CS 898: Tilings and Computation

About the course

Tiling theory, the study of shapes that cover the plane with no gaps and no overlaps, is a fascinating subject that draws ideas from many areas of mathematics and computer science. Results in tiling theory are interesting as advances in mathematical research. Many results also transfer over into applied domains of computer science, particularly computer graphics. And of course, the practice of tilings has numerous decorative applications in art, architecture, and design.

After I give a few preliminary lectures laying out an introduction to tiling theory, we'll survey research from across the topic, from mathematics to computational geometry to computer graphics. We won't restrict attention to the newest papers only—it's not like there's a big annual conference where all the top tiling-theoretic work is published. We'll reach back into the 20th century when appropriate, and we'll occasionally leave the bounds of CS and wade into mathematics papers (without getting too deep into the abstract realms of pure math).

Note for PhD students: Because this course will cover both theoretical and applied topics, you can count it towards either the "Graphics and User Interfaces" or "Algorithms & Complexity" areas of the Comp I requirements (but not both!).

Student responsibilities

Here's a tentative marking scheme for the course, with some preliminary details about each of the categories. The exact weights and details are subject to change before the start of the term.

The course does not include regular assignments or a final exam.

Readings and Resources

Schedule

Here's a tentative schedule for the term. We'll fill up this schedule as students claim papers and dates on which to present them. We may make other adjustments during the term as needed.

Policies

Generative AI

Generative artificial intelligence (GenAI) trained using large language models (LLM) or other methods to produce text, images, music, or code, like Chat GPT, DALL-E, or GitHub CoPilot, may be used under specific conditions in this course with proper documentation, citation, and acknowledgement.  Permitted uses of and expectations for using GenAI will discussed in class and outlined on assignment instructions.

That's the university's boilerplate text. Let me expand on it. Basically, I'm opposed to using Generative AI. I don't trust it to work reliably. When it's wrong, it's often wrong in subtle ways that are easy to miss, precisely because it's tuned for plausibility over correctness. More fundamentally, even if it worked flawlessly, you shouldn't use it. Generative AI certainly does nothing to make you smarter, and there's some evidence that it may even make you dumber (by stunting your critical thinking skills). If you weren't interested in becoming smarter, then why did you come to grad school?

The one place where I can offer some leeway is in using Generative AI to improve English writing. If you aren't a confident writer, then it's OK to treat a system like ChatGPT as a fancy grammar checker: you can feed in your draft text and have it spit out a polished version. It is your responsibility to look over the generated text carefully to make sure its meaning is preserved. You are required to disclose any AI tools that you used to help with writing and must, upon request, provide a transcript of your interaction with the tool.

Mental Health