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).

SUPPLEMENTARY TEXT: Relativity: The Special and the General Theory by Albert Einstein. This can be found as a cheap paperback, but is also available online, for example at "Google books.''

PREREQUISITES: Multivariable calculus and linear algebra (the more, the better!).

ABOUT THE CLASS: This course will be roughly broken into three parts: (1) differential geometry (with an emphasis on curvature), (2) special relativity, and (3) general relativity. We will spend about half of our time on differential geometry. We will then take a "break" and address special relativity. The class will finish (and climax) with general relativity and a discussion of black holes. We will deal at length with the (differential geometry) topics of curvature, intrinsic and extrinsic properties of a surface and manifold. We will briefly survey special relativity (giving coverage that a physicist would consider fairly thorough, but which a geometer would consider a "shallow survey"). In particular, we will "outline" (as the text puts it) Einstein's field equations and derive the Schwarzschild solution (which involves a nonrotating, spherical mass). We will see the differential geometry concepts come to the aid of gravitation theory. We will discuss gravitational redshift, precessions of orbits, the "bending of light," black holes, and the global topology of the universe.

MY TEACHING STYLE FOR THIS CLASS: We will go at a maddening rate. My lectures will follow from the overheads which I present in class and which are available online.

GRADING: Your grade will be determined based on your performance on assigned homework problems. Very roughly, you will be assigned 3 or 4 problems per section we cover.