Which math courses are the most useful for grad. school?

• Courses

Main Question or Discussion Point

I am presently finishing my second year as a combined mathematics and physics major, and I am planning on pursuing graduate school in theoretical physics, as many here no doubt are.

I have already, or will have already taken the standard core mathematics courses: i.e. calculus, linear algebra, ordinary and partial differential equations, complex analysis, and real analysis. However, I have some choice when it comes to which upper year math courses I can take, and so I was wondering what particular topics would be the best preparation for graduate school.

Specifically, I can make the choice between abstract algebra (rings, fields, Galois theory etc.), differential geometry, number theory, further studies in real and complex analysis (I'm not quite sure what this would entail; possibly lots of measure theory), Green's functions and the calculus of variations, and probability.

The choices aren't mutually exclusive, in general; however, if I I choose to focus on abstract algebra, due to unfortunate scheduling conflicts, and prerequisites, I will be unable to take any of the differential geometry or analysis courses. Although, I will be taking an introductory General Relativity course regardless, so I suspect that even if I don't take the differential geometry courses I would get at least a brief introduction to the subject, even if an unsatisfactory one.

Answers and Replies

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Theoretical physics is a meaningless term. Can you perhaps narrow it down a bit? QFT? GR?

Of the courses you listed, probability will be the most useful. This is especially true if you have already had a course in complex variables and linear algebra, and ordinary and partial differential equations. You can probably get the other higher level math courses in graduate school anyway, when (if) you need them. Quantum mechanics and statistical mechanics relies on probability. You can see a lot of probability in astrophysics as well. A great article is Selected Problems in Physics and Astronomy by S. Chandrasekhar.