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I'm finishing my bachelor's in physics and for my masters, where I have a few free choice courses (~5), I'd like to take math courses that would be relevant for a future as a theoretical physicist or applied mathematician.

Rigorously (as in taught by mathematicians) I've had Calculus, Calculus in R^n, Complex Analysis, Linear Algebra, Probability and Statistics and just a small overview of differential equations. I've had more math in physics courses but not in a very rigorous way.

I'm setting my eyes on the following courses:

  • Ordinary Differential Equations
  • Partial Differential Equations
  • Group Theory
  • Stochastic Processes
  • Functional Analysis

Are all of these relevant? Which others could be added to this list?

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    To quote the physicist who taught me string theory: "There is no mathematics that God has not found a use for in string theory."
    – zibadawa timmy
    Commented Mar 30, 2016 at 23:36

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Although the name is not explanatory, a course in "Lie theory", or "Lie groups and Lie algebras" would be very helpful: this is about the influence of large-ish (certainly not finite) symmetry groups, such as rotation groups ("orthogonal groups"...), and more.

Also, "functional analysis" is very hit-or-miss, depending on what one wants. What a potential physicist would want would be "operator theory", especially "unbounded operators". Also, probably, "distribution theory/generalized functions", to be able to cope gracefully with things like Dirac's delta "function". (E.g., to not be at the mercy of semi-ignoramuses who'll happily rant about the non-existence of such a thing, and/or insist on describing it in ways which horribly obscure its utility and sense...)

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All of the courses that you've mentioned could be quite helpful depending on what area of physics or applied mathematics you end up in. The ordinary and partial differential equations courses would be expected in any reasonable graduate program in applied mathematics.

Differential geometry and tensor analysis is very important in many areas of mathematical physics. In my experience, many physics graduate students end up learning a lot of numerical computing and numerical analysis (not quite the same thing.)

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