Math 445: Introduction to Topology I

David Dumas

University of Illinois at Chicago
Spring 2019

[Dyadic disks]
Textbook Topology, 2ed by James R. Munkres. (Prentice Hall, 2000)
UIC library / Google books / Amazon
Lectures MWF at 1pm in 309 Taft Hall
Instructor email david@dumas.io
Instructor office hours To be announced
CRN 39509 (undergraduate), 39510 (graduate)

About the course

Math 445 provides an introduction to topology, which is the field of mathematics concerned with a formalization of the notion of "shape". Most of the course will focus on the area within topology known as point set topology. We will define topological spaces and discuss some important examples, such as metric spaces. We will study a variety of properties of topological and metric spaces, including compactness and connectedness. We will also discuss general methods for constructing new topological spaces from existing ones, such as products, quotients, and subspaces.

We will cover chapters 2–4 in the textbook and selected topics from chapters 5–8.

Documents

Calendar & Grading

This is a condensed summary of some important dates and the weights used to compute your course grade. The course syllabus is the definitive reference for course policies.
Date/time Course grade fraction
Homework Most Mondays (see list below) 50%
In-class midterm Wed Mar 6 20%
Final Exam Mon May 6 30%

Homework

Problem sets and their due dates are listed below. Unless otherwise noted on the assignment, homework is due in class at the beginning of the lecture (i.e. at 1:00pm in 309 Taft Hall).

Typeset solutions are not required. If writing solutions by hand, please make sure they are legible. Staple homework if it spans several sheets of paper. Write your name and the assignment number (e.g. "Homework 1") at the top of the first page.

Many of the homework problems are assigned directly from the primary textbook (Munkres, 2ed).

Lecture titles and textbook sections

Supplementary texts

For students looking for another place to read about the topics from the course, I recommend:

Online resources

LaTeX

Students who are learning TeX / LaTeX and who want to typeset their homework may find this template helpful:
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