THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA Olympiad Winners Honored in Washington Volume IS. Number 4 Eight winners of the U.S.A. Mathematical Olympiad were honored at an awards ceremony at the National Academy of Sciences in Wash• In this Issue ington, DC on June 12. Chosen as first place winner from nearly 3 Letter to 550,000 students, Aleksandr Khazanov, a se• the Editor nior at Stuyvesant High School in New York, became one of six members of the U.S. Inter• national Mathematical Olympiad (IMO) team. 4 Arcadia Review Last summer, Khazanov was a member of the Lto R: Jay Chyung. Andrei Gnepp. Christopher Chang. Graig Helfgott. MAA President Ken Ross. Aleksandr Khazanov. U.S. IMO team which received a perfect score Sarnit Dasgupta. Jacob Lurie. and Josh Nichols-Barrer. 6 Distinguished for the first time in IMO history. Khazanov Teaching A wards will enter Penn State in the fall to study math• South High School in Newton Center, Massa• ematics. He plans to be a college mathematics chusetts; and Craig R. Helfgott, a senior at instructor. He says his father taught him math• Ramaz Upper School in New York City. 9 Interview with ematics since he was age nine. "By showing Along with Khazanov, this is the second con• MAA President me interesting combinatorics problems rather secutive year Lurie and Chang have won the than belaboring arithmetic, he induced in me a Ken Ross USAMO. Lurie also received a perfect score at vigorous interest in mathematics." the IMO last summer. These three individuals 16 1995 SlitTe Awards Top USAMO winners include Jacob Lurie and plus Chyung, Gnepp, and Nichols-Barrer made Samit Dasgupta,junior and senior, respectively, up the six-member IMO team; Dasgupta and 19 1994 MAA at Montgomery Blair High School in Silver Helfgott were alternates. After four weeks of Spring, Maryland; Christopher Chang, a jun• intensive training at the Illinois Academy of Annual Report ior at Henry M. Gunn High School in Palo Math and Sciences in Aurora, they represented Alto, California; Jay Chyung, a senior at West the U.S. in Toronto, Canada, competing with 39 Employment High School in Iowa City, Iowa; Andrei Gnepp, teams from over seventy countries. The IMO Opportunities a senior at Hawken School in Gates Mills, Ohio; took place July 13-15. A report of the compe• Josh Nichols-Barrer, a sophomore at Newton tition will appear in the October FOCUS. AWM Announces 1995 MAA National Election Schafer Prize Winner Did you receive a ballot?

Ruth Britto-Pacumio, ajun• The MAA is conducting its biennial national ior at the Massachusetts election. Due to a mailing problem, ballots to Institute of Technology, is a few zip code areas were not delivered. Bal• the winner of the sixth an• lots have been remailed to members in these nual Alice T. Schafer Math• areas. ematics Prize. The Schafer We want to give every member an opportu• Prize is awarded to an un• nity to vote. If you have not yet received a dergraduate woman in rec• ballot, please notify us immediately. You can Tbe Mathematical ognition of excellence in contact the MAA toll free at 1-800-331-1622. Association of America mathematics and is sponsored by the Associa• A new ballot will be sent to you. Because of 1529 Eighteenth Street. NW tion for Women in Mathematics (AWM). Ms. the possibility that there are still members Wa~hingt()n. DC 20mt1 Britto-Pacumio will receive a cash prize of who have not received ballots, election re• $1000. sults will not be announced until October. See Schafer Prize on page 3 FOCUS August 1995 FOCUS Editorial FOCUS is published by The Mathematical Association of America, 1529 Eighteenth Congratulations Street Northwest, Washington, DC 20036- 1385, six times a year: February, April, One thing that struck me as I was putting together this issue of FOCUS was that, as a June, August, October, and December. profession, we seem to like giving awards for achievements. The two front page articles Editor and Chair of the MAA are about awards ceremonies, and in the pages that follow you will find several more Newsletter Editorial Committee: Keith announcements of awards. We give awards to students for their performance as students J. Devlin, Saint Mary's College of and to faculty for their performance as teachers. California The awards reported in FOCUS are just the tip of the iceberg, the national awards. For Associate Editor: DonaldJ. Albers, MAA most of us, the college or university where we work has its own range of awards for Associate Executi ve Director and Director students and professors, and often for graduate student instructors as well. That's a lot of Publications and Programs of awards. Managing Editor: Harry Waldman, MAA This plethora of academic awards is, I believe, a particularly American phenomenon. I Production Specialist: Amy spent most of my academic career to date in my native England where, although a few Stephenson Fabbri, MAA university departments have prizes for the best undergraduate students, it would never Proofreader: Meredith Zimmerman, occur to anyone to give awards to an instructor for outstanding performance in the MAA classroom. The unspoken assumption is that you don't give an award to someone for Copy Editor: Nancy Wilson, Saint Mary's simply doing their job well. At least, I assume that is the assumption-being an unspoken College of California assumption, no one ever spoke about it, so I cannot know for sure if there is a rationale for not giving teaching awards or if the very idea simply never occurred to anyone. Letters to the editor should be addressed to: Keith Devlin, Saint Mary's College of It's an interesting question. Should we give awards to people for doing well the job for California, P.O. Box 3517, Moraga, CA which they are employed and paid? I am sure the existence of an award does not itself 94575; e-mail: [email protected]. lead to better performance. People excel because they want to succeed, not because they The FOCUS subscription price to are trying to win a prize. The real reward for a semester's good teaching comes at the individual members of the Association is semester's end, when we look back on what we have accomplished and grade the papers, $6.00, included in the annual dues. and maybe receive thanks from a few of our students. So why give awards? (Annual dues for regular members, exclusive of annual subscription prices for Anyone who has spent time at both British and American colleges and universities MAA journals, are $68.00. Student and cannot fail to have noticed that, overall, the standard of teaching in America is far higher unemployed members receive a 66 percent than in Britain. (I deliberately used 'overall' because, as always when human perfor• discount; emeritus members receive a 50 mance is concerned, there are plenty of individuals who buck the trend.) In Britain the percent discount; new members receive a student at a university is still by and large regarded as a bit of a nuisance, someone who 40 percent discount for the first two membership years.) gets in the way of the real work of the day. Though you will certainly find similar attitudes in the USA, my own observations tell me that by and large the climate on this side of the Copyright © 1995 by The Mathematical Atlantic is very different. And awards are, I think, an important part of the picture. Association of America (Incorporated). Educational institutions may reproduce There are surely so many excellent college and university teachers around that most of articles for their own use, but not for sale, them cannot possibly ever win an award. But the very existence of those awards makes provided that the following citation is used: a clear and highly visible statement as to what we, as a profession, think is important. "Reprinted with permission of FOCUS, They affirm what we are about. Awards are not re-wards. They are not incentives. They the newsletter of The Mathematical Association of America (Incorporated)." are a way of saying "This is what we value and what we strive to achieve." And as such, they are very valuable. Second-class postage paid at Washington, DC and additional mailing offices. So I give my hearty congratulations to all those awards winners whose names you will Postmaster: Send address changes to the find in this FOCUS. And I give equally hearty congratulations to all those who did not Membership and Subscriptions De• win an award, but who nevertheless did an excellent job. partment, The Mathematical Association of America, 1529 Eighteenth Street Northwest, Washington, DC 20036-1385. -Keith Devlin ISSN: 0731-2040 Printed in the United States of America. The above opinions are those ofthe FOCUS editor and do not necessarily represent the Printed on recycled paper. official view of the MAA.

2 August 1995 FOCUS

Gale's article seems to agree that Nash Fine, I imagine Gale saying, definitions Letter to the Editor defined the concept, but then it says that deserve credit. But then the right people the concept had been around long before deserve the credit, and Nash is not the right To the Editor: (indeed in the economics literature• person here. Someone else was first, or perhaps many people. But this is no dif• I reply to the lovely article by David Gale didn't Cournot use it?). Consequently, ferent than the situation with theorems. To in the April FOCUS about Nash's game Gale seems to regard Nash's (re)definition name an example from a related area, Kuhn theory equilibrium theorem. I'm glad you of it as a minor event. and Tucker did not invent the Kuhn• allowed the article to include a proof, so This is where I disagree. Mathematicians Tucker theorem. (Kuhn and Tucker even• readers could see how, with the right setup, place too much importance on the theo• tually discovered that it appeared twelve Nash could use the better known Brouwer rems people prove, and not enough on the years earlier in a Master's thesis written at fixed point theorem. However, just as Gale definitions they devise. (The relative im• Chicago by one William Karush.) But they had a quibble with Devlin, I have a quibble portance we ascribe is clear: theorems rightly get the credit for they were the first with Gale. It concerns his comments (last often have people's names attached; defi• to prove it in a context that made its sig• paragraph) on Nash's role in defining game nitions rarely do.) Yet it is definitions that nificance clear. equilibrium. I think Gale underrates Nash's give us the concepts that make thinking contribution. effective and make the theorems possible. Similarly Nash was the first to define his eqUilibrium in a way that made its broad First let me seem to agree with Gale. When Often, especially in applications, it is importance clear-he first put it on the I first learned game theory (from Kuhn enough to have the concepts to make head• map for the general theory of non-coop• and Tucker-Tucker was my thesis advi• way. For instance, I suspect the most im• erative games. As natural as the idea is sor in 1972), and for some time afterwards portant things students can take from a mathematically, it had not been stated in (when I looked only at game theory mate• calculus course are a thorough and intui• this generality, and it wasn't obvious to all rials written by mathematicians), I found tive understanding of the definitions of at first that it was appropriate in this con• the theorem referred to as Nash's theorem derivative and integral, not the theorems text. (It wasn't obvious to von Neumann• and the definition referred to merely as about them. see the article on Tucker in the same April 'equilibrium.' But later I found thatecono• If we mathematicians gave more credit for issue of FOCUS.) But it was appropriate. mists almost universally refer to the defi• definitions, maybe their importance would The definition and theorem together nition as 'Nash equilibrium.' This seemed be appreciated more. Here is a question I caught on (as Gale notes). And so it is very strange to me. The concept is, as Gale tempt people with. Who invented the appropriate that this eqUilibrium be called says, so natural; surely it was around be• modem definition of derivative for func• Nash eqUilibrium. And it is appropriate fore Nash. tions of many variables (i.e., f' is the lin• that we give him credit for it. So about a year ago I asked Al Tucker if ear transformation T so thatfix + h) - fix) Stephen B. Maurer Nash had indeed defined the equilibrium - T(x)h is o(h)). This definition is a tre• Professor of Mathematics concept as well as proved the theorem. Al mendous conceptual (and notational) ad• Swarthmore College said he believed Nash had. They are both vance over what came before, but most Swarthmore, Pennsylvania in his thesis, he said. mathematicians don't even know who is responsible.

Schafer Prize from page 1 will each receive $150. Two Honorable Founded in 1971, AWM was established The Schafer Prize was established in 1990 Mention citations were awarded to Tara to encourage women to study and have by the executive committee of the AWM E. Brendle (Haverford College) and Karen active careers in the mathematical sci• and is named for AWM former president Shuman (Agnes Scott College). The prize ences. Equal opportunity and the equal and one of its founding members, Alice T. presentation will be held on August 5, 1995 treatment of women in the mathematical Schafer, who has contributed a great deal in conjunction with the opening banquet sciences are promoted. There are more than to women in mathematics throughout her at the MathFest in Burlington, Vermont. 4000 members, both women and men, career. The criteria for selection include, from the United States and around the "The selection committee was extremely but are not limited to, the quality of the world, representing all parts of the math• impressed with the quality of the nomi• nominees' performances in mathematics ematical community. nees this year," stated Linda P. Rothschild courses and special programs, an exhibi• (University of California, San Diego), The Alice T. Schafer Mathematics Prize tion of real interest in mathematics, the chair of the 1995 Schafer Prize Commit• is funded by an endowment with con• ability to do independent work, and, if tee. "The selection of these six talented, tinuing contributions coming from AWM applicable, performance in mathematical determined young women was difficult members and others. TheAWM seeks ad• competitions. among the many others who also deserve ditional contributions to belp ensure the In addition to the winner, Wung-Kum Fong recognition." Serving on the committee long-term viability of the prize. Checks (University of California, Berkeley), with Rothschild were Ruth Charney (Ohio made payable to "ATS Prize Fund" may Nancy Heinschel (University of Califor• State University) and Lesley Sibner(Poly• be sent to AWM, 4114 Computer and nia, Davis), and Jessica Wachter (Harvard technic University). Space Sciences Building, University of University) were declared runners-up and Maryland, College Park, MD 20741.

3 FOCUS August 1995 Review of Arcadia, a play by Tom Stoppard

Mark Saul Mathematicians living within striking dis• The critics have been touting the tance of Broadway cannot stay away from connection with Fermat's Last Tom Stoppard's new play Arcadia. When Theorem. This is a red herring, I went, I met two mathematical acquain• designed, I think, to (a) capitalize tances in the audience, neither of whom on the recent news about Wiles knew the other was there. We all knew and (b) tell less about the plot of Blair Brown and Victor Garber on stage that the content of the play was vaguely the drama. There also might be mathematical, but what unfolded on stage (c) some misunderstanding about the and the lights go down, the apple scene surprised each of us. mathematics. In any case, I think I can remains briefly lit, an indication of what is write about some interesting ideas of the First of all, despite the advertisements, and about to be played out. Is knowledge the play without spoiling the experience of even the playbill, it is not a play about a fruit of rationality or of its opposite? seeing it. Stop reading if you don't trust brilliant young woman who proves me. Stoppard's second point is more original Fermat's Last Theorem. Nor is it a femi• and more controversial. He is clearly draw• nist version of Breaking the Code (the play The modern characters are busy, for vari• ing a parallel between the beginning of about Alan Turing, which ran on Broad• ous reasons of their own, unearthing the the romantic era and the intellectual cli• way several years ago). In that play, for details of the lives of their predecessors mate of today. Since we are living in our example, there's one specific moment (or, in some cases, ancestors). In the pro• own intellectual climate, we are all where Alan Turing "solves the problem" cess, they discuss the history of ideas and uniquely unqualified to discuss it. But that of building a computer. The moment was of culture. So Stoppard is not talking about has never stopped us: What We Are Like dramatically staged, and swept one along mathematics at all. Our subject gets is a common theme of modern literature. emotionally. Yet on a rational plane, it's "impleaded" into the argument, perhaps hard to believe that Turing's breakthrough because we've made a hit with the public Is the argument valid? Has the computer, came all at once, or even that he "invented" in settling Fermat. Would the Riemann for example, sparked a revolution from the computer. It is not likely that there was hypothesis have occasioned a drama? Newtonian, or Cartesian, determinism to an epiphany here, like Hamilton's insight Perhaps one day we'll find out. other ways of analyzing nature? It is cer• with quarternions. tainly true, from where I sit, that a belief Stoppard's play is "about" two things. in the exact predictive power of science is Nor is there any in Arcadia. The math• First, it is a discussion of the relationship a characteristic of our era. We have a deep ematics is part of a more general discus• of the romantic era of the early 1800s to and abiding belief that the scientific sion. What is the play about? Well, it's the Enlightenment that preceded it. Part method will give us mastery over our good theater, so this question cannot be of this interpretation, at least as old as environment. Genetics, materials science, answered while standing on one leg. It Hegel, is not original, but seems to me to modern physics, have all given us a lot of concerns a British noble family and their hold up well. It is given vivid color through this mastery. Will research into social is• estate. The action switches back and forth the experiences of the two sets of charac• sues, for example education, evolve simi• from 1809 to the present, sometimes within ters. Because the author is so in control of larly? Or will we move to other approaches, a scene, so that characters from both eras his medium, the result is very lifelike• other "paradigms," in investigating social are sometimes together on stage (but don't not at all a colorized version of an old idea. phenomena? Can the social uses of sci• interact). In an unusual reversal, Stoppard seems to ence, the fruits of rationality, be made The characters in 1809 are busy rethink• view the end of rationality and the begin• susceptible to rational inquiry? ing the Enlightenment. The formal garden ning of romanticism as a fall from inno• The play raises other questions more spe• is being torn up (by a newly invented cence. A rationalist can dream naively of cific to mathematical thought. Does the steam-powered back-hoe) to make way for writing an equation for the motion of ev• investigation of non-linear systems con• an English romantic garden complete with ery particle in the universe. Stoppard im• stitute a revolution? Raymond Wilder says fake ruins and a "hermitage." Lord Byron plies that letting go of this dream and facing that there are no revolutions in mathemat• is a central character in the action (but the chaos of reality is a fall from grace. It ics because progress in math lacks the never appears on stage). And the young is this connection that leads to the per• essential revolutionary characteristic of woman who is a mathematical genius, and sonal issues of his characters, and the ac• rejecting what has gone before. Is this who mentions Fermat only once or twice, tion of the drama. The opening curtain, for correct? is thinking very deeply about fractals, non• example, is a lavishly decorated scene of linear systems, and "iterated algorithms." Arcadia as Paradise, with a woman hand• More generally, how valid are parallels, ing a man an apple. As the curtain rises including Stoppard's own, between the

4 August 1995 FOCUS history of mathematics and the history of Society for Industrial and other aspects of culture? Stoppard' s young Applied Mathematics genius is supposed to have filled a note• NEW book with diagrams zooming in on some The DFT fractal. She saw this as a new way of using mathematics to analyze nature. She asks, iiiLES An Ownert Manual for the "If an equation can describe the curve of Discrete Fourier 7tansform a bell, then surely it can describe the curve FROM William L. Briggs and Van Emden Henson of a bluebell" (although Gauss's major Conceived as an "owner's' manual, this comprehensive book work on statistics came only in the 1840s). explores both the practical and theoretical aspects of the Off, one of the most widely used tools in science. engineering, and Her work, for a variety of reasons, never SIAM computational mathematics. Designed to be accessible to a sees the light of day. But we in the audi• diverse audience, the book is written in an informal style and is ence know this already. Why was it not Solving supported by many examples, figures. and problems. rediscovered by others at the time? If the Least Squares 19951xv + 434pagesl Softcoverl ISBN0-89871-342.Q end of determinism was part of the end of Problems List Price 137.50 I SIAM Member Price 130.00 lOr-tier Code OT45 the Enlightenment, does the mathematics Charles L Lawson of the time reflect it? The lives of Galois and Richard J. Hanson Numerical Solution and Abel are certainly excellent romantic Numerical analysts, of Initial-Value Problems stories, and could even be mistaken for statisticians, and engineers in Differential-Algebraic Equations opera plots. But what about their math• have developed techniques K.E. Brenan. S.L. Campbell. and LR. Petzold and nomenclature for the ematics? It seems to me that the major Many physical problems are most naturally described by mathematical results of the romantic era least squares problems of their own disCipline. This systems of differential and algebraic equations (DAE's). This went counter to any "romantic" trends. well-organized presentation book describes some of the places where DAE's occur. The Cauchy and Gauss, the giants of the era, of the basic material basic mathematical theory for these equations is developed and were busy tightening the screws on the needed for the solution of numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and mechanisms of analysis, not gushing ro• least squares problems can unify this divergence of illustrate the concepts and techniques. Originally published in mantically about new fields of mathemat• methods. 1989. this reprint is the only general DAE book available. ics. And their life stories are strictly for Fall 1995 I Approx. 355 pages Fa1/19951 Approx 260 pages I Softcoverl ISBN 0-89871-353-6 insomniacs. Softcover I ISBN 0-89871·356.Q List Price 129.50 I SIAM Member Price S23.6O IOrder Code CL14 List Price 133.00 The play speaks to the mathematician in SIAM Member Price 126.40 other ways, too. The metaphor of math• Order Code CLU Numerical Solution ematics as a contrast to more fleshly hu• of Boundary Value Problems man endeavors is brought up right at the To ORDER for Ordinary Differential Equations beginning. The young genius asks her Use your credil card Uri M. Ascher. Robert M. M. Mattheij. and Robert D. Russell young tutor to explain the phrase "carnal (AMEX, MasterCard, and VISA): This book is the most comprehensive, up-to-date account of the Call toU free In USA: 1IOO-447-S1AM popular numerical methods for solving boundary value embrace," and he tries to put her off with Outside USA call: 215-382-9800 a counter-question about algebra. Now Fax: 215·386-7999 problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth perhaps it is because I deal chiefly with E-mail: [email protected]'8 Or send cbecil/money order 10: analysis of the numerical methods by using decoupling adolescents, but the view of mathematical SIAM. Dept. BKF095, P.O. Box principles. Although first published in 1988, this republication efforts as a sublimation of sexual expres• 72(fJ, Philadelphia, PA 19101-72(fJ remains the most comprehensive theoretical coverage of the sion seems to me both obvious and under Payments may be made by wil'l! subject matter, not available elsewhere in one volume. exploited. Or is this why they do not seek transfer 10 SlAM's bank: August 1995 I Approx. 592 pages I Softcover I ISBN 0-89871-354-4 PNC Bank, 3535 Market Street. List Price 139.50 I SIAM Member Price 131.601Order Code CLU Fields medalists among people over forty? Philadelphia, PA 19104; ABA Routing 1031000053; Account But the play has it lot of serious things to Name: Society for Industrial and Iterative Methods for say. The dialogue crackles, the acting is Applied Mathematics; Account #8550970454 Unear and Nonlinear Equations superb, the stagecraft is riveting. It did Shipping and Handling: c. T. Kelley miss, for me, an emotional pull. While the lJ.5A: Add $2.75 for the fl/Sl book Linear and nonlinear systems of equations are the basis for central questions of the play are central and $.50 for each additional book. Canada: Add $4.50 for the many, if not most. of the models of phenomena in science and questions of my intellectual life, I did not fl/Sl book and $1.50 for each engineering and their efficient numerical solution is critical to get caught up in the closely related per• additional book. Outside USN progress in these areas. This book, the first to be published on Canada: Add $4.50 per book. nonlinear equations since the mid-I980s, focuses on a small sonal problems of the characters. But oth• All overseas delivery via airmail. ers who viewed it with me did, so maybe number of methods and treats them in depth. I wasn't in the mood. If you're in striking August 19951 Approx. 172 pages I Softcover /ISBN 0-89871-352-8 List Price 132.50 I SIAM Member Price 126.00 lOr-tier Code PR16 distance of Broadway, this is a memorable and exciting evening of theater. Complete rabies of contents and further InfoonatKlll on all S~ pubilCaUons ScIENCE AND INDUSTRY 15 available VIiI S~·s Gopher setVeI" by acCessing gopher.siam.org or Mark Saul is a computer coordinator at ADVANCE WJ1lI MATIiEMAllCS Q- through the World Wide Web at http://www.SJiJm.org. the Bronxville Schools in New York. 5 FOCUS August 1995 SECTION AWARDS FOR

Donato De Felice Donovan R. Lichtenberg Carl C. Cowen, Jr. Allegheny Mountain Florida Indiana Duquesne University University of Southern Purdue University Florida

Herbert S. Wilf Linda R. Sons Eastern Pennsylvania and Illinois Delaware Northern Illinois University of Pennsylvania University

Gerald Lieblich Seigfried Haenisch Thomas F. Banchoff Metropolitan New York New Jersey Northeastern CUNY-Bronx Community Trenton State College Brown University College

Sidney W. Graham Clayton M. Knoshaug Michigan North Central Michigan Technological Bemidji State University University

Thomas Rishel Sylvia T. Bozeman Kuen Hung Lee Seaway Southeastern Southern California Cornell University Spelman College Los Angeles Trade- Technical College

Henry L. Alder Governors will act on these nominations highly successful teaching efforts in which at its meeting on August 5, 1995, in It is a great pleasure to feature on these these talented teachers are involved. The Burlington, Vermont. pages the 1995 recipients of the Awards MAA has every right to be proud to have for Distinguished Teaching who received The committee has been greatly impressed among its members so many dedicated and the awards at the spring meetings of the with the outstanding quality ofthis year's imaginative teachers. sections. awardees. This has made it a great plea• Fortunately there is a way for the mem• sure to read the files on these awardees, The Committee on Awards for Distin• bership of the Association to find out more but also makes the task of nominating the guished College or University Teaching about these teachers: the national awardees national recipients of the awards most of Mathematics is now in the process of make presentations on their successes as difficult. The committee wishes that there nominating at most three of these distin• teachers during the annual meetings at were some way for all members of the guished teachers for the national Deborah which their awards are conferred. These Association to share in the pleasure of and Franklin Tepper Haimo Awards for sessions have become one of the highlights reading the folders on this year's section of the meetings, as is evidenced by the Distinguished College or University awardees to learn of the wide variety of many highly complimentary comments Teaching of Mathematics. The Board of 6 August 1995 FOCUS )ISTINGUISHED TEACIDNG

Wayne W. Barrett W. Wiley Williams I-Lok Chang Intermountain Kentucky Maryland-DC-Virginia Brigham Young University University of Louisville American University

Elgin H. Johnston Steve Ligh Iowa Louisiana-Mississippi Iowa State University Southeastern Louisiana University

Edward M. Landesman James R. Choike William D. Emerson Northern California Oklahoma-Arkansas Rocky Mountain University of California- Oklahoma State Uni- Metropolitan State Santa Cruz versity College

Aparna W. Higgins Richard Koch Ohio Pacific Northwest University of Dayton University of Oregon

William Daniel Kaigh Frank Jones Richard L. Christensen Southwestern Texas Wisconsin University of Texas-EI Paso Rice University University of Wisconsin Ctrs. - Marshfield received on these presentations and the of the national effort to identify, reward, couraging renominations ofteachers who steadily increasing attendance at these and honor this nation's outstanding col• did not receive the Section Award has been events. Because of the very favorable re• lege teachers of mathematics. It appears well received by the sections. Indeed all action by the audiences, these presenta• that a few additional sections have chosen comments, without exception, were posi• tions are now reprinted, at least in summary a section awardee without, for a variety of tive. form, in FOCUS. You might wish to note reasons, notifying the national office of Accordingly, the committee, at its meet• now that the national awardees will make their choices. The national committee ing on January 7, 1995 in San Francisco, their presentations at the Joint Annual wishes to commend the sections' efforts decided to continue these procedures so Meetings in Orlando, Florida, Friday, in establishing procedures for nominating that the rules for the 1996 awards and the January 12,1996, at 3:20 P.M. and selecting carefully the award winning nomination form will be identical to those teachers. The fact that twenty-three of the twenty• in effect this year. This means that those nine sections have notified the national The procedures adopted last year to sim• wishing to make nominations for next office of the selection of a section awardee plify the requirements for documenting year's awards can initiate the process now. speaks well for the support by the sections evidence of success in teaching and en- See Section Awards on page 8 7 FOCUS August 1995 Congratulations to the Newly Elected Members of the MAA Board of Governors

Charles C. Alexander Carole A. Bauer Gerald E. Bergum J. Kevin Colligan Nancy L. HageIgans University of Mississippi Triton College South Dakota State National Security Agency Ursinus College Louisiana-Mississippi Illinois Section Governor University Maryland-DC-Virginia Eastern Pennsylvania Section Governor North Central Section Section Governor and Delaware Section Governor Governor

Gloria C. Hewitt Frederick Hoffman Alexander F. Kleiner Glen E. Mattingly John W. Petro University of Montana Florida Atlantic University Drake University Sam Houston State Western Michigan University Governor At-Large. Florida Section Governor Iowa Section Governor University Michigan Section Governor Minority Interests Texas Section Governor

Ann E. Watkins Patricia K. Rogers Carolyn Connell Thcker California State Uni• York University Westminster College versity - Northridge Governor At-Large. Intermountain Section Southern California Canadian Membership Governor Section Governor

Section Awards from page 7 The national committee urges all mem• Call for Nominations for Section bers of the Association to think of worthy candidates for these awards and nominate Distinguished Teaching Awards them to the appropriate section commit• Nominations for the 1996 Section Distinguished Teaching Awards should be submitted tee. Even if your candidate should not be to your appropriate section officers this fall in accordance with your section's proce• selected as a recipient of the award, re• dures and deadlines. member that a nomination by itself is a distinct honor and also that there is now a Nomination forms will be sent no later than early October from your section secretary simple procedure in place allowing a can• to your department chair and possibly others, such as your department's MAA repre• didate to be nominated again if not se• sentative. Ifyour department chair has not received this form by October 16, check with lected the first time. The larger the pool of your section secretary or appropriate section officer. outstanding nominations, the easier it will be to maintain the high standards for these Henry L. Alder is a professor in the Department of Mathematics at the University of awards so successfully established by the California. Davis and chair of the Committee on Awards for Distinguished College or first four sets of awardees. University Teaching of Mathematics.

8 August 1995 FOCUS Interview with Ken Ross Donald Albers ROSS: I didn't have a choice. Ken Ross Takes the Reigns ALBERS: Did military school get any better? In January of 1995, Professor Kenneth A. Ross of the University of Oregon became ROSS: Well, I pretty much hated that President of the MAA. Ross served the school for a year and a half. And then my MAA for several years as Secretary and folks switched me to another military Associate Secretary. He has arranged so school in the San Fernando Valley for two many national meetings that he claims, "I years that I liked quite a bit. I made up for can do it in my sleep." being inept in sports by being a good score keeper. When I was in the fifth and sixth While still a graduate student, he co• grade in military school, even though the March 11, 1945. after two months in authored with Ed Hewitt the modern clas• school went up to the twelfth grade, I was military school. sic Abstract Harmonic Analysis. Since the score keeper for games. I liked that then, he has written two other highly suc• because the other schools' score keepers in the era before the dishwasher, and so we cessful books, Elementary Analysis: The were usually math teachers. I was a little had a lot of time together washing and Theory of Calculus and Discrete Math• twerp who could keep score as well as the drying dishes. My father was older, busy ematics with Charles Wright. next guy. making money and providing. Ross says that he was on his way to be• Love at First Sight ALBERS: And she had time for Ken. coming a military brat until, at age 10, he met Edith, a magical stepmother, who took ALBERS: At age 10, your luck really ROSS: She had time. Edith had no chil• him under her wing and changed his life. changed. dren other than me. She tried to make me normal and she did succeed, partially. Mili• As President, Ross hopes to foster the work ROSS: My whole life changed starting tary school, even a good one, is not a per• of the Young Mathematicians' Network July 1st, 1946, when I met my stepmother, fect environment for bringing up and to provide support for mathematics Edith. Without her, I would probably have somebody to be normal. After military education reform. He adds, however, that If been a military brat. I'd stayed in mili• school I went to the toughest junior high his agenda is growing. The interview that tary school until the twelfth grade, I would school in Salt Lake and I was quickly follows took place at MAA headquarters have been trained to go into the military. branded because it took me a few weeks to in February of 1995. ALBERS: What do you remember of that stop saying, "Yes, ma'am," and "Yes, sir," Military School first meeting with your stepmother? to the teachers. I was little and vulnerable, and Edith wanted me to be normal and ROSS: I saw this beautiful, tall blonde. It DON ALBERS: What do you remember wear a polo shirt, go to dances, etc. about your early childhood in Utah? was sort oflove at first sight, I guess. I was a cute little lO-year-old and looked like I ALBERS: You seem to have shaken off KEN ROSS: Not much. My memories up was seven, in a little military uniform, and "Yes, ma'am," and "Yes, sir." to age 10 are very limited. said, "Yes, ma'am," and "Yes, sir." And ROSS: Yes, sir! I guess she saw someone ALBERS: How about elementary school? she was 25, which I now realize is pretty worth saving. I wasn't in real trouble, and young. She took over this I O-year-old and ROSS: In the third grade I got all unsatis• I wasn't an unhappy kid. But I certainly we became buddies at once. We were closer had no idea where I was going, and I had factory grades, although I should have only in age than she and my dad, who was 50. gotten unsatisfactory deportment because very little in the way of interpersonal skills. I wouldn't sit still in my seat. So for that ALBERS: A 15 year spread in age versus In military school, I was on my own and I and other reasons, including family prob• 25 years. didn't need the usual interpersonal skills. lems, I got sent off to military school in ROSS: Yep. I obeyed her and I recognized ALBERS: But the two of you talked a lot Los Angeles, which I started in the middle her authority, but we were buddies and we and played a lot. of the year, on January 10, 1945. The first used to have water fights and things like ROSS: Yes. day was memorable in that I thought they that, and wrestle until I got too rough. One had some unfair rules. They had a rule that Sunday we were out driving and we The End of Monopoly you couldn't leave campus for the first stopped for gas. My stepmother and I were two weeks. On the eleventh day, which fighting over the funny papers in the front ALBERS: You played games together, was a Sunday, my ninth birthday occurred, seat and the station attendant said to my too? and I had to stay on campus. That was a dad, "It's okay, don't worry about it; my ROSS: Oh, yes. Except my dad had to bad experience. kids fight too." stop us playing Monopoly because we ALBERS: But you stayed on campus. We talked a lot, too. Fortunately this was would end up not speaking to each other.

9 FOCUS August 1995

We would be partment. I spent at least one summer paint• ROSS: My geometry and algebra teacher absolutely, rig• ing the outside of the building. When I in high school was pretty unpopular with idly unreason• was 16, I spent the summer doing cost most kids, but I liked her. I got along with able and unfair accounting, which was sort of interesting. her. Her name was Charlotte Schroeder. once one of us My dad fired one woman in accounting, She is the first person who pointed out to got the advan• and I ended up training a new woman. me that I' m sort of ambidextrous. One day, tage; we'd just after I got through doing a problem on the ALBERS: Did that lead to an apprecia• go for the kill. board, she asked, "Do you know what you tion for mathematics? did?" And I said, "No." She said, "Well, ALBERS: ROSS: No. When I was a kid, the thing I you drew a square with two hands." Both of you. liked the most was maps. ALBERS: So are you ambidextrous? ROSS: Yes. So ALBERS: Maps? President Ross at 4 or 5. we didn't play ROSS: Yes, nature made me left-handed Monopoly for a ROSS: Maps. I also loved the numbers and I was forced to be right-handed, and long time. I had to wait until I had a daugh• that went with maps. I memorized the so I print left-handed and I write right• ter. populations of all the towns in Utah over handed and do the blackboard with both 2500 and useful facts like that. hands. ALBERS: That was a long wait! At what grade did the change occur, i.e., going from Casino, Anyone? In 1959, when I went to Yale with Ed military school to stepmother to public Hewitt, I was asked to give a talk in the school? ALBERS: Do you have any other special seminar. I don't know whether I was brave memories of high school?You said that in or stupid, but I did it. In the audience were ROSS: Eighth grade. Although the kids school you would run across the street to Felix Browder, Walter Rudin, Shizuo didn't believe that I belonged in that avoid getting beaten up. Kakutani, Phil Curtis, and Hewitt. school. When I arrived, they told me where the elementary school was located because ROSS: In junior high. Right. In high ALBERS: Tough audience! I was little; they said I couldn't possibly school, they were more civilized; the big ROSS: Yes. I'd been writing on the board be more than a fifth grader. I was probably kids would make sure that the dumb tenth about two minutes when I heard "mumble, the smallest kid in every school I went to, graders didn't beat up on us little kids. mumble, mumble," so I stopped and said, and usually smaller than the smallest girl, ALBERS: Were there other interests in "Is anything wrong?" Kakutani was talk• or at least no bigger. high school that you pursued? ing to somebody and there was all this ALBERS: That doesn't seem to have pro• ROSS: I mumbling. They didn't respond so I went duced any serious harm. tried to get a on and the rest of the talk went fine. After the talk, over coffee and cookies, Mary ROSS: True, but I did have to adjust. card club going. I got Ellen Rudin told me what the fuss was. I Getting Home Alive another guy had switched hands. Instinctively, very interested. It early, I learned not to stand in front of what ALBERS: How did you do in public was just the I write. So I would put things up on the school? two of us, so board with one hand and then I'd get out ROSS: I survived. Fortunately, I lived it didn't go of the way and switch hands. across the street from school so I could get far. My dad Heaven home in one piece. was a great card player, ALBERS: Where did you go to college? ALBERS: Were the students actually Ken as a teenager. ("Note that. and my in• tough on you physically? ROSS: When I was sixteen, I went to the unlike Jerry Alexanderson. I've terest came outgrown bow ties.") University of Utah, and I wasn't the big ROSS: They would have been, I think. from him. five-foot-two-inch hulk you see before you But I could go out the door, race across When I was now. There were exactly two women on Highways 89, 91, and 40, and be in my a little kid taking train trips home by my• campus that were small enough to be of dad's business in about a minute. self, I would wander the aisles looking for interest. One of them turned out to be a people to play cards with. And I mean real ALBERS: What was his business? senior and quickly vanished from my life, cards-not Fish! but the other one was still around when I ROSS: Wholesale television, radios, ALBERS: I didn't think card-playing was was a junior. A friend of mine set me up record players, refrigerators, freezers, big in Utah. with my first date, a blind date. When I ranges, etc. went to pick her up, there she was - the ROSS: Well, it was in our family and with ALBERS: Did you help around the busi• very one that I'd been noticing on campus my folks' friends. ness? for two years. I thought I'd died and gone ALBERS: Did you have any teachers in to heaven. She was 4 foot II and looked ROSS: Yes. I worked in the shipping de- high school who had a big impact on you? great in high heels.

10 August 1995 FOCUS

across from the person who people who were big names in numerical solved it-John Selfridge." analysis and computer science. I took a four-week course in which, after four hard I mentioned to Selfridge that weeks, if you had learned it and I hadn't my dad had never finished because it was too complicated, one knew high school, but that he was how to divide on the computer. I was hop• quite good at math. He used ing to go into computing at UCLA. Where it, including algebra, and he would I be now? I would have been right knew little tricks like casting there on the ground floor. But in retro• out nines. My dad knew that spect, I made the mistake of applying too if there was an addition error soon. I sent the application in October, which was a multiple of nine, and when I never heard from them, I didn't then the first thing to do was have the sense to write and ask them about to look for a transposition. Around the table at a birthday party: Ken. Ruth. Jeanie it. I ended up going to the University of The fact that if you transposed Neven. and daughters Laurel. and Emily. Washington. I went to University of Wash• the digits the error will be a ington on the grounds that, since the Uni• multiple of nine seemed like magic to my ALBERS: When did your mathematical versity of Utah had an applied math dad. Selfridge did not know about casting interests expand a bit? department and University of Washing• out nines at that time. ton was a lot bigger than the University of ROSS: There was always somebody bet• ALBERS: Amazing. Utah, surely they would have applied math. ter than me in school, certainly through But they didn't. I've just sort of stumbled high school and in college. So I didn't think ROSS: So he went to the blackboard and into everything. of myself as a math student. Furthermore, after a few minutes he showed me a proof. I had a half-brother in physics who said He created a proof on the spot. My dad "I'm Going to Have to Think" there was no future in math, and who said always thought casting out nines was all you could do with it is teach. He was a magic. I went home and told my dad that ALBERS: Did you have any memorable good physicist, and so I thought I'd prob• it wasn't magic anymore, that this guy undergraduate teachers? ably go into physics. I went through a Selfridge had proved it. That evening with ROSS: I am a better teacher because of whole sequence of majors. My dad had a Selfridge was the start of a nice relation• my own early difficulties with mathemat• business, so first I was a business major. ship. At the end of my visit to UCLA, I ics. When I got to analytic geometry, I But I hung around with a crowd that went home to Salt Lake, and my half• failed the first exam. It turned out to be a thought business was for lowlifes. So I brother just happened to be there. Inci• blessing. It was a blessing that I didn't just switched into chemical engineering be• dentally, I never lived with him, and I didn't get a C+ or something. It shocked me and cause I had a friend in chemical engineer• even know he existed until I was ten. It my response was very intelligent, for a ing. Then a teacher told me I should be in turns out we're very similar in personal• change. I essentially said to myself, "Oh pure science, so I was a chemistry major ity. I said, "I've got this neat book." He God, I'm going to have to think." Math for a while because I liked freshman chem• opened it up, thumbed through it, and said had been all automatic up to that point. istry. Then I was a physics major and, as a condescendingly, "Well, maybe you Algebra was absolutely intuitive and senior, I wrote to five graduate schools in should be a mathematician. "The book was trivial, but suddenly I had failed this exam. math and five graduate schools in phys• Introduction To Number Theory by Hardy My teacher, Ferdinand Biesele, liked me ics. and Wright. And that was my release. After and encouraged me, and I got a C on the that, I was no longer, in my mind, a phys• Between my junior and senior years, I went second exam, and an A on the final. But ics major. down to UCLA to visit, on a job assign• when I saw how he graded the final, he'd ment, following a teacher down there. ALBERS: So your brother's influence was missed all my mistakes. Two teachers While I was there, I met a graduate stu• nontrivial. graded it and all the points taken off were dent, John Selfridge. by the other teacher. I saw that I definitely ROSS: Certainly, in the sense that I wasn't shouldn't get an A. But I got an A in the "Maybe You Should be a going to go into math when there was no course, and ended up being his grader the Mathematician" future, except teaching. next term. ALBERS: Look what you ended up do• ALBERS: Lucky for you. ALBERS: John Selfridge. ing - teaching! ROSS: I was good at grading. I don't think ROSS: One night over dinner with ROSS: I knew I wanted to go into math• Selfridge, and another guy named Ken I would have had the nerve to think about not teaching though. I applied to UCLA being a math major if I hadn't been en• Ralston, I mentioned that I had just bought for grad school because I had spent a sum• a book on number theory and on page 5 couraged by Biesele. At Utah, I also was mer there; in fact, it was the summer where taken under the wing of an applied math• there was a little footnote about an un• all kinds of big names were on campus• solved problem involving prime numbers, ematician named Charles Thorne. He's the I was rubbing elbows with Thompkins, one who took me with him to UCLA. and Ralston said, "Well, you're sitting George Forsythe, Mina Rees, and all these

11 FOCUS August 1995

ALBERS: So at the end of that summer, a half-hour on ring theory, fig• you went back to Utah to finish your se• uring that would be enough since nior year. it was an easy course. So we spent a half-hour on group ROSS: Yes. At Utah I was sort of a pet theory, and there was nothing student, but not a really good student in that we didn't already know. I the sense that in math and physics, I either said, "Should we do the ring got a low A or a high B every time. I theory?" We both replied, finally got philosophical about it. I'd feel "Nah." bad about those B+'s that could have been A- 's, but then I would remind myself that It was a three-hour final, and after I had A-'s that could have been B+'s. And 45 minutes I had done everything besides, you didn't complain in those days. I could do, which was 55 percent I was one of two math majors. of the exam. I couldn't do the L to R: Jeanie Neven. Laurel. Emily. and Ken. other 45 percent. So I sat there I ended up teaching a course when I was and spent the whole next hour trying to a senior. The oldest faculty member had to ROSS: I certainly was not aware of him figure out a key definition. I finally went stop teaching suddenly during the second my first year in graduate school at Wash• up with the exam in my hand and I said, in week of the term, so I taught my own course ington until the math picnic. In those days a very soft voice to Pierce in this very quiet winter and spring term as a senior. I was Hewitt was an MAA lecturer, and he gave room, "Could I ask a question in exchange 19 when I first went into the classroom. some lectures at the University of Utah. for some points?" He responded, very Everyone at Utah asked him how I was ALBERS: What did you teach? softly to his star student, "What can I do doing and he'd never heard of me. So at for you?" And I whispered, "What's an ROSS: College algebra and then trig. the math picnic he came over to the table ideal?" And he said, in a very loud voice, where I was, looked right at me, and said, ALBERS: Did you like teaching right "WHAT'S AN IDEAL?" Every head "Is Ken Ross around here?" away? popped up in that room and I panicked. I threw the exam down, missed the table, After Klee talked to him, Hewitt called ROSS: The first four weeks or so of teach• picked it up off the floor, laid it on the me in and asked, "Would you like to be my ing algebra were horrible. Finally I went table, walked out and avoided Pierce for note-taker and be on my grant?" and I said, to see a graduate student named Hal three or four weeks. "Yes." Moore. I said, "I know what's right or wrong but I can't explain why." And he In the afternoon, I had my topology exam The very first lecture or two were on set said, "Well, didn't you give them the field from Klee. By then I was sick. I had to theory. He was somewhat sketchy and I axioms?" The next day I went to class, and walk out of the exam a couple of times. I really fleshed them out and started a num• without using those words, said, "Here's was absolutely a mess because of the fi• bering system. I started out on the right what everything relies on." I had no seri• asco in the morning. But I was flying high. foot and I was among Hewitt's chosen after ous trouble after that. There were fourteen "prove" or "disprove" a week. From then on, I could do no wrong. questions, and I did ten of them. No one By the way, in those days Hewitt was At the time, I didn't think teaching was else did more than five problems, so I made known as Big Ed. He was intimidating and my calling. I thought I'd go off and be an a big impression on Klee. I thought I was a very demanding teacher. applied mathematician and work for the going to work with Klee. He and I got Navy or something. along just great. He's a really nice person. In the Fast Lane with Big Ed "What's an Ideal?" Klee was going to be away my second ROSS: In the spring of 1959 Hewitt went year, so he asked Ed Hewitt to put me on to Yale. It was a special year of functional ALBERS: Who were your important his grant even though he didn't know me analysis at Yale. Rudin was there, Bert teachers in graduate school? at all. Klee was going to be in Denmark Yood from Oregon was there, as was Phil ROSS: I quickly came under the influ• during my third year, and I ended up work• Curtis from UCLA. I asked Hewitt if I ence of Vic Klee. In my second term at ing with Ed Hewitt. could tag along with him. I was on an NSF Washington, I took a course in topology Hewitt and Ross fellowship, so I didn't have any teaching from him. And I did well, especially on duties. I hardly taught at all until I became the final. I had two final exams on the same ALBERS: Hewitt and Ross and your two a faculty member. Anyway, Hewitt invited day. The first was in an undergraduate volumes on abstract harmonic analysis are, me to go with him in his Mercedes 300SL, algebra course given by Richard Pierce, of course, inextricably linked together, and so I drove across the country with Hewitt and I had been doing essentially perfect are modem-day classics. Ed Hewitt was a in 1959. One day we went 130 miles per work in there. After all, it was an under• very colorful fellow in the minds of many. hour. graduate course and I was a graduate stu• Can you remember your first impressions ALBERS: Wow! dent. When it came to studying for the of him and what it was like to work with final, one of my classmates and I decided him? ROSS: That was in Wyoming. We crossed to spend a half-hour on group theory and Wyoming in the morning. We had break-

12 August 1995 FOCUS fast near the Idaho border and we had lunch ALBERS: And at the end, especially gen• in Nebraska. We did not mess around. "The erous. Fast Lane With Big Ed" has a special ROSS: And I was really coauthor on Vol• meaning for me. ume 2. In Volume I there are 26 sections Before I went to Yale, Hewitt gave me a and three appendices. I essentially wrote problem that I wasn't making much the appendices and two other sections. So progress on. Later he gave me another one. I truly was ajunior author. My job was to I was rooming with Karl Stromberg, my rewrite, to make it more beautiful, more friend and former fellow graduate student, clear, more smooth, and correct. And it all who was at Yale for the year. Every time came out. But he could have reasonably I'd make some progress, Stromberg would regarded me as an editorial assistant. ask another question. That summer I gave I was very careful and very hardworking. Hewitt an 80-page manuscript, and he said, I knew how to write. No one ever taught "Well, this is a thesis." I said, "Oh, how me. That's amazing, but I started writing nice." I was surprised, but Stromberg said Ken and Ruth Ross notes for Hewitt and I knew how to write. it was obvious to him, because I had been I don 'tknow why. I impressed Hewitt more ROSS: I outline a book by section, but answering all the questions that he pep• than he should have been, because I was a otherwise Ijust use a "What do they need pered me with. Stromberg just knew the reliable, responsible note-taker and did to know?" approach. I often organize talks right questions. pretty well. I did well in his class, but I in reverse, and write that way also, in the Earlier that year, before I wrote my thesis, certainly wasn't any better than Stromberg sense that, "Here's the goal. Now, what do Hewitt asked me if I'd be an editorial as• or Wis Comfort. you need to know to understand it?" I don't sistant on his book on abstract harmonic wantto overstate it, but I don 'tthink I ever ALBERS: And you knew how to set up a analysis. I was thrilled to death because I found writing hard. Maybe it's because numbering system. would learn a lot of mathematics from initially I was taking notes from the black• Hewitt and get paid a lot more than as a ROSS: Yes. board, and Hewitt, knowing that I was graduate student. I had no idea that the there, left them to be beautified by me. ALBERS: Were your writing talents book would become Hewitt and Ross. One present in high school? I guess I was lucky because I learned how of the things about Hewitt was that he could to write, given that someone else had al• be anything. Like Lyndon Johnson, any• ROSS: Not that I know of. And I certainly ready done a draft. Hewitt wrote most of thing you say about him is true - some• couldn't write in other subjects. My hand• the chapters, but he didn't write them el• times: S.O.B., petty, mean, generous, kind. writing was so bad that I didn't do very egantly. He wrote them very fast and he For example, when people from Eastern well in English. just made sure they were correct. He was Europe would drop by with monetary prob• ALBERS: But you knew what good math• a dogged, hardworking person who didn't lems, Hewitt would just pull a checkbook ematical writing was. You recognized it. have the patience to beautify. I spent a lot out of his desk and write them a check. of time trying to see what the real point But if you went to his office on the wrong ROSS: Instinctively, so far as I can tell. I was. I cleaned up the notation. I was al• day and wanted to borrow a pencil, he'd had read Natanson's Theory of Functions ways following behind, cleaning up. tell you that that's the tool of his trade and of a Real Variable before working with ask if you would go visit an auto mechanic Hewitt. Natanson really made sense to me. ALBERS: That's a great mental image. and ask to borrow his tools, and give you Klee thought that I wrote very sophisti• ROSS: So I think it's an overstatement to a lecture and just be an S.O.B. cated proofs in topology the year before, say that I knew how to write. I knew how as a matter of fact. What he really meant to write, but I wasn't writing from scratch. Half the Work, Half the Credit was succinct. This is a revelation for me today. I prac• On one of his generous days, when the "I Just Start Writing" ticed rewriting for years, until I wrote my book was completed, he said, "Well, you own book on analysis. did half the work, you ought to get half the ALBERS: Well, how do you write, then? credit." Without that joint authorship, How do you sit down and organize and ALBERS: That book was not done that Hewitt and Ross, I wouldn't be here to• write today? way. day. I probably wouldn't have had the jobs ROSS: Well, mostly I don't work as hard ROSS: No, but it was based on a course that I've had. He was sometimes horrible as Paul Halmos makes it sound. He says that had been given several times. I did to work with on Volume 1. I hasten to add it's hard work and requires great organi• outline that one. The book has six chap• that on Volume 2 it was a different story. zation - I just start writing. If it's really ters. I wrote four chapters in note form On Volume I, I was truly the junior author. complicated, I'll have some sections in and used them as a text in our required And so while he was not very much fun mind, but I just write. course. Then I sent them to Walter some of the time - there was a month Kaufman-Buhler at Springer-Verlag. In where I worked at night to avoid him - he ALBERS: You don't outline. my cover letter, I said, "This is what I've was generous in many ways. got, and this is all I'm going to do unless

13 FOCUS August 1995 you publish it. I'm not going to send it to ALBERS: That's great. months; I went over every sentence again. any other publisher." I figured that if And I found all kinds of little mistakes. ROSS: Without the second editions, third Springer didn't want it, no other publisher The real merit of that book is that it's ac• editions, and all the pain of revisions. should want it. When they gave me the go• curate. Even though he was the brains ahead, I sat down and wrote the other two ALBERS: Just more printings. behind it, it wouldn't have been the clas• chapters and fleshed out the book. That sic you can depend on in hadn't made that ROSS: Yes. took about three weeks. nine-month review. With Len Gillman's help, I had to persuade him that, "You're ALBERS: That's pretty fast. Rochester to Oregon smart enough, but you're not patient ROSS: But ithad all been thoughtthrough. ALBERS: How important do you think enough." And I had to give lots of examples that Hewitt and Ross has been to you? It of mistakes that I found that he would have ALBERS: I'm impressed. certainly is a classic. missed. I just checked every darned de• ROSS: But I was nervous. I had never ROSS: Well, I don't know - would tail. written a book all by myself. I was ner• Leonard Gillman have hired me at the Running Meetings -"I can do it vous because I glossed over the founda• University of Rochester? Probably not. tions. I don't think I tell lies, but I really Gillman just called me out of the clear in my Sleep" didn't want the students to get bogged blue and offered me ajob. When I accepted, down, so I glossed over the foundations ALBERS: You can now, at the tender age he had to go to his dean and make sure it of 59, look back over lots of nice things in and kept going. I was real nervous, but was okay, but those were the good old days. people accepted it from me. They might your life - research, writing good books, not have accepted it from someone they Gillman has been crucial in my career and lots of service to two organizations, had never heard of. There are places in the because he was a friend of Hewitt's. Actu• AMS and MAA. If you were to look back, book where I didn't want to tell the whole ally, I met Gillman and Meyer Jerison in what are the one or two things that have truth. the same sentence. Hewitt introduced us. mattered the most? The only time Gillman ever got mad at me ALBERS: You and Charlie Wright have ROSS: In many ways, the most important was when I announced that I was leaving thing has been service to my department. written a book on discrete math, which is Rochester, and I wouldn't talk about it; I really at some distance from analysis. I've been something of a grind all my life. wouldn't bargain with him. I've done a lot more than my share of ROSS: Which is why I got a coauthor. ALBERS: You missed the west. department duties. I supervised 15 disser• tations. I look back and I see my imprint ALBERS: The big question is, "Why do ROSS: Yes, and remember, I was married you write?" on lots of things in the department - the to a lady who grew up in Seattle. She had graduate qualifying exams, the teaching ROSS: Oh, both of those books came out never been east of Potlatch, Idaho, until evaluation forms, etc. of courses. In the case of the analysis we went to Rochester. I spent the summer course, there was one book which was out of 1963 in Eugene working with Stromberg I like to do things and feel like I'm doing of print and the author, who is an old friend and got an offer from Oregon. When I saw them well. The thing I feel I did best for of mine, on advice of his lawyer in Canada, the possibility of going to Oregon and the MAA and the AMS was to arrange wouldn't let me use a photocopy. So I had being with Stromberg, there was nothing meetings. I did that for twenty years. I to create notes. And then the notes turned Gillman could do. believe I've organized more than 60 meet• ings. into a book. Our administrative assistant ALBERS: Were you married during said, "If we're going to keep having this graduate school? ALBERS: I find the thought of running a be a required course" - which it has be• national meeting absolutely daunting. come around the country, an analysis ROSS: No. I got engaged about three or course between calculus and hard senior four days before I left Seattle. I went to ROSS: I can do it in my sleep. I'm wan• analysis - "If it's going to be a required Rochester for a semester and then I flew dering from your question, but I feel I've course, there ought to be a book available back to Seattle at Christmas and got mar• done well and worked hard. Do I like what for it." So I said, "I'll write one." He didn't ried. Hewitt and I had our blow-up two I'm doing? Yes. Okay, do I wish I was believe me. For the discrete math book, I weeks before the marriage. A real blow• working a little less a week? Darn right. I and six or eight other authors-to-be in 1980 up, not just a tiff. We weren't speaking to work seven days a week, but it's the only were all appalled at what was out there, so each other after the end of Volume I. way I can keep up. we all cranked up and had books out in ALBERS: That sounds serious. ALBERS: You feel that you've done a 1983, 1984, or 1985. Both of my books service for your department. Certainly were in response to perceived needs. ROSS: We didn't get back together until you've done a service for the Association. 1965. When we had finished Volume I, I What drives your service? ALBERS: Both have sold pretty well, too. insisted on going through the entire manu• ROSS: Especially the analysis book. It script again. He thought that I wasn't go• ROSS: Oh, I suppose Freud or someone has had essentially constant sales now for ing fast enough, and that I was delaying would say it's because I'm small and that fifteen years. the book. I delayed the book about nine I didn't always have a very nurturing fam-

14 August 1995 FOCUS ily. That's the psychobabble answer. How But as president I' m still task-oriented and convert them but listen and adapt when do little kids survive? I was definitely a I have to remind myself, "I can get other necessary and desirable. This is an area survivor, and my way of surviving was to people to do the tasks." that needs attention. behave and please. I think that translates into adult service, and over-achieving. Presidential Goals The other goal is professional develop• ment and, again, I don't know that I will Regrets ALBERS:You'reveryearlyinyourpresi• do very much, but I'd like to at least pub• dency, and you still seem to be buoyant licize it and be supportive. So my agenda I thought you were going to ask, what are about it all. You only have two years. is growing. my regrets in life. I have very few. They ROSS: Yes. are very minor. IfI had it to do over again, ALBERS: Thanks very much for taking I wouldn't have quit my piano lessons ALBERS: In your first message, in FO• time to chat about your life and goals. By when I was twelve. Of course, my whole CUS, you indicated that you're going to the way, Ken, what's an ideal? life would have been different without work on communicating to people what a Hewitt, but I really loved probability all president does, which is a good idea. Be• along. I should have gone into probability. yond that, you've laid out some particular CBMS Statement goals. High on your list is improving com• ALBERS: As a student it's easy to miss munication between the young mathema• The members of the Conference Board probability. ticians, who are certainly having a lot of of the Mathematical Sciences, com• ROSS: Well, it's the old mistake one makes difficulty on the job front these days, and posed of the fourteen presidents of the when you're young and in a hUrry. I would with the rest of the community. mathematical sciences organizations have had to take an extra year to stop and ROSS: Yes, but the Young Mathemati• in the United States, support and en• take a series of courses in probability in cians' Network has taken care of a big part dorse the following statement: order to do research in that area. It wasn't of my goal. So I'm more in a position of one of the big three - algebra, analysis, listening and passing information on than A strong mathematics education for and topology. being a communicator. every child is at the very basis of the nation's need for a competent work President Ross ALBERS: What other things do you want force and an informed society, now to accomplish as president? ALBERS: You are now president of the and in the future. To enable all stu• MAA, the organization devoted to pro• ROSS: My goals keep growing as I react dents to acquire a strong mathematics moting collegiate mathematics. It's clear to what I learn is going on. An earlier one education is the prime objecti ve of the that you have a big interest in undergradu• was to increase effectiveness of the MAA's mathematics education reform move• ates, as well as graduate students. One Board of Governors. I see at least two more ment, which was generated at the grass could say your interest in the educational goals that I haven't got very clear in my roots level and propelled by the Na• aspects of mathematics has been strong mind yet. One is to be helpful, supportive, for most of your life. and on the frontline for mathematics edu• tional Council of Teachers of Math• ematics'Standards. ROSS: In a nonprofessional way, yes. And cation reform. The broad mathematical community, as well as the general public, it may pose an interesting problem for me The thrust of this movement is to pro• as president. I have to fight that. I'm task• needs to see the value of the changes in education at all levels. The two main mote a core of serious mathematics oriented. I see a problem and I want to for every student at the primary and solve it. I don't think about it and I don't thrusts are, of course, the NCTM Standards secondary levels as well as to lay a ask questions. Here's an example that's in and its effect on K-12, and calculus re• solid foundation for continuing the my brain right now: the teaching evalua• form broadly interpreted to include pre• tion forms at Oregon. I tried to figure out calculus, linear algebra, abstract algebra, study of mathematics at the post-sec• sensible questions people could interpret, and differential equations at the college ondary level. The reform efforts seek students would understand, and colleagues level. And I am convinced that their fu• to improve student learning by build• would approve of. I kept circulating them tures are linked. ing on the strengths of the past, incor• by my colleagues until I concluded that ALBERS: Go on. porating modem technology, and we had a nice set of questions. But a pro• engaging students actively in the ROSS: I think they're linked only tenu• fessional might have asked, "What is the learning process, always keeping in ously in a technical sense, but very closely goal?" Now that I know more about the mind the needs and aspirations of stu• in the sense that I predict they're both going teaching side of the MAA and assessment dents. and so on, there are all kinds of questions to be a big success or they're both going to be dying in five years. And they're both that I could have thought of. But I just Therefore, these reform efforts de• under some attack. So we need to be pay• never think that way. I organized meet• serve support by society at large as ings for twenty years. That's what I' m good ing attention to the concerns of the people who are opposed to change - convert well as the mathematics community at. And I didn't have to make judgments. in particular. I just had to be organized and responsive. them when they're convertible, not only

15 FOCUS August 1995

1995 Edyth May SliITe Award Winners Contributed Paper Walter E. Mientka Sessions The MAA Committee on Sessions of Since the acceptance by the Mathemati• Mr. Peter Kelley, Saint Albans School, Contributed Papers selects topics and or• cal Association of America of the be• Washington, DC ganizers for contributed paper sessions at quest of the Sliffe estate in 1988, 166 Mr. Charles Koppelman, Wilde Lake national meetings. The committee would high school teachers have been hon• High School, Clarksville, MD be delighted to hear from MAA members ored as winners ofthe Edyth May Sliffe who would like to organize such a session Award for Distinguished High School Ms. Susan Kornstein, Rye Country Day or who have suggestions for topics. All Mathematics Teaching. School, Rye, NY that is required is a title, name(s) and addressees) of organizer(s), and a short The award winners are selected accord• Mr. Michael Marcketti, West High two- or three-sentence description. ing to directives in Ms. Sliffe's will, in School, Iowa City, IA Planning is now underway for the August which she stated that the MAA is "to Mrs. Mary J. Neff, J.P. Taravella High 1996 summer meeti.ng in Seattle, WA and give awards to high school mathemat• School, Coral Springs, FL ics teachers whose teams do well on the January 1997 meeting in San Diego. the American High School Mathemat• Mr. Michael Park, Iolani School, Ho• The deadline for receipt of proposals for ics Examination (AHSME)." nolulu, HI the 1996 summer meeting is December I, 1995; deadline for receipt of proposals for Specific procedures not mentioned in Mr. Richard Rothenberg, Stuyvesant the San Diego meeting is January I, 1996 her will for selecting the winners were High School, New York, NY (January 12, 1996 ifby e-mail orin person determined by the MAA Edyth May Mr. Richard Rukin, Evanston Town• at the Orlando meeting). Information SliffeAwards Committee. They include ship High School, Evanston, IL should be sent to the chair of the commit• soliciting recommendations from the tee, Elizabeth Teles, 1150 I Chantilly Ln, three team members of each of the top Mr. James Trudeau, Homewood• Mitchellville, MD 20721; (703) 306-1668 sixty schools in the 1995 AHSME. Flossmoor High School, Flossmoor, (work) or (301) 262-9586 (home); fax: IL (703) 306-0445; e-mail: [email protected]. The list of the 1995 winners is given below. They receive a cash award, an Dr. Alice Underwood, Texas Academy elaborate MAA certificate, a one-year of Math/Science, Denton, TX membership in the MAA, and a Sliffe Mr. Ronald Vavrinek, Illinois Math• Funding Informal lapel pin. The MAA is pleased to rec• ematics and Science Academy, Au• Science Programs for ognize these outstanding teachers. rora,IL Ms. Dawn Anderson, St. Charles High Ms. Ruth Zucker, Detroit Country Day Youth-Serving School, St. Charles, IL School, Beverly Hills, MI Organizations Dr. John Beam, Bellaire High School, Mr. John Barsby, St. Johns• This one-and-a-half day, hands-on work• Houston, TX Ravenscourt, Winnipeg, Manitoba, shop is sponsored by the Science Link• Ms. Rosemary Benedict, Hopkins Canada ages in the Community Institute, a project School, New Haven, CT Mr. George Kyritsis, Woburn Colle• of the American Association for the Ad• vancement of Science and the DeWitt Mr. Joseph Bettina, Adlai E. Stevenson giate Institute, Scarborough, Ontario, Wallace-Reader's Digest Fund. High School, Lincolnshire, IL Canada September 7 & 8 St. Louis, MO Mr. Dan Butler, Mounds View High Mr.C. G. (Kip) Sumner, Upper Canada School, Arden Hills, MN College, Toronto, Ontario, Canada October 13 & 14 Dallas, TX Mr. Steven R. Conrad, Roslyn High Walter E. Mientka is a professor of November 16 & 17 New Orleans, LA School, Roslyn Heights, NY mathematics at the University of Ne• December 7 & 8 San Francisco, CA braska and the executive director of Mr. Frank Griffin, Cate School, The cost is $190 for registration, recep• Carpinteria, CA the American Mathematics Competi• tions. tion, and meals. For more information, Br. Christian Jones, Christian Broth• contact Stephanie Jensen at (800) 351- ers Academy, Lincroft, NJ 7542.

16 August 1995 FOCUS Board on Mathematical Mathematics Awareness Week a Success Sciences Department The Joint Policy Board for Mathematics (the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Math• Chairs Colloquium ematics) would like to thank the sponsors of Mathematics Awareness Week 1995: the U.S. Army Research Office, Oxford University Press (with offices in New York and Tenth Anniversary Meeting London), and Springer-Verlag (Textbooks in Mathematical Sciellces (TIMS). a new October 20-21, 1995, Arlington, VA undergraduate text series). "Managing While Science and Education Please send news clippings from your Mathematics Awareness Evolve" highlights include Week activities to 1529 18th St NW, Washington, DC 20036. • keynote address by George E. Brown, Jr., ranking minority member of the Com• mittee on Science, U.S. House of Repre• sentatives • sessions on the view from Harvard, the University of Michigan, Stanford, and the University of Texas at Austin • the American Association for Higher Education's project on evolving assess• ment of faculty teaching • an administrator's view of mathemati• cal sciences departments • mathematical sciences employment op• portunities, successes encouraging underrepresented groups, federal re• search and education programs, statis• tics departments and statistics within other departments • successes in undergraduate and calculus reform programs • the annual employment survey Workshops focus on information for new and future chairs; prototype interdiscipli• nary initiatives; changing school math• ematics: challenges and opportunities; concerns and professional roles of new fac• Ulty: lessons from Project NExT; assess• ment in Ph.D.-granting departments; and Then consider joining a highly talented Statistics, Combinatorics and more. And they func• removing barriers to student success. The group of mathematicians whose job it is to deduce tion as a true community, exchanging ideas and goal of this colloquium is to provide de• structure where structure is not apparent, to find working with some of the finest minds-and most partment chairs, chair candidates, and patterns in seemingly random sets, to create order powerful computers-in the country. If you love department leaders with timely, practical out of chaos. problem-solving and like the idea that those solu• information to help as the mathematical These are the mathematicians of the tions will be applied to real world problems, look sciences adjust and adapt in education and National Security Agency. They contribute to the into a career with NSA research to the manifold changes taking solution of cryptologic problems using Number Send your resume to the address below or Theory, Group Theory, Finite Field Theory, Linear contact your campus place and on the horizon. The registration National fee is $160. More information, including Algebra, Probability Theory, Mathematical placement office. Security that for registration, is available from Agency Board on Mathematical Sciences, National Research Council, NAS 315, 2101 Con• The Opportunities of a Lifetime stitutionAve NW, Washington, DC 20418; Attn: M322(A1G), Ft. Meade, Maryland 20755-6000 (202) 334-2421; fax: (202) 334-1684; e• An equal opportunity employer. U.S. citizenship reqUired for applicant and immediate family members. mail: [email protected]. 17 Check out our Web site! http://www.wri.com/ PUT ONE OF THE

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of fascinating books. As I mentioned above, we also publish many notes and MAA 1994 Annual Report documents to assist the profession. I want to single out the Guidelinesfor Programs and Departments in Undergraduate Math• PRESIDENT'S REpORT ematical Sciences, published in February 1993. I urge any department that is reex• amining its role in education (aren't we Taking a Closer Look: all?) to use these guidelines. They are also pertinent when departments are assessed Our Membership, Our Mission by outside reviewers. Another publication, UME Trends, is widely read and deserves Ken Ross No matter how fast your support. As I write this in May, I've been President we move in the Our national and sectional meetings pro• of the MAA for a little over four months. electronics arena, it seems that the possi• vide another service to our members. I urge This has been a very busy time. I will bilities are outrunning us. We already have you to attend the joint AMS-MAA meet• mention some of the high points in this a lot of information about the MAA avail• ing in Orlando next January. This is, inci• report. My predecessor, Don Kreider, ac• able on gopher and on the WorldWide Web. dentally, the tenth anniversary of the complished a great deal and much of my In the future, individuals will be able to famous Tulane Conference which pro• energy is devoted to carrying on activities join the MAA and maintain their mem• voked the mathematics community to take that were initiated during his tenure. Don bership electronically. Some publications a serious look at how we teach calculus. had the pleasure of seeing, during his will be available electronically, and there The MathFest in August 1996 will be in watch, the spectacular performance of the will be other services we haven't even beautiful Seattle. The nature of our sum• U.S. Olympiad team last summer in Hong thought of yet. mer meetings after 1996 is under study at Kong. Recall that our six-member team In the past few years we have substan• this time. We want to be sure that our made history by all having perfect papers. tiall y expanded our services to undergradu• meetings serve our members in the best While nothing is yet definite, we expect ates. The primary vehicle has been student possible way. that the U.S. will host the International chapters across the country. I am pleased Mathematical Olympiad in the year 200 I. to report that I am the coordinator for the When I was elected MAA President, my first major concern was the job market in At this point the officers are taking a very student chapter at the University of Or• mathematics. I am almost a "charter mem• close look at what the MAA is doing and egon. The new and very successful publi• ber" ofthe YMN (Young Mathematicians' what the MAA is about. We are looking at cation Math Horizons is aimed at Network) and I have been in touch with how we can best serve our members in the undergraduates, but it has a much wider several people in YMN. I am by no means context of our mission, which is the fur• audience. It's time for us to target some unique, and I believe that the YMN is therance of collegiate mathematics, inter• services for our graduate students. By the generally heartened by the response of the preted very broadly. Most of my remarks time you read this we will have a Task mathematics establishment. In January the below can be viewed as an elaboration on Force on Graduate Students that will be MAA Board of Governors adopted a reso• this theme. studying ways in which we can better serve graduate students and prepare them for life lution on "Supportive Practices and Eth• Much of what the MAA does can be clas• after graduate school. ics in the Employment of Young sified as professional or faculty develop• Mathematicians" similar to resolutions ment. This includes minicourses and The MAA has been a leader in education adopted by the AMS and other organiza• workshops at national and sectional meet• with our efforts to work toward the goal of tions. See page 12 of the February 1995 ings, special publications that focus on equal opportunities in mathematics for all FOCUS. And watch for my coauthored pedagogy and classroom experiences, Americans. Our SUMMA (Strengthening article "Myths in Math" coming up in the publication of reports and studies of cur• Underrepresented Minority Mathematics October issue. My friendship with my rent practices, etc. However, we haven't Achievement) program seeks to increase coauthor, Charles Mannix, started when analyzed the overall structure of our pro• the representation of minorities in the fields we were both contributors to early issues fessional development efforts, nor have of mathematics, science, and engineering, of the YMN e-mail newsletter, Concerns we determined services that members may and to improve the mathematics educa• of Young Mathematicians. want that we aren't providing. A major tion of minorities. These efforts require An important part of the President'sjob is initiative is to focus on faculty develop• the greatest vigilance and persistence be• to work with our sibling organizations and ment and to make a more concerted effort cause the problems are a reflection of much also to work with other scientific organi• to tailor our membership services to our bigger problems in the larger society. zations and governmental bodies. I will membership needs. And we plan to repli• The most visible work of the MAA is, of just mention one event that may turn out cate successful programs like our NExT course, our fine publications. In addition to be pivotal for mathematics education. project, which has been a powerful source to our outstanding journals of expository CBMS (Conference Board of the Math• of development and networking for col• papers, we have a wide and expanding list ematical Sciences) is an organization of lege teachers who are new to the profes• sion. 19 FOCUS August 1995 fourteen mathematical associations. At a meeting in May, CBMS took a major step FROM THE EXECUTIVE DIRECTOR'S DESK by approving a serious investigation, with outside funding, of the feasibility of the creation of a CBMS Education Partner• The Changing Face of the MAA ship Council. The hope is that this council would initiate projects and take positions Marcia Sward you are in a depart• on education on behalf of the supporting ment that does not organizations. If this works, then math• As the world around us changes at an ever increasing rate, there is comfort in think• yet subscribe to Ho• ematics would have a single voice on edu• rizons, please find a cation comparable to that of the other ing of the MAA as something of a fixed point. After all, the Board of Governors way to make it hap• sciences, like chemistry and physics. pen. Your students While all the CBMS organizations' roles recently reaffirmed, almost word-for• word, the historic mission ofthe MAA: to will thank you, and you will feel great would be important, this council would be about it! especially valuable to the MAA and advance the mathematical sciences, espe• NCTM (National Council of Teachers of cially at the collegiate level. In our pro• Electronic Services Mathematics), the organizations that are grams, meetings, and services, we also find on the frontline of various reform efforts. much that is familiar and comfortable• MAA electronic services have also taken ourjoint national meetings with the Ameri• off during the past year. We now can boast In March I was fortunate to be able to visit can Mathematical Society, our three of our own gopher, World Wide Web page, with Oregon Senator Mark Hatfield for journals and FOCUS, our sections and their and several electronic discussion groups. about half an hour. He is a friend of edu• activities. However, looking more deeply We see electronic communication as a cation in general, and mathematics educa• into today's MAA, we see quite a differ• powerful new means of reaching virtually tion in particular. MAA Executive Director ent picture-an organization that is care• everyone who is interested in collegiate• Marcia Sward and I also made a very pleas• fully scrutinizing itself, and is significantly level mathematics and who wants to learn ant visit to the home of He lam an Ferguson, reshaping its programs to ensure a strong more mathematics, chat with colleagues the widely known mathematician and future effectiveness and success. So while about the teaching and learning of math• sculptor. We saw his entire operation, the MAA of today is founded strongly on ematics, network about job opportunities, which was fascinating. In particular he the mission and programs of the MAA of etc. We are intrigued by the vast new op• showed us the fine piece that the MAA yesterday, and while the traditions of the portunities for professional development commissioned as a gift to NCTM in com• past are still deeply honored, the MAA is via the Internet, and will be experiment• memoration of NCTM's seventy-fifth not the same organization that it was even ing in the coming years with new forms of birthday. This piece was presented to a few years ago. Here are some examples minicourses, dialogue groups, etc., seek• NCTM at its huge April meeting in Bos• of the changing face of the MAA. ing to find the most effective ways of serv• ton. ing the needs of our members and our In fact this is a year of anniversaries. This Math Horizons community. is the fiftieth anni versary of the Canadian Launched in 1994, Math Horizons now Teaching Awards Mathematical Society, which was cel• boasts over 22,000 subscribers, more sub• ebrated in Toronto in June. In early April scribers than any of our three journals. Of In recent years, the MAA has successfully I visited a meeting of the Texas Section at these 22,000, about 1000 are individual. launched a program of awards for distin• Baylor University in Waco. This was a The rest are taken out in bulk by math• guished teaching of mathematics which is splendid occasion at which they were cel• ematics departments and distributed to bringing regional and national recognition ebrating the section's seventy-fifth anni• interested students. Of course, it's the of excellence to the teaching of mathemat• versary and Baylor's one hundred fiftieth quality and relevancy of the content, pro• ics. We are all deeply grateful to Deborah anniversary. Also this year my own Pa• vided by Editor Don Albers and his cadre Tepper Haimo for endowing these awards. cific Northwest Section is celebrating its of eager authors and advisors, that really This year, we extended our awards pro• fiftieth anniversary. has made Horizons a smash hit. Students gram in another direction. Together with I feel that I've only scratched the surface and faculty tell us that Horizons is filling theAMS and SIAM, we established ajoint of all the activities that go on in the MAA. a real need, providing them with a rich award for student research, the Morgan We are blessed with an MAA staff in array of information about careers and Prize, which has been generously endowed Washington and hundreds of volunteer graduate programs, intriguing mathemat• by Brennie and Frank Morgan, parents of mathematicians throughout the country ics-sometimes old and sometimes new• award-winner Frank Morgan of Williams who are dedicated to and work very hard and humor, puzzles, and personal profiles College. It will be exciting to see the im• for the MAA. Noteworthy members of of successful mathematicians. We are ea• pact of this award, not just on the winners, both groups are the Visiting Mathemati• ger to get Horizons in the hands of many but in encouraging and validating the re• cians who work for a year at the MAA more students and faculty because we search efforts of undergraduate students. believe so deeply that every college stu• headquarters. Each has brought special Externally-Funded Projects skills to the enterprise and left an everlast• dent who is interested in mathematics ing imprint on the organization. deserves to have access to Horizons. If SUMMA (Strengthening Underrepre- 20 August 1995 FOCUS sen ted Minority Mathematics Achieve• making set of perfect papers. Congratula• is attracting attention on campuses across ment), founded in 1991, has successfully tions go to the team's three coaches, Anne the country and helping colleges and uni• expanded the number of mathematics• Hudson, Titu Andreescu, and Paul Zeitz, versities reexamine their promotion and based intervention projects in the country and to Walter Mientka, who served as tenure policies. An outcome of the JPBM from fifty in 1992 to a recent 129, with leader of the U.S. delegation. During his report is the establishment of the JPBM another twenty-seven in the planning presidency, Donald Kreider launched a Task Force on the Evaluation of Educa• stages. Through these programs, over joint effort with the National Council of tional Activities of Faculty. This commit• 30,000 minority youngsters have been Teachers of Mathematics (NCTM) to seek tee is charged with the creation of guide• involved in mathematics activities outside new opportunities for greater coordina• lines to aid mathematical sciences of school. SUMMA recently received tion among existing competitions and pro• departments in improving their evaluation funding for development of an archival pose alternative models for new competi• systems. The task force will work record of minority mathematicians and for tions or competition-like activities. This collaboratively with the American Asso• a survey of minority mathematics gradu• task force will make its recommendations ciation for Higher Education's project on ate students. The results of the survey will to the MAA and NCTM by December Peer Evaluation of Teaching. With the help shape the first phase of a graduate 1995. Support for the USA Mathematical downsizing of the Mathematical Sciences student mentoring program. And last, but Olympiad and our participation in the IMO Education Board (MSEB), a painful pro• not least, SUMMA is cooperating with is provided by the Army Research Office, cess dictated by lack of funding, the MAA North CarolinaA&TUniversity and Texas Office of Naval Research, Hewlett• has worked with our colleague organiza• Instruments in a project titled "Collegiate Packard Corporation, Microsoft Inc., and tions to find a way for the professional Curriculum Reform and Community Ac• the Matilda Wilson Foundation. societies to fill the breach. At its spring tion: Opening the Way," which is provid• 1995 meeting, CBMS voted to plan a ing faculty from HBCUs (Historically Journals, Books, and Reports CBMS Educational Partnership Council. Black Colleges and Universities) with During the past year, we have published This is to be an entity representing the training and support in integrating the use 14 books ranging from A Radical Ap• broad mathematical sciences community of calculators in their classroom teaching. proach to RealAnalysis, All the Math that's which is focused on coordinating our vari• The MAA's Project NExT is proving to be Fit to Print, and Algebra and Tiling. We ous educational efforts for greater national a winner. Through it, 66 young mathemat• are delighted that so many outstanding au• impact. Also at its spring 1995 meeting, ics faculty have been networked with one thors want the MAA to be their publisher. CBMS held the day-and-a-halfWorkshop another and with senior mathematicians, We are moving more and more toward on Minority Participation and Achieve• and are developing a broad view of the electronic manuscripts, and are pleased ment in Mathematics. This workshop grew roles and responsibilities of faculty mem• with the decrease in time-to-publication out of the desire to involve theotherCBMS bers and the issues of concern of the math• as well as reduced costs. Our journals are societies more actively in encouraging ematics community. Clearly one of the still our most popular publications, thanks minority participation in mathematics. The greatest benefits of Project NExT will be to the dedicated work of the editors and MAA was able to provide much insight the leadership skills that participants are authors. And FOCUS continues, under and assistance because of the knowledge honing, and from which we will all ben• Keith Devlin's capable leadership, to bring that we have gained over the past ten years efit in the future. All total, the MAA boasts us the latest news in the world of math• in this area, both in creating a more wel• of 30 externally funded projects, includ• ematics. The ACRE (Assessing the Cal• coming organization and in launching in• ing the Interactive Mathematics Text culus Reform Effort) Report, released last tervention programs for minority students. Project (IMTP), Case Studies of Under• January in San Francisco, has provided Planned Giving graduate Mathematics Programs, Statisti• the mathematics community with concrete cal Thinking and Teaching Statistics, Co• evidence ofthe success of the calculus re• In 1994 we launched the Planned Giving operative Learning in Undergraduate form efforts on many campuses, as well as Program, and initiated publication of our Mathematics Education, and the Institute the long road ahead. Guidelines for Pro• newest newsletter, Legacy. Happily the in the History of Mathematics and Its Use grams and Departments in Undergradu• response has been phenomenal! Over 150 in Teaching. Our list of generous sponsors ate Mathematical Sciences is being uti• members have indicated that they would who make these project possible includes lized by departments to assist in examining be willing to consider a gift from their the National Science Foundation, Carnegie their programs. Our career information estates to the MAA. We are in the process Corporation of New York, Exxon Educa• publications have been widely dissemi• of contacting these individuals to discuss tion Foundation, Alfred P. Sloan Founda• nated through the CBMS organizations with them possibilities for restricted or tion, IBM International Foundation, De• and the American CounselingAssociation. unrestricted gifts to the MAA. Ifyou would partment of Energy, Bamberger Memorial consider leaving some portion of your Foundation, and Texas Instruments. Collaborative Efforts estate to the MAA, putting some funds Competitions Among the various collaborative efforts now into a trust for the MAA, or designat• that the MAA has undertaken with our ing the MAA on an insurance policy, please The big news in 1994 was the spectacular colleague organizations are: The JPBM feel free to contact me to discuss the pos• win of our team in the International report Recognition and Rewards in the sibilities ([email protected]). We believe Mathematical Olympiad, with a history- Mathematical Sciences, released last year, See Executive Director on page 34

21 FOCUS August 1995

number of other questions that one could vided me with the MAA Financial Report ask, such as, "Where does funding for the information that I Board of Governors and the officers come need as Treasurer Gerald 1. Porter, Treasurer from?" and "What about the financial and as PIon the In• I am pleased to report that 1994 was a support for the executive staff?" and so teractive Math• good year for the MAA. Financially we forth. The answer is that these costs are ematics Text finished the year with a balanced budget allocated to each of the Association's ac• Project (lMTP). We (see below). The highlight of the year was tivities in proportion to the expenses in• wish her well and the outstanding performance of our team curred by the activity. Thus, for example, thank her for her in the International Mathematical Olym• you might question why our publishing dedication and hard piad held in Hong Kong. Our congratula• efforts ran a deficit of $342,000. Didn't work. we sell enough books? The answer is that tions go to the team's coaches, Anne Outcomes in 1994 Hudson, Titu Andreescu, and Paul Zeitz; if you look at the direct costs of publishing Executive Director of the American Math• the books and the cost of the publications There are several measures of the ematical Competitions, Walter Mientka; department, then that cost was about the Association's fiscal health. These include the chairoftheAdvisory Committee, Dick same as the income received for our books. our general operating budget, grant activ- Gibbs; and of course first and foremost to But when you add the allocated costs of ity, our real estate holding, and our invest- the team itself. $3 14,000 the result is a ~ ______---, deficit of $342,000. Consolidated MAA Balance Sheet It seems like only yesterday that Marcia About 50% of dues in• Sward succeeded Al Willcox as our ex• come is used to pay for December 31 December 31 ecutive director, but Marcia's first five allocated costs on pub- 1993 1994 years have quickly passed. I am pleased to lications and other ac• Assets report that the Board of Governors has ti vities that are not paid Current Assets voted to renew her appointment for an by outside funding Cash $325,655 $29,269 additional five years. She continues to agencies. In 1994 total Liquid Assets 979,437 913,001 provide sound administrative management dues income was $2.2 Accounts Receivable 841,298 728,491 Publications Inventory 320,317 350,375 for the Association while simultaneously million and initiating innovative programs. It is a plea• Prepaid Expense 142,495 163,630 unreimbursed allo• Total Current Assets $2,609,202 $2,184,766 sure to work with her. cated costs were $1.2 As Treasurer, I chair the Committee on million. The other 50% Non-current Assets Management Oversight and Evaluation of the dues pays for Investments (at cost) $993,593 1,648,000 (formerly known as Staff and Services). journal subscriptions. Furniture and Equipment 1,079,182 1,164,725 Building (at cost) 816,455 816,455 This committee is a subcommittee of the At the end of June, Building Improvements (at cost) 1,171,856 1,180,305 (ad hoc) Personnel Committee which has Rhoda Goldstein left Accumulated Depreciation (959,438) (1,131,908) responsibility for reviewing the structure the MAA to pursue Deferred Development Costs 127,780 127,336 of the staff in our Washington headquar• other interests. During Total Non-current Assets $3,229,428 $3,804,913 TOTAL ASSETS $5,838,630 $5,989,679 ters. Our current structure evolved from her six years at the the recommendations of an ad hoc com• MAA she has made a mittee chaired by Felix Haas on which I Liabilities and Fund Balances valuable contribution Current Liabilities served in 1988. The MAA was a different to the Association. As Accounts Payable $450,964 $392,331 organization at that time. Our total budget Associate Director for Accrued Royalties 47,478 55,380 in 1988 was $3.4 million vs. $6.3 in 1994. Finance and Adminis• Other Accrued Liabilities 83,646 90,996 Grant income was $386,000 vs. $1.7 mil• tration, she has super• Prepaid Dues and Subscriptions 1,967,903 2,117,719 Total Current Liabilities $2,549,991 $2,656,426 lion in 1994 and our total assets were $3.3 vised the renovation of million vs. $6 million in 1994. Because of our headquarters and these changes it is appropriate to review Long-term Liabilities the installation of a new the structure of our staff and our manage• Mortgage Payment $338,577 $254,577 computer system. On a Unexpended Grant Receipts 457,105 554,519 ment. We have contracted with Frank B. day-to-day basis she Total Long-term Liabilities $795,682 $809,096 Manley & Company to assist us with this has provided firm fi• Total Liabilities $3,345,673 $3,465,522 study. I believe that this study will enable nancial control. The Fund Balances us to structure our staff in a way that pro• General Fund has been vides maximum support for the activities Unrestricted Fund Balances $945,961 $975,258 in balance four out of of the Association. Restricted Fund Balances 954,887 929,758 the last five years and Endowment 592,109 619,141 You will see below a table titled" 1994 during that time has ac• Total Fund Balances $2,492,957 $2,524,157 Income and Expense." In this table we cumulated a surplus of present the income and expense for our $218,000. On a per• Total Liabilities $5,838,630 $5,989,679 and Fund Balances major programmatic activity. There are a sonallevel she has pro-

22 August 1995 FOCUS ment fund. We discuss each of these. a difficult task since very little is budgeted without bank borrowing. Those capital for contingencies. As a result, in some General Fund The General Fund is the expenditures are depreciated over time. years we have surpluses while there are MAA's unrestricted operating fund. In• The restricted fund in• deficits in others. For that reason we look Restricted Funds come to the General Fund comes from cludes externally funded projects and the at the result over a rolling five-year pe• members' dues, publication sales, inter• riod. American Mathematics Competitions est on working capital and contributions. (AMC). Grant revenues during 1994 to• Expenses include publications, manage• Year General Fund Balance taled $1,699,000. This includes grants to ment, supplies, non-externally funded (rounded to nearest S10(0) support SUMMA, Math Horizons, calcu• program support, allocated building ex• 1994 $4000 lator workshops, the IMTP, and myriad pense, and support of sections. General 1993 ($36,000) other projects thatsupportcollegiate math• Fund expenditures in 1994 totaled $3.9 1992 $97,000 ematics education. The AMC is respon• million out of total expenditures of $6.4 1991 $52,000 sible for operating the high school and million. 1990 $101,000 junior high school mathematics contests as well as the Math Olympiad. During 1994 It is the goal of the Finance Committee $218,000 5 year total AMC income totaled $704,000 while ex• that the General Fund be in balance, and in penses totaled $725,000. 1994 this was indeed the case. The Gen• As is indicated, over the past five years we eral Fund wound up the year with a sur• have an accumulated balance of$218,000. Building Fund Several years ago the Fi- plus of $4000 compared to a deficit of That balance provides us with a cash flow $35,871 in 1993. Managing the budget is to enable us to make capital expenditures See Treasurer s Report on page 24

1994 INCOME AND EXPENSE (Unit = $1000) BALANCE ACTIVITY INCOME EXPENSE BALANCE ACTIVITY INCOME EXPENSE 31 TOTALS 6475 6444 ( 145) Grant Supported Programs 1560 1705 (916) Journals 696 1612 ( 1) Assessment Study in Calculus-NSF 60 61 ( 298) American Mathematical Monthly 357 655 ( 3) Calculator Based Placed Tests-TI 8 11 ( 139) Mathematics Magazine 120 259 0 DC Mathematics Coalition 6 6 ( 163) College Mathematics Journal 95 258 4) Career Information-Dept of Energy 86 90 ( 305) FOCUS 35 340 1) Case Studies-Call for Change 22 23 ( 11) Math Horizons 89 100 0 Dana Foundation-MSEB 19 19 I) Guidelines for Progs & Depts-Exxon 2 3 (317) General Programs and Services 144 461 Int~ractiv~ Milth Text ~rQi~!;t ( 16) AMS Joint Projects 0 16 ( 31) IBM 191 222 ( 11) Awards and Contributions 19 30 ( 3) Regional Sites-NSF 12 15 ( 24) Career Information 2 26 0 Developers Conf-NSF 41 41 ( 19) CMLlEmployment Register 0 19 0 Workshops-NSF 80 80 ( 16) Committees & Representatives 5 21 3) High Schools-NSF 164 167 ( 67) Government and Public Relations 26 93 3) Regional Minicourses-IBM 8 II ( 20) Meetings 30 50 Milth Horizons ( 8) Minicourses 30 38 6) Exxon 15 21 ( 66) Section Support 2 68 8) Hewlett Foundation 22 30 ( 25) Student Chapters 25 50 0 NSF 17 17 ( 44) SUMMA 0 44 I) Sloan 3 4 ( I) Visiting Lecturers & Consultants 5 6 5) Preparing College Teachers-FIPSE 17 22 0 Priming the Pump-NSF 18 18 (342) Books and Pamphlets 932 1274 ( 17) Project NExT-Exxon 65 82 ( 7) Acquisitions 12 19 ( 9) Brink Selected Papers 16 25 ( 5) Statistical Thinking & Teaching-NSF 106 111 ( 15) Carus Mathematical Monographs 50 65 SUMMA ( 12) Classroom Resources 52 64 ( I) CCRCA 7 8 ( 36) Dolciani Mathematical Expositions 78 114 ( 29) Carnegie 155 184 ( 5) MAA Studies in Mathematics 10 15 ( 2) NSA 36 38 ( 9) Miscellaneous Books 27 36 ( 5) Adv Native American Math 20 25 ( 34) New Mathematical Library 132 166 ( 7) NSF 241 248 ( 76) Notes 202 278 0 AMIT-NSF 4 4 ( 10) Placement Tests 43 53 ( 2) Teaching Math with Calculators-NSF 119 121 ( 9) Reports and Pamphlets 6 15 ( I) UME Trends-Calculus Retrosp-NSF 9 10 ( 93) Spectrum 233 326 ( 6) Women and Mathematics-IBM/Others 713 ( 4) UME Trends 39 43 ( 23) Video Tapes 32 55 ( 24) Miscellaneous 47 71 I Management 27 26 ( 21) American Math Competitions 704 725 ( 25) Miscellaneous 20 45 25 American High School Examination 407 382 ( 15) American Junior High School Exam 183 198 1,796 General Income 2392 596 ( 19) American Invitational Math Exam 0 19 1,754 Dues 2164 410 0 USA Mathematical Olympiad 47 47 46 Contributions 120 74 ( 12) International Math Olympiad 67 79 ( 4) Building Fund 108 112 23 FOCUS August 1995

Treasurer's Report from page 23 leadership in both the Building Fund Drive and the actual renovation of the building. nance Committee made the decision to Participation of I know that I will think of John every time separate the Building Fund from the Gen• I enter the building. We all are the benefi• eral Fund so that the expenses associated Women ciaries of his foresight and hard work for with renovation of our buildings would be the MAA. Thank you, John. isolated from the day-to-day operating Carole B. Lacampagne, Chair budget of the Association. Space costs are Investment Fund The MAA Investment The Committee on the Participation of allocated to the General Fund as a fixed Fund includes both restricted and unre• Women (CPW) was established by the yearly charge. This allocation together stricted endowment funds. The earnings Board of Governors in January 1987 to with rental income from our other tenants and capital gains from our investments are foster the participation of women in the and contributions constitute income to the retained with the exception of funds that mathematical sciences, and especially in Building Fund. Expenses include operat• are intended to support specific activities activities of the MAA. The committee ing expenses, debt service, capital im• such as the Sliffe awards to high school has sponsored programs at national meet• provements, and principal payments on teachers. During 1994 we transferred ings, published articles and a short book, our mortgages. Because of the recent reno• $53,000 from the Investment Fund to the made recommendations to the Board of vations on our buildings there is a cumu• General Fund to support these designated Governors, and produced skits on micro• lative deficit in the building fund. As our programs. At the end of 1994 the MAA inequities. mortgages are reduced and interest costs Investment Fund was valued at During the 1994-95 academic year, CPW decline, that income will be used to re• $1,507,589, down slightly from the previ• sponsored a contributed paper session on duce and eventually eliminate this deficit. ous year. While this fund can provide some "Winning Women into Mathematics" at During 1994 our mortgage indebtedness protection against a "rainy day," the total the summer meetings and a panel discus• declined from $338,577 to $254,577 while value is only about 25% of one year's sion on "Recruitment and Retention of our accumulated deficit in the cash build• budget. As we look to the future, we must Women Faculty" at the January meetings. ing fund increased from $325,607 to find additional resources to increase the We also presented our traditional Micro• $355,519. Taking advantage of the favor• Investment Fund. We have begun a pro• Inequity Skits at the summer MathFest. able interest rates, we combined our two gram of planned giving as a first step in mortgages into a new mortgage which we this direction. We have served as an advisory group on plan to payoff in early 1998. various MAA-sponsored proposals to Financial balance sheets and reports indi• promote the participation of women in Next January, John Kenelly will complete cate that the MAA is able to support the the mathematical sciences and are on the his second term as an elected member of leadership position that we have assumed advisory committee for an Association the Finance Committee. John has provided in collegiate mathematics. However, the for Women in Science grant. We have true strength aided in the establishment of the "Pro• 1994 Revenues and Expenditures of the orga- grams for Women and Girls in Mathemat• (with 1993 for comparison) nization is ics," funded by the Tensor Foundation, 1993 1994 seen in the and several CPW members will be re• Revenues committee viewing proposals for Tensor funding at Dues $2,121,000 $2,164,000 lists both at Grant Supported Programs 1,475,000 1,560,000 the summer meeting. Book SaleslPamphletsNideoslUME Trends 917,000 932,000 the national Journal SubscriptionslFOCUS/ level and in Our Taskforce on Statistics on the Par• Math Horizons/Advertising/Royalties 614,000 696,000 the sections. ticipation of Women in the MAA is work• Mathematical Competitions 617,000 590,000 Without the ing in conjunction with the Joint Contributions 134,000 166,000 dedication Committee on Women in the Mathemati• Interest, Dividends, and Capital Gains 120,000 98,000 and hard cal Sciences to have data on the partici• USAMO and IMO 110,000 114,000 work of our pation of women made available by the Building Fund Contributions and Rental 141,000 108,000 members, Miscellaneous 44,000 47,000 various mathematical societies. Our TOTAL REVENUES $6,293,000 $6,475,000 we would be Taskforce on Skits is looking into the incapable of viability of the CPW skits as they are Expenditures advancing currently constituted, and considering Membership Recruitment and Retention $519,000 $410,000 collegiate appropriate changes in the skits format. Grant Supported Programs 1,557,000 1,705,000 mathemat- CPW is working closely with the Women BookslPamphletsNideoslUME Trends 1,184,000 1,274,000 ics. In the fi- Journals 1,550,000 1,612,000 and Mathematics (W &M) program dur• nal analysis, Mathematical Competitions 606,000 599,000 ing this time of change in focus and man• that is the General Programs and Services 479,000 461,000 agement. We are also represented on the Development/Greater MAA Fund 63,000 74,000 real strength MAA-NCTM Taskforce on Competi• USAMO and IMO 110,000 126,000 of the orga- tions. Building Operations 175,000 II 2,000 nization. Miscellaneous Programs 58,000 71,000 TOTAL EXPENDITURES $6301000 $6444000

24 August 1995 FOCUS

SUMMA has awarded sixty-three small discount, as well as an overhead projector SUMMA planning grants, totaling $250,000. Grant• unit donated by Hewlett-Packard. ees have established thirty-five projects William A. Hawkins on both two- and four-year campuses in In December 1994, the BINMAA Col• laborative Task Force completed its work The goals of the MAA's SUMMA Pro• twenty-seven states. These projects now serve more than 1325 students, including of examining the mathematics programs gram are to increase the participation and in BIA institutions and tribal colleges. A representation of minorities in mathemat• 1080 minority students. With SUMMA serving as a catalyst and reviewer of pro• project was designed to bring a new vi• ics' science, and engineering, and to im• sion of mathematics to these settings. A prove the mathematics education of posals, these projects have raised more than $8.5 million in additional public and one-year planning proposal will be sub• minorities. Marcia Sward, the MAA Ex• mitted to the NSF, the Exxon Education ecutive Director, and the MAA Commit• private support. The fourteen 1995 grant recipients are attending a proposal writ• Foundation, and several other private foun• tee on Minority Participation in dations. The BIA has committed $10,000 Mathematics, co-chaired by Robert ing workshop at the Burlington Summer MathFest. and one-fourth of the time of their director Megginson ofthe University of Michigan of education for the planning year. The and David Scott of the University ofPuget SUMMA has completed the third and fi• project directors are Joaquin Bustoz of Sound, oversee the SUMMA Program. nal year of a $703,000 NSF grant to net• Arizona State University, who will spend With the assistance of SUMMA, a work• work intervention projects directed by the 1995-96 academic year at SUMMA shop on minority participation in math• mathematics faculty. The SUMMA Con• as the visiting mathematician, and Lois ematics was sponsored by the Conference sortium (SUMMAC) now has 151 mem• Folsom, SUMMA consultant. bers at institutions in Canada, forty-one Board of the Mathematical Sciences in The development and publication of an May 1995 for CBMS leadership. Discus• states, Puerto Rico, Guam, and the Dis• trict ofColumbia. The SUMMAC projects archival record has been given $27,000 in sions between Professors Uri Treisman of funding by the Sloan Foundation through the University of Texas at Austin, James serve more than 36,000 students, of whom 91 % are minorities. SUMMAC proposal December 1995. The record will list more Turner of Florida A&M University, and than four hundred minority mathemati• the CBMS have been initiated concerning writing workshops have now been held in twenty-six of the MAA sections. To assist cians who have received Ph.D.s in math• continuation of research summer schools ematics or mathematics education. The for minority students at different host with SUMMAC activities, Professor Kathleen Sullivan of Seattle University record and an associated directory will universities. SUMMA would assist with include brief biographical information and recruitment of minority faculty and stu• was the visiting mathematician at SUMMA during the spring 1995 quarter. pictures. They will be available in hard dents. copy and on the MAA Gopher. SUMMAC hosts an e-mail discussion Minority Participation in the group and publishes the Directory of The Sloan Foundation, in collaboration MAA Mathematics-based Intervention Projects, with the National Association of Math• the quarterly SUMMAC newsletter Fo• ematicians, has also given the MAA a grant At the 1995 winter meeting, there were rum, and the Project Director's Handbook. of $30,000 to support a survey of minority five minority governors (including the first The fourth SUMMAC Conference will be mathematics graduate students. This sur• elected by a section) and the first minority held in conjunction with the Orlando win• vey will locate these students and deter• vice-president in attendance. The Ben• ter meeting. Proposals for continuation of mine their needs so as to facilitate the jamin Banneker Room in the MAA SUMMAC have been submitted to the design and implementation of a Graduate Dolciani Mathematical Center (the head• NSF and the Coca-Cola Foundation. Mentoring Network. quarters building) was dedicated May 19 in honor of Benjamin Banneker, a "free The MAA was a subcontractor on the Funding Being Sought man of color" and the first African Ameri• Collegiate Curriculum Reform and Com• SUMMA is planning a collaboration of can mathematician and astronomer. A munity Action (CCRCA) pilot project minority institutions to focus on the campaign to name a room after the first which was funded by NSF and the Hewlett• strengths, needs, and concerns of minor• Hispanic American to earn a Ph.D. in Packard Company. Completed in early ity mathematics departments which have mathematics remains a possibility. June 1995, the pilot involved twenty-five been successful in nurturing minority faculty from nine historically Black col• mathematical talent. Linking these insti• Projects leges and universities (HBCU s). The NSF tutions electronically will facilitate com• has funded a second round for this project The SUMMA Program continues to en• munication between these departments to provide technical assistance to fully courage college and university mathemat• and the larger mathematical community. implement calculator-based curricular ics faculty to initiate or replicate A proposal for $1.2 million over five years reform efforts in calculus for nineteen intervention projects for minority middle will be submitted to NASA. This project faculty from seven HBCUs, Hispanic• and high school students. The Carnegie will include the Graduate Mentoring Net• serving institutions, and American Indian Corporation of New York has funded a work, with electronic communication be• colleges. Each participant will receive a third two-year grant in the amount of tween mentors and minority graduate classroom set of state-of-the-art graphing $376,000 for this project. Since May 1991, students. calculators purchased by the project at a

25 FOCUS August 1995 1994 Best Sellers and New Shoes

Publications had a good year in 1994, reaching an all• time high in book sales of $792,000. The books pro• gram is driven by the Committee on Publications under the dynamic leadership of Jim Daniel of the University of Texas at Austin. Each year the editors of the seven book series of the MAA carefully review dozens of manuscripts and ultimately recommend about fifteen to twenty of the best for publication. The Committee on Publications has proven to be a very fine judge of "book U..·lhiaH.... flesh," finding winner after winner over the years. Some of their choices have been spectacularly successful, earn• ing the accolade "BEST SELLER." When we inform authors that their books are best sellers, they usually smile modestly and express surprise. None of them write with the goal of achieving best sellerdom. Rather they write to communicate mathematical ideas to their col• leagues, students, and others who share their passion for what E.T. Bell called the Queen of the Sciences. If their books happen to sell enough to buy the baby a new pair of shoes, all the better. Don Albers Director of Publications

26 August 1995 FOCUS Best Sellers A Radical Approach to Real Out ofthe Mouths ofMathema• Analysis-Bressoud ticians-Schmalz All the Math That's Fit to Polyominoes-Martin Print-Devlin Problems for Mathematicians Complex Analysis: The Geo• Young and Old- Halmos metric Viewpoint-Krantz Proofs Without Words• Complex Numbers and Geom• Nelsen etry-Hahn Resources for Calculus (in five Cryptology-Beutelspacher volumes )-Roberts Essays in Humanistic Math• Student Research Projects in ematics-White Calculus-Cohen et al Excursions in Calculus• The Lighter Side ofMathemat• Young ics-Guy and Woodrow Exploring Mathematics with The Searchfor E. T. Bell-Reid Your Computer-Engel The Wohascum County Prob• Game Theory and Strategy• lem Book-Gilbert et al. Straffin The Words of Mathematics• Journey Into Geometries• Schwartzman Sved Using Writing to Teach Math• Knot Theory-Livingston ematics-Sterrett Linear Algebra Problem Visualization in Teaching and Book- Halmos Learning Mathematics• Lion Hunting and Other Math- Zimmerman and ematical Pursuits- Cunningham Alexanderson and Mugler Mathematical Cranks• P.S.Ifyoudon'townacopy Dudley of all of these best sellers, More Mathematical Mor• there's still time to order. sels-Honsberger Just call 1-800-331-1622. Numerical Methods that Help finance a new pair of Work-Acton shoes for the baby or Old and New Unsolved Prob• grandbaby. lems in Plane Geometry and Number Theory-Klee and Wagon

------27 FOCUS August 1995

voted to provide plaques to recognize the American Mathematics Competitions top scoring student in those schools which participate in theAJHSME or AHSME for Walter E. Mientka, Executive Director (AMC) three consecutive years. In order to hold Richard A. Gibbs, Chair the line on the costs of the examinations, the CAMC has also begun a campaign to The Committee on the American Math• in the AIME, an increase of over 9000 from solicit corporate sponsors for the AIME ematics Competitions (CAMC) is the 1993. Selected on the basis of their and the USAMO. policy-making body of the American AHSME and AI ME scores, 146 students Mathematics Competitions (AMC), a pro• participated in the USAMO. The eight The mathematical community of the USA gram of the MAA also sponsored by the USAMO winners were honored by the has been invited to host the IMO during SOA. MAT, NCTM, CAS, AS A, MAA at the annual ceremonies in June (a the month of July in the year 2001. Host• AMATYC,AMS, and the ASPA. Thecom• report on the ceremonies appears in this ing the IMO in the USA will provide an position of the committee includes at least issue). The top six students comprised our opportunity for the largest ever assembly one representative from each of the spon• team that participated in the International of mathematics educators and gifted stu• sors, the chairs of the AMC subcommit• Mathematical Olympiad (lMO) in Hong dents from all over the world to partici• tees, the executive director of the AMC, Kong. Their performance was truly out• pate in the greatest challenge to their and the committee chair. standing. As reported in the October 1994 abilities of inquiry and problem solving. FOCUS, our team not only defeated sixty• (It is estimated that by the year 200 I, a The AMC administers the AJHSME, eight other countries, they achieved a per• total of one hundred countries will want to AHSME, AIME, and the USAMO. In fect score on each of the six questions send a team.) In addition, the IMO will 1994, over 560,000 junior and senior high associated with the nine-hour examina• provide for cross-cultural exchanges, con• school students registered for these exami• tion. This was the first time in the thirty• tribute to the promotion of friendship and nations. Over 217,000 students from 31 03 five-year history of the IMO for such an understanding, and create an opportunity schools registered for the AJHSME and accomplishment by any country! for the exchange of information on math• over 339,000 students from 5372 schools ematics syllabi and practice in mathemat• registered for the AHSME. Although the The CAMC believes that the AJHSME and ics education throughout the world. AHSME committee made a decision to the AHSME fulfill their role of both en• try to raise the number of honor roll stu• couraging students to participate in a The members of the CAMC feel that the dents, no one expected over 20,000! There mathematically challenging activity and experience of hosting the IMO and aiding were only 3273 in 1993 and never more identifying the top high school mathemat• its success will be viewed as a milestone than 9000 in previous years. Over 12,000 ics students in the nation. In an effort to in the history of mathematics in the USA. AHSME honor roll students participated increase participation, in 1994 the CAMC

tee members tried to find the cause ofthe ematics by an Undergraduate Student. Student Chapters inactivity by calling many of these insti• The Committee on Student Chapters Aparna Higgins, Chair tutions. Although many reasons were stayed in touch with student chapters given, the most frequent one was that the through Chapter News. With Deborah The Committee on Student Chapters con• chapter advisor had left or was on sabbati• tinues to create and support activities at Frantz of Kutztown University as its edi• cal. We urge all departments to revitalize tor, Chapter News continues to provide a the chapter, section, and national levels an inactive MAA student chapter or, where for students interested in mathematics. forum for all chapters twice yearly. This there is no chapter, to form one. Perhaps newsletter is sent to all chapter advisors, This year, Jane Heckler and Andy Sterrett the most important reward of such an ac• and contains ideas for student activities at were joined in anchoring the work of this tivity is a lifelong affection for, and inter• the chapter level, as well as information committee at the MAA's national office est in, mathematics on the part of the on the national meetings, summer research by Victor Katz. members of a student chapter. opportunities, and careers in mathemat• There are currently 416 MAA student In 1994 we established contact with ics. The Committee on Student Chapters chapters in the country, with a total paid MathCounts, which organizes a contest also provides an opportunity for chapter membership of about three thousand. The for eighth graders. For those MAA chap• advisors to meet with each other and share committee is grateful to the large number ters interested in working with eighth grade interesting chapter experiences at the na• of devoted chapter advisors who form the students in their surrounding communi• tional meetings, where the Committee on lifeline of student chapters of the MAA. ties, we encourage your participation in Student Chapters and Pi Mu Epsilon hold We acknowledge the immense gift of time offering your services of coaching students Joint Advisors' Breakfasts. These break• and energy that good chapter advisors put for the exam, or assisting MathCounts in fasts have been very successful. At the San into their chapters. We know that their other ways. The Committee on Student Francisco meetings, over sixty people at• students find mathematics a rewarding and Chapters is also very pleased to have been tended. enjoyable subject. one of several groups consulted in setting The Committee on Student Chapters grate• This year the committee focused some up the new Frank and Brennie Morgan attention on dormant chapters. Commit- Prize for Outstanding Research in Math- See Student Chapters on page 30 28 August 1995 FOCUS

funds for their travel costs-a significant Visiting Lecturers increase from previous years' percentages! MAA Staff Three of the five identifiable Latino speak• EXECUTIVE Program ers added this year have indicated that their Marcia P. Sward, Executive Director institutions may be able to provide some Mary McLean Bancroft, Executive Assistant Ron Barnes, Chair travel assistance. Four new states have Meredith S. Zimmerman, Executive Secretary In the calendar year 1994, the committee been added to the list of those supplying Development solicited new lecturers and rotated off those lecturers: Idaho (I), Maine (3), Oregon Richard M. Witter, Development Consultant who had served four years, in accordance (I), and Tennessee (I). The booklet now Maureen A. Callanan, Development Assistant with the committee guidelines. The VLP includes speakers from forty-two of the booklet for the 1995-96 academic year is fifty states, the District of Columbia, and PUBLICATIONS AND PROGRAMS being printed. Jane Heckler and Lisa six Canadian provinces. Donald J. Albers, Associate Executive Direc• tor, Director of Publications & Programs Johnson of the MAA have coordinated At the January 1995 national meetings in Lisa Johnson, Assistant to Associate Execu- placement of the contents of the booklet San Francisco, Robert Eslinger of Hendrix tive Director onto the MAA Gopher. The gopher ver• College joined the committee. Represen• Amy S. Fabbri, Production Specialist sion adds biographical information on lec• tatives of the visiting lecturers programs Production and Marketing turers to the standard content of the printed of SIAM and COPSS were invited to at• Elaine Pedreira, Production & Marketing booklet. An announcement on accessing tend and contribute to the meeting. Manager the booklet from gopher appeared in the At the San Francisco meeting it was de• Carol A. Baxter, Assistant Production & Mar• June issue of FOCUS, page 17. For the cided to submit a proposal for a session by keting Manager first time, the booklet was entered on a our committee at the 1996 Orlando winter Beverly J. Ruedi, Electronic Production Spe- computer disk, which will make it much meetings. DeaneArganbright, formerly of cialist easier to update future editions. Whitworth College and now the new chair Chester Blyther, Publications Sales Assistant The 1994 booklet contained 187 lectur• of mathematics at the University of New Shawn Hayden, Publications Sales Assistant ers, including twenty-nine new ones added Guinea, agreed to head up this project. A Editorial in 1994. For the calendar year 1994, of the panel discussion on the Visiting Lecturers Harry Waldman, Journal Editorial Manager 187lecturers listed, sixty reported no talks Programs in the Mathematical Sciences is Programs given; twenty-seven reported giving a to• being developed with representati ves from Jane S. Heckler, Senior Assistant for Programs tal of fifty-six talks plus "several presen• professional societies who administer such April White, Programs Secretary tations." In addition, two speakers noted programs, successful lecturers, minority FINANCE AND ADMINISTRATION multiple invitations to talk at various high lecturer organizations, and colloquium Rhoda D. Goldstein, Associate Executive Di• schools and colleges. Several noted that organizers. A survey of mathematical sci• while they gave a number oflectures, they rector, Director of Finance & Administra• ences departments is intended to gather tion could not attribute them to the MAA book• information and ideas, and the results of Accounting let. One hundred lecturers did not report this survey will be included in the pro• Tracy L. Terry, Accounting Supervisor on their activities. gram discussion. For further information Miranda Hunt, Accounting Assistant Various lecturers made suggestions and! on this program, please contact Deane Kemi Oluwafemi, Accounting Assistant or observations about the program. A de• Arganbright whose e-mail address is Reception sire for advertising the program more [email protected]. Robin Chapman, Receptionist & Office Op- widely, including more contacts with The committee would also like to initiate erations Coordinator groups like AMATYC, NCTM, high informal get-togethers with interested Mailroom schools, and others was mentioned. In MAA lecturers at the annual national Eric Aiken, Mailroom Supervisor response, the committee requested that the meetings (and possibly at some of the sec• Computer Network booklet be distributed to all MAA student tion meetings) to share ideas and discuss Joe Cody, Information Systems Administrator chapter advisors. Contacts with schools suggestions for improving the program. and other mathematics organizations are MEMBERSHIP AND SUBSCRIPTIONS The committee welcomes suggestions and being pursued. The main obstacle seems Kay Lamont, Membership/Subscriptions Man• comments for improving the program. to be money, according to a number of ager Nominations for outstanding speakers for comments received. It has been suggested Janet Petrillo, Membership/Subscriptions As- the program are encouraged. For additional that perhaps this issue needs to be ad• sistant Manager information, nominations, copies of the dressed. Frederica Watson, Membership Assistant 1995-96 VLP booklet, etc., please con• Sarah Knight, Membership Assistant The 1995-1996 booklet contains 208 lec• tact Ron Barnes, Chair, MAA Visiting Rudean Farmer, Membership Assistant turers, including sixty-one new ones Lecturer Program, CMS Department, added. Since forty lecturers rotated off in University of Houston-Downtown, I OFFICE OF MINORITY PARTICIPATION 1994, the net increase in lecturers was Main St, Houston, TX 77002; (713) 221- William A. Hawkins, Jr., Director twenty-one. Of the sixty-one new lectur• 8553; e-mail: [email protected]; fax: Florence Fasanelli, Director of SUMMA In• ers, twenty-three have indicated that their (713) 221-8086. tervention Programs institutions may be able to provide some Lana Bilyeu, Administrative Assistant 29 FOCUS August 1995

Student Chapters from page 28 MAA Board of Governors fully acknowledges the continuing sup• Prior to conclusion of the MAA Business Illinois, Albert D. Otto, Illinois State Univer• port of the Exxon Education Foundation. Meeting in San Francisco, CA, January 1995 sity Part of a grant was used in the academic Officers Intermountain, Lawrence O. Cannon, Utah year 1994-95 as mini-grants to sections to State University President-Elect, Kenneth A. Ross, University implement programs to attract minority of Oregon (95-96) Iowa, Lynn J. Olson, Wartburg College students to participate in section activities President, Donald L. Kreider, Dartmouth Col• Louisiana-Mississippi, Donald M. Bardwell, and national meetings, to implement pro• lege (94-95) Nicholls State University grams for students that illustrate applica• First Vice-President, DorisJ. Schattschneider, Maryland-D. c.- Virginia, Elizabeth J. Te1es, tions of mathematics to contemporary Moravian College (94-95) National Science Foundation and Montgom• society, or to conduct career fairs or oth• ery College Second Vice-President, James A. Donaldson, erwise alert students to the wide variety of Howard University (94-95) Michigan, Hugh L. Montgomery, University careers that are open to those with a sound of Michigan Secretary, Gerald L. Alexanderson, Santa Clara background in mathematics. A total of North Central, John M. Holte, Gustavus University (90-99) $8150 was awarded to nine sections. The Adolphus College Treasurer, Gerald J. Porter, University of Penn• activities funded by these grants include sylvania (92-97) Southern California, James O. Friel, Califor• nia State University at Fullerton career conferences for undergraduates and Associate Secretary, Donovan H. Van Osdol, for junior high school students, a University of New Hampshire (94-97) Texas, John Ed Allen, University of North Texas minicourse or workshop at a section meet• Additional Members of the Board of Gover• Sectional Governors (July 1, 1993-June 30, ing' and prizes for a mathematics paper nors 1996) writing contest. The Committee on Stu• Former President Allegheny Mountain, Kathleen Anne Taylor, dent Chapters has received a fifth grant Leonard Gillman, University of Texas atAus• Duquesne University from the Exxon Education Foundation, tin (89-94) Indiana, Catherine M. Murphy, Purdue Uni• versity at Calumet part of which will be used to fund activi• Deborah Tepper Haimo, University of Cali• fornia-San Diego (94-98) Kentucky, Christine A. Shannon, Centre Col• ties at the section level for the academic lege year 1995-96. Sections have been asked to submit proposals to implement pro• Elected Members of the Executive Commit• Metropolitan New York, Theresa J. Barz, St. tee John's University grams or activities described similarly to Chair. Committee on Sections, Linda C. Hill, Nebraska & Southeast South Dakota, Melvin those mentioned immediately above. Idaho State University (94-96) C. Thornton, University of Nebraska at Lin• coln At the past three national winter meetings, Editor, Martha J. Siegel, Towson State Uni• Karen Schroeder of Bentley College or• versity (91-95) Northern California, John A. Mitchem, San Jose State University ganized Special Paper Sessions of con• Elected Members ofthe Finance Committee Oklahoma-Arkansas, Edward N. Mosley, Lyon tributed papers pertaining to activities at Barbara T. Faires, Westminster College (92- College the chapter and section levels. Many of 97) Rocky Mountain, Celestino G. Mendez, Met• the papers describe the activities of sec• John Kenelly, Clemson University (88-95) W. ropolitan State College of Denver tions which have been awarded an Exxon Governors at Large Wisconsin, Robert J. Fraga, Ripon College mini-grant. Bettye D. Forte, Fort Worth Independent Sectional Governors (July 1, 1994-June 30, School District (93-95) The Committee on Student Chapters con• 1997) tinued to infuse the program for the na• Johnny L. Houston, Elizabeth City State Uni• Kansas, Willard A. Parker, Kansas State Uni• versity (92-94) tional meetings with activities appropriate versity Genevieve M. Knight, Coppin State College for undergraduate members of the MAA. Missouri, Lanny C. Morley, Northeast Mis• (94-96) The Student Lecture at the summer meet• souri State University Patrick D. McCray, G.D. Searle & Co. (94-96) ing in Minneapolis was delivered by Gail New Jersey, Barbara J. Osofsky, Rutgers Uni• Nelson of Carleton College on "What is Eric R. Muller, Brock University (92-94) versity really in the Cantor Set?" It was a wonder• David A. Sanchez, Texas A&M University Northeastern, Karen J. Schroeder, Bentley System (93-95) College fully crafted exposition of a topic usually not seen by an undergraduate. The Stu• Journal Editors (Terms end December 31) Ohio, David E. Kullman, Miami University dent Workshop was an exciting mix of Bart Braden, Northern Kentucky University Pacific Northwest, Harvey J. Schmidt, Jr., (94-98) Lewis & Clark College mathematics and juggling, as two experts in both areas, Joe P. Buhler of Reed Col• John H. Ewing, American Mathematical Soci• Seaway, Stephen R. Cavior, State University ety (92-96) of New York at Buffalo lege and Ronald L. Graham of AT&T Bell Sectional Governors (July 1, 1992-June 30, Southeastern, David R. Stone, Georgia South• Labs presented "The Theory and Practice 1995) ern University of Juggling." At the winter meetings in Eastern Pennsylvania & Delaware, Marvin L. Southwestern, Richard B. Thompson, Univer• San Francisco, William W. Dunham of Brubaker, Messiah College sity of Arizona Muhlenberg College presented a spell• Florida, Lee H. Armstrong, University ofCen• All committee member terms expire at the end binding account of Newton 's contribution tral Florida of the annual winter meeting following the to "Newton's Method" in a talk titled year listed, unless otherwise noted. "Newton's (Original) Method-or- 30 August 1995 FOCUS

Though this be method, yet there is mad• The Student Workshop is "Mathematics ideas and their gifts of time. We welcome ness in't." The ice cream social after the on the Internet," by Dennis DeTurck of Richard L. Poss of St. Norbert College, talk encouraged many in the audience to the University of Pennsylvania. who is also president-elect of Pi Mu Epsi• stay and chat informally. Sonja Sandberg The Committee on Student Chapters has lon, and Terry L. Herdman of Virginia of Framingham State College presented worked hard to contact minority institu• Polytechnic Institute & State University, an informative and interesting workshop tions directly and to discuss the involve• who will be SIAM's representative on this on a use of mathematics in contemporary ment of their students with mathematics. committee. society titled "Mathematics and the AIDS W. Howard Jones ofthe University of the As other groups increase their efforts to epidemic." District of Columbia and Joanne Darken involve undergraduates in mathematics As always, the Hospitality Center at the of the Community College of Philadel• activities, the Committee on Student Chap• national meetings was open and eager to phia have organized this effort. Richard ters hopes that they will avail themselves serve students, providing a place for Jarvinen of Winona State University of the many opportunities we already pro• puzzles, contests, information, and respite headed an effort to bring students from vide. We welcome comments and sugges• from the busy pace ofthe meetings. It was Native American Indian colleges in Min• tions on our work. The MAA Committee staffed by Richard S. Neal of the Univer• nesota to the MathFest in Minneapolis last on Student Chapters is pleased to be of sity of Oklahoma. summer. service to undergraduates interested in mathematics and invites all undergradu• There were fifteen MAA Student Papers Cooperation between the Committee on ates to participate in the many activities at at the summer meetings. The sessions were Student Chapters and Pi Mu Epsilon con• the chapter, section, or national levels arranged, as usual, by Ronald Barnes of tinues to grow. Robert Eslinger of Hendrix described in this report. the University of Houston-Downtown. College acted as the liaison between the The MAA Committee on Student Chap• two organizations. He will be the MAA For additional information on the MAA ters continued to award some funds for Visiting Mathematician for the next aca• Committee on Student Chapters, please travel for student paper presenters. For the demic year, and our committee will have contact Aparna W. Higgins, Chair, MAA first time, the prizes for best presentation another special friend at MAA headquar• Committee on Student Chapters, Depart• carried a cash award of $100 each. Ben ters. ment of Mathematics, University of Day• Fusaro of Salisbury State University Bob Eslinger, Ben Fusaro, and Howard ton, Dayton, OH 45469-2316; (513) worked with the Mathematical Contest in Jones have ended their terms on this com• 229-2511; fax: (513) 229-2566; e-mail: Modeling to get two winning teams from mittee. We thank them for their wealth of [email protected]. the MCM to present their winning solu• tions at the sessions. At the 1995 summer meetings in Burlington, the Committee on Student Chapters continues its tradition of provid• UMETRENDSNews and Reports on Undergraduate Mathematics Education ing exciting programming forundergradu• ates. The Student Lecture is "Cauchy,Abel, Dirichlet, and the birth of real analysis," URGENT by David Bressoud of Macalester College. H you are a loyal reader of UME Trends, please become a loyal sub• scriber. 1994 Year End UME Trends, which is in its seventh year of publication, is hanging by a thread. The present number of subscriptions to UME Trends will not allow us to continue publication Membership beyond January 1996. HERE'S HOW TO SUBSCRIBE: Individual Members • Call 1-800-331-1622 and have your Visa or Mastercard ready, or: • Send a $16 check ($24 outside the US), with your name and address, to the Mathematical College and Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036, or University Faculty 12,682 ·If you are an MAA member, U ME Trends is listed on your 1996 dues notice. Simply check off UM E Trends and send in your $16 payment with your dues, and your subscription will 6,426 Student begin immediately. Industry or Government 3,082 Secondary School Teachers 2,132 IF YOU ARE ALREADY A UME TRENDS SUBSCRIBER: • RESUBSCRIBE to UME Trends when you receive your next subscription notice. Retired or Unemployed 3,108 ·If you are an MAA member, check off UME Trends on your next MAA dues notice. This Other 1,875 will extend your subscription for an additional year beyond your current subscription. Institutional Members 580 • URGE COLLEAGUES with whom you have been sharing your copies of UME Trends to take out their own subscriptions. TOTAL 29,885 • Give GIFT SUBSCRIPTIONS of UME Trends to friends, students, or colleagues.

31 FOCUS August 1995

Barnier, KimA. Barrett, Gregory A. Bastian, The Greater MAA Fund Gary D. Berg, Bernard R. Bernstein, Will• iam D. Blair, Steven E. Blasberg, Austin R. In 1994,953 donors contributed $63,965 to SPONSORS Brown, Robert E. and Rosalie P. Brown, the Greater MAA Fund. The officers of the Donald L. Burkholder, Donald W. Bushaw Association express their gratitude to the Jeanne L. Agnew, Henry L. Alder, William • Roderick P. Caldwell, Benjamin R. Cato, membership for its generous support of this C. Allen, Edward F. Assmus • William W. Stephen R. Cavior, Onn Chan, George E. fund. The names of all 1994 donors, except Babcock, Walter W. Bartlett, Donald Chapman, Jr. *, Theodore S. Chihara, Hubert of those wishing to remain anonymous, ap• Batman, Helen P. Beard, Robert D. Bergstein E. Chrestenson, Sr. Helen Christensen/ pear below. (In Memory of R H Bing), Walter Bernard, George MackiwlRichard McCoartlWilliam Martin Billik, James 1. and Ann F. Bowe, GRAND BENEFACTORS John D. Bradburn, Robert L. Bryant, Milo F. Reddy*, RobertA. Clark, Richard M. Cohn, Bryn, Francis R. Buianouckas, Robert Maria Contessa, James Paul Conway*, Tho• Richard D. Anderson, Tom M. Apostol, Bumcrot, Thomas R. Butts· Nathaniel mas A. Cootz, Samuel G. and Ettie J. Coun• Herbert M. Baruch, Alice C. Beckenbach Chafee, Jean B. Chan and Peter Stanek (In cilman, James P. Crawford, Edmund A. C. (In HonorofAlan C. Tucker), Marvin L. and Crouch· M. Hilary Davies (Wick), Keith J. Memory ofWing Shu Chan), Joyce Conlon* Elaine S. Bittinger, Mary L. Boas, Malcolm Devlin, Anthony B. Di Luna· Clifton E. and Michael R. Vogt*, Helen V. and Norman K. Brachman, Richard A. Hord, Edward Ealy, Gerrit Mark Edris, Jessie A. Engle· Coulson, Michael D. Covney • Guy M. Kitchen, Ravi S. Kulkarni, Hung-Wei Lin, De Primo, Leonard P. Diana, George W. John C. Fenley, Raymond C. and Mary S. Robert G. Maule, Everett Pitcher, Uri Flagg (In Memory of Albert Herbst), Ken• Dinolt, Underwood Dudley • Bernard A. Treisman L. Edison, Marjorie Enneking· J. Sutherland neth W. Fogarty, Susan Forman, James H. and Emily Frame, Lawrence E. Freeman, Freeman, James O. Friel· Sally S. Garber, BENEFACTORS Donald Y. Goldberg, Benjamin F. Ben A. Fusaro· Robert L. Graves • M. E. Gundelfinger, William S. Guthrie*, David Alfred and Dorothee Aeppli, Gerald L. Hamstrom, Bill Hassinger, ThomasA. Hern, E. Guyer· James E. Hall, J. H. Hancock, Alexanderson, Raymond A. Barnett, Bar• Jim and Mary Jane Huneycutt • D. Richard John L. Hank, Adam O. Hausknecht, James bara J. Beechler, William G. Chinn, Betsy litis· Richard E. Johnson· Wilfred Kaplan, B. Herreshoff, Detlev and Yuli Gu Hoffmann, Feagan Colquitt (For the R H Bing Fund in John T. Kearns, Robert C. Knapp, Genevieve Ernest Holmes, Thomas Honold, John M. Memory of Landon A. Colquitt), William L. M. Knight*, Virginia E. Knight· Richard G. Horvath, Laurence G. Hoye· I. Martin Isaacs Duren, Richard L. Gantos, Anna S. Laatsch, Walter R. Lawson, Steven K. Leary, • Martin L. Jautz, Carl G. Jockusch, Russell Henriques, Donald L. Kreider, Morris Margaret L. Lial, Clifford A. Long • Dexter E. Jones· Rosella Kanarik, David B. Kirk, Newman, Henry O. Pollak, Paul J. Sally, A. Magers, William D. Maness, May H. Benjamin G. Klein, Ronald J. Knill, Ignace Marcia P. Sward*, Ling-Erl Eileen Wu Maria, Andrew J. Matchett, Janet McDonald I. (In Honor of Winifred P. Asprey and Marcia Kolodner, Ralph M. Krause, Gary R. GRAND PATRONS P. Sward), David M. Merriell, John A. Krumpholz, David E. Kullman (In Honor of Mitchen, Harriet F. Montague· John D. Neff, G. Baley Price) • Elliott Landowne (In Howard Anton, Lida K. Barrett, Lynn A. Mary M. Neff, John D. Nelligan· Arnold M. Memory of Dunham Jackson), Ronnie Baur, Ronald M. Davis, Leon A. Henkin, Ostebee and Kay E. Smith· Nicholas Passell, Levy*, M. Albert and Joan S. Linton, Charles James R. C. and Joan R. Leitzel, Richard A. Juanita J. Peterson (In Memory of Edward Livingston, R. Lee Livingston*, Nicholas J. and Laura N. Little, Ivan Niven, Robert A. Maurice Beesley), John W. Petro, Donald L. Lord, Norman W. Lord (In Memory of Estella Rosenbaum, Lynn A. and Mary E. Steen, Plank, Gerald J. Porter*, G. Baley Price • Cahan Lord), Leon J. Luey • John J. Alfred B. and Shirley B. Willcox Albert L. Rabenstein, Charles D. Robinson, MacDonnell, J. J. Malone, Joseph S. Mamelak, Heinrich Mantel, William PATRONS Raphael M. Robinson, John C. Roland*, Sharon Ross, Michael M. Rubenstein • Jef• Margulies, Walter Markowitch, Thomas J. Marlowe, Jennie E. Master, David K. Samuel J. Baethge, Carole A. Bauer, John frey R. Sachs, Robert L. Sachs*, Donald Y. Masunaga, Stephen B. Maurer, RaymondA. and Clara R. Bender (In Honor of Prof. and Sakahara, Hans Samelson, Donald E. Mayer, John R. Mayor (In Memory of Mrs. Malcolm S. Robertson), Peter B. Sarason, Jeffrey A. Sarnoff, Doris J. Rudolph E. Langer), Charles W. and Bertha Bjorklund, Stewart E. Boden, Phyllis J. Schattschneider, Joel E. Schneider. John A. M. McArthur (In Memory of Orville G. Cassidy, Jan W. Dash, Jean E. de Valpine, Schumaker, Abdulalim A. Shabazz, Melvin Harrold), William S. McCulley, Robert T. Gregory M. Dotseth, Robert L. Druet, John A. Shader, RichardJ. Shaker, John L. Snyder, and Alice D. Mertz, Barbara W. Meyer, H. Ewing, Barbara and Doug Faires*, Louis Solomon • Elizabeth J. Teles*, John Ernest A. Michael, Arthur F. Miller, G. H. Eugenia E. Fitzgerald (In Memory of Dor• W. Trabert, Thomas W. Tucker • Dirck Miller, Gerald A. Mischke, Richard L. othy Evelyn Nelson Smith), Samuel Uptegrove· Sr. Paul J. Villemure • Joe F. Mortland, Thomas L. Morton, L. T. Moston, Goldberg, J. H. Graham, Curtis Greene, Wampler, Robert and Elizabeth B. Weinstock Robert H. Myers· Togo Nishiura, Steve N. Samuel W. Hahn, Linda C. Hill, Joseph A. (In Memory of Harold Bacon), Alex Nordquist, F. Alexander Norman, Victor T. Hughes, Daniel Kennedy, Eugene A. Weintraub (In Honor of the Tufts University Norton· Ann F. 0' Neill, Paul Olum, Hironori Margerum, Walter and Gretel Mientka, D. Mathematics Department), Chris Wheland, Onishi, Philip Oppenheimer, David B. D. Miller (In Memory ofAlfred H. Clifford), Karen L. Whitehead, John F. Wilkinson • Oulton, Calvin I. Owens· Hiram Paley (In Chester W. Mills, Kenneth R. Rebman, Ken• Anonymous Honor of Lee A. Rubel), John T. Poole, Alan neth A. and Ruth M. Ross (In Memory of G. and Marjorie E. Poorman, Ervin J. Prouse, Karl R. Stromberg), David A. Sanchez, CONTRIBUTORS Calvin M. Pullias· James F. Ramaley, Ken• James F. Sanford*, Maria W. Steinberg, Michele J. Alberg, Kathleen T. Alligood* neth B. Reid, Irma M. Reiner (In Memory of Robert Steinberg, Tina H. Straley, Alan C. and Tim Sauer*, Edward Z. Andalafte • Irving Reiner), Mary B. Rhodes, Neil W. Tucker, Allyn J. Washington, John E. Wetzel Edward D. Baker, Fred E. Ballard, William Rickert, Lucille Ritter (In Memory of Eu• • Anonymous (In Memory of Freida R. Ballard, Fredrick W. Barber, William J. gene K. Ritter), Stanley A. Robinson, Jean- Mangus), Anonymous 32 August 1995 FOCUS

Louis Roque, N. J. Rose • Saturnino L. Salas, Guglielmi· Michael E. Hammett, Charles William E. Siesnick, Karen J. Small, Anita David H. Sanders, Diran Sarafyan, Charles D. Harris, Glen A. Harris, Robert G. E. Solow, Lawrence E. Somer (In Memory M. Schneeberger, Damon Scott, Norman E. Hathway, Francis M. Henderson, Delfin G. of E. T. Parker), Alexia A. Sontag, Betty M. Sexauer, John K. Seymour, Christine A. and Hernandez, Gerald A. Heuer, James F. Speairs, Olaf P. Stackelberg, James W. David L. Shannon, Martha J. Siegel *, David Heyda, Charles F. Hicks, James L. Higgins, Stewart, Allen H. Stix, John R. Stock, Tho• A. Smith, James L. Smith, RichardA. Smith, Gregory A. Hively, Alfred L. Horowitz, mas N. Strickland, Hirosi Sugiyama· Elliot Wilbur L. Smith, Wallace R. Soderquist, David S. Hough, Jonathan W. Hoyle, James A. Tanis, James W. Thomas, James L. Robin N. Soloway, Linda R. Sons, Michael G. Huard, Mark E. Huibregtse, James F. Thornburg, James C. Thorpe, Wolfgang J. J. and Margaret Sormani, Blair Sterba• Hurley, Lee P. Hutchison· Franklin T. Iha, Thron, Kathryn B. Toll, James E. Trefzger, Boatwright, Richard S. Stevens, Danielle C. Nancy J. Ingram, Lynne Ipina Isaacson and Leonard L. Tripp, Jaroslav Tuzar· J. Jerry Struppa* • Laurence R. Taylor, Harold B. Eli Isaacson, Lynn H. Iwamoto· Richard D. Uhl • Gary L. Vance (In Honor of all 1994 Tobin, Mary P. and Hing Tong, Roseanna F. Jarvinen, June R. Jensen, Charles H. Livonia Mathematics Retirees), Mary E. Torretto • Visutdhi Upatisringa • John P. Johnson, Gerald W. Johnson, Luella H. Violett, Paul A. Vodola • Adrian R. Van Alstyne, Richard J. Vance, Wolmer V. Johnson, William B. Johnson, Kathryn A. Wadsworth, Curtiss E. Wall, Nancy J. War• Vasconcelos· Buck Ware, Frank W. Warner, Jones and Sherwin Skar· Paul A. Kaschube, den, John V. and Mary K. Wehausen, An• Bette L. Warren, Alvin M. and Myra White HerbertE. Kasube, Victor J. Katz*, William thony A. Weidner, Tilla Weinstein, Edward (In Memory of Stephen Bergman), Wiener E. Kaufman, George A. Kent, Dorothea A. W. Weissner, Robert A. Welker, Donald C. Lose Enterprises, Pete Wildman· Jeong S. Klip, David I. Knee, James F. Koehler, Roger West, Steven N. Westfall, Frederick J. Yang, Michael Yanowitch • Anonymous (2) P. Kovach, David M. Krabill, Henry A. Wicklin, Robert S. Williams, Patricia S. Krieger,JeanS. Kromer,JohnS. Kronholm, Willis, Izaak Wirszup, Eugene W. Womble, SUSTAINERS Kenneth Kunen • Jackson B. Lackey (In Edward Wong· Nicholas W. Yang, Howard Memory of Aughtum Howard), Nancy L. Sheldon B. Akers, MarthaAliaga, Gerald R. H. Yeager· Stephanie A. Zahrbock, Paul M. Laing, JosephA. Langsam, Arnold Lapidus, Andersen *, Gayle-Jean Angelo, Florence H. Zorn· Anonymous (2) Michel L. and Odile Lapidus, James F. Ashby (In Honor of Donald and Sylvia Lawrence*, Jinoo Lee, Gerald M. Leibowitz, OTHER DONORS Bushaw), Walter Augenstein· James H. o. Alan L. Levine, John B. Lewis, Kathleen E. Bagley, Frederick A. Bakenhus, Joseph A. Lewis and L. Gaunce Lewis, Jr., William A. Joseph Abate, Neil E. Aiken, Fahad AI• Baldinger*, John T. Baldwin, Philip R. Lewis, Joey Liaw, Rudolf B. Lim, Andrew Jalawi, Etienne Archinard, Charles E. Aull· Bartick, Frank P. Battles, Kathleen J. P. Lineberry,AndrewC-FLiu,JohnM. Long, Vivie G. Babb, Charles N. Baker, George A. Bavelas, Kathleen Baxter, Enrique Bayo, Emmet F. Low, Robert B. Lumbert, Norman Baker, Arienne S. Balser, Mary McLean Imogene C. Beckemeyer, Robert J. Beeber, Y. Luther • Kenneth D. Magill, Athena Bancroft*, Adrienne A. Barnhart, Oscar C. Donna L. Beers, Thomas A. Beiter, Vaclav Makroglou, Pir M. Maleki, Josep M. Oriol Benavides, Thomas E. Bengtson, William E. Benes, F. Chal Benson, Simon J. Bernau, Marti, Presciliano Martinez, John C. R. Bennett, Elwyn R. Berlekamp, Geoffrey Andrew C. Berry, Paul R. Bialek, Kurt Bing, Matthews, Ray A. McClanahan, Thomas C. Berresford, Amer Beslagic*, Carlos M. John W. Bishir, AlbertA. Blank, Marilyn J. McConnell, O. C. McGehee, Archie and Lois Betancourt, David G. Bethelmy, Dorothea Blockus, Haig E. Bohigian, S. Elwood Bohn, McKinnon*, Diane T. McNichols, Robert D. Bone, James N. Boyd, Nancy J. Bray, BrentA. Bradberry, Murray Braden, Thelma C. Meacham, James W. Mellender, Gary P. Gary R. Breaux, Richard G. Brown, Louise E. Bradford, Eric C. Branlund, George U. Menzel, Sandra Ann Mertes, Stephen A. O. Bryant· Maureen A. Callanan*, Thomas Brauer, George H. Bridgman, Susan S. Meskin, Gerhard Metzen, Charles W. Carrillo, Edward M. Carroll, Daniel S. Brinckerhoff, Gary L. Britton, John E. Broth• Mitchell, Walter Morris*, Chris L. Mueller, Chesley, Charles C. Chouteau, Robert D. ers, Arthur B. Brown, Ezra A. Brown, Dou• Marvin G. Mundt, Paul F. Murphy· Herbert Cismowski, Michael H. Clapp, Richard glas A. Brumbaugh, James E. Brunner (In Nadler, Norman W. Naugle, Edward O. Coffinberger*, Bruce I. Cohen, Enrique Memory of James Armstrong), Billy F. Nelson, Ali H. Nesin, Ben E. Norman· David Comer-Barragan, Anthony Conciatori, Jo• Bryant, Richard T. Bumby, James W. Butler O. Oakland, Robert F. Olin, Rene E. Olivares, seph F. Conrad, Scott Cooley, Henri Comet, • John F. Cavalier, Ping-Tung Chang, Charles Roger F. Olson, Henry 1. Osner, Robert James L. Current· David B. Damiano, Wil• A. Chapman, Ronald J. Chase, Elly C. Claus, Osserman, Clem Z. Ota, Albert D. Otto· liam D. Dickey, James M. Dolan, Robert S. Daniell. A. Cohen, Flavia Colonna*, Rob• William H. Peirce, Joseph Pekarsky, Stephen Doran, Avron Douglis, Jean Doyen, Regina ert J. and Beatrice Cone, Richard J. A. Pennell, W. T. Puckett· John E. Rawson, C. Dukes • Earl F. Ecklund, Wade Ellis, Jr. Cunningham· Peter G. De Buda, Kotaro Maxwell O. Reade, Francis Regan, Bruce and Jane Ellis (In Memory of Wade and Dokeh, Veronica M. Dort, Harold L. A. Reznick, Robert M. Richardson, Norman Agatha Ellis), Edor Engvall· Arnold L. Fass, Dorwart, James B. Dowling • Elwood G. J. Richert, Stanley J. Rocko, William M. Irwin K. Feinstein, William A. Feldman, Edwards, Alexander S. Elder, George W. Rodgers, Miguel A. Rodriguez-Estrada, Joan Helaman Ferguson, Alan Filsinger, Abraham Ellis, Raymond L. Ely, Susanna S. Epp, R. Rosenblatt*, George M. Rosenstein, B. Finkelstein, William M. Finlay, Roderick Thomas G. Errico, Michael Evan • Frank D. Haskell P. Rosenthal, Shepley L. Ross, Mat• J. Fletcher, Thomas J. Fritsch • Lisl N. Gaal, Faulkner, Ismor Fischer, Charles R. Fleenor, thew B. Rudd, Charles J. Rykken • Mayra Pedro J. Geraldo, Kerry E. Grant, Eric W. Richard J. Fleming, Peter R. Flusser, Herta Alonso San Roman, John M. Sawka, Blin B. Gray, John C. Griffin, Natalio H. T. Freitag, Jiro Fukuta, Stephen A. Fulling • Scatterday, Paul T. Schaefer, John J. Schiller, Guersenzvaig, Wynne A. Guy· Peter J. JosephA. Gallian,Ann C. Garstang, Eugene Anne J. Schimmel, Ernest C. Schlesinger, Hagis, Gena Hahn, Milton W. Harden, Jerry M. Gaydos, Claudia M. Giamati, Maurice John Schue, Sanford L. Segal, Tracey A. M. Hawn, R. B. Herrera, Walton B. Hill, E. Gilmore, Michael J. Gilpin, Ross B. Serle*, Henry Sharp, Ching-Kuang Shene, Jean M. Hom, Joy Hsiao, G. Perry Hudkins, Gingrich, Michael Glass, J. K. Goldhaber, Alpha Shirey, K. Shoemaker, Allan J. Cephas D. Hughes, Patricia M. Hughes, Leonard D. Goldstone, R. N. Goss, Eric J. Silberger, Lloyd D. Simons, Robert C. George A. Hutchinson, John A. Hymo· Jo• and Florence Gossett, Ronald A. Gove, Simonsen, Marguerite G. Simpson*, David seph A. Iaia, Godfrey L. Isaacs, John Ivery Adonis L. Gray, Ronnie Green, Josephine P. A. Singer, John S. Skocik, David L. Skoug, • Peter M. Jarvis, Arthur H. Jerbert, Maria

33 FOCUS August 1995

Guadalupe Jimenez, Wendy R. Jogasurya, Saladin, Luis C. Salinas, N. Paul Schembari, Executive Director from page 21 Marsha Finkel Jones • Nancy E. Kane*, Irene V. Schensted, Hans Schneider, Gre• Miranda Katsoyannis* and Michael gory A. Schou, Betty L. Schulte*, Christo• Paraloglou*, Vernon M. Kays, Michael pher J. Scott, Mark L. Seligman, Antonio that through the Planned Giving Program, Kerrigan, Eric S. Key, John O. Kiltenen, Serraima, Anthony J. Seyko, Jay A. Shapiro* , the MAA will eventually build its endow• Donald R. King, Debra J. Knisley, Deborah Charles M. Shenitz, Jack Silber, Thomas H. ment base to a level which assures service R. Kula, John S. Kulesza*, John F. Kurtzke Slook, Daniel D. Slosberg, Elizabeth L. to the next generation of mathematicians. • W. Clark Lambert, Martin D. Landau, Pe• Smith, Lloyd B. Smith, Samuel E. Smith, ter S. Landweber, Lester H. Lange, Suzanne Robert I. Snell, Charles G. St. Pierre, Brian Conclusion L. Larson, David F. Lawson, Lew E. Lefton, Steigerwald, Michael Stein, Enid M. Katharine Leggat, Robert N. Leggett, Steinbart, Charles I. Steinhorn, Philip P. The MAA is changing as we seek new Solomon Leibowitz, D. A. Lentz, Edward Stich, Emmanuel Stogiannis, Donald W. ways to provide more and better services Lever, Andrew M. Lewis, Teck C. Lim*, Jeng Stokes, Clarence B. Stortz, Jeffrey L. Stuart, to our members, recruit into membership Eng Lin*, Charles Lipp, Clement H. Beverly Suhr, Charles S. Sutton, Ronald and active participation more people who Lutterodt • Elizabeth A. Magarian, Richard Sverdlove, Josef V. Swatek, Andrzej A. value collegiate mathematics, and make 1. Marchand, Jerrold E. Marsden, James R. Szymanski· Jeanette H. Tanaka, Ronald F. the case with the public and the govern• Marshall, Mario U. Martelli, Gus Mavrigian, Thurston, Horace W. Tousley· Yasushi Unai ment about the importance of quality Charles N. Maxwell, Byron L. McAllister, • Jan A. Van Casteren, Richard A. mathematics education for all. And yet in Roy H. McLeod, Robert F. McNaughton, J. VanDervelde, Andrew H. Van Tuyl, many ways, the MAA is still the same G. McPhail, Morris Meisner, John G. Kumaraswamy Velupillai, Robert C. Vow• organization that it was, an organization Milcetich, Michael H. Millar, C. David els • David F. Walnut*, Edward T. H. Wang, Minda, Anna S. Morley*, Cecil A. Morris, Alan Wayne, John C. Weaver, Willes L. where professional friendships can blos• Joseph M. Moser, H. Deon Murphy, Michael Werner, Agnes J. Wieschenberg, Herbert S. som, where young people can be encour• G. Murphy· Saeid Kazemy Naeiny, Donald Willcox, Timothy R. Wilson, Kebenesh aged, where excellence in the teaching and E. Niman, Ronald D. Notestine • Joseph W. Wondimagegnehu, Bing K. Wong, Jerry D. writing of collegiate mathematics can be Paciorek, Helen L. Paisner, Elwood G. Woods, Tadg H. Woods, ScottD. Woodward, recognized and rewarded, and where, in Parker, N. T. Peck, John W. Pennisten, David J. Wydra, N. Convers Wyeth· Anne cooperation with our sibling organizations, Hoshang Pesotan, G. Edric Phillips, John A. L. Young* • Ben F. Zirkle we can inform and influence national poli• Poluikis, Miller S. Puckette • R. Michael cies affecting mathematical education at Range, Bernardo Recaman, Sharon A. *lndicates the names ofthose donors who all levels. Richards, Allan Richert, David W. Roeder, contributed to a Greater MAA Fund me• Linda E. Rogers*, Edouard Ryser· Yves morial to John Melvin Smith. New Fpom the MAA Circles: A Mathematical View Dan Pedoe Revised edition rem. In an appendix, Pedoe includes a biographical sketch of Illuminates the fundamental aspects of college geometry, non• Karl Wilhelm Feuerbach, a little known mathematician with a Euclidean geometry, and other branches ofmathematics where tragically short life, who published his theorem in a slender the circle plays an important role. geometric treatise in 1822. No school or undergraduate mathematics library should be Readers of Circles need only be armed with paper, pencil, without this book. compass, and straightedge to find great pleasure in following London Times Education Supplement the constructions and theorems. Those who think that geom• This revised edition of a mathematical classic originally etry using Euclidean tools died out with the ancient Greeks published in 1957 will bring to a new generation of students will be pleasantly surprised to learn many interesting results the enjoyment of investigating that simplest of mathematical which were only discovered in modern times. And those who figures, the circle. As a concession to the general neglect of think that they learned all they needed to know about circles in geometry in school and college curricula, however, the author high school will find much to enlighten them in chapters deal• has supplemented this new edition with a special chapter de• ing with the representation of a circle by a point in three-space, signed to introduce readers to the vocabulary of circle con• a model for non-Euclidean geometry, and the isoperimetric cepts with which the author could assume his readers of two property of the circle. generations ago were familiar. For example, Pedoe carefully 144 pp,. Paper, 1995 explains what is meant by the circumcircle, incircle, and en• ISBN-O-88385-518-6 circles of a triangle as well as the circumcentre, incentre, and orthocentre. The reader is then well equipped to understand MAA Member: $14.50 List: $18.95 his discussions ofthe nine-point circle and of Feuerbach's theo- Catalog Code: CIRCLESIFOC

34 August 1995 FOCUS MATH HORIZONS IF YOU DON'T GET IT, YOU'LL NEVER KNOW WHAT YOU'RE MISSING! That's right. The September 1995 issue had just appeared filled with exciting articles such as A 15,OOO-Word Proof, Marketing Your Math Skills, Gaggles of Geeks, and much more. Don't continue to miss out. Subscribe now! ~------I Yes! Renew my subscription to Math Horizons. Individual Subscription (Individual subscriptions must be pre-paid) Please send __ copies.

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Mail to: Math Horizons, 1529 Eighteenth Street, N.W., Washington, DC 20036 Fa9S I L ______:.....J FOCUS August 1995 New Fl'om the MAA New Mathematical Diversions Martin Gardner Mathematical jokes, mathematical magic, and a dose 01 lun

Offered here are twenty reprints from Martin Gardner's • The Transcendental Number Pi monthly column in Scientific American. Gardner tells us that • Victor Eigen: Mathemagician his book is a book of "mathematical jokes," if "joke" is taken • Polyominoes and Fault-Free Rectangles in a sense broad enough to include any kind of mathematics • Euler's Spoilers: The Discovery of an Order-I 0 that is mixed with a strong element of fun. Readers of this Graeco-Latin Square book will be treated to a heavy dose of fun, and it is very pos• • The 24 Color Squares and the 30 Color Cubes sible that they will learn some mathematics along the way. • Bridg-it and Other Games Martin Gardner instructs us about mathematics as he enter• Answers are provided for these problems, as well as tains us with his wit and sense of the absurd. Always the mas• references for further reading and a bibliography. Martin ter expositor, the ideas presented in his books have stimu• Gardner's Postscript section provides updates to the problems. lated, challenged and delighted generations of readers. Mar• tin Hollis (in New Scientist) says it best when he says of 272 pp., Paperbound, 1995 Gardner's work, "Should you ever need to explain subatomic particles to a Stone-age man, send for Martin Gardner... He ISBN 0-88385-517-8 leaves open questions open, conveys the thrill of the chase and MAA Member: $16.50 List: $19.95 deals flawlessly with hard and simple ideas alike." Catalog Code: DIVERIFOC Some of the problems you will find here are: • Group Theory and Braids • The Games and Puzzles of Lewis Carroll

A Practical Guide to Cooperative Learning in Collegiate Mathematics Nlncy L. Hlllillns, Blrblrl E. Rlynolds, SDS, Kllth Schwlnllndorl, Drill Vldlkovlc, Ed Dubinsky, Mazln Shlhln, G. Joslph WimbiSh, Jr.

This book will greatly help readers introduce cooperative learn• work that can be expected of students in cooperative learning ing in their own undergraduate mathematics classes. Anyone groups. The authors present methods for monitoring groups interested in cooperative learning will find valuable informa• and dealing with problems that may arise in a cooperative learn• tion in this book. The book reflects the extensive experience of ing environment. They also address the question of student the authors as well as that of over forty colleagues who re• assessment. An extensive and annotated bibliography is also sponded to a survey on cooperative learning. Throughout the included. book cooperative learning is related to educational research results, which are clearly explained in one chapter. 192 pp., Paperbound, 1995 The book includes directions for organizing students into groups ISBN 0-88385-095-8 as well as complete descriptions of what these groups do once MAA Member: $14.95 List: $18.95 they are formed. Examples of group problems and grouped test questions for various mathematics courses illustrate the Catalog Code NTE-37IFOC

36 August 1995 FOCUS New FI'om the MAA She Does Math Real-Lile Problems Irom Women on the Job Marla Parker, ElInor A CIII"I'oom ResouI'ce Fol' Tellchel's of gl'lIdes 8 thl'ough the I/I'st yelll' of college She Does Math presents the career histories of 38 professional • It demonstrates the surprising variety of fields in which math- women and math problems written by them. Each history de• ematics is used. Some examples: scribes how much math the author took in high school and Archaeology: Learn how archaeologists use mathe matics college; how she chose her field of study; and how she ended to study pollen and thus understand the environmental up in her current job. Each of the women presents several prob• changes that occurred in a North American Indian village a lems she had to solve in her job. thousand years ago. There are lots of good reasons to buy this book: Fish Pathology: Learn how a fish pathologist gives medi• • It contains many real-life problems. When students ask you, cine to a large population of fish or helps prevent them from "Why do I have to learn algebra (or trigonometry or geom• getting the "bends." etry)?" you will find many answers in its pages. Students will Ophthalmology: Learn how an ophthalmologist helps a pa• welcome seeing the situations from real-world jobs where tient suffering from double vision by determining the power the math skills you are teaching are actually used. of prism needed in the patient's eyeglasses to correct the • It provides your students with strong female role models. Girls problem. need these role models to help them imagine themselves in 272 pp., Paper, 1995 good, technical jobs. Both girls and boys need these role models to help imagine themselves working professionally ISBN 0-88385-702-2 with women as managers, colleagues, and subordinates. MAA Member: $18.50 list: $24.00 • It supplies practical information about the job market to your Catalog Code: SDMlFOC students. They will learn that they can only compete for these interesting, well-paying jobs by taking mathematics through• out their high school and college years.

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37 FOCUS August 1995 ANMM

DENTS beco of the world's largest on dev,!_ interests of college math- rest an4 citement among your mathematics rage more students to consider careers in the math sciences. MAA Student Chapters are devoted to increasing student involvement with mathematics, careers, and mathematicians at the national and local levels.

Student Chapter members: What some CHAPTERS do: • join the MAA at reduced rates • organize scavenger hunts for high school • receive travel support for paper presenta- students tions at the summer mathematics meetings • publish newsletters distributed to math • receive notification of student activities at majors and alumni math majors the national mathematics meetings which • write articles about mathematics for the include a Student Lecture, a Student Work• school newspaper, and organize a puzzle shop and the Student Hospitality Center • contest • receive career information 8 Pft!sent a campus-wide evening of • automatically become members in • ematics for the non-technical majo the MAA's 29 regional :>eCliOllS • course sor student workshops, arrange for speakers "Bernoulli Boys a

To receive more information on Student Cha-··!I>"III! Jane Heckler, MAA, 1529 18th Street, NW. Washington. e-mail: [email protected] or call 1-800-331-1 MAA.

38 August 1995 FOCUS

E\lPLO' \IE"T OPPOI{ n "!TIES Notice to Employment Advertisers Rates for FOCUS Employment Ad• The Board of Governors of the MAA is asking departments that are considering hiring vertisements are $65.00 per column temporary faculty to one-year positions to convert these to multi-year positions if at all inch (one inch minimum), billed to possible. In addition, those departments that plan to hire temporary faculty for the next the nearest 1/2 inch. 5-10 years are urged to work with their administrations to convert these temporary All advertisements are set with a one• positions to tenure-track positions. line headline, centered, boldface, consisting of the institution name, un• It is our belief that the repeated hiring of temporary faculty not only impedes the career less additional headline information development ofthe young mathematicians holding these positions, but also increases the is provided. Ads will appear in the work load of permanent faculty. An individual in a one-year position must begin search• same language in which they are sub• ing for a new job every October. He or she does not have the time and energy, and, indeed, mitted. can hardly be expected to contribute to the life of the department and of the institution. FOCUS offers a 15% discount for the It is our hope that those departments that have been forced to hire temporary faculty on same advertisement in three or more a regular basis will be able to work with their administrators in order to reduce or consecutive issues. All invoices in• eliminate this practice. clude a tear sheet. Advertising Copy Deadlines: The first of the month, two months prior to publication. FOCUS Continuing Position Brooks/Cole Publishing is published in February, April, June, Department of Mathematics 511 Forest Lodge Road August, October, and December. Southern Illinois University at Pacific Grove, CA 99350 Advertisers should contact: Amy Carbondale Applications are invited for Associate Technical Carbondale, Illinois 62901 Editor. The Associate Technical Editor is directly Fabbri, FOCUS Advertising Coordi• Applications are invited from qualified candi• involved in the acquisition, production, market• nator, The MAA 1529 18th St., NW, dates for a tenure track position at the assistant ing, and support of technology-based products. Washington, DC 20036; (202) 387- professor level beginning on August 16, 1996. Responsible for presigning, developmental, and 5200; fax: (202) 265-2384; e-mail: Ph.D. in mathematics required at the time of ap• quality assurance reviews of new and revised [email protected] plication. Preference will be given to applicants products. Assists with demonstrations at profes• in the areas of combinatorics, dynamical systems, sional meetings, sales rep. and software support ordinary or partial differential equations, prob• rep training. Applicants must have experience in ability and topology. Candidates must have developing and using software in instruction. demonstrated excellence in research. All appli• Address application to Robert Evans, Director of cants must provide evidence of excellence in Electronic Publishing. Alternatively applications teaching and evidence of the ability to teach in may be sent to [email protected]. To English effectively. Send letter of application, be considered applications must be received be• resume, and three letters of recommendation to: fore July 15, 1995. Continuing Position do Ronald B. Kirk, Chair Department of Mathematics Southern Illinois University at Carbondale Carbondale, Illinois 62901 Educational Testing Service (ETS), the nation's leading educational testing and measurement orga• The closing date is October I, 1995, or until the nization, has an immediate opening with an ideal opportunity for professional growth in a stimulating position is filled. SIUC is an equal opportunity! environment. affirmative action employer. Women and minori• The Associate Examiner we seek will develop and assemble tests in mathematics to meet client ties are particularly encouraged to apply. specifications. You will be involved in the research, writing and review of test items and will perform all procedural steps associated with the test development process. Handling preliminary cost esti• mates, developing test-related surveys and studies and arranging/conducting committee meetings are among other diverse responsibilities of the position. Qualifications include a Master's degree in mathematics or computer science, or a closely related field (e.g. mathematics education or measurement and statistics), along with 4 years of related work experience in teaching, testing math or computer science. Additional course work and degrees desir• able. Knowledge of current trends in mathematics/computer science desirable. An equivalent combi• nation of education and experience acceptable. Excellent communication and analytical skills, plus the knowledge a~ abilities to meet the above-described requirements are essential prerequisites. ETS offers a competitive salary, commensurate with experience, a comprehensive benefits pack• age and an environment distinguished by individual achievement. For confidential consideration, please submit a resume, including salary history to: Ms. P. Marks EDUCATIONAL TESTING SERVICE Rosedale Road, Princeton, NJ 08541 Fax: (609) 734-8486 As an Equal Opportunity/Affirmative Action Employer with a commitment to diversity. ETS actively encourages nomina· tions and applications from women, candidates of diverse racial and ethnic backgrounds and differing physical abilities.

39 Calendar National MAA Meetings LOUISIANA-MISSISSIPPI March 1- SEAWAY November 3-4, 1995, 2 1996, Southern University, Baton Rouge, Skidmore College, Saratoga Springs, NY January 10-13, 1996 Seventy-ninth An• LA nual Meeting, Orlando, FL. Board of March 1996, Elmira College, Elmira, NY Governors Meeting January 9, 1996 February 28 - March I, 1997, Millsaps November 8-9, 1996, SUNY College at College, Jackson, MS January 9-7, 1997 Eightieth Annual Geneseo, Geneseo, NY Meeting, San Diego, CA. Board of SOUTHEASTERN April 12-13, 1996, Governors Meeting January 8, 1997 MICHIGAN May 10-11, 1996, Siena University ofAlabama-Huntsville, Hunts• January 7-10,1998 Eighty-firstAnnual Heights College, Adrian, MI ville, AL Meeting, Baltimore, MD. Board of MISSOURI April 12-13, 1996, South• SOUTHERN CALIFORNIA October Governors Meeting January 6, 1998 east Missouri State Univ., Cape Girardeau, 21-22, 1995, Cal Poly tech State Univer• MO sity, San Luis Obispo, CA (joint meeting Sectional MAA Meetings Spring 1997, Missouri Western State Col• with N. California Section) ALLEGHENY MOUNTAIN April 12- lege, St. Joseph, MO TEXAS March 28-30, 1996, Texas Tech 13, 1996, Indiana University of Pennsyl• Spring 1998, Southwest Missouri State University, Lubbock, TX vania, Indiana, PA University, Springfield, MO Spring 1997, Texas Lutheran College, EASTERN PA & DELAWARE Novem• NEBRASKA-SOUTHEAST SOUTH Seguin, TX ber 4, 1995, Penn State University• DAKOTA April 19-20, 1996, Univ. of Spring 1998, Southern Methodist Univer• Ogonta, Abington, PA Nebraska-Kearney, Kearney, NE sity, Dallas, TX April 13, 1996, Millersville University, NEW JERSEY November 18, 1995, WISCONSIN April 12-13, 1996, Univer• Millersville, PA Rutgers University-Busch Macpus, New sity of Wisconsin-Platteville, Platteville, Fall 1996, Delaware State University, Brunswick, NJ WI Dover, DE NORTH CENTRAL October 20-21, ILLINOIS March 1-2 1996, Monmouth 1995, North Dakota State University, Other Meetings College, Monmouth, IL Fargo, ND September 29-30,1995 Twenty-thirdAn• INDIANA November 4, 1995, Taylor April 1996, Hamline University, St. Paul, nual Mathematics and Statistics Confer• University, Upland, IN MN ence, Miami University, Oxford, OH; March 29-30, 1996, Butler University, NORTHEASTERN November 17-18, theme: mathematical modeling in under• Indianapolis, IN 1995, Salem State College, Salem, MA graduate curriculum; principal speakers: October 26, 1996, Rose-Hulman Institute June 7-8, 1995, 1996, Hampshire College, John Casti, Daniel Maki, Philip Straffin. of Technology, Terre Haute, IN Amherst, MA Abstracts for contributed papers and re• quests for pre-registration and housing Spring 1997, Franklin College, Franklin, November 22-23, 1996, University of information should be sent to Prof. Doug IN Massachusetts-Boston, Boston, MA Ward, Dept of Math & Statistics, Miami INTERMOUNTAIN April 19-20, 1996, NORTHERN CALIFORNIA October University, Oxford, OH 45056; (513) Mesa State College, Grand Junction, CO 21-22, 1995, Cal Poly tech State Univer• 529-5815; fax: (513) 529-3841. (joint meeting with Rocky Mountain Sec• sity, San Luis Obispo, CA (joint meeting tion) with S. California Section) October 12-24, 1995 Seventeenth Annual Meeting ofthe North American Chapter IOWA April 26-27, 1996, Cornell Col• March 2, 1996, Sonoma State University, of the International Group for the Psy• lege, Mt. Vernon, IA Rohnert Park, CA chology of Mathematics Education KANSAS Spring 1996, McPherson Col• OKLAHOMA-ARKANSAS March 22- (PME-NA XVII), Columbus, OH. For lege, McPherson, KS 23,1996, Westark Commuity College, Fort more information, contact Doug Owens, KENTUCKY March 29-30, 1996, Smith,AR 253 Arps Hall, The Ohio State Univer• Murray State University, Murray, KY ROCKY MOUNTAIN April 1996, Mesa sity, 1945 North High Street, Columbus, State College, Grand Junction, CO (joint OH 43210-1172; (614) 292-8021;; e• meeting with Intermountain Section) mail: Owens.93@ osu.edu. FOCUS AUGUST 1995 The Mathematical Association of America Second class postage paid al Washington. DC and 1529 Eighteenth Street, NW additional mailing offices Washington, DC 20036-1385