Syllabus
Each pair of weeks corresponds roughly to a chapter of notes.
| Weeks | Topic |
|---|---|
| 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 |