# Math 472: Introduction to Topology

## Colorado State University, Fall 2016

Email: henry dot adams at colostate dot edu
Office: Weber 125
Office Hours:

• Wednesdays 12:50-1:50 in Weber 125,
• or by appointment.

Lectures: MWF 12:00-12:50pm in Engineering E204
Textbook: Basic Topology by M. A. Armstrong.

Overview: This course is an introduction to topology. Topics covered include Euler's theorem, topologies on sets, continuous functions, homeomorphisms, sequences and convergence, metric spaces, compactness, connectedness, path-connectedness, identification spaces, homotopy equivalences, the fundamental group, Brouwer's fixed-point theorem, classification of surfaces.

Syllabus: Here is the course syllabus.

## Homework

Homework 1 (LaTeX Source) is due Friday, August 26.
Homework 2 (LaTeX source) is due Friday, September 2.
Homework 3 (LaTeX source) is due Friday, September 9.
Homework 4 (LaTeX source) is due Friday, September 16.
Homework 5 (LaTeX source) is due Friday, September 23.
Homework 6 (LaTeX source) is due Friday, October 7.
Homework 7 (LaTeX source) is due Friday, October 14.
Homework 8 (LaTeX source) is due Friday, October 21.
Homework 9 (LaTeX source) is due Friday, October 28.
Homework 10 (LaTeX source) is due Monday, November 14.
Homework 11 (LaTeX source) is due Friday, November 18.
Homework 12 (LaTeX source) is due Friday, December 2.

We will have weekly homework assignments. All homework is due in class at the beginning of class. Your homework should be legible and stapled.

## Exams

The exams will be in-class. You will only be able to use your brain and a pen or pencil - no notes, books, or electronic devices. The exams will be comprehensive, except that Midterm 2 will emphasize the material after Midterm 1, and the Final will emphasize the material after Midterm 2.

Here is Practice Midterm 1.
Here is Practice Midterm 2.
Here is a Practice Final.

## Notes

Scans of Henry's lecture notes.

## Schedule

 Date Class Topic Remark Aug 22 Introduction and course overview Aug 24 §1.1 Aug 26 §1.2 Homework 1 due Aug 29 §1.3, 1.4 Aug 31 §1.4, 1.5 Sept 2 §1.6 Homework 2 due Sept 5 Holiday - no class! Sept 7 §1.6, 2.1 Last day to drop or change grading option Sept 9 §2.1 Homework 3 due Sept 12 §2.2 Sept 14 §3.1 Sept 16 §3.2 Homework 4 due Sept 19 §3.3 Sept 21 §3.3, 3.4 Sept 23 §3.4 Homework 5 due Sept 26 §3.4 Sept 28 Review Sept 30 Midterm #1 Midterm through §3.3 Oct 3 §3.4, 3.5 Oct 5 §3.5 Oct 7 Midterm recap and §3.5 Homework 6 due Oct 10 Research talk and office hours Oct 12 §3.5 Oct 14 §3.6 Homework 7 due Oct 17 §5.1 End of course withdrawal period Oct 19 §5.1 Oct 21 §5.1 Homework 8 due Oct 24 §5.2 Oct 26 §5.2 Oct 28 §5.2 Homework 9 due Oct 31 §5.3 Nov 2 Review Nov 4 Midterm #2 Midterm through §5.1 Nov 7 §5.3 Nov 9 §5.3 Nov 11 Class cancelled Nov 14 §5.4 Homework 10 due Nov 16 §5.4 Nov 18 §5.4 Homework 11 due Fall Recess, Nov 21-25 Nov 28 §2.3 Nov 30 §5.5 Dec 2 §5.7 Homework 12 due Dec 5 An introduction to computational topology Dec 6 Dinner at Henry's! Dec 7 Review and class picture Dec 9 Review Final Exam, Monday December 12 Through §5.7 4:10-6:10pm in Engineering E204