**Lectures:** TTh 12:30 -- 1:45, Hayes-Healy 117.

**Office hours:** Th 5-6, Hurley 283 (tentative), or by appointment.

**Syllabus:** We will loosely follow Lee's and do Carmo's books. We will aim to cover material in do Carmo up through chapter 10, and maybe beyond if we have time/inclination. We will cover: Riemannian metrics, connections, geodesics, curvature, submanifolds, Gauss-Bonnet theroem, Jacobi fields, curvature comparison theorems. Here are the lecture notes from when I taught the course in 2021.

**Book:** do Carmo, ``Riemannian geometry.'' Lee, ``Introduction to Riemannian manifolds.''

**Grade:** There will be one take-home midterm, and one take-home final. Your grade will be weighted by: 50% homework, 25% midterm, 25% final.

**Midterm:** Will take place the week of March 18. It will be a take-home midterm. You won't have homework for that week.

**Homework:** There will be regular (~weekly) homework assignments. I will post the homeworks and solutions here as they appear.

- Homework 1 (due January 25) solutions
- Homework 2 (due February 6) solutions
- Homework 3 (due February 13) solutions
- Homework 4 (due February 20) solutions
- Homework 5 (due February 27) solutions
- Homework 6 (due March 5) solutions
- Midterm (due evening of March 22) solutions
- Homework 7 (due April 2) solutions
- Homework 8 (due April 11) solutions
- Homework 9 (due April 23) solutions
- Final Exam