Math 529: Introduction to
Computational Topology (Spring 2022)
Topology studies how a shape or object is connected. In the past few years, there has been an increased interest in the development and use of topological methods for solving various problems in science and engineering. This new line of study is called Computational Topology, Topological Data Analysis (TDA), or Applied Algebraic Topology. Computational topology combines topological results with efficient efficient algorithms to analyze data and solve problems in many fields—biomedicine, phenomics, machine learning, computer graphics and image analysis, sensor networks, robotics, geography, and several others. For motivation, see my TEDx talk on how TDA helps to find hidden structures in data.
This course will present an introductory, self-contained overview of computational topology. There are no prerequisites, but mathematical sophistication at the senior undergraduate level and some familiarity with the use of computer packages such as Matlab or Python are expected. We will cover basic concepts from a number of areas of mathematics, such as abstract algebra, algebraic topology, and optimization. We will also look at algorithms and data structures, and efficient software for analyzing the topology of point sets and shapes.
While there is a recommended book, we will rely a lot on handouts and class notes. Material from several recent (and not-so recent) papers will also be covered. Since the main goal of this course is to expose the audience to this nascent interdisciplinary research area, evaluation will be done through homework (around 7–8 assignments) and a course project. No exams will be given.
|Sat, Jan 8:||The class will meet in VECS 125 (Vancouver) and in Terrell 106 (Pullman).|
|Mon, Jan 10:||We will have class tomorrow (Jan 11) at the usual time. Pullman students can attend on Zoom.|
|Tue, Jan 25:||Check-in hour for today will be 3:30–4:30 pm on Zoom.|
|Wed, Mar 2:||The class will not meet tomorrow (Mar 3). A lecture video will be posted instead.|
|Sun, Mar 20:||The class will not meet this week (Mar 22, 24). Lecture videos are posted instead.|
|Mon, Apr 18:||This week's lectures (Apr 19, 21) to originate in Pullman.|