Diners: Dale Johnson, Dean of the Graduate School; Jim King, Doug Lind, Steve Mitchell, Jim Morrow, Ginger Warfield, faculty; Jon Jay, Liz Rachele, Robert Smith, graduate students.
The evening began with a characteristic ricochet shot. Doug suggested that we all introduce ourselves with a brief mathematical autobiography (or deanical in the case of Dale Johnson). I thought to myself that this was an excellent variant on the as yet unfulfilled plan to run some mini- or quasi-colloquia at which a small number of faculty members sketch, for the benefit of the graduate students, their career autobiographies. As it turned out, I was so busy taking part in the general faculty chorus of "Gosh, really?" that I completely failed to take notice of how any of the graduate students present reacted. But we did also enjoy hearing how they got to our august institution.
Jon introduced the first topic of conversation (which also wound up being the last one--I'll splice the discussions): he remarked that the shift from the pre-prelim state to the post-prelim state was causing him rather drastic culture shock. This was universally agreed to be A) normal and B) unfortunate (to put it mildly.) Liz found the admirable solution of camping out in the library, submerging herself in all possibly relevant references until she had a feeling for the field of her choice. Jim Morrow remarked that the only students he has run into that come into graduate school with an understanding of what mathematical research actually is are those who have taken part in an REU (Research Experience for Undergraduates.) This is an NSF-funded summer project which brings together ten undergraduates (generally but not always about to be seniors) to spend the summer doing research. Jim and Ed Curtis see to it that it really is research--the students are introduced to an area in the theory of networking, told some recent results and a few directions that other students have ventured into, and then turned loose to find problems, think of ways to work on them, and see where they can get to. They are given encouragement, support, and a great deal of assistance in learning to communicate mathematics (especially in writing), but no grades or comparative evaluation of any sort, and no specific directions. A few come out saying that if this is what it is to do math research they would prefer a new edition of the Spanish Inquisition than to ever let it into their lives again. Others, on the other hand, like our own Matt Huddleston, come out saying that this is just what they have been looking for all their lives, charge into graduate school motivated to get the preliminaries out of the way and get back to this great stuff--and have no culture shock whatever.
That's a far cry from being dumped cold turkey into Real Life Research in Mathematics as a reward for surviving the prelims. It is also an extremely intensive, ten week long experience with a five to one student to faculty ratio--not something we can casually reproduce for 30 graduate students a year. But it surely would be nice if somehow some faint echo of such an experience could happen for them.
A comment by Rob introduced the next topic: calculus. Or rather, CALCULUS! We ranged through the difficulties of choosing the optimal format for it, the degree of its impact on our position in the world, the importance of professor/T.A. alignment in jointly teaching it, and what some of the current options are. Dale then sounded an even scarier note by pointing out the incipient baby-boom echo: 9000 more eager young freshmen in the near future. His quotation of a speaker who maintains that "technology is the answer" led to a discussion of what technology can do. What sticks in my mind, though, are two examples technological non-answers. One was Dale's own tale of a video-taped lecture so bad that when the camera panned around to the live-audience class half of them were asleep. Another was Jim King's feeling comment that teaching with computers can add a tremendous richness to a course, but only if you spend about twice as much time as you would on a regular course.
If technology is not the answer, then one might lie somewhere in the range of upping our admission standards and making heavier use of our excellent community college system--but that direction involves a certain number of land mines as well. Simple solutions there ain't.
Back on the subject of Things to do with Calculus, Steve Mitchell pointed out that we have with us for the year David Pengelley, who since leaving the fold here has gone off and built himself a considerable reputation for innovative teaching, most notably at the calculus level. An opportunity which should not be wasted (and we have no intention of doing so!)
Another conversation which made a meteoric passage from one topic to another began with a description of a two-credit graduate seminar on technology which Jim Morrow ran this summer. He set it up to address whatever questions the students in question formulated. This produced questions of a wide range of sophistication, and the seminar appears to have worked out quite well. So well, in fact, that students asked why it doesn't run all year. The answer to this involved faculty teaching loads, the discussion of which always produces sundry bizarre decimals and a random collection of acronyms. As the fog of question marks around the graduate students' heads began to become dense, Doug launched an explanation of the counting system, starting with the external one involving FTE's, etc. It was already interesting before Dale said "Well, actually,..." and absolutely fascinating thereafter!