Math courses for a Physics major (that aren't required)

[lunarstrain]

I'm going into my third year in Physics in fall and I have some room on schedule and would like to take some math courses beyond the requirements at my uni since I enjoy math and want to have a head start in graduate school.

My school only required calculus (up to multivariable calc.), differential equations, linear algebra and a third year physics course I haven't taken yet called "methods in theoretical physics".

Looking at the math courses offered I see a few options but I can't tell which would be best suited for a career in physics.

There's a course on Complex Variables and another on Partial Differential Equations. These would be fairly easy to fit in my schedule since I have all the prerequisites already.
Then there's a couple courses on Abstract Algebra and the Real Analysis > Topology thread.

There are many more but those are the ones I think may be useful. I can take two of these at most without overloading my schedule. If you could tell me anything about these courses and how useful they will be for me (in the near future as I'm likely to forget things after a year or two) then I'd very much appreciate it. Or would this be a waste of time and I'd be better off taking some extra computer science or doing nothing at all?

Thanks

 

[mfb]

I think complex analysis is nice. You probably won't need it directly in physics, but it gives a deeper understanding in analysis in general.
Partial differential equations can be useful, especially for thermodynamics.
Statistics is interesting, too - no experiment works without statistics.

 

[WannabeNewton]

Have you taken a proof based course before (e.g. honors calculus)? Have you had any experience with proofs? If not I wouldn't recommend taking topology nor real analysis. It would be quite a big jump from regular calculus courses + DE to real analysis and/or topology if you have not had much, if any, proof experience. You might want to start off with a more "friendly" class in such a case.

 

[robphy]

Take the PDE course... And maybe the complex analysis course if you can fit it in.

Maxwell Equations for electromagnetism, the wave equation, the heat equation, the Laplace equation, the Schrödinger equation... are PDEs. (One can easily add to this list.) It would be great if the PDE course did some numerical methods.

My $0.02.

 

[lunarstrain]

Thanks for the replies. I forgot to mention that there's a required statistics/thermodynamics course which I'm taking. I'm kind of leaning towards the complex variables because of the deeper understanding. I know that partial DEs are very useful but my differentials course covered some already and Schrödinger, laplace, etc. are covered in the "methods" course mentioned in the OP. I don't know how long it will be until we use the things taught in the math focused course (if there's even anything extra at all) so I'll probably have to ask the profs about that one.

And I did consider the fact that I have little experience in proof based courses. My first year calculus courses tried to do some of both worlds, but I've never taken a course intended for math majors. There is a course designed to introduce such things but I wouldn't be able to fit it. I was hoping since real analysis 1 is a lower year course I could spend extra time figuring that out on my own. I don't know exactly how difficult it would be, do you have any experience with that? I typically do very well in math if that makes any difference.

 

[WannabeNewton]

Real analysis is one of the more difficult of the standard undergraduate math classes in my opinion. Pure math classes will be unlike the regular calc + DE classes you have taken; they won't be nearly as trivial/computational. You could always take a look at introductory real analysis syllabi from various universities and see for yourself if it is within your reach. Regardless, I would have to agree with what robphy and mfb said above in that the PDEs course would be of much more immediate use.

 

[ModusPwnd]

I took extra engineering type math courses when I was an undergrad. Discrete mathematics, PDEs for Engineers and an applied statistics class. In hindsight I would say that they were more useful than the Math Methods for Physics classes that I had to take.

 

[lunarstrain]

Thanks, I am going to look at the syllabi. Assuming that I can handle the extra work to understand real analysis and then next year topology, will the extra work be worth it? I am primarily interested in these courses for their own sake but it seems like it will be fairly difficult and for that amount of work it would be nice to know that I can use this at some point in my career.

Regarding PDE's I have looked at the course material and it looks like there's little difference between what's offered in that course and what's in the required courses (DE's and Methods in theoretical physics). The difference is that the course I was thinking of taking uses a mathematicians approach and goes into more detail with proofs. It would be beneficial but it's offered in the fall and my schedule is very heavy in the fall and very light in the winter so I don't think I will take it.