In this section, Prof. Demaine describes the research-driven focus of the course and how aspects of the course support students in experiencing research.
This course is based on my first area of research in theoretical computer science from when I was a beginning PhD student. At that point, the field was pretty young and there were very few published results. Since then, the field has really exploded; for instance, the National Science Foundation is explicitly funding origami-based engineering as a big area of interest. A lot of the material is very recent, so it is a moving target. Every time I teach it, there is new material to incorporate.
As such, this course champions the notion that research in computer science is not static, but simply demonstrates the best things that we know now. Even if students choose not to come to the open problem sessions, we are always talking about open problems in class: “We still don’t know this, and maybe this is optimal. I would conjecture that, but I don’t know.” In these courses, there is a lot of uncertainty that is not so common—at least not so commonly expressed—in the lower-level courses. But I think that uncertainty is really a key aspect of the world we live in. We do not know the correct answers to most questions, and there is an excitement to the unknown. Even if you are not actively pursuing it, there is a sense that we are still trying to figure out the solution. This uncertainty also serves as an equalizer because there are many things that everyone does not know. It can be comforting, or disappointing, depending on your perspective. I hope that by the end of the semester, after being constantly exposed to that idea (“Oh, open problem here too!”), the students get used to these encounters.
Another spirit of the course is that research is a lot of fun. In folding, there are several fun concepts such as origami design and making new art that actually drive interesting scientific research and have applications to more serious things. But along the way, it is just a lot of fun to be folding paper, exploring, and tangibly experimenting. There are problem sets in 6.849 that ask students to fold something cool and to experiment with the paper.
Problem Sets and Projects
This puzzle, created by Prof. Demaine and Martin Demaine, was assigned as part of the first problem set. Puzzle courtesy of Erik Demaine and Martin Demaine. Photographs of MIT Stata Center, dome, and Simmons Hall © source unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
The problem sets give students a physical, hands-on experience and a problem-solving experience with the material of the course so that they understand the content in a deeper way. The problem sets are intended to drive home a lot of key concepts. Students without a more mathematical background find some of the problem sets harder and others easier. Some students might be really good at the design aspects and less so at the mathematical aspects. The idea is that the course offers something for everyone, and students can enjoy at least part of the problem set and get a lot out of completing the exercises.
The problem sets drop off later in the semester so students can focus on their final project. The project is the big deliverable of the course and comprises most of the grade. This is also where a lot of exciting things happen, so the idea is to give them a lot of time for discovery and exploration in the second half of the semester.
To me, the most exciting projects are the ones that advance the frontier of research. Some of those come from the open problem sessions and others from students working on their own. The sculptural projects that are based around folding or incorporate folding in a nice way are probably the next most exciting. These usually come from the architects, but also from computer scientists and mathematicians. As far as I know, 6.849 is the only MIT computer science course that allows sculpture as a final project! Not too many students take me up on it, but it usually leads to some pretty interesting results.