Choosing math courses for theoretical/mathematical physics (grad school)

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Which of these mathematical courses are useful for theoretical/mathematical physics?

Topology/Geometry-related set of courses
Topology
Integral geometry
Topology of Lagrangian manifolds
Riemannian geometry
Differential forms on Riemannian manifolds

Algebra-related set of courses
Group theory
Ring theory
Lie groups and algebras
Groups and geometries
Superalgebras
Number theory
Model theory
 

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  • #2
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I'm not quite a mathematical physics guy, but I know just a thing or two about what some of it entails. Things like superalgebras and all of the topology and geometry stuff seem to come up in a lot of mathematical physics for sure.
 
  • #3
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Basically all of those topics crop up in mathematical physics somewhere, with the possible exception of model theory (I've never heard of it being used in physics but that doesn't mean that it hasn't). Number theory also has very few uses in mathematical physics, but they do exist (one example: using quantum statistical mechanics to study class field theory). Superalgebras generally crop up in supersymmetry, but I don't know if they have much use outside of that. I don't know anything about integral geometry so I can't comment on that. Everything else you mentioned, though, is widely used in mathematical physics.
 
  • #4
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I think everything you listed except for model theory is used on a regular basis. I also think you cannot limit yourself to Lagrangian manifolds. You need the entire theory of smooth manifolds.

I would also throw in some measure theory and mathematical analysis.
 

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