homeomorphic

Have you finished your PhD yet mate? If so, how did it go and what are you doing for work now???

I took an undergraduate version a long time ago. The graduate level version is a totally different thing. Much more advanced. Most areas in math don't just stop after one or two courses worth of material. Usually, you could fill bookshelves with all the material in one area. It's not something that fits into one textbook. Some people still do research on ODEs.

I'm almost done with the PhD. I would graduate in August (still might), except I'm a little unprepared to apply for jobs, and all that is left in the spring is stuff outside the US. My thesis is on 2-dimensional spin topological quantum field theories and homotopy quantum field theory. It's topology. Sounds very physicsy, but not as much as you would think, given the names.

I'm pretty surprised that ODE is taken in graduate school, I was under the impression that it is taken beforehand. What specifically are you planning to pursue as PhD in Mathematics?