I'll be doing Introductory General Relativity and Graduate Quantum Mechanics II next semester. I still need to choose 2 (or maybe 3, but I don't want to overload too much) from the following:

  • Algebraic Topology I: Sounds useful in both mathematical physics, and things like string theory, so leaning towards taking this one.

  • Number Theory: Sounds interesting, not sure if very useful though. Things like the Riemann-Zeta function will be discussed, and other topics may include elliptic curves etc.

  • Graduate Complex Analysis: My fear is that it may be too focused on proofs, so not sure how useful it'll be as far as use in physics goes. I'm already familiar with the usual complex analysis methods that physicists use, but sharpening my understanding of it can't hurt. How useful would this be to learning the sort of complex geometry stuff that seems indispensible these days (reimann surfaces and complex manifolds etc)?

  • Lie Algebras and Representation Theory: Same concern as the one with complex analysis, i.e offered by the math department and designed for math grad students, so not sure how useful it will end up being.

  • Graduate Statistical Mechanics: Haven't had an undergrad class yet so it may be a bit tough going. Also, its at the same time as the Lie Algebras class.

I would really appreciate it if someone with experience in fields such as string theory, quantum gravity, mathematical physics etc can comment on the relative usefulness of these courses and give their recommendations on which ones to choose. I know that all these topics are potentially useful and I would have to learn them all eventually if I am serious about these fields but which ones are the most immediately useful ones in terms of progressing to the next stage.


closed as off topic by David Z Jan 12 '13 at 8:08

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    $\begingroup$ I think this question should be on academia.stackexchange.com $\endgroup$ – ungerade Jan 12 '13 at 6:13
  • $\begingroup$ Talk to professors in the field you want to go into! One of the things that sets going to a university apart from taking online courses is the access you have to career planning (and networking). Surely you at least have some academic adviser who can serve as a first point of contact. $\endgroup$ – user10851 Jan 12 '13 at 17:40
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    $\begingroup$ Maybe what Warren Siegel says here could be helpful. And please dont forget to read the joke papers,listed under the title "physics parodies" on the same site, they are fun as hell ;-) $\endgroup$ – Dilaton Jan 13 '13 at 9:57
  • $\begingroup$ @Dilaton: Just in case a future visitor is confused, you mean the parodyies section here. That's actually an excellent site! It has an "Introduction to String Field Theory"! Wow, I must read that. $\endgroup$ – Abhimanyu Pallavi Sudhir Aug 25 '13 at 10:41
  • $\begingroup$ @Dilaton: The stuperspace parody is just too funny ... NIce metric tensor (+--+-+++--+-+x=→←/⊕⊗--). $\endgroup$ – Abhimanyu Pallavi Sudhir Aug 25 '13 at 10:50