## Math 362 - Differential Geometry of Curves and Surfaces (Spring 2017)

Instructor: Ben McMillan
Email: bmcmillan@math.stonybrook.edu
Locataion: TuTh 1:00pm--2:20pm in Earth & Space 181

### Course Information:

The course syllabus is here. Some critical points:
• The midterm will be in class on Thursday March 23.
• My office hours this term are Tuesdays 2:30--3:30pm and Wednesdays 3--4pm in Simons 510. I will also be available in the MLC (S-235) on Thursdays 11am--12pm.

### Schedule and Homework:

The following is a tentative schedule for the course. As homework is assigned it will be posted here. You are encouraged to work with others, but please make sure to write up solutions in your own words.

For each homework you turn in, please write an estimate of how long it took you for each problem.

Each week 3 problems will be graded. The ones in parenthesis are ones that I think you will benefit from, but won't be graded. You should still do them!

Week Date Topic(s) Covered Reading Homework
11/24Properties of R^3Chapter 1-23, 5
1/26Smooth maps, curves1-36, 8, 10
2 1/31Geometry of the vector product1-41, 6
2/2Local theory of curves (invariants)1-51, 2, 4, 6, 11
3 2/7Regular surfaces2-21, 8, 11, 12, 13
4 2/14Regular surfaces continued2-216
2/16Differentiable functions on surfaces2-31,(2),3,13,(16)
5 2/21Tangent planes of a regular surface2-41, (2), (8), 21, (24), (25)
2/23Vectors, the first fundamental form2-51 b & d, 3, (9, see pp 76-77)
6 2/28Area2-55, (12), (14)
3/2Oriented surfaces2-6(2), 4, 5, 7
7 3/7The Gauss map3-2(4), (8)
3/9The Gauss map (continued)3-2.
8 3/14Spring Break!..
3/16Spring Break!..
9 3/21Review..
3/23Midterm..
10 3/28What is Curvature3.2
3.3
2, (4), 8, (16)
1
3/30Isometries4.21, 2, (3)
11 4/4Isometries4.2(7), (8), 9, 11
4/6Geodesics4.43, (4), 5a
12 4/11Connections4.33, 8, (9)
4/13Parallel vector fields, geodesics4.44, 15
13 4/18More Parallel transport4.46, 12, (13)
4/20The Gauss Bonnet theorem4.51, (2), 4
14 4/25Local Gauss Bonnet4.5Compute the Euler Characteristic of the projective plane.
4/27Finish proof of Gauss Bonnet4.52, 3
15 5/2So you want to know what is a category None
5/4And some homotopy theory None