Math 225A Class Schedule

Math 225A: Differentiable Manifolds

Class Schedule

The topics are tentative but the due dates are not.

Date	Tentative topic	Homework
9/23	Review of topology and linear algebra	HW1, due 9/30

9/26	Review of differentiation
9/28	Manifolds; examples
9/30	Smooth functions and smooth maps	HW2, due 10/7

10/3	The inverse function theorem
10/5	Submersions
10/7	Immersions and embeddings	HW3, due 10/14

10/10	Tangent spaces, Day I
10/12	Tangent spaces, Day II
10/14	The tangent bundle	HW4, due 10/21

10/17	Cotangent bundles and 1-forms
10/19	Lie groups
10/21	Vector bundles, Day I	HW5, due 10/28

10/24	Vector bundles, Day II
10/26	Tensor products
10/28	Tensor and exterior algebra	HW6, due 11/4

10/31	Differential k-forms
11/2	De Rham cohomology
11/4	Mayer-Vietoris sequence; some homological algebra	HW7, due 11/14

11/7	Integration
11/9	Stokes' theorem
11/11	No class (Veterans Day)	HW8, due 11/18

11/14	Applications of Stokes' theorem
11/16	Evaluating cohomology classes, degree
11/18	Lie derivatives	HW9, due 12/2

11/21	Homotopy properties
11/23	Vector fields
11/25	No class (Thanksgiving break)

11/28	Vector fields and Lie derivatives
11/30	Relationship between d and [,]
12/2	Frobenius theorem

	Final exam is take-home!

Last modified: October 26, 2016.