Math newbie: what to read?

Question

Quick question for you all: what should a high school senior who intends to major in CS and math read to become familiar with proofs, calc, algorithms, etc?

I know that's incredibly broad, basically I'm just looking for any book that could be of use to me, because I am severely undereducated in math. I'm not bad at HS math, I get good grades, and I'm a fast learner, but I haven't had access beyond pre-cal and AP Stats, so I'm severely lacking (no trig, no calc, but I got into purdue!)

Any advice for me? I really need to learn this stuff, and I really want to. Thanks!

Edit: this question is on hold due to its opinion-based nature, so I'll try to edit and clarify a bit. Rather than suggesting the absolute best books for me to read and absolutely study, could you just tell me some books that were helpful to you and your understanding of high-level math? I don't know if that fits the format any better, but it should discourage any arguments over opinion.

Answer 1

I think that number theory and group theory are two subjects that are easy enough to understand with no prior knowledge and most importantly are very good for learning styles in proof writing.

Two good books.

Friendly Intro To Number Theory Silverman ISBN 9780321816191 Edition 4

Book Of Abstract Algebra Pinter ISBN 9780486474175 Edition 2

I hope this helps.

Answer 2

You need to learn trigonometry to understand calculus. You need to learn calculus to understand the set $\mathbb{R^n}$ and its properties. You need to learn those properties to prove things.

Pick up a Stewart's calculus book and begin there.

Oh yeah, and don't get frustrated if it takes you over three hours to understand a concept. That's uncommon, but it's more common to spend days on a concept. :)

Answer 3

One very important subject of mathematics you must learn is Linear Algebra. Calculus is a MUST because it is the foundation for computation. I recommend this book because a provides you a structured foundation for proof strategy. It is one that all higher mathematicians (even me) have read.

So, the path that I recommend to you is finish trigonometry, then Calculus, then get into Basic Set Theory, do Real and Complex Analysis with Multivariable Calculus, then do Linear Algebra. Once you have done that, you will have a VERY strong foundation. With a better foundation, your comprehension of concepts will come easier to you.

Let me know if you need anything else.

P.s., Congrats on getting into Purdue!

Answer 4

You should read Martin Gardner's books more than anything I think. They'll motivate you to learn mathematics far more than a standard text in some subject like trigonometry or basic calculus. Check out http://www.amazon.com/Colossal-Book-Mathematics-Paradoxes-Problems/dp/0393020231/ref=sr_1_1?s=books&ie=UTF8&qid=1419142855&sr=1-1&keywords=martin+gardner+math for instance.