INSTRUCTOR: Alex Voronov
OFFICE: VinH 324
PHONE: 624-0355
E-MAIL ADDRESS: voronov@math.umn.edu. You are welcome to use e-mail to send questions to me.
INTERNET: All class announcements and assignments will be posted on the class homepage http://www.math.umn.edu/~voronov/5378/index.html and NOT handed out in class.
OFFICE HOURS: Tue 2:30-3:30 p.m., Wed 10-11 a.m., Fri 2:30-3:30 p.m., and by appointment.
TEXT: Differential Geometry and Its Applications by John Oprea, 1997.
GOALS: This is an introductory course in differential geometry of curves and surfaces in space, presenting the basics of the theory along with applications. Students should have some background in multivariable calculus (as in the course Math 2263). The course should prepare the student for studying more abstract methods in pure and applied mathematics as well as provide base for further study in geometry and areas of mathematics, science, and engineering which use substantial amounts of geometry.
CONTENT: Chapters 1-6 and 8 of the textbook. Topics include: basic geometry of curves in space, Frenet Formulas, theory of surfaces, curvature, geodesics, metrics, Gauss-Bonnet Theorem, calculus of variations.
GETTING HELP:
FINAL EXAM: The final exam will be given on Tuesday, May 14, 4:00-6:00 p.m. in VinH 301, our regular classroom.
HOMEWORK: There will be weekly problem sets assigned to be turned in. A few problems from each set will be selected at random and graded. You are expected to do your homework regularly during the week (I recommend at least three times a week) and hand it in at the beginning of each Wednesday class, except the first week of classes and the test weeks. The test weeks' homework will be assigned, but not collected. You are encouraged to cooperate in doing homework, forming study groups. (I do not mind if the whole class becomes one study group.) However, everyone should work on every problem; a solution you get together with other students should be written down in your own words. Copying someone else's solution will be penalized. Assignments handed in late will get a 10% penalty per any fraction of a day after 1:30 p.m. on the due day. The maximum penalty is limited to 50%.
I suggest that after each class you review your lecture notes, read the corresponding sections of the text, and do the homework problems from these sections.
GRADING: Based on the two hour tests (15% each), the problem sets (25% total), and the final exam (45%). Grading will be done on curve. I expect the students to be good enough to earn grades not lower than a B-. In principle, depending on your particular performance, you may get any grade between an F and an A+.
INCOMPLETES: Assigned when, due to extraordinary circumstances, e.g., hospitalization, a student is prevented from completing the work of the course on time. Requires that the student has completed a substantial amount of course work at the level of C- or better. A written agreement between instructor and student must be filled out.
IMPORTANT DATES:
Tuesday, January 29 - last day to drop a course and receive a 100% refund.
Friday, February 1 - class and office hours canceled. I am in Washington, D.C., doing an important government job. The class will be rescheduled as a problem solving session before the first test March 6.
Monday, February 4 - last day to drop a course with no approval required and no grade recorded on transcript.
Wednesday, March 6 - Hour Test I.
March 18-22 - Spring break.
Wednesday, May 1 - Hour Test II (and the International Workers' Day).
Tuesday, May 14 - Final examination.