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## Main Question or Discussion Point

I'm a math/physics major, and I just finished my freshman year of college. I have almost 4 months off, so I decided I'd like to teach myself some subject in the realm of math. I've taken vector analysis/calc III, linear algebra, and advanced calculus.

Advanced calc. at my university is, as I understand it, supposed to be a somewhat rudimentary version of real analysis. We used Rudin's text (Principles of Mathematical Analysis), and went through chapter 6 (on integration), skipping sections liberally (ie, we completely ignored Lebesgue integration).

So, what would you recommend I do with myself? I'm looking for something interesting, that doesn't necessarily have to build on what I've already learned (chaos theory, I believe, is like this [am I right?]). I really enjoyed Calc III, so I was thinking about something like fluids, but I'm not sure if I have the background for that.

Any help would be appreciated, I have no idea where to start looking, what books to look into, etc.

Edit: I'll be taking probability and ODE (diff eq's) in the fall, if this is of any consequence.

Advanced calc. at my university is, as I understand it, supposed to be a somewhat rudimentary version of real analysis. We used Rudin's text (Principles of Mathematical Analysis), and went through chapter 6 (on integration), skipping sections liberally (ie, we completely ignored Lebesgue integration).

So, what would you recommend I do with myself? I'm looking for something interesting, that doesn't necessarily have to build on what I've already learned (chaos theory, I believe, is like this [am I right?]). I really enjoyed Calc III, so I was thinking about something like fluids, but I'm not sure if I have the background for that.

Any help would be appreciated, I have no idea where to start looking, what books to look into, etc.

Edit: I'll be taking probability and ODE (diff eq's) in the fall, if this is of any consequence.

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