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So I'm having a tough time deciding between courses next semester. I'm a rising 3rd year undergrad math major whose goal is to get a solid understanding of theoretical physics through advanced math (laugh all you want). So in that view, which one should I choose from

  1. Theoretical Mechanics: This is a graduate level class covering Lagrangian and Hamiltonian Mechanics. I've already had classical mechanics at the undergrad level, but we didn't do Hamiltonians, and at that level a lot of the conceptual details weren't highlighted. I want to do this class because L and H mechanics seem really fundamental to anything you do in theoretical physics and thus a good understanding of them seems essential.

  2. Electricity & Magnetism II: This is an undergrad class which will probably be based on the second half of Griffiths. I know that this material is pretty important (E&M Waves and Relativistic E&M) and I'll have to learn it eventually, but to be perfectly honest, I think I have had enough classes based on Griffiths for a lifetime (2 semesters of Quantum along with E&M I).

As a second question, another choice has been bothering me. In the same view which one class should I choose from:

  1. Statistical Mechanics. Standard first semester undergrad Stat Mech class using Kittel & Kromer.
  2. Graduate-level Algebra. I've already had an undergrad algebra class but this may be useful if I decide to go to grad school for math.
  3. Mathematical Methods. A graduate level class covering calculus of variations, greens functions and PDEs, real waves and group theory.
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You're definitely better off self-teaching Math methods than spending a whole semester on it. If you're not taking much more formal physics, I'd definitely recommend the mechanics couse, especially if it covers classical field theory. –  Jerry Schirmer Jul 27 '12 at 13:43
Three classes of Griffiths is enough for a lifetime? Personally, I would say a whole lifetime of Griffiths is not enough for a lifetime. How I love it! –  Steve B Jul 27 '12 at 21:45

2 Answers 2

I say take the theoretical mechanics class; you sound more interested in it, and that goes a long way to how much you will get out of it. That's not to say that EM2 would be "more of the same." In my EM1 class, we worked up to Maxwell's equations; in EM2, we filled in a lot of the details about dielectrics and material interactions. I don't know that your class would be the same, but EM2 seemed to me to be aimed at providing a foundation for condensed matter kind of stuff.

As for the other class, the graduate level algebra sounds good, but taking two graduate level classes in addition to (presumably) other undergrad classes could be to much to handle. The stat. mech. class would likely be good though as it is really a class in applied statistics. There's plenty of math but with a good dose of application and theory. The math methods class likely won't be much help for you honestly; the math methods classes I took were all pretty much "math for physics majors" classes aimed at teaching us silly physicists enough math to do our work without having to get deep into the theory. As a math major, I expect you wouldn't get much out of it that you wouldn't be able to learn on your own when necessary.

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Yes, for the first choice I'm mostly sure that I'll be doing mechanics. For the second one, I'm still thinking. I was considering math methods because I've taken or know the material to most of the applied math classes that the math department has to offer (calculus, ODEs, PDEs, complex variables etc) and still feel that there's a great deal to learn. You're correct in that grad-level algebra along with Grad Mechanics and Grad Quantum might be too much to handle so Stat Mech may be a good choice. –  Ahsan Jul 27 '12 at 19:39
In my undergrad Math Methods for physics class we covered calculus, ODEs, PDEs, and a bit of matrix math... take it if you like, but be prepared to be disappointed. Also, pick up a copy of the Riley, Hobson, Bence book "Mathematical Methods for Physics and Engineering". It's cheap and very worthwhile. –  AdamRedwine Jul 28 '12 at 12:07

I strongly suggest taking the statistical mechanics class. There's gold in them hills. In particular, if you want to understand the modern formulation of quantum field theory, you will need intuition from statistical mechanics.

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Seems that the questioner is deciding on two courses and yes, mechanics and statistical mechanics are a good choice. –  anna v Jul 27 '12 at 15:37
Yes. I didn't answer the EM2 vs mechanics class because I don't have a strong opinion there. Too much depends on the syllabus and the lecturer. But Stat Mech is something most mathematicians miss out on when they get interested in physics, which is a tragedy. –  user1504 Jul 27 '12 at 15:43
I certainly want to be learning QFT during my senior year. So do you think it's absolutely essential that I have stat mech before doing so or is it also doable concurrently? –  Ahsan Jul 27 '12 at 19:41
It is probably doable concurrently, since most QFT classes start out with free field calculations and 1st order perturbation theory, and wait till 2nd semester for the Wilsonian approach, which is where you want intuition about phases and scaling laws. This is a perverse way to teach the subject, but it's probably still pervasive. –  user1504 Jul 27 '12 at 21:41

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