Section Distinguished Teachingawards

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See Page 3 Section Distinguished TeachingAwards See Page 6 FOCUS August 1993 Table ofContents FOCUS is published by The Mathemati• cal Association of America, 1529 Eighteenth Street Northwest, Washing• ton, DC 20036-1385, six times a year: February, April, June, August, October, Features and December. Editor: Keith 1. Devlin, St. Mary's Col• Fermat's Last Theorem 3 lege ofCalifornia

Associate Editor: Donald J. Albers, MAAAssociate Executive Director, and Director ofPublications and Programs Twenty-Second

Chair ofthe MAA Newsletter Edito• Mathematical Olympiad 5 rial Committee: Joseph A. Gallian, University of Minnesota at Duluth SectionAwards for Distinguished Managing Editor: Harry Waldman, MAA Collegeor University Mathematics

Production Specialist: Amy E. Teaching 6 Stephenson, MAA

Subscribers should address letters to the editor: Keith Devlin, St. Mary's College NSF Conference on Statistics Education 8 of California, Moraga, CA 94575. E-mail: [email protected]

The FOCUS subscription price to indi• vidual members of the Association is The 1992MAAAnnualReport 13 $6.00, included in the annual dues. (An• nual dues for regular members, exclusive of annual subscription prices for MAA journals, are $68.00. Student and unem• Starting an Industrial Postdoctoral Program 32 ployed members receive a 66 percent discount; emeritus members receive a 50 percent discount; new members receive a 40 percent discount for the first two membership years.) Copyright © 1993 by The Mathematical Association of America (Incorporated). Educational institutions may reproduce articles for their own use, but not for sale, provided that the following citation is Departments used: "Reprinted with permission of FOCUS, the Newsletter ofThe Math• ematical Association ofAmerica Editorial 10 (Incorporated), 1993." Second-class postage paid at Washing• ton, DC and additional mailing offices. Personal Opinion 11 Postmaster: Send address changes to the Membership and Subscriptions Depart• ment, The Mathematical Association of America, 1529 Eighteenth Street North• Employment Opportunities 35 west, Washington, DC 20036-1385. ISSN: 0731-2040 Printed in the United States of America. Printed on recycled paper August1993 FOCUS

i = x(x - an)(x+if) Fermat's Last Theorem, in the way proposed by Taniyama. Follow• ing an appropriate re-formulation by Jean-Pierre Serrein Paris, Kenneth Ribet in a Theorem at Last Berkeley strengthened Frey's original con• cept to the point where it was possible to Keith Devlin, Fernando Gouvea,andAndrew Granville provethat the existenceofacounterexample to the LastTheoremwould lead to the exist• After defying all attempts at a solution for different direction, and rests on an amazing ence ofan elliptic curve which could not be 350 years, Fermat's Last Theorem finally connection, established during the last de- modular, and hence would contradict the tookits placeamongthe knowntheoremsof cade, between the Last Theorem and the Shimura-Taniyama-Weil conjecture. mathematics in June ofthis year. theory ofelliptic curves, that is, curves de• termined by equations ofthe form This is the point where Wiles entered the On June 23, during the third of a series of picture.Usingand developingpowerfulnew lectures at a conference held at the Newton i=r +ax+b, methodsofBarryMazur(Harvard),Matthias Institute in Cambridge, British mathemati• where a and b are integers. Flach (Heidelberg), Victor Kolyvagin cian Dr Andrew Wiles, of Princeton (Steklov Institute), and others, Wiles even• University, sketched a proof the Shimura• The path that led to the June 23 announce• tually succeeded in establishing the Taniyama-Weil conjecture for semi-stable ment began in 1955, when the Japanese Shimura-Taniyama-Weil conjecture for an elliptic curves. As Kenneth Ribet, of the mathematician Yutaka Taniyama proposed importantclass ofellipticcurves(thosewith UniversityofCalifomiaatBerkeley, showed that there should be a connection between square-free "conductors"), which includes someyears ago, Fermat's LastTheoremis a elliptic curves and another well-understood those relevant to proving Fermat's Last corollary ofthis result. class of curves, known as modular curves. Oneshouldbe able to establish a connection Theorem. In the years since Fermat made his famous betweenany given elliptic curveand amodu• For the Cambridge conference, Wiles had marginal note in his copy of Diophantus' lar curve, and this connection would announcedhis lectures, a series ofthree given Arithmetica, asserting, without proof, that "control" many ofthe properties ofthe ini• on successive days, with the highly unspe• equations of the form tial curve. cific title "ModularForms, Elliptic Curves, x"+y"=z" Taniyama'sconjecture was made morepre• and Galois Representations." Prior to his lectures, he refused to give a hint as to what have no integer solutions for values of the cise in 1968 by Andre Weil, who showed they mightcontain.Eventhough, by the third exponent n greater than 2, many mathema• how to determine the exact modular curve talk, many in the audience had guessed he ticians, professionals and amateurs alike, that should be connected to a given elliptic mighthave crackedFermat'sLastTheorem, have tried to find a proof. Every few years, curve. few dreamt that he could have proved so the newspapersreportyet anotherpurported In 1971 the first significant evidence in fa• much more, and there was an audible gasp solution, which is subsequently found to be vor of this abstract understanding of as he wrote the final result on the black• lacking in some way. equations was given by Goro Shimura, a board. To understand why Wiles has succeeded Japanese mathematician at Princeton Uni• Given the history of attempts to prove the where so many before himhave failed, one versity, who showed that it works for a very Last Theorem, readers will doubtless view needs to know something ofthe recent his• special class of equations. As a result, this latest announcement with some initial tory ofthe problem. Taniyama's proposal eventually became knownas the Shimura-Taniyama-Weil con• skepticism. But it should be stressed that To number theorists, until the last decade jecture. Wiles' work is not a chain of reasoning as the question seemed completely unassail• strong as its weakest link. Instead it is a able, despite a number of significant Additional evidence in support of the con• bedrock ofideas, solid and rigid, a rich and advances that had been made as a result of jecture came from the fact that its nature profound theory that will hold up even if a attempts to solve it, among them the 19th allowed for a substantial amountofnumeri• few details need altering. Considering the century work of Kummer on cyclotomic cal testing by computer: all curves that were enormouscomplexityofthis workit will, of fields and ideal theory. examined seemed to be modular. course, take time to be absolutely certain that there are no hidden flaws, but the ex• Morerecently, there was GerdFaltings, 1983 But so far, no one knew of any connection perts feel confident that even any necessary proofofthe Mordell Conjecture, which im• between this very abstract conjecture and changes will be possible. Many of these plied that for each exponent, the Fermat Fermat'sLastTheorem.Thingschangeddra• expertswere attendingWiles'talks, and from equationcouldhaveat mosta finite number maticallyin 1986, whenGerhardFrey, from what he said and the way he said it, they of solutions. But, despite much simpler Saarbrucken, discovered a most surprising were satisfied that the techniques are, in es• proofs ofVojta and Bombieri, it seems un• and innovative link between the two. sence, sound. likely that such methods can be modified to Whathe realized was thatifen = an +if,then show that there really are no solutions. it seemedunlikelythat one couldunderstand The situation is a bit like building a bridge across a chasm. Most attempts to solve the Wiles' approach comes from a somewhat the elliptic curve given by the equation Please see Fermat on page 4 FOCUS August1993

Fermatfrom page 3 Last Theorem made by amateurs are like a The Technical Details single span consisting ofmany short pieces Shortly after Wilesfinished his lecture, DrKenneth Ribet, ofthe University ofCalifornia ofwire tied together. One small flaw and the at Berkeley, who was in the audience. sent out the following summary ofthe proofto entire structure collapses. Wiles' solution is colleagues at Berkeley, where the excitement it createdled to its rapidappearance on the much more like a solid concrete and steel Internet. The message is reproduced here with his permission. bridge, erected on firm foundations laid down by many others. Itmay contain many I imagine that many ofyou have heard rumors about Wiles's announcement a few hours small cracks, but the bridgeitselfstill stands, ago that he can prove Taniyama's conjecture for semistable elliptic curves over Q.This and the road crew can comealonglater to fill caseofthe Taniyamaconjecture implies Fermat'sLastTheorem, in view ofthe result that in the cracks. Of course, even solidly built I proved a few years ago. (I proved that the "Frey elliptic curve" constructed from a bridges do fall down occasionally, but the possible solutionto Fermat'sequationcannotbe modular, i.e., satisfy Taniyama'sConjec• natureof Wiles ' work, whichinvolvesmany ture. On the other hand, it is easy to see that it is semistable.) appreciable, profound new ideas, suggests The method of Wiles borrows results and techniques from lots and lots of people. To that this is not such a bridge. mention a few: Mazur, Hida, Flach, Kolyvagin, yours truly, Wiles himself(older papers Taking the bridge metaphor a step further, by Wiles), Rubin... The way he does it is roughly as follows. Start with a mod p represen• one might ask what is to be found on the tation ofthe Galois group ofQwhich is known to be modular. You want to prove that all other side? Well, it is likely that the proofof its lifts with a certain property are modular. This means that the canonical map from the whole of the Shimura-Taniyama-Weil Mazur'suniversal deformationring to its "maximal Heekealgebra" quotientis an isomor• conjecture is at hand, and the consequences phism.To provea map like this is an isomorphism, you can give somesufficientconditions are breathtaking. The face of numbertheory basedon commutativealgebra. Mostnotably, you have to boundthe orderofa cohomology will be altered in a way that we cannot even group which looks like a Selmer group for Sym2 of the representation attached to a guess right now. modular form. The techniques for doing this come from Flach; you also have to use Euler systems a la Kolyvagin, except in some new geometric guise. The story of Fermat's Last Theorem is one ofthe most delightful in mathematics, and if Ifyou take an elliptic curve over Q, you can look at the representation of Gal on the 3• it had to finally be resolved then perhaps it division points ofthe curve. If you're lucky, this will be known to be modular, because of was best to be as the motivation for such a results ofJerry Tunnell (on base change). Thus, if you're lucky, the problem I described startling result. above can be solved (there are most definitely some hypotheses to check), and then the curve is modular. Basically, being lucky means that the image of the representation of Certainly, the method used to obtain the so• Galois on 3-division points is G42, Z13Z). lution is of far more importance to mathematics than the Last Theorem itself. Suppose that you are unlucky, i.e., that your curve E has a rational subgroup oforder 3. Indeed, had it not entered the mathematical Basically by inspection, you can prove that if it has a rational subgroup oforder 5 as well, world the way ithad, as acryptic note by one then it can't be semistable. (You look at the four non-cuspidal rational points of XO(I5).) of the most powerful number theorists the So you can assume that E[5] is "nice." Then the idea is to find an E' with the same 5• world has ever seen, and had it not resisted division structure, for which E'[3] is modular. (Then E' is modular, so £[5] = E[5] is all attempts at a solution for so many years, modular.) You considerthe modularcurveX which parametrizeselliptic curves whose 5• the Last Theorem would have merited little division points look like E[5]. This is a "twist" ofX(5). Itis therefore ofgenus 0, and it has more than a footnote to textbook accounts a rational point (namely, E), so it is a projective line. Over that you look at the irreducible of Pythagoras' Theorem. But the Wiles re• covering which corresponds to some desired 3-division structure. You use Hilbertirreduc• sult, and the work of the many other ibility and the Cebotarev density theorem (in some way that hasn'tyet sunkin) to produce mathematicians that paved the way, is sure a non-cuspidal rational pointofX overwhich the covering remains irreducible. You take to have enormous impact in many parts of E' to be the curve corresponding to this chosen rational point ofX. mathematics. - Ken Ribet, June 23, 1993, Cambridge, England. The next issue of FOCUS willinclude a much more detailed account of Wiles' new proof. Marginal Interest? Dr Andrew Granville, ofthe University of Georgia, spent the last six months at the With Fermat's Last Theorem no longer around as "the most famous unsolved problem in Newton Institute at Cambridge, and attended mathematics," what else can science journalists and writers of popular books on math• the lectures at which Wiles sketchedhis new ematicsuse to spice up their writing?FOCUS invites readers to submittheir own "marginal proof. Dr Fernando Gouvea, a collabora• comment," and the best ones received will be published in a future issue. To qualify, your tor with, andformerstudentof, Mazur; is on problem should be short, simple for the layperson to understand, but should appearto defy thefacultyatColbyCollege. DrKeith Devlin solution by "elementary" methods-except, ofcourse, for the truly marvellous proofthat is the Dean ofScience at Saint Mary sCol• will not fit into the margin of FOCUS, which you may keep to yourself. Send your lege ofCalifornia, andthe editorofFOCUS. suggestions to: Keith Devlin, Editor, FOCUS, School ofScience, Saint Mary's College, Moraga, California 94575, email [email protected]. ~------August1993 FOCUS Twenty-second USA Mathematical Olympiad Winners Honored

Lisa Kolbe with HP 49SX calculators. USAMO Organizer Hewlett-Packardhas been a long-standingcontributorto Winners ofthe Twenty-second USA Math• the USAMO Awards Cer• ematical Olympiad were honored at a two emonies. day celebration in Washington on June 6 and 7. Members of the mathematical sci• On Monday morning, the ences community, the federal government, winners, their parents, and andprivateindustryrecognizedtheirextraor• members ofthe mathemati• dinary achievement and extended their cal sciences community congratulations to the winners. They were: were invited to attend a se• ries of lectures by National Wei-Hwa Huang, First Place, Science Foundation math• Potomac, Maryland ematicians. Dr. Fred Wan, Director, Division of the Robert D. Kleinberg, First Place, MathematicalSciences, and Wales Center, New York Dr.Judith Sunley,Executive Back row: Carol Westfall, AMATYC; Ron Graham, AMS; Mary Officer ofthe Mathematical Lindquist, NCTM; Donald Krieder; MAA; Carol McGill, Mu Alpha Lenhard Ng, Third Place, Theta; Glenn Walker; CAS; Bryan Hearsey, SA; Frank Rhodes, SA. Chapel Hill, North Carolina and Physical Sciences Di• rectorate, welcomed the Front Row: Jonathan Weinstein, Andrew Schultz (1992 winner), Lenny Jeremy D. Bern, Fourth Place, Ng, Robert Kleinberg, Joseph Hundley, Wei-Hwa Huang, Andrew winners on behalf of the Dittmer; Timothy Chklovski, Jeremy Bem. Ithaca, New York NSF.Dr. Keith Crankspoke Andrew O. Dittmer, Fifth Place, on Probability and Computers, Dr. Roubon presented. Engraved silver trays were given Vienna, Virginia Rastamian address was titled,"How toBuild to the winners by IBM representative Dr. a Poker Table: A Mathematician's Ap• James Wynne. The 1993 guest speaker was Timothy Chklovski, Fifth Place, proach," and Dr. William Velez spoke on Dr.Joseph A. Gallian, UniversityofMinne- Hopkins, Minnesota Number Problems in Elementary Number Please see Olympiad on page 33 Jonathan L. Weinstein, Seventh Place, Theory. Lexington, Massachusetts An afternoon tea was the setting for the Joseph A. Hundley, Eighth Place, first USAMO winners' reunion. Itwas Chicago, lllinois a particularly poignant occasion be• cause 1993 winners and alumni THE WHITE HOUSE The festivities began with the Sponsors' honored Professor Emeritus Nura D. June 2. 1993 Reception at the Dolciani Mathematical Turner, whose work and dedication to Center, where MAA officers, representa• the USAMO ceremonies is unsur- I am delighted to extend my congratUlations tives from sponsoring organizations, and the to the winners of the 1993 United States Mathematical passed.TheMAApresented Olympiad. I commend you for the hard work and USAMOSubcommit- dedication that have earned you this special honor. ProfessorTumerwithanen• For those who wl11 participate in the International tee, greeted the Mathematical Olympiad, I am confident that you will graved crystal bowl. represent our country with pride and distinction. winners and their par- The stUdy of mathematics is an admirable and worthwhile pursuit, yielding personal as well as Professor Donald Kreider, academic fulfillment. It CUltivates logical thinking ents. skills, which will prove invaluable throughout your lives. In conjunction with fields such as chemistry, President ofthe MAA, pre• physics, and engineering, mathematics is an essential The sponsoring societ• element in technological innovation and dillcovery. sided at the Awards It underlies the scientific advancements that are helping to protect the environment, improve health ies' representatives care, reVOlutionize information systems, and spur Ceremony.Itwas held inthe economic growth. Our nation has a rich tradition of presented gifts, prais• innovation, design, and discovery, and we will look Lecture Room of the Na• to outstanding young people like you to continue this ing them for their legacy. tionalAcademy ofSciences, Your superlative achievements in lllathellllltics outstanding achieve• reflect the tradition of excellence upon which this where the USAMO medal, country was founded. I send my best wishes for your future success. ment. honoring Gerhard C. Daniel Marino, Dis• Arenstorff, twice a winner trict Sales Manager, of the USAMOandarnem- from the Hewlett• ber of the firstUSA team in J. Thomas Ratchford, Consultant to the International Math• Packard Company, Director ofWhite House Office of presented the winners Science and Technology Policy. ematical Olympiad, was FOCUS August 1993

HenryAlder Section Awardsfor1 A highlightofmost section meetings this spring was theirAwardsfor Distinguished Collegeor UniversityTeaching ofMath• ematics. The Committee on Awards for Distin• guished College or University Teaching ofMathematics is now in the process of nominating at mostthree ofthese distin• guishedteachersfor the national awards. The BoardofGovernorswill act on these nominations at its meetingon August 14, 1993 in Vancouver. The national George E. Andrews James R. Boone Robert Bringham Texas A&M University awardees will be honoredand make pre• Pennsylvania State University University ofCentral Florida Allegheny Mountain Section Texas Section Florida Section sentations at the Annual Meeting in January 1994inCincinnati. For thenames of the recipients of the first national awards, together with their pictures, please see the April 1993 FOCUS, pp. 6• 7. Three of them will make their presentations at the Vancouver meeting on August 15from 2:30p.m. to 5:30p.m. (fordetails, see the April FOCUS, p. 27). The nomination of national awardees from the above list by the national com• mittee has turned out to be a most Kay William Dundas Paul R. Halmos I. Martin Isaacs delightful experience as well as an al• Hutchinson Community College Santa Clara University University ofWisconsin most impossibletask; delightful because Kansas Section Northern California Section Wisconsin Section of the extraordinaryhigh quality ofteach• ing of the section awardees, almost impossiblebecause it is exceedinglydif• ficult to differentiate among these truly outstanding and dedicated teachers. Re• viewing the nomination files of the section awardees has convinced theCom• mittee that it can never do justice to the large numberofsuperb and devoted col• lege teachers of mathematics in the MAA and that being a section recipient of this Award should beconsideredan outstand• Doug Nance David Pengelly Eileen L Poiani ing achievement. As one member ofthe Central Michigan University New Mexico State University St. Peter's College national committee wrote after receiv• Michigan Section Southwestern Section New Jersey Section ing this years' files, "The candidates are all very, very impressive; overall this group is as strong as last year's," and anotherwrites, "it's wonderful to see ex• cellence inalldimensions ofmathematics instruction, ranging from remedial and introductorycoursesto mentorshipat the graduate level." A great deal of the credit for selecting such outstanding candidates belongs to the sections who have so energetically and effectively established procedures for Mel Thornton Alan Tucker Stephen West University ofNebraska SUNY - Stony Brook SUNY - Geneseo Nebraska Section Metropolitan New York Section Seaway Section August1993 FOCUS

identifying and honoring their most de• istinguisbed TetUhing serving college teachers ofmathematics. Establishmentofthese awards has notonly made it possible to identify and honor the most distinguished college teachers of mathematics, but also to emphasize the importance ofexcellence in teaching col• legemathematics.The following quotation from the Secretary-Treasurer ofthe Indi• ana Section, when transmitting the nomination folder of the awardee of that section, is typical, "On behalfofthe Indi• ana Section, let me once again express the enthusiasm we have felt since the initia• James N. Cannon Allan Cochran GeraldDiaz Bringham Young University University ofArkansas United States Air Force Academy tion of the Distinguished Teaching Intermountain Section Oklahoma-Arkansas Section Rocky Mountain Section Awards." On September25, 1993, Section Secretar• ies will be sent information on the nominations for the third (1994) Section Awards. These guidelines will be essen• tially the same for the 1993 Awards; in particular, there will be no change in the nominationform. Watchfordetails inyour section newsletter. Some sections have been concerned that, while the candidates who were nominated were outstanding, the number of nomina• Genevieve Knight Thomas Moore Dale Mugler tions has been smaller than they would Coppin State University Grinnell College University ofAkron Maryland-DC- Virginia Section Northeastern Section Ohio Section have liked. They therefore have devised strategies to increase the numberof nomi• nations. For example, the Northeastern Section sent out a flyer in March urging any member ofthe section to "send a one page letter in support of an outstanding teacher and the Section Committee will ask the candidate's department chair to complete the nomination form." The national committee urges all mem• bers of the Association to think of worthy candidates for these awards and nominate them to the appropriate section commit• J.J.Price Jack M. Robertson David Sprows Purdue University Washington State University Villanova University tee. Even if your candidate should not be Indiana Section Pacific Northwest Section Eastern Pennsylvania and selected as a recipient of the award, re• Delewase Section member that the nomination by itself is a Photoswerenotavailablefrom distinct honor and also that the candidate can be nominated again if not selected the thefollowingAwardWinners: firsttime.The moreoutstanding candidates are nominated, the easier it is to maintain Robert Bryant David Cohen Martha Watson the high quality ofthe awards, so success• Duke University University ofCalifornia • Georgetown College fully established by the first two sets of Southeastern Section Los Angeles Kentucky Section' awardees. Southern California Section Henry L. Alder, University ofCalifornia at Davis, is Chair ofthe Committee on Congratulations to all the Section Distinguished Awards for Distinguished College or Teaching AwardRecipients University Teaching ofMathematics FOCUS August 1993

of process orientation, relying for data on A National Science Foundation frequentfeedbackand authentic assessment. Conference on Statistics Education Common Features of the George ltv. Cobb Projects Mount Holyoke College Comparingthe variousprojectsrepresented "In industry, teachingqualitycontrolexcites courses are built from a list of topics, with at the conferencesuggests a numberoftrends people. In high school, teaching statistics exampleschosen to serve as illustrations. In and challenges in statistics education, al• gets people interested and excited. In col• statistical practice, the priority is reversed: though here, as with any search for patterns, lege, it puts people to sleep. Something's we start with a problem, and choose meth• we must attend to outlyingobservations.And wrong."Thesewords were spoken by Rich• ods we think will help solve it. How closely here, as with any gathering which includes ard Scheaffer, of the University ofFlorida, can a beginning course be modeled on the Robert "Boss" Hogg, we can count on him at an NSF-sponsored conference held in priorities ofactual practice?" Another way to supply one ofthe outliers: Unlike all the Washington, DC on June 28-29, 1992. The to rethink curriculum starts by identifying other projects, which are concerned with three dozen statisticians and NSF officers obstacles to change, then looking for ways particularcurricularmaterialsor courses,the who were in attendanceare amongthe many to get round the obstacles. For an easy ex• Hogg Workshop was a structured discus• who are currently trying to "fix what's ample: to the extent that suitable examples sion of statistics education in general. (For wrong." Mostofthose presentare Principal are hard for teachers to find, they will con• a report ofthe conference, see Appendix D Investigators or co-PIs for the dozen NSF• tinue to rely on data. of"TeachingStatistics"in Heeding the Call funded projects listed in this report. The Yet another way to rethink ourcourses is to for Change) conference also included a dozen teachers think about assessment and TQM. ofstatistics, eachthe inventorofan unusual To me the most striking feature ofthe other eleven projects is that ten of them involve course or distinctive approach. The confer• Assessment: Whyis assessment so impor• labs, albeit in some cases only implicitly. ence was organized by Joan Garfield, tant? PsychologistLaurenResnickhas given The prominence oflabs among the projects UniversityofMinnesota, and myself, Mount the best short answer I know: "We get what appears to confirm what many have sug• HolyokeCollege, with assistance from Nell we assess, and if we don'tassessit, we won't gested,thatstatisticshas beenmoving away Sedransk and William Haver, who were at get it." Or, from an eloquent essay by Grant from mathematical theory, backtowards its the time both Program Officers of the Na• Wiggins, "Oneofmy definitions ofauthen• roots in science. There is a robust variety in tional Science Foundation. Support was tic assessmentis that 'it is composedoftasks the way the projects use labs: for analysis of provided by the NSFunderGrantNo. USE• that we value.' It is not a proxy. It is not an real-world data sets from an archive (Ikem, 9255396. efficientsystemto shakeout a grade. Rather, Magel, Notz et al., Tichenor, Trumbo); for the test should reveal something not only The main purpose of the conference might simulation-based learning (Gilliland, about the student, but about the tasks and be described by borrowing the Bayesian Meeker); and for hands-on production of virtues at the very heart ofthe subject- its phrase, "borrowing strength," in this case data for analysis (Nelson, Scheaffer, standards." (''Towards an AssessmentWor• the strength that comes from exchanging Spurrier). Each of these three uses has a thy ofthe Liberal Arts," in Lynn Steen, ed., ideas, resources, and experiences. To maxi• characteristic advantage. Analyzing Heeding the CaliforChange, MAA 1992.) mize the chance for genuine exchange, the archived data gets students to uncover and I suggestthat the harderwe thinkaboutwhat conference schedule included few formal ''tell the statistical story" of a compelling tasks we truly value, the more likely we are presentations,but many small-groupdiscus• application ofobvious import. Simulations to find that ourcourses change in response. sions. These discussions were planned as providefirst-hand experience with variabil• variations on a sequenceoffourmainthemes: TQM: Perhapsnot surprisingly, this proved ity, focused on a particular concept or (1) Seeing new curricular possibilities to be the most controversial of the confer• method. Hands-on lab activities allow stu• (2) Anticipating resistances to change ence themes. I'll limit myself here to two dents to create data which feel truly their (3) Assessment of student learning observations by David Moore of Purdue own, often the best way to guarantee inter• (4) Total Quality Management (TQM) University: (1) "Faculty don't thinkquality est. Unfortunately, eachofthe three uses has management (especially reduction of un• disadvantages also, and therein lies a chal• ConferenceThemes planned variation) applies to them. Neither lenge to statistics education. Archived data did auto plant managers. Both are wrong." sets deprive students of a role in data pro• Possibilities and Resistances: Mostbe• (2) "The typical college class can be greatly duction, and often the analysis must follow ginning statistics courses still sit at the same improved by caring about the outcome and a well-worn path. Simulationsare at bestre• old local minimum in curricular space. The by attentionto detail,"withouta majorover• creationsofadistantreality,and the hands-on setoftopics,and their sequence,is well worn, haul ofthe process. (TQMpeople say this is measurements a student can make in one and mostclasses, small as well as large, still true of most processes.) More substantial afternoon lab will never compete with the gravitate leadenly to the default format, "I improvement requires a change in the pro• Stanford Heart Transplant data for import. talk, you listen." There are various ways to cess." Our challenge is to continue to seek new push a course away from these inertial pat• ways to offer students the advantages ofall To seek that improvement, we can all re• terns. One is to identify underlying three approaches. assumptions and questionthem, e.g., "Most think our courses from within theTQMframe €t? August 1993 FOCUS Meeting the Challenge: Calculus Renewal MAA Member Receives an A Live Video Workshop "OutstandingTexan" Award How can calculus instructionbe restructured and reformed?Answersto that question will State Representative Gamet Coleman se• love and support me as a person and as a take place in a live video workshop, spon• lected MAA member Jacqueline B. Giles professional educator ... It has taken a col• sored by the National Science Foundation, for an Outstanding Texan Award, in educa• lective effort to get to this level of on Wednesday, October 13,1993. tion. recognition and it will take that same en• The workshop will offer practical insights Giles is a mathematics instructorat Central ergy to reach national and international toalternative curricular approaches and strat• College in the Houston Community Col• goals forAfrican Americansand allAmeri• egies for implementing them. Participants lege System, advisorto the Central College cans in mathematics education and in this workshop will hear from faculty Mathematics Club, the Central College education in general." members developing innovative instruc• Chapter ofthe Society ofHispanic Profes• She continued, "I was surprised to get this tional materials-and from their students. sional Engineers, advisor and consultant to recognition, but Ifeel it is timelyas Iexpect To participate in this video workshop, your OPERATION SMART in District 147.co• to plan more impacting involvement at the institution needs access to a C-Band or Ku• founder of YOUTH VICTORY and the national and international levels of educa• Band satellite down link on the day of the Association ofMricanAmericanMathemat• tion. I already have my mind set to go to an program. In addition you must have a room ics Educators, member of Pleasant Grove international conference in Vancouver, with a video monitor or a projector and a Missionary Baptist Church, and organist for Canada, and to Russia with a delegation of telephone. The telephone will allow you to Ephesus Missionary Baptist Church, mem• mathematics educators. A special thanks is ask questions ofthe participants in the video ber ofthe American Mathematical Society, extendedto my family, DeloydParker, Pas• workshop via an 800 number. Also, con• the Joint Policy Board for Mathematics tor C.L. Jackson, Herbert Hamilton, sider inviting concerned organizations and Public Information Resource Committee, Representative GametColeman, all ofour schools from your area to join you in view• and a member of an ad hoc committee to friends in theTexan LegislativeBlackCau• ing and participating in the Workshop. develop the "Archival Records ofMinority cus, and many more colleaguesand friends. Mathematics in theUnitedStates." Sheholds I thankGodthat this occurred on Mother's The registration fee is $50. Upon receipt of a three year appointmentto the MAA Com• Day weekend because this Mother's Day your registration form and fee, you will be mittee on Faculty Development. is very special for me. Thanks to the Black sent: A facilitator's guide with technical in• Media for allowing me a place to express formation on down linking; camera ready Giles holds master's degrees from Texas my views and articles for more than 21 copy for local advertising;and a "masters" Southern University and Texas A&M Uni• years. Ibelieve the Black Media isour voice viewers guide (to copy for all participants), versity-CollegeStation, withfurther study in education, politics, and community ser• whichincludes an agenda, instructional ob• at the doctoral level in mathematics and vice. Without it we would have the arduous jectives,presenter biographies,background engineering. task of challenging the veracity and con• notes, department-based audit of under• Speakingat the ceremony, held inAustin on tent ofcertain articles, with no alternative graduate instruction, and publisher's May 8, Giles said, "All that I am able to channels of expression, extensions, and information forordering any ofthe curricu• accomplish is made possible by those who analyses." lum materials.

Congratulations to Former MAA President Deborah Tepper Haimo for Receiving the Radcliffe Distinguished Alumna Award in June. FOCUS August 1993 Editorial

If you draw four unit circles centered at the We are, after all, in need of as much good when I left for the United States a decade points (1,1), (1, -1), (-1, 1), (-1,-1), and then publicity as we can get. As mathematicians, later. And though myoid department does add a fifth, smaller circle, centered at the we do not need to be told how important still exist, albeit much reduced in size, in the origin, that just touches each of the other mathematics is, and how relevant it can be mid 1980s it was not at all clear that it would four circles, then this fifth circle is clearly in many walks of life. But how many citi• survive to see the decade out. containedin the square around the outerfour zens, and, more critically, how many Now, for different reasons, the United States circles. lawmakers, have any idea what we do for a higher education system is under severe fi• living? We are supported, ofcourse, in that Do the analogous thing in three dimensions. nancial pressure, and unless administrations most ofus manage to earn a living as math• Place eight unit spheres with their centers at faced with making tough decisions are aware ematicians. But for the most part, we do so the points each of whose coordinates is 1or of the value ofa strong mathematics depart• by teaching, and the expectation is, I am -1. A ninth sphere, centered at the origin, ment' the same can happen at American sure, that what we teach is basic arithmetic which just touches the first eight, will lie colleges and universities as happened to me and algebra skills, toppedofwith a semester within the cube that contains the eight. and my colleagues back in Britain. or two of calculus. Likewise in four dimensions, and five, and So, glossy publications such as the one I A few years ago, when I was working in the so on. And it seems obvious that the same cited above are to be welcomed, as are any British university system, the government will be true for any number ofdimensions. other attempts to convey tothe outside world embarked on ahuge program ofcutsinhigher But, obvious or not, it isn't true. In nine di• that mathematics is a living, breathing, vi• education, a system-wide downsizing that mensions, the central hypersphere just brant discipline, connected to many walks continues to this day, incidentally. My own touches the bounding hypercube, and for oflife.As mathematicians, we must do what university was faced with having to cut its dimension greater than nine it pokes out of our friends in the physical and life sciences largely tenured faculty by a factor ofabout the hypercube. Ifyoudon'tbelieve me,check have been doing for years: we must learn to a third within a period of two years. My itout.All itrequires is astraightforwardcom• bang our own drum--even if, as one ofthe colleagues and I in the MathematicsDepart• putation of Pythagorean distance. articles in the new AMS booklet explains, it ment were concerned that many of our is not possible to discern the shape of that I cannotrecall where or when I first met this friends in other departments would be forced drum from the sound it makes. marvelous little example of the dangers of to leave, and that some departments would "reasoning by dimensional analogy", but I have to close altogether. But we knew that The above are the opinions ofthe FOCUS came across it again in the booklet Whats our jobs were secure. After all, we said to editor, and do not necessarily represent the Happening in the Mathematical Sciences, ourselves, we give all those service courses official view ofthe MAA. published recently by the American Math• tothe scientists, engineers, economists, busi• ematical Society. This excellent and ness students, and so forth. And besides, beautifully produced collection of "news• mathematics is just plain indispensable. Please note paper-level" articlesonrecentdevelopments Well, from a logical point ofview, that was in mathematics, written by mathematics jour• FOCUS editor Keith Devlin has all perfectly correct. As society's logical nalist Barry Cipra, is available in limited experts, we were right on the ball when it moved from Colby College in quantity only, free of charge apart from a came to evaluating our importance both to Maine, where he was the Carter shipping and handling fee of $7.00, directly the university as a whole and to the world at from the AMS (in the USA, phone toll free Professor of Mathematics and large. Unfortunately, the crucial decisions 1-800-321-4267).Itisa"must"for all math• Chair ofthe Department ofMath• were made on political grounds, not logic, ematics department reading and coffee ematics and Computer Science, to and many years of failing to bang the math• lounges, and the FOCUS editor would like ematical drum had left us with an Saint Mary's College of Califor• to commend the AMS for bringing out this administrationthat regardedus as decidedly nia, in Moraga, California, where little gem. It is great publicityfor our profes• dispensable. The departmentof18or so that sion. he is the Dean of the School of I joined in 1977 was reduced to 10 or 11 Science. August1993 FOCUS

he could always add a note ofexplanationto the file. (I later found that this is what Bertrand Russell did in his own files which are now at McMaster University.) But I Personal Opinion agreed that he should do whatever he felt most comfortable with. I believe he did de• stroy the drafts. Also during this archival discussion. Alex Rosenberg, then amember oftheAMScoun• WhyArchive? cil, expressed doubts about the desirability Albert C. Lewis of saving anything at all in archives. But when we met at an archival exhibition set up The premise might seem uncontroversial: if to libraries around the world. They are de• for a council meeting at Texas, he told me mathematics is to have a history, resources posited so that they may be looked at. Why that he had changed his mind after convinc• must be available upon which to base it. But, is this and how do they get there? inghimselfofthe soundness of thefollowing as I hope to illustrate, historical archiving Wehave had experienceduring the past thir• argument. He was himselfdevoted to alge• has not been as straightforwardly automatic teen years with American archives since the braic number theory which even many as, for example, the archiving ofcomputer Mathematical Association ofAmerica and mathematicians regard as a particularly re• files is supposed to be. the American Mathematical Society inves• condite field that is not relevant to much When civilizationis set back by the destruc• tigated the establishment of archives, and else. Nevertheless, he appreciated that math• tion of a library, such as the Central committees, such as ours, have tried to aid in ematiciansrespectedhis interest in the field. University Library at Bucharest in 1989, in the preservationof archival materials. Math• By the same token, if there were people modem times most ofthe loss may consist ematicians have given a wide range of whose fields involved archives, the fact that of printed or machine-readable books and responses to the notion of archives as the he personally did not have such an interest journals which effectively have their back• following three examples from my own ex• did not entitle him to destroy archival ups inother libraries and which can therefore perience atthe University ofTexas atAustin sources. Boxes of material related to his eventually be replaced. But unpublished illustrate. editorship of TheAmerican Mathematical materials at Bucharest, as at other libraries, Monthly arrived shortly afterwards for ad• R H Bing not long after hereturnedtoAustin arerarely duplicated and distributed and thus dition to the MAA archives. became President of the AMS and learned they can never be replaced. It is these, usu• something about archives when a proposal Soon after theArchives forAmericanMath• ally paper documents-correspondence, was made to have the Society jointhe MAA ematics wasestablishedatTexas, itsadvisory personal notebooks, drafts, institutional in establishing a joint archives. Everett committee was informed that Emil records, photographs-whichthe historian, Pitcher, Secretary of the AMS at the time, Grosswald was wondering if anyone would at least, needs. Most mathematicians natu• has given a diplomatic accountofthe fate of be interested in his papers. I did not know rally have a strong historical interest at least this proposal in the chapter "Archives" inA Grosswald but I am told that he was a me• to the extent that they regard establishing HistoryoftheSecondFiftyYears,American ticulously organizedperson who did not like precedence-who discovered what and Mathematical Society 1939-1988, (AMS, loose ends. He sent some material immedi• when was it discovered-as important. 1988). The AMS chose not to establish an ately and arranged for the remainder to be But is there a need to preserve more than archive at that time (they have since desig• bequeathed to the archives in his will. (This publications today? Gazing upon Gauss's nated Brown University as the repository), did come after his death in 1988.) autograph is probably not a source ofinspi• but the affair did have the effect ofinform• I suspect that none ofthese mathematicians ration for doing mathematics. Students' ing some mathematicians about archives, gave much weight, if any, to what motives notes ofHilbert's lectures are probably too their purpose and functioning. Not long af• might be attributed to them in depositing out of date for mathematical purposes to• terwards Bing expressed a concern to me. their papers. On the other hand, archives as day. And is it anyone's business anyway to He had been looking over a file containing reminders ofour mortality are perhaps, not pry into personal correspondence or keep drafts ofa telegram he had proposed on the surprisingly, a subject which some people tabs on who was attending whose lectures? occasion of the rather controversial forced would prefer to avoid altogether ("Let my Some people may doubt that it is, but many retirement ofhis teacher R. L. Moore from family take care of it.") or, on the other, a mathematicians share with historians a de• the University of Texas at Austin in 1969. subject in which some will involve them• sire to find out why and how mathematical The archival discussions had alerted him to selves with a view to affecting history. Is discoveries are made, received, and taught, the fact that these draftsmight be looked at handing over one's papers to an archive an and, as good scientists who want the best in the future. He felt that they could be mis• egocentric gesture? Is it a creation of an evidence, are going to make use ofwhatever understood and he ought to destroy them. I unseemly monument to oneselfor a hubris• such sources ofinformation are available. tried to argue that by doing so he was leav• tic assumption that one's papers will be of ing open the possibility of even more Personal archives, like those ofGauss and interesttohistorians? Psychological motives inappropriate speculations about his stand Hilbert at Gottingen, as well as institutional or motives at that time. I also suggested that archives, do exist and continue to be added PleaseseeArchiveon page 12 FOCUS August 1993

Archivefrom page 11 an effort to counterbalance the inevitable Transportation losses which have occurred and will occur. are, I think, quite irrelevant if a larger view Albert W. Tucker has a despairing tale of is taken. how a box of important files belonging to and the For a start, what are "one's own" papers? one ofPrinceton's well-known mathemati• Considering correspondence with others, cians was inadvertently left in the corridor Mathematical shared work, mutual benefits ofthe teacher• outside his office . The next day, when it student relationship, and other influences, couldn'tbe found, it was discovered that the Sciences each mathematician, and especially offic• box had been picked up by the night ers, editors, committee members, referees, caretaking staffand thrown out. More mas• TheBoardon MathematicalSciencesand and others who participate in the functions sive disappearances have been known to the Transportation Research Board ofthe ofa mathematical society or journal, or in a occur when a department as a whole has National Research Council jointly spon• mathematical department of a school or moved to a new building. sored a symposium in early May on the university or business, is part of a larger changing interactions between transpor• It is easierto throw things out than to contact network. Perhaps it is more egocentric to tation and the mathematical sciences. your local archivist (or one of the national unilaterally withdrawthe backgroundrecord Speakers included representatives of the archives listed below) justas it is easier not ofone'spart in this enterprisethan to assidu• Federal Aviation Administration and the to makebackupsofcomputerfiles. If you or ously try to preserve it. The important thing Federal Highway Administration. someone you knowwishesto considerwhat seems to me to consider the possibility that to archive, our committee stands ready to The rapid expansion ofthe transportation archives are more than monuments to the help with information, advice, and support. system has slowed, and focus has shifted memories ofindividuals or even individual to optimizing the system's uses. Thus the institutions, and that they help form the liv• Albert C. Lewis (Box 57118, Hamilton, mathematical sciences have an evolving ing memoryofthe mathematicalexperience. Ontario L8P 4W9). and more prominent role. Mathematical Whethera mathematician saves all or noth• Other members of the AMS-MAA Com• simulationoftraffic flow, for instance, has ing, and, if something in between, then just mittee on Archives: Andrew M. Gleason increasing relevance: while synchroniz• what, are matters which are probably going (Harvard University); Karen H. Parshall ing traffic lights for normal traffic flow is to continue to be worked out case by case. (UniversityofVirginia);Franklin P. Peterson now routine, designing systems for rush Some idea of the sort of things that have (MIT); EverettPitcher(LehighUniversity); hour is an unsolved problem. Operations been considered worth saving is given by SanfordL. Segal, Chair(UniversityofRoch• research, statistics, mathematical model• Frederic Burchsted in "Sources for the His• ester). ing, and the design and analysis of tory of Mathematics in the Archives of algorithms are areas ofincreasing useful• Archives of American Mathematics: American Mathematics," A Century of ness. FredericF.Burchsted,Archivist,University Mathematics in America, Part lII, 667-674 Archives, SRH 2.109, The University of To cite anotherexample, the FAA is build• (AMS 1988). These can include audio and Texas at Austin Austin, Texas 78713-7330; ing a new, morecomplexair traffic control visual recordings and memorabilia (such as 512-495-4129. system, the software for which will con• R. L. Moore's typewriter with mathemati• tain over a million lines of code. cal symbols) as well as the more common Archives of Mathematics and Mathemati• documents mentioned above. There is in cians: Mark N. Brown, Curator of generalnot yetadangerofflooding archives Manuscripts, The John Hay Library, Brown with an excessive amount of material. At University, Providence,Rhode Island 02912; this point it seems more important to make 401-863-1512.

Contributed Paper Sessions

TheMAACommitteeon SessionsofCon• Planning is now underway for the Au• tributes Papers selects topics and gust 1994summermeetingsinMinnesota organizers for contributedpapersessions and the January 1995 winter meeting in at national meetings. The Committee San Francisco. The deadline for receipt would be delighted to hear from MAA for proposals for eithermeeting January memberswhowouldliketo organizesuch 15,1994. Information should be sent to a session or who have suggestions for the chair of the committee: Elizabeth topics. Teles, 11501 ChattilyLane,Mitchellville, FOCUS isprintedon Recycled Maryland 20721 w(202) 357-7051, h(301)262-9586,e-mail:[email protected]. andRecyclable paperwith soy based inks. Please recycle. The 1992 MAA Annual Report 992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The1992MA President's Message

DonaldL. Kreider

My term as President began at the close of would be the launching of an electronic the annual meetingin SanAntoniolast Janu• database that will facilitate the dissemina• ary, at a session honoring the first recipients tion of information about successful ofthe MAAAwards for Distinguished Col• instructional programs. This would be one lege or UniversityTeaching ofMathematics. of a number of new electronic services that President Haimo, now PastPresident, handed the MAA is preparing to introduce to its me a gavel signifying the beginning of my members. And it would be accompanied by term. I am still hopeful that she will instruct an effort to coordinate a set of articles in me in its use. Her presidency was an active MAA publications and activities at MAA one, marked by many accomplishments.The national and Section meetingsthat will con• MAA Strategic Plan, adoption of the new tribute to the database. The ultimatepurpose Council structure, heightenedcollaboration is to enhancecommunicationamong depart• with our sister mathematical organizations ments who are actively trying new things, to on issues ofconcern to us all, and the imple• make it easierto learn what others are doing, to the meeting and promised a lively future mentation ofthe Awards for Distinguished to celebrate successes, and to learn from for our organizations. Teaching, are some of her legacies. They failures. In May the Executive and Finance paint a picture ofa strong Association, true Committeesapproved moving forward with Ahighlight of the San Antonio meeting was to its roots, yet willing to move forward. such an initiative, building on MAAefforts the celebration of theAmerican Mathemati• already underway, such as the provision of cal Monthly's looth birthday. Part of the In the past several years the MAA, the Math• electronic services. The CoordinatingCoun• program for the meeting was dedicated to ematical Sciences Education Board (MSEB), cil on Education, CUPM, the Committeeon this celebration, including inspiring talks by and other organizations have published a Electronic Services, as well as many other former Monthly editors. The Monthly ban• number of documents that articulate goals committees and editors ofthejournals, need quet itself was one of those rare occasions and strategies for undergraduate mathemat• to be engaged. when nostalgia, reflection, and pride com• ics education. The most recent of these are bine in a most natural way to remind us why the MAA Guidelines for Programs and During the spring I had the opportunity to we love this Association. We all left the cel• Departments in Undergraduate Mathemati• visit meetings of a number of our MAA ebration, and the meetings as a whole, with cal Sciences. Given final approval by the Sections. This is both enjoyable and a re• adeep feeling ofpride in those who nurtured Board of Governors in February, and pub• minderofthe vitality ofour Association that the Monthly over all these years, those who lished in the June issue of FOCUS, the resides at grassroots levels. Contributed gave rise to the MAA itself, and everyone Guidelines will contribute to current efforts paper sessions, special programs for under• who is carrying on the traditions and activi• at revitalizing undergraduate mathematics. graduate students, invited speakers, panels on currenttopics or concerns-allthese, and ties today. What actions should follow their publica• much more, are part of rich programs and The San Antonio meeting will also be re• tion? Certainly, many departments of are embedded in lots of fun and collegial membered for marking the first time in our mathematics have picked up the challenge, interaction. I might also add that this Presi• history that the Board of Governors of the responding to the call for action in creative dent, living as he does in Vermont, finds it MAA and the Council of the AMS met in and exciting ways. The programs ofsectional especially pleasant to visit the southland in joint session to resolve an issue of concern meetings and the national meetings make late winter and early spring. The Section to both organizations. The immediate ques• that clear. But how systemic is the move• meetings are important to the Association. tionwas the moving ofthe I995jointmeeting ment, and to what extent is it addressing the They provide an importantlink betweenour from Denver to another site, as reported in main goal of improving undergraduate in• members, local mathematicalactivities, and the April issue of FOCUS. The prevailing struction in mathematics? This question is work of theAssociation at the nationallevel. effect will be the remembrance ofthe high being pressedupon us ever more strongly by Indeed many more members attend their level of debate and the strong feeling of the foundations that support the MANs Section meetings each year than attend the collegiality that characterized the joint ses• projects. national meetings. sion.There willbefuture issues that similarly This spring I proposed an initiative to report San Antonioprovideda gracious and attrac• test the bonds of cooperation between us, progress in undergraduate mathematicsedu• tive site for the annual meeting in January. It and the precedent set in San Antonio shows cation. The idea is to gather, organize, and was well attended, and well enjoyed. The that we can face such challenges. My con• disseminate information about the creative mathematical programs of both MAA and gratulations go out to presidents Debbie and exciting approaches being taken by AMS were rich and varied. The many re• Haimo and Mike Artin for holding us to• mathematics departments in response to the ceptions and social engagements added to getherandto HenryAlder who demonstrated challenge of revitalizing undergraduate the fun. And the presence of many under• his consummate skill in parliamentary mat• mathematics. A centerpiece ofthe initiative graduate and graduate students added spice ters. @------AA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Ani

Collaboration with other mathematical or• expressions of interest are retained by the ganizations is essential to reaching MAA's Committee on Committees, however, so Inside the goals. Supporting and revitalizing under• many who are not called immediately can graduate instruction, identifying and expect to be called upon in the future. encouraging students who can be future 1992Annual mathematicians, encouraging underrepre• I would like to close this first report with an sented groups to continue their study of observation about the MAA that is of ut• mathematics and to consider careers in most significance to me. Throughout its Report mathematicsand science, and improvingthe history the MAA has operated with civility educationoftomorrow'steachers-allthese and collegiality matched by few otherorga• requirea view ofmathematicseducationthat nizations. Ithas aspired to be an organization transcends the traditional boundaries of opento all who are boundonly by an interest Executive Directors school, college, and graduate school. Thus in mathematics and mathematicseducation. Report 16 the MAAworks closely with the American This is not to say that its record is unblem• Mathematical Society and the Society for ished, however, for there have been incidents Industrial and Applied Mathematics under ofdiscrimination againstAfricanAmerican Committee on Visiting the umbrella of the Joint Policy Board for colleagues in the past, and there were peri• Mathematics. Here we joinhandsin matters ods during which segregationand repression Lecturers 17 ofgovernmentrelations, scienceand educa• in our society at large affected the ability of tion policy, and public awareness of AfricanAmericanstoparticipatefully within mathematics. We workclosely with the Na• the MAA or to feel fully welcome at its CRAFTY 17 tional Council ofTeachers of Mathematics meetings. One would like to say that those and the American Mathematical Associa• days are past. Indeed they are, as measured tion for Two Year Colleges under the by the resolve of MAA officers, the Board Financial Report 18 umbrella of CBAMN (Cooperative Board ofGovemors, and today's MAAmembers, for AMATYC, MAA, and NCTM). Here that we are and will remain an open and we worktogetheron educationalmatters that welcoming organization to all. And we will SUMMA 20 cross the lines ofschools, two-yearand com• take active steps to carry this policyforward. munity colleges, and four-year colleges and Butpast errors cannotbe expunged, and onIy universities. Andfmally, we collaboratewith time can slowlyheal the deep hurt that many Committee on the much larger number of mathematical ofour minority colleagues feel even today. organizations within the Conference Board I report on this matter now because such Sections ...•...... 21 on the Mathematical Sciences. The math• feelings surfaced strongly withinthe South• ematical community has gained the eastSectionand in San Antonio at meetings reputation nationally of "having its act to• of the MAA Committee on Minority Par• MAABoardof gether". Oursolidarity isimportantin gaining ticipation and the National Association of wider support for mathematics. Mathematicians. It is good that they did. It Governors 22 is important that we pay attention. It is es• The MAA is a largely volunteer organiza• sential that we all resolve to redouble our tion. Itcarries out its workthroughindividual efforts to convince every one of our mem• Committee on members, the sections, and its committees bers that they are valued members of our and councils. It has some 150 differentcom• Testing 22 community and that their full participation mittees working on as many different is needed ifwe are to accomplish our goals. programs, and its vitality depends on the I ask all members to join me in this resolve. diversity ofmembers within this structure. Committee on Were we not an open and welcoming orga• The Committeeon Committeesmakes avery nization I am sure that those voices would Student Chapters 23 strong effort to bring new people and new not have been raised at the San Antonio ideas into its nominating process each year meeting. In that I take heart. as it prepares its final recommendations for Publications 24 the President. It delegates to the Council The MAA is in the center of efforts to ad• chairsthe responsibilityfor identifying suit• dress the critical problems in American able candidates to fill committeevacancies, mathematics education. It has taken a lead• and the chairs are chargedto consultwidely. ership role, and through its members and The Greater MAA FOCUS has periodically invited members Sections it is actively engaged at all levels. Fund Honor Roll 26 to volunteerfor committeesthat wouldbe of The work remaining is daunting. But we particularinterestto them. This has resulted continue. in a very large response, much larger than the number ofpositions available. All such Ie 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 ~

From the Executive Director's Desk A Nation at Risk

Marcia P. Sward Ten years ago we were shocked into aware• regular member services, it was insufficient ness of the weaknesses of our educational tolaunchandmaintaindesirablenewprojects system by the report, "A Nation at Risk," and programs. which stated: MAACommitteesDuringhertermas "Wereport totheAmerican people that while MAA President, Lida K. Barrett undertook we can take justifiable pride in what our to open committee membership to a wider schools and colleges have historically ac• pool of members, thus ensuring broaderrep• complished and contributed to the United resentation of members' interests in States and the well-being of its people, the committee deliberations. Deborah Tepper educational foundations of our society are Haimo, after assuming the presidency in presently being eroded by a rising tide of January 1991, sought to reduce duplication mediocrity that threatens our very future as of effort and increase the effectiveness of a nation and a people." committees. With Board of Governors ap• the favored mode for MAAleaders and staff The MAA and Educational Re• proval, she organized MAA committees in to communicate. With guidance from the Council groups according to their basic re• MAA Committeeon Electronic Communi• form "A Nation at Risk" launched a sponsibilities, and appointed oversight cations, the MAA staff began the process of massive educational reform effort in which committeesto coordinateand facilitate their planning for MAA Electronic Services, to the MAA has played an important role, to• work. be launched in fall 1993. gether with its sibling mathematical societies. In the process ofshaping this role Strategic PlanningIn an effort to de• Cooperation with Other and looking for the resources to carry it out, velop a clear vision to guide further change Mathematical Organizations MAA leaders began to look with new eyes within the MAA, President Haimo initiated at the MAA itself - its strengths, weak• a strategic planning process in 1991.A draft Recognitionofthe magnitude and complex• nesses, existing resources, and potential• plan was presented by the Strategic Plan• ity ofeducational reform has spurred more and to build toward a stronger organization ning Committee to the MAA Board of interorganizational cooperation than ever capable ofserving its members well and of Governors in December 1992. The Board before.The long-term collaboration ofMAA providing strong leadership in the educa• reaffirmed the MAA's historic mission, ap• with theAMS and SIAM on public informa• tional reform movement. proving a new mission statement and tion and governmental affairs was program and operational goals, and asked supplemented in 1992 by a new collabora• Much of what they saw was good - out• MAA committees to review the relevant tion among the MAA, NCTM, and standing journals and books, attractive portions of the plan and advise the Boardon AMATYC. Representatives of these orga• national meeting programs, strong Sectional the programs and projects proposed. (See nizations met for the first time at the organizations. But not all. There were, for FOCUS, October 1992, page 3). The strate• International Congress ofMathematics Edu• example, alargenumber ofcommittees (over gic planning effort will not come to full cationinQuebec lastAugusttobegintoshape 1(0), some ofwhich were long overdue for closure until January 1994 when, hopefully, a common agenda. discharge, some of which had overlapping the Board ofGovernors will formally adopt or even contradictory charges, and few of A joint ad hoc Committee on AMSIMAA an MAA Strategic Plan. which had adequately representative mem• Cooperation, chaired by DonaldL. Kreider, reviewed the various joint ventures of the berships. Progress During 1992 Much AMS and MAA, and identified various ad• progress was made in 1992 in several areas And there were other problems: the MAA's ditional areas where collaboration might be addressed in the draft Strategic Plan: historicnationalheadquarters buildings were useful. badly inneedofrenovation; theMAA's com• Electronic Communications puter system was inefficient and out-moded; The Mathematical Sciences Education the MAA had only marginal access to elec• In June 1992 theMAA's 32-memberWash• Board (MSEB) hosted a five-organization tronic communications; and, while the ington Office staff was linked via a Novelle joint planning sessioninOctober 1992.Presi• financial base of the MAA was adequate for network, and staff members gained direct dents and Executive Directors of the MAA, access to the Internet. Email quickly became AMS, SIAM, NCTM, and AMATYC re- ~ MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA An

viewed the strategic plans of the organiza• Committee on and increase participation in the Visiting tions, looking for common interests and LecturersProgram.Consequently,theCom• concerns. Visiting Lecturers mittee addressed its Information Booklets The Conference Boardofthe Mathematical to "Colloquium Chairperson" at each de• Sciences (CBMS) undertook a joint Career The Association's Visiting Lecturers Pro• partment of mathematics in the United Information Program, initiated by theMAA. gram serves departments of mathematics States and Canada with the hope that, if no across the country. Its objectives include such person exists, the department would Student Activity stimulating and expanding the mathemat• appoint one! ics programs in two-year colleges and in As PresidentDonaldKreiderrecently noted Interested departments should arrange for those four-year colleges not offering aPhD in an interview in FOCUS (June 1993), a visit directly with the desired lecturer; at inmathematics; affordingstaffand students "mathematicians have rediscovered stu• that time, they should agree upon expenses. at such colleges with opportunities to meet dents." Ithasbeen gratifying to see theMAA Some lecturers' home institutions have in• and converse with creative mathematical continually build itsstudentmembership and dicated a willingness to subsidize some scientists;communicating newandrelevant student participation. The year1992 saw visiting lecturers' expenses (asterisks dis• applicationsofmathematics and computer continued increases in participation of stu• tinguish these listings in the booklet). Some science to not only the physical sciences dents in sectional and national meetings, and institutions maintain faculty development and engineering, but also the biological and growth in MAA Student Chapters. Fund funds. To assist you, the 1992-1993 Infor• social sciences; and strengthening the rap• raising for a new undergraduate magazine, mation Booklet discusses guidelines for port among mathematicians working for Math Horizons, was also successful. This financial considerations. new MAA publication will be launched in government, industry, and educational in• fall 1993, and will be disseminated in bulk stitutions. Members of the Committee on Visiting Lecturers urge departments to take advan• to all U.S. colleges and universities. The program's 1992-1993 Information tage of the opportunities this program Booklet includes the names of participat• Mathematical Center Fund provides. Furthermore,theCommitteewel• ing lecturers. These lecturers agree to comes suggestions and comments to remain in the programfor four years, after The resources needed to pay for badly improvethe program; you may contact any which they must take at least a two-year neededrenovationofthe Washington Head• Committee member at the appropriate ad• hiatus before the Committee invites them quarters were obtained from generous dress provided inside the Information toparticipateagain. MAA Visiting Lectur• members and friends ofthe MAA. A three• Booklet.The Committeealso solicitsnames ers not only deliver formal presentations year $600,000 campaign was successfully of potential lecturers, particularly from but also meet with students and faculty completed, with contributions now topping states and provinces currently without rep• informally. They will happily discuss op• $630,000. At a gala reception at the San resentation.Ifyou haveheardanoutstanding portunities for graduate study and Antonio meeting, donors were honored and speaker whom you think might further the employment with students, and they will thanked. Seventeen rooms in the MAA's programs objectives as stated above, or, if cooperate with departments to further the National Headquarters have been named in you wish to receive additional information aims oftheir mathematics programs. honor offriends, family, mathematicians of on the program, contact: James G. Ware, renown, and mathematicstextbookauthors. The Committee encourages departments Chair, MAA Committee on Visiting Lec• Conclusion to establish departmental colloquiums with turers, Department of Mathematics, an appointed chair. Such colloquiums will University ofTennessee, Chattanooga, TN These are just a few highlights of MAA foster faculty dialogues and presentations 37403-2598; (615) 755-4545. activity in 1992, but may serve as an indica• tion ofprogress made during the year on a variety offronts. Much has transpired dur• ing the first six months of the current year, CRAFTY and it is now clear that 1993 will be another and a panel on calculus reform and the AP Calculus Program. banner year for the MAA. As Executive CRAFTY met at both the January 1992 Director, I am extremely pleased to be able meetings in Baltimoreand the January 1993 A series of NSF-supported summer work• to report that the MAA is in sound fiscal meetings in San Antonio. In Baltimore shops, directed by Don Small ( a memberof condition, is planning carefully for the fu• CRAFTY organized a contributed paper CRAFTY) through discussions at commit• ture, and is tackling the issues of the day session on innovative first-two-year course tee meetings and another NSF grant for a with vigor and enthusiasm. sequences. CRAFTYalso cosponsoredtwo program ofvisiting,singledepartment work• panel sessions: one on site-testing ofcalcu• shops, is also being developed in the lus reform projects and another on the committee with Martin Flashman as direc• College Board'sAdvanced Placement Cal• tor. culus Program. At the end of the San Antonio meeting, In San Antonio the committee cosponsored Wayne Roberts replaced Thomas Tucker as a poster session on calculus reform projects chair ofCRAFTY. 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA

1992 MAA Financial Report

Geraldl. Porter, Treasurer

This is my first year as Treasurer. I succeed beinbalance. During 1992,theGeneral Fund Don Kreider who served as Treasurer from showed a surplus of $100,700 compared to 1986to 1992.During Don'stenure theMAA a surplus of$52,200 in 1991 on a total bud• made remarkable strides toward puttingboth get of$3.7 million. its financial and physical houses in order. RestrictedFunds:The restricted fund in• The Association has moved from years of cludes externally funded projects and the unbalanced budgets tobalanced budgets, has American Mathematical Competitions repaired and renovated our buildings, and is (AMC).Grantrevenuesduring 1992totaled currently completing installation of a new $1,176,000. This includes new grants to computer system. The Executive team of support, among others, SUMMA, Math Marcia Sward, Rhoda Goldstein and Donald Albers provide sound administrative man• agementfortheAssociationatthe same time as they initiate innovative new programs. Particularpraise is due to Don Albers for the growth of the publications program. Rev• enues have increased more than 50% over the past two years, and an all time high of18 1992 Revenues and Expenditures new titles were published in 1992. In addi• tion, the MAA has taken over responsibility with 1991 for Comparison for publishing UME Trends and plans are well underway for the publication of Math Horizons, our new student publication. Revenues The strategic plan for the MAA is nearing 1991 1992 completion and will provide a map for the Dues $1,964,000 $2,115,000 future ofthe Association. As we implement Subscriptions 445,000 507,000 this plan we are always constrained by lim• Book Sales and Advertising 661,000 835,000 ited resources - more than half of our Interest, Dividends, and Capital Gains 268,000 155,000 unrestricted income comes from members' Contributions 233,000 224,000 dues. Grants are an importantmeans ofstart• Grants and Indirect Cost Reimbursment 945,000 1,176,000 ing programs, but the challengethat we face Contest Fees and Sales 725,000 774,000 is in institutionalizing these programs when Space Rental 101,000 78,000 the grants are finished. Miscellaneous 172,000 183,000 The outcomes in 1992 TOTAL REVENUES $5,514,000 $6,047,000 There are several measures of the Association's fiscal health. These include our general operatingbudget, grant activity, Expenditures our real estate holding, and our investment fund. We discuss each of these separately. Journals and FOCUS $1,422,000 $1,525,000 Membership 475,000 424,000 General Fund: The General Fund is the Books 723,000 1,049,000 MAA's unrestricted operating Fund. Income Sections, Meetings and Joint Programs 232,000 214,000 to the General Fund comes from the Development 59,000 58,000 member's dues, publication sales, interest on working capital and contributions. Ex• Grant Supported Programs 1,095,000 1,312,000 penses include publications, management, Mathematical Competitions 610,000 724,000 supplies, non-externally funded program Building Operations 146,000 141,000 support, allocated building expense and Miscellaneous Programs 225,000 216,000 support of sections. It is the goal of the Fi• nance Committeethat the General Fund will TOTAL EXPENDITURES $4,987,000 $5,663,000 @------AA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annu

Horizons, and the IMTP Project, as well as the continuationofother projects. TheAMC is responsible for operating the high school Consolidated MAA Balance Sheet andjuniorhigh school mathematicscontests as well as the Math Olympiad. During 1992 Assets restricted income totaled $2,058,917 while expenses totaled $2,034,768. December 31, 1991 December 31, 1992 Building Fund: Several years ago, the Fi• nance Committee made the decision to Current Assets separate the Building Fund from the Gen• Cash $126,541 $132,495 eral Fund, so that the expenses associated Liquid Assets 1,449,788 1,233,202 with renovation of our building would be Accounts Receivable 512,577 818,545 isolated from the day-to-day operatingbud• Publications Inventory 243,828 273,938 get of the Association. Space costs are Prepaid Expense 241,571 254,320 allocated to thegeneral fund as afixed yearly charge. This allocation with rental income TOTAL CURRENT ASSETS $2,574,305 $2,712,500 from our other tenants and contributions constitute income to the Building Fund. Non-current Assets Expenses include operating expenses, debt Investments (at cost) $1,009,595 $921,305 service, capital improvements and principal Furniture and Equipment 655,431 862,890 payments on our mortgages. Becauseofthe Building (at cost) 816,456 816,456 recent renovations on our building, there is Building Improvements (at cost) 897,310 930,369 a cumulative deficit in the Building Fund. Accumulated Depreciation (693,509) (809,354) As our mortgages are reduced and interest Deferred Development Costs 134,364 199,434 costs decline, that income will be used to reduce and eventually eliminate this deficit. TOTAL NON-CURRENT ASSETS $2,819,647 $2,921,100 During 1992, our mortgage indebtedness declined from $448,714 to $393,903 while TOTAL ASSETS $5,393,952 $5,633,600 our accumulated deficit in the cash building fund increased from $150,402 to $179,914. InvestmentFund: TheMAAInvestment Liabilities and Fund Balances Fund includes both restricted and unre• stricted endowmentfunds. The earnings and CurrentLiabilities capital gains from our investments are re• Accounts Payable $259,028 $208,967 tained with the exception offunds that are Accrued Royalties 32,247 41,482 intendedto support special activities such as OtherAccrued Liabilities 235,975 162,877 the Sliffe Awards to high school teachers. Prepaid Dues and Subscriptions 1,963,391 1,959,807 During 1992, the investmentfund increased from $1,409,248 to $1,461,980 after taking TOTAL CURRENT LIABILITIES $2,490,641 $2,373,133 account ofa transfer of$42,000 to support designated programs. Long Term Liabilities Summary: I am pleased to report that the Mortgage Payable $448,714 $393,902 MAAhas the financial strength and capable Unexpended Grant Receipts 336,421 364,937 managementrequired to support the leader• ship position that we have assumed in TOTAL LIABILITIES $785,135 $758,839 collegiatemathematics. Balance sheets can, however, only begin to measurethe strength FundBalances ofthe Association. The most important as• Unrestricted Fund Balances $784,833 $943,889 set that the MAAhas is our members. Their Restricted Fund Balances 842,947 977,701 involvement in the many MAA activities at Endowment 490,396 580,038 both the section and national levels provides the energy for the organizationand the foun• TOTALFUND BALANCES $2,118,176 $2,501,628 dation for its activities. TOTAL LIABILITIES AND FUND BALANCES $5,393,952 $5,633,600 ~ 1e1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MJ

the original Carnegie funds had leveraged SUMMA1992-aYear in Review an additional $2.7 million from both public and private sources. Another $50,000 in William Hawkins Small Grants will be awarded in early 1994. The StrengtheningUnderrepresentedMinor• A second minority member ofthe Associa• (Please watch for the announcement in ity Mathematics Achievement (SUMMA) tion, Dr. David Sanchez of Los Alamos FOCUS later this year.) Program of the MAA is a national effort National Laboratory, was elected to the SUMMA Consortium focused on increasing minority participa• MAA Board of Governors in January 1993 tion in mathematics at every level, from as a Governor At-Large. A third minority (SUMMAC) of Intervention elementary through graduate school and member, Bettye Forte of Ft. Worth, was Projects beyond. The goals of SUMMA are to in• elected to represent high school teachers. crease the representationofminorities in the These momentous events occurred at a time SUMMAis now in the second year ofaNSF fields ofmathematics, science and engineer• ofincreasingminority attendance attheJoint grant of $703,000 for three years to network ing and to improve the mathematics Meetings as evidenced by the number of existing mathematics-based intervention education of minorities. Oversight of the minority presenters. The list of minority projects and those it has been assisting. This SUMMA Program is provided by Marcia presentations at Baltimorefilled four pages. SUMMAConsortium (SUMMAC) held its Sward, the MAA Executive Director, and More than 70 committee and/or council inaugural conference in Washington, D.C. the MAA Committee on Minority Partici• positions are held by minority members of in November 1992 for mathematicians di• pation in Mathematics, co-chaired by the MAA; the MAA leadershipcontinues to recting intervention projects. Seventy-five Manuel Berriozabal of the University of work with SUMMA staff and CMPM to directors attended this exciting event where Texas at San Antonio and Sylvia Bozeman involve more minorities in committee ac• theydiscussed mutual concerns andreceived ofSpelman College. tivities. CMPM is working with a variety of copies of the Project Director's Handbook committees to address overall issues ofmi• and the Directory of Intervention Projects SUMMA collaborates directly with a vari• nority participation in the MAA. The which lists 67 mathematics-based interven• ety of mathematics-related organizations campaign for naming a room in the MAA tion projects around the country. A second such as the American Indian Science and headquarters building in honor of Benjamin national meeting of the SUMMAC mem• Engineering Society (AISES), the Ameri• Bannekeris well underway. Acampaign for bers is planned for November 1993 for can MathematicalAssociation ofTwo-Year a room in honor of a prominent Hispanic 100-125 participants. Colleges, theAlliance to Involve Minorities mathematician is being organized. in Mathematics of the Mathematical Sci• SUMMAC funding currently supports ences Education Board, the Benjamin Core Support workshops at mathematics meetings. Sec• Banneker Association, the National Asso• tion workshops are continuing. If your ciation ofMathematicians, and the Society A request for core support has been submit• Section has not had a SUMMAWorkshop, for the Advancement ofChicanos and Na• ted to the National Security Agency. Their please contact the SUMMAoffice. Presen• tive Americans in Science. Members ofthe previous grant of $12,500 ended in April tations about successful projects will take SUMMAstaff have attended and/or partici• 1992. place in Vancouver, British Columbia in August 1993 and in Cincinnati in January pated inthe ICME-7Conference,the annual Mathematics-Based Projects meeting of the Hispanic Association of 1994.Aquarterlynewsletter, the SUMMAC Colleges and Universities, the annual meet• for Minority Students Forum, is now being published. ing of AISES and the ongoing Brownbag The purpose of this SUMMA activity is to Attracting Minorities into Discussions of the Quality Education for encourage college anduniversity mathemat• Minorities Network as part of outreach ac• Teaching Mathematics (AMIT) icsfaculty to initiate orreplicateintervention tivities to various groups. Several NSF or projects for minority middle and high school The National Science Foundation provided U.S. Department of Education conferences students. The Carnegie CorporationofNew funding for one year through 1993 for the have been attended also. York has awarded the MAA a second two• AMIT project. The purpose of the project Minority Participation in the year grant for this project in the amount of was to study the characteristics of under• graduate programs successful in attracting MAA $350,000. (See the article in the April 1993 FOCUS for more details.) This renews a minority students into teaching mathemat• IntheNorthCentral Section,effortsarebeing two-year grant awarded in May 1991. In ics at the secondary level. Special emphasis planned to increase minority participation 1993, 12 faculty were awarded $50,000 in was placed on two-yearcolleges and articu• by involving tribal colleges in their meet• small planning grants up to $5,000. lation concernsbecause of the large number of minorities attending these institutions. ings and activities, building on the model of SUMMAhas encouraged 29 projects in the thePacificNorthwestSection. The SUMMA lasttwo yearsandhas l8morebeingplanned. The study results will be published by the staff receives requests daily from inside and The goal is to have every mathematics de• MAA in the late summer or early fall of outside the mathematics community for in• partment sponsor a project each summerfor 1993. The publication will include invited formation about minority participation in underrepresentedrninorities.Byearly 1993, papers from faculty at minority and major• mathematics. ity institutions, a commissioned survey of ~ MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA An

16 states and 57 colleges ofeducation, and Organization for Mathematics Archival Record of Minority recommendations from a blue ribbon panel for suggested actions by government, the Departments at Minority Insti• PhDs in Mathematics or Math• mathematics/education community, the tutions ematics Education business community and the public. The SUMMAProgramproposesto develop Now that there is interest in minorities who Mainstreaming Projects for a new national collaborative focused on the hold such doctorates, it has proven to be a needs, concerns, and strengths ofmathemat• dauntingtask toidentifythem. Todate, more College Students ics departments at 52 selected minority than 300 names ofminority PhDs in math• This proposedprojectwill assist mathemat• colleges and universities because these de• ematics ormathematicseducationhave been ics departments at majority institutions in partments have the record for nurturing foundfortheArchivalRecord.The SUMMA reexamining their programs, setting goals minoritymathematicaltalent. Planning will Program is collecting pictures as well. It is for minority participation, and establishing be undertaken by SUMMA in cooperation hoped that details will be found about the mechanisms to reach these goals. The focus with key individuals from minority institu• educational accomplishments of all minori• will be on two-year colleges. The project tions and with representatives of minority ties who were U.S. citizens at the time they presently provides technical support to the professional organizations in mathematics• receiveddoctoratesin the mathematical sci• Charles A. Dana Center for Mathematics based fields. ences or mathematics education. and ScienceEducation, University ofTexas MentoringMinorities in Math• at Austin, for a research summer school for Conclusion minority students funded by NSF. The ematics Project SUMMA continues to have a major impact SUMMA Program assists with the recruit• The Mentoring Minorities in Mathematics on the members and structures of the MAA ment of minority faculty and students and Project (MMMP), part of a larger national and discussions are beginning about the in• facilitates meetings betweenDana staffand project, is seeking funding for a pilot in stitutionalization ofSUMMA. The work of faculty at minority institutions. Washington, D.C. and in Baltimore. The increasing minority participation in math• SUMMA also facilitates the participation proposed project is centered on mentoring ematics cannotbe limited to the activities of of minority mathematicians in the MAA 100 minority students in schools in the two SUMMA.As our foreign competitors grow Visiting Lecturers and Consultants Pro• cities on a one-to-one basis. Mentors will be more powerful and as we become more di• grams. This will enable minority and local minority professionals such as doc• verse, we Americans must use our diversity majority mathematics students to see mi• tors, dentists, architects, engineers, as a strength. High wage jobs will be acces• nority mathematicians in a positive setting. mathematicians and scientists whose back• sible only to those well versed in Plans for this component of SUMMA in• ground includes strong mathematics mathematics, "thelanguage ofthe 21st cen• clude the establishment of a database of preparation. The purpose of MMMP is to tury." The entire mathematical community minority mathematics students at various encourage the students to pursue appropri• is needed to ensure that minorities and all levels. ate mathematics and science courses other citizens speak this language. throughout their pre-college education. WilliamHawkinsistheDirectoroftheMAA Office ofMinority Participation

Committee on Sections renew their commitment

The Association has charged the Committeeon Sections with providing assistance to the sections, encouraging communication amongst them, acting as liaison between the sections and the Association's national headquarters, representing the sections to various constitu• encies and acting as a forum for the discussion ofconcerns ofthe various sections. The Chairofthe Committee serves on the Executive Committee of the Association to insure an avenue ofcommunication among all levels. The Committee on Sections continues to review its service to the 29 sections ofthe Association meeting in both the annual (winter) and summer meetings of the Association. The Committee also hosts the Section Officers meeting at these two conferences, with one officer from each section receiving a travel subsidy from the Association for only the summer meeting. However, many officers attend both meetings and a lively discussion is almost always guaranteed on topics of concern to the sections. Section officers will next meet on Sunday August 15, in Vancouver, immediately before the Joint Meetings ofthe Association and the American Mathematical Society with the Canadian Mathematical Society. The Committee encourages officers to forward agenda items to the chair before the meeting. Past meetings have been devoted to Department Guidelines, Mathematical Reform, P6lya Lecturers, Guidelines for Fund to Aid Sections, the new Math Horizons, and subconventions for sections. We look forward to assisting the sections with their endeavors. Section officers and members - how may we help you? 192 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The1992 MJ MAA Board of Governors Committee on Prior to conclusion ofthe MM Business Meeting in San Antonio, January 1993 Testing

Donald J. Albers, The Mathematical As• Rebecca Hill, Rochester Institute ofTech• The Committee on Testing (COT) is con• sociation ofAmerica and Menlo College nology cerned with mathematics testing and Gerald L. Alexanderson, Santa Clara Shirley A. Hill, University ofMissouri at assessmentfor grades elevenand twelve and University Kansas City the undergraduate level. It maintains and routinely improves the MAA's Placement John E. Allen, University ofNorth Texas John H. Hodges, University ofColorado Testing Program. In addition, COTinitiates at Boulder Lee H. Armstrong, University ofCentral and oversees externally funded projects rel• Florida John M. Holte, Gustavus Adolphus Col• evant to its mission, develops position lege statements on issues in mathematics testing David R. Arterburn, New Mexico Institute and assessment and cooperates with other ofMining & Technology Johnny L. Houston, Elizabeth City State MAA committees with related missions University (North Carolina) Donald M. Bardwell, Nicholls State Uni• (e.g., the Committee on the Undergraduate versity John W. Kenelly, Clemson University PrograminMathematics' (CUPM)Subcom• mittee on Assessment). Lowell W. Beineke, Indiana University• Donald L. Kreider, Dartmouth College Purdue University at Fort Wayne MAA Placement Testing Program Bennie R. Lane, Eastern Kentucky Uni- SincethePTP'sinception in 1977, COThas Marvin L. Brubaker, Messiah College versity overseen its activities. In March 1993, more Lawrence O. Cannon, Utah State Univer• Dennis M. Luciano, Western New En• than 300 postsecondary institutions sub• sity gland College scribed to the program. The PTP Program test packet contains twelve tests including Lily E. Christ, CUNY, John Jay College Richard F. McDennot, Allegheny College calculator-based versions of its Arithmetic ofCriminal Justice Alexander Mehaffey, Jr., University of and Skills, Basic Algebra, Algebra, and Curtis N. Cooper, Central Missouri State South Dakota Calculus Readiness tests. Subscribers also University receive anewsletterwhich ispublishedtwice Hugh L. Montgomery, University of a year. The Committeeis currently develop• Larry A. Curnutt, Bellevue Community Michigan ing a new Basic Algebra test, a College S. Brent Morris, National Security Agency calculator-based version of the Advanced William W. Durand, Henderson State Algebra and Trigonometry and Elementary Eric R. Muller, Brock University University Functions tests, and three calculator-based John D. Neff, Georgia Institute ofTech• prognostic tests. In spring 1993, the PTP John H. Ewing, Indiana University at nology began offering custom-designed tests to Bloomington program subscribers. Mary M. Neff, Emory University Barbara T. Faires, Westminster College Funded Projects Ruth D. O'Dell, County College of Susan L. Forman, Mathematical Sciences COT continues to oversee three externally Morris Education Board and CUNY, Bronx funded projects for the MAA: the Calcula• Community College Lynn J. Olson, Wartburg College tor-BasedPlacementTestProgram(CBPTP) Project, the Computer-GeneratedPlacement Bettye D. Forte, Fort Worth Independent Albert D. Otto, Illinois State University Test (CGPT) Project, and Teaching Math• School District Gerald J. Porter, University ofPennsylva- ematics with Calculators: A National James O. Friel, California State Univer• nia Workshop (TMC). sity at Fullerton Kenneth A. Ross, University ofOregon Grants from Texas Instruments fund the Leonard Gillman, University ofTexas at CBPTP Project. This project develops cal• Sharon C. Ross, Dekalb College Austin culator-based placementtestsand prognostic David A. Sanchez, Los Alamos National tests for the PTP test packet. When this Kendall O. Griggs, Hutchinson Commu• Lab project is completed, the PTP will feature nity College six calculator-based placement tests and Martha J. Siegel, Towson State University Deborah Tepper Haimo, University of three calculator-based prognostic tests. Missouri at St. Louis Olaf P. Stackelberg, Kent State University The Fund for the Improvement of John G. Harvey, University ofWisconsin Elizabeth J. Teles, Montgomery College PostsecondaryEducation(FIPSE)funds the at Madison CGPT Project. This project uses item-gen• Ann E. Watkins, California State Univer- erating functions to produce software that, sity at Northridge Please see COT on page 23 ~------1M Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Ann

cally attheendof1992.The tennsofHoward Devitt of the University of Waterloo. As Committee on Anton ofDrexel University and Milton D. usual, the studentpapersessions will be run Cox ofMiami University ended, as did the by Ronald F. Bames of the University of Student Chapters term of Charles A. Cable ofAllegheny Col• Houston -Downtown,and there willbe some lege, who was the first person to strongly travel moneyavailablefor studentspeakers, While continuing to encourage the forma• promote the idea of MAA Student Chap• courtesy ofthe Exxon grant. tion of new chapters and hence to increase ters. All three of these members were with the numberofstudent membersoftheMAA, the committee since its inception. Their ef• Part ofthe Exxon grant will fund awards to the Committee shifted its focus to appropri• forts to start and sustain StudentChapters is Sections which plan student programs on ate programmingand activities for these new behind much ofthe success ofthis activity. contemporary problems of society.Another members. For most students, participating use of the Exxon grant will be to increase in a section or national meeting is an excit• The San Antonio meetings in January 1993 chapter membership for underrepresented ing experience. Students enjoy the provided many activities for students, sup• minorities. W. HowardJones ofthe Univer• invigorating contact with other students of ported by the Exxon Education Foundation sity ofthe DistrictofColumbiais overseeing like interests, the challenge of new prob• grant. JosephA. Gallianofthe Universityof this effort with help from CMPM and lems andthethrillofmeeting mathematicians Minnesota-Duluth gave the Student Chap• SUMMA. whose names they know from their books. ters Lecture on ''Touring aTorus," followed A set ofguidelinesfor SectionCoordinators Nineteen ninety-two was a landmark year, by the popular make-your-own-sundae re• is being prepared and will be sent to all the providing students with such opportunities. ception. A student workshop on "Mathematics via Hands-on Experimenta• Sections to help them plan appropriate pro• InAugust, 1992, Miami University of Ox• tion" was presentedby HerbertR. Bailey of grammingforthegrowing number of student ford, Ohio, hostedthe Pi Mu Epsilon/MAA Rose- Hulman Institute of Technology. A members. Student Chapters Joint Conference - the Joint (with Pi Mu Epsilon)Advisors Break• Increased collaboration with other math• first-ever national mathematics conference fastwasfollowed by apaper sessionfeaturing ematics organizations, such as the AMS, is entirely for students. It was extremely suc• talks by student chapter advisors and sec• expected. cessful, with 29 student papers presented in tion coordinators. This session will be an the MAA sessions. Peter J. Hilton ofSUNY ongoing feature ofthe wintermeetings. It is For additional information on the MAA at Binghamton, gave the MAA invited ad• organizedby Karen J. SchroederofBentley Committee on Student Chapters, contact: dress on "Another Look at Fibonacci and College. Approximately 300 students at• Apama W. Higgins, Department of Math• Lucas Numbers." There were three tended the Second Annual Career Fair at ematics, University ofDayton, Dayton, OH minicourses- ''Tilings''presentedby Doris which 21 companies, laboratories, and as• 45469-2316; telephone: (513)229- 2103;e• W. Schattschneider of Moravian College, sociations discussed opportunities for mail: [email protected]; fax: (513) "Variations on a Spiral" presentedby David mathematicalscientists. ArthurT. Benjamin 229-4000. Kullman of Miami University, and "Envi• of Harvey Mudd College demonstrated his ronmental Modeling" presented by B. A. amazing mental calculations. COTfrom page 22 Fusaro ofSalisbury State University; a Ca• reers Panel Discussion with panelists from The Committeeon StudentChaptershosts a with monitoring, will generate PTP tests. government and industry; and Pi Mu Student Hospitality Center at each national COThas conducted research on the statisti• Epsilon's annual 1. Sutherland Frame Lec• meeting. Richard S. Neal ofThe University cal parallelism of PTP test items and has ture, presented this year by Underwood of Oklahoma runs this center, providing adjusted parameters associated with each Dudley of DePauw University, on "Angle puzzles, contests and information, a place to item-generating function to produce the Trisectors." The programwas notlackingin gather and a friendly respite from the bustle desired parallelism. The software facilitates opportunities for social interaction, what ofthe formal program.At each wintermeet• customization ofPTP tests. ing, a list ofNSF- supportedREUs and other with a pizza party, an MAAreception, the Pi Outreach andTraining Mu Epsilonbanquet, a trip to King's Island, summer research / internship opportunities is made available. In 1993 the Committee developed two po• and the popular MAA Hospitality Center, sition statements: The Use of Graphing where students congregatedto work puzzles DeborahA. Frantz ofKutztown University Calculators on Placement Testsand Appro• and problems, setup dinnergroups and chat! of Pennsylvania continued editing Chapter priate Use of Placement Tests. COT The ExxonEducationFoundationprovided News which is published twice a year. It is members continue to address mathematics its third grant to the MAA's Student Chap• a newsletter for Student Chapter Advisors. and assessment testing issues at national ters. Themoneywas used, in part, to support The year 1993 holds even more in store for meetings; during the past year COT mem• student speakers at the summer meeting. A StudentChapters. The activities ofthe Com• bers have delivered talks at the annual fourth Exxon grant has been awarded for mittee at the summermeetingsin Vancouver meetings of the American Mathematics use in 1993. The Committee on Student will have a Canadian flavor. The Student Association of Two-year Colleges Chapters gratefully acknowledges this con• Chapters Lecture will be given by Richard (AMATYC) and at the MAA's Joint Math• tinued support from Exxon's Education K. Guy ofthe University of Calgary, and the ematics Meeting in San Antonio. COT Foundation. student workshop "Using MAPLE to do continues to offer its minicourse on place• mathematics" will be presented by Stan ment testing at the Association's annual The Committee's structure changed drasti- meetings. .2 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MA

Publications 1992 MAA Titles

A Century of Calculus: Part I, T.M. • Calculus Problemsfor a New Cen• In Praise of Apostol, H.E. Chrestenson, C.S. tury, Robert Fraga Ogilvy, D.E. Richmond, N.J. • Learning by Discovery, AnitaSolow Schoonmaker • Problems for Student Investigation, A Century of Calculus: Part II, T. M. Editors Michael B. Jackson, John R. Ramsay Apostol, D. H. Mugler, D.R. Scott,A 1992 was a banner year for MAA Publica• Sterrett, Jr.,AE. Watkins • Readingsfor Calculus, Underwood tions, with sales topping the $700,000mark, Dudley up by more than $200,000 over 1991.These Excursions in Calculus, Robert M. figures reflect the intense and growing in• Young Statistical Abstract of Undergraduate terest of MAA members in a host of topics Programs in the Mathematical Sci• From Zero to Infinity, Constance Reid in mathematicsand mathematicseducation. ences, Donald J. Albers, Don O. The growth of MAA books is due in the Heeding the Call for Change, Lynn Loftsgaarden, Donald C. Rung, Ann main to our talented and hard-working se• Arthur Steen E. Watkins ries editors who work with Jim Daniel, Chair Statisticsfor the Twenty-First Century, of the Committee on Publications. They, Library Recommendations for Under• series editorial board members, and our re• graduate Mathematics, Lynn Arthur Sheldon and Florence Gordon Steen markable collection of authors are Student Research Projects in Calculus, responsible for the books publishedin 1992. Lure ofthe Integers, Joe Roberts Marcus Cohen,EdwardD. Gaughan, Thanks to Jim Daniel and the MAA book Arthur Knoebel, Douglas S. Kurtz, editors for their great work. Mathematical Circus, Martin Gardner David Pengelley Twenty new books were published in 1992, Mathematical Cranks, Underwood Symbolic Computation in Undergradu• including the best-selling, five-volume Re• Dudley sources for Calculus Collection. The first ate Mathematics Education, Zaven printing 00000sets sold out in less than six Mathematics Book Recommendations Karian for High School and Public Librar• months. RCC was described in a recent The Concept of Function, Guershon ies, Lynn Arthur Steen Mathematics Magazine review as "a trea• Harel, Ed Dubinsky sure trove for the instructor who wants to Resources for Calculus Collection ease into 'calculus reform,' or for one who Two-YearCollege Mathematics Library wants to plunge in with both feet." • Applications of Calculus, Philip Recommendations, Lynn Arthur According to our all-member survey, stu• Straffin, Jr. Steen dents seem to be more important than ever to MAA members. Survey respondents strongly endorsed two new publications projects for students - Math Horizons, the new magazine for students, scheduled to premier late this fall; and Classroom Re• sources Materials, our newest book series. We are very excited about these new stu• dent-oriented projects for 1993.

-Don Albers “I’mdelighted to have the opportunity to work with a great Diredorof group of book-series editors to help continue the MAA tra- Publications dition ofpublishing important, interesting, and well-written material. 7’hanksto technology, thepublishing worldischang- ing and the MAA publications program is changing with it. I hope that Association members will continue to send us the ideas -and manuscripts- we need in order to grow in new

directions. ” -Jim Daniel Chair, Publications Committee A Annual Report The 1992 MAA Annual Report I The 1992 MAA Annual Report The 1992 MAA Ann 1992 Series Editors

Donald W. Bushaw Marjorie Senechal Andrew Sterrett, Jr. Washington State University Smith College Denison University MAA Notes and Reports Carus Mathematical Monographs Classroom Resource Materials

Paul Zorn Anneli Lax St. OlafCollege New York University New Mathematical Library New Mathematical Library

Meyer Ierison Roger Horn Bruce Palka Purdue University University ofUtah University ofTexas - Austin MAA Studies in Mathematics Spectrum Dolciani Mathematical Expositions 92 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The1992MA

Long, John M. Long. ].]. Malone, Marc Mappen (In Memory of Leon Warren Cohen), William The Greater MAA Fund Margulies, AndrewJ. Matchett, Arthur P. Mattuck, Robert G. Maule, Raymond A. Mayer, Jr., Janet McDonald (In Memory of Virginia Felder), In 1992,896 donors contributed $46,654 Alexander Mehaffey,Jr., James W Mellender, Rob• to the Greater MAAFund. The Officers of ert T. Mertz, Shirley G. Miller, Gerald A. Mischke, Samuel Goldberg. Samuel W Hahn, M. E. Charles D. Mooney, Frank Morgan, Thomas L. the Association express their gratitude to the Harnstrom, BillHassinger,jr. ,jerryM.Hawn, Shirley Morton, L. T. Moston, Earle F Myers. Togo membership for its generous support of this A. Hill, Joseph A. Hughes, James E. Huneycutt. Nishiura, Victor T.Norton,Jr., Tom E. Norwood. fund. The names of all 1992 donors, except ThomasE.Ikard, D. Richard Utis. Carl G.Jockusch, Andrew M. Odlyzko, Rene E. Olivares, Anne F of those wishing to remain anonymous, ap• jr., Richard E. Johnson. Wilfred Kaplan, John T. O'Neill, Calvin 1. Owens. Ervin E. Padgett, III, pear below. Kearns,jr., Richard A.Keele,Daniel Kennedy,Edwin Diego Pareja, Nicholas Passell,Rhodes Peele,Sharon M. Klein. Katherine P. Layton, Margaret L. Lial, E. Persinger,]ames M. Pike, Peter R.Pomeroy, Guy• RichardA. Little.William D. Maness, MayH. Maria, Serge Pompilus • Margaret A. Rejto, Charles E. Grand Benefactors Thomas]. Marlowe, David M. Merriell, Harriet F Rickart, David W Roeder, William G. Rosen,john Binnie and Herbert M. Baruch, Jr., Marvin L. Montague, Javier F Moreno-Valle, Benjamin N. D. Rudolph. David H. Sanders, Diran Sarafyan, Bittinger,Malcolm K.Brachman, DeborahT.Haimo, Moyls,]ohnD. Nelligan, Morris Newman, Edward Donald E. Sarason, Richard L. Schauer, Irene V Richard A. Hord, Edward Kitchen, Anonymous C. Nichols. Arnold M. Ostebee, Clem Z. Ota. Schensted, Charles M. Schneeberger, Klaus Murray B.Peterson,johnW Petro, DonaldL. Plank, Schocken, Norman E. Sexauer, John K. Seymour, H. O. Pollak, Bruce T.Prendergast. Grace S.Quinn Abe Shenitzer, FrankC. Sherburne,David L. Sherry, Benefactors • Irma M. Reiner (In Memory of Irving Reiner), MarthaJ. Siegel,CandidoSitia,johnS. Skocik, David Alfred and Dorothee Aeppli, Gerald L. Franklin B. Richards, Raphael M. Robinson.jean• A. Smith,]ames L. Smith, Paul R.Smith, Wilbur L. Alexanderson, Lida K. Barrett, Barbara]. Beechler, Louis Roque, Kenneth A.and Ruth Ross, Sharon C. Smith, Louis Solomon, Robin N. Soloway,David A. William G. Chinn, Jean E. de Valpine, William E. Ross.Jeffrey R.Sachs and Priscilla Cehelsky,John Sprecher, Allen H. Stix, Thomas M. Sturm.Joni L. Dorion, William L.Duren, Emma W Garnett, Marcia A. Schumaker, Richard]. Shaker, John M. Smith, Tamayo-Wilson, Laurence R. Taylor, Roseanna F L. P. Sward, Uri P. Treisman John Snyder, Robert H. Sorgenfrey, Blair Sterba• Torretto, DavidA. TrautmanjavisutdhiUpatisringa Boatwright, Steven N. Strand, Michael T.Surdyk. • John P. Van Alstyne, Wolmer V Vasconcelos, James W Thomas, Thomas W Tucker. Elizabeth Stephanie A. Walborn, Joe F Wampler, Alex GrandPatrons B.and Robert Weinstock (In Memory of Harold M. Weintraub (In Honor of Tufts University Depart• Anna S.andDouglas Henriques, D. D. Miller,Gerald Bacon), Paul T. Witzke (In Memory of George A. ment of Mathematics), Marie S. and William B. ]. Porter, Robert A. and Marjorie Rosenbaum, Paul Parkinson), Jeffrey K. Woodhead (In Honor of G. Wilcox, BrunoWolf, Edward Wong. Anonymous ]. Sally,Jr., Lynn A. Steen, Alfred B. and Shirley Thomas Sallee), David]. Wright. Anonymous (2) (4) Willcox Contributors Sustainers Patrons Clarence M. Ablow, Youness Ahmadian, William William W Adams, Frank A. Adrian, Michael 1. Carole A. Bauer, John and Clara R. Bender (In O. Alltop, Beverly]. Anderson, John A. Ausink, Aissen, Sheldon B. Akers, Yousef Alavi, George E. Memory of Joshua Barlaz), Stewart E. Boden. SheldonAxler. William R.Ballard, Enrique Bayo, Alberts, Allen S. Aldridge, Frank B. Allen, William Nathaniel Chafee,Betsy Feagan Colquitt (In Memory Phillip R.and Kathryn Bender, Charles H. Bertness, C. Allen, III, Alexander A. Ambrioso, Anne L. and of R H Bing). Ronald M. Davis. David V Finch Richard M. Bittman, Peter B.Bjorklund, William D. Donald B. Anderson, Michael H. Andreoli, Ken• and Mary E. Flahive (In Memory of lohn V Finch) and Kathleen Blair, Raymond T. Boute, Thelma E. neth 1.Appel, Florence H. Ashby, Douglis Avron. • Richard L. Gantos,]. H. Graham. Thomas A. Bradford, MurrayBraden, Amos D. Bradley,Gary L. George Bachman, George A. Baker, Fred E. Ballard, Hem, Betty F and Larry L. Hinman. James R. C. Britton, Kenneth A. Brons, Robert E. Brown, John Leon Bankoff, Wayne T. Barnard, Kathleen Baxter, and Joan R. Leitzel, R. B. Lind. Eugene A. E.Bruha, Regina C. and Carl E.Brunner(In Memory JerryP. Becker (In Memory ofE. G. Begle),E.Maurice Margerum, Walter E. and Gretel Mientka, Chester of Robert M. Exner), Richard T.Bumby, Thomas R. Beesley, John B. Bennett, Margretha M. Bentz, W Mills. John D. Neff. Kenneth R. Rebman. Butts, Charles L. Byme,jr.• Raymond]. Cannon, Geoffrey C. Berresford, David G. Bethelmy, Andrea Bernard Sohmer, Olaf P. Stackelberg, Maria W Jr., John E. Carson, William L. and Phyllis Carter, G. Blum, S. Elwood Bohn, William E. Boyce,]ames Steinberg, Robert Steinberg. Alben W Tucker (In Charles A. Chapman, Fen Chen, Hubert E. N. Boyd, Fred F Brack, Murray and Geraldine Memory of R. S. Pieters),. Allyn]. Washington, Chrestenson, Leroy M. Christophe, Jr., Robert A. Braden, George H. Bridgman, Harold F Bright,Susan Stephen S. Willoughby Clark, Philip Cobb, Bruce!. Cohen, Daniel 1. A. S. Brinckerhoff, ArthurB.Brown, Austin R.Brown, Cohen, Michael P. Cohen, Ivan E. Colon, Robert]. Patrick]. Brown, Billy F. Bryant, Donald L. and Beatrice Cone, Thomas A. Cootz, Clyde L. Burkholder, Ralph S. Butcher.John G. Campbell, Sponsors Corcoran, Samuel G. Councilman, James P. Dennis]. Caro, Dennis Carrie, Vasily C. Cateforis, HenryL. Alder, Margaret G. andL.ThomasAldrich, Crawford. Anthony B.Di Luna, George W Dinolt, YunK.Chan,Ronald]. Chase, Charles C. Chouteau, Samuel!. Altwerger, Richard D. Anderson, David JamesA. Donaldson,]amesB. Dowling. CliftonE. John O. Church, Richard C. Churchill, Michael H. R. and Kathy Arterburn. Edward D. Baker, Gre• Ealy,Gerrit Mark Edris, Stanley B.Eliason, Edward Clapp,james H. Cliborn,jane E. Clifford, Leon W gory A. Bastian, Donald Batman, Lynne A. Baur, T. Esty, Frank D. Faulkner, Ian M. Ferris, Paul T. Cohen,RichardM. Cohn,johnE. Crandall,AnnM. Robert D. Bergstein(In Memory ofRHBing),Manuel Fjelstad, Timothy]. Frawley, Michael D. Gilbert, Curran, Philip C. Curtis. Watson M. Davis, Peter P. and Maria Berriozabal, Steven E. Blasberg,]ean E. Ross B. Gingrich, Frank C. Graves, Eric W Gray, G. De Buda, Roger M. Dell, Jean H. Dewallens, and Willard E. Bleick, John D. Bradburn, John D. John W Green, Curtis Greene, Elliot M. Grurnera Charles R. Diminnie, Kotaro Dokeh, Harold L. Bramsen, Milo F Bryn, Robert Bumcrotjs Lily E. Carl Hammer, John L. Hank, Katherine Heinrich, Dorwart, Gregory M. Dotseth, Roy]. Dowling. Christ, A.]. Coleman,]anW Dash, Wayne Dennis, leonA. Henkin, Delfin G.Hernandez, R.B.Herrera, Charles H. Edwards, Elwood G. Edwards, Constance Guy De Primo, Martha Dresher (In Memory of John M. Horvath, M. Gweneth Humphreys, John L. Elko, Herbert E. Elliott, jr., George W Ellis, Melvin Dresher), Robert L. Druet, Underwood A. Hymo. Rosella Kanarik, Zaven A. Karian, Vir• Raymond L. and Gertrude Ely, Gerard G. Emch, Dudley,Charles Everett Dutton. Bernard A, Edison, ginia G. Kasten, Ernest]. Klotz, Roger P. Kovach, Jessie A.Engle, DickranH. Erkiletian, Michael Evan SusannaS.Epp. Barbara T.Faires, Robert W Field• Ralph M. Krause, Gary R. Krumpolz, Dennis E. • Sonia Favela-Vara, John C. Fenley, Emanuel ing, Eugenia E. Fitzgerald,]. S. Frame, James H. Kunimurajs Richard G. Larson, Anneli Lax,Robert Fischer, Ismor Fischer, Marjorie Fitting-Gifford, Freeman. RobertW Gibson, Andrew M. Gleason, N. Leggett, Rudolph B. Lim, Shen Lin, Clifford A. Kenneth E. Fitzgerald, Peter R. Flusser, Gabriel ~ Annual Report The 1992 MAA Annual Report The 1992 MAA Annual Report The 1992 MAA An.,

Fontrier, Stephen H. Forbes, Susan L. Forman.]o• Abdulalim A. Shabazz, Melvin A. Shader, Edward William B.Harrison, Lawrence A. Hart, Neal Hart, seph B. Frechen, Lawrence E. Freeman, Herta T. Shapiro, S.David Shapiro, HenrySharp,Jr., Ching• John C. Hayes, Nola A. Haynes, Vivian E. Heigl, Freitag, Charles H. and Bennye Frick, E. Clare Kuang Shene, CharlesShenitz, Alpha]. Shirey;Dale James B.Herreshoff, StephenR.Hilbert, Francis H. Friedman, Susan L. Friedman, Thomas J. Fritsch, Shisler, Tom E. Shrader, David L. Skoug, Muriel Hildebrand, William M. Hilton, Paul]. Horn, Helen H. Froberg,John N. Fujii .AnnC. Garstang, Skoug, Eddy F. Smet, Lloyd B.Smith,Jr., Samuel E. Charles D. Horvath, Raymond L. Houpy, Cephas Murray Gechtman, Colin M. Glanville, Michael Smith, Rubin Smulin, Charles E. Snygg, Joel H. D.Hughes, Patricia M.Hughes, MarkE. Huibregtse, Glass, Germana 1. Glier, Dennis Glovach, Arthur Spencer, Craig C. Squier, Peter E. Staab, Robert S. Burrowes Hunt.john]. Hwang.JudithE.]ohnson, W Goebel, Leonard D. Goldstone, Robert N. Goss, Stacy, Philip P Stich, Virginia Stover, Thomas N. Robert C. Johnson. Takeshi Kano, Carl E. Kerr, Robert L. Graves, Florence N. Greville, Torrence 1. Strickland, PeteJ. Stuckey, Mary V Sunseri, Jean L. Rose H. Kim, Michael]. Klass, Marcia Klein,James Gurman .James N. Hagler, Gena Hahn, Earl G. Sutherland, Ronald Sverdlove, D. Derk Swain,Josef R.Kochan, Daniel E. Koditschek,John G. Koelzer, Hansen, Frank Harary; William]. Hardell, John G. V Swatek • Norma]. Taber, Richard B.Talmadge, III,Peter M.Kohn, EarlS.Kramer,Gary M.Kretchik, Harvey;Frank S.Hawthorne (In Memory ofLeonard Angus E.Taylor,LeeA.Taylor,Raymond F. Tennant, Henry A.Krieger,Eunice L. Krinsky,HerbertKurss, Schwartz), Dorothy M. Heller, Francis M. P E. Thomas, James c. Thorpe, John A. Thorpe, John F. Kurtzke,Jr.•Fat Cheung Lam, Margaret F. Henderson, Donna W Herrick, Emil R. Herzog, Wolfgang]. Thron, Sally Tippett (In Memory of Land, Arnold Lapidus, Walter R. Lawson, Ruth S. Gerald A. Heuer, James Hewitt, James F. Heyda, Gary R.Tippettl.james N. Tipton, HenryS. Tropp, Lefkowitz, Kathryn Lenz, Richard G Levin, An• Charles F. Hicks,JamesL. Higgins,JohnA. Higgins, Theodora L. Tsakiris, Bryant Tuckerman .Yasushi drew C-F Liu, Thomas P G. Liverman, Edith H. Ellen L. Hocking, Helen R.Hoffman,JeanM. Horn, Unai .JanA. Van Casteren, Richard]. Vance, Dale Luchins, Daniel H. Luecking, Helen H. Luscher. ]. G. Horne, Jonathan B. Horrell, Thomas G. E.Varberg, Sr.Paul]. Villemure .JamesD.Watson, Thomas Madej, RoyA. Magda, Kenneth D. Magill, Hospelhorn, V Dwight House, Fredric T.Howard, John C. Weaver, Waldemar C. Weber, David M. Gregoris A. Makrides, Dennis R. MaIm, James R. Joy Hsiao, Wallace Hummasti, John P Huneke, Wells,WillesL.Werner, Donald C.West (In Memory Marshall, Ronald M. Mathsen, Alafuele Mbuyi• James F. Hurley;LeeP Hutchison, Edward L.Hutton ofR H Bing),ChristopherC.White, Myron E.White, Kalala, Vincent O. McBrien, Donald]. McCarthy, • Franklin T. Iha, Matthew O. Ikle, M. D. Lucille E. Whyburn, Herbert S. Willcox, Pete C. Neil B.McConlogve, Earlena F. McKee, Edward B. Indjoudjian,YoeItokawa, LynnH. Iwamoto .Henry Williams, Eric ]. Wingler, Donald F. Winter, Izaak Mcleod, Jr., Diane T. McNichols, Morris Meisner, G. Jacob, Gerald G. jahn, Hae-pyng jea, June R. Wirszup, Richard A. Witt, Rozelle B.and Bradford Michael]-H Meister, Gerhard Metzen, Richard C. Jensen, Gerald Wjohnson, Paul B.Johnson.Diana Wright .JeongS.Yang,Nicholas W Yang,Howard Metzler, Ronald E. Mickens, John G. Milcetich, Kalish, PaulA. Kaschube,]ohn B.Kelly; William R. H. Yeager,Hisashi Yokota.Gary E. Zablackis,John Michael H. Millar, Deborah]. Miller, G. H. Miller, Kemp, George A. Kent, Thomas C. Kipps, Mary L. M. Zerzan, Francis E. Zimmer, Leon P Zukowski. William R. Miller,Jr., Bryan P Moran, Bernard B. Klaas, Benjamin G. Klein, Elizabeth D. Klipsch, Anonymous (10) Morrel,JosephG. Moser, Ronald G. Mosier, Marvin Robert C. Knapp, Ignace 1. Kolodner, David M. G. Mundt, H. Deon Murphy; Michael G. Murphy. Krabill,Jean S.Kromer,John S.Kronholm, Norbert EdwardA. Nordhaus, Edward Norman, Ronald D. ]. Kuenzi • Jeffrey c. Lagarias, Nancy L. Laing, Other Donors Notestine. Edward Onstott, Jr., Albert D. Otto, John P Lambert, Kenneth C. Lane, Michael L. Neil E. Aiken,]ohn E. Allain, Richard A.Alo, Bertil Harold Oxsen • Joseph W Paciorek, Helen L. Lapidus, William G Leavitt, ArnoldLebow,Joseph Anderson, Michael Anshel, Helen C. Arens • Paisner, Prakash Panangaden, Osborne C. Parch• Lehner, Alan L. Levine, Bingxi Li, Wendell D. Arienne S. Balser, David W Bange, Edward]. ment, Elwood G.Parker,BruceB.Peckham, Stephen Lindstrom, M. A. Linton, Charles]. Lombardo, Barbeau,William H. Barker,Philip R.Bartick,Walter A. Pennell, Ed A. Petron, Esther R. Phillips, Loren Emmet F. Low,Jr., Robert B. Lumbert, Gustave H. W Bartlett,]ohn S. Bartling, Brian D. Beasley, Tho• D. Pitt, Mitchell P Preiss • Francis Regan,James E. Lundbergjalohn]. MacDonnell, ThomasA. Mackey; mas E. Bengtson, William R. Bennett, Irving O. and Patricia Reiland, Bruce A. Reznick, Robert M. Dino M. Mako, Mihalis P Maliakas, Joseph S. Bentsen, Daniel C.Biles,Jerry M.Blackmon, Ashton Richardson, Lawrence B.Richmond,JoyceA. Riley, Mamelak, Heinrich Mantel, Richard]. Marchand, Blair, Dorothee J. Blum, William M. and Ruth Deborah G. Rogers, Robert A. Ropell, N.]. Rose, StephenB.Maurer,Gus Mavrigian,FarleyJ. Mawyer, Boothby; Delmar L. Boyer,ArthurE. Bragg,Fred G. Louis Ross, Peter A. Rothmaler, T.Benny Rushing, John R. Mayor, Charles W McArthur, Thomas Brauer, George U. Brauer,John E. Brothers.johnL. John Russo. Mayra Alonso San Roman, John F. McConnell, Freddie L. Mclaurin, Stephen H. Brown, Richard H. Brown, Heinz A. Bruggesser, Schmeelk, Dawn L. Scholland, Dexter Senft, War• McMullen, Robert F. McNaughton, Jr., Robert C. Andreas Brunnschweiler, Sylvester W Bryant, ren E. Shreve, Donald M. Silberger, Karen]. Small, Meacham, Robert]. Meier, Sandra Ann Mertes, Francis R. Buianouckas.james P Burling, Herbert ChristopherL.Smith, Margaret]. Smith (In Memory Michael A. Miniere, CharlesW Mitchell,Jr., Deane Busemann • Susan L. Callahan, Howard H. of Roland F. Smith), Richard A. Smith, Alexia A. Montgomery, Mabel D. Montgomery, Leone C. Campaigne, Duff G. Campbell, Richard D. Sontag, William L. Soule, jr., Edward]. Specht, Monticone, James D. Moore, Richard A. Moore, Carmichael, James A. Carpenter, I-Chen Chang, Stephen E. Spielberg, Robert R. Spieler, Walter C. RufusA. Moore, Larry]. Morley;Burt]. Morse, Paul Daniel S. Chesley, Chris Christensen, Thomas P Stanley,Richard S. Stevens, T.Christine Stevens, A. F. Murphy; MargaretA. M.Murray;William H. Myers Cieslik,MicheleG. Clement, Martin]. Cohen,James D. Stewart, John R. Stock, Colin Strickland,]. B. • Herbert Nadler, Mark A. Narduzzi, Edward O. Coppola, Mary K.Corbitt, Henri Cornet, Clifton E. Stroud, Jeffrey L. Stuart, Cynthia S. Stubblebine, Nelson, Richard A. Nelson, Joseph D. Novella. Corzatt, CathyM. Cryvoff,Joseph Cunsolo • Brian Stewart G.Swerdlow,]. David Swift,PeterP Szabaga Rodney G. Olinger, Hironori Onishi, Robert F. Doolin, Allen G Dors, Veronica M. Dort, John G. • Choy-takTaam, SteveD.Takle,TalIeeT.Tanimoto, Osserman, David B. Oulton • Hector D. Pacheco, Driscoll, Regina C. Dukes. Earl F. Ecklund, Jr., Robert E. Thomas, Harold Thornton, Charles R. Jingyal Pak, John D. Paliouras, Francis D. Parker, William 1.Eggers, Alexander S. Elder, Wade Ellis, Traina, Po-Son D. Tsao, Heidi A. Tschuemperlin, Suzanne G. Patunas, John A. Paulos, N. T. Peck, Jr., Aaron G. Enright, Ronald]. Ensey, Margarita S. Joseph Tucker, Lisa C. Tucker. Rosario Urso • H. Paul S. Peck, Joseph Pekarsky;John W Pennisten, Escatelljs.Albert B.Farnell, ArnoldL. Fass,John C. R. Van Der Vaart, Andrew H. Van Tuyl • Irene Hoshang Pesotan, Juanita]. Peterson, Robert R. Fay, Irwin K. Feinstein, William A. Feldman, Vaughan (In Memory of Herbert E. Vaughan), Eric Phelps, Marilyn Pierce (In Memory of Richard S. Rosanne M. Ferdico,JesusFerrer, Daniel C. Fielder, F. Verhoeff,William M. Wagner, Curtiss E. Wall,]i Pierce), Vera S. Pless, Ervin]. Prouse, Calvin M. William M. Finlay, Henry C. Finlayson, Che-Kao Sheng Wang, Herbert H. Wathan, George L. Watts, Pullias • Richard Quint.Thomas G. Railey; Max• Fong, Richard C. Fowler, Michael L. Frame, Robert Gerald M. Webster, John Weibel, Anthony A. well O. Reade, Robert W Rector, Raymond M. K. Franz, Austin French, Wolfgang H. Fuchs • Weidner, Harvey M. Weitkamp, Edward C. White, Redheffer, Pamela C. Richards, Steven F. Rieth,Jose Raymond L. Gaillard, Turkan K. and John S. Jr.,Agnes]. Wieschenberg, Patricia S.Willis, Milton Rio,James S.Robertson, Haskell P Rosenthal,James Gardenier, Samuel Y. Gebre-Egziabher, Juergen E. Winger, Robert H. Wood, Michael C. Wu, David W Roth, Emilio O. Roxin, David K.Ruch, Dorothy Gerlach, Doug Girvan, Seymour Goldberg, Luis• J. Wydra. 1.K.Yale. Radu Zaharopol, Lieselotte S. Rutledge, Clarence F. Rydeen, Charles]. Rykken Enrique W Gomez, Arthur Goodman, Hugh Zassenhaus (In Memory of Has]. Zassenhaus), • Donald Y. Sakahara, E. W Sanders, Blin B. Gordon, RonaldA. Gove, Peteris E. Graube, Cheryl Kecheng Zhou • Anonymous (In Memory of Sr. Scatterday,Ernest C. Schlesinger, Gregory A.Schou, L. Gregerson, D. B.Gumaste jsClair R. Haberman, Ruth M. Schickel), Anonymous (2) HorstSchraegle, Manfred R.Schroeder,JohnSchue, Peter J. Hagis, Milton W Harden, Beverly B. Marsha A. Segal, Sanford L. Segal,Arthur G. Settle, Hargraves, Glen A. Harris, Jr., James O. Harris, FOCUS August 1993 The Search for E.T. Bell Also known as John Taine by Constance Reid

EricTemple Bellhasbeen oneofmyheroesfor60years...Icongratu• lateConstanceReidonaremarkableachievement. I hopeitisgreeted withthesuccess it deserves, and revives interest in an extraordinary and multi-talented man. -Arthur C. Clarke

ConstanceReid reveals an engagingstory aboutahighly interesting and complex individual: Eric Temple Bell, as student, husband, father; teacher; mathematician, historian, poet, and sciencefiction pioneer: Thestory ofBell's lifeisfascinating, and thedescription of thepainstaking detective work that unveiled this story is equally fascinating. It is a remarkable piece of work. -Tom Apostol

No onetoday writes aboutmathematics and mathematicians with E.T. Bell more grace, knowledge, skill, and clarity, and no one is going to produce a more delightful, informative, accurate account ofEric gins with the discovery ofan unexpected inscription in an Temple Bell and his work, and that of his alterego, theprolific English churchyardanda seriesofcrypticnotationsin a boy's pioneer of sciencefiction, John Taine. This is afine book. schoolbook. Then comes an inadvertent revelation, by Bell -Martin Gardner himself, in a respected mathematicaljournal...Youwill have Eric Temple Bell (1883-1960) was a distinguished math• to read the book to learn the rest. ematician and a best-selling popularizer of mathematics. His Men ofMathematics, still in printafter almost sixtyyears, Originallyagreeing to write only a profile of Bell, Constance inspired scores of young readers to become mathemati• Reid soon found herselfinvolved in a full-length biography.. cians. Under the name 'John Taine," he also published The discoveries she made in the course ofher five years of science fiction novels (among them The TimeStream, Before research will necessitate a fresh evaluation of his extensive theDawn, and TheCrystal Horde) thatserved to broaden the mathematical work and his science fiction novels as well as subject matter ofthat genre during its early years. therevision ofalmosteverystatementcurrentlyin printabout his family background and early life. In The Search for E.T. Bell, Constance Reid has given us a compellingaccountofthis complicated, difficultmanwho Includes a collection ofover 75 photographs. never divulged to anyone, noteven to his wife and son, the story of his early life and family background. Her book is 384 pp., Hardbound, 1993 thus more ofa mystery than a traditional biography. It be- ISBN 0-88385-508-9 List: $35.00 Member:$28.00 Catalog Number BELL

~------August1993 FOCUS Constance Reid- Why I Write About Mathematicians

There are certain questions these books, A Long WayJromEuclid, introduced me to the cap• that I am often asked in con• tivating figure ofDavid Hilbert and the legendary charm he nection with my writing about exercised over the young mathematicians of GOttingen. I be• mathematics and mathemati• came obsessed with the idea that the general public should cians. First-are you a learn about this unique man. mathematician? No. Then• How did it happen that you write about mathematicians? FormerstudentsofHilbertwerenotencouraging,butultimately it wastheenthusiasm ofone ofthem-Richard Courant-that resulted in myvery nontechnical accountofHilbertbeingpub• It happenedthefollowing way. lished by Springer-Verlag andfalling into the hands, notofthe In 1952 I waswriting shortsto• general public, but ofthe scientific community. A life ofCou• ries, and even considering an rantfollowed-anaturalsequel. I thenturnedtosomeonecloser Constance Reid novel, when my sister Julia to my home in San Francisco-the statistician Jerzy Neyman, Robinson told me abouta pro• who in his eighties was still running the famous "stat lab" he gram her husband, Raphael, a founded at Berkeley. mathematics professor at Berkeley, had written for one of the new electronic computers that had been developed during World War II. In one evening the program, which tested the Today I am being asked still another question in regard to my 257_1, primality of Mersenne numbers beyond 2 had turned up writing about mathematicians: How did I choose E.T. Bell? twopreviously unknown perfectnumbers, thefirst to be ascer• tained in seventy-five years, butwhat I found most interesting I did not really choose Bell. In 1988 I agreed to write a dedica• wasthat although the "giant brain" could work with numbers tory profileofhimfor thesequel to MathematicalPeuple. Ialready far beyond theability ofhuman beingsand the ordinarycalcu• knew from Julia of the inspirational effect ofhis Men ofMath• lating machines of the day, it could not answer the simple ematics. When it appearedin 1937,she wasa mathematicsmajor question that Euclid had asked. How many perfect numbers atasmallcollege in SouthernCalifornia, essentiallya "teachers" are there? college. It was through reading Bell's book that she realized there was something she could do with mathematics besides teach it. She could become a mathematician. So I was not ad• I wrote an article about Raphael's work, which appeared in verse to writing the proposed profile and giving Bell his due as Scientific American. The publisher Robert Crowell read it and the fatherofmathematical biography. How andwhytheprofile asked if I would be interested in writing "a little book about developed into a full-length biography ofa very elusive man• numbers" for him. The result wasFrom Zero toInfinity, a fourth "a cat that cannot be caught," as Marianne Moore said ofT.S. edition ofwhich has been issued recently by the MM. I wrote Eliot-is the story of The Search forE.T. Bell. two more books explaining mathematical ideas to "educated laymen" who had had no more mathematics than I. One of FOCUS August 1993 NEW RELEASES FROM THE MAA

Exploring Mathematics With Your Computer Arthur Engel

Today's personal computer gives its owner tremendous powerwhich can be used for experimental inves• tigations and simulations ofunprecedented scope, leading to mini-research. This book is a first step into conjectures which can then be proved by mathematical reasoning. You will find 65 interesting and substantial mathematical topics in this book, and over 360 problems. Each topic is illustrated with examplesandcorrespondingprograms. The majorgoal ofthe bookisto use the computer to collectdataandformulate conjectures suggested by the data. It is assumed that readers have a PC at their disposal. A 3.5" IBM-compatible disk containing the Pascal programs in the book is packaged with this volume. 264 pp., Paperbound, 1993, ISBN 0-88385-636-0 List: $38.00 .MAA Member: $26.50 Catalog Number NML-35

The Wohascum County Problem Book George T. Gilbert, Mark Krusemeyer, and Loren C. Larson

If you like problem solving, this bookbelongs on yourshelf. This collection of130 challengingproblems, with carefullyworked-outsolutions, ispresentedin the form of "word problems"relating to everyday life in Wohascum County, Minnesota, a rather remote area which is not to be found on any map. Some knowledge oflinearor abstract algebra is neededfor a few ofthe problems, butmostrequire nothing beyond calculus, and many should be accessible to high school students. However, there is a wide range of difficulty, and some problems require considerable mathematical maturity. For most students, few, ifany, ofthe problems will be routine. The book centers on solutionswhich are elegant, instructive, and clear. Often several solutions to the same problem are presented. Some problems have complicated solutions, and many ofthem are quite long. Sometimes solutions are preceded by "Ideas," which can serve as motivation or as hints, or followed by "Comments," which often put solutions in a broader perspective. Indices are provided which may be especially helpful to problem solving classes and to teams of individuals preparing for contests such as the Putnam exam. 244 pp., Paperbound, 1993, ISBN 0-88385-316-7 List: $26.00 .MAA Member: $19.00 Catalog Number DOL-14 @------August1993 FOCUS Excursions in Calculus An Interplay of the Continuous and the Discrete Robert M. Young Printed with eight full-color plates.

Youngprooides amplematerialforany studentorteacher ofcalculustosharpenhisorherinsightinto thesurprisingly diverse waysin whichthesubject impingeson therealmof discrete mathematics...an excellent source ofprojectsfor wellmotivatedstudents. The listof463 references is a valuableaid for those who wish todig deeper: -CHOICE The purpose ofthis book is to explore, within the contextofelementarycalculus, the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point ofview as a unifying principle are continually explored as they interact with traditional calculus. The interaction enriches both. The book is addressed primarily to well-trained calculus students and those who teach them, butit can also serve as a supplementin a traditional calculus course for anyone who wants to see more. The problems taken for the most partfrom probability, analysis, and number theory, are an integral partofthe text. Many point the reader toward further excursions. There are over 400 problems presented in this book. 408 pp., Paperbound, 1992, ISBN 0-88385-317-5 List: $39.00 MAA Member: $31.00 Catalog Number DOL-13

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Attheworkshop,Ri• Starting an Indus• chard Herman, director of the Joint trial Postdoctoral Policy Board for Mathematics (JPBM)inWashing• Program ton, D.C., discussed how to develop "so• A handful ofpostdocs and a few industrial cial contracts" giants are trying to answer the question: between labs, indus• "How can I put mathematics to use in real try, and universities. life?" They are part of a fellowship program The JPBM is an ex• developed by the Institute for Mathematics ecutive action and and itsApplications (IMA) atthe University public policy arm of of Minnesota. the American Math- The IMA fellowship program connects ematical Society,the Richard Herman. Chiar; Joint Policy Boardfor Mathematics; Sam postdoctoral mathematicians with industry MathematicalAsso• Kramer, Associate Executive Director, National Institute ofStandards researchersatcompanies suchasHoneywell, ciation of America, and Technology; John Simpson, Director, Manufacturing Engineering 3M, and Siemens. The postdoctoral students and the Society for Laboratory, NIST. apply their skills in advanced mathematics Industrial and Ap- to industry-based, practical problems while plied Mathematics. "The tangible gain for Honeywell is a prod• working with industry researchers. Now the uct. The intangible gain is a chance to bring AvnerFriedman, director ofthe IMA, spoke Institute is proposingto expandthe program mathematics into Honeywell," said Cox. from personal experience on how the IMA to other universities nationwide. "We feel that it's a great deal. We certainly has initiated and nurtured industry contacts. get our money's worth." The backbone of the IMA program is fac• The workshop also provided faculty mem• ulty mentors who must initiate the bers with an opportunity to hear from and The idea of industrial postdoctoral fellow• partnership between university and indus• talk to industrial postdocs and faculty mem• ships is for both academia and industry to try.At a May 22 and 23 meeting, funded by bers who have successfully establishedjoint leam from each other through technology the National Science Foundation, the IMA mathematics research projects with indus• transfer. Recent PhDs have access to new shared itsexpertisewith prospective faculty try. mathematical knowledge and industry sci• mentors inaworkshop entitled "How toStart entists have access to the most relevant A principal investigator and coordinator of an Industrial Postdoctoral Program." problems facing technology. Furthermore, postdocs at Honeywell, 1. Allen Cox, pro• the fellowships expose young mathemati• "The purpose of this meeting is to attract vided workshop participants with the cians to job opportunities beyond the faculty from around the nation who are in• industry perspective. "I want to talk about traditional scope of college and university terested in starting an industrial postdoc the sensitivities of industry-propriety of mathematics departments. program based on the IMA model and to data, information exchange-that the fac• show them how to nurture relationships with ulty mentors often view as unnecessary The current IMA program began in 1990 industry scientists in their localities," said constraints on research, but industry sees as with four 2-year postdoc fellowships-they WillardMiller,associatedirectoroftheIMA, vital to business," said Cox before the work• have six this year and plan for seven next which was established by the NSF in 1982 shop began. year. The IMA and JPBM are requesting to identify areas in other sciences and indus• that in 1994 NSF begin a full-fledged indus• Cox has worked successfully with both try where mathematical research could be trial postdoctoral program in mathematics Honeywell postdocs, David Dobson and applied. based on the IMA pilot program. The pro• Gang Bao. At the workshop, Dobson de• posed NSF program would fund The faculty mentor must contact industrial scribed his experienceworking on problems approximately 20 new two-year postdocs scientists, find an industrial project suitable modeling the behavior of light as it passes each year, with up to 40 funded in anyone for amathematical postdoctoral student, and through very small optical elements used in year by 1995. get acommitmentfor halfthe money needed lasers, displays, sensors, and other advanced to support the postdoc for two years-ap• technologies based on lightwaves. Bao is Approximately one-tenth of the more than proximately $35,000 per year. Faculty working on the same problem at a more 1,000 new U.S. doctorates in mathematics mentors apply to NSF for the remainder of advanced level of technology. Computer have access to postdoctoral positions each the funding. "Most mathematicians have simulations ofthemathematical modelshelp year.Developmentofindustrial postdoctoral littleexperience making thesecontacts," said test how a devise will work without actually positions could expand the base of math• Miller. 'The IMA workshop is designed to building aprototype. Honeywell iscurrently ematics postdoctoral employment and alleviate any misgivings and give faculty using the computer models in the develop• provide the research maturity necessary for members practical advice for approaching ment of the next generation of cockpit developing top-notch professionals. industry." displays for Boeing aircraft. August 1993 FOCUS

Olympiadfrom page 5

sota-Duluth, who captivatedthe winners and Free Copy! guests with a lecture titled "Touring the Torus." The day culminated with an elegant recep• UME tion and dinnerin the Diplomatic Reception Rooms oftheDepartmentofState.Although unable to attend due to a meeting ofa special 'lrends advisory committee on the Space Station, USAMO Alumnus Richard Mifflin, and his Every other month (]ME Dr. John H. Gibbons, Assistant to the Presi• wife, Cheryl Bosman on the U.S. State De• Trends brings you: dent for Science and Technology, was our partment balcony with the Lincoln Memorial host. He was represented by Dr.J. Thomas in the background. • Reviews of the latest in com• Ratchford, Consultant to the Office of Sci• puter software, instructional enceandTechnologyPolicy,whoread special Ceremonies and travel to the IMO are the videos, books, and much R. greetings from President Clinton. Microsoft Corporation, The Matilda Wil• son Fund, The Army Research Office, The more. Office of Naval Research and the Math• ematical Association of America. • The Whens and Wheres of mathematics education The MAA staff who assisted in making the meetings. events run smoothly and effortlessly were Mary Mclean Bancroft, Robin Chapman, • Tried and tested suggestions Elaine Pedreira, and Amy Stephenson. for teaching undergraduate The eight sponsoring organizations ofthe mathematics you can use in American Mathematics Competitions: the your classroom.

Alfred B. Wilcox, MAA Executive Director Emeritus; David Roselle, President, University ofDeleware YFS! Please send andformer MAA Secretary; and Lynn Arthur Steen, o Former MAA President, and Executive Director of me a free copy of the Mathematical Sciences Education Board. IJME 1.rends. First Place winners Wei-Hwa Huang and And enter my trial subscription for one Robert Kleinberg were presented with the year at the low rate of $16 (foreign $24).If Samuel L. GreitzerlMurray S. Klamkin I am not completely satisfied I can return Award for Excellence in Mathematics at the your invoice marked "cancel" and will conclusion of the dinner. The winners, in ad• owe absolutely nothing. The first issue is dition to othertop scorers, went to train at the USAMO Alumnus Stephen Modzelewski mine to keep. This offer is for new sub• U.S. Military Academy at West Point from scribers only. This offer is good through 1 June 8-July6forthe InternationalMathemati• June 1993. cal Olympiad. The international competition American Mathematical Association of Name held in Istanbul, Turkey July 13-24. Two-Year Colleges, the American Math• Major contributors to the USAMO Awards ematical Society, the American Statistical Association, the Casualty Actuarial Soci• Address ety, the Mathematical Association of America, Mu Alpha Theta, the National City Council of Teachers of Mathematics, and the Society ofActuaries. State Zip

Please send this form to: UME Trend~ 1529 Eighteenth Stree~ NW, Washington, OC 20036, or Joseph A. Gallion, University ofMinnesota-Duluth, call 2021387·5200 delivers his "Touring the Torus" lecture at the Na• tional Academy ofScience. FAX 2021'265-2384 FOCUS August 1993

MAA HEADQUARTERS STAFF MAA President Testifies

EXECUTIVE before Senate Panel in Marcia P. Sward Executive Director Mary McLean Bancroft Executive Assistant NSF Budget Request Meredith S. Zimmerman Executive Secretary Donald Kreider, President ofthe Mathemati• Development cal Association of America, testified before Richard M. Witter Development Consultant the Senate VA-HUDAppropriationsSubcom• Maureen A. Callanan Development Assistant mittee in late May. PUBUCATIONS AND PROGRAMS Kreider, acting on behalf of the Joint Policy Donald J. Albers Associate Executive Director, Director of Board for Mathematics, submitted a written & Publications Programs statement calling for full support of the NSF Lisa Johnson Assistant to Associate Executive Director budget, in particularfor the Division ofMath• Amy E. Stephenson Production Specialist ematical Sciences and the Division of Production and Marketing Undergraduate Education. At the hearing, he Elaine Pedreira Production & Marketing Manager spoke about theimportant connection between Carol A. Baxter Assistant Production & Marketing Manager teaching and research in the mathematical sci• Beverly J. Ruedi Electronic Production Specialist ences. Kathleen H. Knust Publications Sales Assistant The Senate panel will write its version ofthe Phil Moors Publications Sales Assistant VA-HUD spending bill later this summer. Editorial Harry Waldman Journal Editorial Manager Programs TheCollege Mathematics Andrew Sterrett Assistant Director of Programs Journal Special Issue on Jane S. Heckler Senior Assistant for Programs Differential Equations April White Programs Secretary

FINANCE AND ADMINISTRATION The November 1994issue ofthe College Math• Rhoda D. Goldstein Associate Executive Director, Director of ematics Journal will be devoted entirely to Finance & Administration teaching the introductory course on differential Frederica N. Watson Assistant to Associate Executive Director equations. Recent improvements in graphics software make it possible to shift the focus of Accounting the course from analytic methods, which can• Tracy L. Terry Accounting Supervisor not work in all cases, to qualitative methods that M. Denise Witherspoon Accounting Assistant can give surprisingly detailed information about Valerie Cooper Accounting Assistant the solutions. We are looking for fresh ap• proaches to the subject in this spirit, such as: Reception Robin Chapman Receptionist • computer demonstrations or student projects Mailroom • novel ways to present fundamental concepts Eric Aiken Mailroom Supervisor • new applications Computer Network The Board of Editors invites submissions to all Keith Hiatt Computer Network Administrator our regular sections for this special issue: main articles, classroom capsules, student research MEMBERSHIP AND SUBSCRIPTIONS projects, fallacies, media highlights and quota• Kay Lamont Membership/Subscriptions Manager tionsorhumor. Allsubmissions willberefereed. Lori Bryan Woodfork Membership/Subscriptions Assistant Manager For information about submitting an article, Sabrina Mitchell Data Processing Assistant consult the inside cover of a recent issue of the Sarah Knight Membership Assistant CMJ or contact the editor: Bart Braden, Math• OFFICE OF MINORITY PARTICIPATION ematics and ComputerScience Dept., Northern William A. Hawkins, Jr. Director Kentucky University, Highland Heights, KY Florence Fasanelli Director ofSUMMA Intervention Programs 41099. Lana Bilyeu Administrative Assistant Papers for this special issue should be in the editor's hands by November 30, 1993. August1993 FOCUS

Mathematics Chair Search of assistant professor; in exceptional cases, Davidson College however, more advanced appointments may Department of Mathematics Rose-Hulman Institute of Technology is a be considered. Excellence in teaching and school of 1350 strong (mean SAT scores • statistics, including scholarship and consult• P.O. Box 1719 680 math, 540 verbal) science, engineering, ing, and doctorate required. Davidson, NC 28036 and mathematics students. E-mail: [email protected] Please have a vita and three letters of recom• Applications are invited for an entry level ten• The Department of Mathematics consists of mendation on teaching and statistics sent to ure track position in the Mathematics 17 faculty who take teaching seriously. Fac• Statistics Hiring Committee. Evaluation of Department beginning August 1994. Comple• ulty are active in regional and national applications will begin November 15 and con• tion or near completion of PhD is required. A professional organizations and are leaders in tinue until the position is filled. As an EEO/AA candidate must be committed to outstanding curriculum efforts to use computers in instruc• employer, Williams especially welcomes ap• teaching and continuing scholarly activity. tion and to teach innovative curriculum plications from women and minority Computer science background is desirable. combining science, engineering, and math• candidates. ematics. The teaching load will be 5 courses per year. Davidson is a liberal arts college with a Pres• We seek a Chair to begin in Fall 1994. byterian heritage. Send request for more information, inquiries, Williams College A completed application consists of a state• and applications to: Chair Search Committee, Department of Mathematics ment of professional aspirations and goals, Department of Mathematics, Rose-Hulman resume, graduate and undergraduate tran• Institute ofTechnology,TerreHaute, IN 47803, Williamstown, Massachusetts 01267 scripts, and 3 letters of reference (at least one USA. E-mail: [email protected]. Anticipated visiting position for the 1994-95 about teaching). These should be sent to the Phone (812) 877-8391. year, probably at the rank of assistant profes• attention of Prof. L. R. King, Chair, at the ad• dress above. Applications completed by A complete application includes avita, a state• sor; in exceptional cases, however, more November 27, 1993 will receive first consider• ment of mathematical, pedagogical, and advanced appointments may be considered. ation. Davidson College is an Equal administrative philosophy, and three letters of Excellence in teaching, and research and Opportunity Employer; women and minorities recommendation. Evaluation of applications doctorate are expected. Please have a vita are encouraged to apply. begins December 15, 1993. and two letters of recommendation on teach• ing and research sent to Visitor Hiring Committee. Evaluation of applications will Williams College begin November 15, and continue until the Department of Mathematics position is filled. As an EEO/AA employer, Williamstown, Massachusetts 01267 Williams especially welcomes applications Anticipated tenure-eligible position in statis• from women and minority candidates. tics, beginning Fall, 1994, probably atthe rank

DISCOVERING CALCULUS: A PRELIMINARY VERSION FOURIER SERIES AND BOUNDARY VALUE Alan L. Levine and George M. Rosenstein, Jr. PROBLEMS, 5/e Both ofFranklin and Marshall College James Ward Brown and Ruel V. Churchill, 1993

CALCULUS LABORATORIES WITH MATHEMATICA, VOlS. I, II, III AN INTRODUCTION TO MATHEMATICAL Michael Kerckhove and Van Nail, both ofUniversity ofRichmond ANALYSIS,2/e Jonathan W. Lewin and Myrtle Lewin, 1993 AMATHEMATICAL JOURNEY, 2/1 Stanley Gudder, University ofDenver APPLIED AND ALGORITHMIC GRAPH THEORY Gary Chartrand and Ortrud Oellermann, 1993 aEMENTARY ALGEBRA: STRUCTURE AND USE, 6/e Raymond A. Barnett, Merritt College DISCOVERING CALCULUS WITH Thomas J. Kearns, Northern Kentucky University THE HP-28 AND THE HP-48 DISCOVERING CALCULUS WITH FINITE MATHEMATICS WITH COMPUTER-SUPPORTED APPLICATIONS THE TI-81 AND THE TI-85 James Calvert and William Voxman, both ofUniversity ofIdaho DISCOVERING CALCULUS WITH THE CASIO fx-7700 AND fx-8700 CONTEMPORARY STATISTICS: A COMPUTER APPROACH All by Robert T. Smith and Roland B. Minton Sheldon P. Gordon, Suffolk Community College Florence S. Gordon, New York Institute ofTechnology

For more information, contact your McGraw-Hili representative, orwrite: McGraw-Hili College Division, Camp Processing & Control, P.O. Box 448, Hightstown, NJ 08520-0448. Calendar National MAA Meetings August 15-19, 1993 Sixty-eighth Summer Meeting, Vancouver, Northeastern Westfield State College,Westfall, MA, November (Boardof Governors, August 14,1993) 5-6. January12-15,1994Seventy-seventhAnnualMeeting,Cincinnati SeawayOnondagaCommunityCollege,Syracuse,November5-6. (Board of Governors,January 11, 1994) January4-7, 1995Seventy-eightAnnual Meeting, San Francisco (Board of Governors,January 3, 1995) OtherMeetings October8-9,1993Twenty-firstAnnualMathematicsandStatistics Conference,MiamiUniversity, Oxford,Ohio.Theme: TheTeach• Sectional MAA Meetings ing and Learning of Undergraduate Mathematics. EasternPA& Delaware CedarCrestCollege,Allentown,Novem• April 13-16, 1994 Seventy-secondAnnual National Council of ber 13. Teachersof MathematicsMeeting, Indianapolis. For more in• formation, contact: NCTM, 1906 Association Drive, Reston, IndianaIndiana University-Kokomo, October 15-16. VA22091-1593. NewJerseyUnion County College,Elizabeth,NJ, November 13.

FOCUS AUGUST 1993 The Mathematical Association of America Second class postage paid at Washington. DC and addi• 1529EighteenthStreet, NW tionalmailingoffices Washington, DC 20036-1385