There's nothing quite like starting off with a bang! The Brown Bags for the year have just gotten started, and #1 is going to be a very hard act to follow. The idea for it came from a reference in the departmental meeting a couple of weeks ago to an "undergraduate mathematics research laboratory" Peter Sarnak had put together at Princeton. My reaction at the time was that A) I was probably not fully grasping what it was about but B) it sounded very interesting. This week Sarnak was in town to give the annual Milliman lectures, and he kindly consented to be our Brown Bag guest and tell us about the laboratory. I was right on both counts. My grasp being now somewhat better, I shall attempt to explain it.
The explanation starts with a philosophical background: Peter has a firm commitment to the idea that computational experimenation is currently getting a bad rap in mathematics. Gauss and Euler and those guys got huge mathematical mileage out of doing stacks of calculations, looking for patterns and then either proving the resulting conjectures or computing some more and coming up with a counterexample. Nowadays with computer programs capable of, for instance, churning out eigen-values for a 1000 by 1000 matrix at the drop of a hat there's a huge potential for producing batches of results in which to search for patterns or counter-examples. And producing them doesn't require all that much expertise.
That's one element of the origin of the course. Another is Princeton's VIGRE grant. Like ours (like all of them) it mandates vertical integration, with emphasis on involving undergraduates in research.
Those are the two things that made the laboratory desirable. One other indispensable item was that one of Peter's two (2) doctoral students named Steven Miller is outstandingly computer-friendly and student-friendly, and was willing and able to help sift through the possible mathematical topics in search of ones whose computation was within range of current software.
These ingredients came together into a course/laboratory in which students, after being introduced to a bunch of areas amenable to significant computations at an accessible level, take on projects in which they not only carry out computations, but write them up and explain them (in Tek, which they also learn) and put them on the web. It was first offered in 1999/2000 -- and firmly refused. Last year the enrollment figures miraculously rose from 0 to 10, possibly because the course was declared a requirement for junior math majors. Fortunately, once they were pulled in they settled down and did some really good work while, by the sound of it, thoroughly enjoying themselves.
Peter's hope is that this course will not only continue at Princeton but spread to other universities. To that end he has mounted on the web not only student projects but also descriptions of other topics which could be done and haven't been. All are findable at http://www.math.princeton.edu/~mathlab/.
As long as I'm newslettering, I had better fill in on a recent event which is in danger of sliding into oblivion. It was a PFF event, which means I had better do some reviewing: the PFF (= Preparing Future Faculty) project is funded by the NSF, and its major function is to broaden the horizons of graduate students with regard to mathematical academe. Our efforts have had three major components: 1) an opportunity for a small number of students to spend a whole quarter doing a lot of observing and conversing at Settle University and/or Seattle Central Community College; 2) a bunch of mathematico-social events centered around a hot-shot speaker (Alan Schoenfeld last spring, for example) and including a dinner at which graduate students, U.W. faculty members and faculty members from as as many two- and four-year colleges from the area as we can entice in get a chance to converse, and 3) closer to home, a series of dinners at the Marlai Thai Restaurant at which graduate students and U.W. faculty discuss life around our own department from the two different perspectives.
In theory, all these lovely things were due to end as of the end of September. To my great pleasure, we were granted an extension -- in fact, two -- so that we have not only a couple of autumn events, but even possibly one in winter quarter. Meanwhile, however, while all the PFF projects were still theoretically going to fold up shop in September, a final nation-wide meeting was scheduled for the first week-end in October. Its objective was to write a How-To manual designed to help other universities set up PFFish structures. I was invited to bring two graduate students, and chose to invite the two who were last spring's PFF fellows on the SU and SCCC campuses. The success of this ploy can be judged by the letter sent out to all the conference attendees today by Les Sims, one of the organizers:
"The conference was a tremendous success largely because a consensus developed around the excellent suggestion of Gordon Williams and Leah Berman (University of Washington Mathematics PFF students) of an outline for the PFF3 brochure/publication."
It may be borrowed glory from my point of view, but me, I am basking in it! --