Course Staff:

Oliver Knill knill@math
Eric Sui ericsui@college
Hugo Nunez hugonunez@college
Jayanti Leslie-Iyer jleslieiyer@college
Luke Zhu lukezhu@college
Zak Adams zakadams@college

Oliver OH MWF 11-12:30 in 432.

Eric OH Tue from 3:30 to 5 pm in the Dunster DH

Hugo OH Wed 10:30-11:30 Leverett DH

Jayanti OH Sun 10:00 AM-12:00 PM in Adams DH

Luke OH M 9:30am--11:00am Winthrop DH

Zak OH Sat 2-3pm in Leverett DH

Announcements

Class photo: Click for a larger photo.

All documents in one [92 pages PDF] including HW and exams

About one of the homework problems:

Lecture notes

09/02/25 Lecture 1: Introduction ,
09/04/25 Lecture 2: Preliminaries
09/09/25 Lecture 3: Surfaces
09/11/25 Lecture 4: Curves
09/15/25 Lecture 5: Frenet
09/17/25 Lecture 6: Fundamental Theorem
09/23/25 Lecture 7: Hopf Umlaufsatz
09/25/25 Lecture 8: Vierscheitelsatz
09/30/25 Lecture 9: Fundamental forms
10/02/25 Lecture 10: Curvature
10/04/25 Lecture 11: 2-Manifolds
10/09/25 Review week: Theory and Practice
10/16/25 Midterm: in-class and take-home
10/21/25 Lecture 12: Geodesics
10/23/25 Lecture 13: Exponential
10/28/25 Lecture 14: Stokes
10/30/25 Lecture 15: Theorema Egregium
11/04/25 Lecture 16: Gauss
11/06/25 Lecture 17: Bonnet
11/13/25 Lecture 18: Manifolds
11/15/25 Lecture 19: Finite Manifolds
11/20/25 Lecture 20: Curvature tensors
11/22/25 Lecture 21: Relativity
12/04/25 Final: In class

Homework

Exams

Add ons:

Moon Night of November 6, 2025: this is a patch of a spherical manifold.

Click to explore the spherical map. In PSet 1 you worked with a quartic surface. Click on the picture to see a bit more about it: