Math 401 [M]: Introduction to Analysis I

Course Description

This course offers an introduction to real analysis at the senior undergraduate level. Real analysis is a continuation of calculus, and many of the concepts we introduce in this class should be familiar from calculus, e.g., functions, continuity, convergence, etc. But we will introduce these concepts in new, more abstract, contexts. The biggest change from calculus to real analysis is a shift in emphasis from calculations to formal arguments. We will cover Chapters 1--4 from the book Lindstrøm: Spaces An Introduction to Real Analysis. Topics covered include preliminaries (proofs, sets, functions, etc.), completeness, basics of metric spaces, convergence, compactness, and spaces of continuous functions. Emphasis will squarely be on constructing sound mathematical arguments, i.e., proofs.