I.Contents：
This class will cover the theory of curves and surfaces in R^3 in one semester. In the end of the semester, we will prove Gauss- Bonnet Theorem and do some applications. The course will mainly follow Do Carmo’s book, but will avoid the abstract part like regular surfaces. I will provide lecture notes on parametrized surfaces instead. Sec. 2.2, 2.3, 2.7 and 2.8 will basically omitted. Part of sec. 1.7, 3.4 and 3.5 may also be omitted subject to the time limit. I will introduce the notion of regular surfaces, change of parameters etc. before discussing global Gauss Bonnet Theorem. The class will end at sec. 4.5 of the book.
II.Course prerequisite：
It is preferred that students already learned advanced calculus.
III.Reference material ( textbook(s) )：
1.Do. Carmo: Differential Geometry of Curves and surfaces.
2.For report:
L. Mlodinow, Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace
or
R. Osserman, Poetry of the Universe －A Mathematical Exploration of the Cosmos
IV.Grading scheme：
Homework: 10%
Quiz: 10%
Report: 5%
Computer homework: 5%
Midterm + Final: 70% (the higher score will weight 40% and the other weights 30%)
V.Others：