Need some advice about graduate studies in nonlinear dynamics

[kanima]

First off, though I've been reading through these forums for a while now, this is my first post here, so let me briefly introduce myself.

I'm finishing up my third year as an undergraduate in mathematics. Next year, I want to apply to grad school in math, specifically, I'd like to study nonlinear dynamics. While my major is currently pure math, my interests have shifted towards applied mathematics in the past year, so I'd especially like to study dynamics from an applied perspective.

In preparation for that, I've undertaken to self-study at least one subject this coming summer. I'm trying to decide which of the following two subjects would be more important for me: nonlinear dynamics (with Strogatz), or algebraic topology (Hatcher has been recommended to me).

Now you're probably thinking nonlinear dynamics seems like the obvious answer, but let me say some more.

Unfortunately, I won't actually be able to study dynamical systems until the second semester of next school year. The reason for this is that the course is only offered every two years, and in my second year, which is the last time it was offered, I was inadequately prepared for the subject. Although I would mention in my grad school application that I planned on taking the class, I think it might look bad that I hadn't had any real experience with the subject by the time I'd be applying.

As for algebraic topology, my school, which is otherwise considered a good school in many respects, only very rarely offers a course in topology due to budget cuts in the past years (you can imagine that many students, including myself, and many professors, are greatly dismayed at this situation). So by the time I graduate, my only exposure to the field will be from my brief excursions into basic point-set topology covered in my analysis classes. Of course, topology is very important for any student wishing to study at the graduate level, and also very important in dynamical systems.

Something that people on here might ask is: why am I so intent on studying a subject I haven't had classroom exposure to yet? I had considered that, and in fact, the reason I'm asking the question above is that I believe the schools I apply to will be asking the same thing.

All I can say is, I've read quite a bit about the subject, so I'm not completely clueless, I simply haven't studied it in-depth yet. Furthermore, outside of mathematics, my interests lie mainly in the broad domain of pattern formation in nature. Since there's a wide range of fascinating natural nonlinear systems (flocks, neural systems, weather systems, etc.) that exhibit this property, it would be impossible for me to study them all, and so I'd rather look at them from an abstract (mathematical) point of view.

Looks like I made this question pretty long, so hopefully someone will take the time to read it and give me their opinion. Thanks.

(I just realized I might get the answer: study them both. This might not be feasible, as I have other commitments this coming summer, including some research I'll be doing with one of my profs and studying for GRE's. So I'm asking: in case I only have time to study one of the subjects, which one should it be?)

 

[kanima]

I hate to bump this thread, but I realize now (seeing how my post has very few views at all) that I probably chose a bad title; unfortunately I can't change it.

Anyone have any advice as to which of these subjects would be more important in my situation?

 

[diligence]

looks like your mind is displaying some non-linear dynamics in writing a ~300 word question that sums up to: which class should i take?ps: if i were a grad school admissions committee, i'd be more worried about your inability to choose your classes on your own than whether you've taken a NLD class yet.

 

[kanima]

Yeah... I guess went overboard with the question, I was just trying to make it as clear as possible, but perhaps I did the opposite.

Anyway, I'm not really asking about a class I should take, rather about which subject might be preferable for independent study.

I'm not dependent on the replies I get to this post, and I'm quite capable of making my own decision. As things stand, I will probably choose to study dynamics on my own as I personally find that subject more appealing. The only reason I'm asking here is to see if anyone has any good insight, but I can get along quite well if that's not the case.

 

[rezeew]

As a scientist in the field of nonlinear dynamics, I understand your dilemma and can offer some advice. First of all, it's great that you are already thinking about your graduate studies and preparing for them in advance. This shows dedication and passion for the subject, which are important qualities for success in graduate school.

In terms of which subject to self-study over the summer, my recommendation would be to focus on nonlinear dynamics. While it may seem like a disadvantage that you haven't had classroom exposure to the subject yet, it can also work in your favor. Many graduate programs are looking for students who are willing to explore new areas and have a strong interest in a particular topic, and your enthusiasm for nonlinear dynamics will definitely stand out in your application.

Additionally, as you mentioned, topology is an important tool in the study of nonlinear dynamics, so your background in point-set topology from your analysis classes will be helpful. Of course, if you do have some spare time, it wouldn't hurt to brush up on your topology skills as well.

In terms of your interest in pattern formation in nature, studying nonlinear dynamics will definitely give you the tools to understand and analyze these systems from a mathematical perspective. And who knows, you may even have the opportunity to work on some research projects related to pattern formation during your graduate studies.

In conclusion, my advice would be to focus on studying nonlinear dynamics over the summer. It will not only strengthen your application for graduate school, but also give you a solid foundation for your future research in this exciting field. Best of luck to you in your studies and future career!