Math for Physics PhD: Preparing for Top 10 PhD Programs

[ResonantW]

I'm currently a second-year university student considering applying to a PhD program in physics.

I'm leaning towards theoretical physics, although I haven't really experienced enough to make a clear decision. I'm beginning to be involved in research with a theorist this semester, but I was wondering the sorts of math I would need to get into a top 10 physics PhD program.

I've already taken calculus, math methods, a discrete mathematics class, and linear algebra. I'm considering taking real analysis my junior year, and could probably take complex analysis after that during the senior year.

What other math should I take to increase my shots at good graduate schools? What math could I wait until graduate school to take? Should I expect to learn most of my formal math before grad school?

 

[Klungo]

In my opinion, all top 10 schools are a far reach for everyone. Anything you do: more relevant coursework, research, extracurricular societies, etc will improve your chances, but I doubt it would be a significant enough difference. Know that you will be competing with several students who likely have much better credentials. Don't give up though. Its roughly an equal chance for everyone.

Also, it's a bit pointless to just take more math just to boost your chances. Take the extra math either because you love it, or because you see it particularly useful for your intended field in graduate physics.

 

[johnqwertyful]

Don't just take classes because it looks good. Take them because they'll help you.

What area are you interested in? Real analysis is required for a lot of upper division math (at least at my school). So real analysis, then whatever you want to take.

If you're interested in general relativity, topology would be super helpful. If you're interested in a more...computational approach, numerical analysis would be super helpful (numerical analysis is always helpful, regardless of area IMO). Real analysis isn't really the end (for some it is), I've seen it as the gateway to the really cool areas of math. You have to develop the real numbers (and calculus, of course) rigorously before you can do anything cool with them.

Also, upper div PDE or ODE class would be pretty useful.