Textbook:
| Lectures | Sections (from Guillemin and Pollack's book) |
| Week 1 |
§ 1.1+2 Definitions, Derivatives and Tangents
§ 1.3 The Inverse Function Theorem and Immersions § 1.4 Submersions |
| Week 2 |
§ 1.5 Transversality
§ 1.6 Homotopy and Stability Quiz I |
| Week 3 | § 1.7 Sard's Theorem and Morse functions
§ 2.1 Manifolds with boundary § 2.2 One-manifolds and some consequences |
| Week 4 | § 2.3 Transversality § 2.4 Intersection theory mod 2 Quiz II |
| Week 5 | § 3.1+2 Motivation, Orientation § 3.3 Oriented intersection theory § 3.4 Lefshetz fixed-point theory |
| Week 6 | § 3.5 Vector fields and the Poincare-Hopf Theorem § 3.7 Euler characteristic and triangulations Quiz III |
| Week 7 | § 4.1 Introduction § 4.2 Exterior Algebra § 4.3 Differential forms |
| Week 8 | § 4.4 Integration on manifolds § 4.5 Exterior derivative Quiz IV |
| Week 9 | § 4.6 Cohomology with forms § 4.7 Stokes Theorem § 4.8 Integration and mappings |
| Further topics as time permits | |