Math 209,
Manifolds II, Winter 2010
- Lectures: TTh 12:00-1:45pm, JBE 360
- Text: Introduction to Smooth Manifolds
by John M. Lee, Springer 2003
- Instructor: Viktor Ginzburg; office: 353C Baskin Eng.,
email: ginzburg(at)math.ucsc.edu, phone: 459-2218
- Office Hours: Tu 4:00-5:30pm, Th 11:00-12:00pm or by appointment
- Tentative Syllabus: This course is the second course in the
geometry sequence 208-210 and 211. The main theme of the course is
integration on manifolds. Manifolds are curved spaces (such as the
physical space-time, according to some theories) that can be thought
of as a generalization of surfaces to higher dimensions. Among
manifolds are Lie groups, configuration spaces of many physical
systems, and in fact most of the underlying objects of modern
geometry. Manifolds are treated in detail in 208. The goal of 209 is
to develop a theory of integration on manifolds: what to integrate
(differential forms), how to integrate, and the integral theorems
(Stokes' formula). Differential forms are also omnipresent in geometry
and physics. For instance, the curvature of a surface, the area or
volume, and electro-magnetic fields are differential forms. The
notion of a manifold and integration of differential forms are the
most basic elements of the modern geometry language used in
differential topology and geometry, dynamical systems, and theoretical
physics (e.g., relativity and string theory). We will cover Chapters
11-16 of the textbook and some parts of Chapters 18 and 19.
- Coursework: There will be weekly homework sets, one take-home
midterm, and a take-home final.
- Homework Assignments:
-
Take-Home Midterm (pdf file):
due Tuesday 2/23
-
Take-Home Final (pdf file)