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18.S097 | January IAP 2022 | Undergraduate
Introduction to Metric Spaces

### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hour / session

### Prerequisites

18.100A Real Analysis

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

There is no official textbook. Lecture notes will be provided. You may find the following textbooks useful:

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.

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).

Rudin, Walter. Principles of Mathematical Analysis. McGraw Hill, 1976. ISBN: 9780070542358.

### Grading

This class will be Pass/No Record with grading based on assignments and participation. There will be four problem sets, and there will not be any exams.

### Calendar

Lecture # and Topics | Key Dates
--- | ---
Lecture 1: Motivation, Intuition, and Examples | Problem Set 1 out
Lecture 2: General Theory | Problem Set 2 out
Lecture 3: Compact Sets in Rⁿ | Problem Set 1 due
Lecture 4: Compact Metric Spaces | Problem Set 3 out
Lecture 5: The Fixed Point Theorem | Problem Set 2 due
Lecture 6: Where We Go from Here | Problem Set 4 out Problem Set 3 due
| Problem Set 4 due (one week after Lecture 6)

Course Info
Instructor

- Paige Bright

Departments

- Mathematics

As Taught In
January IAP 2022
Level
Undergraduate
Topics

- Mathematics
  Mathematical Analysis

Learning Resource Types
menu_book Online Textbook
notes Lecture Notes
assignment Problem Sets
co_present Instructor Insights