do Carmo, M. P.
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.