MAT 362: Differential Geometry of Surfaces

Spring 2014

Instructor. Michael Anderson, Math Tower 4-110.
E-mail: anderson AT, Phone: 632-8269.
Lectures: Tu/Th: 1:00-2:20pm, in Library N4000

Office Hours. MWF 2-3pm, and by appointment.

Grader. Maryam Pouryahya, Math Tower S-240A.
E-mail: mpouryah AT

Course Description. The foundation of differential geometry is the concept of curvature. The course will focus on understanding this and related concepts very clearly, both geometrically and computationally, for the case of surfaces in Euclidean space. For this, you'll need a solid background in multivariable calculus and linear algebra. We hope to give some idea of how curvature is understood in higher dimensions; this is the basis of Riemannian geometry and General Relativity.

Prerequisites. MAT 205 (Calc III) and MAT 210 (Linear Algebra).

Text. There is no formal text for the class. As a backbone or guideline, we will use the online text:

Differential Geometry: A First Course in Curves and Surfaces
by Theodore Shifrin.

This is a preliminary version of a text to appear and is currently available free online: here
Permission for this use has been obtained. (Shifrin is an old grad student friend).

A more advanced online text, at a level of the lectures in class, is:

Curves and Surfaces, Lecture Notes for Geometry I

by Henrik Schlichtkrull

available as PDF here

There are many other texts that you are encouraged to browse and use as you see fit. Some of these are: These and many others are in the Library (I believe).

Assignments and Grading. There will be one Midterm Exam,

MIDTERM: Date: Tuesday, March 25

This is a TAKE HOME EXAM, due in class on Thursday, March 27 (1pm). You may use or consult texts or course notes, but not others. The material of the exam is all of the course up to and including March 13 (the week before Spring Break).

It will be emailed as a PDF file to all enrolled students on Thursday, May 15, 10am, and due on Tuesday, May 20, 12 Noon.
Bring the exam to my office, Math Tower 4-110, (or put it under my office door before that time).
The material for the exam will be the full semester of course work, but with an emphasis on course work covered since the Midterm Exam.

The Final Exam as PDF is here

There will be regular homework assignments, due roughly once per week. Your grade will be determined via the following percentages: