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Which graduate math courses for mathematical physics

  1. Apr 2, 2014 #1
    Hello, I've started a MS in mathematics at my university and I'm interested in mathematical physics or going to to physics for a PhD. The classes required for the MS are 2 semesters of real analysis, linear algebra, and one semester of algebra, everything else is up to the student to pick and choose from depending on their interest. As an undergraduate I took Fourier's series, and complex variables (different from complex analysis from my understanding, it was mostly applied). Are there classes anyone recommends for an interest in mathematical physics? They are offering an ODE course at the graduate level for the fall, should I look into this course or would the undergraduate version I took to enough? Thank you.

    These are the classes in the catalog:
    Lattice Theory
    Information Theory
    Ordinary Differential Equations
    Partial Differential Equations
    Nonlinear Programming
    Topology I, II, III
    Differential Manifolds
    Axiomatic Set Theory
    Numerical Analysis I, II
    Algebra I, II (Should I look into taking the second, it covers group actions, finite Abelian groups,Noetherian rings, factorization
    domains, and tensor products, but is not required for the MS)
    Intro to Commutative Algebra and Algebraic Geometry
    Representation Theory
    Universal Algebra
    Nonlinear Dynamics I, II
    Complex Analysis I, II
    Measure and Integration
    Real Analysis (This is different from the two semesters required. This one covers Lp spaces, Banach spaces, measure and
    Applications of Tensor Analysis (I think this one is hardly offered though)
    Topics in Differential Geometry (Content Varies)
    Homological Algebra
    Intro to Functional Analysis I, II

    For statistics:
    Elementary Stochastic Processes
    Foundations of Probability (Probability spaces, expectation and conditional expectation, limit theory and law of large numbers)
    Continuous Multivariate Analysis
    Linear Models
    Advanced Theory of Statistics I, II
    Thank you for your help.
    Last edited: Apr 2, 2014
  2. jcsd
  3. Apr 2, 2014 #2


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    Staff Emeritus
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    2016 Award

    Can you give us a list of classes??

    I would definitely recommend anything to do with differential geometry and manifolds. It's totally worth it. It'll help in Classical Mech and GR.

    Functional Analysis is helpful to understand the math behind QM.

    A course on PDE is also something you should consider.

    If there are courses on Lie groups or representation theory, then definitely take those!
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