MATHEMATICS 563 A1
Introduction to Differential Geometry
Fall Semester 2000
Instructor: Takashi Kimura
e-mail: kimura@math.bu.edu

Phone: (617)353-1486 Office: MCS 234

Lectures
MWF 11:00-12:00pm in MCS B31

Text
Differential Geometry and Its Applications, by John Oprea, ISBN 0-13-340738-1, Prentice-Hall, 1997.

My Office Hours
To be announced.

Class Web Page
http://math.bu.edu/people/kimura/Fall00/563/

Content
Geometry is the study of objects such as lines and surfaces as well as their higher dimensional analogs. Differential geometry is an application of the ideas from calculus to characterize geometric objects. An example of a question which differential geometry addresses is, for example, ``What is the proper notion of the curvature of a surface?'' This subject is an active area of research and has various applications in science and engineering, e.g. computer graphics, Einstein's theory of gravitation (general relativity), and so forth. We shall also be using the computer algebra package Mathematica to help visualize these geometric objects as well as to help perform algebraic manipulations. Mathematica is available on the ACS UNIX machines in the computer room in the basement of the Math/Computer Science Building.

Prerequisites
The material in the course is nontrivial so please make sure that you satisfy the prerequesites. The prerequisites to this course are multivariate calculus and some linear algebra. A knowledge of analysis or topology is useful but is not necessary. We will introduce these ideas as necessary. Some knowledge of Mathematica will also be useful although we will introduce this in class.

Homework
Generally, homework will be assigned on a weekly basis and will be due the following week. Late homework will not be accepted. Students may discuss homework with each other (and are encouraged to do so) but all written work must be prepared independently.

Exams
There will be a take home midterm and a take home final.

File translated from TEX by TTH, version 1.60.