I plan on working through "Geometry of Physics" by Frankel. I keep on running into little snags here and there, and I am wondering if that's just part of the process, or whether I am ill-prepared.
For example, in order to understand what differentiability in higher dimensions means (one of the things Frankel assumes you know already), I have been trying to make my way through Spivak's "Calculus on Manifolds". Progress is there, but it's slow.
Is it just me, or is there something incredibly ugly about how Spivak proves the closed interval $[a,b]$ is compact(proof of Heine-Borel theorem)? Am I just missing a lot of "back-story" (i.e. stuff I should be pretty comfortable with already)? Is each page supposed to take me an hour to work through?
Just thought I'd ask others who might have something to share from their experience.