MAT 401: Seminar in Mathematics

Discovery of the Einstein Field Equations

Fall 2016

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 linear algebra, preferably at the level of MAT 310 and vector calculus, preferably at the level of MAT 322, is necessary. A differential geometry course such as MAT 364 would also be very useful background.

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:

Relativity: Special, General and Cosmological, Second Edition, by Wolfgang Rindler, Oxford U. Press, (2006).
This is available on Amazon, and elsewhere, and also as a direct PDF file: here
Also worth studying are the classics
The Meaning of Relativity, 5th Edition, by Einstein, Princeton Univ. Press.
Space-Time-Matter, by Hermann Weyl, Dover Publ.

A good source for the mathematical concepts, (at an advanced level but much weaker on the physics), is
The Geometry of Physics, by T. Frankel, Cambridge Univ. Press.

The course will consist of presentations by both students and the instructor. Grades will be determined by the quality of the student's lectures, as well as participation (asking questions, making comments, and such) during the lectures. Not coming to class regularly will reflect negatively on your grade.

There may also be occasional homework assignments.

Class Time and Place: Tu and Th 11:30 - 12:50, Earth and Space Sciences 183.

Disability Support Services: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disabled Student Services (DSS) office: ECC (Educational Communications Center) Building, Room 128, (631) 632-6748/TDD. DSS will determine with you what accomodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accomodated. All information and documentation of disability 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: and search Fire safety and Evacuation and Disabilities, link

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