September 26-27, 2003
Northern Kentucky University
Members in attendance:
Chris Christensen, Northern Kentucky University
Daniel Curtin, Northern Kentucky University
Richard Davitt, University of Louisville
Charles Holmes, Miami University
Kevin Kirby, Northern Kentucky University
David Kullman, Miami Univeristy
Daniel Otero, Xavier University
Richard Pulskamp, Xavier University
We gathered for dinner Friday evening (typically the most important event of the meeting!) at Brio's Italian restaurant at Newport on the Levee for a wonderful meal. Chris and Dan C. also conducted a short tour of the Levee complex (during which we spotted George Polya--or was it Paul Erdos?--strolling alongside the building), ending in a brief meditation before the Cincinnati skyline at sunset.
We reconvened at NKU's Applied Science Building for the first of our sessions in a planned two-meeting study of the work of George Polya. Beginning as we have in the past with a review of the ethnoculural heritage of our man-of-the-hour, we discussed at length Polya's Hungarian roots, his teachers, his move to Zurich and eventually to the U.S., his illustrious mathematical career and his especial renown for work in mathematical reasoning. We then began our discussion of the main reading, the Introduction and first Chapter of Combinatorial Enumeration of Groups, Graphs and Chemical Compounds (Springer, 1987), the English translation of the influential 1937 paper Kombinatorische Anzahlbestimmungen fur Grüppen, Graphen und chemische Verbindungen (Acta Math., 68, 145-254). The discussion quickly focussed on trying to understand Polya's terminology: what, really, did he mean by the terms figure, configuration, content, and boxes?
On Saturday morning, the members patiently awaited Otero's tardy arrival with the bagels and cream cheese from Panera; juice and coffee rounded out the meal. The discussion then returned to figuring out figures; it's not at all clear that we resolved the issue by the end of the session, either. We did benefit from a reading of the relevant section in Alan Tucker's Applied Combinatorics (Wiley, 1980 -1st ed., 1984-2nd, 1994-3rd, 2001-4th), however. We did manage, barely, to work our way through the text up to the statement of the main theorem in paragraph 16 that states what we now know as Polya's Enumeration Theorem.
Our plan for the winter meeting, tentatively scheduled for January 30-31, 2004, at Xavier University, is to read one or more of the papers on Pedagogy that appears in the fourth volume of Polya's Collected Papers (R. P. Boas, ed., Cambridge, 1974-1984). Also a candidate for study is part of his Mathematics and Plausible Reasoning (Princeton, 1954).
Respectfully submitted,
Danny Otero