Relevant math courses for theoretical physics/applied mathematics? 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...)