Textbook:  "Riemannian geometry" by M. do Carmo.

Course overview: This is introductory course in differential geometry. I expect that you know basics of differentiable manifolds, as described in Chapter 0 of do Carmo's book (and covered in MAT-239). In the class we will cover Chapters 1 through 4 of the textbook plus some extra material on geometry of general bundles. The main objective of the course is to introduce Riemannian metrics, connections and curvature for Riemannian manifolds. All these, are explained well in the textbook (which is one of the best Riemannian Geometry introductory textbooks). On few occasions, I will go outside of the textbook, namely, when we discuss connections and curvature on other bundles. 

Grading: I will assign weekly homework, which will be due on Mondays, in class. The homework score will be 70% of your grade. For the last three weeks of the quarter, I will give every student a paper in differential geometry to read. After reading the paper, you will write a 2-page long description (in your own words) of what is in the paper (there is no need to understand the details of the proofs, although it is nice if you can!). This will count for the remaining 30% of your grade.  

Important dates:

First day of classes: Monday, January 6, 2020.

Holidays: MLK Day (Monday, January 20), President's Day (Monday, February 17).

Last day of classes: Friday, March 13, 2020.

ADA Statement:

The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the quarter to discuss any such accommodations for the course.