Class Home Page for Curves and Surfaces in \({\bf R}^3\): An Introduction to Differential Geometry
MAT 4930, Section 3F84 (17710)
Spring 2019

Most handouts and other information will be available via links or (sub)menus from this page and/or the syllabus page.

• David Groisser's home page, with contact information
• Syllabus and Course Information
• Homework assignments
• Non-book homework problems. (These are part of the Homework assignments, not something additional.)
• Rules for hand-in homework
• Grade-scale page. (Will be updated shortly after each assignment or exam is graded; will not exist until after the first assignment is graded.)
• Miscellaneous handouts
• Dr. Groisser's schedule (with office hours)

What is this course about?

For geometric objects in \({\bf R}^3\) 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, such as the ones here (course announcement), that you (probably) don't know how to answer. This course will be an introduction to these questions and their answers. Topics will include 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.

Prerequisites

MAC 2313, MAC 3474, or the equivalent (Calculus 3), and MAS 4105 (Linear Algebra). These must be completed successfully before taking this course. Note: MAS 3114 (Computational Linear Algebra) does not meet the linear-algebra prerequisite.