Should I Take More Math Courses for Grad School in Physics?

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Physicists typically learn the necessary pure mathematics for theoretical topics in graduate school through a combination of undergraduate math courses and coursework within physics graduate programs. While some foundational math is integrated into physics courses, taking additional classes such as real analysis, abstract algebra, topology, partial differential equations (PDE), complex analysis, and probability/stochastic processes is often beneficial, especially for those pursuing fields like string theory. Students are encouraged to consider their specific interests and future studies when selecting courses. For instance, a second course in linear algebra may significantly aid understanding in quantum mechanics, which is a common subject for upcoming physics graduate students. Ultimately, the choice of math courses should align with individual academic goals and the demands of their intended specialization.
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I'm currently a junior and am wondering how physicists usually learn the pure math required for more theoretical topics in grad school? Is a lot of math taught within the physics grad courses or is it expected to take undergrad math courses? I ask because I'm not sure if I should bother taking real analysis/abstract algebra/topology in my undergrad. Id ask my adviser but my appointment isn't until next week and registration is tonight.
 
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It's normally taught within physics, but PDE or complex analysis might be a good thing to study, or possibly probability/stochastic processes or numerical analysis for some fields. I'm not sure what the really math-oriented people like string theorists do. For someone like that, more math classes would probably be a good idea, but there are books written about topology for physicists, so some people seem to take that route and learn it the physicist's way.
 
Oh I see. I'll be taking PDEs next semester. I've narrowed another choice down to what seems the most useful which is either more linear algebra or complex analysis but I'm pretty stuck on which one to choose. Will a second course in linear algebra help a lot with quantum mechanics? I take quantum next fall.
 
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