Which math courses should i take as a physics student?

[Incand]

I'm trying to decide which math course to take for next term. The one's I think could possibly be useful are:

PDE: Seem to focus on numerical methods. existence, uniqueness, stability, Galerkin methods, Variation formulation, FEM are a few words from the course description. While studying PDE further seems like a good idea I don't enjoy numerical methods to much. There's also a lot of computer labs and hand ins that I probably don't have time for taking this course parallell to my physics courses.

Real analysis: follows rudin. Looks like a lot of fun for me and I suspect I need it if i want to go on studying functional analysis which I think have uses in QM.

Modern algebra: Deals with group & ring theory which I heard is useful i physics. However I feel that perhaps the contents of the course is more directed towards math students and that I probably be better of studying group theory from a physics POV.

I probably can only fit in one course and right now I feel Real analysis looks the most fun and useful for me but I'm not sure. What I'm mostly interested to work in is mathematical physics or possible some other branch of physics with a lot of math in it so I thinking getting a good foundation in real analysis may actually be usefull for me and at the very least it looks fun. Which course would be most usefull for me?

The math I studied so far:
Calculus
Linear algebra
Numerical analysis
Statistics (rather basic course, mostly focused on applications)
Complex variables (self studied)
Mathematical methods for physicists (covers Vector calculus and an introduction to things like tensor calculus, green functions and applications to physics)
Fourier analysis

 

[Dr. Courtney]

Depends on what kinds of physics you see yourself doing in the future. PDE would be great if you see an applied future or want to be employed with just a bachelors.

Real Analysis or Modern Algebra make more sense if grad school is in your future, esp theory.

 

[Incand]

Depends on what kinds of physics you see yourself doing in the future. PDE would be great if you see an applied future or want to be employed with just a bachelors.

Real Analysis or Modern Algebra make more sense if grad school is in your future, esp theory.

I'm aiming for a phd in some math heavy part of physics so theory, beyond that I wouldn't know until I had more physics classes. I'm from Europe and we usually do a master first so that should give me some time as well to decide.

What do you think would be most useful out of real analysis and modern algebra? The thing that makes me say real analys is mainly that it looks more fun as well as being more usefull for future courses. There's also a physics course that cover a bit of group theory using this book https://www.amazon.com/dp/0750305045/?tag=pfamazon01-20 althought we only cover the very basics I'm thinking this may be a better choice. The other thing i wish to get out of these courses is to get better at proofs, in fact I plan self studying some proof book before since most math courses (except perhaps linear algebra) been focusing mostly on calculations rather than proofs.