Math 120A: Differential Geometry
Fall 2014
| Instructor: | Kristen Hendricks |
| Office: | 6617D Math Sciences Building |
| Office Hours: | M 2:15-2:45, W 10-11, R 4-5 |
| E-Mail: | hendricks at math .ucla .edu |
| TA: | Jacob Rooney |
| Office: | MS 2509 |
| Office Hours: | T 11-12, R 1-2 |
| E-Mail: | jhrooney at ucla .edu |
Location and Time
MWF 9-9:50 in Geology 4645. TA discussion section T 9-9:50 in Geology 4645.Content
This course is an introduction to low-dimensional differential geometry. We will study the geometry of curves in two- and three-dimensional space, touching on curvature and torsion, the Frenet-Serret equations, and the isoperimetric inequality. We will next study surfaces embedded in three-dimensional space, covering the notion of a smooth atlas, various types of surfaces, the first and second fundamental forms, and the Gauss map.Textbook
Pressley, Elementary Differential Geometry. Springer (1974). Second Edition. An electronic version of this textbook is available for free through the UCLA network here
We will make use of an appendix of additional exercises published by Pressley, which are here.
You can also find a copy of Classical Differential Geometry by Prof. Peterson here. This may be a helpful supplemental resource.
Prerequisites
Math 115A, Math 131A.
Homework
Homework will be assigned weekly and due at the beginning of lecture on Friday. There will be nine homeworks. Do not submit homework by e-mail. No late homework will be accepted. However, your lowest homework score will be dropped when computing your grade.
You are encouraged to work in groups on your homework; this is generally beneficial to your understanding and helps you learn how to communicate clearly about mathematics. However, you must write up all solutions yourself. Moreover, since crediting your collaborators is an important element of academic ethics, you should write down with whom you worked at the top of each assignment. You should also cite any other sources other than lecture and the textbook (another book, a blog about analysis, etc) you use.
Exams
There will be two in-class midterms on Wednesday, October 29 and Monday, November 24. There will also be a final exam Tuesday December 16, 3:00-6:00 p.m. There will be not be any make-up exams except in extreme and documented circumstances. In particular, note that university policy requires that a student who has an undocumented absence from the final exam be given a failing grade in the course.
Grading
Grades will be computed as follows:
A curve compatible with the department guidelines will be applied to the composite numerical grades. The average will be a B (unless something surprising happens).
Schedule
We will approximately follow the official schedule of topics here. (In fact the chapter numbers online are for a different textbook, but they correspond almost identically to our book.) This means we will cover most of Chapters 1-8. The exact reading will be posted as the quarter progresses.
Homeworks
Homework 1 (Due October 10th). Solutions.
Homework 2 (Due October 17th). Solutions.
Homework 3 (Due October 24th). Solutions.
Homework 4 (Due October 31th). Solutions.
Homework 5 (Due November 7th). Solutions.
Homework 6 (Due November 14th). Solutions.
Homework 7 (Due November 21st). Solutions.
Homework 8 (Due December 5th). Solutions.
Homework 9 (Due December 12th).
Exams