I am currently studying control engineering on a sort of graduate level (mostly on my own).
However every book on the area mentions certain subjects or areas of mathematics (particularly manifolds and canonical forms) that seem too much for an electrical engineer who spent almost all part of it's career doing operational mathematics (integrals, derivatives, Fourier and Laplace transforms).
It is on my personal interest to bridge the theoretical gaps.
For example, I want to get a better understanding of what is meant by Sliding Manifold.
My question in particular is, what would be the prerequisite knowledge in order to approach manifolds?
Doing some research I've gather the next subjects (probably in poor order considering my formation):
1.- Real analysis
2.- Functional Analysis
3.- Abstract algebra
4.- Linear algebra (with focus on vector spaces)
5.- Topology , Differential Geometry . . . ?
I'm sorry if I bother anyone with this question but I really want to learn more in depth to fill mental gaps.