Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 239: Differential Topology
Search by ISBN on Amazon: 978-1-4419-7399-3
|Lectures||Sections (from Tu's book)|
||§1 Smooth Functions on a Euclidean Space
§2 Tangent Vectors in R^n as Derivations
§3 The Exterior Algebra of Multicovectors
||§4 Differential Forms on R^n
|Week 3||§6 Smooth Maps on a Manifold
§8 The Tangent Space
|Week 4||§9 Submanifolds
§12 The Tangent Bundle
|Week 5||§13 Bump Functions and Partitions of Unity
§14 Vector Fields
|Week 6||§17 Differential 1-Forms
§18 Differential k-Forms
§19 The Exterior Derivative
|Week 7||§21 Orientations
§22 Manifolds with Boundary
|Week 8||§23 Integration on Manifolds
For the remaining time, instructors are welcome to cover some of the following topics. Also, some instructors might go faster, and leave time for the following time-permitting topics.
- §15 Lie Groups
- §16 Lie Algebras
- §24 De Rham Cohomology
- Sard's theorem
- Morse theory
- Introduction to Smooth Manifolds, by Jack Lee.
- Notes on Manifolds, by Dmitry Fuchs.