<p>Anything you want to.</p>
<p>If you don’t know what’s out there, here’s a summary:</p>
<p>Chemistry -
There are lots of branches of chemistry. I’m not a chemist, so I can’t tell you all of them, but in general, getting started on organic chemistry wouldn’t be a waste of your time. You might want to do some research on it to see what you really like, though.</p>
<p>(By the way, Caltech’s Organic Chem book is here: <a href=“http://caltechbook.library.caltech.edu/122/[/url]”>http://caltechbook.library.caltech.edu/122/</a> - check it out.)</p>
<p>Biology - There’s a lot here, too. Anatomy, physiology, neurology, biological psychology, etc. Just go through the internet. I’m more of a physics/math guy, and I still can’t get enough of some of the stuff in anatomy and neurology.</p>
<p>Physics - There’s a LOT past AP Physics C in physics. You probably wouldn’t be up to do much quantum mechanics, since it involves a lot of stuff in AP Physics C that you won’t know until the end of your senior year. More on your level would be something like modern physics – relativity, uncertainty principle, schroedinger’s equation, etc. A lot of stuff in modern physics requires calculus, but if you could get a hold of a good textbook that utilizes calculus in only the most fundamental aspects, then that would be a good idea. In particular, I recommend Feynman’s Lectures on Physics. They cover a lot of stuff not included in AP Physics C, and they’re quite easy to understand (of course, it’s Feynman!).</p>
<p>And of course, don’t forget Astronomy.</p>
<p>Math - Stats may be right for you, considering your current level. Also on your current level, you could probably work on number theory or probability theory if it really interests you. If you really want to go advanced, you could consider studying multivariable calculus, linear algebra, or differential equations – linear algebra would probably be the most sensible subject for a person with your experience in math, since it doesn’t require much calculus, and when it does, it’s easy.</p>
<p>Once again, choose something that interests you. You may not be aware of some of the stuff I suggested, and in that case – Google/Wikipedia it.</p>
<p>I doubt Caltech would prefer you independent study any of these courses over another, they just want to see an intense interest in science/math on your part, which independent study often proves. And don’t stress too much over it. I’m not suggesting that you don’t work hard, but I think independent study should be fun and it’s hardly worth it if you’re just doing it for a college application. However, with the variety of topics to study, I don’t think you’ll have trouble finding something that you find very appealing.</p>