================================================================
Topics
----------------------------------------------------------------

Complex integrals and the Cauchy residue theorem
Conformal maps
Linear fractional transformations
Radii of convergence of power series

Classification of compact surfaces

Euler characteristic
Connect sum

Explicit homotopies
Homotopy invariance
Fundamental groups
Homology groups
Cohomology groups
Degrees of maps from S^n to itself

Covering spaces and deck transformations
Covering-space models

Stereographic coordinates for S^n, especially S^1 and S^2.

Change of coordinates for vector fields and forms

1-parameter groups of diffeomorphisms

Critical points and critical values

Lie brackets
Lie derivatives
Using Lie derivatives to show invariance of forms under flows
Converting back and forth between vector fields and flows
Cartan's magic formula
form and vector gymnastics

================================================================
Theorems
----------------------------------------------------------------

Cauchy residue theorem
Liouville's theorem

Lifting lemmas
Seifert-van Kampen
Mayer-Vietoris

Regular value theorem
Poincare' lemma
Stokes' theorem