MA590 On-Line Materials -- Topology

This page contains materials related to the course MA590, Special Topics: Topology.

Course Description

Students should enter the course with an extensive exposure to mathematics at the undergraduate level, including analysis. Students are expected to have well-developed proof-writing skills and a knowledge of set theory, relations and functions at least at the level of MA1971. No previous knowledge of topology is assumed.

Text: Topology, Second Edition by James Munkres Pearson, 2000, 537 pages.

Work Course syllabus: in PDF format. Assignment 1 (due Mon Jan 30): in PDF format. Assignment 2 (due Mon March 13): in PDF format.

Play A knotted molecule with 192 atoms and 8 crossings. The Rolfsen knot table Some propaganda: Dr. Spencer's mantra, in PDF format; an opinionated article on doing university-level math, in PDF format. Examples of categories in mathematics Topological Data Analysis: An important early article on bar codes by Robert Ghrist A popular introduction by Gunnar Carlsson, one of the founders of the subject An essay by Michael Lesnick A survey paper, giving a review of the basic methods, by Larry Wasserman For an introduction to the relevant software, perhaps this paper will help: A roadmap for the computation of persistent homology, by Nina Otter, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, and Heather A. Harrington.