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.