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

  1. May 22, 2012 #1
    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
     
  2. jcsd
  3. May 24, 2012 #2
    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.
     
  4. May 24, 2012 #3
    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.
     
  5. May 24, 2012 #4
    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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