Suggested Reading List
· D. Lovelock and H. Rund, Tensors, Differential Forms, and Variational Principles (Dover 1975)
· B. Schutz, Geometrical Methods of Mathematical Physics (Cambridge 1980)
· C. Isham, Modern Differential Geometry for Physicists (World Scientific 1999)
· M. Henle, Modern Geometries (Prentice Hall 2001)
· S. Carlson, Topology of Surfaces, Knots, and Manifolds (Wiley 2001)
Grades: Homework and class participation, 40%; three tests, 20% each.
Instructor: André Wehner, Olin 111, Ph. 238-5919, e-mail wehner@centre.edu, office hours daily 5 pm to midnight with a short break in between (dinner).
Course Description
This course is meant to introduce you to various methods of modern geometry that are essential in theoretical physics. Our premise is that the basic ideas at the foundations of mechanics, electromagnetism, relativity, and field theory are geometrical and should be approached from this point of view. At the core of these ideas stands the notion of symmetries, which are understood today in terms of Lie groups. In order to develop some Lie group theory for beginners we will cover a wide range of topics including topology, classical and modern differential geometry, and tensor calculus, some of which are only related in a subtle, not always obvious manner. We can dwell longer on any topic that strikes you as particularly interesting. Since the material we hope to cover cannot be found in any single textbook, there is no required text for this course. For information beyond the class notes consult the books listed above and references given therein. Some background knowledge in multivariate calculus is expected.
Three tests will be given January 14, 21, and 28, respectively. They are “closed everything” and should take 90 minutes each. Since every day of this class is equivalent to a week of semester class time, attendance is crucial. Avoid missing class at all cost. Homework and class participation is also an essential part of this class – it accounts for 40% of your grade. The problems will be assigned in class and collected at the beginning of class on test days. You are encouraged to cooperate on the assignments, but you should only turn in your own work. I also encourage you to make use of Maple 7, e.g., for matrix manipulations. Problems on the exams will closely mirror the homework assignments. If you do the homework, you should do fine on the tests.
