Henry Adams

Math 472: Introduction to Topology

Colorado State University, Fall 2016

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

Lectures: MWF 12:00-12:50pm in Engineering E204
Textbook: Basic Topology by M. A. Armstrong. This book is freely available as a PDF to CSU students if you login on the CSU library webpage.

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 Euler's theorem
Aug 26 §1.2 Topological equivalence Homework 1 due
Aug 29 §1.3 Surfaces, §1.4 Abstract spaces
Aug 31 §1.4 Abstract spaces, §1.5 A classification theorem
Sept 2 §1.6 Topological invariants Homework 2 due
Sept 5 Holiday - no class!
Sept 7 §1.6 Topological invariants, §2.1 Open and closed sets Last day to drop or change grading option
Sept 9 §2.1 Open and closed sets Homework 3 due
Sept 12 §2.2 Continuous functions
Sept 14 §3.1 Closed bounded subsets of Euclidean space
Sept 16 §3.2 The Heine-Borel theorem Homework 4 due
Sept 19 §3.3 Properties of compact spaces
Sept 21 §3.3 Properties of compact spaces, §3.4 Product spaces
Sept 23 §3.4 Product spaces Homework 5 due
Sept 26 §3.4 Product spaces
Sept 28 Review
Sept 30 Midterm #1 Midterm through §3.3
Oct 3 §3.4 Product spaces, 3.5 Connectedness
Oct 5 §3.5 Connectedness
Oct 7 Midterm recap and §3.5 Connectedness Homework 6 due
Oct 10 Research talk and office hours
Oct 12 §3.5 Connectedness
Oct 14 §3.6 Joining points by paths Homework 7 due
Oct 17 §5.1 Homotopic maps End of course withdrawal period
Oct 19 §5.1 Homotopic maps
Oct 21 §5.1 Homotopic maps Homework 8 due
Oct 24 §5.2 Construction of the fundamental group
Oct 26 §5.2 Construction of the fundamental group
Oct 28 §5.2 Construction of the fundamental group Homework 9 due
Oct 31 §5.3 Calculations
Nov 2 Review
Nov 4 Midterm #2 Midterm through §5.1
Nov 7 §5.3 Calculations
Nov 9 §5.3 Calculations
Nov 11 Class cancelled
Nov 14 §5.4 Homotopy type Homework 10 due
Nov 16 §5.4 Homotopy type
Nov 18 §5.4 Homotopy type Homework 11 due
Fall Recess, Nov 21-25
Nov 28 §2.3 A space-filling curve
Nov 30 §5.5 The Brouwer fixed-point theorem
Dec 2 §5.7 The boundary of a surface 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