This course will explore the mathematics of folding in 1, 2, and 3 dimensions. We will take an algorithmic approach to solve problems related to folding, exploring from simple concepts to the state-of-the-art. We will also take a look at some open problems in the area and perhaps even collaborate in solving some! Along with math and algorithms, we will have fun folding some origami.

Folding problems have applications in areas such as manufacturing, robotics, and biology.
Several of such problems are easily describibla and remain open.

Prerequisite: Comp160 is required, Comp163 and Comp170 are recommended but not required (concepts needed from these disciplines will be briefly covered in the course).

This is a special topics course and we have freedom to cover any relevant material. We will definitely cover classic results in 1, 2, and 3 dimensions: the problem of foldability, polygonal linkages and the carpenter's rule problem, map folding, geometric constructions, origami design, and flattening and unfolding polyhedra. But the idea is that we can also spend time exploring the state-of-the-art research on topics that you are interested in. For this reason, your participation in class is very important!

** Piazza: **

Sign up here. Communication and materials (including homework) for this course will be posted there.

** Office hours: **

Halligan 206 Mon/Wed 3-4 pm. You can also send me an email and we can try to schedule a more convenient time if that doesn't work for you.

** Expected work and grading: **

You must attend class and **participate** engaging in the discussion.
There will be weekly **homework**, molstly reading assignments but with enventual problems.
You are expected to read academic papers and write a brief one-paragraph summary.
If you didn't understand some concept or proof, you can write it in your summary.
Homework will be due on the beginnign of Tuesday's class. No late homework will be accepted, but I will drop the two lowest scores at the end.

You must submit a **final project** that consists of a proposal due mid semester, a paper describing what you did, and a 15 min presentation that will be scheduled for the final classes.
The only requirement for the project is to demonstrate knoledge aquired in the course in a significant way.
You can, for example, design an origami using an algorithm and describe the process; implement an algorithm/visualization of something covered in class; or solve an open problem! (That will probably give you an A+).

You are required to meet with me mid sementer during office hours to discuss your project proposal.

**
Collaboration is allowed and encouraged. ** However, you must cite **every** source or person you discussed with.
Goup projects are ok (up to 3 people per project) and each group can submit a single paper/presentation as long as the paper clearly states the contributions of each participant.

Your final grade will be:

- 20% participation measured by interactions in class, piazza posting, or submitting questions to me directly (via email or office hours). All you have to do is to do two of the previous per week;
- 40% homework;
- and 40% final project;

** Resources: **