Shoud I take Ring/Field Theory or Complex Analysis?

[chahmquahk]

Having just finished an introductory course on group theory (with some bits of ring and field theory), I am completely enthralled with this type of math. I initially planned on taking Complex Analysis next semester since so many people say it's "useful" for physics (this was also a compromise with my research mentor who was rather annoyed I chose abstract algebra over differential equations this semester) but now I'm undecided as Ring/Field Theory seems like it would be fascinating. On the other hand, both of my physics courses this semester (Hamiltonian Mechanics/Chaos and Quantum Mechanics) started using results from complex analysis (mostly with integration), which was a little disorienting. I know I will eventually take both math courses at some point during my undergrad, but would it be unwise to delay Complex Analysis? If relevant, I am leaning toward mostly theoretical as opposed to experimental/applied physics courses for the rest of undergrad.

Math courses taken: linear algebra, advanced calculus, group theory (all proof-based)

Thanks in advance.

 

[ShayanJ]

Both are beautiful parts of mathematics so I would take both. But since you're asking which one to take first and you need complex analysis soon, so I suggest taking it and waiting for the algebra course. Complex analysis is both useful and beautiful but don't forget to take the Ring/Field stuff later!
I should mention that I don't think going that much inside algebra is useful in physics but its of course worthy for the sake of its beauty.