Goals: To learn the language, fundamental concepts, and standard theorems of analysis. To also learn how to reason deductively from explicit assumptions and definitions in mathematical analysis, thus developing analytic techniques for attacking problems that arise in applied mathematics. Recommended for students considering graduate school in mathematics. Content: An introduction to real analysis with emphasis on proofs of theorems and on problem solving. Topics include properties of the real number system, functions, sequences, limits and continuity, differentiation, integration, and infinite series including sequences and series of functions. Taught: Alternate years, fall. Prerequisites: MATH 3330 and 3550.