These are lecture notes from a special-topics class on computational topology that I have taught several times at the University of Illinois, most recently in Spring 2023. The course focuses on algorithms for curves and graphs in the plane and on other surfaces.
I’m writing everything in Markdown, partly to focus my time on writing instead of typography, and in part to make the final output more accessible by producing HTML and ePub versions. As a result, the notes are typographically rather awkward/ugly. Some day I will figure out how to use Pandoc templates and filters. (Real Soon Now, Honest.)
I drafted most of these notes in Fall 2020 and revised them in Spring 2023; a handful of chapters (13, 16, 26, 27, 29, 30) were first drafted in Spring 2023. Most of the missing chapters either cover material I did not discussed in class, or cover material from my own research papers.
I think I’m about 2/3 of the way to a complete draft of an actual textbook, but even the most polished notes are still very rough drafts.
You are welcome to use these notes, but I would not recommend citing them as a definitive source for ANYTHING.
I honestly don't know when I'll be able to work on these notes again in earnest, or when (if ever) they're likely to be complete. I'll fiddle with them a bit over the summer, but I'm going to be swamped with my real job during the academic year, especially in the fall, I won't teach this class again until 2025 at the absolute earliest.
These notes (and other course materials) are available under a Creative Commons Attribution license (CC BY 4.0).
