HONR 325M - Math 325/425 Real Analysis

You will learn how to write rigorous mathematical proofs and sharpen your logic. We will construct the mathematical formalism that is used to prove all the results used in an introductory calculus sequence. We will start with the definition of the set of real numbers endowed with the field algebraic structure and then systematically study the consequences of defining a metric and imposing the Axiom of Completeness. You will write proofs to classify sequences and real-valued functions of a real variable. By the end of our class, you will (i) be able to read mathematical proofs, (ii) understand analysis arguments and applications in various fields (e.g., physics, computer science, etc.), and (iii) have the foundation necessary for a meaningful study of any higher-level analysis course. Lastly, Real Analysis serves as the ideal introduction to metric spaces in preparation for a course in Topology.