Math 225A:  Differentiable Manifolds

Class Schedule

The topics are tentative but the due dates are not.

Date  Tentative topic
 Homework                                                                          
10/2 (Fri)
 Review of topology and linear algebra
 HW1, due 10/9



10/5 (Mon)
 Review of differentiation
10/7
 Manifolds; examples
10/9
 Smooth functions and smooth maps
 HW2, due 10/16



10/12
 The inverse function theorem
10/14
 Submersions
10/16
 Immersions and embeddings HW3, due 10/23



10/19
 Tangent spaces, Day I
10/21
 Tangent spaces, Day II
10/23
 The tangent bundle HW4, due 10/30



10/26
 Cotangent bundles and 1-forms
10/28
 Lie groups
10/30
 Vector bundles, Day I HW5, due 11/6



11/2
 Vector bundles, Day II
11/4
 Tensor products
11/6
 Tensor and exterior algebra HW6, due 11/13



11/9
 Differential k-forms
11/11
 No class (Veterans Day)
11/13
 De Rham cohomology HW7, due 11/20



11/16
 Mayer-Vietoris sequence; some homological algebra
11/18
 Integration
11/20
 Stokes' theorem HW8, due 11/30



11/23
 Applications of Stokes' theorem
11/25
 Evaluating cohomology classes, degree
11/27
 No class (Thanksgiving break)



11/30
 Lie derivatives HW9, due 12/11 (this is the last day of classes!)
12/2
 Homotopy properties
12/4
 Vector fields



12/7
 Vector fields and Lie derivatives
12/9
 Relationship between d and [,]
12/11
 Frobenius theorem




Final exam is take-home!


Last modified:  September 24, 2020