Advice on what physics classes to take next year

[feuxfollets]

Hey guys, so I'm a freshman and course registration for next year is coming up. I have several thoughts about what to take but I'm not exactly sure what would be best. It's spring break right now for us and I'm going to talk to the undergrad physics advisor in two weeks, but I thought maybe I could get you guys' opinion on this.

This year I took an honors mechanics and I'm currently taking an honors e&m class and a modern physics class. I'm also taking a one year honors sequence of proof based mathematics, covering real analysis, linear algebra, differential equations and multivariable calc. Next semester I plan on taking advanced real analysis, theory of computation, and intro to cognitive science, in addition to whatever physics classes I decide to take.

I guess my main problem is that I don't have the background in math yet to take a lot of the further physics classes because I took proof based stuff this year. I'm enjoying them and I also want to math major, so I don't feel like that was a bad choice. However that leaves me kind of in a weird position for physics...

I could take a one year sequence of proof based complex analysis and partial differential equations. Which means the only physics options available to me next year are vibrations and waves, maybe statistical dynamics (technically I have the prereqs from modern physics but people have told me that I should take a full year of quantum first...), an electrical engineering-ish crash course for physicists, biophysics, and advanced mechanics.
The former 4 are all first semester and the latter is second semester. Unfortunately waves/vibrations and advanced mechanics don't sound terribly interesting to me (that's what people usually take), and I don't think I want to go a whole year with just those classes. There are graduate level classes on general relativity and intro to condensed matter physics; would I be able to handle them second semester of next year? I could take a one-year differential geometry/topology sequence for GR if needed.
I'm not sure if I would gain anything from taking biophysics. I'm not really interested in biochem stuff, but computational neuroscience is something interesting that I'm looking at (applied to some programs on that for this summer).

Alternatively I could take a math class over the summer that goes over PDEs and some complex analysis. That would enable me to take a year of quantum mechanics and electricity/magnetism next year. However the math class over the summer is geared towards engineers and focuses on computation and stuff, and I kind of want to understand the theory behind all of that stuff with the one year math sequence. I guess I could get the books for those classes and self study them over the summer along with the class?

Sorry for the long post. Any advice on what to do would be greatly appreciated.

 

[jtbell]

Alternatively I could take a math class over the summer that goes over PDEs and some complex analysis. That would enable me to take a year of quantum mechanics and electricity/magnetism next year.

Do your QM and E&M really require PDEs and complex analysis as prerequisite? I think at most schools in the US, they require only the standard calculus sequence and a first course in differential equations.

 

[flemmyd]

I'm not sure if this is right, but I think you should try to take upper div mechanics as soon as possible. While the mechanics itself may not be essential, I think a lot of QM use math originally developed in mechanics. Besides, you'll need it to graduate. Might as well be done with it.
I think this is why Goldstein's graduate mechanics text was written in the first place btw.

Also, ask professors and the physics undergrad advisor if they can waive pre-reqs are work around them. Personally, I would try and take mechanics and e&m 1 first semester, and QM 1 and E&m 2 second semester. Finish all the QM you can as a junior.

And it's a bit hard to read what you're situation is. For one, you mention applying to biophysics summer programs, but you also mention a math class over summer. Several of your ideas are scattered... (how does a graduate level CM courses come into play exactly?)
You're getting ahead of yourself planning on how you need to take *insert class* NOW so you can optimize what you can take in your 4 years. It sounds like you intend to take graduate level courses as a sophomore (not that there's anything wrong with that. But will it be that big a difference if you take during the second semester sophomore or some time during junior year?)

 

[feuxfollets]

I guess my main question is, is it better to take a PDE/complex analysis class over the summer so I can take QM/E&M next year, or take a full year of more rigorous and more in-depth PDE/complex analysis and wait until junior year for QM/E&M. In the long run, which would be more beneficial?

Advanced mechanics is offered 2nd semester, and QM and E&M are both one-year sequences starting first semester. I will take advanced mechanics next year definitely.

I mentioned the graduate CM class because, if I go the second route, then the only physics classes that I'll take next year are waves and adv. mechanics, and I really want to take more than just that since neither of those two sound terribly interesting. It isn't really part of any plan. I could take statistical dynamics but I've heard that I should take a full year of QM first; is that true?

The comp neuro thing is at my school so I would be able to take a class with it. I applied to it mostly because the other physics programs don't take freshman. And yea sorry if my ideas sound scattered; they probably are because I still have no idea what I want to do eventually. so I'm trying some things everywhere.

I probably can ignore pre-reqs, but I'm not sure if I want to do that... I don't want my math inabilities to get in the way of learning physics.