Syllabus for Math 518: Fall 2010

Introduction to Differential Geometry

This course is designed to introduce differential geometry to students at the advanced undergraduate and beginning graduate levels through a thorough examination of the basic concepts of the subject in the cases of curves and surfaces embedded in 3 dimensional space. The third semester of calculus, Ma 242, is an essential prerequisite for the course as well as exposure to the subjects of differential equations and linear algebra.

The text for the course is Differential Geometry by John Oprea, 2nd edition published by Pearson/Prentice Hall (New Jersey)

The schedule for topics covered is as follows:

1. Geometry of Curves (Chapter 1) 4 days

2. Surfaces (Chapter 2) 5 days

3. Curvature (Chapters 3 and 4) 8 days

4. Geodesics, Metrics and Gauss Bonnet Theorem 8 days

(Chapters 5 and 6)

5. Calculus of Variations (Chapter 7) 3 days

The topics listed above coincide roughly with the chapters referred to in Oprea. Not all chapters will be covered in their entirety. Topics will be selected as time permits.

Grading for the Course is based on the following data:

2 Tests, I each after chapters 1, 2,and 3 and after chapters 4, 5 and 6

3 problem sets, based on daily homework, due during the course

A Final Exam.

The weights for these are 30% for the test, 50% for the assignments and 20% for the final. The final exam is Monday, Dec 13 from 8 to 11 AM.