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I'm currently a physics major with a year left, and deciding whether to switch into mathematical physics, mathematics or applied mathematics. I'm definitely switching into one of them, as I can meet the requirements for either in my last year and all of them align better with my interests. Speaking of which, at this point I think I want to pursue graduate studies related to chaos theory/dynamical systems. I did a bit of searching and this seems a field that is sometimes studied from an (applied) mathematical viewpoint and at other times from a physics viewpoint.

Not knowing how exactly I want to go about studying this, i.e. I don't know which side interests me more, since it kind of depends on the actual topic, not the approach per se, here's where my quandary comes in. Namely, which of the following courses do you find most crucial if I do indeed want to study the aforementioned fields:

A) Quantum mechanics II, Electromagnetism II [mathematics/math physics/applied maths]

B) Continuum mechanics [mathematics]

C) Intermediate PDE's (a second course in PDE's), Numerical methods [applied maths]

I've grouped this into three separate categories, because if I go with either of the courses in C), then I can't take B). In square brackets I've also listed the programs that I'd need to be in if I want to fit them into my schedule next term.

Personally, I'd like to get a taste of continuum mechanics, but then I definitely can't take either of the courses in C, and what worries me is that those would perhaps be required if I was to approach the subject from a mathematical standpoint in grad school. On the other hand, I'm not sure I could get away with not taking the courses in A if wanted to approach things from the physics side.

What would you recommend?

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I am physicist. My advice: 1) forget about A, it will make you hit your head against a wall to try understand it but will not learn anything about chaos. 2)it would not be a waste of time, but it depends on what specific topics it touches. 3) the most important if you wanna learn chaos seriously.Chaos is a mathematical issue, even if there are many physicists working on the subject (because the equations they use in many branches happen to be chaotic). But you can always learn some basic physics if you need or feel about it. for instance analytical mechanics and then a specific course on chaos theory (but you will be able to do it by yourself once you are good a PDE's.

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Thanks for the reply. The reason I was considering A is that, for example, at my university, I've been told that those courses would probably be required for entry into Physics grad school. So I'm worried that if I apply to approach chaos and dynamical systems from a physics standpoint, I could be rejected for not having those courses. I have done both first parts of the respective QM and EM sequences, though. As for C, I wasn't sure whether more advanced PDE knowledge is as needed in those areas as ODEs, or whether it would be enough to have the basics down. –  Ryker Apr 28 '13 at 3:57
    
well, that changes the picture around, if you plan to enter physics grad school, you should take not only both A) and B), but make sure to ask your adviser or mentor what else. Grad school in physics requires to learn a lot of phyiscs! Your will learn enough about PDE's in advanced course of physics, at least enough of what you need if you decide to work in chaos theory. –  julian fernandez Apr 28 '13 at 4:34
    
Well, like I said, that's the problem. I don't know which approach I'll take, since looking online sometimes the research groups are located in the Physics department, and sometimes in the Maths department. So I need to choose an option that will give me the most leeway in making my decision in the coming months. Unfortunately, I namely only have a couple of days to make the decision about which program to switch to, though. Any further input during with these constraints? –  Ryker Apr 28 '13 at 6:41
    
it is a difficult question, and the key to the answer is only you. My advice. If you love physics, go for the physics phD in chaos dynamics. If you dont really love it, go for math, you will learn much more and you will always find a place in a physics group studying chaos, because you will know more math than them, and they are aware of that! ;) –  julian fernandez Apr 28 '13 at 6:44
    
Hmm, I see. So do you think the focus should be on whether I want to get a PhD in Maths or in Physics, not on the department in which groups dealing with chaos and dynamical systems are located? –  Ryker Apr 28 '13 at 18:07
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