Each pair of weeks corresponds roughly to a chapter of notes.
|1-2||Multilinear algebra, Tensors, Exterior forms|
|3-4||Vector fields and differential forms on open subsets of n-dimensional euclidean space|
|5-6||Integral calculus via forms, Sard's Theorem, Degree theory|
|7-8||Vector fields and forms on manifolds, Stokes's Theorem, Divergence Theorem, Degree theory for manifolds, Gauss-Bonnet Theorem|
|9-10||De Rham theory (cohomology groups of differential manifolds)|
|11-12||More de Rham theory, intersection theory|