I'm turning to you as I find myself in need of help as to how to best go about studying something related to chaos theory/dynamical systems/fluid dynamics in postgraduate school.
I'm currently in my third year of physics and my first question would be what courses would be especially pertinent for me to choose as my electives? Whenever I had the chance thus far, I've taken maths courses as my electives, and I'm also taking the "honors" version of maths courses offered at my university, which are targeted at Maths Honors majors and Mathematical Physics majors. Not only does maths interest me a great deal, I now figure a good mathematical background is essential if I want to go on into aforementioned fields. But what maths courses would be especially relevant if I want to pursue the aforementioned fields?
Thus far I've taken the following mathematics courses: Honors Calculus I and II, Honors Advanced Calculus I and II, Honors Linear Algebra I and II, Introduction to Group Theory, Ordinary Differential Equations and Honors Complex Analysis. I'm taking Linear Algebra III and PDE's next term, and I also heard topology is necessary if I want to go into the fields I mentioned. Is this true? What else would I need?
Note that I realize I probably wouldn't be able to study these fields from a pure maths perspective due to my background, but I'm hoping I'd be able to from a mixed maths/physics one.
Any help here would be greatly appreciated.
edit: For anyone reading this years after the creation of the thread, I actually switched to math in my last year of undergrad, am now doing a Ph.D. in Pure Mathematics, and after taking the required courses hope to start with research this Fall (2016). I'm still keen on looking at dynamical systems, but it's probably going to be ergodic theory/symbolic dynamics/complex dynamics.