This is approximate.
| Date | Material | Problems/Handouts |
| Aug. 30-Sept. 1 | Smooth Manifolds: References: (T)-Chapter 1, (L1)-Chapter 1 |
< Homework 1 |
| Sept.6-8 | Tangent Vectors, The Lie Bracket, Lie Groups | Homework 2 |
| Sept. 11-15 | Lie Groups and Vector Bundles: (T)-Chapters 2 and 3 | Homework 3 |
| Sept. 18-22 | Vector bundles: (T) Chapter 4, 5 | Homework 4 |
Sept. 25- Oct. 13 | Vector bundles, Metrics, Geodesics | Homework 5 |
| Oct. 16- 27 | Geodesics The geodesics, Completeness | Homework 6 |
| Nov. 3-Nov. 17 | Connections on vector bundles and characteristic classes | Homework 7 |
| Nov.17-Dec. 1 | Index Theorem and Applications | Homework 8 |