Instructor: Tobias Holck Colding
Email: colding [at] math . mit .edu
Office: Room E17-342
Office Hours: Wednesdays 8:30 - 9:30AM
Lectures: MW 9:30-11 E17-128
COURSE INFORMATION
Prerequisites: 18.101, 18.950 or 18.952
Text Book: Manfredo do Carmo: Riemannian Geometry; Birkhauser.
10 Weekly Homework.
No final exam but grade will instead be based on the weekly homework.
Homework will be from the book.
Chapters 0 - 12 will be covered in class.
Grader: Nick Strehlke
Email: strehlke [at] mit . edu
Office Hours: E17-301ad, Tuesdays 9-10AM
HOMEWORK
Homework should be turned in to the box in E18.366 (administrative office) by 3pm on the due date. Problems and page numbers refer to the book.
Assignment 1, due Wednesday, September 16: pp. 31 - 34, problems 1, 2, 3, 4, 6, 7, 8.
Assignment 2, due Wednesday, September 23: pp. 33 - 34, problems 9, 10, 12, and pp. 45 - 47, problems 1, 2, 3, 4.
Assignment 3, due Wednesday, September 30: p. 46, problems 5, 6, and pp. 56 - 59, problems 1, 2, 3, 4, 5, 6.
Assignment 4, due Wednesday, October 7: pp. 56 - 59, problems 7, 8, 9, and pp. 77 - 87, problems 1, 2, 3.
Assignment 5, due Friday, October 16: pp. 77 - 87, problems 7, 8, 9, 10, 11, 12.
Assignment 6, due Wednesday, October 21: pp. 77 - 87, problems 13, 14, and pp. 103 - 109, problems 3, 4, 5, 6, 9, 10.
Assignment 7, due Wednesday, October 28: pp. 119 - 123, problems 1 - 8.
Assignment 8, due Wednesday, November 4: pp. 139 - 143, problems 1 - 8.
Assignment 9, due Thursday, November 12: pp. 139 - 143, problems 9 - 12, and pp. 152 - 154, problems 1 - 5.
Assignment 10, due Wednesday, December 2: p. 154, problems 11 (see remark), 12, 13, and p. 207, problems 1, 5, 6. Remark on problem 11, p. 154: Instead of assuming the vector field is bounded away from zero, assume it is bounded.