Introduction to Differential Geometry

**Our FINAL EXAM is scheduled for Wednesday May 13. **

**Our second in-class exam is scheduled for Tuesday April 28. **

**Our first in-class exam is scheduled for Thursday March 5. **

**Lectures: ** Tuesday and Thursday from 10:30 - 11:50PM in 343 Altgeld Hall

**Instructor: ** Ely Kerman,
ekerman@math.uiuc.edu

**Office & Telephone: ** 326 Illini Hall, 265-6710

**Office Hours: **
Thursday 1:00-3:00, or by appointment.

**Textbook (required): ** Theodore Frankel,
The Geometry of Physics, Cambridge U.P. (paperback).

**Course Material: **

1. Manifolds: configuration spaces, differentiable manifolds, tangent spaces, tangent bundles, orientability.

2. Calculus on manifolds: Vector fields, flows, tensor fields.

3. Differential forms and exterior calculus.

4. Integration theory: Generalized Stokes theorem, de Rham cohomology.

5. Riemannian geometry: Riemannian metrics, geodesics.

(Question 5 has been corrected in this version.)