Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Prerequisites
or 18.100P Real Analysis
Course Description
This course provides a basic introduction to metric spaces. It covers metrics, open and closed sets, continuous functions (in the topological sense), function spaces, completeness, and compactness.
Textbooks
Lebl, Jiri. Basic Analysis I: Introduction to Real Analysis, Volume 1. CreateSpace Independent Publishing Platform, 2018. ISBN: 9781718862401. This book is available as a free PDF download. You can purchase a paper copy by following a link at the same site.
Munkres, James R. Topology. Pearson, 2015. ISBN: 9789332549531.
Thomson, Brian S., Judith B. Bruckner, and Andrew M. Bruckner. Elementary Real Analysis. CreateSpace Independent Publishing Platform, 2008. ISBN: 9781434841612. This book is available as a free PDF download (PDF - 5.96 MB).
Grading
This class will be Pass/No Record with grading based on assignments and participation. There will be three problem sets, and there will not be any exams.
Calendar
| Lecture # and Topics | Key Dates |
|---|---|
| Lecture 1: Motivation, Intuition, and Examples | |
| Lecture 2: General Theory | Problem Set 1 due |
| Lecture 3: Compact Sets in Rⁿ | Problem Set 2 due |
| Lecture 4: Compact Metric Spaces | |
| Lecture 5: Complete Metric Spaces | Problem Set 3 due |
| Lecture 6: Where We Go from Here |
