Math learning after Differential Equations?

Question

I made it up to DE(Pre-Calc, Calc I and Calc II with basic stats before that same school) in community college through a special program(I'm poor). I'll have to self-teach from now on but am still very in to math and engineering. What do people usually go to with math after DE?

I'm interested in topology but it looks like there is a lot of other things I need to do first like advanced algebra.

Answer 1

Real analysis if you have not done it so far.

Answer 2

After differential equations, I think you should try learning real analysis at the level of Rosenlicht or so and abstract algebra at the level of Gilbert and Gilbert. These two topics will greatly improve your mathematical maturity and will prepare you for more advanced mathematics.

From here, I would learn complex analysis and venture into topology. You don't need to learn topology after real analysis, but I feel that topology is best understood after learning real analysis well. However I think you must know real analysis well before complex analysis. Complex analysis is almost impossible to appreciate without seeing how.. yucky real analysis can be. From there, the sky is the limit.

Answer 3

If you haven't had the genuine treat of a basic course in complex variables, do that first. Topology is high in my list, but you really must get complex variables under your belt first. It will completely change your take on lots of stuff you have already done.