Geometry of Surfaces

Using methods from calculus and linear algebra, this course develops essential ideas in the study of curves and surfaces in three dimensions. The central focus are the various concepts of curvature that can be assigned to a surface, and how these concepts determine most of the fundamental properties of curves and surfaces. Geometric intuition will be a point of departure from where students will produce rigorous proofs, building on concepts learned in Multivariable Calculus, and preparing the way for the study of Riemannian Geometry.