Sunday, December 21, 2008

More experiments in algo-teaching

(ed. note: think of this as a 'theory'-chaser to take the bad taste of cricket-blogging out of your mouth)

Another experiment that I continued this time was a set of lectures on "fun topics". The idea is to convey some ideas about a fun topic in theoryCS without too much jargon, but with enough meat to indicate that there's something deeper going on beneath the fun stuff.

I run these lectures at the end of the semester (when everyone's worn out already :)), and throw them open to the general public: both times I did this, I got substantial attendance from people not in my class, and at least in one case, someone who attended the lecture last year actually decided to take my class this year.

Not all topics are amenable to such a treatment, but my hope is to build up a suite of such lectures: the nice thing is that they can then be reused for other venues: for example, I've given variants of these talks to freshmen and high school students, and will do an undergraduate colloquium in the math department next semester.

For all of these lectures, I've pilfered shamelessly from the original works, as well as great websites developed by the authors. This post can be viewed as a shout-out and a thank you.

1. Pancake flipping:
Brian Hayes wrote a great article on pancake flipping for the American Scientist. In it, he links it to the problem of genomic rearrangement, and in doing so, ends up with a beautiful tale of the interaction between theoretical problems and practical constraints, all told in context of a topic that everyone can relate to.

I made two-color pancakes in different sizes, and distributed them to the students at the start of class: I briefly described the problem, and let them go at it. It was quite entertaining, and put the more formal discussion later on in context.

2. Zero knowledge proofs
ZK proofs are great for this kind of setting: they are completely counter-intuitive, (and so have the 'bizarre' factor), and are easily explained using popular metaphors. I used Moni Naor's Sudoku demo page, as well as the version of the proof that involves slicing and dicing the puzzle. This was done with class participation (I was the prover, and there were multiple verifiers).

The second demo I ran was the Yao protocol for the Millionaire's problem (how do two millionaires determine which is richer, without either knowing the worth of the other). Again, I did this interactively with class volunteers and an RSA applet to speed things along. More details here.

3. Quantum Computing
No demos for this one, but I gave a crude high level view of what quantum computing is about (about one-step up from the "do everything in parallel" explanation). The main goal here was to convey the basic ideas of what a qubit is, what a quantum circuit looks like, and how the Bell inequalities show that quantum computing is much more bizarre than classical randomness. Here, Dave Bacon/Umesh Vazirani lecture notes proved indispensable, coupled with the Nielsen-Chuang book, and a recent blog post by Michael Nielsen.

4. Computational Origami
I haven't quite worked the kinks out of this one, but the basic idea is to demonstrate the principles behind computational origami (and where the 'computation' comes in) by looking at the question: What shapes can you make by folding, followed by a single cut.

There's a cool backstory to this: essentially the first example of such an algorithm was how Betsy Ross designed the 5 point star for the American Flag, and it lends itself to a nice demo in class.

Secondly, it's a classic example of resource-bounded computation: limiting yourself to one cut. Thus, it makes for a good illustration of how computation appears in all kinds of problems.

Thirdly, computational origami actually shows up in many real-world problems, most notable one involving folding mirrors for a telescope to be launched into space. If we're trying to convey a sense of computational thinking, this is a great example.

The actual problem itself was solved in this paper by Demaine, Demaine and Lubiw. Unfortunately, I have yet to find a way of explaining it that will make sense to non-expert geometers, and that's one weakness with this particular story: Erik's page has some nice examples to demo, but it's hard to convey the deeper algorithmics behind the problem.

Lessons learned:
  • As always, know your audience. What works for a graduate class doesn't work for sophomores, and certainly doesn't work for eigth-graders :)
  • Interactivity is key: if you allow people to participate, they're more involved, and will probably take away something positive
  • Keep it light: resist the urge to get too mathematical. There are many beautiful topics in theoryCS that can be explained without jargon, and many others for which with some effort, jargon can be removed.
  • A 'bizarro' factor helps: In general lectures that I've given, I find that presenting something completely counter to people's expectations catches their attention immediately, and leaves a lasting impression. ZK proofs have that property. Bell's inequality sort of does, but the impact would be more immediate if I could actually run a quantum experiment to demonstrate violation of Bell's inequality ;)
  • Relate it to the real world: again, it's not enough to cite applications: one should try to show them as far as possible. In this regard, the Betsy Ross story is great, because it relates to something everyone (in this country) knows.
My goal is to add one or two such lectures to my arsenal each time I teach the class. For next time, I'm seriously considering running a live auction of some kind to demonstrate some concept in algorithmic game theory (suggestions on how best to do this are always welcome). Are there other such topics that might lend themselves to an entertaining, edifiying and educational experience ?
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