Math 574--Introduction to Computational Topology (Spring 2018)
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
or Applied
Algebraic Topology. Computational topology
combines topological results with efficient
efficient algorithms to analyze data and solve
problems in many fields -- computer graphics
and image analysis, sensor networks, clustering,
robotics, genetics, protein biochemistry, geography,
and others. For a recent overview, check out the
topics discussed in the workshop on
Topological
Data Analysis held at
the IMA a
couple years back.
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 homeworks (around
7-8 assignments of) and a course project. No exams
will be given.
Announcements
Thu, Mar 29: | Today's lecture is canceled. |