Math 543 - Geometry of Physics

Fall 2010

instructor phone # office e-mail
Renato Feres 5-6752 Cupples I, 17

Section information: Classes meet on Mondays, Wednesdays, Fridays, from 3:00PM to 4:00PM, at Lopata Hall 202.

Subject: This is a course on classical mechanics and electromagnetism aimed to provide graduate students of mathematics with a solid acquaintance with these physical theories. The emphasis is on the geometric underpinnings of classical field theories. Topics include: Lagrangian and Hamiltonian mechanics, electromagnetism, and relativity theory. No specific knowledge of physics is assumed, but familiarity with manifold theory at the level of Math 5041 is strongly recommedned. Non-math students are welcome.

Text: Written notes will be provided as the course progresses, in addition to references to articles that can be found on-line and other texts.

Tentative list of topics: I expect that the physical subjects covered in this course will be mainly classical Lagrangian and Hamiltonian mechanics, electromagnetism, and elements of relativity theory (not much general relativity, though), in addition to the relevant mathematics background in differential geometry, Lie theory, and analysis. An optimistic, but not necessarily pie-in-the-sky unrealistic syllabus would consist of the following items:

Coursework: There is a long list of exercises spread out throughout the course notes. Some are easy, some are difficult; some are interesting, others are boring verifications of calculations I didn't want to write down in detail; some are pure math and (for the moment) not so many are really physics but I hope to provide more of the latter. For a final A grade, you are responsible for doing (nicely) 10 of them, of your choosing. You may do them as the course progresses and I will keep track of your accumulated ``exercise credits.''