MATH 322(S) Differential Geometry

Differential geometry describes the shapes of objects from soap films to Universes in terms of curvature. The curvature of a curve can be described in calculus, but it is more complicated to describe the various twistings of surfaces and Universes. In general it requires going a step beyond vectors and matrices to the "Riemannian curvature tensor," which is the key to understanding Einstein's theory of General Relativity, in which mass itself is understood as curvature. Evaluation will be based primarily on classwork, homework, and exams. Prerequisite: Mathematics 211 or permission of instructor.