Section 2E15, Fall 2014
MWF 8th period, LIT 203
Instructor: Dr. David Groisser
Office: Little 308 (southeastern quadrant of building)
Phone: (352) 294-2307
Email: groisser@ufl.edu.
Please note:
- I won’t answer math questions by email.
- I will never provide any grade information by email.
- I won’t answer anonymous email, or email that lacks an informative subject line and your full name.
Office Hours:
Tentatively Monday 5th period (11:45-12:35) and Wednesday & Friday 9th period (4:05-4:55). 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).
Textbook: Loring W. Tu, An Introduction to Manifolds, 2nd edition (2011).
Syllabus (course content):
This course introduces the foundations of manifold theory, what I would usually cover in MTG 6256 (the first semester of a year-long graduate sequence). The course is intended only for undergraduates who have the preparation and maturity for a real 6000-level course. Topics that I expect to cover include a brief review of advanced calculus from a geometric viewpoint; definition and examples of manifolds; maps of manifolds; critical points and the Regular Value Theorem; vector fields, flows, and Lie derivatives; exterior algebra and differential forms; integration on oriented manifolds; Stokes theorem; tensor bundles, and possibly an introduction to Riemannian metrics and Riemannian geometry. Riemannian geometry is a large topic; most of this material will probably be deferred to the second semester (if there is student demand for the usual second semester of the graduate course). Please see course announcement for additional information.
Prerequisites: MAA 4212 and its whole prerequisite-chain.
Pre- or co-requisite: MAS 4301.
Exams, Homework, and Grading: Your final grade will be determined by the following:
- Homework. Depending on the number of students enrolled, I expect to assign and collect from four to eight problem-sets over the course of the semester. I will grade some subset of the problems. How large that subset is will depend on how many students handed in the assignment, how successful they were solving the problems, and how well-written their solutions are. See More about homework below.
- Possible take-home final exam. This may be waived for students who’ve done well enough on homework.
For students for whom a final exam is not waived, the weighting of each of the two grade-components (homework and final exam) will be between 25% and 75% each, and may vary from student to student. Generally I will give more than 50% weight to the component on which you’ve been more successful. (But that does not mean I will give 75% weight to it.)
One of the most important things you must do to learn the material is to go through your notes from each class before the next class, filling in any gaps, trying figuring out anything you didn’t understand at the time, and determining what you still don’t understand and should ask me about. Time permitting, the best thing you can do is rewrite your notes. Do not expect to understand everything I say in class at the time I say it. I will sometimes make comments that are intentionally cryptic, will sometimes deliberately omit some steps in proofs, etc., to force you to think more about something. The deepest understanding will come only when you think about the material on your own. This will take you far more time than the hours we spend together in class.
Attendance: I work hard to prepare my lectures, and I expect all enrolled students to attend all of them, with the usual allowances for illness, emergency, etc. When you must miss a class, please obtain notes from a classmate.
More about homework: Even when homework is well-written, reading and grading it is very time-consuming and physically difficult for your instructor. Please do not make this process more burdensome than it intrinsically needs to be. So:
- The homework you hand in must be neat, and must either be typed (in which cased TeX or LaTeX is preferred) or written in pen (not pencil!), on white paper. Please do not turn homework that is messy or that has anything that’s been erased and written over (or written over without erasing), making it harder to read. If you are writing on both sides of a sheet of paper, do not use paper/ink combinations for which the ink bleeds through from one side of the paper to the other. Anything that is difficult for me to read will be returned to you ungraded.
- Leave enough space for me to write comments. This includes leaving ample margins at the top and bottom and left- and right-hand sides of the page, as well as space between problems.
- Staple the sheets together in the upper left-hand corner. Any other means of attachment makes more work for me. The staple should be close enough to the corner that when I turn pages, nothing that you’ve written is obscured. Also, don’t use paper that’s been ripped out of a spiral-bound notebook; it will make a mess on my floor.
- Write in complete, unambiguous, grammatically correct, and correctly punctuated sentences, just as you would find in (most) math journals and textbooks.
- Partial proofs. If a problem is of the form “Prove this” and you’ve been unable to produce a complete proof, but want to show me how far you got, tell me at the very start of the problem that your proof is not complete (before you start writing any part of your attempted proof). Do not just start writing a proof, and at some point say “This is as far as I got.” Otherwise, when I start reading I will assume that you think you’ve written a complete and correct proof, and spend too long thinking about, and writing comments on, false statements and approaches or steps that were doomed to go nowhere.
Also, I think the following points should be self-evident, and I apologize to anyone who agrees that they’re self-evident and is offended by my saying them. But past experience has taught me that I need to say them explicitly, even in 6000-level classes:
- I assign homework problems because I want you to figure them out, not to send you on a treasure-hunt through the literature. If I limit myself to assigning problems that I think are unlikely to have solutions somewhere in some book, you will not be getting the best education I can give you. When I know that something is a worthwhile problem for you to work on, and even struggle with, I don’t want to have to worry about whether a solution exists in some textbook.
That does not mean you are forbidden ever to look at textbooks. But solutions to homework problems should be your own. If you find yourself looking at a textbook while you are writing up a solution, that solution is not your own.
- You should first try all the problems yourself (alone). After attempting the problems, you may brainstorm with other students in the class for general ideas, but you may not completely work out problems together. You are also not permitted to split the workload with other students, with each student in a group writing up some solutions that all group-members hand in, or that all group-members work from in writing up what they’re going to hand in.
Student Honor Code. UF students are bound by The Honor Pledge, which states:
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We, the members of the University of Florida community, pledge to hold
ourselves and our peers to the highest standards of honor and
integrity by abiding by the Honor Code. On all work submitted for
credit by students at the University of Florida, the following pledge
is either required or implied: “On my honor, I have neither given nor
received unauthorized aid in doing this assignment.”
The Honor Code (here) specifies a number of behaviors that are in violation of this code, and the possible sanctions. Furthermore, students are obligated to report to appropriate personnel any condition that facilitates academic misconduct. If you have any questions or concerns about student conduct, please consult me.
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. See http://www.dso.ufl.edu/drc.
Letter grades and their grade-point equivalents at UF: see https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx.