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FOCUS August/September 2005 FOCUS August/September 2005 FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, FOCUS August/September, October, November, and Volume 25 Issue 6 December. Editor: Fernando Gouvêa, Colby College; [email protected] Inside Managing Editor: Carol Baxter, MAA 4 Saunders Mac Lane, 1909-2005 [email protected] By John MacDonald Senior Writer: Harry Waldman, MAA [email protected] 5 Encountering Saunders Mac Lane By David Eisenbud Please address advertising inquiries to: Rebecca Hall [email protected] 8George B. Dantzig 1914–2005 President: Carl C. Cowen By Don Albers First Vice-President: Barbara T. Faires, 11 Convergence: Mathematics, History, and Teaching Second Vice-President: Jean Bee Chan, An Invitation and Call for Papers Secretary: Martha J. Siegel, Associate By Victor Katz Secretary: James J. Tattersall, Treasurer: John W. Kenelly 12 What I Learned From…Project NExT By Dave Perkins Executive Director: Tina H. Straley 14 The Preparation of Mathematics Teachers: A British View Part II Associate Executive Director and Director By Peter Ruane of Publications: Donald J. Albers FOCUS Editorial Board: Rob Bradley; J. 18 So You Want to be a Teacher Kevin Colligan; Sharon Cutler Ross; Joe By Jacqueline Brennon Giles Gallian; Jackie Giles; Maeve McCarthy; Colm 19 U.S.A. Mathematical Olympiad Winners Honored Mulcahy; Peter Renz; Annie Selden; Hortensia Soto-Johnson; Ravi Vakil. 20 Math Youth Days at the Ballpark Letters to the editor should be addressed to By Gene Abrams Fernando Gouvêa, Colby College, Dept. of 22 The Fundamental Theorem of ________________ Mathematics, Waterville, ME 04901, or by email to [email protected]. By Jeffrey Nunemacher Subscription and membership questions 24 2005 Award Winners for Distinguished Teaching should be directed to the MAA Customer 26 “I Like Change” An Interview with Tina Straley Service Center, 800-331-1622; e-mail: [email protected]; (301) 617-7800 (outside By Don Albers U.S. and Canada); fax: (301) 206-9789. MAA 32 Third Annual Mathematical Study Tour—Home of the Ancient Maya Headquarters: (202) 387-5200. 34 Archives of American Mathematics Spotlight: Copyright © 2005 by the Mathematical Association of America (Incorporated). The New Mathematical Library Records Educational institutions may reproduce By Robin Howard and Kristy Sorensen articles for their own use, but not for sale, 36 What I Learned About…Online Assignment Management provided that the following citation is used: “Reprinted with permission of FOCUS, the By Glenn Ledder newsletter of the Mathematical Association 38 Letters to the Editor of America (Incorporated).” 40 Finding Common Ground in K-12 Mathematics Education Periodicals postage paid at Washington, DC By Michael Pearson and additional mailing offices. Postmaster: Send address changes to FOCUS, 41 U.S. Team Survives Hurricane to Place 2nd in the Mathematical Association of America, P.O. International Mathematical Olympiad Box 90973, Washington, DC 20090-0973. By Steve Dunbar ISSN: 0731-2040; Printed in the United States of America. 42 The Missouri Collegiate Mathematics Competition By Alvin Tinsley and Curtis Cooper 44 Short Takes 2 August/September 2005 FOCUS William McCallum and Ken Ono Named Distinguished Teaching Scholars On June 21, the National Science William McCallum’s research work is in Ken Ono’s work has focused on modu- Foundation named seven Distinguished number theory and arithmetic algebraic lar forms and their relations with ellip- Teaching Scholars, honoring scholars geometry, but he is best known as a leader tic curves. He has obtained remarkable who have achieved success in both re- in the calculus reform movement and results on congruence properties of the search and teaching, and who have suc- one of the main authors of the “Harvard” partition function that are closely related cessfully integrated the two. Among the calculus textbook. He has also been in- to congruences discovered by Ra- recipients are two mathematicians: Wil- volved with the Arizona Winter School manujan many years ago. His work with liam McCallum of the University of Ari- on Arithmetic Algebraic Geometry, undergraduates has successfully involved zona (and a member of the MAA) and which has made this area accessible to them in research, resulting in papers Ken Ono of the University of Wisconsin countless graduate students and schol- published by students and in collabora- Madison. The awards, which are worth ars wishing to learn more about the sub- tion with students. He has also worked up to $300,000 over four years, are “NSF’s ject. NSF reports that “His new work will with K-12 students on projects related to recognition of accomplishments by sci- focus on better communication among number theory. NSF reports that “His entists and engineers whose roles as edu- mathematicians, teachers and math edu- award will help fund summer institutes cators and mentors are considered as cation researchers in a systematic con- that will provide high-school and under- important as their ground-breaking re- tent analysis of problems in algebraic graduate students with a structured re- sults in research,” said NSF Director thinking that should lead to new instruc- search environment. It will also allow for Arden L. Bennet, Jr. The Distinguished tional materials for a broad range of stu- Ono to travel to conduct lectures and Teaching Scholars program has existed dents.” hands-on activities with middle- and since 2001, and has so far honored 34 high-school students alongside Nobel people. Prize and National Medal of Science win- ners.” MAA Election Results Joseph A. Gallian Carl Pomerance Deanna B. Haunsperger President-Elect (2006) First Vice-President (2006-07) Second Vice-President (2006-07) The MAA’s national election concluded at the end of May; 3759 votes were cast, about 35% of them electronically. Joseph Gallian was chosen as President-Elect for 2006, which means that he will be President of the Association in 2007–2008. Carl Pomerance and Deanna Haunsperger will be vice-presidents during 2006–2007. 3 FOCUS August/September 2005 Saunders Mac Lane, 1909-2005 By John MacDonald Saunders Mac Lane was one of the most directly involved in the proofreading of influential mathematicians of the 20th each chapter as it was typed and used to century and was, together with Samuel delight in finding misprints because Eilenberg, a creator of Category Theory. Saunders would say I had an “eagle eye”. Details of this achievement together with He liked to have his students read much other information about his career original source material and had me read can be found in his new book Saunders early papers by Hopf, his papers with Mac Lane, A Mathematical Auto- Eilenberg on K(π,n) spaces, Lawvere’s biography, published by A.K. Peters, Ltd. thesis, as well as Freyd’s, at that time new, in 2005. However, in this article, I will book on abelian categories. present my personal point of view, since Saunders Mac Lane was my thesis At Oberwohlfach he climbed through the advisor, mentor, and lifetime friend. hills with his special walking stick. In the 1970s there were many category meetings I first met Saunders as a graduate student there and many impassioned discussions in Chicago in 1961 when I took a course amongst the participants, especially with him in category theory. I probably about the new developments in topos first came to his attention around that theory. There were discussions during time, when I pointed out a slight error the day and in the evening, and in one of the exercises in his book with arguments too, often with both Eilenberg Birkhoff on Modern Algebra. Saunders Mac Lane and Mac Lane present. Freyd, Lawvere, MAA President 1951-52 Johnstone, Kock, Tholen, Rosicky, Isbell, Saunders’ influence on me did, in fact, suggest some other lemma or theorem Barr and Tierney and many others were extend much further back in time, to that needed proving. involved. Eilenberg’s students were September 1956, when I took a course in always part of the inner circle. Jon Beck’s algebra at Harvard from Andrew Gleason My most important interactions with work, in particular, continues to using the book just mentioned. This Saunders, in fact, took place this way command the highest respect. course resulted in my changing majors when I was a graduate student. He from physics to mathematics, since it insisted on weekly meetings as well as on I remember Saunders’ first wife, Dorothy, convinced me that mathematics had the a progress report from the previous week. quite vividly from the 1974 International richness and mystery that I wished to It was not enough to have read Conference in Vancouver when I had explore further. something — he wanted evidence of many categorists at my house. I met some thought applied to the research Saunders’ second wife Osa at MSRI in In his later years when he had passed problem at hand. In this way he was very 1993. I have a much treasured photo of from his role of advisor and mentor to serious and not nearly as light and Osa, Saunders and my wife standing friend I was constantly amazed by his easygoing as he seemed with some around my son Ian, then 18 months old. tenacity and independence. To give an visitors. I saw her later at notable events like the example, here is a story from when he celebration in Coimbra, Portugal, in was in Coimbra, Portugal, at the At this time in the early 60s, there was 1999, and kept in touch with her up and Category Theory meeting in 1999. After indeed a whirl of categorical ideas through the time of Saunders’ memorial the lectures one day, everyone was urging evolving with visits to Chicago from service at MSRI on May 4, 2005. him to take a cab back to the hotel Eilenberg, Freyd, Lawvere, Beck, and because of the steep walk from the Linton.
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