Differential Geometry
MATH 4250/6250
University of Georgia, Spring 2009

Professor Clint McCrory
Office: 402 Boyd Graduate Studies Research Center, 706-542-2576
Home: 390 Franklin St., Athens 30606, 706-353-6517
Email: clint at math dot uga dot edu

Class meetings
Monday-Wednesday-Friday 12:20-1:10
303 Boyd Graduate Studies Research Center

Office hours
Monday-Wednesday-Friday 1:30-2:30
Tuesday-Thursday 12:30-2:00
or by appointment.

Prerequisites
MATH 2500 (Multivariable Calculus) and MATH 3000 (Linear Algebra)
or
MATH 3510(H) (Multivariable Mathematics II)

Syllabus
The required textbook is Differential Geometry and Its Applications, by John Oprea (second edition, published by the Mathematical Association of America). We will cover chapters 1, 2, 3, and part of chapters 5 and 6: Curves, Surfaces, Curvature, Geodesics, and Holonomy.

There is no required software, but students who have access to MAPLE or MATHEMATICA are encouraged to use these tools. Oprea's book has sections on using MAPLE to investigate curves and surfaces. Another good text (not required) with computer explorations is Modern Differential Geometry of Curves and Surfaces with Mathematica, by A. Gray, E. Abbena, and S. Salamon.

To investigate curves and surfaces, we'll use 3D graphing software developed by David Eigen, an undergraduate student of Tom Banchoff at Brown University: Differential geometry lab

Exams, homework, and grading
There will be two in-class exams and a final exam. Homework will be assigned every week. Your grade will be based on the exams, homework, and class participation. The two exams will count 25% each, homework will count 25%, and the final exam will count 25%. Class participation will be considered in borderline cases.

Note: Some homework problems are from Elements of Differential Geometry, by R. Millman and G. Parker.

Problem set 1
Problem set 2
Problem set 3, part A, Part B
Problem set 4, part A, Part B
Problem set 5, part A, Part B, revision of problem 1(a)
Problem set 6 (Don't hand in.)
Review for Exam 1
Problem set 7 - rework Exam 1
Problem set 8
Problem set 9, part A, Part B
Problem set 10 (revised 3/30) There's no lab in this problem set.
Problem set 11 (Don't hand in.)
Review for Exam 2
Problem set 12, Solutions.
Problem set 13 (Problem A revised 4/22), Solutions.
Problem set 14, Solutions.
Review for Final Exam
Formulas for Final Exam

Exam 1: Friday, February 20, retest Wednesday, March 4. Solutions.
Exam 2: Friday, April 10. Solutions.
Final Exam: Wednesday, May 6, 12:00 - 3:00 pm

Notes from class
Geodesics - sketch proof that geodesics locally minimize distance
Parallel transport - existence and uniqueness of parallel vector fields

Useful links and references
Best jobs - Mathematician is number one!
Schaum's Outline of Differential Geometry, by Martin M. Lipschutz - Useful inexpensive supplementary text, with review of vector calculus. (The notation is not exactly the same as in our textbook.)

All academic work must meet the standards contained in the document A Culture of Honesty. Students are responsible for informing themselves about those standards before performing any academic work.

This page was created on January 3, 2009. It was last revised on May 7, 2009.