Math 651B Spring 2005:

Mathematics of Relativity and Gravitation

Mathematics of Relativity and Gravitation

The course will begin with and move rapidly through the special theory of relativity, a theory that explains how time and space measurements depend on an observer's inertial frame of reference. The main mathematical ingredient for this part of the course will be linear algebra, and the focus will be on Lorentz transformations, hyperbolic rotations, and Minkowski geometry. Following that we will slow down a bit and develop the rudiments of differential geometry needed for an introduction to general relativity, and then proceed to general relativity itself. General relativity is a theory of gravity. It explains gravity in terms of the geometry of spacetime. The unifying theme will be geometry in the context of both flat and curved spacetimes.

INSTRUCTOR: Dr. Klein

OFFICE: Faculty Office Building 127 Phone: 677-7792

email: david.klein@csun.edu

web page: www.csun.edu/~vcmth00m

OFFICE HOURS: Monday & Wednesday 11: 30 to 12: 30 and by appointment

TEXTBOOK: The Geometry of Spacetime: An Introduction to Special and General Relativity, by James J. Callahan, Springer-Verlag Undergraduate Texts in Mathematics, copyright 2000, ISBN 0-387-98641-3 Corrected second printing 2001. Note: Corrections to the textbook are available from:

http://www.math.smith.edu/~callahan/spacetime/errata/errata.html

This pdf file contains a more updated set of corrections:

http://maven.smith.edu/~callahan/spacetime/errata.pdf

GRADING: Grades will be based on homework and a final exam, with each contributing 50% to the final grade for the course. Students may collaborate on homework problems, but each student is expected to understand everything s/he turns in. The final exam will be based on homework assignments and other material from the textbook and lectures. Plus grades (+) and minus grades (–) will be assigned for this course.

COVERAGE: As much of the textbook as time permits.

INTERNET RESOURCE: Relativity on the World Wide Web

Mike's Message Board: http://651b.proboards40.com/index.cgi