Which mathematics courses would you recommend?

[Entangled Cat]

As a quick continuation of the question...what mathematics courses would you (preferably PhD or pursuing a PhD currently) recommend for an undergraduate? I'm interested in high energy/particle physics (I'm working in a lab this summer so we'll see how that goes) and cosmology (no actual experience or coursework experience, just self learning). I do plan on continuing to graduate school and obtaining a PhD although I'm not sure of what topic I want to pursue. Here are some of the courses that I will take for sure:

Linear Algebra I (I have already taken Elementary Linear Algebra)
Differential Geometry I and II
Partial Differential Equations
Calculus of Variations and Integral Equations

My university offers a graduate level course to undergraduates called Linear Algebra II. Here is the course description of Linear Algebra I:

Vector spaces, linear transformations, and matrices. Canonical forms, Determinants. Hermitian, unitary and normal transformations.

Compared to that of Linear Algebra II:

A theoretical course on the fundamental concepts and theorems of linear algebra. Topics covered are: vector space, basis, dimension, subspace, norm, inner product, Banach space, Hilbert space, orthonormal basis, positive definite matrix, minimal polynomial, diagonalization and other canonical forms, Cayley-Hamilton, spectral radius, dual space, quotient space.

Tell me straight; is Linear Algebra II a course worth taking? I am more than willing to provide course descriptions and course planning spreadsheets if necessary. Also, if you have a specific math course in mind, I would love to see if my university has it! So recommend away and I'll get back to you on whether or not it is offered!

Thanks,
Cameron

 

[MarcusAgrippa]

There seems to be quite a lot of overlap between these courses, with one concentrating on linear algebra and the other branching into some analysis.

Both courses are useful. Physics uses a lot of linear algebra. It also uses a lot of infinite dimensional linear spaces. So, if you must chose between them rather than do both, it is a tough decision. I suspect that the theoretical course might turn out to teach you more.

The linear algebra course looks as if it is aimed principally at computer scientists, but I could be wrong. As a physicist, you should aim eventually to know the content of both courses. Physicists need to know everything.