Introduction to Computational Topology

COSC 49.09, Fall 2020

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Hsien-Chih Chang (
Mon Wed 4p–5:50p (Eastern Time)
Office Hours
Fri 4p-5p, Mon 9a-10a (Eastern Time)
Canvas | Syllabus | Projects | Notes for COVID-19


Nov 16
Nov 11
A newer version of Homework 3 has been uploaded (again). As pointed out by a student, there was an error in the erratum of Problem 3 (and also the announcements on Nov 4 below). A k-simplex has k+1 nodes, corresponding to the k+1 shortest paths that share a common intersection. In particular, intersection of two shortest paths corresponds to a 1-simplex. I apologize for the confusion.
Nov 4
A new version of Homework 3 has been uploaded. As pointed out by a student, there was an error in Problem 3. The shortest path complex contains not only the 2-simplices (edges) representing intersections of two shortest paths, it also contains all the k-simplices corresponding to higher-order intersections: construct one k-simplex for every k shortest paths that share a common intersection.
Nov 1
All project proposals have be reviewed and approved. I attached some comments to each of your submissions; all the comments and suggestions are meant to be what they are — suggestions — and you are not required to incorporate them to your project if you don't think they are a good fit. All the project proposals can be found and downloaded on Canvas.
Oct 28
Let's cancel the lecture today.  I will record the lecture on Zoom tonight, and post it on the course webpage; also I'll let you know when I start to record so you can jump in if you happen to be free tonight.  I apologize for the short notice.
Oct 26
Oct 23
Homework 3 is out, due by 11/13 (Friday three weeks from now).
Oct 22
So it was brought to my attention that there is a solution to Problem 2 in Homework 2 without using topology (well, at least not the ones we learned in this class).
Oct 20
A new version of Homework 2 has been uploaded, emphasizing that in Problem 2, the starting and ending positions of the cube and corresponding color labels are given after the preprocessing. Which means you don't have time to look at the whole input map again after a position pair is given.
Oct 19
We had several instable connections and/or voice quality problems to Gather.Town; let's switch to Zoom permanently for future office hours.
Oct 17
It is time to think about your Final Project! The project proposal is due by 10/30 (Friday).
Oct 10
Homework 2 is out, due by 10/23 (Friday two weeks from now).
Oct 7
We will have our make-up office hour today at 3pm at Gather.Town.
Oct 5
The office hour today at 9am has been canceled due to emergencies. I will try to make up for it this week.
Oct 2
A new version of Homework 1 has been uploaded, with some errors fixed:
Sep 25
Homework 1 is out, due by 10/9 (Friday two weeks from now).
Sep 21
I am very sorry that I missed the 9am-10am office hour today. Now I'm on Gather.Town; come if you want to join us!
Sep 14
Sep 9
Homework 0 is out, due by 9/18 (next Friday). All the homeworks should be submitted through Canvas.
If you are now in a different time zone other than the EDT, and in particular if you cannot make it to the lectures, please let me know immediately. We will talk about the logistics of the course on the first day of lecture, and make a decision about the weights between synchronous/asynchronous components afterwards, but I do want to get the inputs from those of you who cannot join the lectures.
Sep 7
Hello, welcome to COSC 49.09! This is the webpage for the upcoming course on computational topology. I'm still preparing for the course; please bear with me! If you see any broken links please do let me know. A few announcements:

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