Differential geometry has two aspects. Classical differential geometry, which shares origins with the beginnings of calculus, is the study of local properties of curves and surfaces. Local properties are those properties which depend only on the behavior of the curve or the surface in a neighborhood of a point. The other aspect is global differential geometry: here we see how these local properties influence the behavior of the entire curve or surface. The main idea is that of curvature. What is curvature? It can be intrinsic or extrinsic. What's the difference? What does it mean to have greater or smaller (or positive or negative) curvature? We will answer these questions for surfaces in three-space, as well as for abstract manifolds. Topics include curvature of curves and surfaces, first and second fundamental forms, equations of Gauss and Codazzi, the fundamental theorem of surfaces, geodesics, and surfaces of constant curvature. 

Units: 1

Max Enrollment: 15

Prerequisites: MATH 302.

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Every other year

Semesters Offered this Academic Year: Fall; Not Offered; Spring