Mathematics 444

Differential Geometry


Differential geometry of curves and surfaces, Frenet frames, differential forms, normal and Gaussian curvature, intrinsic geometry, Riemannian geometry, the Gauss-Bonnet theorem, global structure of surfaces, the theorems of Bonnet and Hadamard. Prerequisites: 207 (Multivariable Calculus), Mathematics 210 (Linear Algebra), and a certain enthusiasm for challenging math classes.

Objectives of the course


Elementary Differential Geometry, Revised Second Edition,
by Barrett O'Neill, Academic Press (Elsevier), ISBN-13 978-0-12-088735-4, 2006 (Required)

Online Resources

Schedule for Spring 2006


Much of our course will center on working through a substantial set of exercises taken from O'Neill's text. A computer algebra system may prove to be invaluable for the more computational exercises. Developing clear, clean, and elegant solutions to those problems, and explaining those solutions to each other, will take up much of our class time. You are then to write up your own versions of those solutions and hand them in as homework. The class discussions represent a community effort and may not extend to all of the exercises for which you are responsible. The homework for this course consists in writing a representation of your own understanding of the solutions to these exercises, whether discussed in class or not. Although the class sessions are collaborative and explorative, writing the homework solutions is an individual effort and is definitive. The goal is to engage and internalize the central mathematical issues of correctness, precision of expression, elegance, and style.

Course Notes and Related Materials


Chris Parrish
Office: Woods Laboratories 120

Location and Time

Monday, Wednesday, 11:00 - 11:55 a.m.
Final Examination: Saturday, May 6, 2-4 pm
Woods Lab 119

Office Hours

Sewanee's tradition of cordial and constructive student-faculty relationships is one of its great strengths, and I am very happy to support that tradition. If you would like to talk with me, please make an appointment, either when you see me in class or in the hallways or in my office (WL120), or by email (, or by voice mail message (x1333).

Homework Day!

Homework is due on Mondays and Wednesdays!


Honor Code

The Honor Code applies to all examinations and written work produced in this course. Plagiarism is copying or imitating the language and thoughts of others, whatever the medium (written papers or computer programs). All work on the examinations must be done individually.


Attendance is required and is an important factor in doing well in the class. All assignments must be completed, and the student is responsible for making up any work missed due to absence. Late work will be accepted ONLY if appropriate arrangements have been made with the instructor PRIOR to the due date. The Dean's Office may be notified after two absences.