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 | |