Math 225A:  Differentiable Manifolds

Class Schedule

The topics are tentative but the due dates are not.

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!


Last modified:  December 1, 2021