Michael Spivak: A comprehensive Introduction to Differential Geometry. Volume 1, Publish or Perish, Inc, Houston, Texas. ISBN: ISBN 0-914098-70-5. xvi+498 pp.
The examination will cover the material in the following chapters:
- 1. Manifolds
- 2. Differential structures
- 3. The tangent bundle
- 4. Tensors
- 5. Vector fields and differential equations
- 7. Differential forms
- 8. Integration
Each oral exam will start with one problem from the list of starting questions. All students are advised to prepare 5 to 10 minute answers to those questions.
Bjørn Jahren's notes on de Rham cohomology are an optional supplement to chapter 8.