## Math 87 (Differential Geometry) - Winter 2004

** Text: **
do Carmo, M. P. Differential Geometry of Curves and Surfaces
, Prentice-Hall, 1976.

** Syllabus**:
We will explore various aspects of the geometry of
surfaces and curves. This will include developing languages to
describe the geometry of a surface both from the point of view of an
astronomer watching the surface as it sits in space, and from
the point of view of a bug living on the surface.
We will emphasize the use of vector calculus tools in developing this
language, hence the use of the term "differential" in this course's title.
(A solid vector calculus background, the equivalent of Math 13,14, or 15,
is required.) We will end the course
by exploring one of the great theorems of mathematics: the Gauss-Bonnet
theorem. The Gauss-Bonnet theorem will allow
us to determine certain global (topological) properties of the surface
from the surface's local geometry.