Math 225A: Differentiable Manifolds
|
Date | Tentative topic |
Homework
|
9/24 (Fri) |
Review of topology and linear algebra |
HW1, due 10/1 |
9/27 (Mon) |
Review of differentiation |
|
9/29 |
Manifolds; examples |
|
10/1 |
Smooth functions and smooth maps |
HW2,
due 10/8 |
10/4 |
The inverse function theorem |
|
10/6 |
Submersions |
|
10/8 |
Immersions and embeddings | HW3,
due 10/15 |
10/11 |
Tangent spaces, Day I | |
10/13 |
Tangent spaces, Day II | |
10/15 |
The tangent bundle | HW4,
due 10/22 |
10/18 |
Cotangent bundles and 1-forms | |
10/20 |
Lie groups | |
10/22 |
Vector bundles, Day I | HW5,
due 10/29 |
10/25 |
Vector bundles, Day II |
|
10/27 |
Tensor products | |
10/29 |
Tensor and exterior algebra | HW6,
due 11/5 |
11/1 |
Differential k-forms | |
11/3 |
De Rham cohomology | |
11/5 |
Mayer-Vietoris sequence; some homological algebra | HW7,
due 11/12 |
11/8 |
Integration | |
11/10 |
Stokes' theorem | |
11/12 |
Applications of Stokes' theorem | HW8,
due 11/19 |
11/15 |
Evaluating cohomology classes, degree | |
11/17 |
Lie derivatives | |
11/19 |
Homotopy propertiesof de Rham cohomology | HW9, due 12/3 (this is the last day of classes!) |
11/22 |
Vector fields | |
11/24 |
No class | |
11/26 |
No class (Thanksgiving break) | |
11/29 |
Vector fields and Lie derivatives | |
12/1 |
Relationship between d and [,] | |
12/3 |
Frobenius theorem | Take-home final will be available on CCLE
at 2pm on Fri 12/3 and is due by 11:59pm on Sun 12/12. |
Final exam is
take-home! |