Math Undergrad Thesis Topic Advice

[gungywamp]

Hello everyone, I was wondering if anyone with more experience than I could give some advice about choosing a topic for my undergrad thesis.

I'm currently a Junior in an Applied Math program, and I am interested in going to graduate school for a Ph.D after I complete my undergrad. I am aware that I should be taking the Math Subject GRE, and that there are a few topics on the exam that I have not been formally introduced to, specifically abstract algebra and topology. I plan to take the exam near the end of the 2011 fall semester, and I will be able to take a course in abstract algebra during the fall. After some talks with my adviser, I have come to the conclusion that it would be worth considering a thesis topic that involves topology, so that I will be forced to do some independent study with direction before the exam.

This is where my question comes in. As a student of applied mathematics, I am most interested in applications, and being relatively uninformed about topology, I was wondering if there are any areas of the field that would appeal to an applied math major. I am still open to just buying some books and studying on my own so that I can free myself up to do a thesis on something I know I am interested in (e.g., pde's, modeling, mathematical physics), but I am still weighing my options. Any advice?

TLDR: What kinds of topics are there in applied topology that would be good for an undergraduate thesis?

 

[ridingonlove]

Have you thought about differential geometry?

http://en.wikipedia.org/wiki/Differential_geometry#Applications_of_differential_geometry

 

[maricoy1219]

we share the same problem..until now i can hardly find a thesis topic in applied math...i don't know...i still don't know to which field i should focus..heeelp..

 

[doodle_sack]

Google it! I googled this: research topics in mathematical physics and found this link
http://www.ma.hw.ac.uk/maths/Research/resdet.html

there are tonnes of other stuff, just google it.

 

[qspeechc]

http://en.wikipedia.org/wiki/Soliton" seem to be an active area of applied math research. Also non-linear partial differential equations and numerical methods. On the more physics side there are things like Hamiltonian dynamics, fluid dynamics etc.

You may want to look in the applied math section in the library and chat to some professors in the field

EDIT: you said with applied topology. Sorry these have nothing to do with topology. Although a little bit of geometry and topology come into Hamiltonian dynamics and symplectic geometry.