Parametrized curves, curvature of curves; Frenet frames, curves with prescribed curvatures, curves on hypersurfaces; principal, Gaussian, and mean curvatures; surfaces in R^3, triangulation and classification of surfaces, Gauss-Bonnet theorem.
Prereq: Grad standing or 2153.01 (254) and either 2568 (568) or 572. Not open to students with credit for 642.