What is this course about? For geometric objects in R3 it's "intuitively obvious" what words like curved, straight, and flat mean. But as soon as you try to nail down these notions, you find some obvious questions, such as the ones here, that you (probably) don't know how to answer. This course will be an introduction to these questions and their answers. Topics will include the Frenet formulas; covariant derivatives; principal curvatures; Gaussian curvature and mean curvature; geodesics; holonomy around a closed curve; and (time permitting) the Gauss-Bonnet Theorem.
- MAC 2313, MAC 3474, or the equivalent (Calculus 3).
- MAS 4105 (Linear Algebra). NOTE:
- MAS 3114 (Computational Linear Algebra) DOES NOT meet the linear-algebra prerequisite.
- This prerequisite will be waived for graduate students in the mathematics department, but will NOT be waived for graduate students in other departments. Graduate students in other departments are welcome to audit the course (see http://www.registrar.ufl.edu/currents/specialregistrations.html#2), but will not be allowed to take the course for credit without specific permission from me.
- Prerequisite does not mean corequisite. All prerequisites must be completed successfully before taking this course.
Text: Barrett O'Neill, Elementary Differential Geometry, revised 2nd edition (2006).
Warning: The UF textbook-listing webpages give the correct ISBN, but just say "2nd edition". The revised 2nd edition, which is the book we'll be using, is not the same as the original 2nd edition (1997).Instructor: Professor David Groisser.
- Office: Little 308.
- Phone: 392-0281, extension 261.
- Email: groisser@ufl.edu. Please include your full name and an informative subject line in all email correspondence with me. I won't answer anonymous email, or email that lacks an informative subject line, or that asks me to open an attachment that I haven't said you should send me.
Office Hours: Tentatively Monday and Friday 8th period (3:00-3:50), and Tuesday 4th period (10:40-11:30). Please come early in the period or let me know to expect you later; otherwise I may not stay in my office for the whole period. See my schedule for updates. Students who can't make scheduled office hours may see me by appointment on most weekdays (but never on a Thursday).
Components of your grade: (THIS IS NOT FINALIZED YET! In particular, the weight of the Homework component may depend on how many students register for the class.)
- Homework (20%-40%, TBD)
- One mid-term exam (20%-30%, TBD). The format (in-class or take-home) is TBD.
- Final exam (30%-60%, TBD). The format (two-hour exam at the time set by the registrar — Thursday, May 3, starting at 12:30 p.m. — or take-home) is TBD.
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."What if you miss an exam? If you miss an exam for a valid reason, I will work out something with you that is as fair as is feasible. In a class like this without cookie-cutter exams, it's impossible for me to write two different exams of exactly the same level of difficulty. It takes me many hours even to try, and hours more to create a grading-scale for an exam taken by just one person. Therefore, unless I'm able to give you the same exam as the rest of the class, and be reasonably certain that there is no information-flow between people taking the exam at different times, I will not give you a make-up exam. Instead, I will just give you a "bye" and simply re-adjust the weights of the other components of your grade.
If you are going to miss an exam due to illness, you should notify me by phone or email before the exam starts (even if it's just a few minutes before).
Attendance policy. Barring valid reasons such as illness, weddings, funerals, family emergencies, and team activities, I expect students to be in class every day and on time, paying attention for all 50 minutes of the period. Coming late to class is disruptive to both your instructor and your classmates.
Currently I plan to take attendance, at least until I learn students' names, but not to factor it into your grade directly. However, students who choose not to regularly attend class (not counting valid reasons such as those mentioned above) should not expect the same consideration in office hours that students with good attendance will receive. Be aware that the University of Florida Attendance Policies contains the following paragraph:
The university recognizes the right of the individual professor to make attendance mandatory. After due warning, professors may prohibit further attendance and subsequently assign a failing grade for excessive absences.Students with a lot of unexcused absences may find themselves dropped from the class with a failing grade.Students with a contagious illness are asked to exercise good judgment and to be considerate of their classmates and instructor when deciding whether to come to class. Coughing and sneezing in an enclosed space like a classroom or office is a wonderful way to spread germs.
Classroom decorum:
- Cell-phone ringers, audible text-message alerts, etc., should be turned off while you are in class. Please also avoid other disruptive or distracting noises, such as the tapping of pencils or feet, or the zipping and unzipping of backpacks several minutes before the end of class.
- Do not use your personal computer in class without express prior permission from me. Ditto for your cellphone, except to receive emergency alerts from UF. In particular, do not read or write text-messages in class.
- Do not read, do the crossword puzzle, etc., while you are in class. If you're too bored to pay attention, do homework.
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."