Course Homework for Math 42 Differential Geometry I
Lectures |
Sections in Text |
Homework Assignment |
Weeks 1 and 2 |
Chapter 1: The Geometry of Curves |
Exercises 1.1.25; 1.2.5; 1.3.7; 1.3.11, 1.3.13, 1.3.19, 1.4.8 parts a, b, c, 1.4.14, 1.5.8 due Friday January 21 at 11:59 PM in Canvas |
Weeks 3 and 4 |
Chapter 2: Surfaces |
Exercises 2.1.1, 2.1.12, 2.1.20, 2.1.22, 2.2.7, 2.2.14, 2.3.9, 2.4.6 due Friday February 4 at 11:59 PM in Canvas |
Weeks 5 and 6 |
Chapter 3: Curvatures |
Optional Homework Exercises 3.1.2, 3.1.9, 3.1.11 (only the first part), 3.2.4 (this exercise is computation hard and is strongly recommended to be done in a group), 3.2.10, 3.4.6 for more adventurous group work you can try Exercise 3.5.10. This homework will not be graded, however if you want to submit it on Canvas anyways this is certainly fine. |
Weeks 7 and 8 |
Chapter 5: Geodesics, Metric and Isometries, Gauss Theorem and Toponogov Theorem (briefly) |
Exercise 5.1.2, 5.1.9 (follow the hint in the textbook, rather than the symmetry proof we discuss in class), 5.1.12, 5.1.13, 5.2.1, 5.4.4, 5.4.6, 5.4.10, 5.4.15 due 11:59 PM on Friday March 4 in Canvas |
Week 9 |
Chapter 5: Geodesics, Metric and Isometries, Gauss Theorem and Toponogov Theorem (briefly) |
Optional Homework not to be submitted |