Which graduate math courses for mathematical physics

[tmbrwlf730]

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
topolgy)
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, IIFor 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.

 

[micromass]

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!