MTH 420/520: TENSORS AND DIFFERENTIAL FORMS (Winter 1999)
This course is a self-contained introduction to the many uses of differential
forms. This approach emphasizes geometric content in a coordinate independent
way; a good analogy is the use of vectors, rather than their components, to
describe a given situation. While we will spend some time developing the
necessary mathematical tools, the emphasis will be on applying these tools to
concrete examples drawn from the physical sciences.
The main prerequisite is a certain amount of scientific maturity, rather than background in a particular area. The only specific requirements are a working knowledge of multivariable calculus and linear algebra.
*Graduate credit for this course has not yet been formally approved.
MTH 437/537: GENERAL RELATIVITY (Spring 1999)
This course is a nearly self-contained introduction to general relativity. We
will study Einstein's theory of relativity, one of the most mathematically
elegant physical theories ever proposed. In essence, this theory says that
gravity is curvature!
After briefly considering special relativity from a geometric point of view we will then study the Einstein field equations. We will examine several special solutions of these equations, including simple cosmological models, such as the Big Bang, and black holes.
The recommended prerequisite for this course is MTH 420/520 (see below).
Further information:
It is strongly recommended that students interested in the relativity
course plan to take both courses, which form a natural sequence. Students
interested in trying to do otherwise are encouraged to discuss this with me as
soon as possible.