Schedule

Here is the tentative course schedule.This schedule is meant as a rough course outline; there will likely be changes as the semester progresses. While we base our syllabus on Wolfgang Kühnel’s Differential Geometry Curves-Surfaces-Manifolds (in the schedule, referred to by [WK]), we occasionally use Do Carmo’s Differential Geometry of Curves and Surfaces ([DC]).

Homework deadlines are on Fridays 11:59pm, unless stated otherwise.

Week of Aug. 26

First day of classes: Monday, August 26

Topics

Introduction

[WK] Ch. 1

Week of Sept. 2

Labor Day: Monday, September 2, NO CLASSES

Topics

Frenet curves

[WK] 2A

Week of Sept. 9

Topics

Plane curves and space curves, Curvature and torsion

[WK] 2B, 2C

Week of Sept. 16

Topics

Frenet equation and the fundamental theorem of curves

[WK] 2D

Homework :HW1 (due Friday 9/20 11:59pm)

Week of Sept. 23

Topics

Global theory of curves, What is a manifold?

[WK] 2F , [Notes on manifold: Available on Blackboar]

Week of Sept 30

Topics

Surface elements and first fundamental form (continued)

[WK] 3A

Homework :HW2 (deadline: Oct 4)

Week of Oct. 7

Topics

Gauss map and curvature, left over material and/or review for midterm 1.

[WK] 3B

Midterm 1: Thur, Oct. 10, 8:00-9:15AM.

More Info: See the Exams and Grading page.

Week of Oct. 14

Fall Break: October 14–15, NO CLASSES

Topics

Gauss map and curvature (continued)

[WK] 3B

Week of Oct. 21

Topics

Surfaces of revolution and ruled surfaces

[WK] 3C

Homework :HW3 (deadline: Oct 25)

Week of Oct. 28

Topics

Minimal surfaces, Covariant derivative

[WK] 3D, 4A

Week of Nov. 4

Topics

Parallel displacement and geodesics

[WK] 4B

Week of Nov. 11

Topics

Gaussuan equation and Theorem Egregium

[WK] 4C

Midterm 2: Tues, Nov. 12, 8:00-9:15AM.

More Info: See the Exams and Grading page.

Homework :HW4 (deadline: Nov 15)

Week of Nov. 18

Topics

Fundamental theorem of surfaces, Guassian curvature in special parameters

Gauss-Bonnet theorem

[WK] 4D, 4E

Week of Nov. 25

Topics

Gauss-Bonnet theorem continued

[WK] 4F

Thanksgiving Break: November 27–Dec 1

Week of Dec. 2

Topics

Gauss-Bonnet theorem continued

[WK] 4F

Homework :HW5 (deadline: Dec 6)

Week of Dec. 9

Last day of classes: Monday, December 9

Topics Review for the final exam and/or left over material.

Homework

No HW

Final Exam: Sunday, 12/15, 12:30-3:30PM

More Info: See the Exams and Grading page.