- #26

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The courses in mathematical physics that are offered in grad school are there for a reason. They expose you to whatever mathematical tools the department feels you'll need to succeed on your way to the PhD.

Most (if not all) schools will not mind a physics PhD candidate sitting in on whatever math courses they want / have time for. You don't need to spend all your time doing proofs and the work required to complete the exams required of mathematicians, but by merely auditing and doing the reading along with lectures, you'd be surprised what you can get from the experience ... plus YOU get to decide what you're really taking away from the course since you get out of it whatever you put into it.

So if you managed to take some algebra, topology, and geometry in undergrad AND have "free time" somehow when you're a graduate physics student, why not audit some grad level algebraic topology or differential geometry or Lie group theory? All of those subjects have a good deal of cross-over into some of the physics you think you like (sorry to say "think you like" like that, but being a sophomore undergrad, you only think you like this stuff now, who knows what will change as your level of sophistication grows in both fields).

Another reason I'd stick away from the masters in math ... unless you find a program that funds masters candidates or offers them TA positions, you'll probably be spending a decent bit of money on the degree (and diverting your eventual PhD in physics by 2-3 years) ... but hey, if you're parents have your education covered or you're already on full scholarship, or you find a fellowship/TA, or you just don't care about money, then maybe the MS in math is still a good idea.

I agree with one of the other guys that posted before: if you end up going into math and pursue it to a PhD ... you're only "kinda" doing physics ... there's a reason people spend 4+ years in graduate level study of physics just to get to the point where you're a "beginning" physicist as far as academics go. Sure, as a mathematician, you may specialize in geometry or PDEs or Bifurcation analysis ... and probably will collaborate with physicists at some point or another ... you're still a mathematician, which is a very different field.

I feel for you with all this stuff, I had a tough time figuring it out myself, and it took me until I was a year into medical school to realize I needed to get out and get back to grad school for this stuff.