Math 412: Topology with Applications

Time: T TH, 10:05 - 11:20AM

Location: West Duke 08A

Instructor: Paul Bendich

Office Hours: Physics 210, M 1-2, TH 12-1

Course Description and Grading Policy

Main Textbooks: We will be using two textbooks. They are Topology: A First Course, by James Munkres and Computational Topology , by Herbert Edelsbrunner and John Harer. I'll refer to them as "T" and "C," respectively, in the syllabus below. We will also use some supplementary handouts, including journal articles.

Date Topics Chapters
Aug. 28 Overview, Introduction, Motivating Examples
Aug. 30 Point-set Topology: Definitions, Examples T: 2-1,2-2
Sept. 4 Product and Subspace Topologies T: 2-4,2-5
Sept. 6 Closed Sets and Limit Points T: 2-6
Sept. 11 Continuity T: 2-7
Sept. 13 Connectedness T: 3-1,3-2
Sept. 18 Compactness T: 3-5,3-6
Sept. 20 Compactness T: 3-5,3-6
Sept. 25 Quotient Topology T: 2-11
Sept. 27 Simplicial Complexes C: III.1
Oct. 2 Convex Set Systems C: III.2
Oct. 4 Point Cloud Triangulations C: III.3,III.4
Oct. 9 Simplicial Homology: Definitions, Examples C: IV.1
Oct. 11 Induced Maps C: IV.1
Oct. 18 Singular Homology, Functoriality
Oct. 23 Matrix Reduction Algorithm C: IV.2
Oct. 25 Relative Homology C: IV.3
Oct. 30 Exact Sequences C: IV.3, IV.4
Nov. 1 Zig-zag Lemma C: IV.4
Nov. 6 Persistent Homology: Intro C: VII.1
Nov. 8 The Persistence Algorithm C: VII.1, VII.2
Nov. 13 Morse Theory and Persistence C: VI.1, VI.3
Nov. 15 Stability Theorems and Homology Inference C: VII.2
Nov. 20 Gene Expression Data C: IX.1
Nov. 27 Extended Persistence C: VII.3
Nov. 29 Protein Docking and the Elevation Function C: IX.2
Dec. 4 Presentations
Dec. 6 Presentations