Syllabus

The following is a tentative syllabus for the course and will be updated as necessary. All associated assignments may be found on the homework page.

Week Lectures Sections in Text Brief Description
1 6/24 §1, 5 Course introduction, set theory
6/25 (Sa) §2, 6, 7

Special Class (10:40-11:45am)

Functions, cardinality of sets, and LaTeX
2 6/27 §12 Topological spaces
6/28 (x) §13 Bases
6/29 §3, 14 Orders and the order topology
7/1 §15, 16 The product and subspace topologies
3 7/4 Independence Day (no class)
7/5 (x) §16, 17 Subspace topology (ctd.),
position of a point in a set, closed sets
7/6 §17 Closure, limit points
7/8 §17 Limit points and Hausdorff spaces
4 7/11 §18 Continuous functions
7/12 (x) §18 Homeomorphisms and topological properties
7/13 Midterm Exam Material through §17
7/15 DF Away (no class)
5 7/18-22 DF Away (no class)
6 7/25 §20 Metric spaces
7/26 (x) §21 Properties of metric spaces
7/27 §19 The infinite product topology
7/29 §23 Connected sets
7 8/1 §23, 24 Products of connected sets, IVT,
path connected sets
8/2 (x) §3, 25 Equivalence relations, connected components,
local connectedness
8/3 §26 Compact spaces
8/5 §26, 27 More on compactness
8 8/8 §27, 31-35 Heine--Borel Theorem,
separation axioms, Urysohn's Lemma
8/10 §30, NIB Manifolds
8/12 §22 Quotient topology
9 8/15 Classification of manifolds
8/17 Classification of manifolds (cont.)
8/19 §51 Homotopies and path homotopies
10 8/22 §52 Fundamental group
8/24 Results in algebraic topology
8/27 Final Exam 3-6pm, Kemeny 105