Math & Science

I'm not too well read in scientific literature, and I'm not sure where to start; are any of you familiar with books about mathematics and science? If so, suggest some of the best you have read.

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james gleick- the information

If you are interested in the philosophy of mathematics, read "Gödel's Proof", by Ernest Nagel and James R. Newman. A relatively non-technical book about one of the hardest subjects of maths.

If you want to really learn college maths with textbooks, I recommend the MIT OpenCourseWare courses as the simplest effective way to master entry-level maths (calculus/linear algebra), but you can use a lot of textbooks for side reading and exercises. Keisler, Meyer and Simmons (all pic related) are good; I recommend Stewart, Spivak and Strang as well.

When you master those, study Rudin's "Principles of Mathematical Analysis". After that, you'll have the knowledge of a junior maths student and be able to fully understand advanced books on topology, algebra, geometry etc.

I haven't studied biology after leaving high school and, for chemistry and physics, I used Halliday and Atkins; both are very good, but your pic related are probably good as well.

For "general reader science", you can't go wrong with the meme books, even though a lot of people in here disregard them. Dawkins's "The Selfish Gene", Sagan's "The Demon-Haunted World", Hawking's "A Brief History of Time" are all very inspirational and cathartic.

If you're up for a challenge, I suggest trying high-school-level maths olympiads training. I know 2 of the 3 proofs books on your image (Polya and Hammack) and they're very good for that. I also suggest Velleman's "How to Prove It", Shklarsky et al.'s "The USSR Olympiad Problem Book" and Bradley's "Problems in Geometry".

Hope that helped. Ask if you have any questions, and I hope you become as amazed with maths as I am. Good luck!

Ignore all the books on the fucking "guides" because they're fucking useless for self study. I can't imagine someone using fucking Lang for "Basic Mathematics." Don't even bother owning a book by lang until you're more than a little comfortable with algebra--and when you are, get his Algebra book as a reference.

If you have absolutely no training in math past precalc/trig I'd pick up "yet another book on analysis" which is a nice somewhat gentle introduction to the subject that works nicely for self study. Do all the fucking problems and read all the fucking concepts until they feel like you've learned nothing at all except that you can somehow do the problems in your sleep. Then pick up a copy of Axler's Linear algebra done right for the best intro to matrices/linear maps. Then get hutherford's linear algebra and that book will be all you need for linear algebra for the rest of your math career. You can also pick up Rudin at this point which is probably the most important book to jumping right into the material. The modern canon on topics covered in Analysis starts with Rudin. Get good at the fucking book at least up until chapter 9 or 10. There's tons of resources online, including youtube videos and step-by-step guides on Davis for doing it. Make sure you're comfortable with the real number line and some of the classic arguments used to prove results about it. Make sure you pay especially close attention to the topological arguments as well. The sooner you are comfortable with Topology the better. For your jump into actual analysis, I'd get Halmos, which is probably the best treatment, along with Stein/Stakarchi's new Princeton series books, which do an awesome job as supplements. Get familiar with the concepts of measure and integration in respect to it, as well as how topology of the real space interacts with the algebra of it. A lot of people will suggest Spivak but I'd honestly skip it and go straight to Calculus on Manifolds at this point if you want a good theoretical basis for multivariate calculus. The book might be a little terse if you've never seen higher dimensional integration (or anything that looks like stoke's theorem), so look online for more elementary applications (any standard multivariable calculus class, which pretty much amounts to one week of useful theoretic material). Let me know if you have any other, maybe more specific questions.

waht r ur credentials

I'll be graduating with a joint BA/MA in maths in one month, already accepted for a PhD program.

I don't understand - I'm using Lang with only pisspoor grade school math and it seems fine?

are you OP?

No just another math retard