Prerequisites: Math 239, Math 201A. Math 250AB recommended.

Textbook: do Carmo, Riemannian Geometry

Syllabus: We will cover the basics of the geometry that one
encounters when one has a metric or connection on a differentiable
manifold. See also the
department syllabus.

Grading: 75% homework, 25% takehome final exam

Homework: Homework will be assigned roughly weekly

Welcome to Math 240A: Differential Geometry

Homework assignments will be posted here as the
course progresses. The takehome final exam is now posted below.

Problem sets

Problem sets will be posted here on Fridays, due the following Friday
in class.
You are encouraged to collaborate with other students, as long as you
do not simply copy their answers.

Problem set #1, due 10/8: Read Chapter 0. Then do exercises
1, 2, 4, 5, 11.

Problem set #2, due 10/15: Exercises 1, 2 of Chapter 1, and
exercises 2 (is this true for any affine connection on a differentiable
manifold?), 3, 4, 8 of Chapter 2.

Problem set #3, due 10/24: Exercise 7 of Chapter 2, and
exercises 1 and 2 of Chapter 3.

Problem set #4, due 10/31: Exercises 4, 5, 6 and 7 of
Chapter 3.

Problem set #5, due 11/7: Exercises 5 and 6 of Chapter 3,
and exercises 2 and 3 of Chapter 4.

Problem set #6, due 11/14: Exercises 4, 6, 7, 8 and 10 of
Chapter 4.

Problem set #7, due 11/21: Exercises 1, 3 and 5 of
Chapter 5.

Problem set #8, due 12/1: Exercises 1, 2, 5, and 12 of
Chapter 6.

Exam

The takehome final exam is due Tuesday, December 9 by 1:00. Obviously,
you are not allowed to discuss it with any of your classmates or anyone
else until after you have handed it in. You may email me with questions
or concerns, but I will not give out any hints individually; if I
determine that a hint is appropriate, I will email it to everyone.