Blackhole image from: http://www.voyagesolarsystem.org/images/DC/image_pow-mod_4zm.jpg
Wormhole image from: http://casa.colorado.edu/~ajsh/schww.html#worm

The East Tennessee State University Department of Mathematics will offer a graduate level class in Differential Geometry (MATH 5310) Term I of Summer 2002 (June 3 - July 8). The class will be held in Sam Wilson Hall, Room 302 at 11:20-12:50 Monday through Friday. This will be a somewhat unconventional introduction to differential geometry. The class meets for only 5 weeks and the instructor, Dr. Robert Gardner, will emphasize applications. Approximately half of the class time will be spent on Einstein's theories of special and general relativity. Therefore the target audience will be physics and mathematics majors. The class will use as a text "Differential Geometry and Relativity Theory, An Introduction" by Richard L. Faber, Monographs and Textbooks in Pure and Applied Mathematics, Volume 75, copyright 1983 by Marcel Dekker, Inc. (ISBN 0-8247-1749-X). For a general introduction to relativity theory, we will use as a supplemental text "Relativity: The Special and the General Theory" by Albert Einstein, available from Random House. For an introduction to more exotic topics (such as black holes, wormoles and time travel), we will refer to the supplemental text "Cosmic Time Travel" by Barry Parker, published by the Perseus Book Group, available in paperback from Amazon.com and Barnes and Noble.

The course will follow the outline:

I. Differential Geometry

1. Curves and Curvature
2. First Fundamental Form (Metric Form) of a Surface
3. Second Fundamental Form (Normal Curvature and Quadratic Form)
4. Geodesics and Christoffel symbols
5. Gauss' Theorema Egregium

1. Inertial Frames and Michelson-Morley Experiment
2. Postulates of Special Relativity
3. Lorentz Transformation
4. Space-Time diagrams
5. Twin Paradox

1. Gravity
2. Field Equations
3. General Relativity and the Bending of Light

Students will be evaluated based on their performance on homework assignemnts.

Dr. Gardner will also offer a Summer Term I Special Topics in Math (MATH 4957) as a senior level class covering similar topics.

For the LATEST information on this course, check out the class homepage at www.etsu.edu/math/gardner/5310/5310.htm.

Hubble image of the core and accretion disk of galaxy NGC 4261 which contains a supermassive blackhole.

Return to Bob Gardner's home page