Senior Year Courses for Graduate School

[PhysicsWiz4]

Hi PF, asking for course advice again.

Currently I am finishing up undergraduate level series in:
Abstract Algebra
Real Analysis
Particle Physics
Topology.

Next fall I will be registering for:
Stat Mech/Thermodynamics (required for physics majors)
Statistics and Probability (required for math majors)
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I can choose from:
Math:
Graduate level Real Analysis
Graduate level Topology
Graduate level Differential Topology (First course in series covering differential geometry)
Physics:
Graduate level Mathematical Methods in Physics
Graduate level Mechanics/EM
Graduate level General Relativity (I have taken the undergrad version)

Which course (or pair of courses) will be most helpful in graduate school for quantum gravity/mathematical physics/high energy theory?

Will I have enough time to take all of these courses in graduate school? (I'm interested in math enough to honestly take all these courses if I had enough time!)

Options:
Take 2 Grad Physics courses
Perceived Pros: Looks better for graduate school/I will be prepared for graduate school
Perceived Cons: Risk of never taking a formal class in graduate level math

Take 2 Grad Math courses
Perceived Pros: Good chance at being able to take even higher level mathematics in grad school
Perceived Cons: Will being going to physics grad school without having taken any grad courses.

Take 1 of each:
Perceived Pros: Good Balance
Perceived Cons: Lack of depth

My perspective is that I want to be able to tackle theoretical/mathematical physics with a sophisticated mathematics tool belt (and because the math is interesting in itself and I can't see myself leaving it behind outright). What should I do?

Thanks!

 

[radium]

I would take GR and differential topology. Differential geometry is very important in GR (in the physics sense) and this way you could get a rigorous course on it and see a physics application.

 

[PhysicsWiz4]

Thanks! Those two are the most prereq heavy, but I am most interested in them! I will definitely consider this option as it seems that it will be most helpful in getting started with research quickly come graduate school.

 

[jbrussell93]

Perceived Cons: Will being going to physics grad school without having taken any grad courses.

And what is wrong with that? If undergraduates were expected to take those classes then they wouldn't be considered graduate classes.

The fact that you're even having this dilemma tells me that you probably don't have anything to worry about as far as getting into a good graduate school. If I were you, I would just take whatever I felt I would be missing out on in graduate school.

 

[radium]

It's actually very good to take grad classes in undergrad. I will have completed 8 (I am graduating in two weeks). It is especially helpful if you want to go into theory. Taking grad quantum my junior year helped my research (in CMT) tremendously. It also helped me do theory research at an REU (they don't normally have theory projects). I got a first author PRL and will be attending Harvard this fall. Doing well in grad courses could not only get you a great letter, it also shows that you can think at the next level since grad courses are conceptually more advanced than undergrad courses and much more mathematically involved.

 

[PhysicsWiz4]

jbrussel93 - Thanks for the vote of confidence! I do hope that that is the case.

radium - Thanks and congrats! I do hope to get a letter of rec from the general relativity professor as I've had him in the past and I've interacted with him before (I hope he remembers me!)

Good luck!

 

[jk]

I would take grad level mechanics or math methods. They will give you a good base to build on for graduate level physics course work

 

[WannabeNewton]

I concur with the above poster. If you've already taken undergrad GR then there is no rush to take the graduate one. If you have free time then you can always self-study advanced GR and take the graduate course once you are in grad school. Taking graduate mechanics/EM would be a much better choice: foundations are everything. Plus with graduate EM under your belt, graduate GR will be much easier if you choose to take it later.

 

[radium]

Honestly, I wouldn't take grad mechanics. Everything you would learn in that you usually will learn in either grad quantum or stat mech. Grad E&M is not really that physical except for the relativistic description. However, you will learn the notation required for that in GR. All of the physics in grad E&M I learned in undergrad (although the grad course I took was not the standard way it is taught so I will take it in grad school again), Jackson is basically just boundary value problems.
Math methods would be a good option if you've never seen the things like certain parts of complex analysis, Green's functions, asymptotic methods, Sturm-Liouville theory, or the calculus of variations.

If you do have the option or taking grad quantum, I would go with that since professors have told me that having a solid understanding of quantum is the most important preparation you can have for doing theoretical research, especially in my subfield.

 

[jk]

Honestly, I wouldn't take grad mechanics. Everything you would learn in that you usually will learn in either grad quantum or stat mech. Grad E&M is not really that physical except for the relativistic description. However, you will learn the notation required for that in GR. All of the physics in grad E&M I learned in undergrad (although the grad course I took was not the standard way it is taught so I will take it in grad school again), Jackson is basically just boundary value problems.
Math methods would be a good option if you've never seen the things like certain parts of complex analysis, Green's functions, asymptotic methods, Sturm-Liouville theory, or the calculus of variations.

If you do have the option or taking grad quantum, I would go with that since professors have told me that having a solid understanding of quantum is the most important preparation you can have for doing theoretical research, especially in my subfield.

Hmm...not sure I would agree with this. If the content of grad mech. is taught in quantum or stat mech , then why do most universities require graduate mechanics? Some of the concepts may be repeated in those classes but they cannot be covered in the same depth as in a class devoted to them.
The OP should probably be having this discussion with faculty at his/her school.

 

[radium]

Many universities actually don't require graduate level mechanics such as Harvard, Cornell, Penn, and MIT.

 

[jk]

Many universities actually don't require graduate level mechanics such as Harvard, Cornell, Penn, and MIT.

And many universities do.

The ones that don't probably assume that the person had covered classical mechanics in undergraduate at the "graduate level", whatever that means. The bottom line is that classical mechanics is a basic requirement for a physicist (and a lot of qualifying exams) so if the OP does not have command of it at a sufficiently advanced leve, it would be a good idea to take it.

 

[radium]

I mean unless you haven't had a rigorous mechanics course where you cover Lagrangian and Hamiltonian mechanics, you don't need to take it at the graduate level since the material is very similar. People have told me the same about E&M although you should take that. However one of my professors who is incredibly famous in condensed matter theory told me that he didn't take grad E&M and that it is not really necessary.

Many schools are actually phasing out Jackson E&M since it is mostly mathematics except for the relativistic formulation which you may even learn in field theory since you are quantizing the classical relativistic theory.

I have taken eight grad classes so far and I have been completely fine with my undergrad knowledge of mechanics. If you are missing something from undergrad, it is more efficient to teach it to yourself than to take a whole course.

 

[jasonRF]

Have you done any research with any faculty in your department? if not, then it might make sense for you to try to spend time doing that and taking fewer grad classes (as long as you can still graduate on time!). If you are already hooked up to do research next year, then ignore me!

jason

 

[Yellowflash]

I have a friend who is currently completing his BsC in Physics and is planning to pursue a PhD. He was facing a similar dilemma and asked for his professor's advice. After that, he took graduate level mechanics and electricity and magnetism (I think he took general relativity or differential topology beforehand though).

 

[mpresic]

I think JasonRF's advice is good. Alternatively, look at what the prospective grad school puts emphasis on. If research (and most do) jasonRF may be right. IF the GRE physics advanced, make sure you have some breadth before depth. (Very few Jackson, Goldstein, Sakurai problems on the physics GRE). I know you can pick up the GRE preparation material at a low level without a formal class in it; but will you. Will that material seem important while you are working on the grad studies.

If I had to answer your original question I would pick Grad methods in Math Physics.
Radium has a lot to say about Classical Mechanics. I should just say I was lucky enough to have two semesters of Classical Mechanics from Goldstein, and Whittaker and Watson, 35 years ago. Since then most grad programs whittled it down to one semester. This is enough of a mistake. To eliminate it completely is unconscionable. I worked in missiles and satellites and I can tell you Marion, or Symon alone does not cut it. I have had to demonstrate techniques to new-hires so I know something about this. Trefil book with the introduction to fluids and solids leans towards my point of view.