Math 529: Introduction to Computational Topology (Spring 2024)
Course Description
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 6
assignments) and a course project. No exams will be
given.
Announcements
Mon, Jan 8: | The class will meet in VECS 125 (Vancouver) and in Webster B8 (Pullman). |
Mon, Jan 15: | I will teach Tuesday's (Jan 16) lecture on Zoom. Check-in hour (2–3 PM) will also be only on Zoom. |
Thu, Jan 18: | I will teach Thursday's (Jan 18) lecture also on Zoom. |
Mon, Jan 29: | This week's lectures (Jan 30, Feb 1) will originate in Pullman. |
Mon, Apr 15: | This week's lectures (Apr 16, 18) will originate in Pullman. |