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I'm a physics major and I'm pretty sure that I'm interested in theoretical physics research. However, I haven't been able to take math courses in a systematic way (as a math major would) due to scheduling difficulties. Therefore, I would like to fill the gaps in my math education by reading books on my own. Are there any suggestions on what topics I should concentrate on and what books are the best, considering that my main objective is to improve my physics insight. (I am very familiar with rigorous proofs and stuff.)

Thanks!

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What math do you know? Do you know multivariable calculus, ODE, PDE? Complex analysis? –  mixedmath Apr 22 '12 at 19:30
    
I know all of the basic math any physics major should know - multivariable calc, ODEs, PDEs, Linear Algebra, complex analysis (cauchy integration techniques, riemann sheets etc..), a little bit of group theory. I'm also fairly familiar with differential geometry and topology since I do gravitational physics research. BUt I would definitely like to formalize my knowledge in those fields by reading a good (challenging) book. I'd like to know what else I can learn to fill in the gaps. Thanks! –  user29712 Apr 22 '12 at 20:20
    
It seems to me now that any future math you learn will be heavily dependent on what area of research you are going into. Is this not the case? That is, other than recommending bigger and better analysis/PDE/complex analysis texts, I don't know what I would recommend –  mixedmath Apr 22 '12 at 23:31
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1 Answer

A short (but might be helpful) answer is to consult the MIT opencourse website. See what you found interesting and you may borrow the book from the library to read it. A good thing is one can learn math entirely on one own with a computer. For physics you need to learn how to do experiments, etc.

A topic you might be interested is differential geometry and geometrical topology if your interest is " theoretical physics research". Similarly you may read functional analysis, PDE, etc....

I also recommend this page which I know since high school and never finished learning from it...

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Thanks for the link!! Yep, I basically follow the MIT open courseware website now. But my main issue with that is that I don't know what will be helpful for me as a physicist. I would definitely love to follow it exactly if I had the time, but I really want to solidify my math knowledge before I go to grad school. –  user29712 Apr 22 '12 at 20:22
    
Why don't you try to study differential analysis? I know nothing about that field, but it should be indispensable if you want to understand any substantial PDE, harmonic analysis, etc. –  Kerry Apr 23 '12 at 2:45
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