Math 500

Schedule Syllabus Homework


This schedule is tentative, and will be updated infrequently.  The homework page will always be up to date.

Date
Section
Topics



Th 8/29

No class.



Tu 9/3

Overview: point-set versus algebraic topology, Brouwer Fixed-Point Theorem
Th 9/5
Ch 2.12-13 Topological spaces, Basis for a topology



Tu 9/10
Ch 2.14-15 Order topology, product topology on XxY
Th 9/12
Ch 2.16-17 Subspace topology, closed sets



Tu 9/17
Ch 2.17-18 Limit points, Hausdorff spaces, continuous functions
Th 9/19
Ch 2.19-20 Product topology, Metric Topology



Tu 9/24
Ch 2.21-22 Metric Topology, Quotient topology
Th 9/26
Ch 3.23-24 Connected subspaces



Tu 10/1
In-class exam

Th 10/3
Ch 3.26-27 (return to 25 later) Compact subspaces
Drop period ends 10/4
Tu 10/8
Ch 3.28-29 Limit point compactness, local compactness
Th 10/10
Fall Break




Tu 10/15
Ch 4.30-31
Countability axioms, separation axioms
Th 10/17
Ch 4.32-33
Normal spaces, Urysohn Lemma



Tu 10/22
Ch 4.34
Urysohn Metrization Theorem
Th 10/24
Ch 4.35
Tietze Extension Theorem



Tu 10/29
Ch 5; Take-home exam out
Tychonoff Theorem
Th 10/31
Ch 9.51-52
Homotopy of paths, fundamental group



Tu 11/5
Ch 9.53; Take-home exam due
Covering spaces
Th 11/7
Ch 9.54
Fundamental group of the circle
Deadline to withdraw 11/8
Tu 11/12
Ch 9.55, 57
Retractions and fixed points, Borsuk-Ulam Theorem
Th 11/14
Ch 9.58
Deformation retracts and homotopy type



Tu 11/19
Ch 9.59
Fundamental group of S^n
Th 11/21
Ch 9.60
Fundamental groups of some surfaces



Tu 11/26
Ch 11.68-69
Direct products and free products of groups
Th 11/28
Thanksgiving




Tu 12/3
Ch 11.70-71
Seifert-van Kampen Theorem, Fundamental group of a wedge of circles
Th 12/5
Ch 11.72-73
Adjoining a 2-cell, Fundamental group of the torus and dunce cap



Tu 12/10
--
Extra day for catch-up



Final Exam