TITLE: Where do I start learning Higher Mathematics?
QUESTION [21 upvotes]: I am 17 years old and I would like to begin learning Mathematics. I am only familiar with Algebra and a bit of Geometry. Do I need to learn Calculus next, or should I try linear algebra? I find myself very interested in number theory. Is there anywhere I can see some sort of tree that shows me prerequisites for different Mathematical studies. I also want to know if there are any websites or resources that can teach me Math formally, using proofs. In high school we never learned math formally or rigorously. Thanks.
Also any books I could get would be appreciated. Keep in mind I am trying to start off, I only know basic Algebra right now, like functions, polynomials, and systems of equations.

REPLY [2 votes]: If you're serious about learning math yes, you have to learn calculus (as well as many other things, but calculus is definitely one of the fundamental first steps).
I am not going to suggest any modern tools, such as online classes etc. I think other people covered that quite well. I will be old-fashioned here and suggest just a book. Yeah, made of paper. And a quite old one actually, that nevertheless is still considered one of the best introductory texts in calculus/analysis.
It is not an easy book. It might be a challenge to start off with it actually, but somehow I have the feeling that it's one of those books that could really make the difference in the future. It's a book that forces you to think. A book that, in order to understand, you have to go through line by line and spend time on it, trying to grasp every concept and filling eventual gaps left here and there by the author (sometimes intentionally, maybe sometimes not).
As I said, it might not be an easy book... well no, it certainly isn't, but it starts from the very basics after all. So if you have some basic math training and you are up for a challenge I think you can have a go with it (I am assuming that you are familiar at least with basic math terminology and symbolism).
Ok, the book I am talking about is Walter Rudin's Principles of Mathematical Analysis. You can have a look here:
http://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X/ref=mt_hardcover?_encoding=UTF8&me=
If you browse a bit through the reviews you can have a feeling of what I'm talking about here. It's a book that even experienced mathematicians love to read. I might be going out on a limb suggesting this, true, but I believe it could be the book that will actually shape you into a real mathematician. Some undergrads may not like it because they say it's too advanced. Unlike you though, they probably wouldn't post questions on math.stackexchange about where to start off with higher mathematics. If your passion is genuine, this might be the book for you. Good luck.