Math 501: Differential Geometry, Spring 2012
Course Notes
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Apart from these notes from Professor Gluck, the course has a textbook which is
Differential Geometry of Curves and Surfaces by Manfredo do Carmo.
| Lecture dates | Notes | |||
| Jan 12, 17, 19, 24 | Curves | |||
| Jan 26, 31, Feb 2 | Surfaces | |||
| Feb 7,9,14,16 | The Geometry of the Gauss Map | |||
| Feb 21, 23, 28 | Intrinsic Geometry of Surfaces | |||
| Mar 1 | The Isoperimetric Problem | |||
| Mar 13, 15, 20, 22 | Geodesics | |||
| Mar 29, Apr 3, 5, 10, 12, 17 | The Gauss Bonnet Theorem | |||
| Apr 19 | The Fary-Milnor Theorem | |||
Homework Assignments
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Homework is usually due on Thursday at 4PM the week after it's assigned. Please put it in the bin on my office door or hand in to me in person if I'm in my office.
Homework is graded using the following scheme:
No work = no mark = 0 pts
Tried unsuccessfully = a check = 1 pt
Got the idea but incomplete = one star = 2pts
Completed the major work = two stars = 4pts
| Due date | Notes covered | Problems | Answers | |
| Jan 19 | Curves | 2,3,5,6,7,8 | HW1 Ans | |
| Jan 26 | Curves | 13,14,16,17 | HW2 Ans | |
| Feb 2 | Surfaces | 0 in email. 1,2,3,4,5 in notes | HW3 Ans | |
| Feb 9 | Surfaces | 14,15,16 in notes. 1,5,14,15 in do Carmo, p. 99-102 | HW4 Ans | |
| Feb 16 | Gauss Map | 3,5,6,7,8,9,11,12,13 | HW5 Ans | |
| Feb 23 | Gauss Map | 15,17,19,20 | HW6 Ans | |
| Mar 15 | Intrinsic Geo | 5,8,10 | HW7 Ans | |
| Mar 29 | do Carmo | 1,5,6,7,12,13,18,20 of 4.4 | HW8 Ans | |
| Apr 5 | GaussBonnet | 2,3,5,6 in notes. 2,3,4 in do Carmo, p. 282-283 | HW9 Ans | |
| Apr 12 | GaussBonnet | 8,9,12,13,14, Lemma 2 | HW10 Ans | |
Exams
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There are two take-home midterms, one on Feb 21st - 28th and the other Apr 10th - 17th. There is no final exam.
Enjoy the Galleries
