Math 424: Honors Real Analysis
Text: M. Rosenlicht, Introduction to Analysis, Dover.
Also, use chapter 17 of Fundamental Mathematics by D'Angelo and West for treatment of integration.
Continuity, compactness and completeness underlie much of modern mathematics and its applications. The course develops these concepts in the metric space setting, after which the fundamentals of calculus are rigorously established.
Chapter 1 - omit
Chapter 2 - The real number system (2 hours)
Chapter 3 - Metric spaces (9 hours)
Chapter 4 - Continuous functions (6 hours)
Chapter 5 - Differentiation (4 hours) - Riemann integration (8 hours)
Chapter 7 - Interchange of limit operations (6 hours)
Leeway, quizzes, and exams: 8 hours
Present the Riemann-Darboux integral using a supplementary source such as chapter 17 of Fundamental Mathematics by D'Angelo and West.