Schedule/Topics/Pre-recorded lecture videos/Notes

Date Topic Videos to watch before Notes Kinsey Reading
12/07 Fundamental group Lecture Notes Parts of 9.2
12/04 Based loops and composition Lecture Notes Parts of 9.2
11/30 +12/2 Brouwer fixed point theorem Lecture Notes
11/20 Homotopy equivalence Lecture Notes Parts of 9.1
11/18 Intro to homotopy Lecture Notes Beginning of 9.1
11/16 Euler characteristic and surfaces Lecture Notes (WARNING: The proof here of invariance of Euler charactertic follows Kinsey Theorem 5.13, which is incomplete. To complete it, one can separately distinguish the surfaces, eg by puncturing and using the homotopy equivalence to a wedge of circles.) 5.4
11/13 Euler characteristic for planar diagrams Lecture Notes 5.3
11/11 Euler characteristic of CW-complexes Lecture Notes Begin 5.3
11/09 Graphs and Trees Lecture Notes 5.2
11/06 Platonic solids and Euler characteristic Lecture Notes
11/04 Platonic solids Lecture (problem with screen-share, but audio seems fine) Notes Platonic app
11/02 Classification of surfaces with boundary Lecture Notes 4.6
10/30 Proof of class. of surfaces, part 3 Lecture Notes 4.5
10/28 Proof of class. of surfaces, part 2 Lecture Notes 4.5
10/26 Proof of class. of surfaces, part 1 Lecture Notes 4.5
10/23 Classification of surfaces Lecture Notes Beginning of 4.5
10/19 + 10/21 Surfaces - orientability and connect sum Lecture Notes Finish 4.3
10/16 Cutting up a Klein bottle Klein Bottle YouTube video None None
10/14 Manifolds and surfaces Lecture Notes Beginning of 4.3
10/12 CW complexes - formal definition Lecture Notes None
10/09 CW complexes Lecture Notes Ch 4.1
10/07 Intro to Cell Complexes Lecture. Mobius tricks YouTube video Notes Ch 4.1
10/05 Quotient spaces Lecture Notes Ch 3.5
10/02 Properties of product spaces Lecture Notes Ch 3.4
9/30 Product spaces Lecture Notes Beginning of Ch 3.4
9/28 Separation axioms Lecture Notes Ch 3.3
9/25 Compactness via open covers Lecture Notes Finish Ch. 3.2
9/23 Subspace, continuity, connectedness Lecture Notes End of Ch 3.1, Beginning of Ch. 3.2
9/21 Basis for a topology Lecture Notes w/ defn error. CORRECTED Notes Ch 3.1
9/18 Metric spaces and topologies Lecture Notes Beginning of Ch 3.1
9/16 Connected sets and intermediate value theorem Lecture Notes Ch 2.5 + parts of Ch 2.6
9/14 Connectedness Lecture Notes Ch 2.5
9/11 Compactness Lecture Notes Ch 2.4
9/9 Continuity (continued) Lecture Notes Ch 2.3
9/4 Continuity Lecture Notes First part of Ch 2.3
9/2 Relative neighborhoods Lecture Notes Ch 2.2
8/31 (No new material) None None None
8/28 Review of Set Theory; Limit points, Closed sets, Limits of sequences Lec part 1: Review of Set Theory; Lec part 2: Limit points, Closed sets, Limits of sequences Notes Part 1, Notes Part 2 Ch 2.1
8/26 Idea of topology, R^n, discs, balls, open sets Lec part 1: Idea of topology; Lec part 2: R^n, discs, balls, open sets Notes Part 1; Notes Part 2 Ch 1, Ch 2.1
8/24 Word search on the torus and Klein bottle None None None
Last modified: Tue Dec 9 18:08:28 EST 2025