Robert H. Gowdy:   Web-page    e-mail

This course is the second semester of a sequence. The first semester, PHYS591: Geometrical Methods of Physics, covered the geometry of manifolds and connections on manifolds. The required concepts will be reviewed briefly in the first lecture of this course, but only for the purpose of establishing notation.

The course will be taught primarily from these web-notes and from the internet resources that are linked to these notes.

There are far too many topics to cover in a semester, so I will start with a few that interest me and let the course evolve from there.

Because Einstein's General Theory of Relativity is very likely to be the correct low-energy limit of any viable theory of gravity, we will spend about half of the semester on it. The initial value structure of the theory and a few useful solutions such as the non-rotating black hole solution of Schwarzschild and the flat Robertson-Walker-Friedman cosmology will be discussed. Some additional topics in general relativity will show up as examples later in the course.

I will leave a large part of the semester to discuss the topic that I know best: The geometry of surface embeddings and projection-tensor fields. That topic turns out to be at the center of current research on what have come to be called 'branes' and is needed to understand the proposed experimental tests for large-scale extra dimensions.

Homework will be distributed and collected as LaTeX files on the web. You will need either Scientific Notebook (SN) or Scientific Workplace (SW) to participate easily since the files are 'wrapped' using the protocol of these programs. The Homework Page presents a table with assignments and solutions. To do a homework assignment for credit, click on an assignment, download the file, and open it using SN or SW, and do the exercises. You will have the full power of a symbolic algebra program to perform or (more often) verify your calculations. When you are satisfied with your work, save it and e-mail the wrapped file to me. I will then insert grades and comments on your work, wrap the file, and e-mail it to you as an attachment.

Once a solution to an assignment has been posted, no credit can be given for that assignment. Each assignment has a due-date listed. The solution will be posted some time after the due-date.

Each homework assignment will receive a grade between 0 and 100 points. Your average homework grade becomes your homework score.

Exams will be given after natural break-points in the material and a final exam will be given at the end of the course. All exams, including the final, will be distributed and collected as LaTeX files on the web. The Exam page presents a table with exams and solutions. The posting of a new exam will be announced on the course home page as "Exam in Progress". To take an exam, click on the latest exam link to download the file, open it using SN or SW and work the problems. Wrap the file, and e-mail it to me. I will then insert grades and comments and e-mail the resulting file back to you as an attachment.

Once a solution to an exam has been posted, no credit can be given for that exam.

Each exam will receive a grade between 0 and 100 points. Your exam average, with the final exam counted twice, becomes your exam score.

The scheduled meeting time for this course is Tuesday and Thursday from 12:30pm to 1:45pm in OLVPH2121. Because the on-campus class is quite small, we may agree to change the time and place. Any such change will be announced on this web-page and in the course forum.

The class meetings provide motivation and communication. This course is set up so that you can do the whole thing on-line and never come to class. However, the course is not self-paced, so you have to keep up with it. You will find that attending class makes it much easier to realize when you are falling behind.

Because the class is small, I will assume that all on-campus students will attend lectures unless I hear otherwise. If, for any reason, you can't make it, I would appreciate an e-mail so that I do not end up preparing a lecture for an empty room.

Note that an online discussion forum is available for the course. It is a good place to ask questions about things that puzzle you because everyone gets the benefit of the discussion. The best way to include mathematical material is just to attach Scientific Notebook files to your messages. If you make forum contributions, I will take those into account when determining your homework score.

Your grade will be determined from two final scores:

The first approximation to your final grade will be determined by the average of these two scores, but I will take both scores into account.

Note: Please contact the appropriate Coordinator of Services for Students with Disabilities to obtain an official memo detailing the academic adjustments or Accommodations which you need.