MAT 401: Seminar in Mathematics

Discovery of the Einstein Field Equations

Fall 2003

Course Description. The goal of this seminar is to understand how Einstein was led to his discovery of General Relativity and the gravitational field equations. Fundamentally, this involves the idea of "general covariance", that the laws of physics are independent of their description in any particular or preferred system of coordinates.
Tracing this path may be quite challenging. We will need to develop some quite sophisticated mathematical concepts, including manifolds and tensors, metrics and curvature. At a minimum, a solid background in vector calculus, preferably at the level of MAT 322, is required. Throughout the course, we will pay close attention to the relations between the physics and the mathematics.
A rough order of the topics to be covered is:

The first three topics will be done quite quickly, in the first few weeks. The bulk of the seminar focuses on the last three topics.

Instructor: Michael Anderson

Texts: There is a large variety of very good texts on this topic, and you are encouraged to search around to find books and sources that appeal to you. The main text for the course is the classic:

The Meaning of Relativity, 5th Edition, by Einstein, Princeton Univ. Press.
This should be in the campus bookstore. Another excellent text, now out of print is:
Essential Relativity: Special, General and Cosmological, by Wolfgang Rindler, Springer Verlag.
There are a number of new and used copies of this (and the presumably similar text ``Relativity: Special, General and Cosmological", by the same author available through, (and maybe elsewhere). Another classic is
Space-Time-Matter, by Hermann Weyl, Dover Publ.
A good source for the mathematical concepts, (although much weaker on the physics), is
The Geometry of Physics, by T. Frankel, Cambridge Univ. Press.

Finally, you'll find a great online source on relativity at all levels, including some free texts, at Relativity on the World Wide Web here, (

The course will consist of presentations by both students and the instructor. It is hoped that the presentations, while clear and rigorous, will be informal and filled with discussion and commentary between the lecturer and the audience. If this goes well, there will be no other formal requirements for the course, besides participation. If not, homeworks or project assignments will be expected. ... - TBA

Class Time and Place: Tu and Th 11:20 - 12:40 a.m., Math Tower, P-131.

Americans with Disability Act. If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disabled Student Services in ECC (Educational Communications Center) Building, Room 128, (631) 632-6748. They will determine with you what accomodations are necessary and appropriate. All information and documentation is confidential.
Students requiring emergency evacuation are encouraged to discuss their needs with their professors and Disabled Student Services. For procedures and information, go the following website:, here