What Courses Should I Take for Graduate School in Theoretical Physics?

[PhysicsWiz4]

Hi everyone, asking for course advice again.

Some background:

I am on a quarter system, this coming winter quarter I am registered for:
General relativity
Elementary Particle Physics (I)
Real Analysis (I)
Modern Algebra (II)

I'm currently a 3rd year physics major finishing up 4th year courses (minus two that I will take next year), so this me a lot of leeway as to what courses I can take my fourth year in college.

What courses should I plan on taking if I want to apply to graduate school in:
Mathematical Physics
Theoretical Particle Physics
Quantum Gravity
?

I might have a chance at taking graduate differential topology/geometry from the math department in my senior year, how helpful will this be in both applying to physics graduate school in the three programs mentioned above? I have enough room to fit a math major, but I wonder what classes I should be taking advantage of in undergrad and which classes I should wait until graduate school to take.

Thanks!

 

[Arsenic&Lace]

The pure math is more useful for the mathematical physics route than for the other two routes, but there's a fairly strong culture in modern theoretical physics which seems to have a lot of interest in pure mathematics. Even old classics like the singularity theorems in general relativity require a strong background in differential topology from what I understand (although I have yet to learn them). My experience having taken general relativity this semester is that much of the understanding is obscured without "some" knowledge of the pure mathematics underlying it; that is to say, more than merely a hand waving development of differential geometry. Unfortunately the math department will bother itself answering mathematical questions which are not really relevant to your physical interests; hence, I suspect one can learn the needed mathematics to study such topics without actually taking courses. A friend of mine took a course in differential geometry from the math department as an introduction, and found it to be mostly (but not entirely) irrelevant to his experience with general relativity, although how much that depended upon the professor who taught the class is an open question.

Hence, I would argue that spending more time on research will be more useful to you than taking more classes, since (I'm assuming from your advancement in your studies) you are independent and mature, and can learn things pretty well on your own with being baby sat through a class. Can you get a professor to work with you on theory? A published paper or at least a compelling argument that you both like and show promise in research will get you further than good grades in math classes, I think.

 

[PhysicsWiz4]

Thanks for the reply! I see that I probably should not let advanced mathematics courses take up a year of slots if I will only be looking at portions of it anyway if I choose to do theoretical physics. Indeed I have taught myself some mathematics before and I should be mature enough to at least attempt to do it again.

Yes! I am working with a professor actually in a small group looking at differential geometry /conformal quantum field theory. We've been working on it together for about a year now, but a lot of it still goes entirely over my head. I will definitely keep at in over the coming years.

Thank you for your words.

 

[Arsenic&Lace]

You can always strike a compromise between say one advanced math course and more research time, and decide for yourself how you feel about the advanced math courses and if they help you in your research; your professor can give you the best advice in this regard.

Don't worry about research going over your head; it took me a about a year before I really felt I had my bearings in my own research (although I'm doing computational biophysics which probably has less intellectual overhead). I would argue that everybody needs at least one introductory course in the fundamentals of any given topic before they can really contribute to it; for me, until I had a semester of statistical mechanics, biophysics was difficult to understand. You'll probably feel much more comfortable after a course in GR/QFT.

 

[kinkmode]

While things like particle physics and general relativity are fun, you probably won't get into much detail in them at the undergrad level. I might suggest really boning up on upper level (graduate level?) E&M, stat mech, and quantum if that is an option. Obviously if you've already taken everything your program has to offer, ignore this advice.

I say this because you will have to take qualifier exams in graduate school. These are often at a difficulty level that is greater than whatever you took in undergrad.

As far as mathematical physics goes, it's true, you'll learn a lot more in a math major. At the same time, if you haven't had courses in differential equations, partial differential equations, curvilinear coordinates, Laplace transforms, Fourier decomposition, and tensors, a mathematical physics course is a good way to see it all in a semester. I left out complex integration since you've taken real analysis.

 

[Arsenic&Lace]

If you're sufficiently advanced (which it sounds like you are) and you have strong reasons to think you'll do well, taking a graduate course is not out of the question.

 

[WannabeNewton]

Even old classics like the singularity theorems in general relativity require a strong background in differential topology from what I understand (although I have yet to learn them).

Actually it doesn't require much beyond the basics. See e.g. Wald "General Relativity" chapter 9; the differential topology and differential geometry involved is quite simple. The mathematical complexities really only come in once you get to the level of Hawking and Ellis "Large Scale Structure of Space-Time".

My experience having taken general relativity this semester is that much of the understanding is obscured without "some" knowledge of the pure mathematics underlying it; that is to say, more than merely a hand waving development of differential geometry.

People generally have different experiences so I can't speak in full generality but one can actually learn a lot of the physics of GR with a minimal amount of math. Hartle "Gravity: An Introduction to Einstein's General Relativity" does exactly this in a brilliant way.

Anyways, OP I would have to agree with one of the other posters that taking grad EM and grad QM would be a much better use of your time than taking grad pure math classes given your stated interests. Don't clutter up your schedule with too many courses though because as Arsenic said you have to make room for research. Good luck!