Math 54
Topology I
Last updated June 17, 2015 12:57:08 EDT

Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.
NOTE ON SECTIONS FOR READING: Munkres uses continuous section numbering, so that the first section of chapter 2 is listed as 2.12 instead of 2.1.

Lectures Sections in Text Brief Description
6/22 1.1-1.3 What is Topology? Intro to Set Operations. Notes for first few chapters (is missing logic stuff like converses,etc.
6/23 1.4-1.10 (skip section 8) Countable and uncountable sets.
6/25 2.12-2.13 Topological Spaces.
6/26 (x-hour) HW First problem session.
6/27 2.14 More bases. Sub-bases.
6/29 2.15 The order topology. The Product Topology (two factors). Subspace topology.
7/2 2.16-17 The subspace topology, ctd. Closed sets and limit points.
7/3 (x-hour) HW Second Problem Session. Emily, Ethan, Jacob, Hayden, Caitlin, Patrick, and Kellie presented solutions.
7/4 Holiday .
7/6 2.17 Limits, Sequences, and Hausdorff spaces.
7/9 2.17 Continuous functions.
7/10 (x-hour) HW Third Problem Session. Sucharita, Kellie, Annie, Cooper, Jacob, and Vincent presented solutions.
7/11 2.18 The product topology.
7/13 2.18-19 Metric Topology.
7/16 2.20-21 Metric Topology, ctd.
7/17 (x-hour) HW Fourth Problem Session. Erez, Paul, Gavin, Harrison, Sam, and Vincent presented solutions.
7/18 Exam First midterm In-class solutions. Take-home solutions.
7/20 3.23 Finish Metric Spaces. Interlude on Quotient Spaces.
7/23 3.24 Connected Spaces. Connected subspaces of the real line. Density of the rationals and irrationals.
7/24 (x-hour) HW Fifth Problem Session. Sean, Erez, Patrick (twice), Ethan, Hayden, and Joe presented Solutions.
7/25 3.26 Products of Connected Spaces. Path-Connected Spaces.
7/26 3.27 Compact spaces. Compact subspaces of the real line.
7/30 3.28 Products of Compact Spaces.
7/31 (x-hour) HW Sixth Problem Session. Harrison, Jacob, Cooper, Vincent, Emily, and Ethan presented solutions.
8/1 4.30 Compact Hausdorff Spaces, Locally Compact Spaces, Heine-Borel Theorem.
8/3 4.30-31 Countability Axioms.
8/6 4.32 Regular and Normal spaces.
8/7 (x-hour) HW Seventh Problem Session. Vincent, Ethan, Sean, Caitlin, Joe, and Paul presented solutions.
8/8 Exam Second Midterm
8/10 4.33 Urysohn's Lemma.
8/13 4.33-34 Urysohn's Lemma, ctd. Prerequisite material for Urysohn's Metrization Theorem.
8/14 (x-hour) HW Eighth Problem Session. Vincent, Cooper, Hayden, Kellie, Sam, and Sean presented solutions
8/15 4.35 Urysohn's metrization Theorem.
8/17 ??? Tietze's extension theorem.
8/20 ??? Intro to Differential Topology
8/21 (x-hour) HW Ninth and Final Problem Session. Hayden, Vincent, Sean, and Emily.
8/22 ??? The Fundamental Theorem of Algebra.
8/25 Exam Final Exam

Dan Crytser
Last updated June 17, 2015 12:57:08 EDT