Well, you can do one of two things (or both really).  You can either prepare yourself for introductory math courses at the college level or start to study pure mathematics. 

Typically when you get into college, you have one to two more years of calculus before you get into pure maths. If you have covered integral calculus up to integration by parts, integration around the axis,and the like, then you would be ready for multi variable calculus and differential equations.  You should also be studying introductory linear algebra and vector geometry during these.  Once you finish multi variable calculus, you can move on to vector calculus, which is like vector geometry and multi variable calculus combined into one.  This was my first 3 semesters of math courses.

This type of calculus typically falls under applied mathematics.  It is what the engineers and the physicists use to do their work.  On the other hand, there is pure mathematics.  This starts off with an introduction to proofs.  After that you can go into a variety of introductory subjects: Modern Algebra, Advanced Calculus (a pure (theoretical) approach to the real numbers), Combinatorics, Discrete math, Linear Algebra, and probably others I can't think of at this moment.

You can go right into proofs without learning calculus at the college level.  Why my university requires differential equations and multi variable calculus for an intro to proofs class, I haven't got a clue.  So it is really up to you.  Myself, I love the pure mathematics, and I have a distaste for applied such as calculus.

An introductory course in linear algebra would also cover transpositions, determinants, properties of determinants, solving systems of equations, and perhaps even an introduction to eigenvalues and eigenvectors.

As for a book for multi variable calculus, I'm not certain.  The book I used was Calculus with Early Transcendentals by Stewart, but this book is big enough to take you through introductory and second semester calc, multi variable calculus, and even has a section on differential equations.

I touched on in breifly in my Pre-cal class, but it didn't really impress me. Maybe a second go would be a good idea.

Identity wrote:

It's never a bad time to study number theory , if you can't find anything else to do, investigate that

How would I go about that? Do you know of any good books?

Do you know of any (non-textbooks) books that would be a good place to start with intro to proofs? What's in an intro to proofs class? I've read many proofs (mostly famous ones) and they didn't seem to difficult to follow. Is there something more to it?

Last edited by bossk171 (2007-09-19 04:07:07)

Maybe I'm not fully understanding the depth of what you're saying, but I feel like all of this is stuff I already know.

Last edited by bossk171 (2007-09-19 07:53:56)

Point made. I don't understand a word of that.

Positive, even/odd, divisible, functions, and relations are all very fimiliar terms, but I guess their meaning runs a little deeper than I realize.

Just to let you know that was a "I have a firm grasp on everything that should be learned in an intro to proofs course" type question.  It is probably a bit advanced for someone who has just taken a proofs course, although not be too much.