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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?2012-04-22
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    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!2012-04-22
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    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 recommend2012-04-22

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