Course Announcement

MTG 6256: Differential Geometry
fall 2004

MWF 6th period (12:50-1:40), Little 233

This year MTG 6256 will be devoted primarily to "classical" differential geometry, the study of curves and surfaces in 3-space. Topics will include a a brief introduction to differential forms (for a deeper treatment of this topic, take Dr. Rudyak's course MTG 7396 this semester), the Frenet formulas and their consequences for curves in R3, orthonormal-frame fields, isometries of R3, differential and integral calculus on surfaces, covariant derivatives, Gaussian curvature, intrinsic and extrinsic geometry of surfaces, geodesics, and the Gauss-Bonnet Theorem. Time permitting, there may be an introduction to abstract manifolds of arbitrary dimension.

Prerequisites for MTG 6256

Advanced calculus and linear algebra. Students entering the class should already be familiar with: A prior course in topology would be helpful but not essential; so would a course in ordinary differential equations at the level of MAP 4305/5304.

Instructor: Professor David Groisser
If you would like to speak with me by phone or in person, please read the instructions on my schedule page before calling, emailing, or stopping by, and please do not call or stop by outside of my designated office hours and advising hours (unless we have previously agreed on an appointment outside those hours). My office is located in the 358 Little Hall area, and you must check in with the receptionist to see me. My phone number is 392-0281, extension 261, and my email address is

Office Hours: Tentatively Tuesday 8th and 9th periods, subject to change as time commitments develop during the semester; see my schedule for updates. You can also see me by appointment any weekday except Thursday , and during the hours listed as "academic advising" on my schedule (but students waiting to see me for academic advising will have priority during those hours).

Text: Barrett O'Neill, Elementary Differential Geometry, 2nd edition.

Exams and Grading: There will be a mid-term and a final.These will probably be two-hour or three-hour exams or take-home exams, so dates and times will have to be arranged. Grades will be based on these exams and on homework. I have not yet decided the percentages for which each component will count; this will depend on how much time I am able to devote to grading homework this semester, and on the number of students who remain registered in the class after the Drop/Add deadline. The homework is likely to count for something between 20% and 50% of your grade, the midterm for something between 20% and 50% of your grade, and the final for something between 40% and 70%.

Homework: will assigned almost daily, and selected problems will be collected sporadically for grading. It is critical that you keep up with the homework, which will be posted on the homework page, even if I fall behind on the grading.

Student Honor Code: Students are expected to abide by the the Honor Code:

We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity.
On all work submitted for credit by students at the university, the following pledge is either required or implied: "On my honor, I have neither given nor received unauthorized aid in doing this assignment."

Religious Holidays: The following is part of the University of Florida Policy on Religious Holidays . "Students, upon prior notification of their instructors, shall be excused from class or other scheduled academic activity to observe a religious holy day of their faith."

Accommodations for students with disabilities: Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the instructor when requesting accommodation.

Last update made by D. Groisser Sun Aug 22 18:41:22 EDT 2004