Winter 2021 STAT 37411

Course: STAT 37411=CAAM 37411

Title: Topological Data Analysis

Instructor(s): Bradley Nelson

Class Schedule: Sec 1: TR 2:40 PM–4:00 PM (Remote)

Textbook(s): Oudot, Persistence Theory: From Quiver Representations to Data Analysis; Edelsbrunner and Harer, Computational Topology: An Introduction; Ghist, Elementary Applied Topology

Description: Topological data analysis seeks to understand and exploit topology when exploring and learning from data. This course surveys core ideas and recent developments in the field and will prepare students to use topology in data analysis tasks. The core of the course will include computation with topological spaces, the mapper algorithm, and persistent homology, and cover theoretical results, algorithms, and a variety of applications. Additional topics from algebraic topology, metric geometry, category theory, and quiver representation theory will be developed from applied and computational perspectives.

Prerequisite(s): Linear algebra, prior programming experience, exposure to graph theory/algorithms.