This is the second half of a course on elementary differential geometry (the first half was taught by Professor Tromba in the Fall Quarter of 1999). Our main objective in this class is to
explore connections between the geometry and topology of surfaces in three dimensional Euclidean space. In particular, we will prove the Gauss-Bonet theorem.
The two main texts we use in this class are Elementary differential geometry, second edition, by B. O'Neill (this is the text which was used in the first half of the class), and
Differential Topology, by V. Guillemin and A. Pollack; however, the course is based mostly on the instructor's lecture notes which are typeset and distributed in the class every week.
The grade is based on the homeworks (which are assigned each week) and
class participation (which is mandatory).