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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.

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 Homework 1 (due Tuesday, January 30): Click here

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) Homework 2 (due Tuesday, February 6): Click here

Week 4 --- February 6 and 8:Compactness, connectedness Textbook Reading: Armstrong, sections 3.2, 3.4 (compactness), 3.5, and 3.6 (connectedness) Homework 3 (due Tuesday, February 13): Click here

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) Homework 4 (due Tuesday, February 27): Click here

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) Homework 6 (due Tuesday, March 13): Click here

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 Textbook Reading: Armstrong, section 7.5 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 Textbook Reading: Armstrong, section 10.1 Wikipedia reference: 3-colourability (Optional) More details on knot theory: An Introduction to Knot Theory Homework 9 (due Tuesday, April 24): Click here (2 pages)

Week 14 --- April 24 and 26:The knot group Textbook Reading: Armstrong, section 10.2 Wikipedia reference: n-colourability (Optional) More details on knot theory: An Introduction to Knot Theory Homework 10 (just for practice, not graded): Click here (2 pages)

Final:11:30AM - 2:30PM, in 740 Evans Testable material: anything testable on Midterms 1 and 2, and anything covered in the classes of April 17, 19, and 24

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