MAT 441: Real Analysis
Undergraduate course, Southern Virginia University, 2024
A rigorous treatment of one-variable calculus: limits, continuity, differentiation, the Riemann integral, metric spaces, and sequences and series of functions.
About the course
Real analysis goes back to the beginning of calculus and asks why it is all true. But for most students the main outcome is not the theorems. It is the thinking: learning to assimilate new concepts and vocabulary quickly, to write precisely and concisely, and to think abstractly and creatively within the constraints of the abstraction. An expert-level mastery of the theory of calculus is a significant byproduct.
Reading quizzes before nearly every class meeting guide students’ study of the text, so class time can be spent on proofs and the ideas behind them.
Textbook: Understanding Analysis, 2nd edition, by Stephen Abbott.
Prerequisite: MAT 343: Linear Algebra.
Syllabus
Helpful resources
- Basic Analysis: Introduction to Real Analysis by Jiří Lebl. A free textbook covering the same material. Useful when you want a second proof of a theorem.
- Paul’s Online Math Notes. When a proof depends on a calculus fact you have forgotten, this is a quick place to review it.