MATH 492: Junior/Senior Honors Seminar in Mathematical General Relativity, Spring 2014

Lecture: Tue 18:40-20:00 Hill-525

Instructor: Shabnam Beheshti
Office: #214, Hill Centre, Busch Campus
e-mail: beheshti[at]math[dot]rutgers[dot]edu

Graduate TA: Moulik Balasubramanian
Office: #622, Hill Centre, Busch Campus
e-mail: moulik[at]math[dot]rutgers[dot]edu

"Office" Hours: We will be holding workshop-style office hours in the Busch Campus Center on Fridays, 14:00-15:30. You can stop by to discuss weekly readings, work on suggested exercises, or practice your presentations with us (over coffee)!


Course Information

Required Course Notes: Curvature of Space and Time, with an Introduction to Geometric Analysis, by I. Stavrov Allen

Recommended Course Textbook: Introducting Einstein's Relativity, by Ray d'Inverno, Oxford University Press 1992 (ISBN: 9780198596868; softcover, 400 pages, $89.95)

A Remark on the Recommended Text: I will be following lecture notes given at an advanced undergraduate summer school on geometric analysis, highlighting the relevant segments of d'Inverno's book for further study. A copy of this text is on reserve at the Mathematics Library (ground floor of the Hill Centre). I will be compiling a reference list for each lecture (see below).

Prerequisites for 640:492: Differential & Integral Calculus, Multivariable Calculus, Ordinary Differential Equations and Linear Algebra. Lectures and coursework will involve computation as well as proofs, so courses such as 640-300 (Math Reasoning), 311/312 (Real Analysis I/II) are also extremely helpful. Any background in Differential Geometry and/or Partial Differential Equations will also be supremely useful. I have included the supplementary background reading list above for your use throughout the term, all of which can be found in our library (or a similar book is available). The "Recommended Readings" will assume you know most of the basic knowledge that this list encompasses.

Background Reading (for above Prerequisites):
1. Vector Calculus, by J. Marsden and A. Tromba. This, or any other calculus textbook covering Green's, Gauss'/Divergence and Stokes' Theorem is highly suggested for a review of chain rule, directional derivatives, gradient, line and surface integrals. Rutgers uses Calculus: Early Transcendentals, by Rogawski (2nd edition). I urge you to have some vector calculus book handy to quickly do the easier calculations suggested in class.

2. Elementary Differential Equations, by W. Boyce and R. Di Prima. Often used as a course textbook for ODEs.

3. Partial Differential Equations, by W. Strauss. A classic textbook in PDE, on which the current Rutgers 423 course is largely based.

4. Introduction to Real Analysis, by R. Bartle and D. Sherbert. Useful for basic calculus proofs on the real line.

5. Differential Geometry of Curves and Surfaces, by M. P. Do Carmo. Beautiful introduction to the fundamental objects of study in differential geometry. His other books are also excellent. Warning: Uses different sign conventions than us.

6. ABCs of Gravity, by X.Y. Zee.

Our (rather ambitious) Course Syllabus: This course will be run in lecture-seminar style. I will describe this setup more clearly on the first day of classes. You will be expected to prepare and present lecture material (typically in groups), complete exercises of varying difficulty, and complete assigned readings in advance of each weekly meeting. Since this course only meets once a week, attendance AND participation are mandatory. You will be responsible for all the material covered in lecture, including announcements, changes to course material as well as exercises and readings.

Grading Scheme: You will submit three homework assignments (Feb, Mar, Apr)and give two presentations. There will be no midterm or final examinations.

It is also important for you to know the Rutgers University Academic Integrity Policy.

Lecture Schedule

Below, I have compiled a variety of other GR-related resources around the web with some brief commentary. Please note that this is by no means an exhaustive list, but some suggestions for places you can go next to learn more!