MA 598 Ralph M. Kaufmann

Ralph Martin Kaufmann
Purdue University; Department of Mathematics
150 N. University Street; West Lafayette, IN
Phone: (765) 494-1205; Fax: (765) 494-0548
e-mail: rkaufman@math.purdue.edu URL: http://www.math.purdue.edu/~rkaufman

MA 59800 - Fall 2021
Topological Data Analysis

Instructor: Ralph Kaufmann

Office: Math 730
Contact via e-mail

Date and Time: MWF 10:30 - 11:20 pm in REC 112

Syllabus
Standard Syllabus components

Office hours: Wed 1-1:50 and by appointment

References: "Computational Topology" by Herbert Edelsbrunner and John L. Harer (CT)
                       "Topological pattern recognition for point cloud data" Acta Numerica. 23: 289-368 by Gunnar Carlsson. (TPR)
                       "Barcodes: The Persistent Topology of Data". Bull. Amer. Math. Soc. 45 (2008), 61-75 by Robert Ghrist.(Bar)
                        "Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition"
                           by G. Singh, F. Memoli and G. Carlsson (Mapper)

more tba.

General References. Munkres: Elements of Algebraic Topology (EAT)
                                   Munkres: Topology
                                   Gelfand-Manin: Methods of Homological Algebra
Electronic resources. Wikipedia (double check content). Mathworld (sometimes a bit terse). n-Lab (sometimes a bit complicated).

NEWS: Welcome. Problem set 2 is Posted.

Homework Problems:
Set 1 will be collected Sep 17

Set 2 will be collected Nov 5

Topics: Topics of lectures past and future. The future does not contain unforeseen changes.

Date	Topics	Reference
8/23	Introduction
8/25	Abstract simplicial complexes, data, graphs and clique compexes.	EAT or any other source
8/27	Singular chains and homology for abstract simplicial complexes	EAT or any other source
9/1	Singular homology for abstract simplicial complexes	EAT or any other source
9/3	Homology for graphs. Examples, connected components and loop number.	Lecture or any other source