Math I'd be Missing out on with a Physics Degree

[Bumpeh]

So I've been reviewing over the courses for a Physics degree at a University I plan to attend. The required math is Calculus I, II, III and Ordinary Differential Equations. I've been told and read in quite a few different places that I should take more math classes, like Partial Differential Equations and Numerical Analysis.

Now, I've seen that the University offers a lot of these good math classes that will help me delve deeper, the only problem is that I'm afraid of going over this "Credit Limit" thing. Basically If I take more than 136 credit hours or something I'll be charged an extra fee. Personally, I think it's kind of dumb, if I'm paying tuition to and fees to take the classes anyway, but whatever, that's not the point.

If I do a minor in mathematics, I'll be taking the four mentioned classes along with Linear Algebra and two other math classes. And since it's a minor, I won't have to deal with the credit limit thing. I feel like that won't be enough to dive into what I really want to dive into, though. If I did the math minor I'd be thinking of taking Partial Differential Equations and maybe Probability and Statistics.

Whereas if I do a dual major in math, I'll be able to cover all those other math classes that would really help, but it would be a very large workload added onto an already large one with the Physics degree itself. Not to mention I'd really like to take some Computer Science classes beyond what's required for the degree and maybe get a minor in that.

So if I were to do the math minor, what would be the best two other math classes to take that would help me on my Physics journey? Should I try for the dual major or not? And if I simply do the minor, how else can I study these mathematics outside of college to get a good grasp on them?

On a side note, the specific area of Physics I'm interested in is Astrophysics and Planetary Science. If that helps narrow down what math classes I should take.

 

[PhotonSSBM]

Linear is absolutely necessary for both your interests. So that's a class you absolutely should take (which you already said you would). Your school should offer (possible at the graduate level) a course on Mathematical Methods in Physics, which will go over a lot of the necessary components of PDE's, Complex Analysis, Fourier Analysis, and if you're lucky some stuff on tensors, group theory, and functional analysis. That's most of what you would need in any physics career, and it's only one 3 Credit Class. A lot of what you don't learn in that class can be picked up by self study at this point and what you study really depends on what you're researching.

If your school doesn't offer that course, the grad schools you apply too should all universally have it as a required course for their grad students to take if they haven't already. And if you're dead set on taking two more math courses anyways, I'd pick PDE's and either Complex Analysis or Fourier Analysis.

 

[Bumpeh]

Oh okay, in the Physics degree program there is a course called Mathematical Physics, I just read the description and it pretty much does cover what you said.

 

[Student100]

On a side note, the specific area of Physics I'm interested in is Astrophysics and Planetary Science. If that helps narrow down what math classes I should take.

Differential geometry and topology might be classes that you'd find interesting, and useful for those interests.

I don't see a real reason to double major, unless that's what you really want to do. Go with the minor, LA, PDE, and CA are generally applicable as a physics major, but dedicated courses in PDE and CA probably aren't necessary, just extremely helpful. I'm surprised LA isn't required for physics majors, and that you don't have the option between PDE and ODE's.

Numerical analysis is neat and useful, but I feel like the majority of it will be picked along the way, sort of like what you need to know for statistics. Most physics classes do a decent job introducing new mathematics to physics majors, but math majors would disagree with that statement. =)