Course overview
The geometry of surfaces is a classical subject, dating back to the 19th century and the work of Gauss. It provides an excellent introduction to the ideas of contemporary differential geometry and Riemannian geometry.
Topics covered are: The inverse and implicit function theorems; submanifolds of Rn; differential forms; Stokes' theorem for submanifolds of Rn. Curvature of curves and surfaces in R3; geodesics. The Gauss-Bonnet theorem. Surfaces of zero gaussian curvature; minimal surfaces.