This is a proof-based introduction to differential geometry, beginning with curves and surfaces in Euclidean space and continuing to intrinsic geometry and Riemannian manifolds. A syllabus can be found here.

The course text is Wolfgang Kühnel, Differential Geometry: Curves–Surfaces–Manifolds, third edition.

Course schedule and notes

Approximate sections of Kühnel are indicated in yellow.

Problem sets

Suggested exercises from Kühnel are listed below. Selected solutions are posted when available.

Project

The group project is worth 25% of the course grade. Groups of two or three will prepare a 6–10 page mathematical expository paper and give a joint presentation. Complete expectations, suggested topics, and the grading rubric are in the project handout.

1. Oct 8 Partner and topic selection
2. Oct 22 Preliminary bibliography and proposal
3. Dec 1 Written report due
4. Dec 3, 8 Project presentations

Project resources