Math 225A: Differentiable Manifolds
Class Schedule
The topics are tentative but the due dates are not.
Date |
Tentative topic
|
Homework
|
9/27
|
Discussion: Review of topology and linear
algebra
|
|
|
|
|
9/30
|
Discussion: Review of differentiation
|
HW1,
due 10/7 |
10/2
|
Manifolds; examples
|
|
10/4
|
Smooth functions and smooth maps
|
|
|
|
|
10/7
|
The inverse function theorem
|
HW2,
due 10/14 |
10/9
|
Submersions
|
|
10/11
|
Immersions and embeddings |
|
|
|
|
10/14
|
Tangent spaces, Day I |
HW3,
due 10/21 |
10/16
|
Tangent spaces, Day II |
|
10/18
|
The tangent bundle |
|
|
|
|
10/21
|
Cotangent bundles and 1-forms |
HW4,
due 10/28 |
10/23
|
Lie groups |
|
10/25
|
Vector bundles, Day I |
|
|
|
|
10/28
|
Class canceled (fire!)
|
HW5,
due 11/4 |
10/29 (Tues)
|
Vector bundles, Day II (lecture and
discussion switched this week)
|
|
10/30
|
Tensor products |
|
11/1 (Fri)
|
Discussion
|
|
|
|
|
11/4
|
Tensor and exterior
algebra |
HW6,
due 11/13 |
11/5 (Tues)
|
Differential k-forms (lecture and
discussion switched this week)
|
|
11/6
|
De Rham cohomology
|
|
11/8
|
Discussion
|
|
|
|
|
11/11
|
No class (Veterans
Day) |
|
11/13
|
Mayer-Vietoris sequence; some homological
algebra |
HW7,
due 11/18 |
11/15
|
Integration |
|
|
|
|
11/18
|
Stokes' theorem |
HW8,
due 11/25 |
11/20
|
Applications of Stokes' theorem, evaluating
cohomology classes |
|
11/22
|
Lie derivatives
|
|
|
|
|
11/25
|
Homotopy
properties
|
HW9,
due 12/6 (this is the last day of classes!)
|
11/27
|
Class canceled
|
|
11/29
|
No class (Thanksgiving break)
|
|
|
|
|
12/2
|
Vector fields |
|
12/3
|
Vector fields and Lie derivatives
(lecture and discussion switched this week)
|
|
12/4
|
Discussion
|
|
12/6
|
Relationship between d and [,],
Frobenius theorem
|
|
|
|
|
|
Final exam
is take-home!
|
|
Last modified: November 7, 2019. |