Math 572b, Differential Geometry, Winter 2004
This course will be an introduction to manifolds and differential
geometry, starting right from the beginning. The topics are chosen to
be of interest in both mathematics and physics, and the material will
be presented in a way that is accessible to students with different
manifolds, vector fields, differential forms, de Rham
cohomology, bundles, connections, curvature, Riemannian and Lorentzian
metrics, geodesics. We will briefly indicate the connections to
Yang-Mills theory, gauge theory and general relativity.
Text: I will use "Gauge Fields, Knots and
Gravity" by John Baez and Javier Muniain as well as
"Differentiable Manifolds" (second edition) by Lawrence Conlon.
Both will be on reserve at the Taylor library.
I am placing orders for both books, so let me know if you
want me to get one or both for you.
Here is a list of supplementary texts
you may like to refer to.
- Instructor: Dan Christensen
- E-mail: firstname.lastname@example.org
- Office: Middlesex 103b.
- Office Phone: 661-2111 x86530.
- Office Hours: after class.
- Class times and location: Tuesdays and
Thursdays 1-2:30 in MC107.
January 13 to April 15, except February 23-27.
linear algebra, multi-variable calculus and permission of instructor.
An acquaintance with metric spaces and/or topology would be great but
is not required.
Presentations: In the second half of the semester,
each student will give one presentation on a topic related to the
course. The scheduling will be worked out later.
Evaluation: Homework will be due roughly every
two weeks. Evaluation will be based upon homework
and the presentations. There will be no tests.
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