Just as a little background, by the time summer comes around, I will have taken mathematics classes up to basic differential equations, multivariable calculus, linear algebra, and some probability theory. In Physics, I will have taken up to classical mechanics and mathematical physics. I want to attempt to learn some topics to give myself an advantage so I won't just be lost in the fall when I have to overload with a bunch of upper level physics and math classes (including Advanced Calculus). I am already planning to attempt to learn programming in C and also mathematical proofs in some way since I've never had to attempt them before (I have a few books I can use, just not sure if I want to just go for really basic math concept proofs or go straight for the intro to real analysis books). My question is: are there any other topics I should look into over the summer? I'm a math and physics major, and I plan to eventually go to graduate school for physics. I was thinking maybe partial differential equations would be a good thing to add, but wasn't sure (if anyone could recommend a book for that, it'd be great).