Questions about recommended courses to prepare for grad school in Physics

[lsaldana]

Hello, I'm currently a 3rd year physics student (will be finishing next year) with some questions about recommended courses which would facilitate my ability to tackle graduate courses. First, due to financial issues I cannot take more than a fixed number of hours in the coming year so I have to chose carefully. My concerns are:

1) I have taken classical mechanics but the course didn't cover Lagrangian and Hamiltonian mechanics, that's covered in a course named classical mechanics II. With my remaining hours, I have to choose between this or Solid State Physics or upper level math. I know that this level of mechanics will be covered in a grad class mech course but I feel a bit afraid about not seeing it before that. Any recommendations?

2) I've taken all required math courses + an upper level linear algebra course but nothing else beyond that. I've learned a lot of other math from physics classes and my advisor recommended to take more physics than math as "you'll learn the math you need there". This summer I'm signing up for probability & statistics and a mathematical methods course (PDE's basically) and I'm also taking a graduate Mathematical Physics course in the Fall. However, I feel like Complex Analysis (the grad math physics course presumably covers this) is mentioned and used a lot in physics and was also contemplating Differential Geometry as I'm taking general relativity and feel it could help further understand the subject which I want to continue studying in graduate school if possible. Are the courses I've mentioned enough or not?

3) Research with a professor is eating up my remaining hours, which is good and bad at this point. We can choose how much academic credit we want to get for research work and it'll count as an advanced elective. Of course, I can always choose to get little (1 or 2 hours) or no credit for it on paper and still participate but I'm under the impression that having strong hours on this will look great when I apply to graduate school. Can anyone enlighten me on this?

All of this is in preparation for graduate school in physics. I want to have a good working , and broad, knowledge from my undergraduate studies. Sorry for the long post but my advisor really sucks and doesn't talk much. Thanks for the help in advance!

 

[FourierFaux]

It sounds like taking that Classical Mechanics II course will be a good idea. The Hamiltonian and Lagrangian are a little exotic the first time you see them. If you really want to get a head start on those, then you can get ahold of a copy of Shaum's Outlines on Lagrangian Dynamics by D.A. Wells. It has much more difficult problems near the end than what your professor is likely to throw at you. I'd only recommend taking the Solid State Physics class in lieu of Classical Mechanics II if you know that you might want to go into Solid State/ Condensed Matter in graduate school.

I think that trying to find an REU for over the summer might be more beneficial than a few extra classes. This may or may not be possible with the research that you're doing with your professor.

Complex Analysis has some useful little tricks, but you can probably teach them to yourself. I'd only recommend Differential Geometry if you know that you want to go into a theoretical branch of physics.

It sounds like you'll be pretty well prepared for graduate school. Good luck sir/miss.

 

[FourierFaux]

It's probably not a good idea to skip Classical Mechanics II.

 

[JaWiB]

For whatever reason, Lagrangians have come up quite a bit in my graduate classical mechanics course, and on our qualifying exams. IIRC there was also a bit on the PGRE.

Still, I didn't find it extremely difficult, beyond solving the DE's that come up sometimes. If you have time, you might try to learn a bit on your own and see if you find the problems difficult. Generally I would say take the classical mechanics course because solid state is probably not a course professors would expect a first-year grad student to have already taken, whereas they will expect you to know a bit of Lagrangian mechanics.

 

[lsaldana]

Thanks for the advice guys. Yeah, I figured Lagrangian mechanics would be something that I shouldn't skip but the Solid State course seems very useful nowadays. In short, the lagrangian mechanics course taught at my university is a pretty dense course and I was wondering how much of the theory I must know beyond knowing what a Lagrangian and Hamiltonian is and a bit of calculus of variations. I've seen some PGRE practice exams and they seem to have maybe 2 or 3 questions on this topic. Do many universities offer grad courses on solid state physics??

As far as the math, I think I'm going to settle with the classes I mentioned before and forget the Complex Analysis/Differential Geometry courses for now, simply don't have time. Thanks.

 

[FourierFaux]

It depends on where you go for graduate school, I would imagine. The PGRE may not emphasize it that much, however, most graduate schools require that you take a Qualifying Exam at some point. This Lagrangian and Hamiltonian Dynamics will usually be strongly emphasized on these. Besides... they're kinda fun once you get the hang of them. :)

Try to find something that will make you happy.