You can peruse some of my introductory lectures on more advanced topics -- I have written several talks aimed at beginning physics graduate students. Except for the last three, which discuss topological quantum mechanics, they are meant cover aspects of mathematics useful for string theorists.
| Title | Notes |
| Introduction to Topology | pdf (761k) |
| Introduction to Rings | pdf (667k) |
| Introduction to Rings II | pdf (894k) |
| Introduction to Modules | pdf () |
| Introduction to Manifolds | pdf (729k) |
| Flows and Forms | pdf (789k) |
| Vector Fields | pdf (684k) |
| Bundles I | pdf (752k) |
| Bundles II | pdf (544k) |
| Introduction to Categories | pdf (962k) |
| Sheaves | pdf (116k) |
| Sheaf Morphisms | pdf (1.1M) |
| Lie Algebra Representations I | pdf (220k) |
| Riemann Surfaces and their Moduli | pdf (121k) |
| The Witten Index | pdf (130k) |
| Perturbative Calculation of the Witten Index | pdf (90k) |
| Non-perturbative Effects | pdf (1380k) |