Striking while the iron is at least tepid, I am attempting a quasi-summary of our conversation. Any comments, expansions, objections, corrections, or mildly relevant flights of fancy that you would like to toss in, I would love to get, and will ultimately blend together into a single document of some sort.
QUESTIONS:
1) What is the goal of our graduate program? Is it simply the
production of doctoral students prepared to join the faculty of some four
year college or university? If so, should it be? The down side is that
students who leave with a Masters leave also with a sense of defeat, or
possibly of having disappointed us. On the other hand, if we invite two
types of application, we create instant elitism, and if we describe the
program as a masters program from which a select few will be permitted to
proceed to a PhD we lower our position in the prestige sweepstakes. Also
confusing to the issue is the fact that many really don't know what they
are going to want, and in any case predicting success or failure from the
entering data is a pretty dicey sport.
One suggestion along the lines of damage-control was to turn the "lame duck" year after prelim failure into active preparation of some alternative sort (or as Top Stoppard put it "Remember to look on every exit as an entrance to somewhere else")
2) Were and are theorems really out there pre-existing and just waiting to be discovered? The real numbers, too? Then where does that put the Riemann Hypothesis?
3) What did they DO to that squid?
IDEAS:
1) Variations on a couple of themes for improving teaching:
graduate students could sign on with a teaching mentor for a quarter.
That could take the form of being an assistant throughout the quarter, and
having regular discussions of the professor's plans and goals and
philosophy, with the student taking on a piece of the teaching (plan
modelled on the English Department's PFF format). Or it could be getting a
professor who has previously taught whatever course the grad student is
about to teach and asking him/her for advice and ongoing availability.
Alternatively, it could take the form of a mini-seminar of everyone in
process of teaching one of the multi-section courses, which might be aimed
at graduate students, but would do participating faculty members no harm
whatever.
The first and third of those ideas could reasonably have a credit or two attached for the grad student and possible fraction of FTE count creditted to the faculty member's load.
Almost anything we did along these lines would have the property of helping to institutionalize the kind of thing the PFF grant is all about.
2) A possibly educational experience for a graduate student would be to shadow a faculty member for a day or longer. It would have to be managed with some care, however, because it has the potential of being mind-bogglingly boring.
3) Another form of helping each other on the teaching front might be to start up an electronic archive of hand-outs from particular courses, especially if the hand-outs were accompanied by brief notes on what they were aimed at, and maybe even how well they worked.
4) On the issue of helping students A) to develop a feeling for what it is to do research and B) to get a running start on doing some, many references were made to Jack's "Icewater Seminar", in which students were required to choose 2 papers from the Forty Top Hits of Diffferential Geometry and give a full formal (colloquimesque) oral report, as well as a written one. Jack set it up to be pretty scary, but clearly with a net positive effect, as reported by John.
5) More on Icewater--it seems as if something of that type might reasonably be substituted for the current general exam.
6) Dave expressed surprise at the number of students who leave after having successfully passed their prelims. Cindy suggested that some, at least, may not realize that their thesis results have as yet any value. Some way of encouraging thesis advisors to give more feed-back might be profitable (though Dave somehow lacked overwhelming enthusiasm for taking on the job of getting and transmitting the feed-back for every relevant graduate student, even though not all 70 are involved!)
7) Given the current oversupply of Math PhD's (as indicated by the undersupply of jobs for same) there is some possibility of converting a few graduate student spots into post-doc positions, with the post-docs supplying enough bodies so that sizes of calculus sections could be reduced to something only moderately unreasonable. The discussion got into something of a tangle of present and future body-count arithmetic.
8) Future dinner suggestion: more graduate students
9) Future departmental suggestion: a day-long retreat to deal with one or another of our specific on-going issues.
10) Repetition of a suggestion already mooted at least twice: have an occasional session where a few faculty members described the route by they arrived at their current exalted position, with possibly a few words about what occupies them from day to day in said position. Probably the best forum for this would be the graduate student colloquium(?)