Office Hours: Mondays 3:00 - 4:00pm and by appointment
Course Description: Differential and topological manifolds, classical groups and associated manifolds, tangent and tensor bundles, vector fields, differential forms, transversality, Sard's theorem, Stokes' Theorem.
Text: Differential Topology, Guillemin and Pollack (ISBN: 9780821851937)
Content: We're aiming to cover most of the book.
Exams: There will be a midterm and a final exam, both take-home.
Midterm: around early March Final: end of April
You will be responsible for the material covered in the lectures, the readings, and the homework.
Homeworks: Homework will be assigned below. It will be due every week or two at the beginning of class on Tuesdays.
Grades:
Overall Score = Hwk 40% + Midterm 30% + Final 30%
Letter grades will approximately follow standard cutoffs, e.g. A>90%, B>80%, C>70% with +/-.
Academic Honesty: Each student will uphold the University of Miami Honor Code.
Guillemin and Pollack, Differential Topology ERRATA (compiled by Shifrin)
Think about all the starred problems, even if not assigned.
Due | Readings | Problems |
---|---|---|
Tues Jan 19 | 1.1-1.3 | 1.1.3,4,6,14,18 (Check the ERRATA!) 1.2.2,4,6,9 |
Tues Jan 26 | 1.3-1.4 | 1.3.1,2,5,6,9 1.4.1,5,7,10 (Actually, consider 9-13) (Deferred: 1.5.2,5,7) |
Tues Feb 2 | 1.5-1.6 | 1.5.2,5,7 1.6.4,7,10 |
Tues Feb 9 | 1.7-1.8 | 1.7.8,9,16,17,18 1.8.5,6,9 |
Tues Feb 16 | 2.1-2.3 | 2.1.3,5 2.2.3 2.3.12,16 |
Tues Feb 23 | 2.4-2.6 | 2.4.1,5,6,7 2.6.3 DUE Mar 1 |
Tues Mar 1 | 3.1-3.3 | 3.2.4,8,11 3.3.2,4,10,13 |
Tues Mar 8 | SPRING BREAK |
|
Tues Mar 15 | MIDTERM Details to come. | |
Tues Mar 22 | 4.1-4.2 | Read |
Tues Mar 29 | 4.2 | 4.2.2,3,12 |
Tues Apr 5 | 4.2, 4.3 | Verify the equations in the middle of pages 163, 164. Do the exerise on page 165. |
Tues Apr 12 | 4.4, 4.5 | 4.4.3, 5, 7, 4.5.1, 2 |
Tues Apr 19 | 4.6, 4.7 | 4.7.8,13 |