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!