What do I study next?

Senior in high-school, finishing up AP Calculus BC. I have a book that covers multivariable calculus, and a book on linear algebra. I'm working through both on my own, and it's going great. Unfortunately, the university I'll be going to won't accept the AP for credit, and I'll obviously need to take the multivariable calculus/linear algebra in a class to prove that I can do it. It'll take about a year for me to be able to actually be able to take any "new" courses in university, essentially. I don't doubt that these courses will be a challenge, it's just that I'd like to be doing something more.

I'm just a bit stumped on what I should be trying to study next. Should I just be attempting problems from contests? Or should I be moving ahead to try and tackle some new material?

This
http://www.amazon.com/Art-Problem-Solving-Basics-Solution/dp/B000TYF8ZE/ref=sr_1_1?ie=UTF8&s=books&qid=1238024912&sr=1-1

Then this
http://www.unl.edu/amc/a-activities/a7-problems/problemUSAMO-IMOarchive.shtml

And finally this
http://www.unl.edu/amc/a-activities/a7-problems/putnamindex.shtml

Once you have mastered these, you shall be a god among men.

Kid who thinks he is a smart faggot.

Here's rapidshares for a bunch of books I have that might be interesting.

>>2
>http://www.amazon.com/Art-Problem-Solving-Basics-Solution/dp/B000TYF8ZE/ref=sr_1_1?ie=UTF8&s=books&qid=1238024912&sr=1-1

Out of print and I can't find a torrent or rapidshare for it anywhere.  I've never seen it before, is it any good?

If you want to do contest problems here's a good starting point.  It's not too difficult, and by the end of it you should be much less intimidated by imo/putnam stuff:

http://rapidshare.com/files/213576842/Problem_Solving_Through_Problems_Larson_.djvu

Here's another problem solving book that seems to have a slightly broader focus than just contests:

http://rapidshare.com/files/213577152/The.Art.And.Craft.Of.Problem.Solving_2ed_Zeitz_0471789011.djvu

>Then this
>http://www.unl.edu/amc/a-activities/a7-problems/problemUSAMO-IMOarchive.shtml

If you've never done contests before, I'd start with the AIME problems instead of the USAMO.  They should be on that same site somewhere.

If you want something a bit more recreational, here's a nice book on FLT that (if I remember) explains the mathematical history of it up to the early 1900's or so, but without requiring much background.  It'll give you some idea of what higher-level math is like without being very demanding.  The author's very good also.

http://rapidshare.com/files/213577477/050_-_Edwards_-_Fermat_Last_Theorem__Springer_1977_.djvu

If you actually do want to do something theoretical, and actually WORK (bleh), then maybe basic abstract algebra is a good place to go from here.  I don't know of any particularly good books for that, but here's a book by an author I like very much, even though I haven't read this book specifically:

http://rapidshare.com/files/213578700/Lang_-_Undergraduate_Algebra.pdf

>>4
>http://rapidshare.com/files/213577477/050_-_Edwards_-_Fermat_Last_Theorem__Springer_1977_.djvu

On second look, that book is more technical than I remembered.  Looking through it might still be interesting though.

>>5
If it's the one I'm thinking of, then it's hardly technical at all.

OP, two recommendations once you get into college.

1. See if you can test out of any of the courses.
2. Talk to a professor and see if you can help him with his research.

>>6
Well it is a GTM.