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Instructor:
E-mail: Office: Phone: Office hours: |
Victoria Sadovskaya sadovskaya@psu.edu 426 McAllister (814) 863-4140 Monday & Friday 1:20-2:10 p.m., Wednesday 3:40-4:30 p.m., and by appointment |
Text:
Real Analysis
by N.L. Carothers.
Course description:
The goal of this course is to develop thorough understanding and
technical mastery of foundations of classical analysis in the framework of metric spaces.
The following topics will be covered: Metric spaces (open and closed sets, connectedness,
convergence, Cauchy sequences and completeness); Maps between metric spaces (continuous
maps and homeomorphisms, stronger continuity properties, contraction mapping principle);
Compact metric spaces (continuity and compactness, total boundedness, coverings);
Baire Category Theorem; Function spaces (spaces of continuous maps, equicontinuity,
Arzela-Ascoli Theorem, Stone-Weierstrass Theorem).
Prerequisites: Math 311M and Math 312H.
Syllabus
pdf