Geometry and Spacetime

The course will examine a number of issues concerning the mathematical and philosophical foundations of the special theory of relativity. The emphasis throughout will be on the "geometric" approach to the theory, and considerable class time will be devoted to a careful study of Minkowski geometry, and its relations to both Euclidean and non-Euclidean (Lobatchevskian) plane geometry. (One of the nicest routes to the latter is via special relativity.)

The course will presuppose familiarity with calculus, basic linear algebra, and (for one topic) formal logic. More advanced prior training in mathematics and/or physics will certainly be helpful.

Instructor: David Malament, SST 757, 824-7374. I can be reached, most reliably, by e-mail: dmalamen@uci.edu. Office hours: Tu 11-12 am, and by appt.

Course requirements: Auditors are welcome. Students who want to take the course for a grade will be asked to submit regular problem sets.

Reading: My lecture notes will serve as a text for the course. They can be downloaded here.

Course Outline with Problem Sets

All problems are from the lecture notes. The due dates listed are all still tentative, and may well be revised.

A. Review of Needed Background Mathematics (4 weeks)

Problem Set #1: 2.1.2, 2.1.4, 2.1.6 (due Tuesday, October 9th)

Problem Set #2: 2.2.2, 2.2.4, 2.3.2 (due Tuesday, October 16th)

Problem Set #3: 2.4.2, 2.4.4, 2.4.6 (due Tuesday, October 23rd)

B. Minkowski Spacetime Geometry and its Physical Interpretation (4 weeks)

Problem Set #4: 3.1.1, 3.1.2, 3.1.3 (due Tuesday, October 30th)

Problem Set #5: 3.1.4, 3.1.5 (due Tuesday, November 6th)

Problem Set #6: 3.2.1, 3.2.2 (due Tuesday, November 13th)

Problem Set #7: 3.3.1 or 3.4.1 (due Tuesday, December 4th)

C. From Special Relativity to Non-Euclidean (Lobatchevskian) Plane Geometry (2 weeks)

Problem Set #8: 4.1.1, 4.2.1 (due Tuesday, December 11th)