Final Exam Review will
take place on Monday, December 14, 10-12 in BA2179.
The Final will take place on
Tuesday, December 15, 10-1 in BA6183.
- It will cover everything we've covered
in class, lecture notes and on homework.
Specifically, it will cover the following material:
- Chapter 3: Everything except functors.
- Chapter 4: Everything except for covering maps.
- Chapter 5: Submanifolds, embeddings.
- Chapter 6: Sard's Theorem, Whitney embedding
theorem for compact manifolds, Transversality.
- Chapter 8 : Vector fields, criteria of
smoothness, sufficient condition for the triviality of
the tangent bundle.
- Chapter 9: Integral curves and integral flows.
- Chapter 12: Everything except tensor products of
vector spaces.
- Chapter 14: Alternating tensors, cotangent
bundle, tensor bundles on manifolds, differential forms,
exterior derivatives.
- Chapter 15: Orientations on vector spaces,
orientations on manifolds.
- Chapter 16: Integration of forms, Stokes's
Formula, applications to De Rham cohomology, Integration
on Riemannian manifolds
- Chapter 17: Mayer-Vietoris sequence, Cohomology
with compact support, degree theory.
- Euler charactersitic of orientable manifolds and
Euler characteristic mod 2.
- Rules for the Final : No
aids
allowed. No
calculators or notes! You can quote results from the
book, lectures and homework.
Here are some practice problems
on recent material to help you prepare for the Final.
I also recommend that you do the following problems from the
book:
- 1-7, 1-11, 2-6, 2-8, 3-1, 3-6, 3-8, 4-2,
4-7, 5-1, 5-6, 5-7, 6-2, 6-9, 8-3, 8-4, 8-11, 9-3d, 9-4,
9-5, 14-7ab, 15-13a