342-0 - Introduction to Differential Geometry

Lectures: Monday, Wednesday, Friday 2:00pm - 2:50pm, Lunt 103
Section Meetings: Tuesdays 2:00pm - 2:50pm, Lunt 103
Course website: www.math.northwestern.edu/~tosatti/idg.html

Instructor:

Valentino Tosatti
Email: tosatti@math.northwestern.edu
Office: Lunt 225

Office hours:

The course is now finished.

Teaching Assistant:

Greg Edwards - gedwards@math.northwestern.edu
Office: Lunt 215
TA Office hours:
The course is now finished.

Course Description:

This course is an introduction to the study of curves and surfaces in three-dimensional space. See the syllabus below for more detailed content information.

Textbook:

M.P. Do Carmo - Differential Geometry of Curves and Surfaces, Pearson 1976.

Section Meetings:

Every Tuesday, 2:00pm - 2:50pm in Lunt 103, starting from September 30, there will be section meetings. All students are required to participate. Normally the section meetings will consist of a discussion lead by the TA followed by a 25-minute quiz. Two of these section meetings (October 21 and November 18) will instead consist of 50-minute midterm exams.

Below you can find some suggested problems to prepare yourself for the quizzes. These are optional and only for your benefit, please do not hand in these problems for grading.

Grading and Final:

The lowest quiz score will be dropped. The class grades will be based on the remaining six quizzes (5% each), the two midterm exams (15% each) and on the final exam (40%). The final exam date is Friday, December 12 from 9:00am to 11:00am in Lunt 103.

There is no make-up for quizzes and exams.


Daily Schedule:


Date Topics Covered Remarks
Sep. 24, 26 The concept of a curve
Sep. 29, Oct. 1, 3 Local theory of curves, arclength, Frenet frame
Sep. 30 Quiz no. 1 (section meeting) Suggested problems: 1-2: 2, 4, 5
1-3: 1, 5(a,b)
Oct. 6, 8, 10 Isoperimetric Inequality, Whitney's Theorem
Oct. 7 Quiz no. 2 (section meeting) Suggested problems: 1-5: 1, 8(a)
Extra exercises
Oct. 13, 15, 17 Surfaces
Oct. 14 Quiz no. 3 (section meeting) Extra exercises
Oct. 20, 22, 24 Smooth functions
Oct. 21 First Midterm
Suggested problems: 1-5: 5
2-2: 1
Extra exercises
Oct. 27, 29, 31 Tangent plane, orientability
Oct. 28 Quiz no. 4 (section meeting) Suggested problems: 2-3: 1, 3
2-4: 2, 8
Extra exercises
Nov. 3, 5, 7 First and second fundamental forms, curvature
Nov. 4 Quiz no. 5 (section meeting) Suggested problems: 2-4: 7, 10, 11, 15
2-5: 1(a,b)
Extra exercises
Nov. 10, 12, 14 Gauß Theorema Egregium
Nov. 11 Quiz no. 6 (section meeting) Suggested problems: 3-2: 2, 3, 4
3-3: 1
Extra exercises
Nov. 17, 19, 21 Geodesics
Nov. 18 Second Midterm Suggested problems: 3-3: 5(a,b,c)
Extra exercises
Nov. 24, 26 Gauß-Bonnet Theorem, Minimal surfaces Extra exercises
Nov. 25 Quiz no. 7 (section meeting)
Nov. 28 Thanksgiving, no class
Dec. 12 Final Exam, 9:00am-11:00am Lunt 103 List of formulas to remember
Extra exercises