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I have taken:

Calc I- III

ODEs

Linear Algebra

Numerical Analysis

Foundations of Math (methods in proofs)

Registered:

PDEs

Topology (Point-set)

Will take:

Abstract Algebra (group theory)

Complex Analysis

I have worked out my schedule for math and physics classes to take, but I'm not sure which of three classes would benefit me best for one of the spaces I can take a course. The three classes I would like to do are Differential Geometry, Interrelations in Math, and Mathematical Methods for Physics.

It's worth noting a few things:

The Interrelations course is somewhat unique, the course description reads "Topics include groups, complex variables, non-Euclidean geometry and differential equations with the theme that any two areas are related. Emphasis on examples, applications, and unsolved problems in contemporary areas such as elliptic curves, geometric surfaces, group-manifolds and modern physics. Appropriate for math majors, and non math majors who are interested in seeing what lies beyond calculus."

The math-physics course would be an independent study. I attend a small liberal arts school, and I am one of two physics students double majoring in math.. I would like to do a survey of different topics, tensors, calculus of residues (I'll learn it in complex, but reviewing won't be bad), differential and integral equations, and some topics in Clifford algebras and dual spaces.

I'm currently doing a little bit of study in differential geometry, specifically of surfaces and geodesics. So I'll have some exposure to the material, although I admit I'm not extremely comfortable with it.

I'm not sure which of the options will benefit me most as a physicist. I'm fairly confident that they will all be beneficial. Any insight or advice is greatly appreciated.