Prerequisites

topics

Lie derivatives, integrable distributions and Frobenius theorem, differential forms, integration and Stokes theorem, de Rham cohomology, including Mayer-Vietoris sequence, Poincare duality, Thom classes, degree theory and Euler characteristic revisited from viewpoint of de Rham cohomology, Riemannian metrics, gradients, volume forms, and interpretation of classical integral theorems as aspects of Stokes theorem for differential forms.

   exams, homework, etc

There will be weekly homework and a take home final. Homework will count for 50% of the grade, the final for the other 50%.

   syllabus

We will cover Chapters 4,5,6,7,8,11 in Spivak's "A Comprehensive Introduction to Differential Geometry" vol. 1 3rd Edition. In addition my notes on manifold theory will also be used.
I'll add what I cover to to table below as we move through the quarter and also update homework assignments.

Date	material covered	homework
1.9	Ch 2
1.11	Ch 2
1.13	Ch 3	Ch 2: 30, 32, 34
1.16	MLK holiday
1.18	Ch 3
1.20	Ch 3,4	Ch 3: 9, 30, 31
1.23	Ch 4
1.25	Ch 5
1.27	Ch 5	Ch 3: 32, 33 and Ch 4: 1, 3
1.30	Ch 5
2.1	Ch 6
2.3	Ch 6	Ch 5: 10, 11, 13, 15a-d
2.6	Ch 6
2.8	Ch 7
2.10	Ch 7	No Hwk
2.13	Ch 7
2.15	Ch 7
2.17	Ch 8 (exclude integration of chains)	Ch 7: 4, 5, 6, 11, 18
2.20
2.22	Ch 8
2.24	Ch 8	Ch 7: 21, 27 and Ch 8: 7, 8
2.27	Ch 11
2.29	Ch 11
3.2	Ch 11	Ch 8: 14, 17, 30, 31, 32
3.5	Ch 11
3.7
3.9		Ch 11: 1, 2, 3, 6, 8, 9
3.12
3.14
3.16
3.xy