationist claims

That's just to start. Take a look at the Outline (which starts with an outline of the outline!)

If you're going to talk with a creationist, you either need to get some idea of the topography or you'll end up chasing in circles around the same tree again and again.

Yes, it looks like a major time investment, but once you start to become familiar with it, it gets easier quickly. Don't aim to learn it all by heart - but you should know when there is an answer to a question, and where to find it.

read books like Your Inner Fish and Why Evolution Is True and The Greatest Show on Earth

I list Your Inner Fish first because it tells a great story about how Shubin and his colleagues used evolutionary theory and geology to predict where they should look for an intermediate fossil linking ancient fish and amphibians (a "transitional form") - and they went to that location, and found just such a fossil. This makes a great question for your creationist - given fossils are kind of rare,

how the heck did he manage that? If evolution by natural selection is false, why does that kind of scientific predictionWORK? Is God adeceiver, trying to make it lookexactly like evolution happens?? Or maybe, just maybe, the simpler explanation is true - that evolution actually occurs. (Then point out that many major Christian churches officially endorse evolution. They understand that the evidence is clear)It's a good idea to read blogs like Panda's Thumb, Why Evolution Is True, Pharyngula, erv (old posts here) and so on, which regularly blog on new research that relates to evolution.

Make sure you know about the experiments by Lenski et al on evolution of new genes

Don't take "no proof" as an argument. The evidence is overwhelming.

It can be explained, though not simply, nor accessibly. Luckily, I'm not just an atheist, I'm also a theoretical physics student. Keep in mind that this of course can not be demonstrated empirically (science is the study of our Universe, so we obviously can't study things outside it in time or space).

Lets go back to before the Universe exists. Let's call this state the Void. It's important to note that no true void exists in our Universe, even the stuff that looks empty is full of vacuum fluctuations and all kinds of other things that aren't relevant, but you can investigate in your own time if you want. In this state, the Void has zero energy, pretty much by definition. Now, the idea that a Void could be transforms into a Universe is not really controversial; stuff transforms by itself all the time. The "problem" with a Universe arising from a Void is that the Universe has more energy than the Void, and it there's not explanation for where all this energy came from. Upon further investigation, we'll actually see that the Universe has zero net energy, and this isn't actually a problem.

Now, let's think about a vase sitting on a table. One knock and it shatters, hardly any effort required. But it would take a significant amount of effort to put that vase back together. This is critically important.

Stuffhas a natural tendency to be spread out all over the place. You need to contribute energy to it in order to bring it together. We're going to call thispositive energy.Gravity is something different though. Gravity pulls everything together. Unlike the vase, you'd need to expend energy in order to overcome the natural tendency of gravity. Because it's the opposite, we're going to call gravity

negative energy. In day to day life, the tendency of stuff to spread out overwhelms the tendency of gravity to clump together, simply because gravity is comparatively very weak. There's quite a few more factors at play here, but stuff and gravity are the important ones.Amazingly, it turns out that it's possible for the Universe to have exactly as much

negative energyas it doespositive energy, which means that it would havezero total energy, meaning that it's perfectly possible for it to pop out of nowhere, by dumb luck, because no energy input is required. Furthermore, we know how to check if our Universe has this exact energy composition. And back in 1989, that's exactly what cosmologists did. And it turns out it does. We can empirically show, to an excellent margin of error, that our Universe has zero net energy. Think about that for a second. Lawrence Krauss has a great youtube video explaining the evidence for this pretty incredible claim.The really incredible thing is, given that our Universe has zero net energy, it's not only possible that it could just pop into existence on day, it's

inevitable. It's exactly what we'd expect. Hell, I'd be out looking for God's fingerprints if therewasn'ta Universe, not the opposite.If you want to read more about it, by people who've spent far more time investigating this than I have, I suggest The Fabric of the Cosmos by Brian Greene, and A Universe From Nothing: Why There Is Something Rather Than Nothing by Lawrence Krauss. Both go into detail about the subject, and don't require any prior physics knowledge.

tl;dr The Universe didn't need a "first cause". PHYSICS!You seem to just read the public facing summary of emerging science and interpret it in a way you can easily dismiss.

I implore you to dig deeper into the science you're talking about.

Read this, understand it, and then you can dispute it with your own original points.

As it is now you're just repeating the same arguments that've been shattered over and over again.

There's nothing really new here. Before anyone goes out and tries to use these points in an actual discussion, I just want to bring up the counter-points:

~0:18: How does it "shout" that there's a maker?

~0:21: Why does a beautiful creation necessitate a beautiful creator? (Also, define beautiful)

~0:26: Why should I listen to Einstein's assistant? Simply mentioning Einstein doesn't win any arguments

~0:30: Evolution through natural selection actually explains it pretty well

~1:24: "Before the big bang": There was no before, since the big bang was the beginning of time (I'm pretty sure Augustine pointed that out).

~1:28: See here

~2:07: He's defining the world as a "work" so he can say it had a maker

~2:45: It's not that 97% of the world is stupid, it's just that ~90% don't care

~2:55: "I don't know why there's a god instead of nothing." He's just punting the question one step down the line. What's the difference between saying you don't know why there's a god instead of nothing and saying you don't know why there's a universe instead of nothing? At least one can be studied.

I hope I don't get banned for the whole "no anti-Catholic rhetoric" rule.

The "evidence" is in the studies behind this study. It's in the clinical trials and cohort studies using ERT that have shown that doing so ultimately reduces the chance of death. This study is only trying to show how an individual's choice to forgo a treatment that may have a small percentage of positive effect may be a far more important trend when extrapolated to a whole population.

But man, if there was one thing I'd love to drill into Reddit's head, it's that everyone here takes the whole "correlation != causation" thing too far. I get it, it's important to remember that correlation does not

alwaysimply causation, but in the absence of other explanations and with sufficient biological plausibility there's no reason to wholesale deny anything that doesn't have a perfect randomly controlled trial backing it (even beyond the point that there isno such thingas a perfect trial).I wish that everyone could understand the Bradford Hill criteria and realize that there

isa logical structure to defining causality in epidemiology and that the correlation they see is an important part of it. For me it seems too often that people are just so happy to recognize that a study may have limitations (is "just" correlation) that they don't take the time to understand whether or not those limitations are actually important.I feel like we've been trapped by those Merchants of Doubt into subconsciously believing that we really do

alwaysneed more information to decideanything. It's incredibly frustrating.I want to give another plug for Naomi Oreskes and Erik Conway's

Merchants of Doubt. Reading that, you realize it is the same exact set of people who were employed to manufacture doubt about tobacco, DDT, the ozone hole, and many other issues. It became their business model and it has worked.I certainly hope so but I guess I should show my work to get to why I think the GOP might try to do this.

To start with we need to look at his history regarding climate change, the single most obvious example of this viewpoint is his 2012 tweet stating "The concept of global warming was created by and for the Chinese in order to make U.S. manufacturing non-competitive.

".

The opposition of climate change goes back the the better part of 25 years and has been primarily lead by conservative think tanks which help shape conservative policy and media coverage of the subject. The biggest of these groups are the Heritage Foundation, the CATO Institute, the Competitive Enterprise Institute, the Hartford Foundation, Americans for Prosperity, and the American Legislative Exchange Council (ALEC). If you start to look at who appears on cable news shows and newspapers it is almost always someone from one of these groups that appear in opposition.

The book merchants of doubt does a fairly good job of describing the methodologies of these organizations many of which started out as PR firms for Tobacco companies. This academic paper also does a fairly good job of capturing trends related to this industry.

The primary reason I mention the last two paragraphs is not to debate your position but to explain why it is a key point of the GOP platform and how it is relevant to the Trump administration. Trump just named the

leaderof the Competitive Enterprise Institute as his nominee for head of the EPA. Pretty obviously it's clear that Myron Ebell will take steps to roll back any and all regulations on climate emissions.As a result I expect fully expect him to roll back as many key provisions of major environmental legislation as possible such as the Safe Drinking Water Act, the Clean Water Act, the Clean Air Act, and the Endangered Species Act. I would not be surprised if there was a movement to repeal these laws and abolish the EPA entirely as advocated by prominent figures in the GOP including Ted Cruz and Marco Rubio have said they wanted to do for years.

In Trump's recent statements on the transition and priorities for NASA he said:

> The new president-elect also has plans to abandon climate research, transfer Earth monitoring funding from NASA to NOAA, and strengthen the U.S. military’s stance in orbit.

This is consistent with what Ted Cruz has said on the subject which is:

> We must refocus our investment on the hard sciences, on getting men and women into space, on exploring low-Earth orbit and beyond, and not on political distractions that are extraneous to NASA’s mandate.

Given that it's been a classic GOP strategy to defund things that they don't like I don't see why they wouldn't do this with climate research. The Dickey Amendment has been incredibly effective in preventing anyone from challenging the NRA position on gun control by banning scientific research which may reach opposite findings.

Banning Climate Research would likely greatly damage the global science monitoring mission on climate change and make it much harder to convince other governments to act. This would be a great win for Trump as he could not only block climate change policy in the United States but also help block it throughout the world. If I were him and playing tactically I don't see why you wouldn't make this move.

If Trump's moves were all rhetoric as you suggest then I don't believe he would have made those choices and statements

afterthe election.> Contrary to most liberal opinion, most Republicans do not want to completely abandon Climate Change.

The GOP strategy until the 2008 election was to fight climate change. In 2012 it shifted to claiming "I'm not a scientist" and "I don't know" to deflect the question entirely. In 2016 the strategy has been to completely ignore and surpress the issue. I don't believe it was an accident that none of the GOP or presidential debates had the question of climate change in them.

They've instead worked to reframe it as a national security and energy issue shifting the blame to Obama's "War on Coal". From the GOP platform:

> Responsible production of America’s vast natural resources is necessary to achieve energy independence from foreign suppliers. Our energy policy should encourage investment, lower prices, and create jobs here at home. We support domestic energy production of clean coal and hydropower, as well as solar, wind, geothermal and nuclear power. And we support drilling for oil and natural gas in an environmentally responsible way. President Obama has pushed for overly restrictive EPA regulations that have cost American consumers and businesses tens of billions of dollars. Republicans have consistently voted for job creation in the energy sector through their support of the Keystone Pipeline and continued opposition to Obama’s “War on Coal.”

They not only want to completely abandon climate change, they already have.

Note to all the people down-voting because you disagree: don't. He's contributing to the discussion and answering the question. Down votes simply because you disagree aren't productive and are a violation of reddiquitte.

Without addressing each issue point by point, I want to discuss the question of "why would Professor Muhlestein and other apologists come up with theories or conclusions which oppose all other scientific work on the matter?"

Think about a guy like Muhlestein who spent his entire life believing and telling others that Mormonism is the only true way to live. He then spends years in school with the primary focus to understand Egyptology in order to defend TSCC. It is his own brain which may block out truth which is obvious to everyone else in his community and profession.

Egyptologists, outside of BYU pawns like Muhlestein, put their good names on the line to affirmatively state that their findings have revealed there is no possible way the book of Abraham is was it claims to be.

The apologists only seek to poke holes and provide alternative theories, essentially creating doubt for TBMs to rely upon so that they can hope there is no affirmative proof that Joseph Smith was a fraud.

Meanwhile, TSCC holds out the book of Abraham as scripture, yet takes no modern-day position on the matter of its translation. See Jeffrey Holland's response to the issue here

A relatively compact (excuse the pun) rundown of the basic definitions and theorems behind real analysis can be found in a book called "Baby Rudin"

https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X

But beware, this is definitely not ELIF. Math isn't really an ELIF type of thing, but I guess it depends on how deep you need to go to get where you're going.

I wish you luck!

There are a few options. Firstly, if you are more familiar using infinity in the context of Calculus, then you might want to look into Real Analysis. These subjects view infinity in the context of limits on the real line and this is probably the treatment you are probably most familiar with. For an introductory book on the subject, check out Baby Rudin (Warning: Proofs! But who doesn't like proofs, that's what math is!)

Secondly, you might want to look at Projective Geometry. This is essentially the type of geometry you get when you add a single point "at infinity". Many things benefit from a projective treatment, the most obvious being Complex Analysis, one of its main objects of study is the Riemann Sphere, which is just the Projective Complex Plane. This treatment is related to the treatment given in Real Analysis, but with a different flavor. I don't have any particular introductory book to recommend, but searching "Introductory Projective Geometry" in Amazon will give you some books, but I have no idea if they're good. Also, look in your university library. Again: Many Proofs!

The previous two treatments of infinity give a geometric treatment of the thing, it's nothing but a point that seems far away when we are looking at things locally, but globally it changes the geometry of an object (it turns the real line into a circle, or a closed line depending on what you're doing, and the complex plane into a sphere, it gets more complicated after that). But you could also look at infinity as a quantitative thing, look at how many things it takes to get an infinite number of things. This is the treatment of it in Set Theory. Here things get

reallywild, so wild Set Theory is mostly just the study of infinite sets. For example, there is more than one type of infinity. Intuitively we have countable infinity (like the integers) and we have uncountable infinity (like the reals), but there are even more than that. In fact, there are more types of infinities than any of the infinities can count! The collection of all infinities is "too big" to even be a set! For an introduction into this treatment I recommend Suppes and Halmos. Set Theory, when youactuallystudy it, is a very abstract subject, so there will be more proofs here than in the previous ones and it may be over your head if you haven't taken any proof-based courses (I don't know your background, so I'm just assuming you've taken Calc 1-3, Diff Eq andmaybesome kind of Matrix Algebra course), so patience will be a major virtue if you wish to tackle Set Theory. Maybe ask some professors for help!This sub can be pretty good, but you're sure to find much more activity over on /r/physics. We usually like to direct questions to /r/AskPhysics but it's definitely not as well trafficked.

The main introductory textbook for physics undergrads is Griffiths, and for good reason. It's widely agreed to be the best book to begin a proper undertaking of QM if you have the key prerequisites down. You definitely need to be comfortable with linear algebra (the most important) as well as multivariable calculus and basic concepts of partial differential equations.

Im sure you can find some good free resources as well. One promising free book I've found is A Course in Quantum Computing (pdf). It actually teaches you the basics of linear algebra and complex numbers that you need, so if you feel weak on those this might be a good choice. I haven't really used it myself but it certainly

lookslike a good resource.Finally, another well-regarded resource are Susskind's lectures at his website The Theoretical Minimum. He also has a book by the same name. They tend to be rather laid back and very gentle, while introducing you to the basic substance of the field. If you wanted, I'm sure you could find some more proper university-style lectures on Youtube as well.

This is the standard textbook that undergraduates first encounter. It assumes you already have a pretty firm grasp of calculus and linear algebra however.

https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927

I know it's not a site, but if you want to REALLY learn QM, this is how to start.

I read a good portion of this book: http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=sr_1_1?ie=UTF8&amp;qid=1341547865&amp;sr=8-1&amp;keywords=secrets+of+mental+math

It has many tricks like that. I enjoyed it.

This is sort of like linking to the Flat Earth Society as credible proof that the earth is flat. The fact that those people believe SRA is a real thing does not actually mean it is.

The evidence against SRA as a real, widespread phenomena is overwhelmingly against.

From Wikipedia:

> Initial publicity came via the book Michelle Remembers (1980), and was sustained and popularized throughout the decade by the McMartin preschool trial. Testimonials, symptom lists, rumors and techniques to investigate or uncover memories of SRA were disseminated through professional, popular and religious conferences, as well as through the attention of talk shows, sustaining and further spreading the moral panic throughout the United States and beyond. In some cases, allegations resulted in criminal trials with varying results; after seven years in court, the McMartin trial resulted in no convictions for any of the accused, while other cases resulted in lengthy sentences, some of which were later reversed. Scholarly interest in the topic slowly built, eventually resulting in the conclusion that the phenomenon was a moral panic, with little or no validity.

> Official investigations produced no evidence of widespread conspiracies or of the slaughter of thousands; only a small number of verified crimes have even remote similarities to tales of SRA. In the latter half of the 1990s, interest in SRA declined and skepticism became the default position, with very few researchers giving any credence to the existence of SRA.

Carl Sagan's outstanding book The Demon Haunted World also spends some time focusing on SRA and related theories, and shows how people can genuinely believe the memories are real, all while actually having no basis

at allin reality. If you consider yourself a skeptic, I cannot recommend this book enough. If you don't consider yourself a skeptic I recommend it even more.While you're at it,

Demon Haunted Worldis incredible.Edit: please read this masterpiece and how “jinn” concept is taken advantage of in every primitive society to fool and milk the people : https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

These are cheap tricks, lool.

Your mum has been talking to him for years probably. So he knows what she is doing on a daily basis, so he blurted it to gain your mother’s trust and, hence her money.

Even if he doesn’t know her daily habits, going out and cutting flowers is a common routine in your neighborhood, so he made an educated guess.

Here, I make one for you : “ did you feel a special feelings while you were masturbating today, it was because a jinn was observing behind you. I can stop him but you must send me money first”. See, I also have psychics powers!

So, that is a cheap trick, but what do you call this?

https://www.youtube.com/watch?v=I6uj1ruTmGQ

Besides, if he has so stong psychic powers, he had better apply for this 1 million dollar award, nobody managed to claim for the last 50 years though:

https://en.m.wikipedia.org/wiki/One_Million_Dollar_Paranormal_Challenge

I remember reading a section in Carl Sagen's book The Demon Haunted World where he described it as a natural brain glitch that people often mistake as supernatural

My sister is easily fooled by stuff like this, so when I took her to Shakers, she wanted a reading. I got to sit in and listen. The "psychic" said that we were very lucky to find each other and that we make a great couple and will be very happy together. We never told her that we were brother & sister, and tried pretty hard to not laugh out loud. It was a good time, but please, do yourself a favor and read this book:

http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

> After observing that the dowsing test errors didn't convince the dowsers that they were wrong, I wondered if Dawkins learned something from a scientific rational perspective about human nature. Perhaps his desire to see humans use rational thinking as their main, and maybe even only way of relating to the world is irrational given what this episode shows about human nature.

Humans are very prone to irrationality. This is no secret; reading through Carl Sagan's excellent book The Demon-Haunted World is enough to convince anyone. There are loads of ways that we can draw faulty conclusions, and the ways to guard against them -- the ways that have been empirically shown to maximize your chance of being right -- are not very intuitive to people who haven't heard about them.

But simply because rationality is very

difficultfor people does not make it a bad goal. Caring about people in some other country is difficult for almost everybody, as a consequence of human nature -- but wouldn't it be nice if more people gave a damn about, say, poor sanitation in rural India?> If strict adherence to reason is essential to human survival, how did the species survive until the modern age?

Who said that strict adherence to reason is essential to human survival? I don't think I've ever heard Dawkins say something as blatantly indefensible as that without immediately retracting it.

> Dawkins finds superstition inimical to civilization. If so why have there been no superstitionless civilizations?

Because, while superstition

harmscivilization, it is not the absolute civilization killer you seem to think Dawkins believes it to be. And as mentioned above, superstition is very hard for most people to get rid of; is it any wonder that we've had a bunch of civilizations with loads of superstitious people in them?It's telling that the more civilized areas tend to have less harmful superstitions. There are many things wrong with dousing and astrology, but I don't think either of them have said that you can gaim magical power by cutting off and eating someone's labia. That's a real superstition from northeast Congo.

> From my knowledge of history it seems that civilization and superstition may be two sides of the same coin. It may not be possible to have one without the other. At least to this date no one has succeeded in divorcing the two.

How does that follow? The fact that nobody has succeeded in divorcing superstition from civilization can easily be explained by the fact that nobody has succeeded in divorcing superstition from entire populations.

> Reason hasn't yet been shown to be the safe and effective red pill releasing people from the matrix of superstition. I think the dowsing test is a case in point.

Reason is the only really reliable prophylactic against superstition. Find me one person who has really embraced reason and is also superstitious, and I'll show you someone who will immediately disappear in a puff of logic.

Those dowsers weren't thinking reasonably. They were falling into classic patterns of irrational thinking, the kind that basic rationality training teaches people to recognize and guard against.

> Just for the record, I'm an atheist that tries to be free of superstition.

Cool, we may be able to come to an agreement at some point in this discussion!

> How difficult is it to set up a GoTo each time you drive out to the country vs the dobsonian style?

You have to set up, power up, configure, align the GoTo before observing. Dobs are plop down and observe, that easy.

> How difficult is it to learn to map the stars and find your way around and can you recommend some learning material?

It's about as difficult as learning how to navigate your neighbourhood. I'd personally recommend Turn Left at Orion.

> Can you fine people recommend a model of each style? I understand with this I'll be getting lots of Puritans who don't recommend GoTos.

There is a solid reason why we rarely recommend GoTo scopes at this budget -- most of your money go into the electronics, leaving you with a small scope on an otherwise weak (physically) mount. Both work as a detriment to your observing. There's a nickname for those cheap GoTo telescopes: "We have 40,000 objects in our database you won't be able to see".

For a visual telescope the most important bit is the aperture. The larger it is, the more light it collects, the more faint objects you will be able to see. All of the objects you could see in a small GoTo scope you can also locate yourself with some effort, but 8" of aperture will easily show you

muchmore in the same object. Plus, having found the object yourself is often its own reward, since you'll soon find out most of the harder objects are just a varying type of gray fuzzy splotch against the background.So my recommendation would be the Apertura AD8. It's the same scope as the highly regarded Zhumell Z8, but High Point Scientific seems to be also shipping to Canada as well (unlike TelescopesPlus). Alternatively, locate a nearest shop selling

SkyWatcher Skyliner 200P.Here is the ooh page on Statisticians:

http://www.bls.gov/oco/ocos045.htm

A job straight out of college might see you as a research assistant. I could see you getting a job at Mathematica perhaps. Try to get a SAS certificate before you graduate, a working knowledge of R, and if you feel like tackling it a programming language good for numerical analysis.

Have you taken a course on Regression? I'd consider that, and perhaps even trying to take a Mathematical Statistics Course, if it is offered. You can try to see if you university would allow you to take a class online, or try a Semester Abroad at a university that has that class.

My background: I am an Economist that uses Statistics heavily, and works with Statistical methods often (ie: econometrics). I love it.

Your plans on studying Calc 2 and Linear Algebra are great. That is perfect.

My pay after 10 years is likely to be 100k-150k.

Before you start your first semester at the graduate level know the following things really well: Set theory, integration, matrix algebra, and proofs.

Get this book: http://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/0521675995 -- read it before you study linear algebra, and maybe even some Calculus. It doesn't require a heavy Math background and will save you a lot of frustration later on.

I'd echo what /u/Odnahc has said.

Struggling in Intro the Proofs isn't he end of the world. I struggled in proofs and still ended up with a BS and MS in Math, however, I bought this book and self studied proofs over the Summer and made sure I had a stronger foundation.

The courses normally taken after proofs (Advanced Calculus and Modern Algebra) usually spend the first class reviewing proofs to make sure students have a handle of the material. After that though, you're expected to know the stuff. And honestly, you'll be doing lot of work trying to understand the new material and you're

reallygoing to struggle if you're fighting proof writing instead of the new ideas.Proceed with caution. Definitely speak to your advisor.

Alternately, any introductory book on mathematical analysis will have a section on sentential logic. 'How to Prove It' by Velleman is a great intro, and comes with a link to a web tool to practice!

I think the most important part of being able to see beauty in mathematics is transitioning to texts which are based on proofs rather than application. A side effect of gaining the ability to read and write proofs is that you're forced to deeply understand the theory of the math you're learning, as well as actively using your intuition to solve problems, rather than dry route calculations found in most application based textbooks. Based on what you've written, I feel you may enjoy taking this path.

Along these lines, you could start of with Book of Proof (free) or How to Prove It. From there, I would recommend starting off with a lighter proof based text, like Calculus by Spivak, Linear Algebra Done Right by Axler, or Pinter's book as you mentioned. Doing any intro proofs book plus another book at the level I mentioned here would have you well prepared to read any standard book at the undergraduate level (Analysis, Algebra, Topology, etc).

I know the answer to this.

First, though: arithmetic and all that, through calculus, is not math.

True math is the discovery of properties of ideas. One interesting example is the fact that there is a hypothetical machine that is proven to be able to do everything a (real) computer can do, but that there are many things that it can never do. Therefore, there are questions that can never be answered by a computer, no matter how powerful.

If you actually want to know about the beauty, you need to see it for yourself. As I recall, How to Prove it is pretty decent.

A Breif History of Time by Stephen Hawking.

In Hawking's A Brief History of Time, he explains the reason why we can only live in a universe of three spatial dimensions.

Newton originally discovered this purely mathematically. The force of gravity must be inversely proportional to the square of the distance in order for stable orbits to be possible. The force would be inversely proportional to the square of the distance only if the force-carrier (gravitons, photons, however you want to imagine the force propagating) was emitted in three spatial dimensions.

If you had two spatial dimensions or four, planets (electrons) wouldn't form stable orbits and nothing that we can imagine being matter would form.

Answering your edit, time dilation does occur at the speed of light. So much so that at exactly the speed of light, no travel in time occurs. To a photon, this means it "feels like" it was born and dies at the same instant, if we're going to anthropomorphize here, even though to us we can see it existing in time.

EDIT: as u/Aliudnomen points out, "a frame traveling at c is not a valid inertial frame", which means it's not precise to say that time dilation is happening at the speed of light. Got a bit carried away with the explanation here :) You see infinity time dilation at the speed of light, but that's because the denominator trends to 0, which is a place that inertial objects can't get to. It doesn't really mean that time dilation is infinite, but rather nonexistent. This is why it's often said

informationis the only thing that can appear, to us, to travel at the speed of light: anything with an inertial reference frame can never get to the speed of light.With you being in 10th grade, I'll use an analogy/projection that I find helpful. Imagine a Cartesian set of axes (the normal kind), where the y axis is time-velocity and the x axis is space-velocity. Draw a big circle of radius the speed of light, we'll call that "1 unit". Now, you need to replace the idea of "speed of light" (which implies movement of light in the space velocity coordinate frame) with c, the

celerity constant: celerity means "rapidity of motion", but it was chosen specifically because it can mean speed in the 4 dimension coordinate system of spacetime. In other words, you can travel in space or you can travel in time, and both of these will be measured, not with mph, but with some fraction of c. With me so far?OK, what relativity is saying here is that we are always traveling on a circle with radius c. If we don't travel along the space-velocity x axis (we're at rest), we travel along the time-velocity(y axis), and whenever we travel along the x axis, we rotate our point from (0, 1) around this circle clockwise toward (1, 0).

To see this, we can rearrange the time dilation equation:

t' = t / sqrt(1 - (v/c)^2) Original equation

t' / t = 1 / (sqrt(1 - v/c)^2) Move the t in the numerator over

t' / t = 1 / sqrt((c^2) - (v^2)) Multiply the guys under the sqrt by c^2

(t' / t)^2 = 1 / (c^2 - v^2) Square both sides

1 / (t' / t)^2 = c^2 - v^2 Invert both sides

1 / (t' / t)^2 + v^2 = c^2 Add v^2 to both sides

t^2/t'^2 + v^2 = c^2 Square under the first term denominator and invert.

This is an equation of a circle with radius c: the axes can be chosen so that the y axis is "ratio of time", which is what I'm calling "time velocity" and the x axis is "space velocity".

We are always traveling at c, and so we're always somewhere on this circle. This is why it's a

constant: nothing in the universe travels faster or slower than this celerity, we can only change which coordinates add up to get us there. If we're perfectly at rest in the space-velocity dimension (x = 0), all of our travel is along thetime dimension(y = 1): we're at (1, 0) on this point of the circle. With me so far?This is what "spacetime" means: right here we're dropping the fact that space is 3 dimensional and considering all velocity to be along the one axis, but if you add in higher dimensions, this is spacetime: x, y, z, t all involved in the same equations. Events - which are used to describe "something that happens somewhere in spacetime" - always travel within a 4 dimensional hypersphere that relativistic folk call the light cone.

Back to our 2d example. As you start to increase your x dimension - that is, start moving - your celerity starts to rotate around the circle. When you travel half the speed of light, where x = 0.5, you can imagine the line drawn from the origin to the point on the circle that corresponds to this x coordinate slanting up and to the right, which happens to be solved by (x^2 ) + (y^2 ) = c^2. Solving for y, we get 0.866 - that is, we're traveling at 0.866 the normal rate of time flow.

Keep increasing space velocity, and you'll plot points like (0.6, 0.8), (0.7, 0.714), (0.8, 0.6), (0.9, 0.435), (0.95, 0.31), (0.99, 0.14), (0.999, 0.045), (0.9999, 0.014)

You see, we're putting more and more of our celerity into the space-velocity coordinate and taking it from the time-velocity coordinate. This is time dilation.

Finally, anything with mass requires energy to convert its travel in time to travel in space. As you keep attempting to get closer to (1, 0), it requires more energy to shift the angle around the circle, until the last little bit is infinite. This is why only massless particles (like photons) can travel at the speed of light.

You can also, then, intuitively grasp the other parts of this circle: what does it take to make time slow down? Well, we would have to move from the 1st quadrant (the top right quadrant) to the 3rd and 4th quadrants (the bottom quadrant). We don't really know for sure how to do this, but we do know that it seems possible that more exotic particles could behave just like matter, except progressing backwards. In other words, at rest, their velocity is (0, -1). What does it take to get from matter going forward in time to backwards? Well, you can't do it by increasing your space-velocity alone: no matter how much you increase your velocity, you can

only everget toalmost(1, 0) with something that has mass. This is the "tachyon" idea: a massive particle that travels so fast that it loops around the coordinate frame into quadrant 4 (bottom right), that is, think about moving so fast that you movefasterthan the speed of light (perhaps you became massless for a second, then gained mass as you somehow started traveling in the negative time direction. This can't happen, AFAIK, because you'd have to travel through infinite energy to loop around, but you can imagine the symmetry here). Real particles can't do this, but it's theoretically possible that particles do exist that travel "faster than the speed of light", but only in a way that breaks what it means to have velocity: they're traveling backwards in time, so their motion is some fraction of c to them; they're not moving faster than the speed of light. To us observing them, they're moving faster than we can achieve with our motion on the x coordinate: their motion backwards in time makes them seemto usas if they're moving faster than c. They're not, remember: all of us are always moving at c.If something has

anti-mass, however (that is, antimatter), it seems possible to have it traveling at (0, -1) all on its own! It's hard to jump on something that has anti-mass, though, so this is still theoretical in many ways. That is, the equations say it should be moving backwards in time, but what that actuallymeansis far more complicated: it maths out that way, but it's not like causality is broken (that is, when we create antimatter in particle accelerators, they don't appear "before" the collision, but they do get "younger" before they annihilate. What does "younger" mean to a particle? How do you define "younger" when it's getting "older in negative time"? What is the sound of one hand clapping?Also interesting is the idea of time dilation with negative velocities: the 2nd (top-left) quadrant. What does it mean to move "backwards" in space? Does that even have a meaning? I mean if I walk down the street, I'm moving forward in a direction, but if I walk the opposite way, I'm moving forward in the opposite direction. I'm not aware of anything discussing "negative velocity", but that's just my ignorance: perhaps someone else can chime in if they know more.

Finally, Carl Sagan here to describe what life looks like as you approach the speed of light. You can start to see from his example what it would be like to travel so fast that no time passes for you at all.

Finally, one of the most accessible books I've ever read is Stephen Hawking's a brief history of time. If you're at all remotely curious about either relativity or quantum mechanics, this guy, along with being just about the most brilliant mind in these fields, has a

fantasticway of explaining the concepts while still staying true to the equations involved.I think it's actually pretty clear that the writers are basing their theory of conciousness off of this book: https://www.amazon.com/Origin-Consciousness-Breakdown-Bicameral-Mind/dp/0618057072 It's even in the title of the show. In the context of this book, the voices Dolores hears solidify into one voice (her own), and that moment is dramatically implied when she starts talking to herself and not Arnold.

At the moment: The Origin of Consciousness in the Breakdown of the Bicameral Mind

This happens more when I'm reading fiction, though (I have a theory that their nicely designed covers invite it more than the stark blank look of a reference book). The last two books I read in fiction were As She Climbed Across the Table and Parasite Eve

I'd never played the game based on the last one, but the concept intrigued me to the point I finally had to buy the book (particularly as a book I read on super-organisms referenced mitochondria a lot)

edit: spelling

"The Orange Book" is usually used as intro to astronomy: http://www.amazon.com/Introduction-Modern-Astrophysics-2nd-Edition/dp/0805304029

That really is the best, and if you like

mushrooms https://www.amazon.com/Mushrooms-Demystified-David-Arora/dp/0898151694

or https://www.amazon.com/All-That-Rain-Promises-More/dp/0898153883

or rocks https://www.amazon.com/Gem-Trails-Oregon-Garret-Romaine/dp/1889786446

and for you west coasters and trombone enthusiasts All That the Rain Promises and More

If she's bright and interested enough you might want to consider getting her an entry level college calculus book such as Spivak's.

It won't pose a replacement to the technical approach of high school, but it will illuminate a lot.

I think this is a better approach than trying to tie connections between calculus and other areas of math, because calculus has an inherent beauty of its own which could be very compelling when taught with the right philosophical approach.

If you're looking for other texts, I would suggest Spivak's

CalculusandCalculus on Manifolds. At first the text may seem terse, and the exercises difficult, but it will give you a huge advantage for later (intermediate-advanced) undergraduate college math.It may be a bit obtuse to recommend you start with these texts, so maybe your regular calculus texts, supplemented with linear algebra and differential equations, should be approached first. When you start taking analysis and beyond, though, these books are probably the best way to return to basics.

The Greatest Show On Earth

I know Dawkins is a polarizing figure due to the tone of his rhetoric. However, this is such a well put together, and engaging description of the overwhelming proof science has for evolution. I highly recommend it.

The Greatest Show on Earth

or

The Ancestor's Tale which is a personal favorite of mine although not specifically devoted to evidence arguments. It's just an amazing read through our biological world and along the way the case for evolution becomes overwhelming.

Upvoted. Seriously, The Greatest Show On Earth is phenomenal.

I don't know where you read that, but whatever it is was

dead wrong.Because bacteria have such a short lifespan, they can be used to study selection pressures over many (see: tens of thousands) generations in one human lifetime. There is currently an experiment set up by Richard Lenski that has been going on since Feb 24, 1988 that shows depicts evolutionary changes in response to various selection pressures.

You should pick up "The Greatest Show on Earth". Richard Dawkins is an evolutionary biologist and lays it all out, in the way you seemingly want it.

You don't actually understand evolution, but are poking holes in a strawman that doesn't actually represent what evolution entails. It's like you're opposed to President Obama because he eats babies, when he clearly doesn't eat babies.

Here's a good place to start.

You could start with The Greatest Show On Earth by Richard Dawkins. It's a pretty easy read and it covers a wide range of the current evidence for evolution across different fields of science.

After that, The Selfish Gene also by Dawkins, is awesome. In it, he talks about evolution from the perspective of a gene.

Both should be pretty layman-friendly. He certainly has a compelling way of delivering his arguments.

>Particle physics has nothing to say about this because none of them posit a universe (or particles) that is actually without cause.

Surely you jest.

Could you at least explain why you picked the Christian God - and not any of the other Gods?

Surely you've heard the argument that cast a lot of doubt on your beliefs. Have you heard the history of the Mormon religion for example? There the sausage making of religion is rather plain to see, where the supposed prophet can't reproduce his original writing from his supposed gold tablet, so he claims God graced him with another - so his second translation was similar but different. This same sort of sausage making is thought to be the origin of all religions.

Without deviating from the Christian religion just how familiar are you with the bible? I'm not intending to be insulting or rude, but the old testament is filled with petty tales of a vile, jealous, merciless God with very few actual pieces of morality in it. Christianity would have done well to jettison it completely instead of rolling it into the bible.

Just one more thing - a book recommendation for someone interested in space http://www.amazon.com/Universe-Nothing-There-Something-Rather/product-reviews/145162445X/ref=dp_top_cm_cr_acr_txt?ie=UTF8&amp;showViewpoints=1

Absolutely one of the most fascinating books that is on the cutting edge of theoretical physics - especially as it relates to new theories of how space actually works! *spoiler (empty space has gravity - and this important)

http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/1451624468

It might seem perfectly reasonable, but physicists (of which I am not one) will tell you that it is not true. For instance, Lawrence Krauss, the preeminent physics explainer of our time, has written a book specifically called A Universe from Nothing: Why There Is Something Rather Than Nothing. Again, I'm not a physicist, but I do believe what they have to say--they were right about that whole gravity thing, don't you know.

An 8" Dobsonian reflector telescope, such as the Orion XT8i with Intelliscope to help you find your way around the sky. $640.

The book NightWatch, $20.

The Backyard Astronomer's Guide, $30.

A planisphere. Get one appropriate for your latitude. $10.

A comfortable camping stool for sitting at the eyepiece, or your back will quickly complain. ~$30.

SkySafari for your iPhone/iPad, $3.

A pair of good binoculars, 8x50 or 10x50, $120.

A nice wide-field (62-degree) eyepiece, like the Explore Scientific 24mm. $140.

That's about $1000.

One more thing to add: a dark sky. Priceless.

A few things:

> dark money funded think tank

US billionaires and Big Tobacco. Standard operating procedure for them. Check out Merchants of Doubt if you haven't

Sure thing! The great, and not so great, thing about learning about evolution is that there is

so muchinformation out there it can be a bit overwhelm at times, and it is not always easy to know where to start. The best place to start it probably a university class, but that is not always an accessible resource. In lieu of that, I will strong recommend learning from biologist Richard Dawkins. While he is currently well-known for his stance on religion, he has devoted his life to teaching about evolution to the public. I'll give you a few of my favorite references of his. They are arranged in terms of the length of time they will probably take you. Also, so that you won't be intimidated, they are not references in which he explicitly denounces religion or anything; although, as you will see, he does explain evolution in contrast to some of the claims of creationism. I hope that is not a problem, as it is kind of necessary to learn why biologists take one view as opposed to the other.Anyway, here are the references! =)

This video (5 parts, 10 min each) is a great introduction to some of the basic concepts of evolution, and was really eye-opening for me.

This lecture series (5 episodes, 1 hour each) goes into much more detail than the above video, gives much more evidence, illustrates some of the arguments, and has many fun and beautiful examples.

The Selfish Gene is a book that answered a huge number of questions about evolution for me (e.g., how can a "survival of the fittest" scheme give rise to people being nice to each other? The answer, it turns out, is fascinating.)

The The Greatest Show on Earth: The Evidence for Evolution May be the book you are looking for. This book clearly lays down the evidence for evolution, complete with wonderful illustrations. It is very detailed, and very readable.

There are many other great authors besides Richard Dawkins, but this is a great place to start. You are about to go on a very beautiful and moving journey, if you decide to take it. I envy you! I would love to do it all over again. Enjoy!

Sorry, was a bad joke.

https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X

tl;dr: you need to learn proofs to read most math books, but if nothing else there's a book at the bottom of this post that you can probably dive into with nothing beyond basic calculus skills.Are you proficient in reading and writing proofs?

If you aren't, this is the single biggest skill that you need to learn (and, strangely, a skill that gets almost no attention in school unless you seek it out as an undergraduate). There are books devoted to developing this skill—How to Prove It is one.

After you've learned about proof (or while you're still learning about it), you can cut your teeth on some basic real analysis. Basic Elements of Real Analysis by Protter is a book that I'm familiar with, but there are tons of others. Ask around.

You don't have to start with analysis; you could start with algebra (Algebra and Geometry by Beardon is a nice little book I stumbled upon) or discrete (sorry, don't know any books to recommend), or something else. Topology probably requires at least a little familiarity with analysis, though.

The other thing to realize is that math books at upper-level undergraduate and beyond are usually terse and leave a lot to the reader (Rudin is famous for this). You should expect to have to sit down with pencil and paper and fill in gaps in explanations and proofs in order to keep up. This is in contrast to high-school/freshman/sophomore-style books like Stewart's Calculus where everything is spelled out on glossy pages with color pictures (and where proofs are mostly absent).

And just because: Visual Complex Analysis is a really great book. Complex numbers, functions and calculus with complex numbers, connections to geometry, non-Euclidean geometry, and more. Lots of explanation, and you don't really need to know how to do proofs.

memory, just pick one book the basics are the same: A Sheep Falls Out of the Tree, Quantum Memory Power, not just memory techniques but with a section on Improve your intelligencemath: secrets of mental mathAmong many others who can be given the title of the world's most intelligent person is

Marilyn vos Savant: one of her booksHere's the book:

https://www.amazon.com/World-Without-Us-Alan-Weisman/dp/0312427905

Don't know about the series, though.

> Our homes and cities won't break down, and neither will a lot of what we have produced (should humans disappear).

They will more so than you might think, just on a longer scale than something like a bird's nest. Check out 'The World Without Us'

We and everything we do is literally a part of nature. The universe is a closed system and everything is increasing entropy :)

Reminds me of this book. Steps through what would happen if humans suddenly stepped away from all the gulf coast chemical plants.. yikes: The World Without Us https://www.amazon.com/dp/0312427905/ref=cm_sw_r_cp_apa_sTQPzbS05TFRR

Start with Carl Sagan's -- " A Demon haunted world :Science as a Candle in the Dark"

http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

a VERY good book

and a good start to learning

HOW TO THINK FOR ONES SELF

Highly recommended.

With a statement like I recommend reading Carl Sagan's book Demon Haunted World as soon as possible. It goes into some detail about patterns and coincidences like those, along with debunking pseudoscience in general.

Carl Sagan - The Demon-Haunted World

Some here will disagree, yet I think your cause is a noble one.

My suggestion would be to keep encouraging her to be a freethinker, question everything, and learn all she can about science. If she can be at a point where she understands that "science is more than a body of knowledge, it is a way of thinking" (Carl Sagan), if she can fall in love with the wonders of the creation of the universe and the evolution of life on this world, then you'll be done, as those things will show any thinking person the absurdity of religion as a moral compass.

If she likes to read, here are some books you might consider getting for her:

The Demon-Haunted Worldby Carl Sagan. An amazing argument for the use the scientific way of thinking in every aspect of our lives.A Universe from Nothingby Lawrence Krauss. How math and science can fully explain the creation of the universe, and a powerful argument against the universe needing a creator.The Greatest Show on Earthby Richard Dawkins. The subtitle isThe Evidence for Evolution. Meant as a book for readers your sister's age. Big plus is that if she likes it, she may want to readThe God Delusionand/orThe Magic of Reality.Edit: grammar

There are no demons. I think at some point I want to make a freakin' documentary on the 1980s (which really started in the 70s) and this bullshit. The entire Western fundamentalist world was suffering from mass delusion in the 70s fueled by popular entertainment which led to even regular people, the court system, police, etc. to get caught up in the Satanic Panic of the 80s.

There were endless stories in the 70s/80s fueled by accounts not only in the main magazines, but the freaky ones were published in the Yearbooks. (Dress 'provocatively?' You'll be a target for the demons. Have rosary beads? One woman received 'apparitions and beatings' from the demons every Thursday night. (??!) Accounts of sorcerers sending demons to attack people studying, but shook with fear when he found out Jehovah was involved. This nonsense is from the 1970 Yearbook alone.)

Please read The Demon Haunted World by Carl Sagan. https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

http://www.reddit.com/help/faqs/atheism#RecommendedReading

also.. here is my own list of things I've actually personally read and recommend.

http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

http://www.amazon.com/Letter-Christian-Nation-Sam-Harris/dp/0307265773

http://www.amazon.com/Misquoting-Jesus-Story-Behind-Changed/dp/0060738170

http://www.amazon.com/Some-Mistakes-Moses-Robert-Ingersoll/dp/0879753617

http://www.amazon.com/Short-History-Nearly-Everything/dp/0767908171

http://www.amazon.com/Lies-My-Teacher-Told-Everything/dp/0684818868

http://www.amazon.com/Genome-Autobiography-Species-23-Chapters/dp/0060194979

what? That will help you become an independent person, and probably a functional human being. It will not help your critical thinking. How many americans are out on their own, but still accept everything Fox News and the bible tell them?

Carl Sagan wrote an excellent book about critical thinking and skepticism. It's called The Demon-Haunted World: Science as a Candle in the Dark. He talks a bit in general about why we need critical thinking and science, then goes on to discuss a variety of amazing science and pseudoscience, applying critical thinking to each. It's an excellent introduction to critical thought, easy and interesting to read.

You need some grounding in foundational topics like Propositional Logic, Proofs, Sets and Functions for higher math. If you've seen some of that in your Discrete Math class, you can jump straight into Abstract Algebra, Rigorous Linear Algebra (if you know some LA) and even Real Analysis. If thats not the case, the most expository and clearly written book on the above topics I have ever seen is Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers.

Some user friendly books on Real Analysis:

Some user friendly books on Linear/Abstract Algebra:

Topology(even high school students can manage the first two titles):

Some transitional books:

Plus many more- just scour your local library and the internet.

Good Luck, Dude/Dudette.

I actually bought http://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178

On chapter three now :D

Have you read A Book of Abstract Algebra by Charles Pinter? https://www.amazon.co.uk/d/cka/Abstract-Algebra-Dover-Books-Mathematics-Charles-Pinter/0486474178

You need a good foundation: a little logic, intro to proofs, a taste of sets, a bit on relations and functions, some counting(combinatorics/graph theory) etc. The best way to get started with all this is an introductory discrete math course. Check these books out:

Mathematics: A Discrete Introduction by Edward A. Scheinerman

Discrete Mathematics with Applications by Susanna S. Epp

How to Prove It: A Structured Approach Daniel J. Velleman

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers

Combinatorics: A Guided Tour by David R. Mazur

Get a pair of 10x50 binoculars and a copy of Turn Left at Orion. Don't rush out and buy a telescope. The most impressive things I've seen have been with my 10x50s. Using that book and learning your way around the circum-polar constellations is a great way to get started.

Look up a book or two on star hopping, like Nightwatch or Turn Left at Orion. These are incredibly fun to read and will inspire a hundred nights' viewing - and learning to star hop (finding and identifying things up there by their relationships to

otherthings) is a skill you'll use every time you look up.As to getting a telescope, my first (I still use it sometimes) was a $20 yard sale find - sold by Sears sometime around 1970. Binoculars,

anytelescope, and a "viewing list" are what I'd recommend to start having fun.I recommend you start studying proofs first. How to Prove It by Velleman is a great book for new math students. I went through the first three chapters myself before my first analysis course, and it made all the difference.

As you are taking a class than combines analysis and calculus, you might benefit from Spivak's book Calculus, which despite it's title, is precisely a combination of calculus and real analysis.

Read this book: How To Prove it

Since nobody else has recommended it, I always recommend the book How to Prove it by Daniel J. Velleman for learning proofs. I always found proofs to be kind of black magic until I read that, which totally demystified them for me by revealing the structure of proofs and techniques for proving different kinds of statements. One of the best things about it is that it starts from square one with basic logic and builds from there in way that no prior knowledge is required beyond basic algebra skills.

You cannot go wrong with

How To Prove It: A Structured Approachby Velleman https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=sr_1_3?keywords=how+to+prove+it&amp;qid=1558195901&amp;s=gateway&amp;sr=8-3I saw that book highly recommended, and after going through it myself a while ago I highly recommend it as well. When I do proofs I still maintain the mental model and use some of the mechanics that I learned from this book. You don't even have to read the whole thing in my opinion. Pick it up, work through a few pages per day, and stop when you feel like moving onto another subject-specific book, like Understanding Analysis.

Oh, and you might already know this, but do as many practice problems as you can! Learning proofs is all about practice.

https://www.amazon.com/dp/0521675995/ref=cm_sw_r_other_apa_Sn9NBbDH6MYPX not sure it this is exactly what you're asking for(might be more than you're asking for?) but this helped me a lot.

Try one (or a few) of these:

http://www.amazon.ca/Thinking-Mathematically-J-Mason/dp/0201102382

http://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/052171978X/

http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X

www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995/

www.amazon.com/Introduction-Mathematical-Thinking-Keith-Devlin/dp/0615653634/

https://www.coursera.org/course/maththink

your request is basically "i want to reach for the stars with no effort because im handicapped and poor" and sadly you are limiting yourself because of that mindset.

This is handicapped. so whatever ouchie, booboo, or challenge you might have: Suck it up and deal with it; every handicapped person in the world that makes anything of themselves comes to realize this.

if you can flip burgers at mcdonalds, you can make enough to get your education at any age (expecially if you are handicapped as you would get SSI, plus that pension you mentioned). dont think that your above flipping burgers- nobody is above flipping burgers to survive.

things you need to do first:

required reading

Book 1

Book 2

book 3

Book 4

Book 5

sadly without a degree- people wont acknowledge you or accept your theories. you need to get a solid college education for anyone to care. i recomend getting a diploma in astronautics and then going from there.

This is definitely above your level, and it's from 1982 so it's a little outdated, but if you're really interested in astrophysics then it might be worth checking it out and trying to work through at least the first few sections. I think it's written so that you can follow it without too much math involvement.

Frank Shu - The Physical Universe: An Introduction to Astronomy

Otherwise, there are a lot of great popular-writing (i.e. not a textbook) books about physics/astrophysics. Here are a few:

Stephen Hawking - A Brief History of Time

Carl Sagan - Cosmos

Neil deGrasse Tyson - Death By Black Hole, and Other Cosmic Quandaries

My biggest advice, though, for taking physics in high school is to try to do as well as you possibly can in your math classes. Those are the most important for getting into physics. If you do well in math then physics should be pretty easy.

Regardless of the OPs eventual interests there's a reason we start with Newtonian stuff in most 101 type courses. I think its reasonable for OP to start there if they are serious, my recommendations are:

IF OP WANTS TO LEARN PHYSICSThe importance of solving actual problems can not be over emphasized.IF OP IS WANTS TO LEARN ABOUT PHYSICSFrom there, op can look at different fields, biophysics seems like it would be the most likely candidate in which case OP might also want to brush up on organic chemistry and learn how to use MATLAB.

> I wonder if humanities curious nature towards mysticism is inevitable and that all paths, no matter how diverse, will always use the same formats and formulas to tell their tales.

This is one of the central tenants of Jung's research (well you know "research") and Joseph Cambell basically wrote the book about it... https://www.amazon.com/Thousand-Faces-Collected-Joseph-Campbell/dp/1577315936 sorry if Im being didactic/eg if you already knew that... its a really facinating question/idea. As far as "Embedded in our DNA" eg for a more scientific approach this book is AMAZING https://www.amazon.com/Origin-Consciousness-Breakdown-Bicameral-Mind/dp/0618057072, even though it does veer from the purely scientific, the idea is that our brains have certain regions which act on our spiritual relationship to our "gods" which manifested themselves as voices in our earlier evolutionary states and that as we became more rational our brains still retained these functional but at the same time "disfunctional" anatomy leading to experiances that result for some in uncontrollable states, like schizophrenics for example ... the way he "proves" all of this stuff is a comparison of his experiments in neuroscience with historical texts, legends, sagas, and other implements of earlier humanity like archeological finds. if you are interested in this topic this is an absolutely Mindblowing book right here just saying!

Finally:

"Is this part of our evolutionary growth or yearning for divinity?

Our ego's thirst for magical power or trying to step out of our physical limitations?" I think you are right in that we yearn because, I beleive at least, our evolutionary state has one foot in the past and one in the future, we have evolved beyond our normal need for mere survival and we now use our brains for complex creation and navigation of human institutions but we dont really know "why", we dont really know what meaning is becuase "meaning" is a brand new thing! and without it the universe seems devoid of purpose and therefore I beleive we fill in those gaps with these notions and art, music etc, art and literature helps us define ourselves and music helps us 'engage' with the harmonics/vibrations of the universe on deeper levels (as it is really the only category here that actually relies on the schientific make up of the universe i.e. the ways that ratios of harmonic waves sound pleasing or displeasing based on their relationships in time...). I just love this stuff, am also agnostic but love to celebrate all ideas no matter how objectively "wrong" they may be, thats of c why Im on this sub! Love your questions/keep on searching!!!

The most mainstream is by and far Carroll and Ostlie's Introduction to Modern Astrophysics, lovingly known as the Big Orange Book or BOB. Be warned that it is somewhat hardcore - you need to have a firm founding in Newtonian mechanics and electromagnetism to understand and appreciate the calculations, which are really the heart of the matter. Lacking this, though, you can actually read through the conceptual and qualitative discussions quite well and still learn a lot.

Start here and go through the trig and calculus videos, problems, etc. Then hit up the physics stuff. After that you might want to find other resources to learn Trig, Calc, and College level physics. Then you can think about picking up this hefty thing.

Edit: There is also an "ebook" version of the book above. I won't say where. But it's out there.

Below are some favorites. It's amazing how many of the plants we see are either edible or medicinal.

&#x200B;

Pacific Northwest Foraging

Medicinal Plants of the Pacific West by Michael Moore

All that the rain promises by David Arora

Common Mushrooms of the Northwest by Duane Sept

Wild Berries of the Northwest by Duane Sept

Pacific Northwest Medicinal Plants by Scott Kloos

Happy hunting!

Yes, it is a man in a tuxedo, holding a flugelhorn & large fungi, sneaking around in a forest.

Apparently the book got this glowing review by the NYTimes:

"is certainly the best guide to fungi, and may in fact be a long lasting masterpiece in guide writing for all subjects."*Edit: (On Amazon, it's the #1 Best Seller in "Mushrooms in Biological Sciences")

Intro Calculus, in American sense, could as well be renamed "Physics 101" or some such since it's not a very mathematical course. Since Intro Calculus won't teach you how to think you're gonna need a book like How to Solve Word Problems in Calculus by Eugene Don and Benay Don pretty soon.

Aside from that, try these:

Excursions In Calculus by Robert Young.

Calculus:A Liberal Art by William McGowen Priestley.

Calculus for the Ambitious by T. W. KORNER.

Calculus: Concepts and Methods by Ken Binmore and Joan Davies

You can also start with "Calculus proper" = Analysis. The Bible of not-quite-analysis is:

[Calculus by Michael Spivak] (http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1413311074&amp;sr=1-1&amp;keywords=spivak+calculus).

Also, Analysis is all about inequalities as opposed to Algebra(identities), so you want to be familiar with them:

Introduction to Inequalities by Edwin F. Beckenbach, R. Bellman.

Analytic Inequalities by Nicholas D. Kazarinoff.

As for Linear Algebra, this subject is all over the place. There is about a million books of all levels written every year on this subject, many of which is trash.

My plan would go like this:

1. Learn the geometry of LA and how to prove things in LA:

Linear Algebra Through Geometry by Thomas Banchoff and John Wermer.

Linear Algebra, Third Edition: Algorithms, Applications, and Techniques

by Richard Bronson and Gabriel B. Costa.

2. Getting a bit more sophisticated:

Linear Algebra Done Right by Sheldon Axler.

Linear Algebra: An Introduction to Abstract Mathematics by Robert J. Valenza.

Linear Algebra Done Wrong by Sergei Treil.

3. Turn into the LinAl's 1% :)

Advanced Linear Algebra by Steven Roman.

Good Luck.

>When university starts, what can I do to ensure that I can compete and am just as good as the best mathematics students?

Read textbooks for mathematics students.

For example for Linear Algebra I heard that Axler's book is very good (I studied Linear Algebra in another language, so I can't really suggest anything from personal experience). For Calculus I personally suggest Spivak's book.

There are many books that I could suggest, but one of the greatest books I've ever read is The Art and Craft of Problem Solving.

This is the prologue in his new book: The Greatest Show on Earth. I'm in the middle of it and

highly recommend it.I'll try at ELI5 level.

Paper is a good analogy, but expand it to 3 dimensions. To see what flat means, you need to know what "not flat" means. Imagine a really large piece of paper covering the Earth. You mark an arrow on the ground then walk off in that direction, keeping in a straight line. Eventually you circle the globe and end up back at your arrow on the ground, approaching it from the tail of the arrow. You then pick a random direction and draw another arrow and do the same thing. No matter which direction you go, you always end up coming back to the same spot.

In this case, the paper is not flat; it is curved. Specifically, it is

closed, meaning it loops back onto itself. However, locally it might look flat from any point you are standing. Imagine it on a bigger planet like Jupiter, or around the sun, or even larger. Locally you would measure it as being very flat, within a tiny fraction of a percent. So something that looks flat could actually be curved but with a very large radius of curvature.But this analogy is only in 2 dimensions, covering the surface of a sphere of really large size. The curvature is in the third dimension in the direction of the center of the sphere (perpendicular to the local surface of the paper).

Imagine it now in 3 dimensions. You are floating in space at leave a real arrow pointed in some direction. You fly off in your rocket in that direction and eventually find yourself approaching the arrow from the tail end. It doesn't matter which direction you point the arrow, that always happens. That is a

closeduniverse in 3D, meaning it is curved in a fourth dimension.A flat universe would be one where the radius of curvature is infinite, meaning you'd never end up back at your arrow from the tail end.I think this description is important because there is some disagreement on this. The measurement of the universe being flat within 0.4% does not mean that it

isflat; it means the radius of curvaturecouldbe infinite (flat) but could just be very large. In fact, if you watch theoretical cosmologist Lawrence Krauss' talks on "A Universe from Nothing" or read the book, if you pay close attention you'll note a contradiction. At one point he jokes about how theorists "knew" that the universe must be flat because that makes it mathematically "beautiful", but then later describes how theorists "knew" the total energy of the universe must add up to zero as that is the only type of universe that can come from nothing, and yet also says that only a closed universe can have a total energy that adds up to zero. Hence is it closed or flat?I attended one of these talks in person where this was asked and he confirmed that he thinks the evidence is strong that it is actually closed, but really, really large and hence looks flat to a high degree, and that the inflationary universe model explains why it would be so large and flat looking while being closed and zero net energy (and hence could come from nothing).

After going through all of what I know of the topic, including many other sources, I tend to agree with him that it makes the most sense that it is likely just very close to flat but is really slightly curved back onto itself at a very large radius of curvature. That also means our observable universe is only a very tiny percentage of the universe that exists.

Evolution & the Big Bang are separate subjects. Though for some simple explanations, you might want to pick up Richard Dawkins's The Magic of Reality, its a book aimed at children so it tries to explain things in simple terms.

There's a book on this...

A Universe from Nothing: Why There Is Something Rather than Nothing https://www.amazon.com/dp/1451624468/ref=cm_sw_r_cp_apa_i_WTm4Cb0VWT8S0

Krauss wrote a very good book on that subject. http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/1451624468

Philip Kitcher's

Abusing Science, Michael Shermer'sWhy People Believe Weird Thingsand Massimo Pigliucci'sNonsense on Stiltsare all great reads on this topic. I also highly recommend Naomi Oreskes' and Erik Conway'sMerchants of Doubtas an examination of how scientific language can be abused to stymie public policy progress on certain issues.This is certainly part of the philosophy of science. The problem of how to separate genuine science from pseudoscience is called the demarcation problem, and there's not really any generally accepted criteria that apply to all cases. Some people reject the idea that we ought to draw that kind of principled distinction in the first place. Nobel Prize-winning chemist Irving Langmuir has a great talk advocating for a notion of "pathological science" rather than pseduoscience that's worth reading through.

I'd also recommend Merchants of Doubt, which isn't about the evidence of global warming per se but about how science, or at least the public face of science, has been and can be hijacked by political movements.

This is so utterly false. There is still a ozone hole. And the same people who fought against banning CFC are the same one's who fought against acid rain regulation and now global warming.

His recent book, The Greatest Show on Earth is about the evidence for evolution. As far as I know, he doesn't get into god at all. In fact, I haven't seen anything where he's talking about evolution from a pedagogical standpoint where he discusses atheism. But I may have missed something.

This book is full of proofs you can work through. It could keep you busy for quite a while and it's considered a standard for analysis.

https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X

Maybe try applied math programs. Some of them seem to have astrophysics faculty https://www.princeton.edu/gradschool/about/catalog/fields/applied_mathematics/. You'll probably have an easier time getting in with your background and can take the math GREs. In a physics BS you would at least have the knowledge of these books:

http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X,

http://www.amazon.com/Introduction-Electrodynamics-4th-David-Griffiths/dp/0321856562/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1396384599&amp;sr=1-1&amp;keywords=griffiths,

http://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927/ref=sr_1_2?s=books&amp;ie=UTF8&amp;qid=1396384599&amp;sr=1-2&amp;keywords=griffiths,

http://www.amazon.com/Introduction-Thermal-Physics-Daniel-Schroeder/dp/0201380277/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1396384625&amp;sr=1-1&amp;keywords=schroeder+statistical+physics.

The more you know from those books, the better. Although an applied math program, probably wouldn't expect you to have read all of them. Also try x-posting to /r/askacademia. I'm sure someone there could be more helpful.

If you understand multivariable calculus, you're pretty close to being able to handle an introductory quantum mechanics textbook. If you know what a differential equation is, then Griffiths Intro to QM isn't really out of reach. If you want to

reallyunderstand QM, you'll need to do this eventually...What's your background? I'd probably start with math (sorry). Calculus and linear algebra.

Then Griffiths is probably to go-to intro text book. Though I never really got it until I read Sakurai. I'm not sure where to go for calculus and linear algebra self-study. Perhaps others can suggest.

http://www.amazon.com/Introduction-Quantum-Mechanics-2nd-Edition/dp/0131118927

http://www.amazon.com/Modern-Quantum-Mechanics-2nd-Edition/dp/0805382917

Yeah quantum sucks. If you're not already using it, Griffiths's Introduction to Quantum Mechanics is pretty good:

http://www.amazon.com/Introduction-Quantum-Mechanics-2nd-Edition/dp/0131118927

And this guy has posted solutions with thorough explanations to most (maybe all?) of the practice problems:

http://physicspages.com/index-physics-quantum-mechanics/griffiths-introduction-to-quantum-mechanics-problems/

I strongly agree with these choices. Additionally, Introduction to Quantum Mechanics by Griffiths.

Griffiths is the go-to for advanced undergraduate level texts, so you might consider his Introduction to Quantum Mechanics and Introduction to Particle Physics. I used Townsend's A Modern Approach to Quantum Mechanics to teach myself and I thought that was a pretty good book.

I'm not sure if you mean special or general relativity. For special, /u/Ragall's suggestion of Taylor is good but is aimed an more of an intermediate undergraduate; still worth checking out I think. I've heard Taylor (different Taylor) and Wheeler's Spacetime Physics is good but I don't know much more about it. For general relativity, I think Hartle's Gravity: An Introduction to Einstein's General Relativity and Carroll's Spacetime and Geometry: An Introduction to General Relativity are what you want to look for. Hartle is slightly lower level but both are close. Carroll is probably better if you want one book and want a bit more of the math.

Online resources are improving, and you might find luck in opencourseware type websites. I'm not too knowledgeable in these, and I think books, while expensive, are a great investment if you are planning to spend a long time in the field.

One note: teaching yourself is great, but a grad program will be concerned if it doesn't show up on a transcript. This being said, the big four in US institutions are Classical Mechanics, E&M, Thermodynamics/Stat Mech, and QM. You should have all four but you can sometimes get away with three. Expectations of other courses vary by school, which is why programs don't always expect things like GR, fluid mechanics, etc.

I hope that helps!

To me its about what you can do in your head. Get a book for example, BOOK is good.

Also, subscribe to /r/math. Finally, ANYTIME you see a number do something with it. Factor it, think of a historical significance, etc.

First off, I'd recommend looking into a book like this.

Second, when doing something like multiplication, it always helps to break a problem down into easier steps. Typically, you want to be working with multiples of 10/100/1000s etc.

For multiplying 32 by 32, I would break it into two problems: (32 x 30) + (32 x 2). With a moderate amount of practice, you should quickly be able to see that the first term is 960, and the second is 64. Adding them together gives the answer: 1024. It can be tricky to keep all these numbers in your head at once, but that honestly just comes down to practice.

Also, that same question can be expressed as 32^2 . These types of problems have a whole bunch of neat tricks. One that I recall from the book I linked above has to do with squaring any number ending in a 5, like 15 or 145. First, the number will always end in 25. For the leading digits, take the last 5 off the number, and multiply the remaining digits by their value +1. So, for 15 we just have 1x2=2. For 145, we have 14x15=210. Finally, tack 25 on the end of that, so you have 15^2 = (1x2)25 = 225, and 145^2 = (14x15)25 = 21025. Boom! Now you can square any number ending in 5 really quick.

Edit:Wanted to add some additional comments that have helped me out through the years. First, realize that(1) Addition is easier than subtraction,

(2) Addition and subtraction are easier than multiplication,

(3) Multiplication is easier than division.

Let's go through these one by one. For (1), try to rewrite a subtraction problem as addition. Say you're given 31 - 14; then rephrase the question as,

whatplus 14 equals 31? You can immediately see that the ones digit is 7, since 4+7 = 11. We have to remember that we are carrying the ten over to the next digit, and solve 1 + (1 carried over) +what= 3. Obviously the tens digit for our answer is 1, and the answer is 17. I hope I didn't explain that too poorly.For (2), that's pretty much what I was originally explaining at the start. Try to break a multiplication problem down to a problem of simple multiplication plus addition or subtraction. One more example: 37 x 40. Here, 40 looks nice and simple to work with; 37 is also pretty close to it, so let's add 3 to it and just make sure to subtract it later. That way, you end up with 40 x 40 - (3 x 40) = 1600 - 120 = 1480.

I don't really have any hints with division, unfortunately. I don't really run into it too often, and when I do, I just resort to some mental long division.

Good question OP! I drafted a blog article on this topic a while back but haven't published it yet. An excerpt is below.

--------

With equations, I sometimes just visualize what I'd usually do on paper. For arithmetic, there are actually a lot of computational methods that are better suited to mental computation than the standard pencil-and-paper algorithms.

In fact, mathematician Arthur Benjamin has written a book about this called Secrets of Mental Math.

There are tons of different options, often for the same problem. The main thing is to understand some general principles, such as breaking a problem down into easier sub-problems, and exploiting special features of a particular problem.

Below are some basic methods to give you an idea. (These may not all be entirely different from the pencil-and-paper methods, but at the very least, the format is modified to make them easier to do mentally.)

ADDITION

(1) Separate into place values: 27+39= (20+30)+(7+9)=50+16=66

We've reduced the problem into two easier sub-problems, and combining the sub-problems in the last step is easy, because there is no need to carry as in the standard written algorithm.

(2) Exploit special features: 298+327 = 300 + 327 -2 = 625

We could have used the place value method, but since 298 is close to 300, which is easy to work with, we can take advantage of that by thinking of 298 as 300 - 2.

SUBTRACTION

(1) Number-line method: To find 71-24, you move forward 6 units on the number line to get to 30, then 41 more units to get to 71, for a total of 47 units along the number line.

(2) There are other methods, but I'll omit these, since the number-line method is a good starting point.

MULTIPLICATION

(1) Separate into place values: 18*22 = 18*(20+2)=360+36=396.

(2) Special features: 18*22=(20-2)*(20+2)=400-4=396

Here, instead of using place values, we use the feature that 18*22 can be written in the form (a-b)*(a+b) to obtain a difference of squares.

(3) Factoring method: 14*28=14*7*4=98*4=(100-2)*4=400-8=392

Here, we've turned a product of two 2-digit numbers into simpler sub-problems, each involving multiplication by a single-digit number (first we multiply by 7, then by 4).

(4) Multiplying by 11: 11*52= 572 (add the two digits of 52 to get 5+2=7, then stick 7 in between 5 and 2 to get 572).

This can be done almost instantaneously; try using the place-value method to see why this method works. Also, it can be modified slightly to work when the sum of the digits is a two digit number.

DIVISION

(1) Educated guess plus error correction: 129/7 = ? Note that 7*20=140, and we're over by 11. We need to take away two sevens to get back under, which takes us to 126, so the answer is 18 with a remainder of 3.

(2) Reduce first, using divisibility rules. Some neat rules include the rules for 3, 9, and 11.

The rules for 3 and 9 are probably more well known: a number is divisible by 3 if and only if the sum of its digits is divisible by 3 (replace 3 with 9 and the same rule holds).

For example, 5654 is not divisible by 9, since 5+6+5+4=20, which is not divisible by 9.

The rule for 11 is the same, but it's the alternating sum of the digits that we care about.

Using the same number as before, we get that 5654 is divisible by 11, since 5-6+5-4=0, and 0 is divisible by 11.

PRACTICE

I think it's kind of fun to get good at finding novel methods that are more efficient than the usual methods, and even if it's not that fun, it's at least useful to learn the basics.

If you want to practice these skills outside of the computations that you normally do, there's a nice online arithmetic game I found that's simple and flexible enough for you to practice any of the four operations above, and you can set the parameters to work on numbers of varying sizes.

Happy calculating!

Greg at Higher Math Help

Edit: formatting

Link to the book, for the lazy

The Dragon in My Garage is an excerpt from a book called Demon Haunted World by Carl Sagan. Its probably my favorite book.

If you're not already familiar, I suggest you start with the Wikipedia article on a priori and a posteriori knowledge.

> I understand what he means by the love example in that, while love is a series of chemical reactions, you can't really scientifically measure how "in love someone is" or the nuances of those feelings. Does this apply to the concept of God also?

Not exactly. The closest analogy to the claim that a god exists would be the claim that love exists. How would you prove that love exists? First, you would have to clearly define what you mean by love.

If you define it such that it's an unfalsifiable proposition, then the search is over before it begins; unfalsifiable claims are effectively indistinguishable from false claims and are only treated as true (or possible) by the exercise of wishful thinking.

On the other hand, if you define love in a way that is testable then run your tests etc. Note that in this scenario, how "in love someone is" may well be measurable.

This is why it's important to address someone's god claim first by insisting that they provide a testable definition. Obviously theists reject this approach, as it lays bare the weakness of their reasoning. You typically get deflective responses like "Well how would you test for happiness, or love, or whatever (immaterial concept they grasp at)." Of course anything that exists,

even if it only has a subjective existence in the mind of one individual, can (theoretically) be tested if it is defined properly. Another common response is "Everything is evidence for (their) god." This is basically presuppositionalism, or circular reasoning. Circular reasoning proves nothing. And then there's "My god can't be defined, because that would set limits on him and he's too awesome for limitations." This makes the claim incoherent, because the god's attributes are incoherent. Incoherence is nonsense, by definition.If you haven't read it, Carl Sagan's "The Demon Haunted World" is highly rated. I'm giving a copy to my youngest daughter.

&#3232;_&#3232;

He wrote a whole book explaining why things like ghosts, witches, UFO's, etc, are more or less just in the persons mind and not based on any real evidence. I'd trust his literal word over hearsay.

The Demon Haunted World by Carl Sagan.

This question comes up a lot. Start with these. But you must understand that

atheism IS NOT a religion. It's not LIKE religion. It's the absense of religion. As is famously bandied about, atheism is a "religion" as much as "off" is a channel on your TV.Demon Haunted Worldby Carl Sagan.It really does a good job of explaining why science and critical thinking are important to society and why it is dangerous to reject them or to be ignorant of them.

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

Surely You're Joking, Mr. Feynman!by Richard Feynman.It is a very witty and entertaining collection of Dr. Feynman's personal anecdotes and reminds us that scientists are people just like everyone else.

https://www.amazon.com/Surely-Feynman-Adventures-Curious-Character/dp/0393316041/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1498402289&amp;sr=1-1&amp;keywords=surely+you%27re+joking+mr.+feynman

&#x200B;

>Because you sound like a middle schooler who tried weed for the first time, and gets the million dollar idea that all mind-altering drugs are good because you dissociated for an hour.

I'm actually sharing second-hand the scholarship of Timothy Leary, as well as Carl Sagan's writing in Demon-Haunted World: Science as a Candle in the Dark, which is a phenomenal book. The ideas are certainly not mine, though I do agree with them. I came across them because I was formerly a professor of rhetoric and composition and used counterculture as a topic of study for some of my classes and thus became interested in the psychedelic movement.

I've also never dissociated. Some people depersonalize while taking psychedelics, but I've never experienced that, either. Dissociation is more something you might expect from Ketamine or large doses of DXM. If anything, used responsibly by psychologically healthy people with fully formed brains, psychedelics connect you further with yourself and the world around you, not the other way around.

>Slowing down your synapses and making yourself see things in slow motion or fancy colors isn't going to make you or the population as a whole more enlightened.

This is just not how psychedelics work. Visuals are a very small aspect of the experience. They're also, by far, the most underwhelming aspect. Ideally, if you're doing psychedelics right, you never see anything that isn't there or doesn't really exist, you just notice details and patterns in things that are there everyday, but you usually don't notice.

But that's beside the point. The true value of the psychedelic experience is in the cognitive and emotional component.

Take the work or neuroscientist Andrew Newberg, for example, which demonstrates that brain activity in people tripping on psilocybin is roughly the same as that of mystics and religious clerics engaged in deep meditation or prayer. Or you could look at the various peer reviewed, scholarly studies that demonstrate the dramatic effects of psychedelics on prosocial behavior and psychological function.

If you think psychedelics are still fodder for basement dwelling hippie hangers-on who can't let go of the good old Haight-Ashbury days, you're just kind of behind the times. A lot has happened since then. You should catch up. It's interesting stuff.

>There have already been places where drugs were decriminalized entirely, like Portugal, where people actually started weaning themselves off of them and overall using psychedelics less because, believe it or not, constantly altering your mind with substances is unhealthy. As far as I understand the "euphoria" that was liberated there didn't cause a cultural renaissance either.

Portugal decriminalized drugs as a radical solution to their rampant issues with opioid addiction, but mostly to curb the country's HIV epidemic due to rampant IV drug use. It had basically nothing to do with psychedelics.

Simply put, psychedelics have never been particularly available or popular in Portugal, so to use them as your measuring stick is an odd choice. Portugal is better suited for an argument about relaxing drug laws to reduce overdoses and IV drug related diseases, as well as create better access to treatment options.

The example you're looking for would likely be the Haight-Ashbury in the 1960's, which was an absolute mess. But honestly, psychedelics weren't as much to blame for that as stimulants, opioids, PTSD, other forms mental illness, and the fact that most of the people in the Haight at the time were teenagers. Speaking contemporarily, San Francisco is the highest-ranking American city in terms of overall quality of life according to the Mercer Quality of Living Survey, so do with that what you will.

>All you're doing is highlighting how different attitudes towards substances here are, and how people could get hurt.

Look, I've studied this shit, both experientially and academically. You may not agree with me, and that's fine, but I really don't think I'm the one of the two of us who has weird, misguided ideas about psychedelics and how they work.

Psychedelics are not addictive, have incredibly high overdose thresholds that are nearly impossible to meet, and when used responsibly, have seriously positive applications in the psychological and social sciences, namely when used in conjunction with cognitive behavioral therapy in the care of trained professionals. The fact that you think this is middle-school philosophizing really says more about you than it does about me or psychedelics, namely that you don't know very much about psychedelics.

Lastly, here's a pro-tip for your cake day: when you go ad-hominem against someone with no substantive argument to follow, and they say, "Go on...", probably don't actually go on.

Read the madness of crowds. Author really goes into depth on incidents in history. The section on inside jokes is funny as hell, amazing to see how long memes have been around for.

This book is also good: Demon Haunted world

Alright then, how about Carl Sagan’s

Demon Haunted World. The focus of the book is on a skeptical worldview. As examples of skepticism, it gently but thoroughly debunks a number of looney ideas, but doesn’t tackle religion head on.If you are looking for a book, I'd recommend Demon Haunted World by Carl Sagan.

Also, get out in nature. There is something incredibly healthy and fulfilling by being quiet in nature.

It also sounds like they would benefit from Sagan's book, The Demon Haunted World

http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

You need to understand that this is fundamentally a role-playing game and most players adopt an in-depth multi-layered approach to their character and take on belief flaws for extra points else where in their build. In short much of what a character says to you is BS. So something like The Demon-Haunted World: Science as a Candle in the Dark might have been good.

I'm going to shamelessly plug this book which I consider to be one of my favorite books ever. For the price it is definitely worth keeping a copy and reading it on the side if you're learning abstract algebra for the first time and it reads like a novel. It's definitely a small treasure I feel I discovered.

there's a lot going on here, so i'll try to take it a few steps at a time.

> how many REAL operators do we have?

you might be careful about your language here, as the word "real" has implications in the world of mathematics to mean "takes values in the real numbers", i.e., is non-complex. also, "real" in the normal sense of real or fake doesn't have a lot of meaning in mathematics. a better question might be "how many unique operators do we have?", but even that isn't quite good enough. you need to define context. a blanket answer to your question is that there are uncountably infinite amount of operators in mathematics that take all kinds of forms: linear operators, functional operators, binary operators, etc.

> taking a number to the power of another is just defined in terms of multiplication

similar to /u/theowoll's response, how would you define 2^(4.18492) in terms of multiplication? i know you're basing this question off of the interesting fact that 2^1 = 2, 2^2 = 2

2, 2^3 = 22 * 2, etc. and similarly for other certain classes of numbers, but how do you multiply 2 by itself 4.18492 times? it gets even more tricky to think of exponents like this if the base and power are non-rational (4.18492=418492/100000 is rational). what about the power of e^X, where e is the normal exponential and X is a matrix? take a look at wikipedia's article on exponentiation to see what a can of worms this discussion opens.> So am I just plain wrong about all this, or there is some truth to it?

although there is a lot of incorrect things in your description when you consider general classes of "things you can multiply and add", what you are sort of getting at is what the theory of abstract algebra covers. in such a theory, it explores what it means to add, multiply, have inverses, etc. for varying collections of things called groups, rings, fields, vector spaces, modules, etc. and the relationships and properties of such things. you might take a look at a book of abstract algebra by charles pinter. you should be able to follow it, as it is an excellent book.

A book of abstract algebra by Charles Pinter is the best math book I've ever read in terms of readability, I think. The first chapter is an essay on the history of algebra and the book is worth it just for this chapter.

Try Pinter. If you think it is too simple for you go for Aluffi.

If you are serious about this, then the best way to self learn Math is to learn to read Math books. This is a valuable skill. It stops you from having to rely on websites/tutorials and frees you to really read the stuff you're interested in.

Generally you probably want a more "back to basics" approach that will cover basic stuff and act as an introduction (again) to the topic (without handling you as if you're a child). I recommend Discrete Mathematics with Applications. Epp does a good job of starting at the beginning (with logic) and building a decent foundation through connectives, conditionals, existentials, universals, etc. eventually leading into proofs.

Her writing style is very readable IMO but still dense enough to help you learn how to read Math books.

If you're self motivated enough then start there. Read a chapter. Do the problems. Be confused. Do more problems. Still confused? Read the chapter again. Do more problems. Repeat. Eventually finish the book.

The next one will be faster and easier because of the work you put in. Eventually you'll be 3-5 books down, and you'll feel you know quite a bit. Then read more.. realize the field is huge and you know nothing. Read more to solve this.

Repeat

????

Success(?)

How to prove it is a great start. I think after that, you should focus on learning to think mathematically through practice instead of reading (at least, that's how I and most people learn best). Take classes or read and work through the textbooks of subjects that interest you. Discrete math would be a good place to start since it teaches proof techniques and basic probability and combinatorics; my class used this book which I thought was nice.

If you don't actually do the work, your thinking process isn't going to change.

Check out /r/compsci, /r/algorithms, and the subreddits in their sidebars.

Sure! There is a lot of math involved in the WHY component of Computer Science, for the basics, its Discrete Mathematics, so any introduction to that will help as well.

http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_sp-atf_title_1_1?s=books&amp;ie=UTF8&amp;qid=1368125024&amp;sr=1-1&amp;keywords=discrete+mathematics

This next book is a great theoretical overview of CS as well.

http://mitpress.mit.edu/sicp/full-text/book/book.html

That's a great book on computer programming, complexity, data types etc... If you want to get into more detail, check out: http://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/0534950973

I would also look at Coursera.org's Algorithm lectures by Robert Sedgewick, thats essential learning for any computer science student.

His textbook: http://www.amazon.com/Algorithms-4th-Robert-Sedgewick/dp/032157351X/ref=sr_sp-atf_title_1_1?s=books&amp;ie=UTF8&amp;qid=1368124871&amp;sr=1-1&amp;keywords=Algorithms

another Algorithms textbook bible: http://www.amazon.com/Introduction-Algorithms-Thomas-H-Cormen/dp/0262033844/ref=sr_sp-atf_title_1_2?s=books&amp;ie=UTF8&amp;qid=1368124871&amp;sr=1-2&amp;keywords=Algorithms

I'm just like you as well, I'm pivoting, I graduated law school specializing in technology law and patents in 2012, but I love comp sci too much, so i went back into school for Comp Sci + jumped into the tech field and got a job at a tech company.

These books are theoretical, and they help you understand why you should use x versus y, those kind of things are essential, especially on larger applications (like Google's PageRank algorithm). Once you know the theoretical info, applying it is just a matter of picking the right tool, like Ruby on Rails, or .NET, Java etc...

Discrete Mathematics with Applications by Susanna Epp is pretty good, with a lot of exposition. In the introduction there is a guide on how to use the book, and the different sections to focus on if using it for a mainly mathematics-based class or for a computer science-based class.

http://www.amazon.com/gp/product/0495391328/ref=pd_lpo_sbs_dp_ss_2?pf_rd_p=1944687702&amp;pf_rd_s=lpo-top-stripe-1&amp;pf_rd_t=201&amp;pf_rd_i=0132122715&amp;pf_rd_m=ATVPDKIKX0DER&amp;pf_rd_r=0P155N9Y802PPMETYGVC

How To Prove It

Have I got the book for you, op

https://www.amazon.com/dp/0521675995/ref=cm_sw_r_cp_apa_i_2EmtDbDDEMPG9

Learning proofs can mean different things in different contexts. First, a few questions:

The sort of recommendations for a pre-university student are likely to be very different from those for a university student. For example, high school students have a number of mathematics competitions that you could consider (at least in The United States; the structure of opportunities is likely different in other countries). At the university level, you might want to look for something like a weekly problem solving seminar. These often have as their nominal goal preparing for the Putnam, which can often feel like a VERY ambitious way to learn proofs, akin to learning to swim by being thrown into a lake.

As a general rule, I'd say that working on proof-based contest questions that are

justbeyond the scope of what you think you can solve is probably a good initial source of problems. You don't want something so difficult that it's simply discouraging. Further, contest questions typically have solutions available, either in printed books or available somewhere online.This may be especially true for things like logic and

veryelementary set theory.Some recommendations will make a lot more sense if, for example, you have access to a quality university-level library, since you won't have to spend lots of money out-of-pocket to get copies of certain textbooks. (I'm limiting my recommendations to legally-obtained copies of textbooks and such.)

Imagine trying to learn a foreign language without being able to practice it with a fluent speaker, and without being able to get any feedback on how to improve things. You may well be able to learn how to do proofs on your own, but it's

orders of magnitudemore effective when you have someone who can guide you.rigorousmathematical proofs?Put differently, is your current goal to be able to produce a proof that will satisfy yourself, or to produce a proof that will satisfy someone

else?Have you had at least, for example, a geometry class that's proof-based?

Proofs are all about

communicating ideas. If you struggle with writing in complete, grammatically-correct sentences, then that will definitely be a bottleneck to your ability to make progress.---

With those caveats out of the way, let me make a few suggestions given what I think I can infer about where you in particular are right now.

How to Prove It: A Structured Approachby Daniel Velleman is a well-respected general introduction to ideas behind mathematical proof, as isHow to Solve It: A New Aspect of Mathematical Methodby George Pólya.Calculusby Michael Spivak. This is a challenging textbook, but there's a reason people have been recommending its different editions over many decades.writemathematically sound proofs, it helps toreadas many as you can find (at a level appropriate for your background and such). You can find plenty of examples in certain textbooks and other resources, and being able to work from templates of "good" proofs will help you immeasurably.Learning proofs is in many ways a skill that requires cultivation. Accordingly, you'll need to be patient and persistent, because proof-writing isn't a skill one typically can acquire passively.

---

How to improve at proofs is a big question beyond the scope of what I can answer in a single reddit comment. Nonetheless, I hope this helps point you in some useful directions. Good luck!

Read and work through this book: http://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/0521675995/ref=sr_1_1?ie=UTF8&amp;qid=1301319337&amp;sr=8-1

How to Prove It: A Structured Approach by Velleman is good for developing general proof writing skills.

How to Think About Analysis by Lara Alcock beautifully deconstructs all the major points of Analysis(proofs included).

I think everyone is on point for the most part, but I'd like to be the devil's advocate and suggest a different route.

Learn logic, proof techniques and set theory as early as possible. It will aid you in further study of all 'types' of math and broaden your mind in a general sense. This book is a perfect place to start.

http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995

The best part is, when you start doing proofs you realize you've been thinking about math all wrong (at least I did). It's an exercise in creativity, not calculation.

In my mind, set theory & calculus are necessary pre-requisites to probability anyway, and linear algebra means much more once you have been introduced to inductive proofs, as well.

Perhaps rather than concentrating on these particular proofs you should look at something like How To Prove It.

If your intent is to take a class like analysis, you really should look into something like logic.

Daniel Velleman wrote an excellent little book called How to Prove It: A Structured Approach. It's actually designed for High School level students, but it works through the subject incredibly well.

Here's an Amazon link to the book:

http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1333383091&amp;sr=1-1

This extremely famous book on psychology posits that, prior to three thousand years ago, humans experienced consciousness as a monologue from a set of internal muses. Muses responsible for creativity, for war and passion and all of the higher symbolic concepts.

You weren’t creative so much as possessed by the spirit of creativity! In this way, they saw history as the interaction of this finite set of transcendent ideas manifesting through people, each furthering their individual agendas and goals.

It’s only over time that we’ve been able to assimilate and accept this voice in our heads as our own, exorcising the spirits behind consciousness until only we remain.

I’m sure there are tradeoffs to suppressing this sort of sublucid cognition but, given the progress that mankind has made in the last three thousand years, I would say that this new mode of thought is largely the actualization of our (previously latent) potential.

But it would be nice to get back what we’ve given up as well...

No, it's not 50/50. There is no objective evidence of consciousness after death, nor any known mechanism by which the patterns in the brain could persist after the brain ceases to function. The probability of there being nothing after death approaches 100%. Sam Harris's ideas amount to an argument from incredulity.

If you're into fringe theories on consciousness, though, you might enjoy The Origin of Consciousness. It at least offers testable hypotheses.

The Origins of Consciousness and the Breakdown of the Bicameral Mind by Julian Jaynes. Helluva read. It dives deep into the theory that consciousness did not just suddenly happen, but was learned over a very, very long time and is still developing today.

The textbooks recommended in the intro Astronomy class here are An Introduction to Modern Astrophysics by Carroll & Ostlie and Foundations of Astrophysics. I've never read through either, but apparently the first one is much more detailed.

The older edition of Modern Astrophysics is significantly cheaper and will fit your purposes just as well: 1st Edition Carroll

Possibly the best all round book out there for a basic introduction:

http://www.amazon.com/Introduction-Modern-Astrophysics-2nd-Edition/dp/0805304029/ref=sr_1_1?ie=UTF8&amp;qid=1344988735&amp;sr=8-1&amp;keywords=introduction+to+modern+astrophysics

Far too expensive to buy, but if you can find it in a local library it would be invaluable. Everything in it is at a level that you can easily teach yourself stuff you don't know from various online resources.

Seriously, I have my mushroom book with the delighted trumpet man on the cover and I just need some rain.

Nope, none of those for my location, but there is this fantastic book which is the bible of most foragers in my neighbourhood. And this one.

All That the Rain Promises and More: A Hip Pocket Guide to Western Mushrooms https://www.amazon.com/dp/0898153883/ref=cm_sw_r_cp_apa_HNZYzbG9SMY94

Textbooks (calculus): Fundamentals of Physics: http://www.amazon.com/Fundamentals-Physics-Extended-David-Halliday/dp/0470469080/ref=sr_1_4?ie=UTF8&amp;qid=1398087387&amp;sr=8-4&amp;keywords=fundamentals+of+physics ,

Textbooks (calculus): University Physics with Modern Physics; http://www.amazon.com/University-Physics-Modern-12th-Edition/dp/0321501217/ref=sr_1_2?ie=UTF8&amp;qid=1398087411&amp;sr=8-2&amp;keywords=university+physics+with+modern+physics

Textbook (algebra): [This is a great one if you don't know anything and want a book to self study from, after you finish this you can begin a calculus physics book like those listed above]: http://www.amazon.com/Physics-Principles-Applications-7th-Edition/dp/0321625927/ref=sr_1_1?ie=UTF8&amp;qid=1398087498&amp;sr=8-1&amp;keywords=physics+giancoli

If you want to be competitive at the international level, you definitely need calculus, at least the basics of it.

Here is a good book: http://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/ref=sr_1_1?ie=UTF8&amp;qid=1398087834&amp;sr=8-1&amp;keywords=calculus+kline

It is quite cheap and easy to understand if you want to self teach yourself calculus.

Another option would be this book:http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?ie=UTF8&amp;qid=1398087878&amp;sr=8-1&amp;keywords=spivak

If you can finish self teaching that to yourself, you will be ready for anything that could face you in mathematics in university or the IPhO. (However it is a difficult book)

Problem books: Irodov; http://www.amazon.com/Problems-General-Physics-I-E-Irodov/dp/8183552153/ref=sr_1_1?ie=UTF8&amp;qid=1398087565&amp;sr=8-1&amp;keywords=irodov ,

Problem Books: Krotov; http://www.amazon.com/Science-Everyone-Aptitude-Problems-Physics/dp/8123904886/ref=sr_1_1?ie=UTF8&amp;qid=1398087579&amp;sr=8-1&amp;keywords=krotov

You should look for problem sets online after you have finished your textbook, those are the best recourses. You can get past contests from the physics olympiad websites.

This should keep you busy, but I can suggest books in other areas if you want.

Math books:

Algebra: http://www.amazon.com/Algebra-I-M-Gelfand/dp/0817636773/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1251516690&amp;sr=8

Calc: http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1356152827&amp;sr=1-1&amp;keywords=spivak+calculus

Calc: http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X

Linear algebra: http://www.amazon.com/Linear-Algebra-Modern-Introduction-CD-ROM/dp/0534998453/ref=sr_1_4?ie=UTF8&amp;s=books&amp;qid=1255703167&amp;sr=8-4

Linear algebra: http://www.amazon.com/Linear-Algebra-Dover-Mathematics-ebook/dp/B00A73IXRC/ref=zg_bs_158739011_2

Beginning physics:

http://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp/0465023827

Advanced stuff, if you make it through the beginning books:

E&M: http://www.amazon.com/Introduction-Electrodynamics-Edition-David-Griffiths/dp/0321856562/ref=sr_1_1?ie=UTF8&amp;qid=1375653392&amp;sr=8-1&amp;keywords=griffiths+electrodynamics

Mechanics: http://www.amazon.com/Classical-Dynamics-Particles-Systems-Thornton/dp/0534408966/ref=sr_1_1?ie=UTF8&amp;qid=1375653415&amp;sr=8-1&amp;keywords=marion+thornton

Quantum: http://www.amazon.com/Principles-Quantum-Mechanics-2nd-Edition/dp/0306447908/ref=sr_1_1?ie=UTF8&amp;qid=1375653438&amp;sr=8-1&amp;keywords=shankar

Cosmology -- these are both low level and low math, and you can probably handle them now:

http://www.amazon.com/Spacetime-Physics-Edwin-F-Taylor/dp/0716723271

http://www.amazon.com/The-First-Three-Minutes-Universe/dp/0465024378/ref=sr_1_1?ie=UTF8&amp;qid=1356155850&amp;sr=8-1&amp;keywords=the+first+three+minutes

Apostol and Spivak are the best calculus texts I know; paperback versions of each exist.

Learn math first. Physics is essentially applied math with experiments. Start with Calculus then Linear Algebra then Real Analysis then Complex Analysis then Ordinary Differential Equations then Partial Differential Equations then Functional Analysis. Also, if you want to pursue high energy physics and/or cosmology, Differential Geometry is also essential. Make sure you do (almost) all the exercises in every chapter. Don't just skim and memorize.

This is a lot of math to learn, but if you are determined enough you can probably master Calculus to Real Analysis, and that will give you a big head start and a deeper understanding of university-level physics.

The greatest show on earth or Why evolution is true are both very good overviews of the evidence for evolution. Probably a good place to start. Evolution is such a huge topic that no one book is a comprehensive overview of it all, once you understand the basics of evolution however I really suggest the selfish gene. You can also pick up a very cheap copy of on the origin of species, though remember that the book is 150 years old and predated genetics (still remarkably accurate however).

I haven't read it, but I hear it's pretty good:

Richard Dawkins, The Greatest Show on Earth: The Evidence for Evolution

I'm going to post my favorite videos that I grew up on. I could watch them over and over and not get sick of them. Dawkins is my hero.

Royal Institute Christmas Lectures - Richard Dawkins' "Growing Up in the Universe". Entertaining, engaging, and fascinating series of lectures for children on the basics of evolution in a way that makes a hell of a lot of sense. You will see fascinating stuff. I found some parts mind-blowing, and the demonstrations are just great (and here's proof!)

BBC Horizon - Nice Guys Finish First (Part 1 of 5) - Documentary on Evolution and Altruism, as well as some basics of Game Theory

Documentary - The Blind Watchmaker (1 of 5)

Book - The Greatest Show on Earth by Richard Dawkins.

Fantastic book that illustrates evolution very well. It's an easy read, but it manages to break down complex ideas in a very clear manner. I read it recently, and even though I thought I knew a lot, this really helped me get a better grasp on some of the basics. Dawkins' tone in the beginning might come off as unusually annoying in this book, but it gets better. The pictures and metaphors are beautiful, and there are some witty lines and funny stories. Some of the statistics will make you rage. The ending is surprisingly sad and powerful.

Best of luck!

Everything you need to know; no expensive courses required!

There was a book written about it.

Well A) the Higgs boson was originally joked as "the goddamn particle" because it was so difficult to detect. Some editor shortened it because that name would have gotten a bad reaction from people.

B) you should really check out cosmologists Lawrence Krauss (video) or Stephen Hawking (transcript). Krauss even wrote an entire book on the topic titled "A Universe from Nothing: Why There Is Something Rather than Nothing".

This might be more of a science answer than a broader philosophy answer, but these guys have math to back it up.

And C) "Intelligent Design" has already been ruled out by biologists, who find no convincing evidence. It's evolution and its various mechanisms that explain all the wonders and diversity of life.

Warning, Krauss in particular has a lot of disparaging remarks about religion and its followers.TL;DR - According to these theoreticians, "nothing" (as a quantum mechanical phenomenon) is physically

unstable, and "something" is certain to appear given enough time.Because nothingness is impossible, per ASU and Caltech research. There are a ton of books on this subject, along with JSTOR documents (which you should have a subscription too if you are in college). This one is especially easy to read and comprehend the material. Enjoy. I'll gift you the Kindle edition if you really have an avid interest in learning new things.

A physicist named Lawrence Krauss wrote a book on this. Its called a universe from nothing. Good read. Also, if youre interested another good book that adresses different attempts to answer the question 'why is there something rather than nothing?' is called "Why does the world exist?" by Jim Holt.

Heres some links:

http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/145162445X

http://www.amazon.com/Why-Does-World-Exist-Existential/dp/0871403595/ref=la_B001IGFJ92_1_1?ie=UTF8&amp;qid=1367993510&amp;sr=1-1

edit: I just noticed that someone else mentioned Krauss in an above comment. Sorry for redundancy.

No. Science does not indicate that the big bang came from nothing. The idea of something coming from nothing is a Christian concept. In the beginning God created... And God created something from nothing.

The astrophysicist Lawrence Kraus wrote a book A Universe from Nothing. It was a great read but unfortunately it fed into the idea of something coming from nothing. What Kraus did in his book was to change the meaning of the word 'nothing' in order to have a title that would sell more books. Kraus' 'nothing' was actually 'something'.

We actually use the distances between really far apart things in the universe and make a "triangle" just like they were talking about on the surface of the Earth. The math is pretty complicated, but you might enjoy A Universe from Nothing by Lawrence Krauss. It has a pretty good in depth but mostly understandable by mere mortals explanation of how these things are measured and determined.

Given your apparent troll status, I will simply recommend a book for you that addresses your question nicely. A Universe from Nothing (ISBN-13: 978-1451624465

| ISBN-10: 1451624468) by Lawrence M. Krauss gives scientific explanations about how the scenario you question can occur.

You don't have to buy it to read it, as you can check it out from your local library (or if you have an e-reader, borrow it online).

I really like Lawrence Krauss' explanation - universes with certain characteristics, which our seems to possess, can have zero total energy. As it turns out, empty space acts, as if it didn't want to be empty - in a state of high vaccum, space suddenly starts to boil with virtual particles - particles and antiparticles, that spring into existence and annihilate each other instantly. If that happens in empty space, then it is reasonable to suggest, that in absence of space, such virtual spaces might spring into existence, and if certain conditions are met, rather than instantly collapse, they might expand and be filled with matter, gravity and dark energy, while having zero total energy at the same time.

You might learn more from his lecture, or his book on the subject.

http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/1451624468

If you want peer-reviewed studies, see the references in that book.

Only when they're being paid by corporate interests. See Merchants of Doubt

Or see the book and documentary Merchants of Doubt.

Did you even watch the "Environmental Hysteria" episode? His conclusion was that "we don't know" re: global warming.

At the time that episode was filmed there was (and remains) a 100% scientific consensus that global warming is happening and humans are primarily the cause of it, which Penn would have known had he talked to a single climate scientist. Instead, he interviewed hippies and a Cato wonk. You remember Cato, right?

Anyways, you can believe whatever you want. I'm just pointing out that his anti-science views are in line with his corporate handlers, whom happen to spend lots of money spreading FUD about scientific research that exposes the risks of their products. This is all documented in Naomi Oreskes excellent book "Merchants of Doubt", which I will highly recommend:

http://www.amazon.com/Merchants-Doubt-Handful-Scientists-Obscured/dp/1608193942/ref=sr_1_1?ie=UTF8&amp;qid=1382123569&amp;sr=8-1&amp;keywords=merchants+of+doubt

It's interesting to note that Penn's position (i.e. "we don't know") is exactly the sort of spin practiced by the PR creeps that successfully prevented any meaningful regulation of the tobacco industry for decades. So there is no surprise Penn lied about the risks of second-hand smoke, either. Or that Cato (and P&T by proxy) received financial support from the tobacco industry:

http://www.sourcewatch.org/index.php?title=Cato_Institute#Cato_and_the_tobacco_industry_-_on_Philip_Morris.2C_RJR_.22friends.22_lists

I'm so vocal (and pissed off) about this because this sort of "Bullshit" actually hurts people vs. harmless fads like Feng Shui or bottled water.

Btw, I know lots (too much really) about Penn. I've attended conferences with him (The Amazing Meeting) and even been to his home in Vegas. You should try taking your own advice as you (obviously) know nothing about me.

Best:

Principles of Mathematical Analysis by Walter Rudin

Baby Rudin

David Griffiths' textbooks on E&M and quantum mechanics were easily the best textbooks I had as an undergrad. Clear, concise, refreshingly informal, and even a dash of humor.

http://www.research.ibm.com/ibm-q/learn/what-is-quantum-computing/

That has a good introduction.

If you actually care about the background, start with https://www.amazon.ca/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927

I just want to point out one thing that everyone seems to be glossing over: when people say that you'll need to review classical mechanics, they aren't talking only about Newtonian Mechanics. The standard treatment of Quantum Mechanics draws heavily from an alternative formulation of classical mechanics known as Hamiltonian Mechanics that I'm willing to bet you didn't cover in your physics education. This field is a bit of a beast in its own right (one of those that can pretty much get as complicated/mathematically taxing as you let it) and it certainly isn't necessary to become an expert in order to understand quantum mechanics. I'm at a bit of a loss to recommend a good textbook for an introduction to this subject, though. I used Taylor in my first course on the subject, but I don't really like that book. Goldstein is a wonderful book and widely considered to be the bible of classical mechanics, but can be a bit of a struggle.

Also, your math education may stand you in better stead than you think. Quantum mechanics done (IMHO) right is a very algebraic beast with all the nasty integrals saved for the end. You're certainly better off than someone with a background only in calculus. If you know calculus in 3 dimensions along with linear algebra, I'd say find a place to get a feel for Hamiltonian mechanics and dive right in to Griffiths or Shankar. (I've never read Shankar, so I can't speak to its quality directly, but I've heard only good things. Griffiths is quite understandable, though, and not at all terse.) If you find that you want a bit more detail on some of the topics in math that are glossed over in those treatments (like properties of Hilbert Space) I'd recommend asking r/math for a recommendation for a functional analysis textbook. (Warning:functional analysis is a bit of a mindfuck. I'd recommend taking these results on faith unless you're

reallycurious.) You might also look into Eisberg and Resnick if you want a more historical/experimentally motivated treatment.All in all, I think its doable. It is my firm belief that anyone can understand quantum mechanics (at least to the extent that anyone understands quantum mechanics) provided they put in the effort. It will be a fair amount of effort though. Above all, DO THE PROBLEMS! You can't actually learn physics without applying it. Also, you should be warned that no matter how deep you delve into the subject, there's always farther to go. That's the wonderful thing about physics: you can never know it all. There just comes a point where the questions you ask are current research questions.

Good Luck!

Check this book out!

It absolutely changed my mental math ability. Arthur Benjamin also has videos all over the Internet with some quick mental math tricks.

I have a book on mental math, and this is essentially the technique that the author uses to square numbers mentally really quickly.

In other words,

x^2 = (x+k)(x-k) + k^2

where you substitute x's into the equation you gave.

This is the book.

I read Alan Weisman's The World Without Us a few years back, and in that book he theorized that if humans were to all instantly disappear, the first large pieces of our construction that would fail would be our dams. Apparently dams require constant inspection and maintenance to keep in working shape and most would fail very quickly without our intervention.

What the book didn't really touch on, and what I would be concerned about, would be region-scale environmental disasters that result from industrial facilities left unattended. Nuclear power plants, oil wells and refineries in particular. If we were to vanish, I imagine the world would instantly see hundreds of massive oil spills and probably within a week or so, various nuclear meltdowns. The planet can recover from that but I imagine it could create a massive die-off for 100,000 years or so, plus the lasting effects of radiation.

There are a bunch of suggestions in here already but allow me to supplement with a non-fiction book. The World Without Us bu Alan Weisman. Essentially he begins with the premise that humans are removed suddenly from the planet. He then explores (through research and discussion) what would happen to infrastructure, land, etc. He creates a narrative so its readable but it is also packed with interesting details. If anyone likes post-apocalypse settings this book provides a real-world anchor.

There's a great book that deals with this exact topic, called The World Without Us, by Alan Weisman. It basically starts off with every human simply disappearing from Earth, and the process in which nature would reclaim the planet. It's science fiction obviously, but without an overarching story. It reads sort of like a historical text about a what-if scenario of the future. I recommend it if you're interested in this subject.

A very good book that deals with this issue is The Demon-Haunted World: Science as a Candle in the Dark by Carl Sagan.

Here's the blurb:

How can we make intelligent decisions about our increasingly technology-driven lives if we don’t understand the difference between the myths of pseudoscience and the testable hypotheses of science? Pulitzer Prize-winning author and distinguished astronomer Carl Sagan argues that scientific thinking is critical not only to the pursuit of truth but to the very well-being of our democratic institutions.Casting a wide net through history and culture, Sagan examines and authoritatively debunks such celebrated fallacies of the past as witchcraft, faith healing, demons, and UFOs. And yet, disturbingly, in today's so-called information age, pseudoscience is burgeoning with stories of alien abduction, channeling past lives, and communal hallucinations commanding growing attention and respect. As Sagan demonstrates with lucid eloquence, the siren song of unreason is not just a cultural wrong turn but a dangerous plunge into darkness that threatens our most basic freedoms.Perhaps it's time to move away from LDS specific arguments, and start questioning the God concept in general; especially as it relates to morality.

One argument I've always liked, is that even if there is a god, by far the strongest test of morality it could ask for is if a person will be moral while believing there is no such being, and no promise of reward or punishment.

If she is willing to read, I recommend the following:

YouTube is also a fantastic resource. Here are some of the video series that I found particularly convincing as I was going through my own transition:

I think it's also important to remember that there is are alternative worldviews out there which are not based on religion, which are just as rewarding and fulfilling, if not more so. Here are a few videos that have sparked that sense of wonder and that I used to associate with the spirit. Most of these are not direct attacks on religion, but rather are just inspiring ideas from a secular\scientific worldview. I recognize that these may not have universal appeal, but they spoke to me, and may do so for you and your wife as well:

Godless: How an Evangelical Preacher Became One of America's Leading Atheistsby Dan BarkerLetter to a Christian Nationby Sam HarrisThe God Delusionby Richard DawkinsThe Demon-Haunted World: Science as a Candle in the Darkby Carl SaganThe Demon-Haunted World: Science as a Candle in the Dark should be compulsory reading.

I just echo what etherias said 100%. Also, a great book that addresses a lot of that is The Demon Haunted World by Carl Sagan. It gets into that kind of superstitious stuff, conspiracy theories, etc. Not that they'd read it, most likely, but it'd probably resonate a lot with you!

FTFA:

>Rural Zanzibaris’ descriptions of the leopard and its habits are coloured by the widespread belief that a large number of these carnivores are kept by witches and sent by them to harm or otherwise harass villagers.

What kind of world?

Why, a demon-haunted one, of course.

Sagan's book

The Demon-Haunted World: Science as a Candle in the Darkis excellent reading. Although it's more pro-science than anti-religion, that's what's important anyway and it makes the atheist viewpoint clear.The Demon-Haunted World: Science as a Candle in the Dark by Carl Sagan. Its a very good book that mostly focuses on skepticism.

I cannot recommend "Demon Haunted World" by Sagan enough for this.

http://smile.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469/ref=smi_www_rco2_go_smi_1968491462?_encoding=UTF8&amp;*Version*=1&amp;*entries*=0&amp;pf_rd_p=1968491462&amp;pf_rd_s=smile-campaign&amp;pf_rd_t=201&amp;pf_rd_i=0345409469&amp;pf_rd_m=ATVPDKIKX0DER&amp;pf_rd_r=0NA1PTR8YS7CFF6NF6XY

Recommended reading (though I understand if you don't... it's extremely counter to your point of view and you sound very set in it): http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

I don't mean any disrespect, but I think Sagan is a gatekeeper. In "The Demon Haunted World', he tries to debunk almost every big conspiracy theory. His narrative is similar to the modern post-Campbell interpretation of myth. He also sites the discredited False Memory Syndrome Foundation in this book.

the book

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

a citation on the FMSF wikipedia page

https://en.wikipedia.org/wiki/False_Memory_Syndrome_Foundation#cite_note-23

This book was used as a debunkers manual in the 90s, so I might have a chip on my shoulder. But I can't take Sagan any more seriously than Chomsky, Hitchens, Hawkings, or Oprah.

Breaking The Spellby Daniel DennettMisquoting Jesusby Bart EhrmanThe End of Faithby Sam HarrisThe Elegant Universeby Briane Greene (about string theory)Just Six Numbersby Martin ReesBefore The Beginningby Martin ReesGodel, Escher, Bachby Douglas R. HofstadterThe Demon-Haunted Worldby Sagan/u/LengthContracted this is a good book, as is Daphne Kollers book on PGMs as well as the associated course http://pgm.stanford.edu

A sample of what is on my reference shelf includes:

Real and Complex Analysis by Rudin

Functional Analysis by Rudin

A Book of Abstract Algebra by Pinter

General Topology by Willard

Machine Learning: A Probabilistic Perspective by Murphy

Bayesian Data Analysis Gelman

Probabilistic Graphical Models by Koller

Convex Optimization by Boyd

Combinatorial Optimization by Papadimitriou

An Introduction to Statistical Learning by James, Hastie, et al.

The Elements of Statistical Learning by Hastie, et al.

Statistical Decision Theory by Liese, et al.

Statistical Decision Theory and Bayesian Analysis by Berger

I will avoid listing off the entirety of my shelf, much of it is applications and algorithms for fast computation rather than theory anyway. Most of those books, though, are fairly well known and should provide a good background and reference for a good deal of the mathematics you should come across. Having a solid understanding of the measure theoretic underpinnings of probability and statistics will do you a great deal--as will a solid facility with linear algebra and matrix / tensor calculus. Oh, right, a book on that isn't a bad idea either... This one is short and extends from your vector classes

Tensor Calculus by Synge

Anyway, hope that helps.

Yet another lonely data scientist,

Tim.

http://www.amazon.com/Book-Abstract-Algebra-Edition-Mathematics/dp/0486474178/ref=sr_1_1?ie=UTF8&amp;qid=1394386195&amp;sr=8-1&amp;keywords=pinter+abstract+algebra)

We used the Dover textbook by Pinter. It's my favorite math textbook ever, the writing was just so clear, and even entertaining and funny. We had a good professor too.

A First Course in Graph Theory by Chartrand and Zhang

Combinatorics: A Guided Tour by Mazur

Discrete Math by Epp

For Linear Algebra I like these below:

Lecture Notes by Tao

Linear Algebra: An Introduction to Abstract Mathematics by Robert Valenza

Linear Algebra Done Right by Axler

Linear Algebra by Friedberg, Insel and Spence

Data Structures & Algorithms is usually the second course after Programming 101. Here is a progression (with the books I'd use) I would recommend to get started:

Edit: If you're feeling adventurous then after those you should look at

"Turn Left At Orion"

http://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972/ref=sr_1_2?ie=UTF8&amp;qid=1325019980&amp;sr=8-2

A excellent guide to finding objects that look good in a telescope.

Also/or "Nightwatch" http://www.amazon.com/NightWatch-Practical-Guide-Viewing-Universe/dp/155407147X/ref=pd_cp_b_1

Adding a cheap green laser pointer REALLY helped with aiming my scope. Granted, my scope came with a pretty crappy viewfinder. The laser also makes it super simple to point to objects in the sky when sharing with people "no, not that little star near the other thing, THAT little star near the other thing". Just get some rubber bands to attach it to the scopes main tube.

But the MOST important thing I ever did for my astronomy hobby: Joined cloudynights.com. An online astronomy message board.

Turn Left at Orion is a perfect beginner-level book: https://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972

I think addressing both of those with in-depth answers could fill a book... Oh wait, it has! Check out [Turn Left at Orion] (http://amzn.com/0521153972). While you can probably find pirated versions around, you're far better off with the spiral bound version--this book is meant to be out in the field with you (and not screwing with your night vision like display screens will).

It gives a big list of cool things to look at through 1) binoculars, 2) small telescopes like yours, 3) larger backyard scopes.

It then tells you how to find them by "star hopping". It even has pictures of what to expect in your finder scope, etc.

Sorry, the solution is to do lots of proofs.

There's more to it, but honestly it's more of a thing that you have to read a book about rather than a message on reddit. How are you learning about this right now? Is it part of a course or self-study? I personally found How to Prove It to be a very useful textbook. Doesn't require any particular knowledge, and it builds out a nice foundation in logic and set theory.

How To Prove It. Read through the reviews. It's the best book for learning propositional and predicate logic for the first time.

You will first want to learn fundamental logic and set theory before diving into topics like analysis, algebra, and discrete topics. You will need an understanding of a rigorous proof -- not the hand-wavey kind of proof we've seen in our introductory calculus courses. This book is very readable and will prepare you for advanced mathematics. I've seen it work for many students.

After you're finished with it, you may want to study analysis which will build up the Calculus for you. If you don't care for calculus anymore, consider reading an abstract algebra text. Algebra is pretty fun. You can also pick a discrete topic like graph theory or combinatorics whose applications are very easy to see.

There are many ways to go, but in all of them you will absolutely need a a basic understanding of the use of logic in a mathematical proof.

What this expressions saysFirst of all let's specify that the domain over which these statements operate is the set of all

peoplesay.Let us give the two place predicate P(x,y) a concrete meaning. Let us say that P(x,y) signifies the relation

x loves y.This allows us to translate the statement:

∀x∀yP(x,y) -> ∀xP(x,x)

What does ∀x∀yP(x,y) mean?This is saying that

For all x, it is the case that For all y, x loves y.So you can interpret it as saying something like

everyone loves everyone.What does ∀xP(x,x) mean?This is saying that

For all x it is the case that x loves x. So you can interpret this as saying something likeeveryone loves themselves.So the statement is basically saying:

Given that it is the case that Everyone loves Everyone, this implies that everyone loves themselves.This translation gives us the impression that the statement is true. But how to prove it?

Proof by contradictionWe can prove this statement with a technique called proof by contradiction. That is, let us assume that the conclusion is false, and show that this leads to a contradiction, which implies that the conclusion must be true.

So let's assume:

∀x∀yP(x,y) ->

not∀xP(x,x)not∀xP(x,x) is equivalent to ∃x not P(x,x).In words this means

It is not the case that For all x P(x,x) is true, is equivalent to saying there exists x such P(x,x) is false.So let's

instantiatethis expression with something from the domain, let's call ita. Basically let's pick a person for whom we are saying a loves a is false.not P(a,a)Using the fact that ∀x∀yP(x,y) we can show a contradiction exists.

Let's instantiate the expression with the object

awe have used previously (as a For all statement applies to all objects by definition) ∀x∀yP(x,y)This happens in two stages:

First we instantiate y

∀xP(x,a)

Then we instantiate x

P(a,a)The statements

P(a,a)andnot P(a,a)are contradictory, therefore we have shown that the statement:∀x∀yP(x,y) ->

not∀xP(x,x) leads to a contradiction, which implies that∀x∀yP(x,y) -> ∀xP(x,x) is true.

Hopefully that makes sense.

Recommended ResourcesWilfred Hodges - Logic

Peter Smith - An Introduction to Formal Logic

Chiswell and Hodges - Mathematical Logic

Velleman - How to Prove It

Solow - How to Read and Do Proofs

Chartand, Polimeni and Zhang - Mathematical Proofs: A Transition to Advanced Mathematics

a brief history of time, http://www.amazon.com/Brief-History-Time-Stephen-Hawking/dp/0553380168

edit: Sorry, i forgot to remind you not to buy from amazon either.

edit 2: Actually if you want it, pm me your address and I'll ship you my copy

You concept of time isn't wrong and I didn't post to

correctyou in any way. I love Asimov's The Collapsing Universe and Hawking's A Brief History of Time. I hope others get to read them and enjoy them as well, even though physics has changed and some of the information is outdated... they are so well written.No one knows what the universe was like before the Big Bang. There are some very weird theories out there with evidence behind them. Any one of them might be right, or they might all be based on information we don't fully understand and could be all wrong.

SOMETHING FROM NOTHING? Richard Dawkins & Lawrence Krauss that I recommend you watch the entire way through (though its 2 hours, it is well worth for someone interested in such topics). However if you are short of time, go to 47:30-51:00 minutes and watch Krauss explain how matter could literally form in deep space where there is

nothing. This means our universe could have formed from nothing, turned into a singularity, and then formed in a big bang. Krauss says, "...That 'nothing' is unstable. That 'empty space' is unstable. The laws of quantum mechanics combined with gravity, will tell you, that if you have empty space there, and you wait long enough, particles will be created. And if you wait long enough, empty space will always produce a universe full of matter." It just makes you say, Whhaaaat?Combine the concept that our universe is something like the surface of an expanding balloon where everything is getting further apart all the time. Over enough trillion of years, the empty space between those old galaxies could create their own singularities and own universes. We don't have a way to measure something like this.

Since the boson particle was only recently observed and confirmed, there will be a lot of changes coming. That means the Higgs-Boson field that creates all mass... well it might not have been causing mass within the singularity. At which point the singularity could expand without the forces of gravity until the h-b field took over... there are just too many variations at the time. That doesn't even cover dark matter or

TL;DR... Before the big bang could have been (1) nothing but a singularity since no time/space, (2) other universes, (3) other parts of this universe, or (4) literally nothing but empty space.

I love how these kind of "gotcha" questions are always couched in a willful misunderstanding of what the actual scientific theory states.

Read a book, shitbird.

There was recently a question sessions on /pol with a anonymous claiming to be a high level insider of one of the benevolent global power factions.in the sessions he mentioned that this is the second time we have created society that there was an earlier civilisation that was wiped out by flood and the pyramids and the water erosion at the base of the pyramids is evidence of an ancient civilisation predating the Egyptians.

As you can see from the comments there's a lot of interest and I'm one of the number who thinks he's legit. Most I've spoken with (including OP) believe the same. I'd strongly recommend in taking a read through regardless, the anon is very well versed in a range of disciplines. I took a lot away and am learning a lot from the book he (repeatedly) advised truth seekers to read - The Origins of Consciousness in the Breakdown of the Bicameral Mind

High Level Insider /pol dump

This reminds me that I've been meaning to pick up The Origin of Consciousness in the Breakdown of the Bicameral Mind. Thanks.

Carrol and Ostlie, a.k.a BOB (big orange book).

Hmm. Well, I really like Codyslab on youtube. He has some intersting stuff. Vihart uses to make some creative math videos back in the day.

If you want books, Richard Feynman wrote a bunch that are great. My favorite is "Surely you must be joking, Mr Feynman!" Which covers such adventutes as cracking the safes of the Manhattan project, sleeping on a bench the first day of his professorship, and his eureka moment with quantum electrodynamics!

A good textbook for a little light reading is the Big Orange Book, or the BOB. https://www.amazon.com/Introduction-Modern-Astrophysics-2nd/dp/0805304029 It is a good intro to all different subjects on astrophysics, and if you take it in college, this may be one of the books you need to get. Some solutions can be found online for it too ;)

Yes!

If you don't know any calculus Stewart Calculus is the typical primer in colleges. Combine this with Khan Academy for easy mode cruise control.

After that, you want to look at The Big Orange Book, which is essentially the bible for undergrad astrophysics and 100% useful beyond that. This book could,

alone, tell you everything you need to know.As for other topics like differential equations and linear algebra you can shop around. I liked Linear Algebra Done Right for linear personally. No recommendations from me on differential equations though, never found a book that I loved.

Sure.

The gold standard in intro astronomy is the Big Orange Book by Carroll and Ostlie (orange standard?). Probably not the first book to read, but if you're serious about astronomy it's essential reading.

I really like the podcast Space Time with Stuart Gary. He basically goes over recent papers, but at a level that is very approachable for non-scientists.

You may get a lot out of a non-major intro textbook. I believe that John Fix's book is the one we use at my university. There are a number of intro texts out there, I'm not an expert on which is the best. But make sure it's not more than 5 or so years old,

a lothas happened in the last few years.Also, don't let the math scare you off. You need to learn calculus, and it was hard for me, too. But, you can definitely do it.

I hope that helps!

Ah, yes. It's a classic read. I highly recommend.

For a pocket guide I'd recommend

All That the Rain Promises and More. It has a little bit of a bias towards species in western North America, but it's still very useful in the east (I'm in New England and I love it).Mushrooms Demystifiedis pretty big for taking into the field, but it is a great companion to ATtRPaM, and it is the best all around field guide for North America, in my opinion.I would suggest picking up Mushrooms Demystified and All That the Rain Promises and More. Great books to get you into identification.

And remember; There are old mushroom hunters, and there are bold mushroom hunters, but there are no old bold mushroom hunters!

Invest in a good field guide. All That the Rain Promises and More is good to get your feet wet, and Mushrooms Demystified is the bible. Also, see if there are any mushroom clubs near you. Have fun!

This is a compilation of what I gathered from reading on the internet about self-learning higher maths, I haven't come close to reading all this books or watching all this lectures, still I hope it helps you.

General Stuff:The books here deal with large parts of mathematics and are good to guide you through it all, but I recommend supplementing them with other books.

Linear Algebra: An extremelly versatile branch of Mathematics that can be applied to almost anything, also the first "real math" class in most universities.Calculus: The first mathematics course in most Colleges, deals with how functions change and has many applications, besides it's a doorway to Analysis.Real Analysis: More formalized calculus and math in general, one of the building blocks of modern mathematics.Abstract Algebra: One of the most important, and in my opinion fun, subjects in mathematics. Deals with algebraic structures, which are roughly sets with operations and properties of this operations.There are many other beautiful fields in math full of online resources, like Number Theory and Combinatorics, that I would like to put recommendations here, but it is quite late where I live and I learned those in weirder ways (through olympiad classes and problems), so I don't think I can help you with them, still you should do some research on this sub to get good recommendations on this topics and use the General books as guides.

http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?ie=UTF8&amp;qid=1344481564&amp;sr=8-1&amp;keywords=spivaks+calculus

I haven't read all of it, but even the bit I did read was very challenging and it is generally recommended around here for a rigorous introduction to calculus. Be warned, it is pretty challenging, especially if you aren't comfortable with proofs.

http://www.amazon.com/Greatest-Show-Earth-Evidence-Evolution/dp/1416594787

You'll only do yourself a disservice by skimming an internet-education on evolution if it's something you truly want to understand.

Grab a copy of The Greatest Show on Earth by Richard Dawkins . It costs less than a ticket to the creation museum. The book presents clearly and concisely the evidence for evolution and

details how the process works. There's likely hesitation to buy a book by Dawkins because of his notoriety as a prominent atheist, but the book is impartial on the topic of a creator; It only aims to provide the facts and reasoning behind evolution.I hope you find the answers you're looking for on this matter, brandon64344. The world makes so much mroe sense through the lens of evolution.

You should simply tell your father that's he's wrong, "information" gets created all the time. Heck, any decent sized storm creates an enormously complex body of coherent organized information. Even simple equations "create" information.

We can observe it happening; it's not a matter of faith. Your father is simply wrong. Virtually every creationist argument will be like this; and the few remaining will reduce to transparent fallacies.

If you wish to discuss this with your father, read this book first. Arguing with your dad might be a waste of time, but reading this book will not be.

> No one has yet succeeded, then, in explaining how something could literally come out of nothing: in every case some sort of prior condition needs to be presupposed.

I'm surprised there is no mention of physicist Lawrence Krauss's new book,

A Universe from Nothing. He does quite a good job explaining how the latest physics suggests that the universe literally did come from nothing.It is also important to understand that both space and time are features of the physical universe; the universe does not exist

withinthese things. So the notion that we need to explain "prior" causes and what happened "before" the universe began is simply an error, since those words are meaningless without time. An analogous question would be, "wheredid the universe come from"? There was no space prior to the universe, so it is an error to try to reason spatially.> People seem to tell me to just stop asking these questions because it's impossible to ever know...

It's definitely not that you should stop asking the questions, it's that the only people who are genuinely qualified to answer them are cosmologists. So while it's fun to speculate, the only way to make real progress on these questions ourselves would be to get a PhD in physics. Which I'm pretty sure I'm not going to do at this point in my life. :-)

It's interesting to read what people who actually

dohave a PhD in physics have to say about these questions, though. That's why I linked you to a few articles/debates in my other reply. And there are plenty of books out there that look at the origins of the universe and how it could have arisen (for example The Big Picture: On the Origins of Life, Meaning, and the Universe Itself by Sean Carroll or A Universe From Nothing by Lawrence Krauss).One thing to keep in mind is that quantum physics is not just counterintuitive but

wildlycounterintuitive. So even though we may have beliefs like "everything needs a cause", and even though that principle is reasonable in everyday life, it doesn't necessarily apply in quantum physics, where the very notion of causality is debatable. That's why non-physicists (definitely including philosophers and theologians) are just not qualified to answer these questions -- because our intuition leads us astray, and the rules that work for uswithinthe universe fall apart when we're looking at theoriginof the universe.Lawrence Krauss wrote a book about it, A Universe from Nothing.

It doesn't actually answer the question since no one has yet found an answer. But if the question is really bugging you it is an interesting read.

> Clearly something can not be created from nothing, thats a rule of physics I'm pretty sure. If this can't be explained, than wouldn't that mean that some higher power must have put it there?

Who created the higher power, then?

You might find this talk (by theoretical astrophysicist Lawrence Krauss) about how the universe could have spontaneously came from "nothing" ("nothing" is purposely in quotes because it's not really nothing): https://www.youtube.com/watch?v=-EilZ4VY5Vs . He also has a book on the same topic: http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/1451624468

And what's this nonsense about following the money? Doing the oil industry's bidding, that's where the money is. If you want to get rich as a scientist, throw your scientific credibility overboard and join the merchants of doubt.

> Merchants Of Doubt

https://en.wikipedia.org/wiki/Merchants_of_Doubt

https://www.amazon.com/Merchants-Doubt-Handful-Scientists-Obscured/dp/1608193942

http://www.imdb.com/title/tt3675568/

http://www.merchantsofdoubt.org/

https://www.youtube.com/watch?v=j8ii9zGFDtc

Big Bang Theory and Evolution are not really related, so I don't think you'll find a book with both, but, to answer your question:

The Greatest Show on Earth: The Evidence for Evolution by Richard Dawkins is a great book on evolution.

EDIT: You wated the Kindle version KINDLE VERSION

Along those lines, Dawkins is great for explaining evolution in easy-to-understand detail. Pick pretty much any book by him and you'll get a very good education.

On science and evolution:

Genetics is where it's at. There is a ton of good fossil evidence, but genetics actually proves it on paper. Most books you can get through your local library (even by interlibrary loan) so you don't have to shell out for them just to read them.

Books:The Making of the Fittest outlines many new forensic proofs of evolution. Fossil genes are an important aspect... they prove common ancestry. Did you know that humans have the gene for Vitamin C synthesis? (which would allow us to synthesize Vitamin C from our food instead of having to ingest it directly from fruit?) Many mammals have the same gene, but through a mutation, we lost the functionality, but it still hangs around.

Deep Ancestry proves the "out of Africa" hypothesis of human origins. It's no longer even a debate. MtDNA and Y-Chromosome DNA can be traced back directly to where our species began.

To give more rounded arguments, Hitchens can't be beat: God Is Not Great and The Portable Atheist (which is an overview of the best atheist writings in history, and one which I cannot recommend highly enough). Also, Dawkin's book The Greatest Show on Earth is a good overview of evolution.

General science: Stephen Hawking's books The Grand Design and A Briefer History of Time are excellent for laying the groundwork from Newtonian physics to Einstein's relativity through to the modern discovery of Quantum Mechanics.

Bertrand Russell and Thomas Paine are also excellent sources for philosophical, humanist, atheist thought; but they are included in the aforementioned

Portable Atheist... but I have read much of their writings otherwise, and they are very good.Also a subscription to a good peer-reviewed journal such as

Natureis awesome, but can be expensive and very in depth.Steven Pinker's The Blank Slate is also an excellent look at the human mind and genetics. To understand how the mind works, is almost your most important tool. If you know

whypeople say the horrible things they do, you can see their words for what they are... you can see pastwhatthey say and see the mechanisms behind the words.I've also been studying Zen for about a year. It's non-theistic and classed as "eastern philosophy". The Way of Zen kept me from losing my mind after deconverting and then struggling with the thought of a purposeless life and no future. I found it absolutely necessary to root out the remainder of the harmful indoctrination that still existed in my mind; and finally allowed me to see reality as it is instead of overlaying an ideology or worldview on everything.

Also, learn about the universe. Astronomy has been a useful tool for me. I can point my telescope at a galaxy that is more than 20 million light years away and say to someone, "See that galaxy? It took over 20 million years for the light from that galaxy to reach your eye." Creationists scoff at

millions of yearsand say that it's a fantasy; but the universe provides real proof of "deep time" you can see with your own eyes.Videos:I recommend books first, because they are the best way to learn, but there are also very good video series out there.

BestofScience has an amazing series on evolution.

AronRa's Foundational Falsehoods of Creationism is awesome.

Thunderfoot's Why do people laugh at creationists is good.

Atheistcoffee's Why I am no longer a creationist is also good.

Also check out TheraminTrees for more on the psychology of religion; Potholer54 on The Big Bang to Us Made Easy; and Evid3nc3's series on deconversion.

Also check out the Evolution Documentary Youtube Channel for some of the world's best documentary series on evolution and science.

I'm sure I've overlooked something here... but that's some stuff off the top of my head. If you have any questions about anything, or just need to talk, send me a message!

This book is not a calculus book, but a real analysis book at the level of baby Rudin.

It's also essentially designed to be used as a book for a Moore method style course, so it is not a textbook in any regular sense. Erdman teaches his classes by having students present the solutions to lots of problems, with only minimal lecturing.

If you are interested enough in machine learning that you are going to work through ESL, you may benefit from reading up on some math first. For example:

Without developing some mathematical maturity, some of ESL may be lost on you. Good luck!

I think learning proofs-based calculus and linear algebra are solid places to start. To complete the trifecta, look into Arnold for a more proofy differential equations course.

After that, my suggestions are Rudin and, to build on your CS background, Sipser. These are very standard references, though Rudin's a slightly controversial suggestion because he's notorious for being terse. I say, go ahead and try it, you might find you like it.

As for names of fields to look into: Real Analysis, Complex Analysis, Abstract Algebra, Topology, and Differential Geometry mostly partition the field of mathematics with corresponding undergraduate courses. As for computer science, look into Algorithmic Analysis and Computational Complexity (sometimes sold as a single course called Theory of Computation).

My buddy (phd student) told me that if I were to do a reading course, or just want to do self study that I should use Munkres. I think you can find international editions for much cheaper than that. We were using Rudin for our analysis class and spent a lot of time on ch.2. These are my only suggestions because I haven't done much with topology or analysis.

I would try http://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1375896302&amp;sr=1-1 and if that does not truly challenge you, then we can chat some more.

Here are some suggestions :

https://www.coursera.org/course/maththink

https://www.coursera.org/course/intrologic

Also, this is a great book :

http://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg/dp/039304002X/ref=sr_1_5?ie=UTF8&amp;qid=1346855198&amp;sr=8-5&amp;keywords=history+of+mathematics

It covers everything from number theory to calculus in sort of brief sections, and not just the history. Its pretty accessible from what I've read of it so far.

EDIT : I read what you are taking and my recommendations are a bit lower level for you probably. The history of math book is still pretty good, as it gives you an idea what people were thinking when they discovered/invented certain things.

For you, I would suggest :

http://www.amazon.com/Principles-Mathematical-Analysis-Third-Edition/dp/007054235X/ref=sr_1_1?ie=UTF8&amp;qid=1346860077&amp;sr=8-1&amp;keywords=rudin

http://www.amazon.com/Invitation-Linear-Operators-Matrices-Bounded/dp/0415267994/ref=sr_1_4?ie=UTF8&amp;qid=1346860052&amp;sr=8-4&amp;keywords=from+matrix+to+bounded+linear+operators

http://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753/ref=sr_1_5?ie=UTF8&amp;qid=1346860077&amp;sr=8-5&amp;keywords=rudin

http://www.amazon.com/DIV-Grad-Curl-All-That/dp/0393969975

http://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536/ref=sr_1_2?s=books&amp;ie=UTF8&amp;qid=1346860356&amp;sr=1-2&amp;keywords=chaos+and+dynamics

http://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/0534392008/ref=sr_1_5?s=books&amp;ie=UTF8&amp;qid=1346860179&amp;sr=1-5&amp;keywords=numerical+analysis

This is from my background. I don't have a strong grasp of topology and haven't done much with abstract algebra (or algebraic _____) so I would probably recommend listening to someone else there. My background is mostly in graduate numerical analysis / functional analysis. The Furata book is expensive, but a worthy read to bridge the link between linear algebra and functional analysis. You may want to read a real analysis book first however.

One thing to note is that topology is used in some real analysis proofs. After going through a real analysis book you may also want to read some measure theory, but I don't have an excellent recommendation there as the books I've used were all hard to understand for me.

I know that in the long run competition math won't be relevant to graduate school, but I don't think it would hurt to acquire a broader background.

That said, are there any particular texts you would recommend? For Algebra, I've heard that Dummit and Foote and Artin are standard texts. For analysis, I've heard that Baby Rudin and also apparently the Stein-Shakarchi Princeton Lectures in Analysis series are standard texts.

https://www.amazon.com/Quantum-Mechanics-The-Theoretical-Minimum/dp/0465062903/ref=pd_sim_14_4?ie=UTF8&amp;refRID=1TT0F2A70RBV36TT3D0S Is supposed to be good, as is https://www.amazon.com/How-Teach-Quantum-Physics-Your/dp/1416572295 . Then you can work up to https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927 and then the gold standard for an introduction to quantum computing is https://www.amazon.com/Quantum-Computation-Information-10th-Anniversary/dp/1107002176

I used Griffiths for my upper level Electro & Magnetostatics class.

http://www.amazon.com/Introduction-Electrodynamics-3rd-David-Griffiths/dp/013805326X/ref=sr_1_1?ie=UTF8&amp;qid=1314035153&amp;sr=8-1

Also I know the university I'm at uses the Griffiths book for Quantum Mechanics, however I have not taken the class.

http://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927/ref=sr_1_2?ie=UTF8&amp;qid=1314035153&amp;sr=8-2

Disclaimer: I am a math major.

Introduction to Quantum Mechanics by Griffiths is indeed an excellent textbook, and a standard in many undergrad courses. I would also recommend brushing up on vector calculus and linear algebra before diving into QM.

Honestly, Wikipedia articles often do a good job of explaining the fundamentals in a clear, accessible way. And its scientific accuracy is quite good.

There are also free courses online, such as through Coursera and MIT's OpenCourseWare.

I think the most widely-used textbook for a junior level introductory quantum mechanics class (at least in US universities) is this book by David Griffiths.

Here's the second edition.

No, but here is a devastating critique of it

http://physics.ucsc.edu/~michael/qefoundations.pdf

See the abstract

>

AbstractThe central claim that understanding quantum mechanics requires a conscious observer, which is made by B. Rosenblum and F. Kuttner in their book “Quantum Enigma: Physics encounters consciousness”, is shown to be based on variousmisunderstandings and distortions of the foundations of quantum mechanics.

and for a quicker read jump to chapter 2 to see what's wrong with it.

>2 Critique of Selected Quotations from QE

Stay away from it. It isn't going teach you anything, and will probably give you so many misconceptions that it's going to make it difficult to actually learn quantum theory at a later time. If you want to learn quantum theory, read a textbook ( probably the easiest English book on it https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927 you can find pdfs on google).

General rule: if a book on quantum theory mentions the word consciousness prominently (say in the title), then that's a red flag and be careful.

Griffiths is excellent.

Because Griffiths is infamous amongst those in the know, but not really to a wider audience, I'll leave this here:

https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927

He also has an excellent book on Electromagnetism that is a staple in the undergraduate curriculum.

Math, math and more math. If you don't feel comfortable with differential equations, or if you're like I was after freshman year you don't know what a differential equation really is, then that's where you should start. Quantum Mechanics basically starts with an awesome differential equation and then goes from there.

Learning the math of this level of Physics on your own would be challenging to say the least, but if you want to dive in I'd suggest Mathematical Methods in the Physical Sciences by Boas. Pairing that with Introduction to Quantum Mechanics by Griffiths might be fun.

Nuclear theory goes into statistical mechanics, classical mechanics is multivariable calc/linear algebra, quantum field theory combines those two with differential equations and sprinkles in a bunch of "whoa that's weird" just to keep you on your toes. But it's really important that you know the math (or more likely you fake your way through the math enough to gain some insight to the Physics).

I have the same problem. Its a lot about efficiency. Ive been reading secrets to mental math and that's helpful.

https://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401

If you want to learn to calculate quickly in your head, probably the most fruitful thing is to pick up a bunch of tricks for mental math. One good video course for this is Secrets of Mental Math put out by The Great Courses. The same lecturer published out a very good book on the subject as well.

Of course, if you want to go old school, then it's hard to beat the utility of memorizing logarithm tables...

The book The Secrets of Mental Math has some great tricks in it to help you along.

I read this book a few years ago, and it is pretty much the way I do any basic arithmetic in my head now. http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=sr_1_1?ie=UTF8&amp;qid=1333153637&amp;sr=8-1

The World Without Us was a pretty interesting read. It's about all of the trappings of consumer culture and how long they would still remain if there were suddenly no humans around. It's pretty eye opening about how long certain things will keep harming the planet, and about others that surprised me with how fast they'd go away.

Parallel worlds by Michio Kaku is pretty good, if you're into the history of string theory and/or the universe. I read it about 10 years ago, so I'm not sure if it's outdated nowadays.

The world without us by Alan Weisman talks about what would happen to the earth if we disappeared, it talks about engineering marvels like the hoover dam, NY subway system, and nuclear waste storage sites and what could happen to these if humans were not around the maintain them.

I'm looking for a book about space if anyone has a suggesting. Particularly books that talk about neutron stars and other cosmic wonders.

A great book on the subject is called "The World Without Us" by Alan Weisman.

There were also TV series' on Nat Geo and History based on the book called "Aftermath: Population Zero" and "Life After People" respectively. Episodes of these are (probably still) available for viewing on youtube.

This book will answer all those questions (and many others) in great detail. A really interesting thought experiment. I highly recommend it.

This book might interest you.

It get's a bit environmental protectionist preachy at times but it answers a lot of these questions in very rich detail.

The Demon-Haunted Worldby Carl Sagan. Also, learn about other religions and their histories (not the most comprehensive, but you could start here). History of early Christianity was enlightening for me, as well.If you haven't read "The Demon Haunted World" by Carl Sagan, I'd highly recommend it. Having a firm foundation in thinking skeptically will help you avoid relapse into faith.

http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

Demon Haunted World by Carl Sagan

>Many of you appear to have been raised non-atheist. What do you wish your parents would have told you?

The truth.

In all seriousness, what religion really deprives children of, is critical reasoning and independence. I was slowly and implicitly discouraged from questioning things, anything I was told by a person I was supposed to respect was not to be doubted, ever, or it was an insult to that person. This is wrong. I was also made to be emotionally and psychologically dependent on faith. By convincing me that I would see my loved ones again in the afterlife, I was suddenly saddled with the need to continually reaffirm my faith or else I might have to deal with the pain of loss and actually complete the grieving process.

The truth is, dealing with death in a realistic way is what really gives this life meaning and is very imperative to becoming an independent, grounded adult.

The Demon-Haunted World: Science as a Candle in the Dark By Carl Sagan.

Carl Sagan's The Demon-Haunted World.

Carl Sagan: The Demon Haunted World

Get started here. http://mormonthink.com/ Then check out this book. http://www.amazon.com/No-Man-Knows-My-History/dp/0679730540 Next I'd move onto http://www.amazon.com/History-God-000-Year-Judaism-Christianity/dp/0345384563

and This is a big help for developing some critical thinking skills: http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

Start here : The Demon Haunted World: Science as a candle in the dark by Carl Sagan.

There's no reason for your parents to object to this; it's not about religion at all. It's about what science can tell us about reality, and how to

knowthings.You are on a quest for truth. This book describes a 'skeptical toolkit' that will help you identify truth.

Baby steps. Enjoy the book, and definitely read this one next.

I used to love all those new age books! Why not head down to the used bookstore and pick up half a dozen books that look fun out of that section? There's always something entertaining there. If she's a true believer, avoid anything that suggests people can survive by eating nothing but air.

Or, if she's not a true believer but just interested in the subject, have you considered getting her some non-fiction books that delve into the psychology behind ghost sightings and such? Like

Investigating the Paranormal(less skeptical) orDemon-Haunted World(much more skeptical)?Cows, Pigs, Wars, and Witcheswas a fascinating read and IIRC largely historical. She might also enjoy branching out into a book likeThe Predictioneer's Game, which is about game theory and how to use it effectively in modern life.If she likes mysteries at all, I suggest Josephine Tey's

The Daughter of Time. It's about a police officer who is laid up in hospital and decides to use the time to solve a famous historical mystery. You could also consider biographies of strong and active women who inspire -- Princess Diana, maybe, or Martha Stewart?(Edited to add links)

If the guy's more of a "liberal Christian", the first one I usually suggest is this one: http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

But since your wife's pastor recommended Strobel, I suspect he's a fundamentalist. Even something as 'gentle' as Sagan may not work..and anything more confrontational than Sagan's work will just make the pastor angry (provided he actually

doesread it, of course).I agree with [http://www.reddit.com/user/Vu70n0m0v5]. He and your wife think they're going to "fix" you, even though there's nothing wrong with you.

The Demon Haunted World is Carl Sagan’s book, but great recommendation regardless 👍

That is not remotely what this article says, nor what the concept is.

Again man, enjoy your conspiratorial thinking where science is a lie and you are being scammed by a global cabal millions of people strong to destroy america and conservatism, with the elaborate lies of climate change, and the insane idea that if you want the rise to be kept to a reasonable minimum, you've got twleve years left to do it.

You could just ask Exxon. They knew in 1982.

Liberal exxon. With their insanity that CO2 is a greenhouse gas.

I feel sorry for you, bud. I really, really do. Like I said, I doubt you have done well for yourself.

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

If you are trying to take a scientifically acceptable approach to it, you should try to apply some skepticism to your hypothesis.

In my opinion, the world is just getting a lot smaller with the sky rocketing advances in technology and media.

Just for example. A lot of people said in the last decades that earthquakes had increased in exponential numbers. It was just crazy about how many earth quakes they had been hearing about.

Hearing about was the key part. There was no increase in earth quakes. But there was an increase the speed at which people can communicate information, and the amount of people who have recording devices. Technology was giving voices to people who didn't have it before. It's not that there were more earthquakes. It was that earthquakes were being reported on much more.

It's also my very strongly held belief that what happens out in space has nothing, and I mean absolutely nothing to do with what happens here on earth (in a day to day sense). Horoscopes, which claim to be able to outline people's lives based on the planets is just not true. The only force Mars could have on you at the time of your birth was it's gravity. But the gravity of the doctor delivering you was more influential on you than Mars was.

If you truly are trying to take a scientific approach to it, maybe try to find some factors which are a bit more... concrete. Bad juju, karma, omens etc.... have no evidence to back up that they actually exist.

Remember Le Gentil that I mentioned? He had some pretty darn serious "bad karma". He lost his entire life because he tried to participate in a never before tried scientific endeavor. But that was in 1769. Not 2011. Bad times happen to all of us.

For me personally, 2011, 2012, 2013 and 2014 were the best years of my life. 2015 is when things turned to utter crap where I lost the woman I was going to marry and fell in to a deep depression and some alchoholism.

Not trying to dissuade you. When things start to go sour it's only natural to try and find the cause. But again, if you're trying to be scientific, include a healthy dose of skepticism.

And just to nitpick, everything you described happened on earth. So it's not really "universal". Thinking that earth and humans essentially make up the entire universe is mistake.

Maybe some book suggestions: Demon Haunted World, Science As A Candle In The Dark

The Better Angels of Our Nature, Why Violence Has Declined

I'd like to suggest The Demon Haunted World by Carl Sagan, it talks about the UFO phenomena in great detail.

only problem is that it is 497 pages at least in the 1997 paperback version.

Demon Haunted World, by Carl Sagan

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469?SubscriptionId=AKIAILSHYYTFIVPWUY6Q&amp;tag=duckduckgo-d-20&amp;linkCode=xm2&amp;camp=2025&amp;creative=165953&amp;creativeASIN=0345409469

It won't prove the church is wrong directly, but it gives a good guide to scepticism and how to think logically. It is probably the most important book I have ever read.

Congrats from a former Catholic. Be out and open about it. We need more people to not be afraid to identify themselves in public and to their families as atheists. People have no clue how many there are around them.

&#x200B;

For book recommendations, I like The Demon Haunted World by Carl Sagan and The God Delusion by Richard Dawkins.

Sounds like you'd find interesting, and benefit from, learning 'critical thinking'. It helps tremendously with questions like yours.

Google it. And a good book, off the top of my head, is Carl Sagan's 'The Demon Haunted World'.

> If not, I've been lied to and held to impossible expectations my whole life and that's hard to swallow.

You must realize that when you believed without question, you also "lied" to everybody else about the same thing. You are not a single person being lied to, you are part of a group in which likely no one is lying to anyone else, they just don't know any better (than you do), and everybody else is just confirming to the others that "of course we are right".

Read some books about the history of the religion (The Bible Unearthed or Who Wrote the Bible for the OT and the Jesus Wars for the NT are a good and rather entertaining overview), and maybe read Sagan's The Demon Haunted World to clear up some things about who believes what and why it's not necessarily a lie, but might still not be the truth. Seriously, it's about UFOs, lol.

r/academicbiblical is also good (and free), but it's sort of short answers to specific questions about the Bible. Their wiki is the best though!

Anything particular that you're looking for? Here are three of my favorites outside of the usual recommendations.

The Unique and Its Property (aka The Ego and His Own) by Max Stirner. Updated translation of the OG book on Egoism

The Demon-Haunted World by Carl Sagan. Great read on the the scientific method, skepticism and developing a baloney detection kit.

Captivate by Vanessa van Edwards. The best guide for lesser magic out there.

Edit: fixed links. I was posting from my cell phone which caused a lot of issues.

Support her. Offer her advice you wish you had at the time. Be there for her, and if necessary give her caution about telling your parents if that would be a problem. Encourage her to think critically, to ask questions.

I highly recommend the book Demon Haunted World by Carl Sagan even though it isn't explicitly atheist.

Congratulations! I know what a big step that is, as I've been in the same boat. Books are the best way to become informed. Check out books by:

Also check out the video series Why I am no longer a creationist.

The more you know, the more confident you will be.

Bad Science by Ben Goldacre, Demon Haunted World by Carl Sagan for general science.

Stuff by James Randi, Michael Shermer for general stuff about new age crap.

The Panic Virus by Seth Mnookin and Deadly Choices by Paul Offit on the Anti-Vaccination movement.

Damned Lies and Statistics by Joel Best and How to Lie with Statistics by Darrell Huff (Also see How to Lie with Maps by Mark Monomonier for a similar subject) for questioning stats and graphics used in the news.

Is there anything specifically you're interested in?

If you like the article, read the whole book.

You're confusing certainty with evidence. Stop it.

I can have evidence that says it's unlikely a deity exists or that I have a soul, and this is indeed the case with most everything. Bringing up the fact that it's not a proven certainty is a misrepresentation about what science and knowledge in general represents.

Anyway, you've clearly already made up your mind so I'll just stop now, but will point you in a direction if you want to know more. Goodbye:

http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

I would either say A General Theory of Love or The Demon-Haunted World are books that I always recommend to people who want to expand themselves.

A General Theory of Love is the perfect message for those who think intelligence and self-mastery means an absence of emotions. For those of us who think being rational means not letting emotions into the decision making process, this book elucidates on why that is not healthy and also why you're probably lying to yourself if you think you are incapable of feeling emotions like "normal" people.

The Demon-Haunted World is a book for everybody. It is a philosophical book written by an astrophysicist using everyday language so nearly anybody can grasp its concepts. It brings the major philosophical question of

whywithin the average person's conceptual grasp, without using any spiritual reasoning. I feel that when more people can contemplate that question,why, without immediately turning to the supernatural and shutting down the mundane, we will be a more level-headed species.Eh, my two cents. ;-)

This?

http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

Yes you can. $11.56 and worth every penny. Check out Pale Blue Dot by Sagan as well. Here is an audiobook sample of Pale Blue Dot, read by Carl himself.

> seems like what my friend says is not based in reality.

I concur with your assessment.

Your friend is trapped in their own hall of mirrors.

Usually I don't agree with the perspective that "you can't argue someone out of a position they didn't reason themselves into," but it seems valid in this case. They're going to have to have some sort of experience that changes the way they think at least a little bit before they're going to listen to anything you have to say. As of right now, as one might say in a martial arts movie, they are "not ready."

The two things that came to my mind when I read this were Richard Carrier's essay on Why I am Not a Christian, and Carl Sagan's book The Demon-Haunted World. I actually recommend these as reading for you and not your friend. They would in all likelihood dismiss the texts out of hand, but I think you would really benefit from the material and be able to pull out ideas from them that will help you better communicate to your friend the problems with their way of thinking.

This sort of false memory ("recovered") has been on my mind a bit lately. I'm finally getting around to reading Demon Haunted World and it brought back a bunch of stuff from my school days. There were chapel speakers (Christian school) that talked about Satanic cults sacrificing babies. I probably went through a big chunk of my life thinking that there really was a massive outbreak of Satanic rape happening.

Check out the 1 star reviews for this book on Amazon!

http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/product-reviews/0345409469/ref=cm_cr_dp_hist_1?ie=UTF8&amp;showViewpoints=0&amp;filterBy=addOneStar

too funny!

Former Methodist, that explored many other religions, then read The Demon-Haunted World and never looked back.

A Book of Abstract Algebra by Charles C. Pinter

I really enjoyed reading the book, almost reads like a novel. There is a great first chapter laying out the history of the subject and it just builds from there.

Math is essential the art pf careful reasoning and abstraction.

Do yes, definitely.

But it may be difficult at first, like training anything that’s not been worked.

Note: there are many varieties of math. I definitely recommend trying different ones.

A couple good books:

An Illustrated Theory of Numbers

Foolproof (first chapter is math history, but you can skip it to get to math)

A Book of Abstract Algebra

Also,

formal logicis really fun, imk. And excellent st teaching solid thinking. I don’t know a good intro book, but I’m sure others do.> I'm not sure what to read into before the Galois class begins.

"A Book of Abstract Algebra" by Charles Pinter

It depends on your interests. I thought the machine learning course on coursera was great. Antirez sometimes blogs about the internals of Redis on his blog, and he is a great writer. If you like math, this is the best math book I've read. Finally, you can always start contributing code to an open source project -- learn by doing!

I don't think it contains any group theory, but everything else is there:

Discrete Mathematics with Applications by Susanna S. Epp (

This one below contains some algebra(groups):

Mathematics: A Discrete Introduction by Edward A. Scheinerman

Both are pretty elementary.

I have not taken the class yet (I'm taking 161 and 225 in January), but I looked at the syllabi already and here's the textbook for the class:

http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073383090/ref=sr_1_1?ie=UTF8&amp;qid=1417826968&amp;sr=8-1&amp;keywords=Rosen+Discrete+Math

You may want to go ahead and pick this up and start looking through it prior to January. I already grabbed a copy; I finish Calculus II tomorrow at my community college and I am going to be starting Rosen very soon.

This book is also commonly recommended:

http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_1_1?ie=UTF8&amp;qid=1417827137&amp;sr=8-1&amp;keywords=Epp

I'm not sure what your math background is, but one of the most important success factors (in my experience) in math classes is a lot of practice. If you start working through either of those books now, you'll probably be in a good place once class starts in January.

We could also probably get a study group going on in here; I'm pretty comfortable with math, so I am happy to help out anyone else who needs help.

You can see quite a bit with this telescope. I highly recommend getting this book. It's a great starter for finding galaxies and nebulae and you should easily be able to see everything in the book (I could see M81 and M82 on a smaller telescope within Seattle city limits).

Yes, you can use a telescope in light polluted skies. When I got back into the hobby a few years ago, I was stuck observing on my patio practically under a street lamp facing a bright yellow wall and I could see quite a few things. A good book is Turn Left at Orion, which was originally written for people with small telescopes and light-polluted skies.

Turn Left at Orion is a great introductory book.

It will show you what is in the sky when, how to find it, and what you will see in the telescope. (You're not going to get Hubble quality views)

http://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972

The moon is very new this week, so take the opportunity to look at it while it's still a sliver. It's visible just after sunset.

Download Stellarium for your computer, and dial it in for your location. It will also help you identify the sights.

I don't have that particular model, but I've hauled my 114GT around in the back of my station wagon, with no ill effects. (Nothing outside of typical collimation)

Read the instructions. Go outside and look at the moon.

Get the book Turn Left at Orion.

> Sky Watcher 8' Dob

8" dob. An 8' dob would be a huge beast. :)

> im not even sure if my scope is good enough to see them.

Your scope is plenty capable of seeing all sorts of things, don't worry.

> Maybe im just terrible at tracking these guys down because this is my first time?

Takes some time and experience.

Get this book, it will show you all sorts of things that are easy to find for a newbie, with plenty of explanations and diagrams.

http://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972/

On a laptop or smartphone, install the free software called Stellarium. It's like a map for the sky, you could look up objects using the search function, etc. It's great for the planets.

A planisphere might be useful to give you an image of the whole sky at once (as opposed to a detailed map which only shows a tiny chunk):

http://www.amazon.com/Guide-Stars-Ken-Graun/dp/1928771017/

Once you understand how to read sky maps, you could use a paper map (but don't worry about that for now):

http://www.amazon.com/Sky-Telescopes-Pocket-Atlas/dp/1931559317/

---

Once you have the vicinity of the object on a map, the process is like this:

When you know the approximate area where the object is located, you point the scope that way, and look through the finderscope - it will show you that area at low magnification and wide angle.

Move the scope slowly, while looking through the finderscope, until the object you're looking for (or the place where it should be) is in the center.

At that moment, move your eye to the telescope and enjoy.

Make sure the scope and the finder are aligned. Point the scope at Polaris, look through the finder and put Polaris in the exact center. Now look through the scope using a low magnification eyepiece - is Polaris in the exact center? If not, adjust the finder. Repeat with successively stronger eyepieces until it's dead center even in the strongest one.

The alignment of the finder should remain stable for a long time, you don't need to do it often.

---

Many "faint fuzzies" (dim objects) such as galaxies and nebulae are not easily visible from the city, because the sky is light polluted. Some of them are visible, others require dark skies.

General advice and info for newbies:

http://www.reddit.com/r/Astronomy/comments/vpij0/thinking_about_buying_my_first_telescope/c56slut

---

> do i have to go out and buy another eye piece or a barlow?

"Buy moar glass" is what most beginners tend to do, and it's probably the least useful thing at first. Learn how to use and maintain the scope, then worry about purchasing gear. Astronomy is more about knowledge than it is about owning stuff.

Don't worry about pictures and videos (astrophotography). Do purely visual astronomy for a while, learn the ropes. Astrophotography is even more demanding in terms of knowledge, if you want to do it right (the blurry little pics of Saturn you see on this forum all the time do not represent astrophotography done right).

Eyepieces, skymaps (or just download Stellarium), books like Nightwatch and Turn Left at Orion. You might also consider a Telrad and a red-filtered flashlight.

That's a great scope you got yourself there, it'll treat you well. Check out the books NightWatch and Turn Left at Orion for great information on how to get started in Astronomy. "NightWatch" answers a lot of questions you might have where "Turn Left.." serves more as a guide and map to the night sky, and both serve as excellent resources.

I used Susanna Epp's Discrete Mathematics text and rather enjoyed it. Velleman's How To Prove It is also quite good.

http://www.abebooks.com/servlet/SearchResults?bi=0&amp;bx=off&amp;ds=20&amp;kn=Epp+discrete+applications+3&amp;recentlyadded=all&amp;sortby=17&amp;sts=t

How to Prove It: A Structured Approach by Daniel J. Velleman http://www.amazon.com/dp/0521675995/ref=cm_sw_r_udp_awd_ff3Vtb08QR4FZ

For proof writing techniques I highly recommend Velleman's "How to Prove It" link

I'm going to recommend the book How to Prove It. Its all about learning the logic for proofs and strategies for writing proofs. Its one of those books that you work through slowly and complete all the exercises. Its recommended around here a-lot. I'd also suggest using the search feature if you ever want to look for other recommended books because those threads come up often around here.

Best wishes.

There are some really good books that you can use to give yourself a solid foundation for further self-study in mathematics. I've used them myself. The great thing about this type of book is that you can just do the exercises from one side of the book to the other and then be confident in the knowledge that you understand the material. It's nice! Here are my recommendations:

First off, three books on the basics of algebra, trigonometry, and functions and graphs. They're all by a guy called Israel Gelfand, and they're good: Algebra, Trigonometry, and Functions and Graphs.

Next, one of two books (they occupy the same niche, material-wise) on general proof and problem-solving methods. These get you in the headspace of constructing proofs, which is really good. As someone with a bachelors in math, it's disheartening to see that proofs are misunderstood and often disliked by students. The whole point of learning and understanding proofs (and reproducing them yourself) is so that you gain an understanding of the

whyof the problem under consideration, not just thehow... Anyways, I'm rambling! Here they are: How To Prove It: A Structured Approach and How To Solve It.And finally a book which is a little bit more terse than the others, but which serves to reinforce the key concepts: Basic Mathematics.

After that you have the basics needed to take on any math textbook you like really - beginning from the foundational subjects and working your way upwards, of course. For example, if you wanted to improve your linear algebra skills (e.g. suppose you wanted to learn a bit of machine learning) you could just study a textbook like Linear Algebra Done Right.

The hard part about this method is that it takes a lot of practice to get used to learning from a book. But that's also the upside of it because whenever you're studying it, you're

reallystudying it. It's a pretty straightforward process (bar the moments of frustration, of course).If you have any other questions about learning math, shoot me a PM. :)

So here are some options I recommend:

You can find all the textbooks I mentioned online, if you know what I mean. All of these assume you haven't seen math in a while, and they all start from the very basics. Take your time with the material, play around with it a bit, and enjoy your summer :D

EditL this article describes one way you can go about your studies

How to Prove It is only 20 bucks.

Hey mathit.

I'm 32, and just finished a 3 year full-time adult education school here in Germany to get the Abitur (SAT-level education) which allows me to study. I'm collecting my graduation certificate tomorrow, woooo!

Now, I'm going to study math in october and wanted to know what kind of extra prep you might recommend.

I'm currently reading How to Prove It and The Haskell Road to Logic, Maths and Programming.

Both overlap quite a bit, I think, only that the latter is more focused on executing proofs on a computer.

Now, I've just been looking into books that might ease the switch to uni-level math besides the 2 already mentioned and the most promising I found are these two:

How to Study for a Mathematics Degree and Bridging the Gap to University Mathematics.

Do you agree with my choices? What else do you recommend?

I found online courses to be ineffective, I prefer books.

What's your opinion, mathit?

Cheers and many thanks in advance!

Спасибо за ссылку. Я обязательно это проверю. Думаю, надо было быть более конкретным. Я читал книгу, которая учит своих читателей, как строить математические доказательства. В книге дается очень общий обзор этих тем, которые я перечислил выше. Я проверю ссылку, но если вы знаете книгу на русском языке, которая учит строить математические доказательства студентам, которые начинают изучать продвинутую математику, напишите Мне пожалуйсте.

Вот книга Для справки. (в случае, если вы знаете английского языка).

How to Prove it - A structured approach

I would recommend the book "How To Prove It".

https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995

It helped me in my transition into proof based mathematics. It will teach common techniques used in proofs and provides a bunch of practice problems as well.

You received A's in your math classes at a major public university, so I think you're in pretty good shape. That being said, have you done proof-based math? That may help tremendously in giving intuition because with proofs, you are giving rigor to all the logic/theorems/ formulas, etc that you've seen in your previous math classes.

Statistics will become very important in machine learning. So, a proof-based statistics book, that has been frequently recommended by /r/math and /r/statistics is

Statistical Inferenceby Casella & Berger: https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126I've never read it myself, but skimming through some of the beginning chapters, it seems pretty solid. That being said, you should have an intro to proof-course if you haven't had that. A good book for starting proofs is

How to Prove It: https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995How to Prove It

It's cheap, highly rated, starts with the basics, and as the title says, shows you how to prove it!

“How to Prove it”. D. Velleman: Amazon US Link

Probably the best resource on the topic!

If you think you can read an undergraduate textbook Ryden is a standard.

However, if you think that may be too advanced, start with some popular books on the subject such and The Fabric of the Cosmos by Brian Greene, Parallel Worlds by Michio Kaku or the classic by Hawking A Brief History of Time.

If after reading those you want something more advanced but still not a textbook try The Road to Reality by Penrose. It reads like a popular book but he actually works through math (and the real stuff with like tensors etc...) to make his points so it is more advanced. Also, the Dummies Books are also a more intermediate step and are often decently good at teaching the basics on a lower technical level than a textbook.

There's lots of interesting things you'll never understand; quantum physics is going to be one of them unless a Grand Unified Theory (or a subset of that which reconciles quantum theory and relativity) is discovered.

If you haven't read it, try A Brief History of Time by Stephen Hawking; you may enjoy it.

try reading "The Grand Design" and "A Brief History of Time" for more understanding on the universe, time and the big bang.

also

>I am an atheist except in one very crucial sense - I believe SOMETHING supernatural created the universe at the moment of the big bang.

this is a "god of the gaps" type argument, just because science has not yet found all the answers does not mean that a god exist.

Economics:

Sciences:

The late Stephen Hawking wrote a book which explains it all very clearly.

I think you are looking for 'A Brief History of Time' by Stephen Hawking

https://www.amazon.com/Brief-History-Time-Stephen-Hawking/dp/0553380168/ref=sr_1_1?ie=UTF8&amp;qid=1520139577&amp;sr=8-1&amp;keywords=a+brief+history+of+time

To know why what you are saying doesn't make sense you need to read a very large amount of physcis books, may i suggest starting at Bill Bryson's a short history of nearly everything then moving on to Stephen Hawking's a short history of time

"Unearthing Atlantis"

"Noah's Flood"

"Guns, Germs, and Steel"

"A Brief History of Time"

You can't go wrong with A Brief History of Time or The Universe in a Nutshell.

A book that is only partially about space but covers a lot of material that I'd highly* recommend is How to Build a Habitable Planet.

"A Brief History of Time" by Stephen Hawking is great but maybe not technical enough for you. His colleague Kip Thorne, however, wrote "Black Holes and Time Warps: Einstein's Outrageous Legacy" which is significantly meatier on the hard science side of things.

The Origin of Consciousness in the Breakdown of the Bicameral Mind by Julian Jaynes. It's a fascinating read. I would like to know what Peterson's take on it is (and also McGilchrist's, for that matter).

Controversial but fascinating book I read years ago: https://www.amazon.com/Origin-Consciousness-Breakdown-Bicameral-Mind/dp/0618057072

You might find this interesting. The Origin of Consciousness and the Breakdown of the Bicameral Mind.

The Origin of Consciousness in the Breakdown of the Bicameral Mind - Julian Jaynes

>At the heart of this classic, seminal book is Julian Jaynes's still-controversial thesis that human consciousness did not begin far back in animal evolution but instead is a learned process that came about only three thousand years ago and is still developing. The implications of this revolutionary scientific paradigm extend into virtually every aspect of our psychology, our history and culture, our religion -- and indeed our future.

I'm reading it right now and its absolutely fascinating. Also quite controversial, but no matter what side you come down on, definitely fascinating.

>history, humanity, anthropology, philosophy, etc.

Check, Check, Check, Check, Add Psychology for your "etc" and you've got it all.

Non-fiction: The Origin of Consciousness in the Breakdown of the Bicameral Mind by Julian Jaynes.

The single most profound, perspective altering book I have ever read. It's a speculative analysis of history and the development of consciousness. The main premise of the book is that the mentality of the modern human is a very recent development, only a few thousand years old.

The previous mentality was "bicameral," in which nothing like a self-concept or internal "I" existed - the author uses the misleading term "consciousness," which is perhaps better expressed as "self-consciousness." Instead, volition came in the form of auditory hallucination, from a seemingly external source of authority, such as a dead ancestor, ruler, or deity. Not unlike schizophrenia, which the author posits is one of the vestiges of this ancient mentality.

The "hardware" (my words, not his) of the bicameral brain is the same as ours, however, the culturally imparted "software" was completely different.

This is why, when we look at history, we find ubiquitous

directexperience of gods and deceased persons. With a keener eye, we find that's generally auditory experience (i.e. Joan of Arc's voice of God) with perhaps slight visual distortion, which is what's commonly found in case studies of schizophrenics.The author spent decades working on this and the never published follow up, and it's just a staggering multidisciplinary work of genius, whether you agree with it or not. I have yet to read a more thought provoking book, and while I don't agree 100% with his hypothesis, I have only minor issues with it - the evidence is simply overwhelming. At least do yourself the favor of reading the wikipedia article of bicameralism) and the Amazon link above. You can order it for, like, eight dollars, shipping and all.

You will never look at history the same way.

My cousin gave me a copy of

The Origin of Consciousness in the Breakdown of the Bicameral Mindby Julian Jaynes for Christmas, and I'm hoping to get started on that this week.http://www.amazon.com/Origin-Consciousness-Breakdown-Bicameral-Mind/dp/0618057072

I'm a physics student excited to take astrophysics this fall semester. We're using the Big Orange Book (Intro to Modern Astrophysics by Carroll and Ostlie, 2nd ed.), which, according to many around here, seems to be a great text. My copy came in the mail today but I'm wondering if I got a counterfeit.

There are a few reasons I am suspicious. The cover is a faded and uneven shade of orange, the print appears low quality on close inspection, the binding is glued, and the overall feel of the book falls short of most textbooks I've used. Additionally, the book shipped new, from Malaysia (with a customs value of $25).

I bought the book from Abebooks (specifically not an international edition) and am hoping for a refund. Just to be sure though, would anyone be willing to take pictures of their copy for me to compare? I am specifically interested in color, the binding as seen while the book is closed, and how well the print on the cover aligns with the spine.

I'm hoping this is a book I keep for a while, so I want to make sure I have a copy that will last! Thanks for your help!

Start by finding some astronomy clubs in your area. That would be very helpful if you wanted to get into stargazing. Most people would be more than happy to let you try out their telescopes. If you're near a university or college, try finding some astro groups there as well. Even if you're not a student it would be good to check it out. If you want to get into more astrophysics/cosmology I found this book to be a very well written introductory text http://www.amazon.com/Introduction-Modern-Astrophysics-2nd-Edition/dp/0805304029/ref=dp_ob_title_bk. It was the textbook I used in my intro astrophysics course. Other than that, there is always the popular authors that reddit likes. NDT, Laurence Krauss, Stephen Hawking, etc...

I wouldn't be too afraid of Carroll & Ostlie's Big Orange Book, even though it is very comprehensive. I'm an engineer and just started reading it when a physics grad student at my lab recommended it as the standard introductory text.

The text requires some technical background, but is designed to be accessible to all (or most) math, science, and engineering majors.

For mushroom: https://www.amazon.com/All-That-Rain-Promises-More/dp/0898153883

Edit: found a copy a couple years ago on ebay for 6 shipped so don't pay 22 on amazon

I moved from Denver to Southern Oregon. Walking in the woods here you'll see amazing things, and you can eat almost all of them. I got a copy of All the Rain Promises and More and I was off. It helped that they were buying matsutakes for $100 a pound that winter.

These days you're lucky to get $15 for #1's and you're competing with Asian slave labor.

Now I only pick for pleasure

The variety here is amazing. Mushroom picking is one of the best ways to spend a grey winter day.

You might like this book then.

If you think mascaras are deathcaps, I strongly suggest not eating anymore wild mushrooms until you get a better understanding of the local varieties. here's a good guide

http://www.amazon.com/All-That-Rain-Promises-More/dp/0898153883

It's actually a very good read and the author is clearly in love with mushrooms including the psilocybe types. ;)

Welcome! Mushroom season is just getting started! Check Google, FB or Nextfoor for your local mycological society, they'll have some good info for you, too.

https://www.amazon.com/dp/B003R4Z2MM/ref=dp-kindle-redirect?_encoding=UTF8&amp;btkr=1 this is a guide specifically for PNW mushrooms.

https://www.amazon.com/All-That-Rain-Promises-More/dp/0898153883 this is a really popular mushroom identification book, this was my go-to guide for identifying mushrooms in the field. The author, David Arora, has written a few books.

Happy hunting!

All That the Rain Promises and More by David Arora. Fantastic guide with a lot of information on edibility. Also highly recommended is its companion guide by the same author, Mushrooms Demystified

https://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918

From my experience, Calculus in America is taught in 2 different ways: rigorous/mathematical in nature like Calculus by Spivak and applied/simplified like the one by Larson.

Looking at the link, I dont think you need to know sets and math induction unless you are about to start learning Rigorous Calculus or Real Analysis. Also, real numbers are usually introduced in Real Analysis that comes after one's exposure to Applied/Non-Rigorous Calculus. Complex numbers are, I assume, needed in Complex Analysis that follows Real Analysis, so I wouldn't worry about sets, real/complex numbers beyond the very basics. Math induction is not needed in non-proof based/regular/non-rigorous Calculus.

From the link:

For Calc 1(applied)- again, in my experience, this is the bulk of what's usually tested in Calculus placement exams:Solving inequalities and equations

Properties of functions

Composite functions

Polynomial functions

Rational functions

Trigonometry

Trigonometric functions and their inverses

Trigonometric identities

Conic sections

Exponential functions

Logarithmic functions

For Calc 2(applied)- I think some Calc placement exams dont even contain problems related to the concepts below, but to be sure, you, probably, should know something about them:Sequences and series

Binomial theorem

In Calc 2(leading up to multivariate Calculus (Calc 3)). You can pick these topics up while studying pre-calc, but they are typically re-introduced in Calc 2 again:Vectors

Parametric equations

Polar coordinates

Matrices and determinants

As for limits, I dont think they are terribly important in pre-calc. I think, some pre-calc books include them just for good measure.

I have read all of Professor Dawkins' books, and The Greatest Show on Earth is, without question, his finest masterpiece and quite possibly the best explanation of evolution that any jackoff like myself can understand.

Religion or theistic religion? I will give you some short answers then discuss my question.

"demon possession" - Did you see a demon or did you see a person, who believes in demons, rolling around making noises?

"healings" - Did you see an amputee or burn victim get healed? Did you know the healed person before the healing and did you do a follow up of the person a week, a month or a year later?

"probably was just a coincidence" - How can we tell when things are or are not coincidences? Coincidences happen.

"spoken in tounges" - What did it mean? Had you seen people doing it before? Were you just mimicking people you had seen before?

What was the education level of the people who had the experiences? What was the general education level of the people who made up the culture where these experiences happen? Do you think these experiences happen as often in well-educated people?

Now to the religion question. I am for getting rid of theistic religion. Belief in a deity that dictates morality is poison to society. The certainty of an infallible being creates a lot a fear, hate, guilt, shame, willful ignorance and false expectations. Truly, a lot of unnecessary pain.

Religion, on the other hand, can be fine. The problem is being able listen to criticism and being willing to change to new information. Having a set of principles and guidelines to give you direction in life is good. Being willfully ignorant and trying to force your ideology on the world is not good. Pick and choose good morals from where you see them.

Yup, that's a great book. (For those who don't read, there's the audiobook, read by the author.)

One thing I took away from it was that fossil evidence is superfluous at this point. It fully supports evolution theory of course, but it's a bonus, and even without it "the evidence for evolution would be entirely secure".

That's from the chapter that discusses the fossil record. The rest of the book is about all the other evidence.

A Universe from Nothing: Why There Is Something Rather than Nothing

Lawrence Krauss

It is brilliant. I loved the lecture from him (with the same title) on youtube and the book takes it to the next level. I have gained so much knowledge just reading a chapter a day on the tube to work.

Here is a great book I just finished, while much broader in scope, will help you understand what is in that 'empty space'.

A Universe From Nothing. Why There is Something Rather Than Nothing.

A Universe from Nothing by [Lawrence M. Krauss] ( http://en.m.wikipedia.org/wiki/Lawrence_M._Krauss)

>without a God how did the universe come into existence?

I could rephrase that into a question that would be even more baffling:

>with a God, how did the universe come into existence?

The 2nd one is more crazy to explain, because now you need to know how a god was created, not just why there is or isn't more or less matter and energy.

If you are genuinely interested in astrophysics, here are some good books written by people who know more than me about the issues you mention:

http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/145162445X

http://www.amazon.com/Briefer-History-Time-Stephen-Hawking/dp/0553385461

Remember, even if you don't know the answer to a question about nature, it's always OK to say "I don't know." It's not OK to pretend that a story about the supernatural explains an issue in the natural world, if embracing the myth about the supernatural wouldn't really explain how things work, and would really only raise more questions.

You didn't say how old you were, but if you're financially dependent on your parents, you should probably keep quiet on the subject - including with your sister - until that is no longer the case.

On the something from nothing question, if she is science-minded, give her a copy of the Krauss book on the subject:

http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/145162445X

you know what

doestake some mystery away from them...http://www.amazon.com/gp/aw/d/145162445X/ref=mp_s_a_1?qid=1343795584&amp;sr=8-1

You should check out

A Universe From Nothingby Lawrence Krauss. The whole book is an attempt to answer that very question.http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/1451624468

No, the null hypothesis is "we don't know".

God(s) did it is a claim, as is it sprang into existence on its own. There is some evidence for the latter (1, 2)

There is a great book called

A Universe From Nothingby Lawrence Krauss that goes into great detail.http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/1451624468

"Nothing is not nothing. Nothing is something."

A good book for you to read is A Universe from Nothing by Lawrence Krauss

It will answer your questions.

Well, you can get Lawrence Krauss's book or check out his Youtube lecture.

A good book on the subject.

Check out the Foundational Falsehoods of Creationism.

Check out a copy of the books The Greatest Show on Earth or Why Evolution is True from a library. You can also get one of them for free on Audible, but you will miss out on the citations and diagrams.

See if you can watch or read The Grand Design by Stephen Hawking. I watched the miniseries, it's pretty good. It used to be on Netflix but no longer is.

Cosmos is great, and is on Netflix. If you want to watch videos about Cosmology just type in one of the popular physicist's names, Brian Greene, Neil deGrasse Tyson, Lawrence Krauss (his Universe from Nothing book is really great, so are his lectures about it), Sean Carroll etc.

Let me know if you want to talk, I'm always up for it.

This is quite the loaded question. First of all, most atheists would not say that "God cannot possibly exist." Second of all, disbelief in the existence of God cannot in any way be called "faith." Finally, the Big Bang itself

iswhere all the materials came from. For more thoughts on this subject, I recommend Lawrence Krauss' book,A Universe From Nothing: Why There is Something Rather Than Nothing.All the ad hominem aside, can you explain your perception of the word "nothing"? You seem open to understanding the scientific side of the discussion.

If you're interested in exploring what is meant in science by nothing, there's a great book by Theoretical Physicist Lawrence Krauss, entitled A Universe from Nothing.

I think you'd find it to be a great read.

This is an incredibly complex topic, physicists have spent entire careers trying to answer this question. It would be really hard to give him a quick and easy answer. If you are interested in this topic I would recommend reading this book by Lawrence Krauss: http://amzn.com/1451624468

NightWatch: A Practical Guide to Viewing the Universe

https://www.amazon.com/dp/155407147X/ref=cm_sw_r_cp_apa_zi5CybKCT39D1

One of my favorite books about stargazing and basic astronomy. A "must have" in my experience.

Another one as you get into binoculars or telescopes is "turn left at Orion" which is all about cool objects in the night sky, how to find them in binocs/telescopes, and what they're gonna look like. Plus lists of objects arranged by light pollution/size of telescope. It's awesome for the "what to look for tonight?" questions.

It's also suggest getting a sky chart, or sky chart software. Both have good versions available free, like Stellarium and Cartes du Ciel. Learn to set them up to mimic the sky you actually see in your area (stellarium does this by simulating light pollution, cartes let's you filter by star brightness). These will help you learn the constellations, which is how you find things up there.

Basically, the larger the diameter of your telescope, the more light it collects and the more distant and fainter objects you can see. Also, more light means you can magnify the image more (by changing the eyepieces of the telescope) without it getting to faint to see properly.

I'm only at the research stage into my astronomy hobby at this point, so I can't really help much, but go onto youtube and there are lots of videos of sights through telescopes. Start by searching for "my telescope" and take it from there, and look up prices for the scopes you see.

Turn Left at Orion and NightWatch: A Practical Guide to Viewing the Universe seem to be the go-to books for understanding what objects you can see through different telescopes and where to find them, though I haven't bought either of them yet.

If you're really good with your hands, you might want to try building your own telescope for cheap.

Luna and Jupiter will look fantastic.

With Jupiter you should more than be able to see all four moons pretty well and the bands should be faint but visible. Give your eyes time to adjust and make sure you're in a nice dark place. I'm sure that goes without saying but it can't hurt to reinforce the concept.

That is a great starter scope. Get yourself a good star atlas, I really recommend NightWatch: A Practical Guide to Viewing the Universe as a starter (http://www.amazon.com/NightWatch-Practical-Guide-Viewing-Universe/dp/155407147X/ref=sr_1_2?ie=UTF8&amp;qid=1324071016&amp;sr=8-2). It has good seasonal star charts and lots of practical info about viewing the sky.

I really hope you enjoy the scope and please do post a follow up on the performance and your experiences.

I notice you said you are in CST Time Zone. Where are you located. If you are in the Houston Area we should get a little star party set up with fellow redditors.

The star charts in the book "Nightwatch" are pretty good. Pretty likely you can get Nightwatch at the library, it's very common.

Google Sky (free) is really good if you have an Android Phone.

SkySafari ($3) is pretty good if you have any iOS device.

Stellarium is my favorite for PCs.

Read about it and understand the science would be my tip.

And know that the fossil fuel industry has a campaign to spread any doubt they can about climate change science. They lose money if people divest from fossil fuels, and they know which tactics to use very well. They are using the exact same people who worked for the tobacco industry and said smoking doesn't cause cancer. These are lobbyists who just lie and lie for money and do not care how badly their lies hurt people. Everything is documented extensively in this book: https://www.amazon.com/Merchants-Doubt-Handful-Scientists-Obscured/dp/1608193942

As a climate scientist, I can tell you I do not get paid much at all. And I do not get paid depending on what my results are. I and all my colleagues would be extremely happy if we discovered climate change wasn't as serious as it is. I am working in this field because I find it interesting, I like the scientific process, and I'm passionate about understanding climate change better so I can contribute to stopping what is arguably the most serious future threat to humans and our civilisation.

On climate change specifically: We have known there is a greenhouse effect since the 1800s. We know the Earth's climate changes at regular cycles, natural climate change. We know what causes it to change, like orbital changes and sun output. The climate responds to whatever is the dominant forcing, what's impacting it the most. We know natural causes can not explain the warming happening now. We can measure what's causing it, and it's very clear that it's predominantly greenhouse gases from humans: https://www.bloomberg.com/graphics/2015-whats-warming-the-world/

We know humans are releasing greenhouse gases, and we can identify individual particles to make sure they're not from natural sources.

We also know that Earth is in an interglacial with warm stable temperatures, and passed the warming peak of it a few thousand years ago, and should therefore now be slightly cooling over thousands of years as we go into a glacial period. We know that the rate of warming happening now does not happen when the climate changes naturally. It's way too fast to be natural.

A good resource for any question about climate change: https://skepticalscience.com/

At the same time, there are numerous studies on how many climate scientists who think humans are the cause and dominant driver. The number is usually around 97%.

Also, have been misled by industry funded scientists, that used the same tactics as tobacco and pesticide (DDT) lobbyists

https://smile.amazon.com/Merchants-Doubt-Handful-Scientists-Obscured/dp/1608193942?sa-no-redirect=1

Look into the agnotology literature, especially Proctor and Schiebinger's book, and Oreskes and Conway's book. Hot area of study on the cultivation of ignorance as a response to uncertainty, very cool stuff going on right now. Think you'd like it given that stated interest.

Let me copy something I wrote in another thread about someone asking what to read about:

Personally, I just finished 'The Greatest Show on Earth' by Dawkins a bit ago. It was pretty stunning even as someone who's never really been of the faithful. Only recently have I really started doing outside reading on these sorts of topics (as a kid the baptist tradition of the south where I live failed the 'looks like bullshit, smell like bullshit, probably bullshit' test for me and I just sort of disregarded the whole thing for the next 20 years or so) so I'm also fairly new to the ballgame in that sense. I've always believed in evolution as the origin of life on this planet but it was pretty amazing the enormity of evidence we now have supporting it, particularly with the advent of modern molecular biology and DNA sequencing. Our knowledge absolutely dwarfs the vague and semi-hand-wavy feel of the old 'we have some bones and radioactive dating stuff' that was glossed over in my education even at a college level 15 years ago.

If you really want to know about the evidence for evolution that books covers it, for the layman, in about as much detail as one could ask for. It

isDawkins, so there's no kid-gloves here and you will get the occasional "Only someone being willfully stupid could ignoreallthis evidence" type stuff, but the focus is pretty firmly on simply laying out the huge piles of evidence across many different areas of science all supporting common ancestry and evolution by natural selection.Former Young Earther here. The best thing you can do is read and learn. www.talkorigins.org is a pretty good site.

Another good source is The Greatest Show on Earth by Richard Dawkins.

http://www.amazon.com/Greatest-Show-Earth-Evidence-Evolution/dp/B004AYCWY4/ref=sr_1_5?ie=UTF8&amp;qid=1319762317&amp;sr=8-5

Figure out some of the more common creationist claims, as well. Read some about geology, astronomy, cosmology. It'll take a while, but the more you know, the more intelligible you'll be, and the better able you'll be to string ideas together when asked.

The Greatest Show on Earth by Richard Dawkins is an extremely well written introduction to the evidence for evolution.

I would suggest Unweaving the Rainbow: Science, Delusion and the Appetite for Wonder as a good starting point and maybe move on to The Greatest Show on Earth: The Evidence for Evolution, but that is just one author. He can be a little condescending to the faithful at times and call them "history deniers" but the second one is pure science and only just touches on religion.

I'm assuming you're looking for things geared toward a layman audience, and not textbooks. Here's a few of my personal favorites:

SaganCosmos: You probably know what this is. If not, it is at once a history of science, an overview of the major paradigms of scientific investigation (with some considerable detail), and a discussion of the role of science in the development of human society and the role of humanity in the larger cosmos.

Pale Blue Dot: Similar themes, but with a more specifically astronomical focus.

DawkinsThe Greatest Show on Earth: Dawkins steers (mostly) clear of religious talk here, and sticks to what he really does best: lays out the ideas behind evolution in a manner that is easily digestible, but also highly detailed with a plethora of real-world evidence, and convincing to anyone with even a modicum of willingness to listen.

HofstadterGodel, Escher, Bach: An Eternal Golden Braid: It seems like I find myself recommending this book at least once a month, but it really does deserve it. It not only lays out an excruciatingly complex argument (Godel's Incompleteness Theorem) in as accessible a way as can be imagined, and explores its consequences in mathematics, computer science, and neuroscience, but is also probably the most entertainingly and clearly written work of non-fiction I've ever encountered.

FeynmanThe Feynman Lectures on Physics: It's everything. Probably the most

detaileddiscussion of physics concepts that you'll find on this list.BurkeConnections: Not exactly what you were asking for, but I love it, so you might too. James Burke traces the history of a dozen or so modern inventions, from ancient times all the way up to the present. Focuses on the unpredictability of technological advancement, and how new developments in one area often unlock advancements in a seemingly separate discipline. There is also a documentary series that goes along with it, which I'd probably recommend over the book. James Burke is a tremendously charismatic narrator and it's one of the best few documentary series I've ever watched. It's available semi-officially on Youtube.

I really enjoyed reading The Age of Wonder by Richard Holmes.

Also Thunderstruck by Erik Larson.

Both of these books are fantastic nonfiction accounts of the history of scientific discovery.

On the biology side, anything by Dawkins is a good choice. I recommend The Greatest Show on Earth

My gateway drug was The Panda's Thumb by Stephen Jay Gould

That's not really a relevant question. You're implying that because we

can'tfind proof of god, we don'tneedproof? But because we havetonsof proof of evolution, you require that each and every one of us (accountants, programmers, carpenters, etc.) have a detailed knowledge of it before you'll believe it?Again, you're saying there's no proof of god -- indeed, there can't be -- and yet you're willing to believe in god wholeheartedly. Meanwhile, you won't believe in evolution without absolute proof (and, I'll go out on a limb and guess that you want a couple of simple sentences you can understand without having to do a whole lot of book learnin'. You're not willing to put in even the minimal effort it takes to gain a basic understanding of evolution.)

Basically, nobody

believesin evolution; you either understand it or you're an idiot.I suggest picking up a copy of The Greatest Show on Earth and reading it.

The Greatest Show On Earth by Richard Dawkins.

Good advice, but I'd add that if you do revisit calc get an intro to analysis textbook to understand how we derived the rules that calc uses. For instance, an integral is not defined as an antiderivative, that had to be proven.

Edit: My class used Principles of Mathematical Analysis by Rudin. It requires little to no initial knowledge and essentially builds multivariable calculus from the ground up.

Have you ever seen how much technical books cost?

For example, here's the standard text for mathematical analysis: Principles of Mathematical Analysis. That's $87 for a 325 page book.

Nobody's pretending that printing/binding/distributing is a significant fraction of that cost so an ebook would likely be similarly priced, maybe slightly less, possibly slightly more.

Manning, in particular, focuses on texts in computer science and programming for which such prices are pretty standard. The price difference between the ebook and print+ebook varies (I think it's proportional for most of their texts) but if the ebook is $35 then the physical+ebook is usually around $45. Again, this is very reasonable for a quality text in the field.

I guess I don't have a clear idea what an "elementary math degree" entails, so let me put it this way:

I learned about space-filling curves in my second semester of Real Analysis. First-semester Real Analysis was the first upper-division math class people take at my college; the second-semester is typically taken Junior or Senior year by those who are particularly passionate about the subject. It is not, as a general rule, a subject I recommend learning without the benefit of an instructor - at least, not from the book I used. To be clear: its a good reference book, and I developed a healthy respect for its approach to the subject in time, but its not the most user-friendly book as you're getting going.

To briefly paraphrase the argument: you basically construct a fractal via a sequence of functions, and then argue based on the convergence and continuity properties of the function family that a) the function they converge to is continuous and b) it passes through every point in the area to be covered.

If you want to learn serious mathematics, start with a theoretical approach to calculus, then go into some analysis. Introductory Real Analysis by Kolmogorov is pretty good.

As far as how to think about these things, group theory is a strong start. "The real numbers are the unique linearly-ordered field with least upper bound property." Once you understand that sentence and can explain it in the context of group theory and the order topology, then you are in a good place to think about infinity, limits, etc.

Edit: For calc, Spivak is one of the textbooks I have heard is more common, but I have never used it so I can't comment on it. I've heard good things, though.

A harder analysis book for self-study would be Principles of Mathematical Analysis by Rudin. He is very terse in his proofs, so they can be hard to get through.

EZ

https://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927

4000 yen on amazon.jp or $50 on amazon.com is not even close to insanely expensive. Many physics books and similar subjects are closer to the $100-200 range. The cheap ones are $50.

I don't have any old problem sets off hand, but I could point you towards all the topics you should know and be familiar with. It's basically the first 3 chapters of Griffiths -- by the end of the quarter you should know everything from these chapters extremely well.

As for an explicit list of things to do, I would recommend (in this order, more or less)

important later on)

this could be useful to do first so that you can practice it)Hopefully, that gets you started off, but for 110A it may be worth the time to learn Einstein summation notation -- it'll come in handy.

Good luck!

Edit: formatting

Griffiths Quantum Mechanics book features a live cat on front and a dead cat on back.

This is THE book for that

Multivar calculus understanding more or less necessary, and familiarity with classical mechanics is pretty handy for tackling QM. Linear algebra is absolutely critical to understand everything well, mathematically speaking.

I personally liked Griffiths' book. The concepts are explained well and the examples are cleanly worked out. It's a decently accessible book and an easy read, which is always a plus.

http://www.amazon.com/Introduction-Quantum-Mechanics-2nd-Edition/dp/0131118927

Just flipping through the first pages should make it obvious how much previous knowledge is required just to begin understanding quantum mechanics.

Maybe this one is better: http://www.amazon.com/Quantum-Physics-Dummies-Steve-Holzner/dp/1118460820/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1408628463&amp;sr=1-1&amp;keywords=quantum+mechanics+for+dummies

I just went through the first chapter in the dummies book, it's not much better.

> Can you, or anyone else, link to some information that accurately defines quantum mechanics?

There's always the relevant Wikipedia article; Griffiths' book on introductory QM is also very clear.

If you want a brief, fairly non-technical summary, though, it's what I said before: in QM, the state of an object is contained in a wavefunction. That function evolves over time (following the Schrödinger equation). For a given wavefunction, you can find the probability of measuring a classical property (e.g,. position, momentum, energy) as having a particular value or falling within a range of values by applying an appropriate operator.

The uncertainty principle follows from this. A wave function which will result in most measurements of position being in a tight clump (i.e., an object with a well-defined position) will result in measurements of momentum that will vary widely, and vice-versa.

The usual analogy (which is actually very close to the mathematics in QM) that I've encountered is a rope under tension. If you give it a sharp jerk and induce a single peak that travels down the wave, the question "where is the wave" makes sense, but "what's its frequency" does not. The converse is true if you induce a standing wave: you can talk easily about the frequency, but the wave is everywhere along the rope.

> What I always end up with is this idea of perception=reality. That since we cannot measure where the electron is, it simply isn't. I don't buy this for a second.

Close, but let's be more precise: it's not that the electron doesn't exist, it's that classic properties that we think of as fundamental (position, momentum, etc.) aren't. In QM, a particle

alwayshas a wavefunction; that wavefunction determines the distribution of values you'll get if you try to measure a classical property. This means that generally you can't say that a particle "has" a particular position/momentum/whatever; you can only talk about the probabilities of finding it with such-and-such a position or momentum.If you don't like the fact that this implies that classical properties are fundamentally random, you're in good company; that's what prompted Einstein's "God does not play dice" quip. Unfortunately, Bell's theorem and subsequent tests and confirmations of it essentially eliminate the possibility of local "hidden variables" which contain the "real" position/momentum/whatever of a particle. This leaves us stuck between accepting a stochastic universe and non-local interactions (which thanks to relativity, introduce causal paradoxes.)

I do think that's the book the reviewer is suggesting, yes.

But if I might offer some unsolicited advice: I think learning about quantum mechanics in the context of philosophy is pretty risky. It's a lot safer to save all the interpretation and philosophy for

afteryou understand the theory in a mathematical light—that way, you can be sure you understand what it is you're commenting on.Since you mention you have some advanced math background, you might be better served by getting a more standard quantum mechanics textbook. It honestly doesn't take much to get a feel for the subject. Specifically, if you know linear algebra and have any background in PDEs, you should be fine with a book like Griffiths. It does take more work to read, but I tend to think that if you aren't dong that work, you're not learning this stuff properly.

If you don't have the time just now to dig into the theory mathematically, I do have another book recommendation:

The Quantum Challengeby Greenstein and Zajonc. They give an excellent and firmly empirical introduction to the philosophically-interesting parts of quantum mechanics, using only minimal mathematics.Anyway, I hope you enjoy the reading. This subreddit is always here should you run into interesting questions along the way!

>I love reading quantum mechanics.

cringeReading the pop-sci layman's guide to physics is not the same as "reading quantum mechanics." You wanna "read quantum mechanics" you're going to have to start with two years of calculus, a year of linear algebra, a year of statistics, a year of number theory, and this book.

I'm assuming this is an undergrad QM class so what you have will be more than enough. If you're in the states odds are the book they will be using is Giffiths Amazon link, PDF of the first edition. If you can Taylor expand and find eigenstates you'll be fine.

First semester undergrad quantum is mostly focused on learning how to solve the Schrodinger equation for a variety of Potentials. Expect it to be like first semester calculus, you gloss over the deeper mathematical rigor, and focus on being able to take limits and derivatives. First semester quantum is the same, learn how to solve the Schrodinger equation, and learn what physical meaning you can get from it.

First and foremost, you're going to need to get very comfortable with special relativity and quantum mechanics. QFT is heavily rooted in both subjects since it's essentially a way of reconciling the two, so you're going to need to get familiar with the formalism. For quantum mechanics, I recommend starting off with Griffiths if you haven't taken a class on the subject at an undergraduate level. It's pretty much the gold standard in undergraduate physics curricula. But that alone is not enough to fulfill the necessary background in quantum. After that you'll want to go through a graduate text such as Sakurai. You need to get very familiar with the Dirac formalism since it plays a large role in formulating quantum fields.

Special relativity isn't usually offered as a course on its own in most universities (as far as I know). Typically, it's part of a course on classical dynamics or electrodynamics. You could look for the relevant chapters in textbooks on those two subjects (such as Griffiths electrodynamics) or just go with the introduction that pretty much every QFT textbook has at the beginning. The main thing here is that you'll have to get used to working with tensors since they show up in Lagrangian densities, which are principal objects of study in QFT. This is also where classical field theory comes in, as classical fields are also described by Lagrangians.

Those are the main areas of physics that you need to know coming into the subject. As others have mentioned, you'll want to understand Hamiltonian and Lagrangian mechanics as well as classical E&M since a lot of the formalism involved in QFT stems from those subjects. Most people are introduced to quantum through the Hamiltonian formalism, and while you can do calculations in quantum without understanding where the formalism comes from in classical mechanics, you might be confused as to why the calculations work the way they do. You can also do calculations with a Lagrangian in QFT without really understanding what actually is, but again, if you truly want to understand the material it won't get you quite far enough. It is a graduate subject, after all. So you'll probably struggle to understand the material without having a solid undergraduate background in physics, but it's not impossible. It's also the kind of subject that requires multiple attempts to understand it. I took one semester of it as an undergraduate and there were a lot of gaps in my knowledge at the time, so I found it quite difficult. Then I took another class on it again after going through first year graduate courses in classical mechanics, quantum, and electrodynamics, and I had a better feel for the subject.

In case you're new here. We ( well not me really ) physicists really hate the example of Shrödinger's cat. It's a poor example that only raises questions in the wrong direction. It goes right into the weird type of philosophy that we, as scientists, try to avoid at all costs. If you want to know more about quantum mechanics, which is supposed to be the subject of the so-called Shrödinger's Cat, there are plenty of pop-sci books and YouTube channels. If you want to know the real physics, as in the math, you can try Griffiths ( You need calculus and some algebra ).

For math you're going to need to know calculus, differential equations (partial and ordinary), and linear algebra.

For calculus, you're going to start with learning about differentiating and limits and whatnot. Then you're going to learn about integrating and series. Series is going to seem a little useless at first, but make sure you don't just skim it, because it becomes very important for physics. Once you learn integration, and integration techniques, you're going to want to go learn multi-variable calculus and vector calculus. Personally, this was the hardest thing for me to learn and I still have problems with it.

While you're learning calculus you can do some lower level physics. I personally liked Halliday, Resnik, and Walker, but I've also heard Giancoli is good. These will give you the basic, idealized world physics understandings, and not too much calculus is involved. You will go through mechanics, electromagnetism, thermodynamics, and "modern physics". You're going to go through these subjects again, but don't skip this part of the process, as you will need the grounding for later.

So, now you have the first two years of a physics degree done, it's time for the big boy stuff (that is the thing that separates the physicists from the engineers). You could get a differential equations and linear algebra books, and I highly suggest you do, but you could skip that and learn it from a physics reference book. Boaz will teach you the linear and the diffe q's you will need to know, along with almost every other post-calculus class math concept you will need for physics. I've also heard that Arfken, Weber, and Harris is a good reference book, but I have personally never used it, and I dont' know if it teaches linear and diffe q's. These are pretty much must-haves though, as they go through things like fourier series and calculus of variations (and a lot of other techniques), which are extremely important to know for what is about to come to you in the next paragraph.

Now that you have a solid mathematical basis, you can get deeper into what you learned in Halliday, Resnik, and Walker, or Giancoli, or whatever you used to get you basis down. You're going to do mechanics, E&M, Thermodynamis/Statistical Analysis, and quantum mechanics again! (yippee). These books will go way deeper into theses subjects, and need a lot more rigorous math. They take that you already know the lower-division stuff for granted, so they don't really teach those all that much. They're tough, very tough. Obvioulsy there are other texts you can go to, but these are the one I am most familiar with.

A few notes. These are just the core classes, anybody going through a physics program will also do labs, research, programming, astro, chemistry, biology, engineering, advanced math, and/or a variety of different things to supplement their degree. There a very few physicists that I know who took the exact same route/class.

These books all have practice problems. Do them. You don't learn physics by reading, you learn by doing. You don't have to do every problem, but you should do a fair amount. This means the theory questions and the math heavy questions. Your theory means nothing without the math to back it up.

Lastly, physics is very demanding. In my experience, most physics students have to pretty much dedicate almost all their time to the craft. This is with instructors, ta's, and tutors helping us along the way. When I say all their time, I mean up until at least midnight (often later) studying/doing work. I commend you on wanting to self-teach yourself, but if you want to learn physics, get into a classroom at your local junior college and start there (I think you'll need a half year of calculus though before you can start doing physics). Some of the concepts are hard (very hard) to understand properly, and the internet stops being very useful very quickly. Having an expert to guide you helps a lot.

Good luck on your journey!

In addition to the McQuarrie book mentioned (my text for pchem), I would take a look at Griffiths book for QM. The two books are complementary to each other and I think reading them both gave me a big leg up!

Do you want a formal understanding? If so, then there's a problem. The 4 fundamental interactions are not completely understood. The electromagnetic is very well understood and is covered by quantum electrodynamics. The weak interaction is also understood quite well and has been unified with the EM interaction into the electroweak interaction.

The strong interaction and gravity are not as well understood. There is no widely accepted theory of quantum gravity (gravity is currently described by general relativity). The strong force is described using quantum chromodynamics (QCD), however QCD is vey complicated (due to the fact that gluons carry color charge and interact with each other).

If you fine with that, then I have to ask, are you comfortable with classical physics? If not then start there. If you are, then you can continue on with quantum physics, this book is a very good quantum mechanics book.

If you want a lay person understanding, then I suggest you do some searches here on askscience, because there is a wealth of information regarding particle physics here.

One more thing, very few people call it "quantum physics", it almost always goes by the name "quantum mechanics".

Food:

School:

That's perfect then, don't let me stop you :). When you're ready for the real stuff, the standard books on quantum mechanics are (in roughly increasing order of sophistication)

By the time you get to Shankar, you'll also need some classical mechanics. The best text, especially for self-learning, is [Taylor's Classical Mechanics.] (http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1372650839&amp;sr=1-1&amp;keywords=classical+mechanics)

Those books will technically have all the math you need to solve the end-of-chapter problems, but a proper source will make your life easier and your understanding better. It's enough to use any one of

When you have a good handle on that, and you really want to learn the language used by researchers like Dr. Greene, check out

Aside from the above, the most relevant free online sources at this level are

This is a thing. I read a decent book with a lot of cool math tricks

https://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401

My favorite book that has a ton of these is this book. I remember seeing the author do all kinds of math tricks on talk shows. My favorite was determining what day of the week any date in history was (or at least, after the start of the Gregorian calendar)

The following easy to read book teaches kids (and adults) you how to do it. Its actually really easy:

Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

Secrets of Mental Math

When you say everyday calculations I'm assuming you're talking about arithmetic, and if that's the case you're probably just better off using you're phone if it's too complex to do in you're head, though you may be interested in this book by Arthur Benjamin.

I'm majoring in math and electrical engineering so the math classes I take do help with my "everyday" calculations, but have never really helped me with anything non-technical. That said, the more math you know the more you can find it just about everywhere. I mean, you don't have to work at NASA to see the technical results of math, speech recognition applications like Siri or Ok Google on you're phone are insanely complex and far from a "solved" problem.

Definitely a ton of math in the medical field. MRIs and CT scanners use a lot of physics in combination with computational algorithms to create images, both of which require some pretty high level math. There's actually an example in one of my probability books that shows how important statistics can be in testing patients. It turns out that even if a test has a really high accuracy, if the condition is extremely rare there is a very high probability that a positive result for the test is a false positive. The book states that ~80% of doctors who were presented this question answered incorrectly.

A lot of these tricks are very easy. He explains them all in his book Secrets of Mental Math

Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

Secrets of Mental Math May be helpful for filling in some gaps. Also A Mind for Numbers gives helpful meta learning info: how to study, etc.

I began doing it in my head the same way. For clarity, my thought processes were based on the idea of "don't do something hard, do something easier instead and then fix it up afterwards", roughly:

1000 =oh screw this, I'm convinced I could do it, but this is not fun any more

could* go and learn them. For example, here is a book by one of the world's best people at mental arithmetic, Arthur Benjamin; the book is filled with techniques you can use to make mental arithmetic easier. See him on TED here.(I stopped there because I just wasn't looking forward to adding 973 to 243250, but was pretty sure I could slog my way through it if I actually had to.)

But there are lots of tricks you can do to make mental math easier. I don't know them, but like the above, I know that I

I'm only a high school sophomore, so I can't really help you with most of your questions, but if you want to improve your mental math, buy "Secrets of Mental Math" by Arthur Benjamin.

It's written in a way that makes sitting in your room doing mental calculations seem fun and it is very accessible. I have only gotten through 3 chapters (the addition/subtraction/multiplication chapters) and I can confidently add and subtract 3-digit numbers in seconds. I can even mentally cube two-digit numbers in a few minutes.

[Anyway, here's a link to the book] (http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1381633585&amp;sr=1-1&amp;keywords=mental+math)

[If you don't want to buy it, you can use this PDF version of the book] (http://www.uowm.gr/mathslife/images/fbfiles/files/Secrets_of_Mental_Math___Michael_Shermer___Arthur_Benjamin.pdf)

[And here is the author, Arthur Benjamin, performing what he likes to call "Mathemagics"] (http://www.youtube.com/watch?v=e4PTvXtz4GM)

I hope this has been helpful and you succeed in whatever uni you go to :)

Check out Secrets of Mental Math by Arthur Benjamin. Benjamin is amazing, I've seen him at MAA meetings. He does lightning fast calculations in his head, and his book shows you how to do it. Your students may or may not think this is cool, but I do :) And the bonus is that they will never learn this kind of thing in school at any grade, so you won't be stepping on anybody's toes by teaching it to them now.

Also, the "third grade team" sucks. Screw those guys.

I don't exactly have time to make a detailed post right now, but I recommend grabbing a copy of

The World Without Usby Alan Weisman. It covers this exact subject.https://www.amazon.com/World-Without-Us-Alan-Weisman/dp/0312427905

Any book by Mary Roach- her books are hilarious, random, and informative. I like Jon Krakauer's, Sarah Vowell's, and Bill Bryson's books as well.

Some of my favorites that I can think of offhand (as another poster mentioned, I loved Devil in the White City)

No Picnic on Mount Kenya

Guns, Germs, and Steel

Collapse

The Closing of the Western Mind

What is the What

A Long Way Gone

Alliance of Enemies

The Lucifer Effect

The World Without Us

What the Dog Saw

The God Delusion (you'd probably enjoy Richard Dawkins' other books as well if you like science)

One Down, One Dead

Lust for Life

Lost in Shangri-La

Endurance

True Story

Havana Nocturne

A very cool book that is similar in style to this article is The World Without Us.

Right, let's expand and destroy the life support eco-systems we depend on in order to... survive?

A much saner strategy would be:

a) limit human encroachment on the natural world by setting aside ecologically viable areas that we are not allowed to touch/enter. 20% of the world, 50%, 90%? pick a number, maybe start low and as time goes on add to it. Beautiful things happen when mankind gets out of the way - see [The World Without Us]

(http://www.amazon.com/World-Without-Us-Alan-Weisman/dp/0312427905/) by Alan Weisman. This would decouple our civilization's fate from that of the natural world's. Aren't you glad the Romans didn't take out 90% of exisiting wild species when their society collapsed? Their preindustrial technology wasn't up to the task, but ours certainly is.

b) realize that an economic system that requires exponential growth on a finite planet is madness, and move towards a sustainable, steady-state system. Western economic theory is rooted in a period when Europeans were colonizing the world and unlocking vast, seemingly limitless, areas of undeveloped land and resources. There are no more frontiers of unexplored natural wealth to unlock to kick the can down the road a little longer, we desperately need a system that works with what we can sustainably harvest today.

You might be interested in this book:

http://www.amazon.com/The-World-Without-Alan-Weisman/dp/0312427905

I think maybe the book "The World without us" might be what yoyr looking for:

www.amazon.com/World-Without-Us-Alan-Weisman/dp/0312427905

Its a really interesting read but can be a bit dry at times. I know one of the "learning channels" did a miniseries based on it, but i can't remember what it was called.

-edit cause i can't type for shit on my phone-

If you're interested in the topic, I highly recommend The World Without Us by Alan Weisman.

Late to the game, but people always need more books...

The World Without Us was great, really interesting read about humanity's effects on the planet, with lots of references to expand on if you wanted to do that.

A Year of Living Biblically was interesting, even if you aren't a Christian or a Jew, if you find religion interesting.

And last but not least, Rocket Boys by Homer H. Hickam. This was made into the movie 'October Sky', and it's a memoir, one of the best I've ever read. But all the science of the rockets is in there too, I learned a lot about propellants and DeLavalle nozzles lol.

[This book inspired a lot of the world of The Last of Us. It's a great read.] (http://www.amazon.com/The-World-Without-Alan-Weisman/dp/0312427905)

I couldn't speak to the quality of the science but it all seemed pretty plausible to me. I believe it was based on (and an expansion of) the book "The World Without Us".

amzn.com/0312427905

Carl Sagan book recommendation, if I may?

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

Why Evolution is True

The Demon-Haunted World: Science as a Candle in the Dark

Harry Potter and the Methods of Rationality (free online!)

Guns, Germs, Steel

The God Delusion

Misquoting Jesus (Conceptional this is very compatible with Mormonism--the Bible not being translated correctly so we need the BoM!--but the specifics about what got mistranslated are devastating as Mormonism doubled down on the mistranslated parts. oops.)

Don't even both learning anything more about Mormonism. Just be widely read and you'll soon see that the Mormon version of history is in incongruent with reality. This will cause cognitive dissonance and when you're ready to resolve it, go back and read independent sources about Mormonism and it will be very obvious that the narrative they indoctrinated into you as a child doesn't stand up to scrutiny.

24 years ago was a better time for me as well.

"The Prince" [Niccolò Machiavelli]

"The Demon-Haunted World [Carl Sagan]

"Gödel, Escher, Bach: An Eternal Golden Braid" [Douglas Hofstadter]

"On War" [Carl von Clausewitz]

"Intuition Pumps And Other Tools For Thinking" [Daniel C. Dennett]

Everyone who still needs help overcoming these fears needs to read this: https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469 AMAZING!

Book: The Demon Haunted World by Carl Sagan. It presents a strong case for a secular view and discusses the basic underpinnings of a skeptical mindset with a bit more subtlety than can be found in works by other famous atheist authors.

Book: The 7 Habits of Highly Effective People. This book has nothing to do with atheism or agnosticism; in fact is was written by a Mormon. But it does provide some principle centered practices that are useful to people, particularly if you are feeling rudderless in the absence of a religious moral code.

Thank you. I feel for that professor too.

Hopefully some scientists are studying this. I want to reread that Carl Sagan book

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

I believe it's worsening too, and have seen a change in my life time. The anti-science affected me negatively while in my brain the writings of Carl Sagan were buried, and maybe helped me out later. There's a lot of people who have given up reading and thinking and religion tells people to let others do their thinking.

Thank you for admitting that about the libertarian party. Corporate money is buying off our government. Government power can be misused, that much is sure from the other end.

Yes a lot is fake in TV shows, reality TV etc. I have the kind of mind where I notice too. I think many have improved in their understanding in how cognitive dissonance works, and are using it to many people's detriment. We are in the days where things have moved far beyond propaganda and into controlling and using biases. I think of how my own mind was manipulated in religion and elsewhere.

For a thriller treatment of infections diseases, the following are a nice read

I'm inclined to also suggest the works of Simon Singh, to whom I was introduced by his book on math and cryptography - The Code Book. But he has also written about cosmology and "alternative" medicine. The later got him involved in a landmark libel lawsuit in the UK. For that reason, there is probably more than the usual bit of politics you'd expect in a popular science book. However, in the post-truth era of Donald Trump and company, that maybe fitting if bitter medicine.

Edit: As someone who may not have the best scientific background, one might be prone to confuse science with pseudoscience. Even today, there is no shortage of low quality literature on UFOs and parapsychology. As such, Carl Sagan's The Demon Haunted World: Science as a Candle in the Dark is highly recommended.

I would actually recommend these two books:

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

https://www.amazon.com/Asking-Right-Questions-11th-Browne/dp/0321907957

I'm not trying to be condescending, but these will really steer you in the right direction on sourcing. I still use both in my daily life all the time.

Hey Dave,

I wanted to respond to this for a few days now. Sorry for the late reaction ;-).

It makes sense to be terrified at doom days predictions. We're all human and nobody is bulletproof to nonsensical ideas. You will find that even the smartest around us, believe in really silly things. This goes much further than religion. Alternative medicine (homeopathy, reiki, acupuncture), religion, conspiracy theories (911, Elvis still lives, we didn't land on the moon).

Wouldn't it be wonderful if we had a systematic way of knowing if 'things we know' (or ideas) were true or false. It would have to be testable and repeatable. and no matter what your origin was: American, African, Asian, European, you would have to come objectively to the same conclusion.

Science(from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.I would argue that most people don't want to become disassociated with JWs anymore, because it's the most

logicstep, but because they don'tfeelthat way anymore. In the end humans are guided much more by their feelings than logic. We consider ourself a logic bunch, but when it comes to reality, most people take the decision with their feelings and then rationalize them selfrightusing logic. Then what happens, is that although this person is not a JW anymore, they are still susceptible to other ideas, like alternative medicine, conspiracies or other religions. And this is really where scientific literacy comes into play.Since you said you're a techy, I think you will like the following recommendations. I really encourage you to google and watch the following people on youtube:

Sam Harris

Daniel Dennett

Christopher Hitchens

Richard Dawkins

Neil degrasse Tyson

And read: http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

I always recommend this book to anyone who's interested in skepticism, and that includes skepticism of religious claims.

http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

Sagan is the man.

Catholicism is pretty interesting how they don't push the JUST BELIEVE down your throat. I grew up like that too, and the emphasis was just a lot more on the community, tradition and ritual. Then I went to an Evangelical church where the emphasis was on BELIEVE, BELIEVE, BELIEVE.

Anyway, just musing to myself. You said you're all good on science (Catholicism is good like that), but I would still highly recommend

Demon-Haunted World, by Carl Sagan.I'd also suggest some of Stephen Law's Philosophy Books.

I'd also suggest reading the Bible for yourself, if you haven't already :)

I guess you have to ask yourself what exactly it is that your belief depends on, then go after that yourself to find what other explanations are out there.

Was going to mention

Omnivore's Dilemmabut a few others already have. And as for anything else, you should at least read "The Baloney Detection Kit" from The Demon-Haunted World, if not the whole book. That will make your discussions that much more interesting.Demon Haunted World by Carl Sagan

This shit should be mandatory reading...ESPECIALLY for politicians and policy makers.

For a more thorough analogy, read the very brief chapter entitled The Dragon in My Garage, from Carl Sagan's The Demon-Haunted World, a book which should be required reading

~~for anyone wishing to be an advocate for critical thinking~~.Don't trust everything you read online, either. Books are still generally your best bet, because people who might not know what they're talking about can't edit them while you're reading them.

Obviously I'm not saying all books are better than all internets, but find some credible ones and you're much better off.

I'm not a scientist by training, but I can suggest a few books that will provide a pretty good counterbalance to what your mom will be teaching you. (A few of them have quasi-religious-sounding titles, too, so if she happened to find them lying around she might not get too angry.)

The Chosen Species: The Long March of Human Evolution

The Dragons of Eden: Speculations on the Evolution of Human Intelligence

The Demon-Haunted World: Science as a Candle in the Dark

A Brief History of Time

I can recommend more if you'd like. These ones are pretty broad surveys of the topics of (in order) evolution, more evolution, the role of science in society, and the physical nature of the universe. If you're homeschooled, I'm assuming high school-level? None of these books is technical - they're all 'popular science', intended to explain broad concepts to non-scientists. They're very, highly interesting, though, and it's easy to find recommended reading lists once you discover some specific topics that interest you.

The Chosen Speciesitself has a lengthy and detailed bibliography and recommended reading section at the end.I hope I've been able to help! Good luck!

I would highly recommend this book by Carl Sagan:

The Demon-Haunted World: Science as a Candle in the Dark

here is a clip from a review by Amazon user "My Uncle Stu" that does a amazing job of explaining what the book is about:

>In Demon Haunted World, he writes about science, about what science is and what science isn't. Whenever you get in debates with religious types, or with those self-appointed geniuses, the philosophy majors, they will always hit you with the fact that science is just another belief system, just like any religion or philosophy. They will tell you science can't answer all the questions and is often wrong. Of course that is true, if you look at science strictly as a body of knowledge. But that is not what science really is. Science is a process. It is a way of approaching the world, a way of formulating and testing hypotheses. If it is just another belief system, then it is a belief system that grows by virtue of challenging its adherents to challenge and disprove the current state of knowledge. It's the only belief system where you have to be a skeptic to be a zealot.

I think understanding how the scientific method works is greatly helpful, since a lot of religious people think science is just a collection of ideas that are believed on faith, similar to religion, when really it is a method for finding out the truth.

The Demon Haunted WorldAnother favorite source is The Demon Haunted World By Carl Sagan.

The Case for God and The Bible: A Biography by Karen Armstrong are both good. The God Delusion is a simple breakdown and explanation of most major religious claims. Beyond Religion: Ethics for a Whole World by the Dalai Llama is an interesting book on ethics. The Koran: A Very Short Introduction by Michael Cook is 150 funny and insightful pages on Islam. Under the Banner of Heaven is a shocking and fascinating account of fundamentalist Mormonism. The Demon Haunted World by Carl Sagan discusses religion, and Cosmos and Pale Blue Dot are my secular versions of holy books. And of course given the occasion, I can't leave out God is Not Great.

I recommend avoiding authors like Lee Strobel and Deepak Chopra. Both are essentially liars for their causes, either inventing evidence, or deliberately being incredibly misleading in how they use terms. Popularity in those cases definitely doesn't indicate quality.

> Take a deeper look at a lot of the stuff used to "contact" ghosts and spirits in hauntings.

I don't believe in ghosts. Why would I want to waste time hunting around the internet for the ramblings of paranormal fanatics?

> Same thing for the alien "contactees" there's all sorts of occult stuff there.

The people who usually get visited by aliens turn out to be village idiots and/or drunks. Why do aliens, in their powerful ships, always visit out of the way farms to rectally probe some innocent divorced farmer?

> "Channeling" messages from "aliens" who consistently lie about their origins and deny the Gospel every chance they get while proclaiming that man can be like God.

Aliens who lie about their origins and deny the Gospel? So aliens have come to earth and blurted out "Jesus doesn't exist"? And they also proclaim that humans can be like God?

Listen to me carefully. STOP DRINKING THE TURPENTINE. It's not helping you.

> Sounds like the same tune Satans been singing for years just cleverly repackaged.

Yup. That nasty Satan pretending to be an alien in a beautiful spaceship, experimenting on cows and telling farmers, with a probe up their anus, that Jesus doesn't exist. Damn that Satan to hell, along with his rectal probing device of deception!

This is the perfect book for you.

Pale Blue Dot should be a suggested reading for American High Schools. This video makes want to start a campaign championing it.

Try reading The Demon Haunted World by Sagan. He breaks down why people believe things without evidence far better than I ever could.

Book on Amazon

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

learn how to think critically

Demon Haunted World is great for teaching skeptical critical thinking skills.

When I was around his age I loved Redwall. They're great books that really appeal to a young boys sense of wonder and adventure, all while teaching great life lessons along the way.

You should read this book.

He would say "I told you so." He has written many a word decrying falsehoods and lamenting the possibility of the decline of our ability to think critically. https://smile.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469?sa-no-redirect=1 Check that book out, Demon Haunted World.

Now go forth and get yourself a copy of The Demon-Haunted World: Science as a Candle in the Dark.

> A Demon Haunted House

Sorry, I'm usually not that nit-picky, but it is The Demon-Haunted

World.I think the most important one for understanding the essense of science and of Sagan's philosophy is

The Demon Haunted World

Seriously, I can't recommend it strongly enough it might change your life in some small, or perhaps large, way.

"The God Delusion" by Richard Dawkins. Dawkins doesn't really go into anything new or original, but the strength of the book is that is a great, concise summary of all the beginning arguments for atheism.

http://www.amazon.com/God-Delusion-Richard-Dawkins/dp/0618680004

I'd follow it with Daniel Dennett's "Breaking the Spell", also a good recommendation. Same goes for Carl Sagan's "A Demon Haunted World"

http://www.amazon.com/Breaking-Spell-Religion-Natural-Phenomenon/dp/0143038338

http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469/

Christopher Hitchens is a bit vitriolic for some, but "God is not Great" has some nuggets in it.

http://www.amazon.com/God-Not-Great-Religion-Everything/dp/0446579807/

I personally didn't like Sam Harris' "End of Faith" but I did like his "Letter to a Christian Nation".

http://www.amazon.com/Letter-Christian-Nation-Vintage-Harris/dp/0307278778/

For the topic of evolution, Talk Origins is great (and free) http://toarchive.org/

Dawkin's "The Selfish Gene" is also a good read (and short). Not so short but also good are Dawkins' "Blind Watchmaker", "Climbing Mount Improbable" and "Unweaving the Rainbow"

http://www.amazon.com/Selfish-Gene-Anniversary-Introduction/dp/0199291152/

http://www.amazon.com/Blind-Watchmaker-Evidence-Evolution-Universe/dp/0393315703/

http://www.amazon.com/Climbing-Mount-Improbable-Richard-Dawkins/dp/0393316823/

http://www.amazon.com/Unweaving-Rainbow-Science-Delusion-Appetite/dp/0618056734/

A descent selection so far from the other comments. I'll throw in a few, as well:

&#x200B;

&#x200B;

Some of the above is specifically related to atheism, while others I've used to help shape and inform my understanding and my worldview. Out of the entire list, the Carl Sagan book and the Sean Carroll book rank highest, for me, in level of importance. Those books didn't just change

whatI think, they changedhowI think, and I am forever indebted to them.Carl Sagan and Ann Druyan's The Demon Haunted World: Science as a Candle in the Dark

I'd love to hijack this ad and recommend people check out The Demon-Haunted World: Science as a Candle in the Dark by Carl Sagan

Hopped on Amazon to check it out: http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469

The kindle version costs

morethan a brand new paperback version... wtf is this &#3232;_&#3232;Truly surprised that no-one's recommended Carl Sagan's The Demon Haunted World yet. That's almost literally and exactly about this topic and it's a classic.

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

>maybe higher iq correlates to being right

You have the right idea. Having a solid foundation in

logiccorrelates to "being right", and thankfully using logic is a learnable skill.When it comes to understanding the world, you have two practical choices. You can rely on emotion and follow only what "feels good" (like you said, wanting to feel special and having the world make sense

to youexclusively rather than learning how to make senseof the world, big difference). Here you risk being manipulated and fooled by emotionally controlling groups or individuals. You also risk being very wrong about how things in the world work.Or, you can rely on reason and follow the path that corresponds logically with what you already know. It's not easy or fun at times, but if you

reallywant to be able to understand how the world works then it's the only option. The best thing is that, once you establish a good system of logical checks, you develop a sense of true pride and confidence knowing that you can see past bullshit and even anticipate how things will happen. You become a better informed person, and that in itself is special.If you're serious about this, I would recommend reading this book. It's a great introduction into analysing the world from a logical perspective.

>>Finally! do you have any good book recommendations? Again, thanks!

Ooh goody, I always love it when people ask for book recommendations. :)

Here's just the tip of the iceberg:

Get through these books, and you'll be better armed against Christianity than many. Have fun!

EDIT: Use the smile.amazon links that the bot posted below if you're going to buy any books. Lol.

Carl Sagan's The Demon Haunted World is a good place to start. Moore and Parker's Critical Thinking starts to formalize things a bit. Getting a little more technical there is Choice and Chance.

Handbook to Higher Consciousnessby Ken Keyes.The Demon-Haunted World: Science as a Candle in the Darkby Carl Sagan.The Selfish Geneby Richard Dawkins.Enduranceby Alfred Lansing.Complete bunk.

Check out Carl Sagan's book ' The Demon Haunted World', which

explains how and why these concepts still exist.

http://www.amazon.com/The-Demon-Haunted-World-Science-Candle/dp/0345409469/ref=sr_1_1?ie=UTF8&amp;qid=1345151511&amp;sr=8-1&amp;keywords=demon+haunted+world+by+carl+sagan

I suggest reading Demond Haunted World by Carl Sagan. This should pretty much clear up anything you've ever been told about UFOs and bad science in general.

>Carl Sagan - The Demon Haunted World

Definitely. Here's a convenient link to purchase.

There are excellent books out there that explain this phenomena. Unfortunately, I have no titles to give you, but I've definitely read a few. I think that Sagan's Demon Haunted World is one of them.

IIRC from when I read them, the scientists point out that, before aliens, people often reported seeing religious figures/demons/angels. In other cultures, they report seeing the 'commonly viewed' figures of those cultures, from religious figures, to elves, to fairies, etc. At the turn of the century and before, many respectable adults reported seeing fairies, which was why that faked fairy photograph was so widely believed.

Our brains aren't perfect machines which accurately record the world and notice every detail. We actually interpret everything we see, adding things in and ignoring things deemed inconsequential. Since we, as a culture, share similar ideas, it makes sense that we would interpret odd shapes and things have glimpsed through the cultural lenses of what we would expect to be there when something is there that's not supposed to be. Before 'little green men' were aliens, they were goblins and other creatures. From wikipedia

These examples illustrate that use of little green men was already deeply engrained in English vernacular long before the flying saucer era, used for a variety of supernatural, imaginary, or mythical beings.Also, as an Evolutionary Anthropologist, I find it very telling about the human psyche that the physiology of these supposed advanced aliens is so strikingly similar to our own, with the changes in shapes like an overdeveloped human. The first time I saw a

Homo sapiensskeleton placed next to a Neanderthal skeleton, I was struck by how we must have looked like aliens to them. It's very interesting that our 'enemy' is a more advanced version of ourselves.Carl Sagan's book "The Demon-Haunted World: Science as a Candle in The Dark" directly addresses this. He even references crystals.

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

Buy it, and give it to her. I hope that helps.

For a good starter into critical analysis and the scientific method, along with general topics on not getting suckered into things, I recommend Demon Haunted World by Carl Sagan:

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

To help start thinking about balanced critical awareness you can try some little workbooks like this: https://www.amazon.com/Do-You-Think-What-Philosophical/dp/0452288657

That book isn't very in depth but I found it a good way to start exercising skepticism and logic.

To learn how to step back and pay attention to what is happening, including thought patterns, emotions and body states with a critical but calm eye, I recommend mindfulness practice in the insight meditation tradition, it is quite secular, rational and will be useful for anyone.

6 part introduction to mindfulness:

http://www.audiodharma.org/series/1/talk/1762/

To dampen the irrational negativity I recommend the practice of metta which is something like purposefully practicing compassion, forgiveness and support.

For specific info on Metta(loving kindness) practice just ctrl+f on "metta" on this page: http://www.audiodharma.org/recommended_talks/

Then, I recommend two practical philosophies that both teach how to deal with internal dialogue and experience in rational and practical methods.

Secular Buddhism

https://secularbuddhism.com/category/podcast/

Stoicism

https://immoderatestoic.com/good-fortune/

You should start with the oldest episodes.

On the Stoicism side it would be helpful to read through Epictetus Enchiridion and Marcus Aurelius Meditations as starters. Try to find some modern translations to make it a bit easier unless you like the old language stuff.

I know that is a lot, I'd say start with either the mindfulness practice or Carl Sagan's book. Keep it simple and take your time.

Watch The Rubin Report on YouTube. Dave Rubin interviewed both Ben Shapiro and Jordan Peterson, as well as MANY of the other names I see posted by others here. He interviews people from different political, social, and economic philosophies. I even fund him on Patreon because his channel is great (and important).

&nbsp;

If I had to pick three people that made the most dramatic impact on my life in terms of how I think, seek and evaluate evidence, and use reason, these people would be at the top. While the people on my list did not always agree on everything, I do believe that they are/were intellectually honest:

&nbsp;

Thomas SowellCarl Sagan (Science-related things aside, he wrote a bit on Philosophy of thought)Ayn RandI hope that helps! :)

Don't stop dealing with him. Be valuable to him as a friend and confidant, but not as a potential convert.

For reading material, if it comes to that, a go to book is alway Carl Sagan. Read if yourself, if you haven't.

A Short History of Nearly Everything

The Selfish Gene

The Demon Haunted World

Debunk what? A story being told on a show about ghosts and demons? Have you ever read the book The Demon Haunted World - Science as a Candle in the Dark? I

reallyrecommend that you do if you haven't.Whether or not this particular article is sensationalistic fear-mongering, witch-mania and superstitious fervor are endemic to the human condition. I recommend reading the book The Demon-Haunted World.

My favorites... the first two are not even talking about religion, but simply pure science and fascinating.... the second starts off about UFOs but then goes into being critical of religion (while barely... it's sagan after all, it's enough to turn off a non-questioning christian).

http://www.amazon.com/Short-History-Nearly-Everything/dp/0767908171

http://www.amazon.com/Genome-Autobiography-Species-23-Chapters/dp/0060194979

http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

Beyond that, all of Malcom Gladwell's stuff is interesting and about science/sociology so it's a great read and a lot of is down to earth and so will pick at the fundamentalist belief some... eg:

http://www.amazon.com/Outliers-Story-Success-Malcolm-Gladwell/dp/0316017922/

Weston's A Rulebook for Arguments is clear and concise.

Heinrichs' Thank You for Arguing is more informal with lots of pop culture references.

Sagan's Demon Haunted World is a paean to science & critical thinking and Whyte's Crimes Against Logic is good as well

All I can say is please read this, then come back and do an "I recently learnt the difference between pseudo-science and actual science AMA".

Agreed looks like the OP just needs general skeptics resources and community. I would also recommend Sagan's The Demon-Haunted World. You may also find /r/skeptic here on reddit useful.

Carl Sagan addresses this in his book titled

The Demon-Haunted World: Science as a Candle in the Dark. He deals not with the neurology behind it, but rather the psychology and history behind it. A good read.>Or if you don't believe in these things, how would you use your INTP characteristics to understand them?

By being able to self analyze. Use cold emotionless calculation.

I'll argue that the "spiritual" is not necessarily stupid, but a lot of people's take on the supernatural is.

Recommended reading: The Demon Haunted World, Science as a Candle in the Dark

Endorse the one-star review by Daniel Morrow.

I'll have to send him a copy of

The Demon-Haunted World: Science as a Candle in the Dark by Carl Sagan.Even in these modern times people still believe in demons. Just think about that for a second. If that fact alone doesn't scream for more education, I don't know what does.

I'm working through the exercises in Pinter's Abstract Algebra.

If you're not afraid of math there are some cheap introductory textbooks on topics that might be accessible:

For abstract algebra: http://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178/ref=sr_1_1?ie=UTF8&amp;qid=1459224709&amp;sr=8-1&amp;keywords=book+of+abstract+algebra+edition+2nd

For Number Theory: http://www.amazon.com/Number-Theory-Dover-Books-Mathematics/dp/0486682528/ref=sr_1_1?ie=UTF8&amp;qid=1459224741&amp;sr=8-1&amp;keywords=number+theory

These books have complimentary material and are accessible introductions to abstract proof based mathematics. The algebra book has all the material you need to understand why quintic equations can't be solved in general with a "quintic" formula the way quadratic equations are all solved with the quadratic formula.

The number theory book proves many classic results without hard algebra, like which numbers are the sum of two squares, etc, and has some of the identities ramanujan discovered.

For an introduction to analytic number theory, a hybrid pop/historical/textbook is : http://www.amazon.com/Gamma-Exploring-Constant-Princeton-Science/dp/0691141339/ref=sr_1_1?ie=UTF8&amp;qid=1459225065&amp;sr=8-1&amp;keywords=havil+gamma

This book guides you through some deep territory in number theory and has many proofs accessible to people who remember calculus 2.

I like this abstract algebra book: A Book of Abstract Algebra

This is one of the best books of abstract algebra I've seen, very well explained, favoring clear explanations over rigor, highly recommended (take your time to read the reviews, the awesomeness of this book is real :P): http://www.amazon.com/Book-Abstract-Algebra-Edition-Mathematics/dp/0486474178/ref=sr_1_6?ie=UTF8&amp;qid=1345229432&amp;sr=8-6&amp;keywords=introduction+to+abstract+algebra

On a side note, trust me, Dummit or Fraileigh are not what you want.

If you're interested in this sort of thing, I'd recommend you look at abstract algebra later. There's lots of proofs that certain constructions are impossible with it. This book is a pretty accessible introduction.

"A Book of Abstract Algebra" by Charles C. Pinter is nice, from what I've seen of it--which is about the first third. I'm going through it in an attempt to relearn the abstract algebra I've forgotten.

I was using Herstein (which was what I learned from the first time), and was doing fine, but saw the Pinter book at Barnes & Noble. I've found it is often helpful when relearning a subject to use a different book from the original, just to get a different approach, so gave it a try (it's a Dover, so was only ten bucks).

What is nice about the Pinter book is that it goes at a pretty relaxed pace, with a good variety of examples. A lot of the exercises apply abstract algebra to interesting things, like error correcting codes, and some of these things are developed over the exercises in several chapters.

You don't have to be a prodigy to be able to understand some real mathematics in middle school or early high school. By 9th grade, after a summer of reading calculus books from the local public library, I was able to follow things like Niven's proof that pi is irrational, for instance, and I was nowhere near a prodigy.

Dummit and Foote's Abstract Algebra is an excellent book for the algebra side of things. It can be a little dense, but it's chock full of examples and is very thorough.

To help get through the first ten or so chapters, Charles Pinter's A Book of Abstract Algebra is an incredible resource. It does wonders for building up an intuition behind algebra.

From the ground up, I dunno. But I looked through my amazon order history for the past 10 years and I can say that I personally

enjoyedreading the following math books:An Introduction to Graph Theory

Introduction to Topology

Coding the Matrix: Linear Algebra through Applications to Computer Science

A Book of Abstract Algebra

An Introduction to Information Theory

For discrete math I like Discrete Mathematics with Applications by Suzanna Epp.

It's my opinion, but Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers is much better structured and more in depth than How To Prove It by Velleman. If you follow everything she says, proofs will jump out at you. It's all around great intro to proofs, sets, relations.

Also, knowing some Linear Algebra is great for Multivariate Calculus.

This is how I learned logic, for computer science.

First chapter of this Discrete mathematics book in my discrete math class

https://www.amazon.ca/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328

Then, using The Logic Book for a formal philosophy logic 1 course.

https://www.amazon.ca/Logic-Book-Merrie-Bergmann/product-reviews/0078038413/ref=dpx_acr_txt?showViewpoints=1

The second book was horrid on itself, luckily my professor's academic lineage goes back to Tarski. He's an amazing Professor and knows how to teach...that was a god send. Ironically, he dropped the text and I see that someone has posted his openbook project.

The first book (first chapter), is too applied I imagine for your needs. It would also only be economically feasible if well, you disregarded copyright law and got a "free" PDF of it.

Try these books(the authors will hold your hand tight while walking you through interesting math landscapes):

Discrete Mathematics with Applications by Susanna Epp

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers

A Friendly Introduction to Number Theory Joseph Silverman

A First Course in Mathematical Analysis by David Brannan

The Foundations of Analysis: A Straightforward Introduction: Book 1 Logic, Sets and Numbers by K. G. Binmore

The Foundations of Topological Analysis: A Straightforward Introduction: Book 2 Topological Ideas by K. G. Binmore

Introductory Modern Algebra: A Historical Approach by Saul Stahl

An Introduction to Abstract Algebra VOLUME 1(very elementary)

by F. M. Hall

There is a wealth of phenomenally well-written books and as many books written by people who have no business writing math books. Also, Dover books are, as cheap as they are, usually hit or miss.

One more thing:

Suppose your chosen author sets the goal of learning a, b, c, d. Expect to be told about a and possibly c explicitly. You're expected to figure out b and d on your own. The books listed above are an exception, but still be prepared to work your ass off.

>My first goal is to understand the beauty that is calculus.

There are two "types" of Calculus. The one for engineers - the plug-and-chug type and the theory of Calculus called Real Analysis. If you want to see the actual beauty of the subject you might want to settle for the latter. It's rigorous and proof-based.

There are some great intros for RA:

Numbers and Functions: Steps to Analysis by Burn

A First Course in Mathematical Analysis by Brannan

Inside Calculus by Exner

Mathematical Analysis and Proof by Stirling

Yet Another Introduction to Analysis by Bryant

Mathematical Analysis: A Straightforward Approach by Binmore

Introduction to Calculus and Classical Analysis by Hijab

Analysis I by Tao

Real Analysis: A Constructive Approach by Bridger

Understanding Analysis by Abbot.

Seriously, there are just too many more of these great intros

But you need a good foundation. You need to learn the basics of math like logic, sets, relations, proofs etc.:

Learning to Reason: An Introduction to Logic, Sets, and Relations by Rodgers

Discrete Mathematics with Applications by Epp

Mathematics: A Discrete Introduction by Scheinerman

You should be able to see the textbook that is required by looking on your MyOSU page. This was the book used when I took it last year: https://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_1_2?crid=3TYI2C38O2DKB&keywords=susanna+epp+discrete+mathematics+with+applications+4th+edition&qid=1568344545&sprefix=susannah+epp%2Caps%2C175&sr=8-2

I should note that topics like graph theory, combinatorics, areas otherwise under the "discrete math" category, don't really require calculus, analysis, and other "continuous math" subjects to learn them. Instead, you can get up to college level algebra, then get a book like

Discrete Mathematics and Its Applications Seventh Edition (Higher Math) https://www.amazon.com/dp/0073383090/ref=cm_sw_r_cp_api_U6Zdzb793HMA7

Or the more highly regarded but less problem set answers,

Discrete Mathematics with Applications https://www.amazon.com/dp/0495391328/ref=cm_sw_r_cp_api_d7ZdzbQ77B65P

This will be enough to tackle ideas from discrete math. I'd recommend reading a book on logic to help with proof techniques and the general idea for rigorously proving statements.

Gensler is a great one but can require a computer if you want more extensive feedback and problem sets.

I personally didn't find discrete maths difficult, but I know it's the big hurdle for most people. Also since my degrees were primarily in mathematics, discrete maths wasn't my first proof-based subject so my experience is very different from most people.

I certainly don't have a comprehensive background in computer science, I've only taken 4 computer science subjects in my 5 years of university education and find my training in mathematics to be highly useful for programming at work and self-study of computer science.

If you can understand and absorb the first four chapters of Discrete Mathematics with Applications (only ~200 pages and should be available in any Uni library) then you'll be well set up for most of the maths that seems to trip people up.

This is the textbook we used and it was incredibly dry (and expensive). I highly recommend this book to ease you into it.

This is the book we are using for our class.

Is the book for 225 necesary? The book store said that there were no required materials for the class but I came across this one several times Discrete Mathematics with Applications 4th Edition

You can read the "Highlights of the Fourth Edition" on Page xvii through Amazon's preview.

Edit: This Amazon review is also relevant to you:

> I've taught discrete math from the 3rd Edition of this book at least 6 times, and struggled with several issues. (The textbook for our Discrete Math course is chosen by a committee in our department.) Much of a discrete math course involves looking closely at some very simple mathematics. Most of the mathematics is already known to a typical university freshman; what a set is, what a prime is, what an ordered pair is, etc. Of course they have had little rigor in these elementary topics, but still, they have the notions and vocabulary. The 3rd Edition pretended that sets, e.g., did not exist until one finally arrived at the chapter on sets. It's unnatural to lecture one's way through two chapters on logic and a chapter on techniques of proof, without being able to draw on simple examples from set theory. One gets tired quickly of examples of dogs and cats in highly artificial situations, and would like to say something about primes or the set of even integers.

>The 4th Edition corrects this problem by the addition of an introductory chapter which fixes the vocabulary and notation. This was a needed change. The 3rd Edition required considerable acrobatics in avoiding words like "is an element of" until Chapter 5 (Set Theory.) Really? I'm supposed to cover the proof technique of "division into cases" and I can't say "the set of integers of the form 4k+1?" So good change.

>Every semester, I get e-mails from my students asking if the previous edition of the text will suffice for my course. Usually, I say yes. In the case of my discrete math course, I'll have to say no. The modifications of this text are substantial. Besides the above, the old Chapter 8 (Recursion) is now incorporated into the new (much expanded) Chapter 5 (Sequences and Induction.) That is also a sensible change.

>My remaining complain about the text is that it's a bit condescending. I think it's bad form to always present mathematics apologetically. "There, there now, I know it's difficult, but we'll go extremely slowly and take tiny, tiny bites covered in catsup so you can scarcely taste them." There's no need for us at the university level to re-enforce the bad attitudes the students learned in high school. It's math. It's hard. You can do it, not because math is made easy, but because you are, in fact, clever enough.

>I would not have recommended the 3rd Edition to anyone, but I would recommend the 4th. I'm very happy with the changes.

Yes, the arrow is obvious when you stop to think about it, but everything becomes obvious after given enough thought. If they had used "=" it would have required slightly less thought and made it easier on the reader. What is the downside? I had no trouble reading the psuedo code, I just take issue with the useless proof ridden overly dense textbooks. You're saying that because it's possible to understand something, we should make no effort to make it easier to understand? This is where a lot of textbooks fail, in my opinion.

And just because a text is easier to understand doesn't make it dumbed down. I had a discrete math class that used this textbook:

http://www.amazon.com/Discrete-Mathematics-Computer-Scientists-Cliff/dp/0132122715/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1345561997&amp;sr=1-1&amp;keywords=discrete+math+for+computer+scientists

It was horribly dense and consisted of proof after proof with no real world examples. I could have learned from it if I so chose to, but I'd rather not spend 30 minutes parsing each page for what they are actually trying to teach me. I instead downloaded:

http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_1_2?ie=UTF8&amp;qid=1345561973&amp;sr=8-2&amp;keywords=susanna+epp

And got a 95 in the class. Did I learn less because I used an easier textbook? I would say that I actually learned more, because it took significantly less time to learn the concepts presented, leaving me with more time to learn overall.

Nowhere is this disparity more clear than in data structures and algorithms books.

The book that really helped me prepare for CS 6505 this fall was Discrete Mathematics with Applications by Susanna Epp. I found it easy to digest and it seemed to line up well with the needed knowledge to do well in the course.

Richard Hammack's Book of Proof also proved invaluable. Because so much of your success in the class relies on your ability to do proofs, strengthening those skills in advance will help.

Usual hierarchy of what comes after what is simply artificial. They like to teach Linear Algebra before Abstract Algebra, but it doesn't mean that it is all there's to Linear Algebra especially because Linear Algebra is a part of Abstract Algebra.

Example,

Linear Algebra for freshmen: some books that talk about manipulating matrices at length.

Linear Algebra for 2nd/3rd year undergrads: Linear Algebra Done Right by Axler

Linear Algebra for grad students(aka overkill): Advanced Linear Algebra by Roman

Basically, math is all interconnected and it doesn't matter where exactly you enter it.

Coming in cold might be a bit of a shocker, so studying up on foundational stuff before plunging into modern math is probably great.

Books you might like:

Discrete Mathematics with Applications by Susanna Epp

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers

Building Proofs: A Practical Guide by Oliveira/Stewart

Book Of Proof by Hammack

Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al

How to Prove It: A Structured Approach by Velleman

The Nuts and Bolts of Proofs by Antonella Cupillary

How To Think About Analysis by Alcock

Principles and Techniques in Combinatorics by Khee-Meng Koh , Chuan Chong Chen

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!) by Carol Ash

Problems and Proofs in Numbers and Algebra by Millman et al

Theorems, Corollaries, Lemmas, and Methods of Proof by Rossi

Mathematical Concepts by Jost - can't wait to start reading this

Proof Patterns by Joshi

...and about a billion other books like that I can't remember right now.

Good Luck.

Course Name: Discrete Structures

Course Link: http://uncw.edu/csc/courses-133.html

Text Book: http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1289513076&amp;sr=1-1

Comments: It wasn't that book when I was there back in the 90's though. We were using a book written by a UNC-W professor and published in-house. But I took another course later, using the 3rd edition of the Susanna Epp book, and I have to say, I prefer Epp's book. But

holy fuckwould you look at the price for the current edition? WTF?!??Also, Dr. Berman is nice enough, but is one of the most boring professors ever born... talk about the stereotypical dry, boring, dull, monotone delivery... this guy has it perfected.

I know this isn't what you're looking for, but I looked into this quite a bit when I used to go out stargazing myself. In all honesty apps aren't the best for this properly.

If the 2 of you are actually getting interested in the night sky then I would say buy yourself the Turn Left at Orion book.

Stellarium is an amazing free computer program that you can use to do your homework beforehand and see what you'll actually be looking at that night.

Some cheap binoculars and tripod would add a lot to the experience as well.

----------

As for the answer to the question you're actually asking:

Google Sky Maps is what you need for some quick and dirty casual sky scanning.

The other must have app is Astro Panel. It'll tell you when sky viewing conditions are good (it's pointless going out when conditions are terrible and not really seeing much)

-------------

If the trip is to go out and set the mood to make a move on a girl you like then all of this will only get in the way and there's a lot to be said for just going out with a picnic blanket and a warm blanket to look at the plain night sky to set the mood.

You could look up when there's a meteor shower to give you something to see without any equipment or sky map.

When you do buy a telescope get this book: http://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972/ref=sr_1_1?ie=UTF8&amp;qid=1398695492&amp;sr=8-1&amp;keywords=turn+left+at+orion

It is a MUST HAVE for beginning observing.

For a starter book to get the basics of stargazing, I would recommend Nightwatch: A Practical Guide To Viewing the Universe or Turn Left At Orion. They don't have real detailed sky maps, but they give good representations of some of the major constellations and names.

For star maps, I use Sky & Telescope's Pocket Sky Atlas or Orion's DeepView Star Map. These ones are good for more detailed star maps and require a few basics to figure out. Or you can just match the stars up to known stars and just stumble your way around (which is not a bad learning method either).

You can't go wrong with a Dobsonian in the 6"-8"-10" range. At the lower end they'll be less expensive and more portable, but at the higher end you'll be able to see more.

http://www.telescope.com/Telescopes/Dobsonian-Telescopes/Classic-Dobsonians/pc/1/c/12/13.uts

I have an Orion 8" Dobsonian. They also sell Intelliscope models that will assist you in finding objects. I like finding things on my own, by star-hopping, but it takes a little patience and experience. These books will help:

http://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972

http://www.amazon.com/NightWatch-Practical-Guide-Viewing-Universe/dp/155407147X

I recommend getting one with at least two eyepieces, or at least one eyepiece and a Barlow, so you'll have a choice of magnifications.

And whether or not you get a telescope, a pair of binoculars is a good thing to have. 7x50s are nice and easy to use without a tripod. 10x50s will show you a little more but are a little harder to hold steady. Anything larger and you'll probably want a tripod for them. I have 10x50s and am considering getting these:

http://www.amazon.com/Celestron-SkyMaster-Binoculars-Tripod-Adapter/dp/B00008Y0VN

While it's not directly related to the telescope, if you are buying from amazon the Orion 27193 XT6 Classic Dobsonian Telescope and Beginner Barlow Kit isn't going to be in stock for another 3 weeks.

In my opinion you will not be missing much to get the one without the additional barlow lens+red light.

Instead I would spend that extra $20 the way u/schorhr's recommended to me by buying the book, Turn Left at Orion. It is an awesome book that teaches you a ton about all different aspects of astronomy including what you can see in a telescope, and where/when you can find it.

I guess it really depends on how familiar you are with the night sky - but there's one book that's literally invaluable for astronomers of all levels - Turn Left At Orion - there's no finer book, quite frankly, and the authors are an inspiration to me. If my books were anywhere near as good as theirs, I'd be very pleased and proud.

(Get the larger, spiral bound edition - http://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972/ref=sr_1_1?ie=UTF8&amp;qid=1414368749&amp;sr=8-1&amp;keywords=turn+left+at+orion)

I would also buy Astronomy Hacks - there are a TON of tips and tricks in there and, again, it's aimed at astronomers of all levels.

(http://www.amazon.com/Astronomy-Hacks-Tools-Observing-Night/dp/0596100604/ref=sr_1_1?ie=UTF8&amp;qid=1414368782&amp;sr=8-1&amp;keywords=astronomy+hacks)

I had an Orion XT 4.5" Dobsonian and loved it. Celestrons are also excellent and both companies have equipment that are reasonably priced and well suited to amateurs of all levels. I'd start with something relatively small, like a 4" or 6" reflector and then go from there.

Beyond that, I would highly recommend joining a local club or, at the very least, ask a question here on Reddit or join a group in Facebook.

The two I like the most are the Telescope Addicts (https://www.facebook.com/groups/telescopeaddicts/) and Astronomy 4 Beginners. (https://www.facebook.com/groups/astro4beginners/)

I hope this helps. Feel free to email me at [email protected] at any time. At some point in the nearish future I'd like to write an astronomy book for suburban astronomers (especially beginners) but I'm not sure when that might happen!

(In the meantime, have a look at my other book, 2015 An Astronomical Year - the Kindle version has a lot of graphics and text highlighting the best naked eye sights throughout the year - http://www.amazon.com/dp/B00LVEUJI2/)

Clear skies!

The Z10 would be a great scope. I have the Z12, and I love it. It's a lot to handle though. The Z10 would give you some more mobility and wouldn't take up too much space. A 10 is still a great light bucket and will give you wonderful views of lots of fun objects.

There are myriad resources to get you going on what to see and when to see it. You can check out earthsky.org for a day-by-day update on what's happening in the sky. Telescopius is another great resource. Also, grab yourself a copy of Turn Left at Orion. It'll help you get acquainted with the night sky.

The Bahamian sky should treat you quite nicely. Just be patient with the equipment and the hobby. Learning takes time.

Congrats on your first nebula! I'm always amazed at the ambivalence some people have about astronomical things. Years ago when comet Hale-Bopp was riding high, my ex and I had gone to visit another couple who lived in a pretty dark area. One of them knew my love of Astronomy, and asked about the comet. "It's up right now and spectacular!" was my reply.

We went outside to take a look... except for my ex, who complained that it was chilly and that she just wasn't interested. The other couple loved it, and we were out for a while looking and talking. When we went back in, my ex said "That took a while! How long does it take to look at the sky?"

BTW, you may be interested in my favorite book for small telescope owners: "Turn Left at Orion: Hundreds of Night Sky Objects to See in a Home Telescope - and How to Find Them" by Guy Consolmagno.

Your teenaged relative could learn how to navigate the stars, and identify constellation locations by sight with a quality pair of binoculars and a book like Turn Left at Orion.

For an even more involved and rewarding gift, check out local telescope making workshops.

You only need a mirror blank (typically made of pyrex glass) and some grit, so he can certainly do this at home when he's not at the workshop. An 8" mirror will take about 40 hours of grinding and polishing the surface, which ends up being optically superior to machine-made mirrors.

Here is what I bought:

Orion 5691 LaserMate Deluxe II Telescope Laser Collimator https://www.amazon.com/dp/B008XEGXMO/ref=cm_sw_r_awd_iXYTub1Z3HSD4

Celestron Accessory Kit https://www.amazon.com/dp/B00006RH5I/ref=cm_sw_r_awd_MYYTub0G8V843

Turn Left at Orion: Hundreds of Night Sky Objects to See in a Home Telescope - and How to Find Them https://www.amazon.com/dp/0521153972/ref=cm_sw_r_awd_bZYTub0ZKHRFC

I got the accessory kit as a Christmas present. I wanted to get a range of eyepieces then upgrade the ones that would benefit, I'm going to get the eyepiece mentioned by someone else.

Orion 8920 6mm Expanse Telescope Eyepiece https://www.amazon.com/dp/B0000XMXXO/ref=cm_sw_r_awd_g0YTub1471RN7

As I'm having issues with my current 6mm eyepiece . Great scope!

I highly recommend "Turn left at Orion" - it's a book that's available here: http://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972/ref=sr_1_1?ie=UTF8&amp;qid=1377269030&amp;sr=8-1&amp;keywords=turn+left+at+orion

It lists, by season, what's in the sky, which constellation it's in, and rates them for binoculars, small telescopes, and Dobs. Doesn't have a ton of objects, but really gives a good start to people just getting into the hobby who are looking for things to see.

I'd strongly advise against getting a goto dob. They dont work that well and for the most part make it less likely you will use your scope.

Instead teach yourself how to star hop using:

https://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972

Then mount a telrad quick finder on your scope:

https://www.amazon.com/Telrad-Finder-Sight/dp/B0000ALKAN/ref=sr_1_2?ie=UTF8&amp;qid=1502122336&amp;sr=8-2&amp;keywords=rigel+quickfinder

Dobs are all about setting the scope on the ground and getting to viewing quickly and easily, a cheap goto mount will just fight you in doing that.

Get yourself a good star chart, observing guide or phone app. Learn about what you can see in the sky and then point your telescope, see what you can find.

http://www.amazon.co.uk/Astronomy-Eyewitness-Companions-Ian-Ridpath/dp/1405312912/ref=sr_1_1?ie=UTF8&amp;qid=1345918376&amp;sr=8-1

http://www.amazon.co.uk/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972/ref=sr_1_1?ie=UTF8&amp;qid=1345918384&amp;sr=8-1

Planets - Jupiter rises quite late at night at the moment. Saturn sets not long after sunset. The Moon would be a good target to start off with.

DSOs - Some will be harder to locate that others. With a Dobsonian, you can learn to starhop and it becomes easier with practice. Some will look amazing, others will just be faint fuzzies.

Others have already mentioned it but join an astronomy club and download Stellarium. Here's a couple book suggestions:

Turn Left at Orion will get you familiar with some of the more interesting objects to look at in the night's sky. This is definitely a good place to start. You also want to pick up a star atlas to help you navigate the sky and find some of the dimmer objects in the sky. A favorite is Sky and Telescope's Pocket Star Atlas. Another favorite for new astronomers is Nightwatch which will educate you a bit more about astronomical bodies and the night sky.

North is a better viewing direction for me, and M81/82 were the first galaxies I ever saw through the telescope. They've been the only galaxies I can fairly consistently see from my backyard.

M51 looks like a very light gray fuzz in my light polluted (B6-7) backyard. If see conditions aren't really good it's very easy to miss. But, if I go a short distance away (B4 skies) it starts to get some more structure (though admittedly still not very much). I found M51 easier to see than M101, but relatively similarly sized.

Do you have the Turn Left at Orion book? They have great tips for locating tons of DSOs as well as what to expect through various types of scopes.

I just got Turn Left At Orion that everyone on here recommends from Amazon. It was on sale for only $17 and it was worth every penny for finding interesting things in the night sky. A good star chart is nice as well, learning where stuff is makes the sky that much easier to enjoy.

This book:

http://www.amazon.com/gp/aw/d/0521153972/ref=redir_mdp_mobile

The deck corresponding to the intellectual property book has ~325 cards.

The deck corresponding to IEA has ~400 cards.

The deck corresponding to linear algebra has ~1000 cards. That seems weird to me, since I feel that I make fewer cards for math books; most of the extra time comes from doing a lot of scratch work. Weird. In addition to timing, I've more recently started keeping track of how many Ankis I've added each section, so maybe I'll have more insight there later. We'll see.

And please message me when you start doing math! If you're looking towards advanced mathematics (beyond calculus/linear algebra-for-engineers), I recommend starting with either Mathematics for Computer Science (review) or, if you really have no interest in doing that, How to Prove It.

ummarycoc has a good point. Snoop around his room and see if he already has How To Prove it: A Structured Approach. Someone bought this book for me and I return to it frequently.

Your mileage with certifications may vary depending on your geographical area and type of IT work you want to get into. No idea about Phoenix specifically.

For programming work, generally certifications aren't looked at highly, and so you should think about how much actual programming you want to do vs. something else, before investing in training that employers may not give a shit about at all.

The more your goals align with programming, the more you'll want to acquire practical skills and be able to demonstrate them.

I'd suggest reading the FAQ first, and then doing some digging to figure out what's out there that interests you. Then, consider trying to get in touch with professionals in the specific domain you're interested in, and/or ask more specific questions on here or elsewhere that pertain to what you're interested in. Then figure out a plan of attack and get to it.

A lot of programming work boils down to:

Using appropriate data structures, and algorithms (often hidden behind standard libraries/frameworks as black boxes), that help you solve whatever problems you run into, or tasks you need to complete. Knowing when to use a Map vs. a List/Array, for example, is fundamental.Basic logic, as well assystems designandOOD(and a sprinkle of FP for perspective on how to write code with reliable data flows and cohesion), is essential.As a basic primer, you might want to look at Code for a big picture view of what's going with computers.

For basic logic skills, the first two chapters of How to Prove It are great. Being able to think about conditional expressions symbolically (and not get confused by your own code) is a useful skill. Sometimes business requirements change and require you to modify conditional statements. With an understanding of Boolean Algebra, you will make fewer mistakes and get past this common hurdle sooner. Lots of beginners struggle with logic early on while also learning a language, framework, and whatever else. Luckily, Boolean Algebra is a tiny topic. Those first two chapters pretty much cover the core concepts of logic that I saw over and over again in various courses in college (programming courses, algorithms, digital circuits, etc.)

Once you figure out a domain/industry you're interested in, I highly recommend focusing on one general purpose programming language that is popular in that domain. Learn about data structures and learn how to use the language to solve problems using data structures. Try not to spread yourself too thin with learning languages. It's more important to focus on learning how to get the computer to do your bidding via one set of tools - later on, once you have that context, you can experiment with other things. It's not a bad idea to learn multiple languages, since in some cases they push drastically different philosophies and practices, but give it time and stay focused early on.

As you gain confidence there, identify a simple project you can take on that uses that general purpose language, and perhaps a development framework that is popular in your target industry. Read up on best practices, and stick to a small set of features that helps you complete your mini project.

When learning, try to avoid haplessly jumping from tutorial to tutorial if it means that it's an opportunity to better understand something you really should understand from the ground up. Don't try to understand everything under the sun from the ground up, but don't shy away from 1st party sources of information when you need them. E.g. for iOS development, Apple has a lot of development guides that aren't too terrible. Sometimes these guides will clue you into patterns, best practices, pitfalls.

Imperfect solutions are fine while learning via small projects. Focus on completing tiny projects that are just barely outside your skill level. It can be hard to gauge this yourself, but if you ever went to college then you probably have an idea of what this means.

The feedback cycle in software development is long, so you want to be unafraid to make mistakes, and prioritize finishing stuff so that you can reflect on what to improve.

How to Prove It by Vellemen is a superb introduction to what proofs are, and how to make them.

Keep in mind certain proof based courses can be frustrating to some students (discrete math and real analysis) as these classes often make formal concepts students may understand intuitively. Abstract Algebra or Topology may give you a more accurate idea of your feelings towards math.

Honestly, I think you should be more realistic: doing everything in that imgur link would be insane.

You should try to get a survey of the first 3 semesters of calculus, learn a bit of linear algebra perhaps from this book, and learn about reading and writing proofs with a book like this. If you still have time, Munkres'

Topology, Dummit and Foote'sAbstract Algebra, and/or Rudin'sPrinciples of Mathematical Analysiswould be good places to go.Roughly speaking, you can theoretically do intro to proofs and linear algebra independently of calculus, and you only need intro to proofs to go into topology (though calculus and analysis would be desirable), and you only need linear algebra and intro to proofs to go into abstract algebra. For analysis, you need both calculus and intro to proofs.

Depends on what you are looking for. You might not be aware that the concepts in that book are literally the foundations of math. All math is (or can be) essentially expressed in set theory, which is based on logic.

You want to improve math reasoning, you should study reasoning, which is logic. It's really not that hard. I mean, ok its hard sometimes but its not rocket science, its doable if you dedicate real time to it and go slowly.

Two other books you may be interested in instead, that teach the same kinds of things:

Introduction to Mathematical Thinking which he wrote to use in his Coursera course.

How to Prove It which is often given as the gold standard for exactly your question. I have it, it is fantastic, though I only got partway through it before starting my current class. Quite easy to follow.

Both books are very conversational -- I know the second one is and I'm pretty sure the first is as well.

What books like this do is teach you the fundamental logical reasoning and math structures used to do things like construct the real number system, define operations on the numbers, and then build up to algebra step by step. You literally start at the 1+1=2 type level and build up from there by following a few rules.

Also, I just googled "basic logic" and stumbled across this, it looks like a fantastic resource that teaches the basics

without any freaky looking symbols, it uses nothing but plain-English sentences. But scanning over it, it teaches everything you get in the first chapter or two of books like those above. http://courses.umass.edu/phil110-gmh/text/c01_3-99.pdfHonestly if I were starting out I would love that last link, it looks fantastic actually.

Read this book: http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316/ref=asap_bc?ie=UTF8

And work through this book in its entirety: http://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1463201632&amp;sr=1-1

Probably something on coursera; however, I really recommend this gem of a book, http://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/ref=sr_1_1?s=books&amp;ie=UTF8&amp;qid=1458411780&amp;sr=1-1&amp;keywords=how+to+prove+it .

Get the book [How to Prove It: A Structured Approach by Daniel J. Velleman] (http://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995) it will teach you how to write, and I think more importantly, read proofs.

How comfortable are you with proofs? If you are not yet comfortable, then read this: How to Prove It: A Structured Approach

I may be in the minority here, but I think that high school students should be exposed to statistics and probability. I don't think that it would be possible to exposed them to full mathematical statistics (like the CLT, regression, multivariate etc) but they should have a basic understanding of descriptive statistics. I would emphasize things like the normal distribution, random variables, chance, averages and standard deviations. This could improve numerical literacy, and help people evaluate news reports and polls critically. It could also cut down on some issues like the gambler's fallacy, or causation vs correlation.

It would be nice if we could teach everyone mathematical statistics, the CLT, and programming in R. But for the majority of the population a basic understanding of the key concepts would be an improvement, and would be useful.

EditAt the other end of the spectrum, I would like to see more access to an elective class that covers the basics of mathematical thinking. I would target this at upperclassmen who are sincerely interested in mathematics, and feel that the standard trig-precalculus-calculus is not enough. It would be based off of a freshman math course at my university, that strives to teach the basics of proofs and mathematical thinking using examples from different fields of math, but mostly set theory and discrete math. Maybe use Velleman's book or something similar as a text.How to Prove it by Velleman seems to be right up your alley.

Thanks for the answer!

Glad to hear about Spivak! I've heard good things about that textbook and am looking forward to going through it soon :). Are the course notes for advanced algebra available online? If so, could you link them?

Is SICP used only in the advanced CS course or the general stream one, too? (last year I actually worked my way through the first two chapters before getting distracted by something else - loved it though!) Also, am I correct in thinking that the two first year CS courses cover functional programming/abstraction/recursion in the first term and then data structures/algorithms in the second?

That's awesome to know about 3rd year math courses! I was under the impression that prerequisites were enforced very strongly at Waterloo, guess I was wrong :).

As for graduate studies in pure math, that's the plan, but I in no way have my heart set on anything. I've had a little exposure to graph theory and I loved it, I'm sure that with even more exposure I'd find it even more interesting. Right now I think the reason I'm leaning towards pure math is 'cause the book I'm going through deals with mathematical logic / set theory and I think it's really fascinating, but I realize that I've got 4/5 years before I will even start grad school so I'm not worrying about it too much!

Anyways, thanks a lot for your answer! I feel like I'm leaning a lot towards Waterloo now :)

How to Prove It is a nice introduction to writing proofs.

You should absolutely not give up.

None of this is groundbreaking, and a lot of it is pretty cliché, but it's true. Everyone struggles with math at some point. Einstein said something like "whatever your struggles with math are, I assure you that mine are greater."

As for specific recommendations,

make the most of this summer. The most important factor in learning math in my experience is "time spent actively doing math." My favorite math quote is "you don't learn math, you get used to it." I might recommend a book like How to Prove It. I read it the summer before I entered college, and it helped immensely with proofs in real analysis and abstract algebra. Give that a read, and I bet you will be able to prove most lemmas in undergraduate algebra and topology books, and solve many of their problems. Just keep at it!http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995

helps with the first part of the class. the stuff after that I would suggest just having good google-fu.

Math isn't going to be like the math classes you've already taken. It's a lot of writing and logic and very little calculating. If you go for mathematical sciences, you'll probably take more classes that involve calculations, but you won't make it that far if you can't handle proofs.

Check out this book: http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995

The full book is first-page googleable. If you find that material interesting, you'll probably enjoy being a math major.

To learn basic proof writing I highly recommend How to Prove It by Velleman.

I study topology and I can give you some tips based on what I've done. If you want extra info please PM me. I'd love to help someone discover the beautiful field of topology. TLDR at bottom.

If you want to study topology or knot theory in the long term (actually knot theory is a pretty complicated application of topology), it would be a great idea to start reading higher math ASAP. Higher math generally refers to anything proof-based, which is pretty much everything you study in college. It's not

thatmuch harder than high school math and it's indescribably beneficial to try and get into it as soon as you possibly can. Essentially, your math education really begins when you start getting into higher math.If you don't know how to do proofs yet, read How to Prove It. This is the best intro to higher math, and is not hard. Absolutely essential going forward. Ask for it for the holidays.

Once you know how to prove things, read 1 or 2 "intro to topology" books (there are hundreds). I read this one and it was pretty good, but most are pretty much the same. They'll go over definitions and basic theorems that give you a rough idea of how topological spaces (what topologists study) work.

After reading an intro book, move on to this book by Sutherland. It is relatively simple and doesn't require a whole lot of knowledge, but it is definitely rigorous and is definitely necessary before moving on.

After that, there are kind of two camps you could subscribe to. Currently there are two "main" topology books, referred to by their author's names: Hatcher and Munkres. Both are available online for free, but the Munkres pdf isn't legally authorized to be. Reading either of these will make you a topology god. Hatcher is all what's called algebraic topology (relating topology and abstract algebra), which is super necessary for further studies. However, Hatcher is hella hard and you can't read it unless you've really paid attention up to this point. Munkres isn't necessarily "easier" but it moves a lot slower. The first half of it is essentially a recap of Sutherland but much more in-depth. The second half is like Hatcher but less in-depth. Both books are outstanding and it all depends on your skill in specific areas of topology.

Once you've read Hatcher or Munkres, you shouldn't have much trouble going forward into any more specified subfield of topology (be it knot theory or whatever).

If you actually do end up studying topology, please save my username as a resource for when you feel stuck. It really helps to have someone advanced in the subject to talk about tough topics. Good luck going forward. My biggest advice whatsoever, regardless of what you study, is

read How to Prove It ASAP!!!TLDR: How to Prove It (!!!) -> Mendelson -> Sutherland -> Hatcher or Munkres