Real Analysis

MAT 3015

Analysis and geometry are at the roots of such basic areas of mathematics as general topology, geometric topology, differential geometry, functional analysis, measure theory, probability theory, dynamical systems, and differential equations, to name a few. This course introduces students to set theory, general topology, metric spaces, measure theory, Lebesgue integration, and function spaces. Though the basic structure of analysis was set in the nineteenth and the beginning of the twentieth century, we will explore such up-to-date applications as analysis of fractals or applications to financial calculus through some of the projects.