i'm currently taking a course on manifolds and i can't seem to decide whether it's too much or too little in terms of actual content
so far we've had
>definition of manifolds & examples (quite long)
>smooth functions
>tangent spaces, derivations, tangent bundle
>vector fields, lie derivative, bracket, bump functions
>integral curves & flows
>homotopy, fundamental group, covers, lifts, universal cover, deck transformations, covers of manifolds, totally discontinuous actions (quite long)
>differential forms on R^n and on manifolds, closed 1-forms, covers and 1-forms, period homomorphism
>paracompactness and partitions of unity
>orientations, orientation cover
>submanifolds
next chapter's gonna be manifolds with boundary and Stoke's theorem for n-forms, with a final chapter on geometrical structures

i'm struggling with some of the material and can't help vacillating between
>maybe it's quite a lot to take in at once
and
>i'm a fucking idiot, this isn't that difficult and if anything we should be learning more

if you have taken a manifolds class in your bachelor, what was it like?