Math 535 syllabus
Real Analysis I
An introduction to real analysis. Topics include: the metric topology of the reals, limits and continuity, differentiation, Riemann-Stieltjes integral. Prerequisite: An undergraduate course in Advanced Calculus or Introductory Real Analysis, and basic proof-writing skills.
Textbook: Walter Rudin, Principles of Mathematical Analysis (3rd ed.), McGraw-Hill, Inc. (New York), 1976, ISBN–13: 978–0070542358 or a text at a similar level chosen by the instructor.
Chapters 1-6 of Rudin’s text (and possibly Chapter 7, depending on student preparation). Course work: Graded homework is an important part of the course. Written in-class exams are encouraged, since masters students must take a written qualifying exam in Real Analysis.
Students will gain a rigorous understanding of the foundations of mathematical analysis and a strong working knowledge of the essential concepts, theorems and techniques. They will also become more experienced in solving problems, constructing proofs and communicating mathematical ideas effectively. Specific topics include: fundamental properties of the real numbers; metric topology, continuity, compactness and connectedness; rigorous development of the derivative and the Riemann- Stieltjes integral. Sequences and series of functions, uniform convergence and the Stone-Weierstrass theorem may be covered in this semester if time permits.
Updated: September 23, 2014