# Math 142, Spring 2018

### Information for students

Syllabus
bCourses Site
Piazza Site
DSP students should speak to the instructor as soon as possible, even if you don't have a letter yet.
Guidelines on what to do if you think you may have a conflict between this class and your extracurricular activities. In particular, you must speak to the instructor before the end of the second week of classes.
Academic honesty in mathematics courses: A statement on cheating and plagiarism, courtesy of Michael Hutchings.
How to get an A in this class, courtesy of Kathryn Mann.

### Textbook

The required text for this course is M.A. Armstrong's Basic Topology. It can be downloaded on a campus connection. You may also find Topology (2nd edition) by James Munkres helpful, and I suggest it for going deeper.

(will be updated throughout the course)
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Week 1 --- January 16 and 18: Topological spaces, continuous functions
Optional Reading: Believe It, Then Don't: Toward a Pedagogy of Discomfort
Textbook Reading: Armstrong, sections 2.1 and 2.2

Week 2 --- January 23 and 25: Continuous functions, identification spaces
Textbook Reading: Armstrong, sections 2.2, 3.4, 4.1, and 4.2

Week 3 --- January 30 and February 1: Identification spaces, compactness
Textbook Reading: Armstrong, sections 4.2 (ident. spaces), 3.1, 3.3, and 3.4 (compactness)

Week 4 --- February 6 and 8: Compactness, connectedness
Textbook Reading: Armstrong, sections 3.2, 3.4 (compactness), 3.5, and 3.6 (connectedness)

Week 5 --- February 13 and 15: Homotopy
Textbook Reading: Armstrong, sections 5.1, 5.4 (homotopy), and 5.2 (fundamental group)
Homework: No homework this week!

Week 6 --- February 20 and 22: Review & Midterm 1
Midterm 1 is on Thursday in class.
Testable material: Material from Armstrong (below), homeworks, anything in class (except metrisation)
Material covered from Armstrong: 2.1, 2.2 (but not Thm 2.9cd or Thm 2.10 forward)
3.1, 3.2, 3.3 (but not Thm 3.11), 3.4 (but not Thm 3.14), 3.5 (but not Thm 3.23, Cor 3.24, Thm 3.25, Thm 3.27), 3.6 (up to end of Thm 3.29)
4.1, 4.2 (but not the cone construction, nor Lemma 4.5 up to projective spaces [but from the latter on is testable])
5.1, 5.4 (up to but not including Thm 5.17, and from Thm 5.19 to the end)

Week 7 --- February 27 and March 1: Fundamental group, calculations
Textbook Reading: Armstrong, sections 5.2 and 5.3
Homework 5 (due Tuesday, March 6): Click here (corrected typos in 3b and 4)

Week 8 --- March 6 and 8: Fundamental group calculations
Textbook Reading: Armstrong, sections 5.3, 5.4, and 4.4 (examples 1-3, 6)

Week 9 --- March 13 and 15: Fixed points, manifolds
Textbook Reading: Armstrong, sections 5.5, 5.7, 7.1
Reading: Chapters 2-3 of Introduction to Topological Manifolds (mainly: Ch. 2 from page 38; Ch. 3, pages 73-77)
Reading: Classification of closed, connected 1-manifolds (we will also do non-closed)
Homework 7 (due Tuesday, March 20): Click here (updated: 2b is fixed, and optional)

Week 10 --- March 20 and 22: Classification of surfaces
Textbook Reading: Armstrong, sections 7.1, 7.5
Reading: Chapter 6 of Introduction to Topological Manifolds
Reading (optional): John Conway's ZIP proof of the classification of compact surfaces
Homework 8 (due Tuesday, April 3): Click here (2 pages; it's shorter than it looks)

Week 11 --- April 3 and 5: Seifert-Van Kampen, classification of surfaces
Reading: Chapter 10 (pp 251-261, 264-267) of Introduction to Topological Manifolds
Homework: No homework this week!

Week 12 --- April 10 and 12: Review & Midterm 2
Midterm 2 is on Thursday in class.
Testable material: Material from Armstrong and Lee (below), homeworks, anything in class (except higher homotopy groups)
Material covered from Armstrong: 4.4 (but only discrete groups)
5.1, 5.2, 5.3 (no path/homotopy lifting lemma questions), 5.4, 5.5
7.1, 7.5
10.4 (up to and including Thm 10.12; no path/homotopy lifting lemma questions)
Material covered from Lee: Chapters 2 (from p38), 3 (from p73, only discrete groups), 6 (up to p178), 9 (for reference), 10 (pp251-257, 264-267)
Classification of 1-manifolds
Descriptions/notations of some manifolds: projective space, spheres, tori, balls, surfaces
Homework: No homework this week!

Week 13 --- April 17 and 19: Knot theory
Wikipedia reference: 3-colourability
(Optional) More details on knot theory: An Introduction to Knot Theory