In this project-based course we will learn about some developments in computer assisted explorations of topology---an area known as Computational Topology. The goal will be to motivate some useful applications of abstract notions from topology, starting by analyzing real world data.
No need to purchase any texts. But just to get a glimpse, here are some texts I may refer to.
- Edelsbrunner & Harer, Computational Topology
- Zomorodian, Topology for Computing
- Munkres, Elements of Algebraic Topology
- Stillwell, Classical Topology and Combinatorial Group Theory
The (group) projects can be a) examples of topological data analysis of some publicly available large data set or b) implementation of topological algorithms on generated data.
To receive a grade for the course, students will be required to give a beamer presentation of the project and write a short blog describing the project.