MATH 4997 - Fall 2015

Vertically Integrated Research: Big Data and Topology

In many applications data (of numerical information) can be represented by a point set in an n-dimensional space. Computational topology focuses on the computational aspects of topology, and applies topological tools to analysis of those data sets. Topological tools of simplicial homology, shape and discrete morse theory will be presented. Algorithms and software for the analysis of the topology, connectivity and shape of point sets will be explored. Projects will be either a software exploration implementation on a point data set of interest to you or a presentation of recent papers in the area.

Prerequisites: Math 2057 (Multivariate Calculus), Math 2085 (Linear Algebra) (or Math 2090) or equivalent, or permission of the instructors.

Text: Computational Topology by Herbert Edelsbrunner and John L. Harer

This course will cover new material: Chapter 4: Simplicial Homology, Chapter 5: Duality & Chapter 6: Morse Functions.

Section 1 Instructor: Dasbach, Stoltzfus Email:
Class: 244 Lockett: 3:30 MWF Office: 306/258 Lockett URL:
Lockett Office Hours: 9:30am MW & TBD Office Fax: 225.578.4276 Office Phone: 225.578.1656

Grades and Evaluation: The class will be divided into several groups each mentored by a post-doc or advanced graduate student. Each group will make in-class presentations during the semester. There will be a variety of introductory and more advanced topics so that every level of mathematical maturity can be accommodated. Attendance is mandatory. We will meet each Monday & Wednesday as a group with presentations. Wednesday is also reserved for the (Virtual) Topology Seminar on current topics. The Friday time period will be for individual group meetings, unless otherwise notified by group email. If it is necessary for you to be absent, please communicate with one of the instructor in advance (in non-emergency cases.)

Grades: Based 50% on class participation & attendance and 50% on the in-class presentation. Letter grades based on a 10-point grading scale. A plus-grade is marked if you are in the top 20% of the decile for a letter grade and a minus grade if you are in the bottom 30% of the decile.

Neal W. Stoltzfus   Fall 2015