Convex Geometry, Func. App

3 Credits · Level: Undergraduate

Convexity is an important concept in advanced mathematics, with important applications to optimization, economics, materials science, and other fields. In this elementary introduction, we will study convex sets, hyperplanes, linear functionals, separating hyperplanes, supporting hyperplanes, Helly's Theorem, Kirchberger's Theorem, the isoperimetric problem, polytopes, Euler's formula, convex duality, linear programming, convex functions, distance functions, continuity and differentiability properties of convex functions, and optimization and convexity. We will consider examples taken from optimization, economics and materials science.