Prerequisites: Graduate Standing.
A rigorous review of the topology of, and of the functions on, the real line and more general metric spaces. Topics include sequences, including sequences of functions, completeness, compactness, continuity, uniform continuity, and differentiation.
Outcomes: Students will master the mathematical rigor behind undergraduate real analysis and obtain preparation for further graduate courses in analysis and its applications.
A rigorous review of the topology of, and of the functions on, the real line and more general metric spaces. Topics include sequences, including sequences of functions, completeness, compactness, continuity, uniform continuity, and differentiation.
Outcomes: Students will master the mathematical rigor behind undergraduate real analysis and obtain preparation for further graduate courses in analysis and its applications.