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?
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...)