Prof: Dr. George Kamberov
| Phone: | (201) 216-5486 |
| E-mail: | gkambero at stevens.edu |
| Office hours: | Wed 5-6PM & by appt, ATI 2nd Floor Lieb |
Announcement: The course WeBCT site will be available by the end of the week
We will use WeBCT only for
Communication
e-mail
discussions
Homework and test postings and submissions
Tracking grades (progress)
To accommodate students auditing the course all other information including
syllabus, grading policies, and references
is posted on this "open" website.
Course Overview
This course is an introduction to the geometry of curves and surfaces. Topics include tangent vectors, tangent bundles, directional derivatives, calculus on surfaces, curvature, Riemannian geometry and geodesicsCourse Description
Prerequisites
Text
Syllabus and Class Notes
- Lecture 1: Intro: Euclidean vector and affine spaces, curves in space
- Lecture 2: Local geometry of curves in space
- Lecture 5: Isoparametric inequality (see Ch 1.7also)
- Lecture : Regular Curves
Final Grade
Homeworks Go to WeBCT
Prerequisites
- Math 227
Textbook: Manfredo Do Carmo, Differential
Geometry of Curves and Surfaces, Prentice Hall, ISBN 0-132-12589-7
Draft Syllabus
- Curves
- Regular surfaces
- Manifolds, tangent vectors, differentiable maps, the tangent and co-tangent bundles
- Riemannian metrics, the first fundamental form
- Orientation, geometry of the Gauss map
- Isometric immersions, intrinsic and extrinsic notions of curvature
- Parallel transport, geodesics
- The Gauss-Bonnet theorem
- The exponential map
- Rigidity theorems
Final Grade:
Assignments 50%
Final exam: 30%
Midterm exam 20%
Stevens Institute, Department of Computer Science
Last Update: 01/15/06