Course Announcement

MAT 4930, Spring 2012
Curves and Surfaces in Three-Dimensional Space: An Introduction to Differential Geometry

MWF 6th period (12:50-1:40), Little 221

For geometric objects in R3 it's "intuitively obvious" what words like curved, straight, and flat mean. But as soon as you try to nail down these notions, you find some obvious questions that you (probably) don't know how to answer. For example:

In this course we will answer questions such as the ones above. Technical names for some of the topics we will cover are: the Frenet formulas; covariant derivatives; principal curvatures; Gaussian curvature and mean curvature; geodesics; holonomy around a closed curve; and (time permitting) the Gauss-Bonnet Theorem.

In addition to being beautiful in its own right, the theory of curves and surfaces (which forms the basis of differential geometry) has many modern-day applications, including computer-assisted design, graphics, and animation. Higher-dimensional differential geometry also has great importance in many areas of theoretical physics, among them General Relativity.

Prerequisites for this course:

  1. MAC 2313, MAC 3474, or the equivalent (Calculus 3).
  2. MAS 4105 (Linear Algebra). NOTE:
    • MAS 3114 (Computational Linear Algebra) DOES NOT meet the linear-algebra prerequisite.
    • Prerequisite does not mean corequisite. All prerequisites must be completed successfully before taking this course.
Click here for syllabus

Last update made by D. Groisser Mon Nov 28 17:09:44 EST 2011