I'm currently a physics major with a year left, and deciding whether to switch into mathematical physics, mathematics or applied mathematics. I'm definitely switching into one of them, as I can meet the requirements for either in my last year and all of them align better with my interests. Speaking of which, at this point I think I want to pursue graduate studies related to chaos theory/dynamical systems. I did a bit of searching and this seems a field that is sometimes studied from an (applied) mathematical viewpoint and at other times from a physics viewpoint.
Not knowing how exactly I want to go about studying this, i.e. I don't know which side interests me more, since it kind of depends on the actual topic, not the approach per se, here's where my quandary comes in. Namely, which of the following courses do you find most crucial if I do indeed want to study the aforementioned fields:
A) Quantum mechanics II, Electromagnetism II [mathematics/math physics/applied maths]
B) Continuum mechanics [mathematics]
C) Intermediate PDE's (a second course in PDE's), Numerical methods [applied maths]
I've grouped this into three separate categories, because if I go with either of the courses in C), then I can't take B). In square brackets I've also listed the programs that I'd need to be in if I want to fit them into my schedule next term.
Personally, I'd like to get a taste of continuum mechanics, but then I definitely can't take either of the courses in C, and what worries me is that those would perhaps be required if I was to approach the subject from a mathematical standpoint in grad school. On the other hand, I'm not sure I could get away with not taking the courses in A if wanted to approach things from the physics side.
What would you recommend?