THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA Mathematician Awarded Nobel Prize Volume 14, Number 6 Keith Devlin The awarding of the Nobel Prize in econom• It was the application ics to the American John Nash on October of Nash's work in eco• II th meant that for the firsttime in the 93-year nomic theory that led to history of the Nobel Prizes, the prize was his recent Nobel Prize, In this Issue awarded for work in pure mathematics. which he shares with fellow American John When the Swedish chemist, engineer, and phi• Harsanyi and German 3 MAA Secretary's lanthropistAlfred Bernhard Nobel established Reinhard Selten. Report the awards in 1901, he stipulated chemistry, Nash's contribution to physics, physiology and medicine, and litera• the combined work ture, but did not create a prize for mathematics. 4 Joint Mathematics which won the award It has been rumored that a particularly bad was in game theory. Meetings Update experience in mathematics at high school led to this exclusion of the "queen of sciences", or Nash's key idea-known nowadays as Nash 6 Search Committee it may simply be that Nobel felt that math• equilibrium-was developed in his Ph.D. the• Diary ematics was not, in itself, of sufficient sis submitted to the Princeton University relevance to human development to warrant Mathematics Department in 1950, when Nash its own award. Whateverthe reason, the math• was just 22 years old. The thesis had taken him 10 Networks in ematicians have had to make do with their a mere two years to complete. He had received FOCUS own special prize, the Fields Medal, though both his B.S. and M.S. degrees in an equally this differs significantly from the Nobel Prize rapid three-year period starting in 1945 and fin- by being restricted to mathematicians who are 13 More on the MAA less than 40 years of age. See Nobel Prize on page 5 Gopher Growing Optimism that Fermat's Last Theorem 14 Project NExT is Launched has been Solved at Last old problem. On June 23, 1993, speaking to a Keith Devlin packed audience at a mathematics conference 17 News from the Hopes rose dramatically in late October that at Cambridge University'S Newton Institute, Sections Fermat's Last Theorem might have been Wiles had outlined a proofof a technical result solved at last, when, on October 25th, about elliptic curves (a special case of the 25 Personal Opinion Princeton mathematician Andrew Wiles re• Shimura-Taniyama Conjecture), and claimed leased two manuscripts claiming to prove the that this result implied Fermat's Last Theorem result. The first of these papers, a long one as a consequence. The connection between the 33 Employment titled "Modular elliptic curves and Fermat's full version of the Shimura-Taniyama Conjec• Opportunities Last Theorem", contains the bulk of Wiles' ture and Fermat's Last Theorem had been argument. The second paper,titled "Ring theo• established by Kenneth Ribet of UC Berkeley retic properties of certain Heeke algebras", in 1986. was written jointly by Wiles and a colleague, Though the bulk of Wiles' enormously com• Richard Taylor, and provides a key step Wiles plex proof was agreed to have been correct, The Mathematical uses in his proof. within a few weeks a significant mistake was Association of America The new announcement came justover a year discovered in the part of the argument that led 1529 Eighteenth Street, NW to the Last Theorem itself. Washington, DC 20036 afterWilesmade hisinitialdramatic announce• ment that he had solved Fermat's 350-year See Fermat on page 3 You've been good this year. Give yourself a treat! See page 30 FOCUS December 1994 FOCUS Editorial

FOCUS is published by The Mathematical Association of America, 1529 Eighteenth The Calculus Ultrafilter Street Northwest, Washington, DC 20036• 1385, sixtimes a year: February,April, June, In September, William Dunham and I were the guests on National Public Radio's Talk August, October, and December. ofthe Nation, an hour-long talk show with listener phone-ins. The event that occasioned Editorand Chairofthe MAA Newsletter NPR to devote an entire show to mathematics was the publication in the late summer of Editorial Committee: Keith J. Devlin, our two most recent books, Dunham's The Mathematical Universe (Wiley) and my own Saint Mary's College of California Mathematics: The Science ofPatterns (W. H. Freeman, Scientific American Library). Associate Editor: Donald J. Albers, One of the phone-in comments came from a listener in California-Jim, I believe his MAA Associate Executive Director and name was-who suggested that high schools spend far too much time teaching students Director of Publications and Programs calculus, and that the time might be better spent providing instruction in other subjects. Managing Editor: Harry Waldman, MAA Radio being the medium it is, the responses Bill and I gave led the conversation in the direction of the ubiquity of mathematics, and then the host moved us on to other matters. Production Specialist: Amy S. Fabbri, MAA We never did get a chance to come back to what I think is a particularly important matter. The plain truth is I agree with the listener. I think schools do spend too much time, far Proofreader: Meredith Zimmerman, too much time, teaching calculus. Come to that, I think colleges and universities spend MAA too much time teaching calculus as well. Copy Editor: Nancy Wilson, Saint Mary's College of California In fact, I did begin my response by saying I thought the listener's point had some validity, but I quickly thought better offollowing up on the matter when I realized that I could not Letters to the editor should be addressed to: possibly make my case adequately in the 'sound bite' form of a radio talk show. When Keith Devlin, Saint Mary's College of treading on sacred and hallowed ground, one should tread slowly and warily. And the California, P.O. Box 3517, Moraga, CA 94575; e-mail: [email protected] world of mathematics knows no ground more hallowed than the teaching of calculus. The FOCUS subscription price to individual I guess it is time I defined my terms. By 'teaching calculus' I (and presumably the listener members of the Association is $6.00, from California) mean the kind of activity that, judging from the results it produces, included in the annual dues. (Annual dues concentrates on developing in the student the ability to differentiate and integrate lots of for regular members, exclusive of annual functions. In nearly 25 years of college and university mathematics teaching, I have subscription prices for MAA journals, are encountered scores and scores of students who had become quite expert in performing $68.00. Student and unemployed members this task. Just over halfway through that 25 year period, I started asking those highly receive a 66 percent discount; emeritus members receive a 50 percent discount; new proficient differentiators and integrators to explain to me, in as simple a fashion as they members receive a 40 percent discount for could, just what the processes of differentiation and integration actually are, and what the first two membership years.) exactly are those things called functions that these two processes appear to act upon. Copyright © 1994 by The Mathematical Ifyou have ever tried this, you will surely not be surprised when I say that I almost never Association of America (Incorporated). received an answer that indicated any real understanding on the part of the student. Sure, Educational institutions may reproduce some could give the standard limit definitions, but they clearly did not understand the articles for their own use, but not for sale, definitions-and it would be a remarkable student who did, since it took mathematicians provided that the following citation is used: "Reprinted with permission of FOCUS, the a couple of thousand years to sort out the notion of a limit, and I think most of us who newsletter ofThe Mathematical Association call ourselves professional mathematicians really only understand it when we start to of America (Incorporated)." teach the stuff, either in graduate school or beyond. But I was not looking for a regurgi• tation of a formal definition. What I wanted was some sense of what the calculus is all Second-class postage paid at Washington, DC and additional mailing offices. about. Why was it invented? What were the basic intuitions that Newton and Leibniz Postmaster: Send address changes to the drew on in order to arrive at the notion of (what we now call) differentiation? Why was Membership and Subscriptions De• it necessary to develop an elaborate calculus, a battery oftechniques to compute deriva• partment, The MathematicalAssociation of tives and integrals? What did they think of the fundamental theorem of calculus, and why America, 1529Eighteenth Street Northwest, was that result so important? Washington, DC 20036-1385. Having students who graduate from high school, or college for that matter, without being ISSN: 0731-2040 able to differentiate or integrate does not bother me--especially since computers can do Printed in the United States of America. Printed on recycled paper. the whole job faster and more reliably than people. But having students graduate without a sense of what the calculus is about bothers me greatly. The invention of the calculus was an enormously significant event in the history of humankind, having ramifications that affected most aspects of our lives in one way or another. We fail our students badly if we do not convey to them some sense of that giant leap for mankind. A few will need to know the how of calculus, and that need can be handled when it arises. In contrast, I think all should be aware of the what and the why. ~i1------December 1994 FOCUS For me, the present, sorry situation is Fermat from page 1 Institute in the History summed up by a remark made to me by a Part of the reason why mathematicians senior colleague at my college, with whom were so ready to give Wiles the benefit of of Mathematics and its I was speaking shortly after the radio the doubt when he made his original June broadcast. Striving to find a way to con• 1993 announcement was that his track veythe fundamental idea ofthe differential record was so good. He was not prone to Use in Teaching calculus in a one-minute sound bite, I had jumping to conclusions. Moreover, the likened it to a movie film, where the effect Would you like to teach a course in the new techniques he had developed clearly history of mathematics? Does your col• of continuous motion is achieved by the represented a major advance that stood a sufficiently rapid sequencing of a series legeor university plan tooffer suchacourse high chance of working. True to his known of still pictures. My colleague, an accom• soonfor prospective teachers to implement caution, Wiles refused to release a copy of the recommendations of the MAA, NCTM plished economist who had taken plenty his manuscript. He wanted to wait until it of calculus courses in his time, said that it and NCATE? Do you want to learn how had been thoroughly combed for hidden was only when he heard me make that the history of mathematics will help you errors by a small number of close col• in teaching other mathematics courses? remark that he finally had any inkling of leagues. just what the whole thing was about. He Ifyou answered "yes" to any oftheseques• had, you see, been taught the how, but no Hiscaution proved well founded whenone tions, you are invited to apply to attend an one had even tried to explain the what and of the inevitable number of small errors MAA Institute in the History ofMathemat• the why.Like the vast majority of students, turned out to be not so small after all. ics and Its Use in Teaching. The MAA calculus had been presented to him as a Given Wiles' previous caution, his deci• expects to receive funding for this insti• large collection of mysterious procedures, sion to release his work leads to increased tute, which will take place at American whose invention could only have come confidence that this time, he is probably University, Washington, DC, June 5-23, from a mind very different from the rest of right. The newly released manuscript was 1995, and for three additional weeks in humanity. In his case, that had been over circulating privately among a small num• June 1996, with work continuing through thirty years ago. But as far as I can see, ber of experts for several weeks before an electronic network during the academic things have not changed very much since Wiles released it, and the inside word is year 1995-96.The teaching staff will con• then. I think they should. that it looks good. In an e-mail message sist of well-known historians of -Keith Devlin broadcast over the Internet on October mathematics, including, in the first year, 25th, number theorist Karl Rubin of the Y.Frederick Rickey,VictorJ. Katz, Steven The above are the opinions ofthe FOCUS Ohio State University said, "While it is H. Schot, Ronald Calinger, Judith editor, and do not necessarily represent wise to be cautious for alittle while longer, Grabiner, and Helena Pycior. Activities at the official view ofthe MAA. there is certainly reason for optimism." the institute will include reading of origi• nal sources, survey lectures, small group The overall outline of the argument Wiles projects, field trips to three great libraries, has just released is broadly similar to the and discussions of methods of conducting one he described in Cambridge. a history of mathematics course. Partici• mittee to construct slates of candidates pants will be prepared to make Secretary's Report for President-Elect, and the two Vice• presentations on their work at the Joint Presidents for the 1995 election. Elected Mathematics Meetings. G. L. Alexanderson were Lida K. Barrett, John H. Ewing, Applications are strongly encouraged from The Board of Governors met in Minne• Raymond L. Johnson, Sharon C. Ross, faculty teaching at small institutions, at apolis, Minnesota, on August 14, 1994. and Alan C. Tucker (chair). minority-serving institutions, and institu• The following isareport of actions taken. On recommendation of the Committee tions that prepare secondary teachers. A new Hedrick Lecturer was confirmed on the Edyth May Sliffe Awards, a new Facilities at American University are fully by the Board: our First Vice-President, set of awards was added to honor junior accessible. Dormitory space for families Doris Schattschneider,of Moravian Col• high school teachers. Up to now Sliffe of participants is available. lege. She will be the Hedrick Lecturer Awards were awarded only to teachers For more information and application for theMathFestin Burlington, Vermont, in senior high schools. In addition the forms, write to V.FrederickRickey, Math• August 1995. Board approved anewprize foroutstand• ematical Association of America, 1529 ing research in mathematics by an Eighteenth St., N.W., Washington, DC The Board elected Professor Paul Zorn undergraduate.The prize willbe awarded of St. OlafCollege to be the successorof 20036-1385, or contact him bye-mail at jointly with the American Mathematical [email protected]. Completedapplications Professor Martha Siegel as editor of Society. Mathematics Magazine. Professor will be due by March 15th and applicants Zorn's five-year term as editor will be• The Board passed a resolution of con• will be notified of their acceptance by early gin in January 1996. gratulations to Professor Dirk J. Struik April. for the occasion of his one-hundredth (Note: This institute will be conducted subject The Board elected a Nominating Com- birthday, September 30, 1994. to the MAA receiving funding.) ------@D FOCUS December 1994 vania State University), Marilyn E. Mays Joint Mathematics Meetings Update (North Lake College), and Alan C. Tucker AMS-MAA Session Activities of Other Organizations (SUNY at Stony Brook) as respondents. Panelists for the session You're the pro- The title of the Association for Women in The MAA panel discussion on the Math• fessor, what next? on Friday morning Mathematics' Noether Lecture given by ematical preparation ofthe technical work include Kenneth P. Bogart (Dartmouth Judith D. Sally on Thursday morning is force on Thursday morning also includes College), Donald W. Bushaw (Washing- Measuring Noetherian Rings. Bruce Jacobs (Peralta Community College ton State University), Daniel L. Goroff The title oftheAWM panel discussion on District) as a panelist. (Harvard University), Edward P. Merkes Wednesday afternoon is AWM: Why do From noon to 1:00 P.M. on Thursday there (University of Cincinnati), Robert R. we needitnow?The National Association will be an MAA Northern California Sec• Phelps (University ofWashington), Rich- of Mathematicians' Claytor Lecturer is tion business meeting and election of ard D. Ringeisen (Old Dominion James H. Curry (University of Colorado, section vice-chair. University), Stephen Rodi (Austin Com- Boulder), who will speak on Saturday af- The AMS Committee on Education will munity College), Ivar Stakgold, ternoon on Endomorphisms and sponsor a panel discussion on Saturday (University of Delaware), and Guido L. factorization ofpolynomials. morning, Can we evaluate teaching or Weiss (Washington University, St. Louis). NAM's Cox-TalbotAddress will be given research in the mathematical sciences? AMS Session on Friday eveningby WilliamA. Hawkins, Recent reports urge departments to give The Committee on Science Policy panel Jr. (University of the District of Colum- more weight to teaching in evaluating fac• discussion on Friday at 3: l5p.M. is titled Is bia, and the MAA), on Some perspectives ulty. Many argue that this makes no sense there a better way to support mathemat- aboutmathematics and underrepresented since it is impossible to evaluate teaching. ics?: A comparative view. Panelists from American minorities. Others counter that it is just as difficult to the U.S., Canada, and Europe will describe The Mathematicians and Education Re- evaluate research, but somehow we do it. systems of supportin their countries, what form Network (MER) banquet is on This panel, organized by Ronald G. Dou• they see as the best and worst aspects of Thursday evening at 6:30p.M., not on glas (SUNY at Stony Brook and chair of those systems, and how they relate to the Wednesday evening. the AMS Committee on Education), will current U.S. system. The MAA panel discussion, Forum on the provide a range of views on the problems MAA Session mathematical preparation ofK-6 teach- of evaluating teaching and research in the mathematical sciences. Panelists are Wil• The contributed papersession on Recruit- ers on Thursday morning includes Judith liam P.Thurston (Mathematical Sciences ment and retention of women faculty is Roitman (University of Kansas) as mod- Research Institute), D. J. Lewis (Univer• sponsored by the MAA Committee on the erator; Mercedes A. McGowan (William sity of Michigan), andAlan H. Schoenfeld Participation of Women, not the Joint Rainey Harper College), and Paul R. Committee on Women in the Mathemati- Trafton (University of Northern Iowa) as (University of California, Berkeley). cal Sciences. presenters; and Jerry L. Bona ( Pennsyl- The MAA session Shaping up: Expecta• tions for high school mathematics on Saturday afternoon includes Hyman Bass (Columbia University) as moderator; and Undergraduate Research Prize Announced Richard Askey (University of Wisconsin, The American Mathematical Society and the Mathematical Association ofAmerica Madison); Gail Burrill (Whitnall High have established the joint Prize for Outstanding Research in Mathematics by an School, Wisconsin); Wade Ellis (West Undergraduate Student. Point and West Valley College); and A. The prize is to be awarded to an undergraduate student (or students having submitted Wayne Roberts (Macalester College), as joint work) for outstanding research in mathematics. Any student who is an under• panelists. graduate in a college or university in the United States or its possessions, Canada, or There will be an MAA poster session on Mexico, is eligible to be considered for this prize of $1000 and a certificate. A few Research by undergraduate students on honorable mentions may be made, for which a certificate is awarded. Saturday from 3:00 P.M. to 5:00 P.M. spon• sored by the CUPM Subcommittee on The prize research need not be confined to a single paper; it may be contained in Undergraduate Research in Mathematics, several papers. The paper, or papers, to be considered must be submitted while the the Mathematical and Computer Science student is an undergraduate; research paper(s) cannot be submitted after a student's Division of the Council on Undergradu• graduation. Publication of the research is not required. ate Research, and the Committee on The research paper, or papers, may be submitted for consideration by the student or Student Chapters. Posters are invited by a nominator. All submissions for the prize must include at least one letterofsupport which describe either mathematical re• from a person familiar with the student's research, usually a faculty member. search projects of individual undergraduate students or the way inwhich This year's prize will be awarded for papers submitted no later than June 30, 1995. undergraduate research is organized and Papers to be considered for this prize should be sent together with supporting mate• encouraged at agiven institution. Prospec• rials to Professor Robert M. Fossum, Secretary, American Mathematical Society, tive exhibitors should contact John Dept of Math, University of Illinois, 1409 W Green St, Urbana, IL 61801. Greever (Harvey Mudd College). December 1994 FOCUS

Nobel Prize from page 1 In his thesis, Nash proved that in any game caught by the police, and, during the course ishing in 1948, at the Carnegie Institute of there exists at least one set of mixed strat• of separate interrogations, are offered the Technology (now called Carnegie Mellon egies, with one for each player-a following choice. Ifone confesses and the University). The thesis was titled "Non• so-called Nash-equilibrium point-such otherdoes not, the confessorgoes free and cooperative Games". that no player can improve his or her po• the othergoes to jail for a long sentence; if sition by changing strategy. At a neither confesses, each goes to jail for a A short version of Nash's Ph.D. thesis ap• Nash-equilibrium point no one can im• short time; if both confess, each receives peared as an announcement in the prove his or her position, and adoption of an intermediate jail sentence. Proceedings ofthe National Academy of those mixed strategies results in a stable Each reasons that he is better off confess• Sciences in 1950; that version, with a one• situation. page proof, was titled "Equilibrium ing because if the other confesses, he points-in n-person games". A reworked Nash used methods from topology to prove receives an intermediate sentence by con• version of the entire thesis was published the existence of an equilibrium point. His fessing and a long sentence by not in Annals ofMathematics in 1951, with result applies to any finite, non-coopera• confessing; if the other does not confess, the title "Non-cooperative Games". tivegame involving any number of players. he goes free by confessing and receives a (The word "finite" here refers to the fact short sentence by not confessing. Since In his thesis, Nash used Brouwer's fixed that the number of possible strategies is each reasons this way,each confesses, and point theorem (1926) to prove the exist• limited; "non-cooperative" means that no so each is given an intermediate sentence. ence of an equilibrium point. Both the communicationbetween players may take The strategy whereby both confess is the Proceedings announcement and the An• place, and no alliances may be formed.) nals version use the more general Nash equilibrium in the game because Kakutani's Fixed Point Theorem (1946) Game theory began to be applied in eco• neither can improve his position by chang• in place of Brouwer. Nash credits this sim• nomics following the publication of the ing his strategy (because to renege on plification of the proofto a suggestion by book Theory of Games and Economic confessing means jail for a long time). Behaviorby John von Neumann and Oskar David Gale, now professor emeritus of What seems paradoxical about this situa• Morgenstern in 1944. Their analysis was mathematics at the University of Califor• tion is that, if both suspects continue to largely limited to games involving only nia, Berkeley, then a graduate student in protest their innocence, they would both two players. Nash's proofof the existence mathematics at Princeton. receive a short sentence. And yet, com• of at least one equilibrium point in the mon sense logic compels them both to Game theory-theabstract study of games much wider class of non-cooperative confess and end up spending longer time (draughts, chess, poker, and so forth)• games with any numberof players has had behind bars. becomes relevant to the more serious a major impact on modem economic aspects oflife when its results are applied theory. Ifyou think of economic behavior Born in West Virginia in 1928, Nash was in warfare, political conflict, or economic as a game in which there are well-defined appointed research assistant and instruc• competition. The game theorist examines rules, and all the players try to maximize tor at Princeton in 1950, and worked as a the strategies the players in such a "game" their payoffs, then in general it will be consultant for the Rand Corporation dur• may adopt. possible for any given player to improve ing the summers of 1950and 1952.In 1951 A pure strategy in a game is a complete his or her position by changing strategy. he was appointed a Moore Instructorat the plan for every possible situation that the Consequently, players will keep changing Massachusetts Institute of Technology, player might encounter during the course their strategies until they reach a Nash• where he was promoted to assistant pro• of play. When the pure strategies of all equilibrium point at which no player can fessor in 1953 and to associate professor players are submitted to an umpire, the improve his or her position. In some cases, in 1957. In 1956-57, 1961-62, and 1963• entire course of play and the payoffs to the this analysis makes it possible to predict 64, he was a visiting member atthe Institute players are determined. the likely strategies that economic actors for Advanced Study. After resigning his will adopt in the long run-namely, those professorship at MIT in 1959, he was a However, not all games can be solved with at a Nash-equilibrium point at which no research associate there in 1966-67. pure strategies, and players must then use player can change to improve his or her Since the mid-1960s, Nash has lived in the a mix of pure strategies by choosing the outcome. probabilities with which each pure strat• Princeton area. As a visiting research col• egy is played. For example, in the simple An illustration of Nash's notion of an equi• laborator in the Mathematics Department, game where two players simultaneously librium point that has a perplexing twist in he makes use of computing and library put down a penny, with one player win• its tail is provided by the so-called facilities in orderto carry out his own pro• ning if they both match (both heads or both "Prisoner's Dilemma" devised by Nash's gram of independent research. advisor atPrinceton, mathematician Albert tails) and the other winning otherwise, the Nash is a recipient of the von Neumann Tucker, a topologist turned game theorist. pure strategies are "heads" or "tails" and Theory Prize from the Operations Research Tucker created the paradox in 1950, the the mixed strategies are the random fre• Society of America, and is a fellow of the same year Nash wrote his thesis. quencies with which a player chooses to Econometric Society. play these pure strategies. The Prisoner's Dilemma asks us to imag• ine a scenario where two suspects are FOCUS December 1994 have done this, since many have little to secretary's watchful eyes. Search Committee say about the fact that one of the respon• sibilities of the position, as stated in the As a final touch, our secretary saves the Diary advertisement, is to supervise secondary cancelled stamps from the applicants' school student teachers. Silence on this envelopes and sends them to a convales• Edward F. Aboufadel topic is, of course, not the kiss of death as cent home. The home is somehow able to far as I am concerned, and perhaps when raise money from the cancelled stamps. The search continues for the perfect math I am done reading all of the folders, I'll Graduate students take note! instructor. In this episode, our diarist be• discover that practically no one has any• Polonius. What do you read, my lord? gins his ascent, then breathes deeply through thing to say about supervising secondary Hamlet. Words, words, words. a grueling schedule ofinterviews at the ER school student teachers. After all, it is not Shakespeare's Hamlet in Cincinnati. Intrepidly he struggles tofind a common responsibility in academia, al• that Yesamong Maybes andNos as the num• though it is an important one. December20, 1993: Working an hour ber of applications climbs to over three or two a day, I have now read through 167 hundred! Watch your step... December14, 1993: The big Reading application folders. Some are complete, oftheApplications continues. I have come while others are missing letters of recom• I read, much of the night, and go south in across two applicants so far that I think are mendation, but I am getting the gist of the the winter. promising, and I wonder if the other mem• quality of our applicants. Of the 167 ap• T S. Eliot bers of the search committee will feel the plications, I have ranked about a fourth of "The Burial of the Dead" same way that I do. I guess I will find out them as either a Yes or a Maybe. The Waste Land next Tuesday. It is interesting to see the many ways that The greatest misfortune that ever befell This week we are sending out our flyer to schools send out letters of recommenda• man was the invention of printing. Print• mathematics education departments that tion. At some schools, there seems to be ing has destroyed education. we have on a list. Our ad was in FOCUS an office which coordinates the sending last week, and it is also now available on of the letters, so for some applicants, we Benjamin Disraeli e-MATH, so by now people should know have received just one envelope with all Lothair about our position. That, in fact, seems to three letters in it. These packets often in• December 4, 1993: Today I began be the case, as during the past few days we clude a page that states that the applicant reading the application folders. I read have been averaging twenty to twenty-five has waived his or her rights to see the let• through fifteen of them in about ninety new applications per day. (The count on ters. For other applicants, the letters come minutes. At that rate, if we were to receive Friday was 107, so we must be closing in in one at a time, and we have applicants one thousand applications, I would spend on 150 as of this writing.) Perhaps with that have only one letter of recommenda• one hundred hours reading through them. the semester ending, people are finding tion, while others have two or three. Afew Let's hope we don't get that many. more time to send letters out. have eight or nine. In our advertisement, we asked for three. What can I say about the folders I read? It I talked to our secretary today to see how was very interesting. At the risk of sound• she is dealing with the flood of mail to the There are two types of recommendation ing like a form rejection letter, let me say search committee. She is spending practi• letters. There are the "wonderful research" that there are a lot of accomplished people cally her whole working day processing letters and the "wonderful teaching" let• out there. Some have very impressive re• applications. In the mornings, she finishes ters. A colleague of mine tells me that ten search backgrounds, while others have a dealing with the previous days' bids for years ago the letters were more balanced. lot of teaching experience. our position, which includes sorting out Concerning the "wonderful teacher" let• the documents and preparing the "we've With approximately twelve pieces of pa• ters, it troubles me a bit that practically received your application" form letters. per per candidate in hand, I have to grade everyone of our candidates is either "an The new mail comes in around noon, and these candidates as Yes, Maybe, or No. exceptional teacher," "an effective then she starts over again. Our secretary (Again, the question I am trying to answer teacher," "an excellent teacher," "an ex• has an undergraduate assistant who helps is, "Should we interview this person?") emplary teacher," "a tremendous teacher," her a few afternoons a week. I suggested Twelve pieces of paper can actually tell "an accomplished teacher," "the best TA. that we should hire another undergradu• you a lot. You get a sense of where a who ever worked for me" or "in the top atejustfor the month of Decemberto help candidate's priorities are from what is sent. 25% of the TA.s at Whatchamacallit U." us with these applications, but our secre• Judging from these letters of recommen• When it comes to applying for jobs, there tary just laughed that sardonic laugh of dation, I start to wonder why people think is one approach-the scattershot ap• someone who has worked at an institution there is a crisis in undergraduate math• proach- for which we young (and not so long enough to know. ematics education. ("Maybe it is because young) mathematicians have become fa• Apparently a few of our intrepid appli• the extraordinary teachers need to spend mous. This approach is to take advantage cants view our hiring contest as some sort too much time looking for jobs," our dia• of computers and copy machines and to of lottery and have applied twice, I sup• rist says sarcastically.) apply for any position that comes along. It pose to increase their odds. So far none of is clear to me that some of our candidates Tomorrow morning at 8:00 A.M., the com- these wily folk have slipped past our {~------December 1994 FOCUS mittee meets to trade opinions about these of resumes of applicants that is provided cants as they worry about their futures. applicants. Our goal is to come up with a by the ER, so each of us had a short list of There are also some new wrinkles in the list of people we would like to interview numbers to contribute. Wecombined these job market this year. I hear that more in Cincinnati (if those people are at the lists together into our List of Potentials. schools are using e-mail to handle appli• Joint Mathematics Meetings, of course). Next we took out our list of quarterfinalists cations and rejections. One friend told me December 21, 1993: As I awoke this that we developed last month to see which that he had already received a few e-mail morning, a tropical storm was blowing of them were participating in the ER. We rejections. through Connecticut. It was windy, rainy, found that eight out of our list of thirty In the ER, at least one school yesterday and mild. I fought the storm, walking from quarterfinalists were participating. Sur• sought to discourage certain applicants my car to Engleman Hall. A few minutes prisingly there were a few of those eight from requesting an interview with that later, we started our meeting. who were notonour List of Potentials. We school. To those people who had already figured that this was due to the limitations For an hour and a half, we compiled our sent the school an application and whom of the ER resume form. With the addition "votes" on individual applicants. When the school had put on the Probably Not of these people and a few on-site appli• all was done, we had a list of about thirty list, this school sent notes reminding those cants, our List of Potentials grew to thirty applicants that we will be looking for in people of their low status in the process members. Cincinnati. (I'll call this group our and strongly suggesting that they not re• quarterfinalists, and we will add to this Employers are allowed up to twenty re• quest an interview with that school. This list after the holidays.) Many of the job quests, so we had to cut some of the thirty. is probably not a bad idea, provided that seekers pointed out in the cover letters that To do this we went through the resumes the note was a reminder and not an initial they would be at the winter meetings, and one by one, exercising less generosity in announcement. most of those said that they would be en• our judgments than we did initially. When This morning the chair picked up our in• rolled in the EmploymentRegister.Wewill the smoke cleared, we had actually reduced terview schedule. Sixteen of our seventeen see what happens next month. our List of Potentials to seventeen, and we requests were met. Of the sixteen, seven submitted that list to the ER. It is premature for us to send out rejection were mutual requests, which means that letters. Most applicants' files are incom• Next we decided on a schedule for the the applicant also requested us. The other plete. We've decided to contact some of interviewers. Sometimes we will have two twenty-fourinterviews will be with people our leading candidates to remind them to interviewers, sometimesjustone. I will be that we did not request, but who requested send the rest of their documents in. (Let• interviewing for all of the Thursday after• us. Of those twenty-four, nine labelled ters of recommendation, in particular, can noon time slots and a few of the Friday Southern Connecticut a "high-priority" be slow in coming.) afternoon slots. request. Tomorrow I am driving west to see my Participating in the ER takes a lot of time. Finally the chair informed me yesterday parents, brother, and niece for afew weeks, Our Wednesday afternoon meeting alone that since Christmas, the number of appli• and then I am driving to Cincinnati. The lasted ninety minutes. I am not getting to cations for our position doubled. We now other committee members who are going as many sessions as I have in past winter have over three hundred applicants. I have to Cincinnati are flying in, so I'min charge meetings. a lot of reading to do when I get back to of bringing the various catalogs and flyers Southern next week. I'm observing that, as in past years, some that we will be giving to our interviewees applicants are leaving notes in the employ• January 15, 1994: Saturday night. at the Employment Register. When we all ers' message boxes, requesting interviews Late yesterday afternoon we completed get to Cincinnati, we will meet up with the outside of the ER. Related to this is the our forty interviews. I participated in four• committee chair who will coordinate our atmosphere of anxiety among the appli- teen of them. For a few of them, I was the activities there. Happy Holidays! lone interviewer. When I worked with January 13, 1994: Thursday morn• someone else, I was the lead questioner ing. I have arrived in Cincinnati, and the about half of the time. Joint Mathematics Meetings are well un• derway. The marquee on the Cincinnati Convention Center announces simply, "Welcome Mathematicians." Three members of our search committee are here, including myself, and we met yesterday afternoon to get organized for the Employment Register (ER). Over five hundred people have registered this year as applicants in the ER. Our first task was tochoose as many as twenty of these people for our interview request list. Before we Left: Coming in... 500 application files met, each of us had looked over the book Above: Going out... letters a/rejection ------@ FOCUS December 1994

Each interview was fifteen minutes long, have much time to discuss their disserta• and not just the decision of the interview• and a typical interview went something tion work. ers. On the other end of the spectrum, we like this: Ifthere was any time left, we often asked couldn't express too much enthusiasm to At the beginning, we gave the applicant a the applicant if he or she had any ques• promising candidates, pretty much for the copy of thejob announcement and the one• tions of us. A few asked about the cost of same reason. page description of Southern Connecticut living in Connecticut. Next week the committee will meet to sort State University that! wrote before Christ• Now, some of the applicants were clearly out our impressions of the interviewees. mas. Often, but not always, the applicant not suited for the job. I asked other com• would give us a vita that we could refer to Interviewers (including myself) com• mittee members whether or not we should during the interview. This was helpful. mented that after several interviews, it was just tell these people right then and there hard to remember if a certain question had Wethen said to the interviewee something not to expect a call from us, but it was felt like, "In our department we have approxi• that this should be a committee decision See Committee Diary on page 15 mately eighty mathematics majors. Many are in the Applied Mathematics program, a few are pursuing B.A. degrees in math• ematics, but the majority is seeking the B.S. in mathematics with secondary edu• NUMERICAL cation teaching certification." (Ifsomeone MATHEMATICS wants to teach high school mathematics and wants certification from us, we re• quire that the person earn a B.S. in mathematics. Some other schools do not Numerical Mathematics do this, but I think it is a sound idea.) A Laboratory Approach We continue: "This position has many S. Breuer and G. Zwas responsibilities, the primary one being to "For someone wishing to learn thenumerical approach supervise these certification students, par• to mathematics, thiscan bea book ofgenuine value. Recommendedfor undergraduates at all levels. " ticularly when they are doing their student - S. Puckette, Choice teaching. What kind of background do you Numerical Mathematics is a unique book that presents rudimentary numerical have in secondary education that would mathematics in conjunction with compurationallaboratory assignments. No relate to this responsibility?" (Wearerather previous knowledge ofcalculus or linear algebra is presupposed, and thus the book lucky to have a position unusual enough is tailor-made for undergraduate students, as well as prospective mathematics that we can quickly get to the point. I teachers. The material in the book emphasizes algorithmic aspects ofmathematics, wonder how it would work if we were which are made viable through numerical assignments, in which the traditional looking for an Applied Math person? I "chalk-and-talk" lecturer turns, in pan, into a laboratory instructor. It guides the would hope we could develop a pointed student to create the algorithm required for any given assignment expressed in whichever programming language is used on the basisofthe underlying mathematics. question or two to ask at the ER.) The computational assignments cover iterative processes, area approximations, There were many different responses to solution oflinear systems, acceleration ofseries summation, interpolative the question. If the applicant had some approximations, and construction ofcomputer-library functions. Throughout the book, strong emphasis is put upon vital concepts such as error bounds, precision background in secondary education (e.g., control, numerical efficiency, computational complexity, as well as round-offerrors used to be a high school mathematics and numerical stability. The book is not a numerical methods book, containing teacher; received certification in some ready-made computational recipes, but it is the authors' belief that the material state; was involved in a program in gradu• presented in this book is pan and parcel ofthe mathematical foundations that ate school that included high school should be acquired by a student in the microcomputer era. teachers), then we asked probing questions Contents: about these activities. We might have Mathematics in a Numerical Laboratory/Iterations for Root Extraction/Area asked, "What teaching methods did you ApproximationlLinear Systems-An Algorithmic Approach/Algorithmic use in your classes?" or, "What do you Computations of1t and elConvergence Acceleration/Interpolative Approximation/ know about the NCTM Standards?" or, Computer Library Functions "What is your opinion of the Standards?" 1993 280 pp. 44040-8 Hardback $49.95 Another responsibility of the position is For more information, please contact Sebastian Thaler at to teach undergraduate mathematics Cambridge University Press courses, so we asked the interviewees which classes they believe they could teach. We asked about their college teach• ing experience and about their use of technology in the classroom. We did not «~------December 1994 FOCUS Gardner on Gardner: JPBM Communications Award Presentation In the summer of1994, the Joint Policy BoardforMathematics presented its Communi• cations Award to Martin Gardner at his home in Hendersonville, North Carolina. Conferring the award was ProfessorBob Fennell, chair ofthe DepartmentofMathemati• cal Sciences at Clemson University. Following are excerpts oftheir conversation. Bob Fennell: Martin, I've admired your ematician, more ajoumalistof mathemat• books and articles for many years. And on ics. behalfof the Joint Policy Board for Math• Mathematics has its own peculiar beauty, ematics, it'smy sincere pleasure to be here and that's about all I can say about it-the to present this Communications Award to Most mathematicians find it very hard to fact that it all works out so rationally and you for your books and articles on the write for the general public, they're on so beautifully. There's something eerie theory of mathematics and clear commu• such a high level that they can't bring it about the way mathematical proofs work nication of ideas. We have a certificate down to where non-mathematicians can out, and that's always intrigued me. Ever and a check for $1,000 to present to you. understand it. I can'timagine, Paul Erdos, since I was in high school I've been fond The certificate reads, "American Math• for example, writing a popular article on of mathematics, but strictly as an amateur. ematical Society, Mathematical number theory. Actually, I majored in philosophy at the Association of America, and Society for University of Chicago and I had the privi• Fennell: Do you think there's a place for Industrial andApplied Mathematics grants lege of taking a seminar from the great using recreational mathematics in the this, The Joint Policy Board for Mathemat• Rudolph Camap, and that was the most classroom? ics Communications Award, to Martin exciting course I think I ever took, so one Gardnerin recognition of exceptionalcre• Gardner: I'vealways thought that thebest of my main interests is in the philosophy ativity and sustained contributions in way to get students interested in mathemat• of science. communicating mathematics in numerous ics is to give them something that has a books and articles, and in the'Mathemati• Fennell: Martin, you have no formal col• recreational flavor: a puzzle, a magic trick, cal Games' column in Scientific lege training in mathematics. How did you a paradox, or something like that. I think American." I present this to you and con• chose writing mathematics to be your ca• that hooks their interest faster than any• gratulate you. reer? thing else. I recall when I was taking geometry in high school in Tulsa, I had Martin Gardner: Well, thank you very Gardner: Actually,I got into writing about finished doing the work and I was playing much. Thank you. mathematics quite by accident. I did an around with trying to figure out how to article for Scientific American on Fennell: Martin, you've been very suc• win a game oftic-tac-toe, and I was play• hexaflexagons in 1957. I had heard about cessful in communicating the power and ing around with a pencil and a sheet of hexaflexagons from friends of mine in the beauty of mathematics to the general pub• paper, and the geometry teacher came magic community. They were playing lic. I'dlike to ask you why you think you've around and saw what I was doing. She around with these strange objects and, as been so successful. snatched the paper away and said, "When you know, the great Feynman, Richard you're in my class, I want you to work on Gardner: Well,thank you very much. I've Feynman, was one of the coinventors of mathematics and nothing else." That's said before, and I'll say it again, that if you hexaflexagons, so it made an interesting always amused me because I think teach• write about mathematics for the public, story. Gerry Piel, who was at that time the ing children aspects of tic-tac-toe is a popular writing on mathematics, it's good publisher of Scientific American, called wonderful way to introduce them to com• not to know too much about mathematics, me into his office after they had bought binatorial geometry, numbertheory, game and I think that's one of the secrets of the this article and asked me if there was theory, all kinds of things. Just that simple kind of writing that I do. I know math• enough similar material like this around little game leads them into very signifi• ematics only up to a certain level, and to make a column. I said I thought there cant areas of mathematics. beyond that it's very difficult for me to was. So I rushed around New York to the understand. I have to work so hard to un• old bookstores and bought as many books Fennell: Well, we've talked a lot about derstand anything that I'm writing about, on mathematics as I could, especially in mathematics and recreational mathemat• that it makes it easier for me to explain it the recreational field. The next month the ics and all your interests. Would you like perhaps in a way that the general public column started under the title "Mathemati• to comment on where you think mathemat• can understand. I am not a mathematician cal Games." So that's how I began. I have ics fits in the real scheme of things? in any creative sense of the word. I love to thank Gerry Piel for that. Up until then, Gardner: Mathematics is not only real, mathematics and I enjoy writing about it, I had never written anything about math• but it is the only reality. That is that the but I don't like to pose as a genuine math- ematics. See Gardner on page 33 FOCUS December 1994 Networks in FOCUS

Gopher and the ~ Internet Gopher e 1991-1993 University of Minnesota. Mathematics ~ Abstract for SchoolStat ~ DoWIlload SchoolStat (SchoolStat. sea. hqx) Archives: Part Two ~ Readme file for SchoolStat

Earl D. Fife & Lawrence Rusch Figure 15: Starting Window for Downloading a File The first part ofthis article appeared in the previous issue ofFOCUS. Note that because information is continually being addedto the Mathematics Archives, by the time this is printed, the menus may have additional or somewhat modified entries. Figure 16: Progress Window in Downloading a File As mentioned in part one of this article, down menu activated by clicking the pull• then double-click on Download there are several differences between what down arrow in the upper left-hand corner SchoolStat, whereupon the window in happens for the Macintosh user and for of each window which can be used tojump Figure 16 appears. When the decoding is the DOS or UNIX user. We observed a back to previous selections. See Figure complete, a dialog box appears (Figure cosmetic difference with the interface 14.) 17), prompting you to select where to put using icons rather than text. Another way the file. the interface differs is that unless other• After the selection of where to store the wise instructed, each selection generates file is made, the downloading now pro• a new window, so moving to earlier selec• ceeds with regular updates on the number tions is just a matter of choosing an of bytes received until the transfer is com• appropriate window. (There is also a pull- plete. The file that arrives is usually a Statistics "self-extracting archive," as indicated by Internot Gopher ©1991-1993 University of Minnesot•. the extension .sea. To uncompress the file, all that is necessary is to double-click the rn Search Abstracts and Readme Files of Statistics Programs file's icon. LJCurveFit , LJDataDesk Professional (Commercial) I LJExpFit (ExpFit .sea. hqx) i!~if A third commentfor the Macintosh user is LJlnterPlot Demo (Inter~~:~::: ~Il! that some telnet client should be on the LJJl1P Demo 2. 0 ::::::; Macintosh so that menu items requiring it ~mi LJLinear Regression Calculator (LinRegressCalc. sea. hqx) can be selected and executed properly. LJtlac Dendro, et al. (tlultivariate]rogs.sea. hqx) ~l~ LJtlacCurveFit Perhaps the most widely used telnet client (t1acCurveFitl 03. sea. hqx) I'~i~,..~.~.:~.i. LJProbability Calculator (ProbCalc .sea. hqx) ,,;;c, is the public domain NCSA Telnet. If a LJProbability Theory by True B&SIC (Commercial) Ii telnet selection is made in TurboGopher, LJ SchoolStat (SchoolStat. sea. hqx) ~ the telnet client is automatically started. LJScientist Spreadsheet (sciensp .sea. hqx) .... I

~ collection of all of your bookmarks and IGl TurboGopher f I c:::l PowerBook •.. choose one which will provide you imme• diate access to this particular site. Again, one of the advantages of the go• - pher program is that it provides a means for organization of materials from many - different sites. For example, if the user - chooses Matlab, then the resulting menu seue as: is depicted in Figure 20. Materials from five different sites are represented there. ===1(_)• A similar example is the Calculus Reform item. The menu is shown in Figure 21. Figure 17: Dialog Boxfor Saving a Downloaded File The first item gives you information (from e-MATH.ams.com, the American Math• =0 The Mathematics Rrchiues 0= ematical Society's gopher) on how to join the calc-reform discussion group. The ~ Internet Gopher@1991-1993 University of Minnesota. second item (from the site ~ About the trathematics Archives Gopher - mir.maths.soton.ac.uk in Great Britain) ~ Organization of the trathematics Archives Gopher - contains an archive of many messages LJ Software (Packages, Abstracts and :Reviews) from this discussion group. Even though LJTeaching traterials and Other Information these sites are not mentioned, they can be LJOther trathematics Gophers and Anonymous FTP Sites identified: on the UNIX server, this can be ~ Submitting traterials to the trathematics Archives done by pressing the = key; on the MSDOS ~ Other Ways of Accessing the trathematics Archives machine, this can be done by pressing Alt• ~What is Gopher? (adapted from Texas ~ &n's Gopher) f followed by Alt-i; in WSGopher, select LJInformation About Gopher (from Univ . Minnesota) the Info on Item on the File menu option; and in TurboGopher, this information is available through the Get Attribute Info - selection of the Gopher menu option. As a - side note, the Mathematics Archives would ¢I¢IIIIII I¢I¢ \!j like to expand this section of the archives Figure 18: The Home Menu with TurboGopher to include information from other sites which have been involved withexperimen• tation in calculus reform. Bibliography Finally, to complete the journey through CHANCE Database the Mathematics Archives "gopher hole," Calculus Reform we look at another major area from the Geometry Forum (Swarthmore) Life Sciences main menu, Other Mathematics Gophers Mathematica and Anonymous FTP Sites. Its menu is Mathematics Archives Newsletters shown in Figure 22. Matlab Numbers In these nine categories are contained San Antonio Math Meetings Poster Sessions (Jan. 1993) gopher links to other sites of interest to mathematicians. There is overlap between Figure 19: "Teaching Materials and Other Information" Menu the links here and in the first two main menu items of the Mathematics Archives. Regarding the third entry in Figure 22, it MATLAB Primer Information is worth noting that as of the writing of Download MATLAB Primer (Plain TeX version) this article, over sixty mathematics depart• Download MATLAB Primer (Postscript version) ments worldwide have gopher servers. Download MATLAB Primer (Spanish Plain TeX version) Download MATLAB Primer (Spanish Postscript TeX version) Links to all those known to the authors are MATLAB Users Group Digest included in this third entry. The fifth and MATLAB faq sixth entries have many items, so are too MATLAB-based Textbooks largefor display here, but contained therein The MathWorks MATLAB Digest are links to software archives, databases comp.soft-sys.matlab Newsgroup of software, software and book publish• Figure 20: MATLAB Menu ers, governmental agencies, computer ------@ FOCUS December 1994

manufacturers, etc. pher client by choosing the item Applica• tion from the menu Configure; it is Navigating the Internet There are two kinds of gopher programs: probably more convenientto set up a book• Keith Devlin a gopher server and a gopher client. Ifyou mark to the Mathematics Archives in this justwant to access other gophersites, then client. Pocket Guides to the Internet is a series of all you need is a gopher client. If you or six books written by Mark Veljkov and your department want to provide infor• For additional information, the reader is George Hartnell. Published by mation via gopher then a gopher server is referred to 2 and 4, two popular sources Mecklermedia, II Ferry Lane, Westport, required. Both ofthese programs for vari• for the Internet. The former is especially CT 06880, (203) 226-6967, each one is 40 ous platforms are available by anonymous useful for the Macintosh user because it to 60 pages long. The volumes cover, in ftp from boombox.micro.umn.edu in the comes bundled with all the necessary soft• order, the following topics: subdirectory pub/gopher. ware to connect a Macintosh with the Internet, including MacTCP and 1. Telnetting Two pieces of information are needed to TurboGopher. 2. Transferring Files with File Transfer access a gophersite: the Internet address Protocol (FTP) and port number. The Mathematics Ar• References 3. Using and Navigating Usenet chives can be reached by gopher at 4. The Internet E-Mail System archives.math.utk.edu with port 70. Most IDeGray, R. W. "The Internet and BITNET• 5. Basic Internet Utilities gophers use the standard port 70, but some An Agora for Mathematicians." FOCUS 13 6. Terminal Connections. use adifferent port. Togopherto the Math• (February 1993): 15-17. Each starts with the same eight-page in• ematics Archives from a UNIX machine, 2Engst, A. The Internet Starter Kit for troduction to the Internet before getting type the command Macintosh. Hasbrouck Heights, NJ: Hayden Books, 1993. down to the task announced in the volume gopher archives.math.utk.edu 70 subtitle. The guides are simply and clearly 3"The Internet-Getting Started." FOCUS 13 written, and should provide an adequate To gopher there using TurboGopher, se• (June 1993): 21-24. introduction to novitiates trying to make lect Another Gopher from the File menu "Krol, E. The Whole Internet User's Guide and their first tentative steps into cyberspace. and enter the archives.math.utk.edu as the Catalog. Sebastopol, CA: O'Reilly & Associ• server name and 70 as the port. The Math• ates, 1992. My first reaction when I heard about this ematics Archives has a Gopher+ server, 5Wachsmuth,B. G. "The Internet: Some Tools series was that it was an excellent idea, so that box should also be checked. Simi• for Efficient Usage." FOCUS 13 (December and approached the publisher with a re• larly with WSGopher, select New Gopher 1993): 15-17,19-21. quest for review copies for FOCUS. from the File menu and enter the Having read all six volumes, I still think archives.math.utk.edu as the server name Earl D. Fife teaches in the Department of they can be of great use to newcomers to and 70 as the port; also check the Gopher Mathematics at Calvin College. Lawrence the Internet, but for the more experienced Plus box. On the PC Gopher III client, you Ruschteaches in the DepartmentofMath• user I am not so sure there is any real ad• enter this information for the home go- ematics at the University ofTennessee. vantage to splitting the material into six volumes. It may even be a disadvantage. For one thing, the volumes are not really -Calculus Reform Discussion Information pocket-sized. Though each one is thin, their <0> -Calculus Reform Discussion List dimensions measure six by nine, largerthan <0> Bowdoin College Bowdoin College Information the average paperback book. <0> Colorado School of Mines Second, almost any Internet use requires <0> Duke University knowledge of procedures spread over sev• Georgia Tech SUNY Albany eral of the guides, so a user will have to <0> San Antonio Math Meetings Poster Sessions (Jan. 1993) buy and have available all six. This is clearly inefficient as a reference source.

Figure 21: "Calculus Reform" Menu However, I am afairly experienced Internet user, long past the stage of information overload that greets a newcomer trying to <0> Electronic Journals <0> Electronic News and Discussion Groups master the system. For the beginner, a 300• <0> Mathematics Departments page instruction book might well remain <0> National Science Foundation Gopher (STIS) unopened on the shelf, while six bite-sized <0> Other Mathematics Software Sources & Information installments might not be so off-putting. <0> Other Organizations of Interest to Mathematicians So, while I cannot recommend the series <0> Preprints and Reports as a reference source for the more experi• <0> Societies <0> TeX enced Internet user, it could be of great help to the beginner. Figure 22: "Other Mathematics Gophers and Anonymous FTP Sites" Menu @------December 1994 FOCUS TheMAA Gapher-Ifyau haven't seen ityau 're missing aut!

Here is just a sample ofwhat you're missing:

• Information on the Joint Mathematics Meetings in San Francisco • Index ofthe College Mathematics Journal • Anewlisting ofProfessionalDevelopmentActivitiesofferedaround the country • New MAA Publications such as Lion Hunting and Other Mathematical Pursuits and All the Math That's Fit to Print • Largest Known Primes • and much more! You can access the MAA Gopher several different ways. If your computer runs a gopher client, or you can log into a computer with a gopher client, you can access the MAA Gopher by typing: gopher gopher.maa.org You can also connect on the WorldWide Web at: URL http://www.maa.org/

Carnegie Small Planning Grants The Strengthening Underrepresented Minority Mathematics Achievement (SUMMA) Program of the MAA is pleased to announce that funds are pending from the Carnegie Corporation of New York for a fifth round of Small Planning Grants. The planning grants (up to $5,(00) are to encour• age mathematics faculty to initiate intervention projects serving underrepresented minority middle and high school students. The deadline is March 15, 1995. The full solicitation will appear in the February 1995 issue of FOCUS. For a copy ofthe solicitation, please contact the SUMMA Pro• gram, Mathematical Association ofAmerica, 1529 18th Street, NW, Washington, DC 20036; (202) 387-5200; fax: (202) 265-2384; e-mail: [email protected]. ------~ FOCUS December 1994 Project NExT Launched James R. C. Leitzel and T. Christine Stevens Sixty-six Project NExT fellows gathered expected, the first class of fellows was on August 12th in Blegen Hall on the cam• expanded to include 66 individuals, pus of the University of Minnesota. Thus rather than the originally anticipated began a series of presentations, discus• number of 60. sions, short courses, and interactions that The sixty-six fellows include 33 men spread over three days prior to the open• and 33 women holding positions in 30 ing of the summer MathFest activities in different states. The institutions repre• Minneapolis. Project NExT was launched! versity ofArizona), and the St. Olaf Project sented include two-year and four-year of Arnold Ostebee and Paul Zorn (St. Olaf The fellows eagerly participated in all of colleges, comprehensive state universities, College). This was followed by a panel the workshop sessions, and, much to the and research institutions. There are repre• discussion on the broader issues of calcu• delight of the co-directors, organized and sentatives from 23 of the 29 MAA sections. lus reform. Later that day, the fellows carried out several events on their own. Fifty-two of the fellows received their elected to have their own discussion groups These events ranged from special sessions Ph.D.s in 1993 or 1994. on a variety of topics. These included on topics of particular interest to several The Minneapolis workshop included more methods for working with students in of the participants, to informal discussions than 20 hours of special sessions. As the groups, changing the culture in depart• at nearby local establishments, to discus• keynote speaker, MAA President Donald ments, utilizing writing in mathematics sions in dormitory lounges lasting late into Kreider spoke of the new "contract" that classrooms, and issues centering around the night. is being forged between mathematics and teacher preparation. That evening, a panel Recognizing that the movement to "re• society at large. He noted that mathemati• discussion on the faculty member as form" the teaching of undergraduate cians can no longer expect society to teacher and scholar featured Tracy mathematics presents special challenges provide the "unquestioned support" that Bibelniecks (University of Minnesota), to those just entering the profession, may have been the rule in prior decades, Richard Herman (JPBM, University of Project NExT was developed to provide and he suggested that one way to re-estab• Maryland), Jerry Lodder (New Mexico not only an overview of current issues in lish the connection between mathematics State University), Doris Schattschneider the teaching and learning of undergradu• and contemporary society would be for (Moravian College), and William Velez ate mathematics, but also to build a college and university faculty to teach the (University of Arizona). network of peers and more experienced students we have, not the ones we wish we The final day ofthe workshop began with mathematicians to provide advice and on• had. a presentation by Carl Leinbach going professional support. This project On the next day, John Baldwin (Univer• (Gettysburg College) and Marvin of the MAA is funded by the Exxon Edu• sity of Illinois atChicago), Ronald Biggers Brubaker (Messiah College) on the use of cation Foundation for a three-year period. (Kennesaw State College), Gail Burrill technology in upper division courses. This first class of Project NExT fellows is (Whitnall Public Schools in Wisconsin), Following this presentation, and again an extremely impressive group. Their ap• and Janet Ray (Seattle Central Commu• meeting in smaller groups, the fellows plications contained personal statements nity College) discussed the changes they discussed using writing to teach mathemat• about teaching, each displaying a high de• have observed in the students who enter ics with David Smith (Duke University), gree of pedagogical sophistication, and colleges and universities. They noted dif• using projects in discrete mathematics with many oftheapplicants were already wres• ferences in preparation and demographics, Jerry Lodder, and developing a sophomore tling with some of the major issues as well as changes in the expectations that laboratory course with Margaret Robinson confronting undergraduate mathematics students who have been educated accord• (Mount Holyoke College). This was fol• education. Because so many of the appli• ing to the NCTM Standards will bring to lowed by a group discussion on these cants were so well qualified, and because their undergraduate courses in mathemat• alternative approaches to instruction. the institutional support was higher than ics. The fellows then had some hands-on Susanna Epp (DePaul University) shared experience with vari• with the fellows some of the results of ous calculus reform research in collegiate mathematics edu• efforts. Insmall work• cation and pointed to some issues that still ing groups, they need attention. discussed problems The workshop closed with a presentation from Project CALC by Joe Gallian (University of Minnesota• (Marcelle Bessman, Duluth) on the importance of "finding your Frostburg State Uni• niche in the profession." His comments versity), the Harvard clearly addressed some of the fellows' Consortium materials deepest concerns and earned him a stand- (William Velez, Uni- @------December 1994 FOCUS ing ovation. It was an appropriate and and their home institutions. Inaddition to stimulating conversation with a master the workshop and MathFest last August, teacher. the fellows are expected to attend the Joint MM Mathematics Meetings in San Francisco Fellows were also expected to participate and the 1995 summer MathFest at the in the MathFest. Special sessions were of• University of Vermont. The task of the co• PLACEMENT fered for them on pre-calculus directors, James R. C. Leitzel (University mathematics (David Dudley, Phoenix of Nebraska-Lincoln) and T. Christine Community College), using graphing cal• Stevens (St. Louis University), has been TESTS... culator technology in the teaching and made a bit easier by the enthusiasm and learning of mathematics (Frank Demana, talents of the fellows, who have taken it can help solve your The Ohio State University), and the com• upon themselves to plan a program of puter algebra system DERIVE (Leinbach college's mathematics activities for Project NExT participants at placement problems and Brubaker). In addition, the fellows the joint meetings in San Francisco. They were invited to attend MAA committee also have made several suggestions for en• • Dothe membersofyourmathemat• meetings and other special activities. hancing the workshop experience for the ics department complain that the next class of fellows. Project NExT will One goal of Project NExT is to build a students intheir classes arenotwell be featured in the program of the Joint network of peers and more experienced prepared for their courses? mathematicians to provide professional AMS-MAASpecial Session organizedby support as the fellows launch their own the Mathematicians and Education Reform • Doyourstudents complain thattheir careers. The intense workshop experience Network (MER) during the San Francisco mathematics courses are too hard got this network of peer support off to a meetings. or too easy? running start. Building on the fellows' time Project NExT is supported, in part, by a • Do your facultyadvisors relyprima• together in Minneapolis, the MAA has es• three-year grant from the Exxon Educa• rilyupon scores on aptitudetestsor tablished a special electronic network for tion Foundation. The second group of onhighschool mathematics courses them and selected "mentors" from the fellows will be chosen in the spring of taken in makingrecommendations mathematical community. That network 1995. Further information about Project to students about their initial col• has already been quite active in discuss• NExT can be obtained on the MAA Go• lege mathematics courses? ing issues of teaching and learning, such pher or from James R.c. Leitzel at the If your answers to these questions as how to structure groups for group learn• University of Nebraska, e-mail:jirnleitz@ are YES, you should know about the ing in the classroom and how to assess unlinfo.unl.edu. writing in mathematics classes. The vari• PLACEMENT TEST PROGRAM (PTP) ety of the fellows' institutions and teaching For a list ofthe Project NExT Fellows, of the Mathematical Association of assignments is reflected in these discus• see page 16. America. This program assists two• sions. The comments of the more and four-year colleges and experienced mathematicians who have James R. C. Leitzel is a professorofmath• universities with the development of joined the network provide a resource for ematics at the University ofNebraska, and on-campus placement programs to these new fellows that reaches beyond their co-director ofProject NExT; T. Christine assess the mathematical skills of new home schools. Stevens is a professor ofmathematics at students objectively and fairly when St. Louis University, and co-director of they enter college. Project NExT is a full year of commit• Project NExT. ment on the part of the individual fellows Colleges and universities pay an an• nual fee to subscribe to PTP. This Committee Diary from page 8 progam provides up-to-datetests and placementtesting information to its Haven for processing, just like the others, been asked yet. To help us keep track of subscribers. things, we had a comment sheet on each and we will decide on Yes, Maybe, or No candidate that we filled out, and we re• for each one. The MAA's Committee on Testing ferred to it during the interviews. also offersfree consulting services to So there were over five hundred applicants any college mathematics department in the ER, and there were sixty-nine em• Someone could make a mint, rolling a that is planningto initiate a local ployers. Some other employers told me food-and-coffee cart around that big in• mathematics placement program or terview room. that they have received over four hundred seeking ways to improve its ongoing applications sofar for one position. At least Inour message box, we found a number of program. one school is trying a method where ap• items. Some people put their resumes in plications are screened immediately when Formore information or to subscribe, (and nothing else). Others put whole pack• they arrive, and the people who are obvi• write or call: MM PT Program, MAA, ets in. We are treating either a resume or a ously inappropriate for the position get 1529 Eighteenth Street, NW, packet as aformal application. That means rejection letters quickly, which follows the Washington, DC 20036, that we will bring each one back to New "Mattix plan" available over e-MATH. 1-800-331-1 MM. To be continued... FOCUS December 1994 North Central 1994-1995 Project NExT Fellows Lynne Baur, Carleton College, Northfield, MN MAA Section of Faculty Appointment Thomas Ratliff, St. Olaf College, Northfield, MN Deirdre L. Smeltzer, University of St. Thomas, St. Paul, MN Allegheny Mountain Kevin Strobel, University of Minnesota, Minneapolis, MN Jeongsook Kim, Wheeling Jesuit College, Wheeling, WV Northeastern Eastern PennsylvanialDelaware Julian Fleron, Westfield State College, Westfield, MA Cheri Boyd, University of Scranton, Scranton, PA Sandra L. Rhoades, Smith College, Northampton, MA Douglas E. Ensley, Shippensburg University, Shippensburg, Northern California PA Julie Suzanne Glass, California State University-Hayward, Kathleen Madden, Lafayette College, Easton, PA Hayward, CA Camille A. McKayIe, Lafayette College, Easton, PA Ohio Robert C. Stolz, Lafayette College, Easton, PA Greg Bishop, College of Mt. St. Joseph, Cincinnati, OH Illinois Heather Hulett, Miami University, Oxford, OH Jon M. Clauss, Augustana College, Rock Island, IL Luiz Felipe Martins, Cleveland State University, Cleveland, Paul R. Coe, Rosary College, Riverforest, IL OH James P. Marshall, Illinois College, Jacksonville, IL Steve Morics, Oberlin College, Oberlin, OH Sharon K. Robbert, Trinity Christian College, Palos Heights, Oklahoma-Arkansas IL Philip Crow, Southern Nazarene University, Bethany, OK Michael Sullivan, Northwestern University, Evanston, IL Mary Ellen Foley, University of Oklahoma, Norman, OK Indiana Janet C. Woodland, University ofArkansas, Fayetteville, AR Georgia Tolias, Purdue University-Calumet, Calumet, IN Pacific Northwest Barbara J. Wahl, Hanover College, Hanover, IN Jennifer McNulty, The University of Montana, Missoula, MT Intermountain Tom Roby, Reed College, Portland, OR Michael Patrick Prophet, Idaho State University, Pocatello, Rocky Mountain ID Erik S. Van Vleck, Colorado School of Mines, Golden, CO Iowa Southeastern Mark Johnson, Central College, Pella, IA Dennis Evans, Coker College, Hartsville, SC Douglas Mupasiri, University of Northern Iowa, CedarFalls, Mark Charles Ginn, Austin Peay State University, Clarksville, IA TN Robin Arnie Pennington, Wartburg College, Waverly, IA Arnaldo Horta, Jr., Armstrong State College, Savannah, GA Kimberly J. Regnier, Northwestern College, Orange City, IA Elsa J. Newman, West Georgia College, Carrollton, GA Kansas Emily E. Puckette, Duke University, Durham, NC CynthiaWoodburn, Pittsburg State University, Pittsburg, KS Bettina E. Schmidt, Auburn University-Montgomery, Louisiana-Mississippi Montgomery, AL Judith L. Covington, LSU at Shreveport, Shreveport, LA Scott A. Smith, Columbia College, Columbia, SC MD-DC-VA StephanieTyler, University of'Tennessee-Martin, Martin, TN Todd G. Will, Davidson College, Davidson, NC Clara S. Chan, Virginia Polytechnic Institute, Blacksburg, Analee Witt, Austin Peay State University, Clarksville, TN VA Olga Yiparaki, Agnes Scott College, Decatur, GA Samuel Bruce Smith, Washington College, Chestertown, MD Metropolitan New York Southern California Michael A. McDonald, Occidental College, Los Angeles, CA Laurel Cooley, York College-CUNY, Jamaica, NY Missouri Texas Jose H. Giraldo, TexasA&M University, College Station, TX AlbertJ. Goodman, University of Missouri-Rolla, Rolla, MO Ruth Gornet, Texas Tech University, Lubbock, TX Michael Hilgers, University of Missouri-Rolla, Rolla, MO Gertrud L. Kraut, University ofTexas at Tyler, Tyler, TX Ilene H. Morgan, University of Missouri-Rolla, Rolla, MO Ruth Ingrid Michler, The University of North Texas, Denton, Timothy Robert Ray, Southeast Missouri State University, TX Cape Girardeau, MO Wasin So, Sam Houston State University, Huntsville, TX Nebraska-Southeast South Dakota Wisconsin Peter Gavin LaRose, Nebraska Wesleyan University, Fe S. Evangelista, University of Wisconsin-Marathon Lincoln, NE Center, Wausau, WI New Jersey AsumanOktac, University of Wisconsin-Oshkosh, Oshkosh, Wen Yao Zhang, Union County College, Cranford, NJ WI Anthony D. Thomas, University of Wisconsin-Platteville, @------Platteville, WI December 1994 FOCUS News From The A one-week summer workshop titled "Mathematical Modeling Workshop," pre• sented byJefferson Hartzler (Pennsylvania Sections State University), and directed by Marvin Brubaker (Messiah College), was held at The vitality and diversity of the MAA are that college. evident in the work of the sections of the Association. Below are descriptions of Florida The twenty-seventh annual meet• ing of the Florida Section was held some of the activities and programs ofthe town, Pennsylvania, featured invited February 25th-26th at Daytona Beach sections over the past year. speakers Joseph Gallian (University of Community College in Daytona Beach, Allegheny Mountain The Allegheny Minnesota, Duluth) speaking on "The Florida. The meeting included twenty-four Mountain Section held its annual meeting Mathematics ofIdentification Numbers"; contributed papers, meetings of depart• April 8th and 9th on the campus of West Carl Pomerance (University of Georgia) ment chairs, a meeting of the Florida Virginia University in Morgantown, West on "Fermat's Little Theorem"; Kenneth Two-Year College Mathematics Associa• Virginia. About 100 persons were in at• A. Brakke (Susquehanna University) on tion (FTYCMA), and a meeting of tendance, including about 20 students. "Soap Films and Covering Spaces"; and SIGCALM. Dennis Runde (Manatee Mary Ellen Rudin (University ofWiscon• John Maceli (Ithaca College, Ithaca, New Community College) presented a sin) on "The Rationals and the Irrationals." York), presented a minicourse titled "Stu• minicourse, "TI-85 Applications in the JoAnne S. Growney (Bloomsburg Univer• dent Projects in Calculus," in which 12 Pre-Calculus and Calculus Courses." Ple• sity of Pennsylvania) gave a luncheon members of the section participated. nary speakers were Underwood Dudley presentation, "Mathematics in Poetry." There were four invited addresses. Susan (DePauw University) who spoke on Forman (Mathematical Sciences Educa• The spring section meeting was held "Angle Trisectors," Donald L. Kreider tion Board), spoke on "PromotingFaculty jointly with PSMATYC, the Pennsylva• (Dartmouth College and past-presidentof Growth in Undergraduate Mathematics." nia State Mathematical Association of the MAA) who spoke on "The Roots of The section's 1993Distinguished Teacher, Two-Year Colleges, at Harrisburg Area Recursion in Mathematics," and P.J. ProfessorGeorge Andrews (Pennsylvania Community College in Harrisburg, Penn• McKenna (University of Connecticut) State University), spoke on "Ramanujan, sylvania on March 12, 1994, and featured who spoke on "Nonlinear Oscillations in Continued Fractions, and Educational talks related to the teaching ofmathemat• Suspension Bridges." Invited lectures Reform." Robert Davis (Rutgers Univer• ics. The four invited addresses were were given by Don Hill (Florida A&M sity), spoke on "Analyzing How Students "Calculus: Concepts, Computation, Com• University), Linda Smith and Moana Think About Mathematics." Sonja position, and Cooperation," by David A. Karsteter (Tallahassee Community Col• Sandberg (Framingham State College) Smith (Duke University); "The Harvard lege), and Scott H. Hochwald (University spoke on "The Mathematics of Epidem• Calculus Consortium and the Reform Pro• of South Florida) speaking on "Teaching ics." gram in Mathematics," by Andrew Math atAfrica University," "Seeking Pat• Gleason (Harvard University); "Using a There was a social hour followed by a terns and Connections in Sequences," and Graphing Calculator toEnhance theTeach• banquet Friday evening at which the 1994 "Tales from the Harmonic Series," respec• ing of College and IntermediateAlgebra," Distinguished Teaching Award was pre• tively. by Stanley R. Clemens (Bluffton College); sented in absentia to Professor David M. Professor Fredric Zerla (University of and "Teaching Undergraduate Mathemat• Bressoud (Penn State-University Park). South Florida) received the Distinguished ics Using Technology," by Roseanne Faculty and student talks followed, and Service Award for 1994. Professor James Hofmann (Montgomery County Commu• the evening finished with a pizza party. Wahab (Rollins College) was the recipi• nity College). Nine workshops were Saturday featured eight sessions of con• ent of the Distinguished University presented. tributed papers, 13 by faculty members Teaching Award. Sessions for student-contributed papers and ten by students. Four regional meetings occurred this year were held at each meeting, with a total of The section's business meeting was held in addition to the annual meeting. eleven student presentations. The student at breakfast on Saturday. paper contest winner,Jennifer Orehowsky, The section gave a volume of the New The section held its Tenth Annual Allegh• Ursinus College, was presented with a Mathematical Library toeach of the thirty• eny Mountain Section Summer Short certificateand acheck by ProfessorAyoub five top scorers in Floridaon theAHSME. Course, "A Mathematical Sampler, 1647• Ayoub, organizer of the contest. Profesor In addition, the section assisted with ex• 1900," byWilliamDunham ofMuhlenberg , William Dunham of Muhlenberg College penses for three students presenting papers College, June 13-17, 1994. received the 1994 EPADEL Section Dis• at the annual section meeting, and for two Eastern Pennsylvania and Delaware tinguished Teaching Award, and outgoing students to go to the national summer The EPADELSection sponsored two regu• President Nancy Hagelgans of Ursinus meeting in Minneapolis. lar meetings and a one-day student College was presented a plaque in recog• Illinois The seventy-third annual meet• conference on careers in mathematics. The nition of her many contributions to the ing of the Illinois Section was held at fall section meeting on November 13, EPADEL Section. Parkland College in Champaign, Illinois, 1993, at Cedar Crest College, in Allen- April 22-23, 1994. It was organized by ------@ FOCUS December 1994 LaVerne McFadden and Caroline Institute of Technology); "Using a Labo• There were twelve student papers; a panel Goodman of that college. There were 142 ratory Approach to Teaching Basic discussion, "Teaching the History of Math• registrants. Concepts of Group Theory," by Ellen ematics"; eleven contributed papers; and The group heard fifteen invited talks; four Parker (DePauw University); and "The three computerdemonstrations: "Creative student papers; an opening address, "Pro• Asymptotic Behavior of the Zeros and Approaches to Mathematical Visualiza• moting Faculty Growth in Teaching and Poles of the Normalized Pade tion," by Deane Arganbright (Whitworth Scholarship," by Susan Forman (director Approximants to exp(z)," by Amos Car• College, Spokane, WA), "Calculus Using of College and University Programs for penter (Butler University). Mathematica,' by Keith Stroyan (Univer• the Mathematical Sciences Education At the spring meeting, students C. Chris• sity of Iowa), and "Using XLISP-STAT Board, on leave from Bronx Community topher Smith (TaylorUniversity) and Stacy for Teaching and Consulting," by Russell College); and a closing address, "Break• Bogataj (Saint Mary's College) spoke on V. Lenth (University of Iowa). ing Drivers' License Codes," by Joseph "Simulation of the Rivest-Shamir-Alder• Kansas The annual meeting of the Kan• Gallian (University of Minnesota, Duluth). man (RSA) Cryptology Scheme," and sas Section was held at the University of Graham Evans (University of Illinois) "Pitching Statistics," respectively. In con• Kansas, March 11-12, 1994, with eighty• gave a banquet address on "Mathematics junction with the meeting, the section held one people attending. and Music, the Musings of a Beginning its twenty-ninth annual Indiana College There were five workshops: "Proposal Cellist." Fred Rickey, Bowling Green State Mathematics Competition. Writing," by William Hawkins (director University, led a minicourse, "Using His• The Indiana Section's Distinguished of the MAA SUMMA project); "The tory in the Mathematics Classroom." Teaching Award was presented to David Hewlett Packard HP48 in Undergraduate Four student teams participated in a math S. Moore (Purdue University) and its Dis• Mathematics Courses," by Robert D. contest arranged by J.B. Stephen, student tinguished Service Award was presented Adams (University of Kansas); "Using chapter coordinator (Northern Illinois to Billy Rhoades (Indiana University). Software to Teach Concepts to Business University). The Indiana Section is glad about the MBA Students," by Teresita S. Salinas The section's Distinguished Service Award state's participation in the AHSME and (Washburn University); "Calculator Ac• was presented to Neale Fadden (Belleville the AJHSME. At its spring meeting, the tivities/Projects for Enhancing Student Area College); the section's Award for section presents plaques to the state win• Involvement in College Algebra and Pre• Distinguished College or University ners on these exams. calculus," by Marilyn Carlson (University of Kansas); and "Interactive Electronic Teaching was given to Ronald M. Shelton Intermountain The Intermountain Sec• Laboratories for Calculus and Geometry (Millikin University). tion of the MAA convened at Westminster of Surfaces," byThomas Banchoff(Brown College in Salt Lake City, Utah, April 8-9, The Illinois Section is the home of Patrick University). Banchoff also delivered the D. McCray (G. D. Searle and Company, 1994. Lance Littlejohn (Utah State Uni• talk "Beyond the Third Dimension: From Skokie, Illinios) who is a newly-elected versity) gave a short course on orthogonal Flatland to Hypergraphics." governor-at-large of the Association. polynomials and was awarded the section's There were sixteen contributed papers, The Illinois Section sponsors ahigh school Distinguished Teaching Award. A panel discussed the limited employment in math• seven student papers, and three panel dis• lecture program which brings mathemati• cussions. Traditional in the section is a cians from local colleges, universities, or ematics and stressed the need for employer and employee to treat each other with dig• breakfast meeting at which issues related businesses to high school classes or math• to mathematics education in Kansas are ematics clubs. nity,honesty,and fairness. After the annual banquet, Kenneth Ross, who grew up in discussed. Indiana The fall 1993 Indiana Section Salt Lake City, reminisced about the math• Kentucky The annual meeting of the meeting at Indiana University Kokomo ematics instruction he had received there Kentucky Section washeldApriI8-9, 1994 featured a tour of Delco Electronics Cor• and some of his most-remembered teach• at Morehead State University, with total poration and a SUMMA workshop ers, many of whom were known to section attendance of ninety-six people. The meet• presented by Bill Hawkins of the MAA. members. This brought back many nos• ing included ashort course, "Calculus from Mathematical presentations included an talgic memories. an Historical Perspective," by Daniel invited address by Elliot Tanis (Hope Otero (Xavier University), and a work• College, Michigan), titled "Random Num• Iowa The Iowa Section met jointly with the ASA and IMATYC at Grinnell Col• shop by John Kenelly (Clemson bers In, Answers Out: Maple V University), titled "Priming the Pump for Simulations." lege, Grinnell, Iowa, April 15-16, 1994. Former P61ya Lecturer Patricia Rogers Curricular Change." The meeting offered The spring 1994 section meeting at (York University) spoke on "Classroom its social, "Aftermath," after an invited DePauw University included an invited Climate and Other Issues," and on "You address Friday night by Keith Devlin, address, "Linear Algebra and Serious Can't Do That in MY Classroom: Cur• editor of FOCUS, followed in turn by a Applications," by Gilbert Strang (MIT); riculum Transformation and Mathematics pizza party specifically for student mem• and papers, "Solving Systems of Polyno• Education." James Hall (Deere and Com• bers. The section had informal mial Equations," by Gene Freundenburg pany) spoke on "Neural Networks and announcements and discussions at its Sat• (Ball State University); "Newman Poly• Genetic Algorithms: Applications in Fi• urday morning breakfast meeting. nomials," by Bart Goddard (Rose-Hulman nance and Engineering." There were two invited addresses, eigh- @------December 1994 FOCUS teen contributed papers from faculty, and The section held its annual spring meeting The Metropolitan New York Section is the six student papers. April 15-16, 1994 at Saint Mary's Col• home of Aleksandr L. Khazanov This year the section is proud of lege ofMaryland,with ninety- four faculty (StuyvesantHigh School, New YorkCity); Kentucky"s AHSME participation and of and seventy-three students registered. The Khazanov is a member of the United the results ofits efforts to increase student section offered a workshop on SPSS by States' history-making 1994 IMO team. participation in its meetings. It also has Alham El-Hage Tannouri (Morgan State Michigan At the annual meeting of the increased participation of faculty from University). There were both student and Michigan Section at Alma College, April two-year colleges; the Kentucky Section faculty paper sessions. The three invited 29-30 1994, out-of-state speakers were of the MAA and the Kentucky MATYC addresses were "Conceptual Issues in Leonard Gillman (University ofTexas at cooperate in publishing new letters to• Conservation of Biological Diversity," by Austin), Underwood Dudley (DePauw gether. The section offers three newsletters Robert McKelvey (University of Mon• University), Kay Somers (Moravian Col• each year. tana); "Visual Clustering, Modes, and lege), and PrasadTetali (AT&TBellLabs). Nonparametric Density Estimation," by Louisiana-Mississippi The Louisiana• Provocative talks included "Down with David Scott (Rice University); and "Some Mississippi Section held its annual Determinants," by SheldonAxler (Michi• History of Fermat's Last Theorem," by V. meeting March 4-5, 1994 at Nichols State gan State University), "(Down With) Frederick Rickey (Bowling Green State University, with an attendance of255, one Angle Trisectors," by Dudley, "Some Ir• University). hundred ofwhom were students. The sec• reverent Thoughts about the Teaching of tion has worked to provide activities of The 1994 John M. Smith Distinguished Mathematics," by Gillman, and interest to students, and this meeting of• Teaching Award was presented to David "Reversibility and Reciprocity," by Tetali. fered a studentcompetition, studentpaper Lay (University of Maryland). A concert featured Gillman on piano and sessions, and a panel discussion on ca• The Maryland-DC-Virginia Section is the Ernest Lloyd (Central Michigan Univer• reers. home of Jacob A. Lurie (Montgomery sity) on cello. The beautifully organized meeting in• Blair High School, Silver Spring, Mary• The section's Award for Distinguished cluded a workshop on graphing calculators land)whois a memberof the United States' College or University Teaching was pre• and dynamical systems, and panel discus• history-making 1994 IMO team. The sec• sented to Jerrold Grossman (Oakland sions on calculus reform and mathematics tion is also the home of Genevieve Knight University), author and teacher, one of education. Leonard Gillman spoke on (Coppin State Collegein Baltimore, Mary• whose students testified, "(his class) re• "Some IrreverentThoughts on the Teach• land) who is a newly-elected mains, for many of us, our best learning ing of Mathematics." Highlights of the governor-at-large of the Association. experience. It convinced me of the sig• meeting included a Cajun reception, a Metropolitan New York The Metropoli• nificance of mathematics." The section's crawfish boil, and a concert by Gillman tan New York Section held its annual Distinguished ServiceAward wentto Jean on the piano, and Carol Dale on flute. meeting on May 1, 1994 at the U.S. Mer• Calloway (professor emeritus at Kalamazoo College), whose substantial Maryland-De-Virginia The annual fall chant Marine Academy in King's Point, contributions to the section includefound• meeting of the Maryland-DC-Virginia New York. There were eight contributed ing the High School Visiting Lecturer Section was held on November 12-13, papers and two invited addresses, "What program. John Kiltenen was thanked for 1993, at Montgomery College, Takoma are the Best Sphere Packings?" by John his many years of outstanding service as Park, Maryland. The meeting program H. Conway (Princeton University), and newsletter editor. featured a banquet, two invited speakers, "You Can't Do That in MY Classroom," a panel discussion and workshop, and five by Pat Rogers (York University). Ruth Favro (Lawrence Technological contributed paper sessions, including one The section is proud of its Mathematics University) reportedthat the annual Michi• made up entirely of student presentations. Awareness Week activities, which in• gan Mathematics Prize competition for Keith Devlin (Saint Mary's College and cluded proclamations from Governor high school students had about 16,000 editor of FOCUS) spoke on "Whose Mario Cuomo and Mayor Rudolph W. participants from about four hundred Mother Is It?: In Search of a Mathemati• Giuliani of New York City. These were schools. Each year, volunteer members of cal Theory of Communication"; circulated to local media. The section also the Michigan Section grade the written Underwood Dudley (DePauw University) held a well-attended program at John Jay solutions for Part II of the test, and the spoke on "Angle Trisectors"; Elizabeth College of Criminal Justice, where Pro• section organizes an awards day to recog• Teles (Montgomery College), Genevieve fessor Charles Peskin of NYU-Courant nize the accomplishments of the top one Knight (Coppin State College), and Jim spoke on computer heart simulation, and hundred students. For the next three-year Sandefur(Georgetown University) offered ProfessorH.M. Edwards, also ofCourant, period, the competition will be hosted by the panel discussion, "NSF Innovation spoke on Fermat's Last Theorem. Grand Valley State University. Grants: New Opportunities"; and Teles The section held its eighteenth annual Co-sponsored by the Michigan Section, presented a workshop on "Grant Oppor• Mathematics Fair at Pace University. the Michigan Calculus Network, tunities for Innovation in Collegiate Awards were given to the student winners MichMATYC, and Western Michigan Mathematics."A workshop, "EnergySys• ofthe fair and to the highest local scorers University, the Fifth Annual Michigan tems Modeling," was a follow-up meeting in the Putnam and AHSME competitions. Conference on College Mathematics was of the June 1993 section workshop. held at Western Michigan University in ------@ FOCUS December 1994 Kalamazoo, Michigan, on March 12,1994. fifteen contributed papers and a panel dis• (Boston University). The topic was "Strategies for Teaching." cussion to update federal- and state-funded For the third year in a row, the very active Missouri The spring meeting of the Mis• programs in the Nebraska-Southeast South Northeastern Section has offered its spring souri Section was held jointly with the Dakota Section. dinner meetings; this year there were five Missouri Council of Teachers of Math• The section presented its Award for Dis• such meetings. Its one-day minicourse, ematics (MCTM), April 8-9, 1994 at tinguished Teaching to Jim Lewis "Teaching the Introductory Statistics Missouri Southern State College. (University of Nebraska). Course," was led by Robin Lock and Ri• The meeting was preceded by a two-and• New Jersey The fall meeting of the New chard Cleary. a-half hour short course on using the Jersey Section at Union County College The section is looking forward to its fall history of mathematics in the classroom, included talks by Israel Gelfand, William presentation, "Mathematical Aspects of and a two-and-a-half hour workshop on Dunham, TillaWeinstein, andJohn Ewing; the Music of Bach," by Victor Hill. This is MATLAB. The Missouri Mathematics and a SUMMA workshop. The spring an event that should be well received by Association for the Advancement of meeting at Rutgers University included the general community, as well as by Teacher Training conducted a business talks by Thomas Banchoff, Joseph mathematicians. meeting and presented a speaker. There Rosenstein, and John Conway. There were The Northeastern Section is the home of were two panel discussions, one on "Ca• student speakers and sessions for contrib• two members of the United States' his• reers in Mathematics," and one on uted papers. At both meetings there were tory-making 1994 IMO team: Noam M. "Assessment of Student Learning for Im• book exhibits by commercial publishers, Shazeer (Swampscott High School, proving the Undergraduate Major in door prizes, and a silent book auction. The Swampscott, Massachusetts) and Mathematics." section thanks James Magliano and Jo• Johnathan Weinstein (Lexington High Invited addresses were given by Martha seph Rosenstein for serving as hosts for School, Lexington, Massachusetts). the meetings this year. Siegel (Towson State University and edi• Northern California The annual meet• tor of Mathematics Magazine) on The 1994 New Jersey Section Award for ing of the Northern California Section of "Mathematics, Industry, and Jobs"; by J. Distinguished Teaching of Mathematics the MAA was held at San Jose City Col• Wanzer Drane (Department of Epidemi• was presented to Richard Bronson lege in San Jose, California, on Saturday, ology and Biostatistics, School of Public (Fairleigh Dickinson University). February 12, 1994. There were 210 par• Health, University of South Carolina) on North Central The fall meeting of the ticipants. The program consisted of five "Correcting for Selection Bias in a Male North Central Section was held at the invited talks: Jean Pedersen (Santa Clara Sample Survey"; and by Ron Harrist (Bi• University of North Dakota, October22nd University) spoke on "From Geometry to ometry, School of Public Health, and 23rd, and featured invited addresses Number Theory"; Keith Devlin (Saint University of Texas at Houston-Health by Wally Sizer (Moorhead State Univer• Mary's College) on "How Do You Know Science Center). Drane also delivered an sity) and Polya Lecturer Patricia K.Rogers This IsATitle?"; Nelson Max (Livermore after-banquet address, "Use of Geographic (York University). Laboratory) on "Light Scattering from Information Systems (GIS) as a Tool for The spring meeting was held April 22nd Surfaces and Volumes"; Edward F. Investigating the Relationship between Schaefer (Santa Clara University) on Electrical Power Lines and Cancer." and 23rd at Winona State University. John Fulton (University of Missouri-Rolla), "Wiles' Proof of Fermat'sLast Theorem;"; There were twenty-eight contributed pa• Keith Devlin (Saint Mary's College), and and Constance Reid on "Searchingfor Eric pers, five of which were from students. Dave Uherka(University of North Dakota) Temple Bell." There was a reception for students on Fri• gave invited addresses. Mark Krusemeyer Professor Jane Day (San Jose State Uni• day night, co-sponsored by Missouri (Carleton College) received the section's versity) was presented with the Northern Southern Kappa Mu Epsilon. Outstanding Teaching Award, and Gerald California Section Award for Distin• Invited speakers at the meeting were spon• Bergrum was honored with the section's guished College or University Teaching. sored by a private foundation, the host Meritorious Service Award. In 1995 the section will hold a two-day college, and the MAA. Northeastern A major project for the joint meeting with the Southern Califor• Nebraska-SE South Dakota The annual Northeastern Section this year was the nia Section at California Polytechnic State meeting of the Nebraska-Southeast South workshop for students, "Mathematics University in San Luis Obispo. Dakota Section of the MAA was heldApril Opens Doors to the World: Careers in the Ohio The annual spring meeting featured 22-23 on the campus of Nebraska Mathematical Sciences." With students a keynote address by S. Brent Morris (Na• Wesleyan University, Lincoln, Nebraska. and faculty attending from as far away as tional Security Agency) titled "Magic, There were fifty-five people in attendance Nova Scotia, the day was an extremely Card Tricks, and the Perfect Shuffle." the first day and forty-five the second. successful one for all participants. Many Other invited addresses were given by Kenneth Ross (University of Oregon and requests were made for future workshops. Alice Silverberg (Ohio State University) President-Elect of the Association) spoke A highlight of the section's spring meet• on "Fermat's Last Theorem and Elliptic on "Understanding and Sensitivity of the ing was the presentation of the section's Curves"; Joe Kennedy (Miami University) Job Market," and on "The Mathematics of Award for Distinguished College or Uni• on "Lights and Strings and Things"; and Card Shuffling." In addition, there were versity Teaching to Robert L. Devaney Tom Hem (Bowling Green State Univer- ~------December 1994 FOCUS sity) on "The Image of a Circle-When public school teachers of mathematics in 85 calculator. There was a banquetat which Eigenvalues Do Not Quite Cut It." The each of the two states, Oklahoma and Fernando Gouvea spoke on "A Marvel• spring meeting always involves students Arkansas. ous Proof"; there were twenty-one to a high degree and did so again this year. PacificNorthwest The Pacific Northwest contributedtalks from among the seventy• In addition to the presentation ofeighteen Section held its annual meeting June 16• five participants at the meeting. papers by students, there were a pizzaparty 18, 1994, jointly with the Western Region The section gave A. Duane Porter (Uni• and a microcourse, "Problem-Solving For of the AMS, at the University of Oregon, versity of Wyoming) its Award for Fun and Profit," by Darrell Horwath and in Eugene, Oregon, with 229 people reg• Distinguished College or University Leo Schneider (John Carroll University). istered. The section enjoyed five student Teaching ofMathematics. The section now The annual summershort course was given papers, which were reports of NSF REU awards a free MAA student membership by Hugh L. Montgomery (University of projects from last summer. Students were to its top-scoring Putnam Exam student Michigan) titled "Computational Labora• feted with a pizza party at lunch the sec• each year; it awards certificates ofrecog• tories in Number Theory." ond day. The section arranged local nition to high scorers on theAHSME, and As a new venture, the section is starting a housing with U of0 graduate students for organizes a reception in Denver for mathematics essay contestfor undergradu• students who were presenting papers. AHSME achievers. ates this year. Invited talks were presented by Carl Seaway The Seaway Section held its Oklahoma-Arkansas The fifty-sixth Pomerance (University ofGeorgia), "Wit• annual fall meeting at OnondagaCommu• annual meeting ofthe spirited Oklahoma• nesses ofcomposite numbers," and Doris nity College in Syracuse, New York. It Arkansas Section of the MAA was held Schattschneider (First Vice-President of was held jointly with NYSMATYC. Sam March 25-26, 1994, at Harding Univer• the Association), "Was Eschera Mathema• McInroy (Corning Community College) sity in Searcy, Arkansas. There were tician?" There were twelve contributed offered a banquet address, "Mathematics, seventy-five regular and ninety-two stu• papers; a panel discussion, "TheBaby and Mother, and Menschenwerk: A Pictorial dent registrations. One hundred ten people the Bathwater,' chaired by Stu Thomas Essay on the Mathematical Shapes and attended the Friday night banquet. There (University ofOregon); three minicourses; Principles Found in Nature and Society." were sixty-eightcontributedtalks, includ• a grant-proposal writing workshop, by The John F. Randolph Lecture in Math• ing thirty-three student talks and two others Florence Fasanelli (MAA's SUMMA of• ematics Education was given by Israel delivered at a special session on "College fice); and a salmon bake. Kleiner (York University) on "AHistory• And University Mathematics Curricular Millie Johnson (Western Washington of-Mathematics Course for Teachers, Reform Projects Funded by the NSF," University) received the section's Distin• Based on Great Quotations." There was a chaired by John Watson (Arkansas Tech guished Teaching Award, and presented a session of student papers, featuring five University). talk titled "TheMathematics of Meanders: papers. Continuing its series ofworkshops on using technology in the classroom, the At the meeting, James Leitzel (University Rivers, Channelization, Floods, and the Environment." section offered the workshop "Using ofNebraska at Linclon), supported by the Graphics Calculators in FiniteMathemat• National ScienceFoundation, led a related Rocky Mountain The annual meeting of ics.t'byJack Graver(SyracuseUniversity). faculty workshop titled "Hands-OnWork• the Rocky Mountain Section was held shop on NSF Proposal-Writing and April 15-16, 1994, on the campus of the The spring meeting ofthe section was held Evaluation."A free conference on careers South Dakota School ofMines and Tech• at the State University of New York in mathematics was led by RobertEslinger nology in Rapid City, SouthDakota. It was (SUNY) atAlbany, April 22-23, 1994, with (Hendrix College), with special funding organized by Donald Teets and Janet 160 people attending. Professor Steven from the Exxon Foundation through the Burgoyne of that school. The keynote Hilbert (Ithaca College) was presented national office ofthe MAA. Nearly ninety address was "What Have Elliptic Curves with a framed certificate honoring him as students registered for this event. Got to Do With ItT' by Fernando Gouvea the section's 1993-94 Distinguished Col• lege Teacher of Mathematics, conferred The section welcomed Keith Devlin as its (Colby College). CelestinoMendez (Met• by Section Chair H. Joseph Straight invited speaker for the meeting. Prof. ropolitan State College of Denver and (SUNY Fredonia). ProfessorRebeccaHill Devlin's topic was "Whose Mother Is It?: governor of the section) chaired a panel was recognized for her service as gover• The Search for a Mathematical Theory of discussion on "TheNew NCTM and MAA nor of the Seaway Section. William Everyday Communication." Thomas Assessment Standards and TheirImplica• Siegmann (Rensselaer Polytechnic Insti• Banchoff was warmly received as the tions for MathematicsHigherEducation." tute) gave an after-dinner address on Nathan A. Court Lecturer, speaking on The section is particularly concerned with computer calculus and workshop calcu• "Visualizing DifferentDimensions: From articulation with the NCTM and with the lus at Rensselaer. Flatland to Interactive Hypergraphics." Standardsfor school mathematics. Itvoted Invited addresses were "Viewing and The winner of the third annual Distin• to add three representatives ofthe NCTM Calculating the Roots of a Polynomial guished College or University Teaching to the section's Executive Committee this Equation are as Easy as Coloring a Flag of Mathematics Award was Lisa Mantini year. Red, White, and Blue, or Hiking along a (Oklahoma State University). The section Tom Kelley (Metropolitan State College Continental Divide," by William F. Lucas continuedits tradition ofhonoring two top ofDenver) offered a workshop on the TI- (The Claremont Graduate School); "Soap ------~ FOCUS December 1994 Bubble Clusters, Including New Results of mathematics. The symposium was or• were "A Fast 'N' Best Optimal Assign• by Undergraduates," by Frank Morgan ganized by Bucky Allen (Francis Marion ment Algorithm with Applications to (Williams College); and the 1994 Harry University). Multitarget Tracking," by Roy Danchick M. Gehman Lecture, "Imaging the Inte• Southern California The annual fall (Senior Staff Engineer, TRW); "Wiles' rior of the Body with Electric Fields," by meeting of the Southern California Sec• Proofof Fermat's Last Theorem," by Ed• Margaret Cheney (Rensselaer Polytech• tion was held jointly with the American wardF. Schaefer(Santa Clara University); nic Institute). Beverly H. West (Cornell Mathematical Society at the Harvey Mudd and "Eigenvalues of Finite Toeplitz Ma• University) presented a workshop, "Teach• campus of The Claremont Colleges on trices," by Estelle Basor (California ing Differential Equations with Interactive November 6, 1993. There were three in• Polytechnic State University). Computer Graphics." Contributed paper vited addresses: "Myths of Mathematics," The 1994 Southern California Section sessions included ten faculty papers and by Morris W. Hirsch (University of Cali• Award for Distinguished College and eight student papers. fornia, Berkeley); "When Algebra Met University Teaching was awarded to Pro• The Seaway Section is the home of Jer• Topology," by Melvin Henriksen (Harvey fessor Mario U. Martelli (California State emy Bem, (Ithaca High School, Ithaca, Mudd College); and "Recent Court Rul• University, Fullerton). NewYork),amemberofthe United States' ings on Apportioning Fractions," by H. Southwestern The annual meeting of the history-making 1994 IMO team. Arthur DeKleine (Cal Poly, San Luis Southwestern Section of the MAA was Southeastern The Southeastern Section Obispo). There was an invited lecture/ held at Glendale Community College, had three excellent invited speakers for its demonstration, "ComputerExperiments in Glendale, Arizona. Since this was a joint annual meeting at Carson-Newman Col• ODEs: Cats, Scrolls, Chaos," by Courtney meeting with ArizMATYC and with the lege: Jack Brown (section lecturer,Auburn Coleman (Harvey Mudd College) and two Arizona Mathematics Consortium, there University) spoke on "Restriction Theo• Harvey Mudd students, Benjamin was a nice mix of two-year and four-year rems in Real Analysis"; Amassa Beechick and F. Leo Parker. There was a college faculty. Friday morning, April 8th, Fauntleroy (North Carolina State Univer• student poster session and three contrib• the group enjoyed a talk byCarl Pomerance sity) chose as his topic, "Hyperbolic uted papers. (MAA P61ya Lecturer). On Friday after• Geometry and Fermat's Last Theorem"; The Southern California Section received noon and Saturday morning were andAndrew Granville(University of Geor• an Exxon Education Foundation grant via contributed paper sessions. gia) spoke "Some Remarks about the Proof the Committee on Student Chapters which In conjunction with the Friday evening of Fermat's Last Theorem." Three short provided for enhanced student participa• banquet, which was held on the new Ari• courses were offered: "History of Math• tion in its two meetings. In particular, the zona State University-West campus, the ematics," by Billy Bryan (Vanderbilt grant supported a student postersession at group toured the new campus and saw the University); "Mathematical Economics," the fall meeting, described above, and electronic classrooms. The guest speaker by John Baxley and John Moorhouse seventeen papers presented by eighteen at the banquet was Mutiara Bays, who (Wake Forest University); and "Statisti• students representing nine colleges and combined mathematics and origami. Steve cal Programming on the TI-81," by universities, making up the contributed Shew (Glendale Community College) re• Richard Stephens (Western Carolina Uni• paper session at the spring meeting. ceived the section's DistinguishedTeacher versity). In addition, the Exxon grant supported a Award. A tour of Glendale Community Two popularevents for students attending symposium on contemporary problems in College's High-Tech Centers was a high• the meeting were the pizza lunch which society, Mathematical Modeling of Envi• light of the meeting; many people left the the section provided for them and the fac• ronmental Problems, atthe spring meeting. conference with new ideas on using com• ulty advisors of student chapters, and the The symposium consisted of three papers: puters in the teaching of mathematics. TA Rush which was held in conjunction F. M. Fujioka (U.S. Forest Service) on Texas The annual meeting of the Texas with this lunch. The section was pleased "Weather by the Numbers"; E. Section was held April 7-9 at Texas A&M to recognize the high achievementof Craig Cumberbatch (Claremont Graduate University inCollege Station, Texas.High• Gentry on the Putnam Exam by the pre• School) on "Fog Capture"; and T. Dolan lights of the meeting included the sentation of a $100 check. Mr. Gentry's (Environmental Applications) on "Math• presentation ofthe section's Distinguished score on the exam was the highest in the ematical Modeling of Soil Vapor Service Award to Professor James R. section. Extraction." Boone (Texas A&M University) and the The section's Award for Distinguished Ali Zakeri, student chapter coordinator, presentation of the section's 1994 Distin• College or University Teaching was pre• recognized the student speakers at the guished College or University Teaching sented to John D. Neff (Georgia Tech), meeting's luncheon and presented books of Mathematics Awardto Professor Montie and the section's Distinguished Service as prizes to the student winners of the prize G. Monzingo (Southern Methodist Uni• Award was presented to James G. Ware lottery. Student chapters in the Southern versity). (University of Tennessee at Chattanooga). California Section raise funds by selling There were forty-five contributed papers Supported by a grant from the Exxon mathematical trinkets at section meetings and eleven student papers at the meeting. Education Foundation, the section spon• and by printing and mailing the section's In addition, Bert Waits (Ohio State Uni• sored an undergraduate symposium of annual newsletters. versity) led a short course on the use of workshops on environmental applications Invited addresses at the spring meeting See Sections on page 33 @------December 1994 FOCUS ANMM • HAPTE .!!!

FACUI.: UDENTS be~.f the world's largest profession ation devoJl.-tr;:interests of college math- ematics. Inc terest an.eYcitement among your mathematics students. rage more students to consider careers in the mathematic sciences. MAA Student Chapters are devoted to increasing student involvement with mathematics, careers, and mathematicians at the national and local levels.

Student Chapter members: What some CHAPTERS do: .... join the MAA at reduced rates .... organize scavenger hunts for high school .... receive travel support for paper presenta- students tions at thesummermathematics meetings .... publish newsletters distributed to math .... receive notification of student activities at majors and alumni math majors the national mathematics meetings which .... write articles about mathematics for the include a Student Lecture,a StudentWork- school newspaper, and organize a puzzle shop and the Student Hospitality Center .... contest .... receive career information . 8Pr's~nt a campus-wide ~venin~ of ma .... automatically become member.s... inJl....• emetics for the non-technical major: the MAA's 29 regional Sectio.~i n-.... course sor student workshoPs..,. s.tu" ets, arrange for speakers wit career conferences.... I math- "Bernoulli Boys and ematics co nc ," student paper "Mathematics· sessions

To receive more information on Student Chapters Jane Heckler, MAA, 1519 18th Street, NW, Washington, DC e-mail: [email protected] or call 1-800-331-1MAA.

______~.t.\ LV PUT ONE OF THES

ON EVERY ONE OF THESE

FOR JUST ONE OF THESE.

How are universities around the puts you in charge. You choose matica site license. We'll work world putting Mathematica® on where you want Mathematica, together to customize one to fit every computer on campus for what kinds of computers you your school's needs. •.'.. as little as $1 per stu- want it on, how you want to net• ... dent? They are tak- work it in your labs, and how 1-800-441-MATH (6284) . ing advantage of much you want to invest. And [ll.S, and Canada) • new Mathematica site you can save up to 90% off the licenseprograms. In fact, site already-reduced acade• Call us about asite license for your campus and ask licenses at over 700 universi• mic price. for afree copy ofthis ties have made Mathematica If you're excited booklet, Mathematica accessible to millions of stu• about preparing more Flexible Academic dents without breaking the students for tomorrow by teach• Purchase Programs. schoolbudget. ing with the world's leading This new series of flexible, technical computing system affordable site license programs today, talk to us about a Mathe- Wolfram Research

Mathematics is availablefor: Macintosh· PowerMacintosh• Microsoft Windows• Microsoft Windows NT• MS-DOS • SunSPARC • HP• Hitachi. DEC Alpha OSF/1. RISC. VAXNMS .IBM RISC. sm. NEC PC. NEC EWS. NEXTSTEP. CONVEX. andothers.

Corporate headquarters: WolframResearch. Inc••+1·217·398-0700; fax: +1-217-398-0747; email: [email protected]. Europe: Wolfram Research EuropeLtd.•+44-(0)1993-883400; fax:+44-(0)1993-883800; email: info-euro®Wri.com Asia: WolframResearch Asia Ltd.(Tokyo otticel+8H013-5276-0506; fax: +81-(0)3-5276-0509; email: info-asia@WrLcom

© 1994Wolfram Research, Inc,Mathematica andMathUrt/( areregistered trademarks of Wolfram aesearcnInc,Mathematica isnotassociated withMamematca Policy Research, Inc.orMathTech, Inc All otherprodlJCt names mentioned areueoemares 01theirproducers December 1994 FOCUS

PERSONAL OPINION Table I: Doctoral Degrees LA. % of Women among those receiving degress from Time For I II III I-III IV V U.S. Cit ALL %F 81-90 15 18 21 17 25 20 Advancement %F 1991 16 21 21 18 29 21 24 20 Mary Beth Ruskai %F 1992 17 20 29 20 27 21 24 21 %F 1993 22 22 24 22 28 26 28 24 Because pre-college attrition is so high, LB. # of Women receiving degress from discussions of underrepresentation of women in science, mathematics, or engi• # in 1981-90 435 230 229 894 865 neering often leave the impression that # in 1991 70 39 29 138 49 33 112 220 there is only a minor role for college fac• # in 1992 73 38 39 150 46 27 103 223 ulty and research mathematicians. # in 1993 95 42 44 181 65 40 145 286 However, the number of women mathema• reached that at which they receivedPh.D.s several things occurred simultaneously: ticians has been substantial for many years. from group I departments alone!" The the percent of women receiving Ph.D.s Not only have women received over 20% group II (but not group III!) departments from group I departments jumped from a of the Ph.D.s in mathematics earned by did sometimes hire at a higher rate, but previous high of 17% to 22%; the distri• U.S. citizens every year since 1982, but in only in years when the group I hiring rates bution of women receiving Ph.D.s from recent years women have received nearly were low. This suggests that the group II groups I, II, and III was more uniform; 50% of undergraduate and 25% of doc• and III departments will hire women only groups II and III began to hire afew women toral degrees in mathematics. Despite if they can get group I women, but not if from groups II and III as well as I, IV,and recent progress, there is evidence that they have to settle for group II. Unpub• V; women were hired by doctoral institu• women continue to advance more slowly lished AMS data.' giving further tions at a rate slightly (very slightly) higher than men, and are less likely to have their breakdowns confirms this-women are than that at which they received Ph.D.s; achievements recognized than men. Dur• rarely hired into group II and III depart• and jobs were becoming increasingly ing the last two years, as chair of the ments from groups II and III, although scarce. The result was widespread claims AMS-ASA-AWM-IMS-MAA-SIAM substantial numbers of men are. In 1993, of, "Women are getting all the jobs.'?' Joint Committee on Women in the Math• ematical Sciences (JCW), I have reviewed A Personal Story a great deal of data. It has been a sobering WhenI wasagraduatestudentinthe '60s, eventhemostinsufferablemalechauvinists experience to realize the extent of the dis• never questioned my ability-no matter how inappropriate and perverted they re• parity that remains. gardedmy studyofscience,theyconcededthatawomanwhocouldsurviveingraduate schoolat Wisconsinwas capable.In 1972,near the previousnadir of the job market, I believe that mathematicians could do I reluctantlytook a postdoctoralresearchpositionfor the fourthconsecutiveyear,but much more to advance the careers of jun• decidedtoseekandacceptnothinglessthanaregularfacultypositionforthefollowing ior women, and that this responsibility is year.Moreover, in thefallof 1972,ElliottLiebandI completedtheproofof the strong shared by the entire mathematical com• subadditivityof quantum mechanicalentropy, a problem which we had worked on munity, men as well as women. Mentoring duringmy 1971-72postdocatMIT.Thisresult,whichhad beenanopenconjecturefor junior women should not be left to the five years, had gained enough notoriety in some circles that its solution would be increasing, but still overburdened, pool of expected to make one competitivein most markets. senior women. Afewmonthslater,a visitorwasvociferouslyholdingforthinthemathematics depart• AreWomen Getting All the Jobs? mentloungeaboutthe pressuretohire women.He allegedthathis departmenthadno The current job crisis in mathematics has womenapplicantsand he wouldgladlycreate a positionifsomeonelike me applied. been accompanied by claims that women So I asked for the name of his university-it turned out that I had just received a are getting a disproportionate share of the rejectionletter from his chair in the mail I opened before lunch! positions. The data tells a different story. In May,Rockefellerofferedme a postdocfor whichI had not even applied,but I still I have culled and summarized some data had no facultyoffers.By June, I finallyhad a one-yearpositionas VisitingAssistant from the annual AMS-IMS-MAA data Professorat the Universityof Oregon.Yet,whenI reportedthe offer,one male math• surveys. Table I shows the percent and ematician said (to my face), ''They must have been desperate to hire a woman." number of women among Ph.D.s from NeverthelessI enjoyed three years at Oregon,reachingthe tenure-tracklevel before different types of departments, whileTable decidingto move on. II shows corresponding data for those who Reasonablepeoplemay,ofcourse,disagreeaboutthe relativemeritsofindividualsfor received their first position at different certain appointments, However, honest disagreements should not be distorted into types of institutions. I From 1988-92 the tales of outrageousfavoritism, and those who hear such anecdotes third-andfourth• rate at which women were hired by doc• hand should regard them with considerableskepticism. Moreover, the existing data torate-granting mathematics departments does not show any evidencefor systematicpreferentialtreatment. increased steadily until in 1991 it finally ------@ December 1994

Table II: First Position of New Doctorates by Type of Department II.A. % of Women among those receiving first position at I-V+RI I II III I-III IV V RI D* MB 1988 13 26 7.5 14 26 0 17 15.5 18 20 1989 8 21 13 12 24 28 12 14.5 24 35 1990 12 16 19 15 31 22 9 16 19 18 1991 13 24 17 17 22.5 21 15 17.5 21 30 1992 21 17.5 12 18 8 57 16 18 18 30 1993 26 25 26 26 38 60 33 29 24 25 88-93 16 22 16 17 26 28 17 19 21 27 II.B. # of Women receiving first position at I II III I-III IV V RI D* M B 1988 II 11 4 26 9 3 38 14 14 1989 9 10 7 26 8 4 3 41 20 38 1990 12 8 13 33 10 4 3 50 16 19 1991 15 12 11 38 9 4 5 56 19 41 1992 23 7 6 36 2 4 10 52 15 42 1993 28 13 15 56 15 6 10 87 17 32

When, for perhaps the first time in history, 91, and 92, the number of "unfilled" po• much better. In fact, as shown in Table IV, women finally began to get their fair share sitions reported by both group II and group the proportion of women among tenured (any excess being well within the limits of III departments was always greater than faculty at groups I, II, and III was about statistical fluctuations), some men began the number of women actually hired! The 4%,5%,5.5%, respectively in 1991 and to cry "foul." nature of these unfilled positions is un• 1992. However, it jumps to 11-12% at clear-they may have disappeared, or master's and 15% at bachelor's depart• The AMS also publishes data on new hires been filled late. In any case, factors other ments. This differential is not simply a at all levels. The data for 1991 supports than competi tion from talented women are historical artifact; women continue to be the hypothesis that group II hires women primarily responsible for whatever diffi• disproportionately hired by bachelor's only if it can attract the kind of topnotch culties men currently encounterin finding institutions. In 1992 about 46% of tenured women group I has finally begun to re• jobs.' women mathematicians were at four-year cruit. True equality will be achieved not colleges, as well as 46% of untenured when the top mathematics departments Whereare Women Getting Jobs? women, i.e., both juniorand senior women finally have a few more tenured women, Women are far more likely to have posi• were equally likely to have positions at but when the group II departments stop tions at institutions with high teaching four-year colleges. By contrast, only 28% recruiting group I caliber women and start loads than at research-oriented Ph.D. in• of tenured and 33% of untenured men were hiring group II caliber women! stitutions. While a great deal of attention at such departments. Similar patterns hold However, Table III also contains some has been focused on the lack of tenured for 1991 and 1993. striking data about the numberof recruited women at "top ten" departments, only a Is this disparity a result of a greater appre• positions which were not filled. In 1990, few of the less prestigious departments do ciation of the rewards of teaching at Table III: New Doctoral Hires by Type of Department four-year colleges by women? This ques• I II III I-III IV V I-V M B tion cannot be answered until we are sure - -- _.-.------that every woman has the opportunity to 1990Total# Hired 144 74 157 375 461 68 18 215 220 pursue a mathematics career with the con• %F 13 16 16.5 15 22 17 16 23 20 #F 19 12 26 57 15 3 75 49 44 vex combination of teaching, research, and # Unfilled 24 17 32 73 18 2 93 46 42 administration that is best suited to her ------talents and interests. 1991 Total # Hired 170 73 131 375 61 19 455 220 402 %F 15 7 14 13 23 10.5 14 20 23 ButAre They Visible? #F 26 5 18 49 14 2 65 45 94 # Unfilled 9 14 34 57 20 12 89 66 51 It is certainly heartening that many of the ------young women coming out of graduate 1992Total# Hired 145 81 120 346 52 20 418 188 399 %F 18 23 16 18.5 21 IO 18 27 28 school are finally getting the opportunity #F 26 19 19 64 11 2 77 50 112 to begin their careers in good research # Unfilled 7 21 25 53 19 3 75 36 47 departments. However, most of these po• 1993 Total # Hired 163 65 152 380 62 30 472 233 331 sitions are not tenure-track. Ii The %F 14 34 22 21 31 23 22 23 23 substantial number of women who re• #F 23 22 33 78 19 7 104 53 77 ceived Ph.D.s from 1975-88 is not # Unfilled 12 9 13 34 15 4 53 25 55 reflected in the 5% of tenured women cur- 8)------December 1994 FOCUS rently in doctoral departments. Will the Table IV % Women among Tenured Doctoral Faculty* women Ph.D.s of the '90s fare better, or I II III I-III IV v M B will attrition also pare their ranks? Rather # of Depts 39 43 88 170 250 1000 than taking a "wait and see" attitude, the mathematics community should actively Fall 1991 4.2 5.2 5.5 5 7 3 11 14 promote the advancementofjuniorwomen Fall 1992 3.8 5.3 5.5 5 6 6 12 15 into the senior research ranks. Fall 1993 4.9 5.9 6.5 6 6 5 11 15 *Response rates are high (> 90%) for groups I-III, but significantly lower for groups IV, V, M, Career advancement does not consist en• and B. Therefore, the extrapolated data groups IV,V,M, and B are less reliable and show greater tirely in getting job opportunities at good fluctuations from year to year than that for groups I-III. However, figures are given to 0.1% for research institutions, or even in publish• groups I-III solely to indicate trends, and not as an indication of accuracy. ing in top notchjournals. Recognition and contactsalso play an importantrole. There• References for Tables I-IV fore, women mathematicians have long The primary sources were the second reports of the annual AMS-IMS-MAA survey for the years been concerned about the paucity of 1988-1993. These were published in Notices ofthe AMS as follows: women speakers at mathematics research 1988, vol. 36 (May/June 1989): 533-538; 1989, vol. 37 (July/August 1990): 658-663; 1990, vol. conferences. Although the situation is 38 (May/June 1991): 411--417; 1991, vol. 39 (July/August 1992): 573-581; 1992, vol. 40 (July/ improving, there are still far too many August 1993): 601-609; 1993, vol. 41 (July/August 1994): 598-605. conferences with no or few female speak• Data in Tables I and II above come from the tables denoted 2A and/or 2B in these reports. Data ers. The data summarized in Table V for in Table III above comes from the tables denoted 3B in the 1990-93 reports. Data in Table IV above comes from the tables denoted 3C and 3D in the 1991-93 reports. Additional data was AMS special sessions of invited twenty• obtained from the following articles in Notices ofthe AMS: minute talks illustrates one aspect of the Jackson, A. "Top Producers of Women Mathematics Doctorates." 38 (September 91) 715-720. problem. In sessions with only male orga• "1991 Annual AMS-MAA Survey (First Report)." 38 (November 1991):1086-1094. nizers, 7-8% of speakers were female; in "1993 Annual AMS-IMS-MAA Survey (First Report)." 40 (November 1993): 1164-1171. those with at least one female co-orga• Because cultural factors inhibit many number willing to confrontand fight them nizer, 15-16% of speakers were female. women from applying for awards or invit• is comparably small. As a result, a small Carefulexamination ofmeeting programs ing themselves, it is particularly important number of "bad guys" can have a dispro• and discussions withcolleagues have con• that senior researchers nominate and en• portionately large effect. I doubt that vinced me that this pattern is typical of courage them. affirmative action results directly in hir• many other meetings, and is the result of ing more women; its utility is primarily as Let me emphasize that I am not advocat• the following phenomenon: Men tend to a tool for diminishing the effect of the ing differential standards, but an expansion invite primarily well-established women malicious minority. who could also be hourlong speakers, of the existing network process to insure while female organizers include more the inclusion of women. It is not at all Only a few cases of hiring, promotion, promisingjunior women and lesser lumi• unusual to find that including more women speaker selection, etc. are really clear cut. naries. When junior women are actually raised standards. The essence of We do not live in an ideal world where overlooked, they may miss the exposure my recommendation is simply to make a every decision can be based upon pure and contacts that are essential to profes• small but concerted effort to insure that merit. Because most people have both sional growth and career advancement. promising women are not lost or over• good and bad points, detractors can al• However, it is not unusual for organizers looked. The current pool of ways find something if they look. The to include junior (male) colleagues. In mathematically talented young women is difficulty is to distinguish between a bona addition to including more senior women a vital resource which the mathematical fide criticism and an excuse to hide big• among the major speakers, organizers community ought to do everything pos• otry and double standards. Even when the should seek out junior women who are sible to develop. The existence of other "goodguys" win, the process ofairing and beginning to contribute to an area, par• pools of mathematical talent should not defeating irrelevant complaints can have ticularly if the meeting includes shorter tempt us to squander this unprecedented a detrimental effect on a junior faculty talks. opportunity, but challenge us to find ways member's career. I have seen too many of utilizing all the wealth. young women falter eitherbecause no one But conferences are only one aspect of a bothered to provide a necessary "push" at larger problem. The research community What Should We DoNext? critical times, or because detractors man• should take a more active role in advanc• Past experience has shown that the most aged to prevail. ing the careers ofpromisingjuniorwomen modest effort inevitably produces some Some people will point out that similar by suggesting them as speakers; inviting backlash. Despite the negative anecdote things can happen to young men also, and them to workshops at the various math• recountedin the box, I have also had many there are certainly cases in which men, as ematics institutes; encouraging them to positive experiences and very supportive well as women, have beenunfairly treated. apply for grants and fellowships; giving male colleagues. However, although I am What I find unfortunate is that, instead of savvy advice on grant proposals; nomi• convinced that the number of truly mali• being a stimulus toward fairness, this ob• nating them for awards; etc. In otherwords, cious and bigoted people is very small, I servation often becomes an excuse to doing all the things that someadvisors have am also increasingly convinced that the always done for their best male students." tolerate discrimination or double stan------@ FOCUS December 1994

Table V: AMS Special Sessions (Math Research) Meeting Organizer # of Women Speakers # of Total Speakers % Women A Consortium to Jan 91 San Francisco 22 244 9% 6 sessions Worn Co-Org. 12 100 12% Advance Women in 8 sessions Men Only 10 144 7% Jan 92 Baltimore 18 206 9% Mathematics 1995 none. Worn Co-Org. omitted-teaching & history only 12 sessions Men Only 18 206 9% If funded by the NSF, a consortium of 1992 Section Meetings 69 812 9% seven mathematics departments will II sessions Worn Co-Org. 28 193 14% begin offering special programs designed 41 sessions Men Only 41 619 7% to encourage talented women under• Jan 93 San Antonio 40 404 10% 4 sessions Worn Co-Org. 16 73 22% graduates to pursue advanced degrees in 17 sessions Men Only 24 331 8% the mathematical sciences. 92 & 93 Joint Summer Meeting 25 340 8% Summer Programs for Freshmen and 3 sessions Worn Co-Org. 8 44 18% 21 sessions Men Only 17 296 6% Sophomores: *Carleton and S1. OlafCol• Jan 94 Cincinnati 18 287 6% leges will offer a four-week program to 3 sessions Women Co-Org. 8 68 12% develop students' skills in conjecture, 12 sessions Men 10 219 5% proof, and the use of mathematical soft• Total Above 192 2293 8% ware. * SUNY Stony Brook's six-week 27 sessions Women Co-Org. 72 478 15% programwill involveeach studentin cre• III sessions Men Only 120 1815 7% ative problem solving in both pure and N~tes: .Prep~red f~om unpublished AMS data and/or a rough survey of meeting programs, both pnmar~ly using first name recognition with foreign names and initials assumed male unless applied mathematics. recognized. Only.math research sessions were included; those on history, undergraduate re• Summer Programs for Juniors: * The search, mathematics education, and meetings were excluded. George Washington University will of• fer a six-weekprogramof intensive short dards. Senior faculty not only have a re• scientists and engineers acquiring permanent courses leading to interesting open prob• sponsibility to be honest themselves, but residency in the U.S. in 1991 and 1992. Fur• lems. * Mills College will continue to to fight for their junior colleagues when thermore, nearly half of the scientists were operate its successful six-week Summer necessary. classified as mathematicians and computer Mathematics Institute, where students scientists by the Immigration and Naturaliza• References tion Service. By contrast, NRC data indicate participatein intensive interactive semi• that mathematicians and computer scientists nars led exclusively by active women I In these AMS-MAA reports, group I consists mathematicians. * Mt. Holyoke College of the top 39 Ph.D.-granting math departments constitute less than 10% of doctoral scientists (20% if one excludes social scientists). One in the U.S.; groups II, the next 43, group III, will offer an eight-week program in the remaining doctoral math departments; needn't be xenophobic or unappreciative of which small groups of students will work group IVconsists of statistics departments; and the contributions of foreign immigrant math• with faculty on researchproblems. *The ematicians to be concerned about this group V of doctoral programs in applied math University of Michigan atAnnArbor will imbalance. Moreover, in view of anecdotal and/or operations research. M and B denote operate an eight week research program departments which grant Master's and evidence that these immigrants were over• whelmingly male, it seems clear that the recent in which each student will work one-on• Bachelor's in mathematics respectively. The one with faculty on ongoing projects. symbol RI is used for research institute (e.g., advances of junior women are an exceedingly minor factor in the current tight job market. lAS or MSRI) and D denotes the combined Junior Year at Chicago: * The Univer• total of I-V + RI, i.e., new doctorates whose "The non-tenure-track positions range from prestigious research instructorships at top in• sity of Chicago will host promising first position was in a non-industrial research students who wish to deepen and broaden environment. stitutions to exploitive one- and two-year their mathematical background in an 2Although excluding groups II and III Ph.D.s temporary positions. The large number of from the doctoral hiring pool may be justified, women in non-tenure-track positions is partly intensive year ofstudy in mathematics. the actual hiring pool is somewhat higher than a consequence of their finally getting a higher share of the research instructorships. However, All seven programs will provide advice group I alone, since groups I and II do hire a and information about graduate schools significant number from group V, and group it is worth noting that in 1993 women held III from group IV. only 6% (10 of the 156) tenure-track positions and careers in mathematics. at group I departments versus 19% (68 of 360) 'Don McClure, AMS-ASA-MAA data com• of the non-tenure-track positions. Instructors are urged to bring this an• mittee chair (1987-1993), sent the JCW a nouncement to the attention of their summary of this data. "For those who want more detailed sugges• tions, see M.A. Olmstead, "Mentoring New students. For more information and ap• "Jackson, A. "Jobs, Grants, and the New Faculty: Advice to DepartmentChairs," CSWP plication materials, please send email to Ph.D."Notices of the AMS 40 (July/August Gazette 13 (August 1993), pp. I, 8-11. [email protected] or write to 1993): 588-90; "Are Women Getting All the CAWM, clo Summer Mathematics In• Jobs?" Notices of the AMS 41 (April 1994): Mary Beth Ruskai is a professor ofmath• stitute, Mills College, Oakland, CA 286-87. ematics at the University ofMassachusetts 94613. "The NSF data bureau recently reported sub• in Lowell. Her e-mail address is stantial increases in the number of foreign [email protected]. @------December 1994 FOCUS CALCULUS REFORM: A RETROSPECTIVE A SpecialJanuary Issue of

r-~~--~--

NEWS AND REPORTS ONUNDERGAADUATE MATHEMATICS EDUCATION .:

Calculus Reform-already involved, thinking about it, wonder what it is and how it's doing? Be sure to read theJanuary issue ofUME Trends and learn about:

• The history of calculus reform

• Overview and critique of calcuIus reform projects

• Assessing calculus reform efforts

• Calculus reform in Minority Institutions

• Calculus reform in Two-Year Colleges

• Using technology in calculus reform

• Dissenting views on calculus reform

• A practical guide to calculus reform

The special issue will be mailed to all members ofthe MAA, AMS, SIAM, and AMATYC. ------@ FOCUS December 1994 You've been good this year. Give yourself a treat!

Lion Hunting and Other Algebra and Tiling The Lighter Side Mathematical Pursuits Sherman Stein and Sandor Szabo of Mathematics A Collection ofMathematics, Verse, Often questions about tiling space or a Proceedings of the Eugene Strens and Stories by Ralph P. Boas, Jr. polygon lead to other questions. For Memorial Conference on Recre• Gerald L. Alexanderson instance, tiling by cubes raises questions ational Mathematics and its about finite abelian groups. Tiling by tri• and Dale H. Mugler, Editors History As a young man at the Institute for Ad• pods or crosses raises questions about vanced Study in Princeton, Ralph Philip cyclic groups. From tiling a polygon with Richard K. Guy and Robert Eo Boas, Jr., together with a group of other similar triangles, it is a short step to inves• Woodrow, Editors tigating automorphisms of real or complex mathematicians, published a light-hearted In August of 1986 a special conference on fields. Tiling by triangles of equal areas article on the "mathematics of lion hunt• recreational mathematics was held at the soon involves Spemer's lemma from to• ing" under a pseudonym (1938). This University of Calgary to celebrate the pology and valuations from algebra. sparked a sequence of articles on the topic, founding of the Strens Collection. Lead• several of which are drawn together in this The first six chapters of Algebra and Til• ing practitioners of recreational book. ing form a self-contained treatment of mathematics from around the world gath• Lion Hunting includes an assortment of these topics, beginning with Minkowski's ered in Calgary to share with each other articles that show the many facets of this conjecture about lattice tiling of Euclid• the joy and spirit of play that is to be found remarkable mathematician, editor, writer, ean space by unit cubes, and concluding in recreational mathematics. Martin and teacher. Along with a variety of his with Laczkowicz's recent work on tiling Gardner says of recreational mathemat• lighter mathematical papers, the collection by similar triangles. The concluding chap• ics: "I don't know of any better way to includes Boas' verse and short stories, many terpresents a simplified version of Redei 's hook the interests of students." theorem on finite abelian groups: if such of which are appearing for the first time. The papers in this volume represent a trea• a group is factored as a direct product of Anecdotes and recollections of his numer• sure trove of recreational mathematics by subsets, each containing the identity ele• ous experiences and of his work and a star-studded cast: Leon Bankoff, Elwyn ment, and each prime order, then at least meetings with many distinguished math• Berlekamp, H.S.M. Coxeter, KenFalconer, one of them is a subgroup. A remarkable ematicians and scientists of his day are also Branko Griinbaum, Richard Guy, Doris geometric implication of this result is included. Schattschneider, David Singmaster, developed in Chapter 2. The mathematical articles in this collec• Athelstan Spilhaus, Stan Wagon,and many tion cover a range of topics. They include Algebra and Tiling is accessible to un• others. dergraduate mathematics majors, as most articles on infinite series, the mean value You will not soon find another collection of the tools necessary to read the book are theorem, indeterminate forms, complex of wonderful articles on recreational math• found in standard upper division algebra variables, inverse functions, extremal prob• ematics by a more distinguished group of courses, but teachers, researchers and pro• lems for polynomials, and more. authors. If you are interested in tessella• fessional mathematicians will find the tions, Escher, tiling, Rubik's cube, Boas' wit and playful humor are reflected book equally appealing. Beginners will pentominoes, games, puzzles, the arbelos, in the verses included in this collection. find the exercises and the material found Henry Dudeney, or change ringing, then The verses reflect the phases of his career in the appendices especially useful. The this book is a must for you. as author, editor, teacher, department chair, "Problems" section will appeal to both and lover ofliterature. Asection of the book beginners and experts in the field. The If you believe that recreational mathemat• describes the feud that Boas supposedly had book could serve as the basis of an under• ics must be the mathematics that is fun, with Bourbaki. Also included are many graduate or graduate seminar, or a source then look no further, for TheLighterSide amusing anecdotes about famous mathema• of applications to enrich an algebra or of Mathematics is full of fun. ticians. geometry course. 376 pp., Paperbound, 1994 We profit from Boas' labor, and treasure it 224 pp., Hardcover, 1994 ISBN 0-88385-516-X as an inheritance. We should allow our• ISBN 0-88385-028-1 List: $38.50 MAA Member: $29.00 selves in some measure to walk along his List: $34.00 MAA Member: $26.00 Catalog Code: LSMAIFOC path. This collection will allow the reader Catalog Code: CAM-25/FOC a glimpse of that path. 240 pp., Paperbound, 1994, ISBN 0-88385-323-X List: $35.00 MAA Member: $25.00 Catalog Code: DOL-15/FOC Order form on page 32 December 1994 FOCUS All the Math Preparing for a Assessing Calculus That's Fit to Print New Calculus Reform Efforts Articles from the Manchester Conference Proceedings A Report to the Community Guardian Anita Solow, Editor James R. C. Leitzel and Alan C. Tucker, Editors Keith Devlin Among the background papers presented Assessing Calculus Reform Efforts: A Between 1983and 1989 Keith Devlin, re• at this 1993 conference are overviews of Report to the Community provides a re• search mathematician, author, and developmental projects in calculus reform, view of various aspects of the calculus educator, wrote a semi-monthly column precalculus reform at the college level, and reform movement. This study gives an on mathematics and computing in the mathematics curriculumreform at the high assessment of the current attitudes and in• English national daily newspaper, The school level. In addition, there are back• volvement of mathematical sciences Manchester Guardian. This book isacom• ground papers on the current status and departments-theirfaculty and students• pilation of many of those articles. It is special problems and potential forcurricu• in efforts to revise calculus instruction. witty, entertaining, and easy to read. lar reform in community colleges, and in colleges with large proportions of minor• A key finding of the assessment study is The mathematical topics range from ity students. The remaining two that how calculus is taught has changed simple puzzles to deep results including background papers summarize the results more than what is taught. The changes in open problems such as Faltings Theorem of the MAA Survey of the current state of instructional practice, more frequent use and the Riemann Conjecture. Youwill find calculus reform at the college level and of technology, and increased focus on articles on prime numbers, how to work changes in the AP Calculus Program. building students'conceptual understand• out claims for traveling expenses, calcu• ing are finding their way into both lating pi, computer simulation, patterns The core of the meeting program was a pre-calculus and post-calculus mathemat• and palindromes, cryptology, and much series of four concurrent workshops on ics courses. This has encouraged increased more. Content, Teaching Strategies, Institutional Context, and Course Context. Reports from interest in research about how undergradu• This book is meant for browsing by any• each workshop form the second part of the ate students learn mathematics. Many of one who regularly reads a serious volume. In these reports, each workshop the institutions that currently report using newspaper and has some interest in mat• group examines the future of the reform reform materials in experimental sections ters scientific or mathematical. Keith movement from the perspective of their have plans to move their efforts to course• Devlin tells us "from the mail I received topic. wide adoption in the near future. The fact Iknow that the readers ofthecolumn were that in the past two years over 95% of in• a varied bunch. They ranged from stu• The contributed papers, the third part of stitutions using a reform text continue dents at schools in their early teens the volume, represent the best thinking on using a reform text the next year (for at (occasionally even younger!), to retired calculus and precalculus reform from those least some sections) indicates that calcu• people in their nineties (often the ones who are actively involved in the move• lus reform is likely to be around for the who best succeed in cracking the brain ment. foreseeable future. teasers I occasionally included in my ar• The fourth part of the volume is a collec• Data is provided on the number of institu• ticles); from prison inmates to executives tion of brief descriptions of a number of tions at each of the levels of postsecondary in the computer industry; from truckers developmental projects in the calculus and education that are engaged in reform ef• to schoolteachers; both men and women." precalculus reform movements. The list• forts and also given is information on It you think that nothing of interest has ing of projects is a valuable resource faculty and student involvement and re• happened in mathematics since the time providing helpful information about a di• views of texts produced by some of the of Pythagoras, this book will change your verse set of projects. PreparingforaNew major curriculum development projects. mind. Keith Devlin presents mathemat• Calculus should be read by every math• The appendices to the report include brief ics as a living human enterprise, both a ematics educator who teachers at the descriptions of selected calculus reform science and an art. calculus or precalculus level. texts and a complete listing of the NSF awards made during the seven years of the 345 pp., Paperbound, 1994 250 pp., Paperbound, 1994 Calculus Initiative. ISBN 0-88385-515-1 ISBN 0-88385-092-3 List: $32.50 MAA Member: $25.00 List: $25.00 100 pp., Paperbound 1994 Catalog Code: ATMAFOC Catalog Code: NTE-36/FOC ISBN 0-88385-093-1 List: $15.00 Catalog Code: NTE-37/FOC

You've been good this year. Give yourself a treat! ------@ FOCUS December 1994

..UNITEDST4TES Statement of Ownership, Management, and Circulation Linear Algebra Problem Book _POS7aLSERVICE,. IReqiJirocll>y39U.S.C.3685) 1.P\tIIclIIOtIl1Ie 2.PubIcdonNo. 3. FIlIng0-. Paul Halmos FOCUS 0 17 1 3111- P 1014 10 November 28, 1994 4.....~ 5. No. of ...... P\MIhed e.ArnJIIl SubIcrtpIon Pnc.

8~~n:lm;:D~ero~:~r ~~( Feb. ~ April, M1ufIt.J six Indlv. Member $10 This is a book for mathematicians at all levels. Paul Halmos tells 7. ~....AddrMt01Knowl'n 0IIce of PublIcdon (SttNt. CII)C Co&ny.s.M. Mel ZJPH) (Not Pm,.,) us, "Even if I know some answers, I don't think I understand a 1529 Eighteenth St., NW. Washington, DC 20036-1385

subject until I know the questions. The questions in mathematics •. ~~AdlneIof~Ol'a.nen.IIlullrwuOfllclotPublllher(NatPrlnW) are called problems-and although I learned some linear algebra 1529 Eighteenth St. J NW. Washington. DC 20036-1385 a long time ago, until now I have made no serious effort to exam• •. FlA HImel end Cor!fI!t! M!!InpAdcnuM of F\bliIheI', EdIeDr, Mel MIn!pinpEd10r (Do Not L..~ Blankl NIIIINr ""-.J~~ActtNf) The Mathematical .as e cc a e t i cn of Alilerica. 1529 Eiehteenth St. I NW ine the problems that the solutions are based on. I wrote this book Washington. DC 20036-1385

to organize those questions-problems-in my own mind." EcIIDr fNIm--.d~" AUiIiIlg AtkJrea) Keith J. Devlin. School of Science. St. Mary's College of California This book can be either the main course or the dessert for some• Moraga. CA 94575 MiInlgIngEdtor ~ and CompI«e MtIIHngAddtea) one who needs linear algebra-and nowadays that means every Harry Waldman. 1529 Eighteenth St., NW, Washington. DC 20036-1385 user of mathematics. It can be used as the basis of either an 1D.Owner(llOlllllNllby.COtJ)OIal/Cn, .. ,..,.-.d-**-"..ba.aled-.d-.o~telyft«Nller,.flMllNandaddruHlof~~ orltoltln(J 1 patf*WOttrlOlWoIl'tt' ..,amountol,*,,*,. " notownedby. ~"..,..,.,..Mtdadlnfl. oIlhaindiWdua/CMNIIa rrxm~" official course or a program of private study. ~~~a::'':':':r',=,'':.::::~=-==~tofNO'l~multbag/vMI. tflhl~.

Full Name Malll AddNU If used as a course, the book can stand by itself, or if so desired, The Mathematical Association of Americ 1529 Eighteenth St., NW

it can be stirred in with a standard linear algebra course as the Washington, DC 20036-1385 seasoning that provides the interest, the challenge, the motiva• tion that is needed by experienced scholars as much as by beginning students.

11. Known BonctloIdItI,~, Mel Oller 8ec:urtty HoIcIM OwnIngorHoIdng 1 ~ orMen of Total A/noI.I'ltof BondI, ~. 01' Olhar The best way to learn is to do, and the purpose of this book is to _ .• nono."""' .....~.::..._ I c...... "..._. get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, '0.. . for security and completeness, provide the detailed answer. 340 pp., 1994, Paperbound 12. ForCCllTlPtiIion by nonpoIIt orgIRUIll:lrIaaulloriz«:lto rnaIlat 1IJlIClaI ....n. purpoM.lunctIon. Md nonprofit statui oflhl orgariUlion lind !he ~ ISBN 0-88385-322-1 ___ lor ItIdlnIInco'nIIDIUJlCIeM: (Chac*OM) ID.....NoC 0wlgtcI DuringPr8cdng 12 MonI1s o Hu ChMgMt DwWlgPrK!d'lO12 Months List: $35.00 MAA Member: $25.00 {lfetwlpad.~me..'.ubmII~oIcMnr1aMft'lIM ..r.m.rnJ

Catalog Code: DOL-16/FOC 1S.PWlIcalIonName 1

L "Ral No. CopIM (Nat p,.... Run) 30,490 26,500 b.~.::or~c;."::~, (Nct_ StrMIVwxIors,IlndCcu*rs.lel a a

(2) PMdorAeql-*l Mall &mcrlptionl j'lr'It:IWI~'PrDd~COpie$) 24,514 23,247

c. TomIPIlid.m'or Ae4lMtIdCircuIIllon (&In 01 16b(1) end 16b(2}) 24,514 23,247

clFrHDiIlI'ttMAIonbyMeill 3,818 tsM¥*t, ~taty, end OIhIr FiN) 2,789 f~ /Send order The MAA, Eight;;;th Street, ('Ifto;or~) this 1;;: 1529 NW-: -, I. FrM Ditt!tPulIon 0UtIlM the Mall (C'..Im"., (Jt 0 0 1Washington, DC 20036,1-800-331-1622; FAX: (202) 265-2384 r.TotalFrN DIItrlbullon (Sum of 15dand 1S.) 3,968 2,789 1Quantity Catalog Number Price g. 'rot.lOlltribulloo(Sumoll5cand15f} 28,482 26,036

1 _ h.CopinNot~d (1) OfIioIlJH, Leftovers. Spolild 2,008 464

,------(2) Return from News Agents 0 a 1 r.Total (Sumol15g, 1$11(1), and 1511(2)) 30,490 26,500 1 ~ Paid Ind/or Requnted CirculatiOn (1&: 115g x 1(0) 1 TOTAL 16.This S1a1~nlofewn.oopwlll bllprimld int. Dec. 1994 Issue 01 ltIit publiCafton 0 Checllbox ilnol reqUired to publistl

1 Membership Code _ 11.SignaturlandTilItofEcMIor.Publiahlr,BusinN$ManI~r.orOwnir y~ ?~ Datil November 28, 199 Membership/Subscriptions Manager 1 (Please mpy the first six digits that appear on the top line ojyour mailing label) ICIr1Ityhi"I InformationlumiIhId 0I'I1tI1l1orm Is true and complill Iun<»rslendIhIt anyone who fumishes .IISI 01"mllIading Ir'lformalion on thiStorm or who omtt. rMlllrial 01"inforTTW.tion rlQUIIfed on 1I'l1form may bllll.CjlCt 10crtrTllnlllMnctionI (inchJdinfJfirIIs.m impri«Jnm,ml) 8ncL1or civil sanctions 1Name (/rtchJ6ngrrUtiplldama~.andclvll~$)

Address Instructions to Publishers I 1. 01this lorm with your postmaster on or before 1, annually. a of the completed lorm lor Completeand file one copy OCtober Keep copy your recorde. State Zip Code 2. Include in Me,.,. 10 and 1" In cases where the l1ockholder or MCuri!y holder is a truttN. the name of the person or corporalion for whom the IrwiN illlCllng. AIaoinclude the names and IKk1I1lSI8I of individuals who ere stockl'lolde,. who own or hold 1 percent or more of Ihe total atn04.IflIof bonds, mortgages,or other MCurttles of the publishing corporation. In Item 1" if none, check box. Use blank ,heelS H IPayment 0 Check o VISA o MASTERCARD morespace ill required. 3. Be sure to lum'-h all information called for In lIem 15, regarding circulation. F.... circulation mUSI be shown in Items 15d, e. and t, •. "the publication had second-cJass authOrization as a general or requester publication, this Statement 01 Ownership. Management, and ICard Number Circulation must be published: il must be printed in any lse:ue In October or the lir'Slprlnted issue atler October. if the publication is not publlIhecl dUrlng Oclober. IS' E.. 5. In Item 16, indicate dille 01the Issue In which thlI Statement 01OwnerVllp will be printed I Ignature xplratIon Date 1 fl. ttem17 muslbe signed. o~ Foreign Orders Please add $3.00 per item ordered to cover postage and Fdure to file or publish a nhHnenl of maylead to auapenaion of IIfICOnd.cIus authorization

1handling fees. The order will be sent via surface mail. If you want your order 1 PS Form3526, CIctrJbtIr 1994 (~....rs.) ~tbyair,~lIbeh~~end~uaprofu~~icefury~ord~ !~~.2\------\J~/ V December 1994 FOCUS

Gardner from page 9 Sections from page 22 NAZARETH COLLEGE Department of Mathematics & entire universe is made of matter, obvi• graphing calculators in calculus and dif• Computer Science ously. And matteris made ofparticles. It's ferential equationscourses, and Joe Lakey Nazareth College invites applications for a ten• made of electrons and neutrons and pro• (University of Texas at Austin) offered a ure-track position in mathematics, effective Fall, 1995. Doctorate in mathematics or mathematics short course on wavelets. Department tons. So the entire universe is made out of education, and demonstrated interest and excel• particles. Now whatare the particles made chairs, institutional representatives, two• lence in teaching required. Responsibilities out of? They're not made out ofanything. year college faculty members, and MAA include 4 courses per semester (at various lev• The only thing you can say about the real• student chapter advisors and student rep• els), and continued scholarly growth. Preference ity ofan electronis to cite its mathematical resentatives met in special sessions. given to qualified candidates committed to the "reform" movement in undergraduate mathemat• properties. So there's a sense in which Wisconsin The annual meeting of the ics, and the preparation of mathematics teachers. matter has completely dissolved and what Wisconsin Section was held April 22-23, Nazareth College is a thriving, independent, co• is left is just a mathematical structure. 1994 at the University ofWisconsin, Eau educational, liberal arts college with an Mathematical structure has a reality ofits Claire, with 180 registrants, forty ofwhom undergraduate student body of approximately own and it's independent of the human were students. There was a large number 1400.The College is located near Rochester, New mind. Or, to put it another way, if intelli• of student papers, many the result of col• York, the third largest city in the state. Rochester gent beings were suddenly to disappear laborative work among students. The is noted for its cultural diversity. Salaries are com• petitive. from the universe, the Andromeda galaxy section's first attempt at offering a student would still have a spiral structure, whether poster session was declared a success; al• Send letters of application, resume, transcripts, anyone was observing it or not. Or, to put though only four posters appeared, they and the names and addresses of three references it in terms of number theory, if two dino• to: Professor Nelson Rich, Nazareth College, were well-appreciated. The section also 4245 East Avenue, Rochester, NY 14618-3790. saurs met two otherdinosaurs in a clearing, provided a pizza party for students as an E-mail: [email protected] will be con• there wouldbe four dinosaurs even though alternative to the banquet, as the section sidered as received until the position is filled. there would be no humans around to ob• has learned that students often do not en• EOE/AA. serve this event or to count, and even joy the banquet; now students have a though the dinosaurs didn't know how to choice. University of North Dakota count. So this is the sense in which I think The section is proud of its work on build• Mathematics Department mathematics is independent ofthe human ing a program of high school and middle Grand Forks, ND 58202-8376 mind. There are a lot of mathematicians Applications are invited for an expected tenure• school mathematics contests in the State. now who try to argue the reverse and make track position at the assistant professor level in It is continuing to encourage colleges and mathematics dependent on humanculture. one of the three areas, mathematics education, universities in the state to offer scholar• I simply can't understand what they're differential geometry or combinatorics, begin• ships linked to achievementon the several ning August 16, 1995. Teaching loads are three talking about when they say that. mathematics contests. The section supports courses per semester. Applicants must possess a strong commitment to teaching and research. The Joint Policy Board for Mathematics both the national mathematics contests and a statewide contest of its own. Doctorate required. Salary and fringes competi• Communications Award is sponsored by tive.ln your letter of application, state clearly the the American Mathematical Society, the area, of the above three, in which you are quali• MathematicalAssociation ofAmerica, and fied. Send current CV, copy of transcripts and the Society For Industrial and Applied three letters of reference to: Selection Commit• Mathematics. tee, Mathematics Department, University of North Dakota, P.O. Box 8376, Grand Forks, ND Constructivist Methods in Teaching 58202-8376. Closing date: February 15, 1995. UNIVERSITY OF REDLANDS Undergraduate Mathematics The University of Redlands Departmentof Math• ematics invites applications for a tenure-track 1995 Faculty Workshops at Purdue University position at the assistant professor level begin• ning September 1, 1995.Responsibilities include We inviteyou tojoinour intensive workshops on AbstractAlgebra,June 1-11, or Calculus.May teaching six undergraduate courses per academic 25-June 11.Our approach is based on: year, including computer-based courses; direct• ing student research projects; and engaging in • cooperative learning in a computerized environment scholarly activity. Requirements for the position • nine years of experience with alternative methods of teaching various mathematics topics include the Ph.D. in mathematics (any area of • a large research and development international project, funded by the National Science specialization is acceptable) and evidence of Foundation excellence in and commitment to undergraduate NO PREVIOUS COMPUTER EXPERIENCE IS REQUIRED teaching. We are seeking a person who is com• Partial supportfor travel and living expenses will be available. Take-home software and written mitted to meeting the educational needs of an materials will beprovided at nominal cost. For information and application forms, contact: Ed increasingly diverse student population. Dubinsky or Terry Loro, Department of Mathematics, Purdue University, W. Lafayette, IN The University of Redlands is a selective, pri• 47907, (317) 494-1982; e-mail: loro@math. purdue.edu. vate, comprehensive university located in sunny Application forms must be received by March 3, 1995 Southern California. It enrolls 1500 undergradu• ------@ates in liberal arts and sciences and in small FOCUS December 1994 professional programs in business, music, and ate and UMTYMP calculus component It has an undergraduate enrollment of approxi• communicative disorders. coursework. Work with the Director on under• mately 2000 full-time students and 1200part-time graduate curriculum development and K-12, To apply, send a letter of application which in• students. It also has a branch campus in undergraduate and graduate programs and activi• cludes a statement of teaching philosophy, Englewood Cliffs devoted primarily to adult ties which are educationally innovative. Conduct curriculum vitae, and three letters of reference learners. The normal teaching load is 12 credits (at least two of which must address teaching) to: research with the Director and senior staff lead• per semester. The Mathematics Department has ing to the publication of articles and materials a full-time position available beginning in Au• Dr. Mary Scherer, Chair, Mathematics Search, related to these programs. Qualifications: Ph.D. gust, 1995.Duties include teaching undergraduate Department of Mathematics, University of degree in mathematics, with extensive teaching mathematics courses, including some develop• Redlands, P.O. Box 3080, Redlands, CA 92373• experience at the undergraduate level required. mental courses. A Master's degree is required; a 0999. Research and publication experience and involve• Doctorate is required for tenure. Preference will Application deadline is February I, 1995. De• ment in educationally related programs, and be given to candidates with experience in prob• partment representatives will attend the mathematics research publications desirable. ability or in analysis. The position is contingent AMS-MAA Joint Meetings in San Francisco, Experience with innovative educational programs on budget approval. The review of applications California, January 4-7,1995. The University of for talented secondary school students or under• will begin on February I, 1995, and will continue Redlands is an Equal Opportunity employer, and graduates desirable. Send curriculum vitae, 3 until the position is filled. Send a letter of appli• especially encourages women and members of letters of recommendation (including at least one cation and a curriculum vitae to Search under-represented groups to apply, even if their letter detailing teaching experience and educa• Committee, Mathematics Department, Saint career paths have been unconventional. tional involvement), and statements on both Peter's College, Jersey City, NJ 07306. Please teaching/educational and mathematical interest enclose a self-addressed, stamped postcard for UNIVERSITY OF SOUTHERN and background to Dr. Harvey B. Keynes, School acknowledgment of your application. Saint of Mathematics, University of Minnesota, 127 COLORADO Peter's College is an EO/AA employer and com• Vincent Hall, 206 Church Street SE, Minneapo• plies with Title IX of the Education Amendments Department of Mathematics lis, MN 55455-0487. Closing date for receipt of of 1972 and with Section 504 of the Rehabilita• 2200 Bonforte Boulevard application 1/31/95. THE UNIVERSITY OF tion Act of 1973. Pueblo, Colorado 81001-4901 MINNESOTA IS AN EQUAL OPPORTUNITY Applications are invited for two tenure-track EDUCATOR AND EMPLOYER. SUNY GENESEO positions, each requiring a doctorate in mathemat• Two year, tenured track position (lnst. Asst. Prof.) ics. Candidates must demonstrate a strong Boston College - Department of open Fall 1995. Experience in and commitment commitment to excellence in teaching and teach• Mathematics to excellence in undergraduate teaching. Ph.D. ing a culturally diverse student population. Strong Boston College invites nominations and appli• preferred. Specialty: applied mathematics. Clos• communication skills are essential, and ongoing cations for a tenured position in the Department ing date: Feb. I, 1995. Send: vita, three letters of scholarly activities are expected. The University of Mathematics at the level of Full, or possibly recommendation, transcripts, statementof teach• of Southern Colorado is building a multicultural Associate, Professor. Qualifications include the ing philosophy to Donald Thrasher, SUNY, I faculty and strongly encourages applications from Ph.D. in the mathematical sciences, a strong College Circle, Geneseo, NY 14454. AA/EOE. female and minority candidates. Send letter of record of scholarship, and a commitment to teach• Women and minorities are encouraged to apply. application which includes a statement of pro• ing at the undergraduate and master's levels. An fessional goals, current resume, copy of graduate applicant's area of research should be compat• transcripts, and three letters of reference ( two The University of Montana ible with those of the department; these include, must commenton teaching) to Roger W.Johnson, Department of Mathematical Sci- but are not limited to, analysis, dynamical sys• Search and Screen Committee. Evaluation of ences tems, number theory, probability and statistics, applications will begin immediately and continue The Department of Mathematical Sciences has and topology. The position will be available on until positions are filled. USC is an AA/EO em• openings for two tenure-track Assistant Profes• September I, 1995. ployer. sors beginning Fall 1995. One position each in Boston College is a Jesuit University, enrolling Operations Research and Statistics are available. SCHOOL OF MATHEMATICS, approximately ten thousand undergraduate and A doctorate in Mathematical Sciences and acom• UNIVERSITY OF MINNESOTA four thousand graduate students. The Department mitment to excellence in teaching and research of Mathematics includes twenty-one full time Assistant Professor, Mathematics, 2-Year Tem• are required. Research must be compatible with faculty, and offers undergraduate programs in porary Position, for recent Ph.D.s especially interests of current faculty members in the de• mathematics and computer science, as well as interested in several areas of curriculum devel• partment in Operations Research and Statistics. opment and mathematics education in a major graduate programs leading to the MA and MST The department offers B.A., M.A., M.A.T., and degrees in mathematics. mathematics department. These areas include Ph.D. degrees in several areas of mathematics. A graduate training, undergraduate curriculum re• Applicants should submitacurriculum vitae along longer jobdescription may be obtained by anony• form, and programs for mathematically gifted with a cover letter, and are invited to include mous ftp at ftphost.umt.edu in the subdirectory / secondary school students. This position will be names of references. Send all materials and in• pub/math (read 'readme' first) or by calling the a 9-month, non-tenure track appointment with quiries to: W. J. Keane, Chair, Department of phone number below. Applications (including the School of Mathematics, with a 2-year initial Mathematics, Boston College, Chestnut Hill, MA resume, graduate transcripts, and 3 letters of rec• period, and renewable forup to 2 additional years. 02167; e-mail: [email protected]. Review ofappli• ommendation) should be sent to: Don Work under the supervision of the Directorof the cations and nominations will begin on January I, Loftsgaarden, Chair, Department of Mathemati• Mathematics Special Projects Office with the 1995, and continue until the position is filled. cal Sciences, University of Montana, Missoula, University's Talented Youth Mathematics Pro• MT 59812. Phone: (406) 243-4171, e-mail: Boston College is an Affirmative Action/Equal [email protected] (questions only). gram (UMTYMP), departmental initiatives, and Opportunity employer. developing various grants. Projected salary Screening of applicants will begin on January 16, 1995, and continue until the positions are $32,000-$34,000 for the academic year 9/ 1-6/15 Saint Peter's College depending on qualifications. Summer appoint• filled. The University of Montana is an equal Department of Mathematics ments on externally funded projects may be opportunity/affirmative action employer. available. Responsibilities: Teaching undergradu- Saint Peter's College, an urban Catholic Jesuit Institution, is located in Jersey City, New Jersey. @------December 1994 FOCUS

Moorhead State University August 1995. Ph.D. in mathematics in the area of mathematics and have a record of or show poten• Tenure-track position at rank of assistant profes• combinatorics, graph theory, optimization, or tial for in-service teacher education, grant sorto begin September, 1995.APh.D. orEd.D. in control, evidence of excellent teaching ability, procurement, research, and publication. mathematics education is strongly preferred. Sub• and strong interest in research are required. Du• Sam Houston State University has a strong tradi• stantial progress towards terminal degree is ties include teaching undergraduate and graduate tion of quality in mathematics teacher education, required. Eligibility for licensure at some level courses, engaging in research activities, partici• providing a variety of innovative programs for K-12 and good communication skills are required. pating in course and curriculum development, preservice and in-service teachers of mathemat• Preference will be given to candidates with evi• and directing graduate students. Initial screening ics at the elementary, secondary, and two-year dence of successful teaching experience at the of applications will begin on January 10, but the college levels. An unusually cooperative rela• K-12 and college level. Interest or experience in position will remain open until filled. Send tran• tionship exists with the Department of Curriculum teaching a mathematics methods course for the scripts and curriculum vitae, and have three letters and Instruction, which offers complementary elementary education majors and evidence of abil• of recommendation sent to: course work in professional education. Division ity to work effectively as a member of a teaching Prof. Brian M. O'Connor curricula include computer science, mathemat• team are desirable. Duties include teaching math• Search Committee Chairperson ics, and statistics. Undergraduate and graduate ematics education methods courses, elementary Department of Mathematics major and minor programs in mathematics with education content courses, and undergraduate Box 5054 supporting courses in computer science and sta• mathematics courses. Other responsibilities in• Tennessee Technological University tistics are offered for prospective secondary clude advising secondary mathematics education Cookeville, TN 38505 school teachers. In addition, the Division offers majors, developing in-service workshops, work• FAX: (615) 372-6172 mathematics minors at the BS and M.Ed. levels ing on assigned committees, and maintaining an e-mail: [email protected] for elementary school teachers. Apreservice MA appropriate level of professional activity. The AN AA/EEO/ADA EMPLOYER program for two-year college mathematics fac• teaching load is twelve hours per semester, which ulty is available. San Houston State University, may include supervising student teachers. Screen• a member of the Texas State University System, ing of applications will begin January 20, 1995. Elon College with 96 undergraduate, 76 graduate, and one Applications are invited for one or two perma• Completed applications must include a resume, doctoral program, is one of the larger state-as• nent positions at the assistant professor level. MSU Standard Application Form, graduate and sisted institutions of higher education in Texas. Applicants must hold a Ph.D. in Mathematics by undergraduate transcripts, and three letters of ref• Approximately 13,000 students and 500 full- and the effective date of appointment, August 1995. erence. Apply to Ronald Jeppson, Chair, part-time faculty enjoy the advantages of pictur• A strong commitment to teaching at the under• Mathematics Department, Moorhead State Uni• esque Huntsville, Texas (rated as one of the best graduate level is required. Preference will be versity, Moorhead, Minnesota 56563, (218) small cities in America), and close proximity to given to candidates with experience in teaching 236-2274. Moorhead State is an equal opportu• the Houston Metroplex, 60 miles south of cam• and a demonstrated interest in curriculum devel• nity/affirmative action employer and educator. pus. opment. Evidence of experience in statistics, applied mathematics and interdisciplinary study Review of applications will begin on January 15, GUILFORD COLLEGE is desired. Elon is a private, liberal arts college 1995, and continue until the position is filled. To Department of Mathematics Greens- with 3500 students located between Greensboro apply, submit a letter of application, full curricu• boro, North Carolina and Burlington, within an hour's drive of several lum vitae, transcripts, and three letters ofreference Tenure-track position in mathematics at a selec• colleges and research universities. The mathemat• to: Professor Ronald A. Stoltenberg, Mathemat• tive Quaker affiliated liberal arts college of ics department has 10 full-time faculty members ics Education Search Committee, Sam Houston approximately 1600 students. Applicants must be and 45 undergraduate majors. A representative State University, Huntsville, Texas 77341-2206. enthusiastic about teaching service courses (es• will be attending and interviewing at the San Sam Houston State University is an Equal Op• pecially elementary statistics) and a wide range FranciscoAMS/MAAmeetings in January 1995. portunity and Affirmative Action Employer. of courses in the major, and should have interdis• Applicants interested in being interviewed should Women and members of minority groups are ciplinary teaching interests as well. They also need submittheir applications by December 15, 1994. encouraged to apply. to be enthusiastic about teaching students with Otherwise applications will be reviewed begin• diverse mathematical preparations and abilities, ning on January 20, 1995. Send letter of OHIO UNIVERSITY and about promoting undergraduate research with application, vita, undergraduate and graduate Department of Mathematics capable students. Candidates must have com• transcripts, and three letters of reference to: Dr. The Department of Mathematics is accepting pleted, or be near completion of the Ph.D. in Rosalind Reichard, Associate Dean forAcademic applications for the position of tenure-track as• mathematics (all specialities considered) and Affairs, Campus Box 2163, Elon College, NC sistant professor in the field of mathematics should show evidence of an active continuing 27244. Minority and women candidates are en• education. The position begins September 1, research program. Three courses per semester is couraged to apply. Elon is an EOE institution. 1995. The candidate must be qualified to teach the standard teaching load. Applicants should send courses entitled "Teaching of Mathematics in AMS Application Cover Sheet, letter describing MATHEMATICS POSITION Secondary Schools," and "The History of Math• teaching interests and philosophy, vita, transcripts, ematics." The candidate should also be able to and three recommendations to George R. Gordh, Specialty in Mathematics Education supervise the mathematics sequence for elemen• Jr., Department of Mathematics, Guilford Col• Sam Houston State University The Division of Mathematical and Informational tary education majors. The salary is competitive lege, Greensboro, NC 27410. Application and there is an excellent benefits package. Appli• materials should be sent by January 9, 1995 to Sciences is seeking applicants for a tenure-track position for a specialist in mathematics educa• cants must have a Ph.D. in either mathematics or ensure full consideration. Women and minorities mathematics education before September 1,1995. are encouraged to apply. AA/EOE. tion. Rank and salary are negotiable. Applicants should have the equivalent of a master's degree Send resume and three letters of recommenda• in mathematics and hold a doctorate in math• tion to Mary Anne Swardson, Chair, Department TENNESSEE TECHNOLOGICAL ematics or mathematics education. The successful of Mathematics, Ohio University, Athens, Ohio UNIVERSITY candidate will possess the interest and ability to 45701. The deadline for applications is January Department of Mathematics develop and teach mathematics content courses 31,1995. Ohio University is an Equal Opportu• Applications are invited for a tenure-track posi• for prospective teachers. Preference will be given nity/Affirmative Action Employer. tion at the rank of Assistant Professor, available to persons who have a strong background in ------~ FOCUS December 1994 Northeast Missouri State University comite de selection, de son interet pour la forma• anticipate a doctorate in mathematics and mas• Three positions are expected to be available in tion des maitres du secondaire en rnathernatiques ters-level competency in computer science or a August 1995: tenure-track Assistant or Associ• et de sa capacitc a donner des cours de doctorate in computer science and masters-level ate Professor of Mathematics Education, mathernatiques adaptes aux futurs enseignants competency in mathematics. The successful can• tenure-track Assistant Professor of Mathemat• du secondaire. didate is expected to be able to offer some ics, and temporary Instructor. Tenure-track Avoir la capacite de faire de la recherche in upper-level courses in computer science and in• positions required appropriate doctoral degrees mathematiques. troductory courses in both areas. The department or expected completion dates prior to August 31, is searching for a person who is an excellent Pouvoir enseigner en francais, 1995; Instructor positions require at least a mas• teacher and has a strong commitment to the lib• ters degree. Candidates for the Mathematics Serontconsideres comme des atouts: - une bonne eral arts. Continued excellence in teaching and Education position should have the commitment connaissance du systerne denseignement research are required for tenure. and ability to continue the development of an secondaire au Quebec, - la capacite a integrer Please have a letter of application, vita, and three excellent, innovative graduate program prepar• dans une des equipes de recherche existantes de letters of recommendation, at least one of which ing secondary teachers. This involves supervising departement, - une formation complernentaire addresses teaching, sent to the chair of the de• interns and requires substantial driving. For the dans un domaine lie a I'enseignementsecondaire. partment. Review of applications will start I tenure-track mathematics position, an interest in INFORMATION L'Universite Laval applique un February 1995 and will continue until the posi• teaching numerical analysis or computer science programme dacces a l'egalite qui consacre la tion is filled. As an AAlEOE employer, Denison is preferred, but not required. Teaching loads are moitie des postes vacants a I' engagement des encourages women and people of color to apply. nine semester hours for tenure-track positions, femmes. Las candidatures feminines et les twelve hours for instructors. Candidates should candidatures de jeunes presentant un grand Northern Kentucky University supply evidence of potential for excellence in potentiel sont particuliercment encouragees. teaching, advising, research, and service appro• Conformernent aux exigences prescrites en Department of Mathematics and priate forthe position they seek. Applicants should matiere d'immigration au Canada, la priorite sera Computer Science send a vita, statement of teaching philosophy, accordee aux citoyens canadiens et aux residents Tenure-track position in mathematics beginning transcripts of undergraduate and graduate study, permanents du Canada. Le salaire est detetrnine August, 1995, pending funding. Doctorate in a and three letters of reference to Dr. Eric Howard, par Ie convention collective suivant I' anciennete mathematical science required. Quality teaching, Division Head, Mathematics and Computer Sci• et Ie rang universitaire accordes. Les personnes continued scholarly activity, and service required. ence, Northeast Missouri State University, interessees sont priees de faire parvenir, avant Ie Good oral and written communication skills Kirksville, MO 63501. Review of applications 31 janvier 1995, a I' adresse cidessous, une copie mandatory. Will teach a wide range of under• will begin January 16, 1995 and continue until de leur curriculum vitae, des tries-a-part de graduate mathematics courses. Normal teaching the positions are filled. Northeast is a highly se• quelques publications recents ou tout autre tra• load is twelve hours/semester. Send letter of ap• lective public liberal arts and sciences university vail de recherche et deux lettres de plication, curriculum vitae, transcripts or and an AAIEO/ADA employer. recommendation ternoignant de leurs aptitudes summary of graduate work, and three letters of professionnelles tant en recherche qu ' en recommendation to: Dr. Gail Wells, Chair of DEPARTEMENT DE enseignement. Claude Lemaire, dDirecteur Search Committee, Department of Mathematics/ MATHEMATIQUES ET DE Departement de mathernatiques et de statistique Computer Science, Northern Kentucky Univer• sity, Highland Heights, KY 41099-1700. STATISTIQUE UNIVERSITE Universite Laval Sainte-Foy (Quebec) Canada GIK 7P4 Applications reviewed as received; interviews LAVAL begin February 15, 1995. NKU is located seven POSTE POUR LE Western Carolina University miles from Cincinnati, Ohio and enrolls approxi• BACCALAUREAT EN Department of Mathematics mately 12,000 students. The Department of ENSEIGNEMENT SECONDAIRE Mathematics and Computer Science, with 200 and Computer Science (MATHEMATIQUES) computer science majors and 100 mathematics Assistant!Associate Professor tenure-track posi• Le Dcpartement de rnathernatiques et de majors, offers courses in mathematics, computer tion, beginning August 1995. Ph.D. in statistique sollicite des candidatures pour un poste science, and statistics. NKU is an AAlEOE ac• mathematics required. M.S. or B.S. degree in de carriere specialernentconsacre an baccalaurent tively seeking the candidacy of minorities and computer science will enhance application. Du• en enseignement secondaire (voies women. ties include teaching mathematics courses from mathernatiques). L'ENTREE EN FONCTION freshman through master's levels and possibly EST LE IER JUIN 1995. computer science courses. Excellence in teach• Dartmouth College fonctions La fonction principale de la personne ing and continued scholarly activity are expected. The Department of Mathematics has an opening recrutee sera d'enseigner des cours de Send resume, transcripts, three reference letters for a tenure-track Assistant Professor in Modern mathernatiques destines aux estudiants du to: Lee Minor, Coordinator MATH SEARCH Analysis, with initial appointment in the 1995• baccalaureat en enseignment secondaire et COMMITTEE, Dept. of Mathematics & CS, 1996 academic year. A candidate for the position deffectuer toute tache universitaire en relation Western Carolina University, Cullowhee, NC must be committed to outstanding teaching at all avec ce programme. 28723. Send inquiries to: [email protected]. levels of the undergraduate and graduate curricu• lum and must give evidence of a well-regarded Elle devra faire de la recherche et pourra etre Deliberations on completed applications will research program that shows real promise for the requise pour effectuer dautres taches begin January 6, 1995; later applications will be future. Candidates with several years of experi• universitiaires, notamment lenseignerncnt accepted until position is filled. AAIEOE. ence should in addition be ready to direct Ph.D. d autres cours et la supervision d estudiants des theses. To create an atmosphere supportive of deuxierne at troisierne cycles. Denison University Mathematics and research, Dartmouth offers new faculty members Criteres de Selection Detenir un doctorat en Computer Science Department grants for research-related expenses, a quarter of rnathernatiques ou un dipl6me juge equivalens. Granville, OH 43023 sabbatical leave for each three academic years in Les candidatures des personnes qui sont proches The department invites applications for a tenure• residence and flexible scheduling of teaching d "obtcni r un doctorat seront eg alernent eligible position at the rank of assistant professor responsibilities. The teaching responsibility in considerees. Faire la preuve, a la satisfaction du beginning fall 1995. Candidates must hold or mathematics is four courses spread over two or three quarters. The department encourages good ,@------December 1994 FOCUS teaching with a combination of committed col• emphasizes teaching however, scholarship and script of doctoral studies, and three letters of leagues and bright, responsive students. Though service is expected. Minimum qualifications: recommendation) to: Edwin Hawkins, Chair, first priority is to appoint a modem analyst, our Doctorate in mathematics, mathematics educa• Department of Computer Science, Math, and second priority is a mathematical statistician with tion, or operations research; demonstrable Engineering, Mesa State College, P.O.Box 2647, strong interests in signal processing. Exceptional computer skills, sufficient to use the Center's soft• Grand Junction, CO 81502, (303) 248-1654. To circumstances could lead to making the appoint• ware. Preference will be given to candidates who insure consideration, the entire application pack• ment in some third field or at a higher level than have experience directing a mathematics learn• age should be received by January 18, 1995.Mesa assistant professor. To apply, send a letter of ap• ing center. Consideration will be given to State College is anAAlEOEemployer. Mesa State plication, curriculum vitae, and a briefstatement candidates who expect to complete all degree College is a drug-free workplace. All employees of research results and interests. Also arrange for requirements by August 15, 1995 (essential for of the College must agree to abide by our drug• four letters of reference to be sent, at least one of appointment). Correspondence must identify the free policy as a condition of employment. which addresses teaching, and, ifthe applicant's title of the position. Letter of application and native language is not English, the applicant's resume, including the names and telephone num• Computer Science, Meredith College bers of three references (no letters of reference, ability to use English in a classroom. All applica• Assistant!Associate Professor and Director of please) must be received by JANUARY 20, 1995. tion materials should be addressed to Betty Computer Science. Ph.D. in Computer Science Harrington, Recruiting Secretary, Departmentof Address correspondence to: Dr. Robert V.Mark, or Computer Information Systems; a strong in• Dean, School of Arts and Sciences, Box B, State Mathematics, 6188 Bradley Hall, Dartmouth terest in teaching; a commitment to undergraduate College, Hanover, NH 03755-3551.Applications University of New York, College of Technology, liberal arts and computer science education. Farmingdale, NY 11735.The College is an Equal completed by February I will receive first con• Meredith College is a church-related women's sideration. Dartmouth is committed to Opportunity/Affirmative Action Employer. college with a stable environment of about 2000 Affirmative Action and encourages applications students. Apply to Dr. Virginia Knight, Depart• from African Americans, Asian Americans, His• Continuing Position ment of Mathematics and Computer Science, panics, Native Americans, and women. Inquiries Department of Mathematics Meredith College, 3800 Hillsborough St., Ra• about the progress of the selection process can be Southern Illinois University at leigh, NC 27607; inquiries to vknight@ directed to C. Dwight Lahr, Recruiting Chair. Carbondale Carbondale, Illinois mercury.interpath.net. Meredith College is an 62901 Equal Opportunity Employer; women and mi• Dartmouth College Applications are invited from qualified candi• norities are encouraged to apply. John Wesley Young Research Instruc- dates for a tenure-track position at the assistant torship in Mathematics professor level beginning on August 16, 1995. Franklin & Marshall College The John Wesley Young Research Instructorship Ph.D. in mathematics required. Preference will Lancaster, PA 17604-3003 in Mathematics is a two-year post-doctoral .ap• be given to applicants in the areas of algebra, Assistant Professor of Mathematics pointment for promising new or recent Ph.D.s combinatorics, ordinary or partial differential Visiting Assistant Professor of Mathematics whose research interests overlap a department equations, probability and topology. Candidates Undergraduate mathematics department has aten• member's. Current departmental interests include must have demonstrated excellence in research ure-track entry-level position and a visiting areas in algebra, analysis, combinatorics, com• or potential for such. Applicants should provide position renewable for two or three years, start• puter science, differential geometry, logic and evidence of excellence in teaching, and foreign ing Fall 1995. Ph.D. expected by Sept. 1995. For set theory, number theory, probability and topol• applicants must provide evidence of the ability tenure-trackjob, preference will be given to can• ogy. Teaching duties of four ten-week courses to teach in English effectively. Send letter of didates specializing in algebra, number theory or spread over two or three quarters typically in• application, resume, and three letters of recom• discrete math. Teaching: 5 courses per year. Con• clude at least one course in the instructor's mendation to: Continuing Position c/o Ronald B. tinued scholarly activity expected. Send resume; specialty and include elementary, advanced and Kirk, Chair, Department of Mathematics, South• graduate and undergraduate transcripts; four let• (at instructor's option) graduate courses. Nine• em Illinois University at Carbondale, Carbondale, ters of recommendation, two of which address month salary of $35,000 supplemented by Illinois 62901 The closing date is December I, teaching ability; list of courses taught, including summer (resident) research stipend of $7,778 1994 or until the position is filled. SlUC IS AN applicant's responsibilities andAMS Application (two-ninths). Send letter of application, resume, EQUALOPPORTUNITY/AFFIRMATIVEAC• Cover Sheet to: Alan Levine, Chair. The deadline graduate transcripts, thesis abstract, description TION EMPLOYER. Women and minorities are for the tenure-track position is January 20, 1995. of other research activities and interests if appro• particularly encouraged to apply. Consideration for the visiting position begins priate, and 3 or preferably 4 letters of January 20; applications accepted until position recommendation (at least one should discuss Mesa State College announces two tenure-track filled. Franklin & Marshall is committed to cul• teaching) to Betty Harrington, Department of positions in Mathematics at the Assistant or As• tural pluralism and strongly encourages Mathematics, 6188 Bradley Hall, Hanover, NH sociate Professor level beginning mid-August applications from minorities and women. EOEI 03755-3551. Applications received by Jan. 15 1995. Required are an earned doctorate in math• AA. receive first consideration; applications will be ematics by May 1995; a demonstrated ability to accepted until position is filled. Dartmouth Col• provide high quality teaching in lower division, Franklin & Marshall College, Dept. lege is committed to affirmative action and upper division, and developmental levels; strong of Mathematics strongly encourages applications from minori• interest in integration of new mathematical tech• Lancaster, PA 17604-3003 ties and women. nology; and a commitmentto campus service and professional development. Preference will be Assistant Professor of Mathematics SUNY-Farmingdale given for outstanding teaching atthe college level. and Computer Science Director of the Mathematics Center and As• Consideration will be given for graduate teach• Tenure-track entry-level position in undergradu• sistant Professor of Mathematics - fall 1995 ing assistantships with sole responsibility. Good ate mathematics department starting Fall 1995. anticipated tenure-track vacancy-to direct the communication skills are also required. Commen• Ph.D. expected by Sept. 1995.Teaching: 5 courses operations of a mathematics learning center and surate with education, experience and rank, per year in mathematics or 4 courses in computer to teach a 112 load. Teaching responsibilities will anticipated salary would be in the low $30,000. science. Continued scholarly activity expected. range from remedial through all levels of under• Send application package (letter of application, Send resume; graduate and undergraduate tran• graduate mathematics. The Department statement of teaching philosophy, resume, tran- scripts; four letters of recommendation, one addressing teaching ability in computer science ------@ FOCUS December 1994 and one in mathematics; list of courses taught, The University of Akron liberal arts and sciences college of 1700 students including applicant's responsibilities and plan for Department of Mathematical Sciences located near Burlington, Vermont. Duties include future research to: Professor Jay Anderson, by Instructor or Assistant Professor teaching 3 courses per semester, research or pro• January 20, 1995. Franklin & Marshall is com• An Instructor orAssistant Professor (tenure-track) fessional development in mathematics, and mitted to cultural pluralism and strongly position available in January 1995. Primary re• service to the department and the college. Send encourages applications from minorities and sponsibilities involve general education, more application, including resume and 3 letters of women. EOE/AA. specifically the coordination and teaching of recommendation, at least one which addresses Mathematics for Elementary Teachers and Col• teaching, to Dr. Z Kadas, Chair, Department of Murray State University lege Algebra courses. Applicants should possess Mathematics, Saint Michael's College, Department of Mathematics at least a Masters degree in mathematics or math• Colchester, VT 05439. Screening of applicants & Statistics ematics education. The university offers begins December 15, 1994, and continues until the position is filled. SAINT MICHAEL'S COL• Applications are invited for a tenure-track posi• competitive salaries and excellent fringe benefits. tion in mathematics education starting August I, The University of Akron is the third largest state LEGE ISANAFFIRMATIVEACTIONIEQUAL 1995. Candidates must have a doctorate in math• university in Ohio. The department offers a Bach• OPPORTUNITY EMPLOYER. ematics or a doctorate in mathematics education elors degree in mathematics, applied with at least a masters degree in mathematics, in• mathematics, computerscience and statistics, and Mathematicians. Iterated Systems, Inc., the hand, by starting date. Evidence of outstanding a Masters degree in mathematics, applied math• global leader in fractal image compression, is teaching, a successful record of scholarly activ• ematics, and statistics. All material (application seeking mathematicians for challenging research ityorthepotential for continued scholarly activity, letter, curriculum vitae, unofficial copy of gradu• on fractal image compression. Graduate work in and a strong commitment to teacher education ate transcripts, and three letters of reference) mathematics, knowledge of fractal geometry, and are required. Responsibilities include a maximum should be sent to: Dr. Neal C. Raber, Chair, Math• C programming skills required. Understanding three courses teaching load, continuing research/ ematics Search, Department of Mathematical of image science and C++ an advantage. lSI of• scholarly activities, and university/departmental Sciences, The University of Akron, Akron, OH fers competitive salary and comprehensive service. The person who fills this position will 44325-4002. Review of completed applications benefits. For consideration, send resume to: Iter• teach a range of mathematics courses, including will begin November 15, 1994, and continue until ated Systems, Inc., Suite 650, Dept. MFB 1094, content and method courses for prospective K• the position is filled. Women and minorities are 5550 Peachtree Parkway, Norcoss, GA 30092 or 12 teachers, seek external funding to conduct encouraged to apply. The University of Akron is e-mail: [email protected]. FAX: (404) workshops and seminars for public school teach• an equal education and employment institution. 840-0029. We will respond only to candidates ers, and work in collaboration with public schools selected for an interview. An Equal Opportunity to help implement the Kentucky Education Re• Bowdoin College Employer MIF/DN. form Act. The application package must include Brunswick, Maine 04011 a letter of application, vita, copies of graduate Mathematics Department: Tenure-trackAssistant The University of Scranton transcripts, and a statement which addresses the Professorship starting Fall, 1995. Initial appoint• Mathematics Department applicant's experience and interest within thefield ment for three years with renewal possible. The University of Scranton, a Jesuit university of mathematics education. The immigration sta• Seeking candidates with primary research inter• with over 3,500 undergraduates, anticipates an tus of non-U.S. Citizens should be indicated on ests in one of the following fields: operations opening in the academic year 1994-95 for an entry the vita. All applicants must meet federal guide• research, mathematical economics, numerical level assistant professor of mathematics, tenure• lines for working in the U.S. For full analysis, or geometry (AMS subject classifica• track. Applications are invited from qualified consideration, applications must be completed tion numbers 51,52,53,65, or 90). Ph.D. required candidates seeking a teaching environment where by December 16, 1994. Send the application and strong research record or potential expected. research isencouraged and supported. Applicants package and direct three letters of recommenda• Normal teaching load is two courses per semes• should have a doctorate in mathematics or near tion to: ter. A record of superior undergraduate teaching completion. We are especially interested in indi• Dr. Robert Pervine, Search Committee Chair is expected. Review of candidates begins De• viduals able to teach Probability/Statistics, Department of Mathematics and Statistics cember I, 1994, but applications will be Applied Mathematics, or Mathematics Educa• Murray State University considered until position is filled. Send completed tion. Submit a vita, copies of transcripts, and three P.O. Box 9 AMS application cover sheet, resume, and 3 let• letters of recommendation attesting to teaching Murray, KY 42071-0009 ters of recommendation to James E. Ward, Chair, and research ability to Mathematics Faculty Department of Mathematics, Bowdoin College, Search Committee, University of Scranton, Murray State University ois an equal education Brunswick, ME 04011. Include e-mail address. Scranton, PA 18510-4666 or phone (717) 941• and employment opportunity M/F/D AA em• Bowdoin College is committed to equal opportu• 4233. The Department will be interviewing at ployer. nity through affirmative action. Women and the San Francisco meeting Employment Regis• members of minority groups are urged to apply ter in January. The University of Scranton is an Mathematics, Assistant Professor, and invited to identify themselves as such. AffirrnativeActionlEqual Opportunity Employer. Tenure-track An anticipated opening for Fall 1995 to teach Saint Michael's College High-school level mathematics teacher, pre• the full range of math courses from algebra Department of Mathematics algebra through calculus, also to assist with through calculus, and in area of expertise. Ph.D. Colchester, Vermont physics and chemistry at an innovative private required. Excellence in teaching and current c1ass• boarding school in central Oregon. Minimum 2• room pedagogy, academic advising, and the Applications are invited for a tenure-track posi• tion at the Assistant Professor level to begin Fall 3 years classroom teaching experience required. ability to direct undergraduate research are es• Assertive individuals possessing solid leadership sential for the successful applicant. Send vita, 1995. Qualifications: Ph.D. in Mathematics or Statistics; evidence of the potential for excellence and counseling skills to work closely with stu• letter of application, official transcripts, and dents. Send resume to: Mt. Bachelor Academy, names/addresses of three references by January in undergraduate teaching; commitment to schol• arly activity. Preference given to candidates with 246301 E. Hwy 26, Prineville, OR 97754 Attn: 15, 1995 to: Dr. Richard Melka, Mathematics Personnel Director. FAX (503) 462-3430. Search Committee, University of Pittsburgh at expertise in Statistics, Applied Mathematics, or Bradford, 300 Campus Drive, Bradford, PA fields which can be made accessible to under• 1670 I. AAlEOE. graduates. Saint Michael's is a selective, Catholic @------December 1994 FOCUS Assistant Professor of Mathematics research institution on a modem campus with Mathematics with 3 different emphases: Pure Grand Valley State University, an institution one of the most ethnically diverse student bodies Mathematics, Applied Mathematics, and Teach• committed to teaching excellence, solicits appli• in the nation. Persons with an intrinsic commit• ing Credential in Mathematics. Faculty members cations for a tenure-track assistant professorship ment to, knowledge of, and familiarity with take turns teaching all courses in the department to begin August 1995. Doctorate in an area re• diversity issues are strongly encouraged to ap• and participate in teaching college-wide courses lated to the teaching of mathematics required. ply. such as Freshman Writing Seminars and other Candidates should have a sincere desire to teach Associate Professor in Mathematics Educa• interdepartmental courses. Send cover letter, curriculum vitae, statement of teaching philoso• courses from prealgebra through precalculus with tion: Expert in applying modern technology to opportunities to teach in the area of math educa• the learning and teaching of mathematics in K• phy, and three letters of recommendation to Dr. Sharad Keny, Chair, Department of Mathemat• tion. Candidates must have a strong mathematical 12 classrooms. Should be committed to background. Acomplete application must include qualitative and quantitative research methods. ics, Whittier College, P.O. Box 634, Whittier, a cover letter, vita, a copy of graduate transcripts, California 90608. Review of completed applica• at least three letters of recommendation (at least Associate Professor in Educational Technol• tions will begin on January 15, 1995. Whittier two of which focus on the applicant's teaching ogy: Expert in instructional designs for College is an EOIAAE. ability and potential), and a personal statement educational software, including software tools that addresses the applicant's teaching philoso• built upon constructivist learning models. Should University of Oklahoma phy, and experience with and expectations be committed toexperimental evaluation designs. Successful applicants will employ theoretically Chair, Department of Mathematics regarding the use of technology in teaching at Nominations and applications are invited for the this level. Send these materials to: Faculty Search grounded research in the service of school re• form, will teach and carry out a program of position of Chair of the Department of Math• Committee Department of Mathematics and Sta• ematics. The appointment is to be effective by research and scholarly work in education, and tistics, Grand Valley State University, Allendale, the start of the Fall 1995 semester or earlier. Can• will contribute to the development of new gradu• MI 49401. Applications will be accepted until didates must possess an earned doctorate, a January 13, 1995. EEO/ANADA. ate degree programs for teachers and educational researchers. The Department is particularly noted substantial record of research achievement, a commitment to excellence in teaching, and lead• for its strength in educational technology. Assistant Professor of Mathematics ership and administrative abilities appropriate to Grand Valley State University, an institution To Apply: Send resume with a complete list of a department that is dedicated to a balanced pro• committed to teaching excellence, solicits appli• publications and reports; three recent publica• gram of quality research and teaching. The cations for a tenure-track assistant professorship tions; and names, addresses, and telephone Mathematics Department has over 30 faculty and to begin August 1995. Ph.D. in mathematics re• numbers of four persons who can provide recom• approximately 70 graduate students. There are quired. Applications from individuals working mendations if the Department requests them to active research programs in a wide range of top• in all areas of mathematics will be considered, Dr. Henry Jay Becker, Chair of the Search Com• ics. The scientific activity of the Department is but preference shall be given to applicants work• mittee, Department of Education, University of further enhanced by a substantial endowment for ing in the areas of discrete mathematics, California, Irvine, CA 92717-5500. Deadline for discretionary funds. The Department offers pro• operations research, dynamical systems, or ap• receipt of applications is December 31, 1994. grams for the bachelor's, master's, and Ph.D. plied mathematics. Responsibilities include The University of California is an Affirmative degrees. Candidates should send a cover letter, teaching twelve hours per week at the level of ActionlEqual Opportunity Employer committed vita, selected reprints, and names and addresses precalculus and above, maintaining an active to excellence through diversity. of four referees (at least one of whom could ad• program of professional development, and stu• dress the candidate's administrative abilities) to: dent advising. A complete application must Whittier College Dr. Paul Goodey, Chair Search Committee include a cover letter and vita, a copy of graduate The Department of Mathematics invites applica• Department of Mathematics transcripts, at least three letters of recommenda• tions for a tenure-track position, assistant University of Oklahoma tion (at least two of which focus on the applicant's professor level,to teach undergraduate mathemat• Norman, Oklahoma 73019-0315 teaching ability and potential), and a personal ics courses beginning Fall 1995. Qualifications: statement that addresses the applicant's teaching Screening will begin on November 1,1994, and Ph.D. in Mathematics (completed by summer of continue until the position is filled. philosophy, experience with and expectations 1995), evidence of quality teaching, and poten• regarding the use of technology in teaching, and tial for scholarly growth. Preference will be given The University of Oklahoma is an Equal Oppor• experience with and/or interest in conducting a to candidates with experience in teaching under• tunitylAffirmative Action Employer. Womenand program of undergraduate research. Send these graduate courses, with an appreciation for liberal minorities are encouraged to apply. OU has a materials to: Faculty Search Committee Depart• artseducation, and whose expertise complements policy of being responsive to the needs of dual• ment of Mathematics and Statistics Grand Valley current faculty. The department offers a major in career couples. State University Allendale, MI 49401 Applica• tions will be accepted until January 13, 1995. EEO/ANADA. Teaching Undergraduate Women Headed for a Ph.D. University of California, Irvine Iffunded by the NSF, a Consortium of seven institutions will begin in 1995 to teach Associate Professor in talented women undergraduates selected nationally, in summer programs designed to Mathematics Education help motivate and prepare them to head for Ph.D. degrees in the mathematical sci• Associate Professor in ences. Four of these (at Carleton and St. Olaf Colleges, SUNY Stony Brook, The Educational Technology George Washington University, and Mills College) may employ women mathemati• The University of California, Irvine, seeks appli• cians to teach in their programs; dates, subjects, and levels of students may vary. cants for two tenured Associate Professorships in the Department of Education for the 1995-96 The Consortium is setting up a registry of women mathematicians who wish to be academic year. Candidates should be broadly considered for such positions. For further details please send email to knowledgeable scholarlresearchers with a Ph.D. millssmi @ella.rnills.eduorwritetoCAWM, c/o Summer Mathematics Institute, Mills in a relevant field and a strong coherent record of College, Oakland, CA 94613. publication in refereed journals. UCI is a leading ------@ Calendar National MAA Meetings MICHIGAN May 5-6, 1995, Grand WISCONSIN April 7-8, 1995, Univer• ValleyState University, Allendale, MI sity of Wisconsin-Green Bay, Green January 4-7, 1995Seventy-eighthAnnual MISSOURI April 7-8, 1995, Central Bay, WI Meeting,SanFrancisco(BoardofGov• Missouri State University, ernors, January 3, 1995) Warrensburg, MO Other Meetings August 6-8,1995 SeventiethAnnualJoint NEBRASKA April 1995, Creighton Bienni~l Summer Meeting. University of Ver• University, Omaha, NE April 20-22, 1995 Thirtieth Soc~­ mont-Burlington, Burlington, VT NORTH CENTRAL April 21-22, Kappa Mu Epsilon (Math Honor Le~ls 1995, Carleton College, Northfield, ety) National Convention, Fort Sectional MAA Meetings MN College, Durango, CO. For more m• NORTHEASTERN June 9-10, 1995, formation, contact Arnold Hammel, ALLEGHENY MOUNTAIN April 7• Bates College, Lewiston, ME Central Michigan University, Mt. 8, 1995, Duquesne University, NORTHERN CALIFORNIAOctober Pleasant, MI 48859; (517) 774-3543. Pittsburgh, PA 21-22, 1995, Cal Polytech State Uni• February 8-11,1995 Sixth SIAM Con• FLORIDA March 3-4, 1995, Valencia versity, San Luis Obispo, CA (joint ference on Mathematical and Community College-East Campus, meeting with S. California Section) Computational Issues in the Orlando, FL OKLAHOMA-ARKANSAS March Deosciences, San Antonio, TX. For ILLINOIS March 31-April 1, 1995, 31-Aprill,1995,SouthwesternOkla• more information, contact SIAM Con• Monmouth College, Monmouth, IL homa State Univ., Weatherford, OK ference Coordinator, (215) 389-7999, INDIANA March 31-April1, 1995,Tri• PACIFIC NORTHWEST June 15-17, e-mail: [email protected]. State University, Angola, IN 1995, Whitman College, Walla Walla, INTERMOUNTAIN April 7-8, 1995, August 14-20, 1995 Symmetry: Na.tu• WA ral and Artificial Third Idaho State University, Pocatello, ID ROCKY MOUNTAIN April 21-22, Interdisciplinary Symmetry Congress IOWA April 21-22, 1995, University of 1995, University of Southern Colo• and Exhibition, Washington, D.C. (Old Northern Iowa, Cedar Falls, IA rado, Pueblo, CO KANSAS April 14-15, 1995, Wichita Town Alexandria). Contact: Gyorgy SEAWAY ApriI21-22, 1995, Hobart & Darvas, Symmetrion -The Institute for State University, Wichita, KS William Smith Colleges, Geneva, NY KENTUCKY March 31-April1, 1995, Advanced Symmetry Studies, P.O.Box SOUTHEASTERN March 31-Aprill, 4, Budapest, H-1361 Hungary; tel: +36• Transylvania University, Lexington, 1995, University of North Carolina• 1-131-8326; fax: +36-1-131-3161; KY Asheville e-mail: [email protected];DenesNagy. I"OUISIANA-MISSISSIPPIMarch3• SOUTHWESTERN April 7-8, 1995, 4, 1995, Mississippi State University, Institute of Applied Physics, Univer• University of Texas at El Paso Biloxi, MS sity ofTsukuba, Tsukuba Science City, SOUTHERN CALIFORNIA October MD-DC-VA April 7-8, 1995, Thomas Japan 305; tel: +81-298-53-6786; fax: 21-22,1995, Cal Polytech State Uni• Nelson Community College, Hamp• +81-298-53-5205; e-mail: nagy@ versity, San Luis Obispo, CA (joint ton, VA kafka.bk. tsukuba.ac.jp . meeting with N. California Section) METROPOLITAN NEWYORK May TEXAS March 30, 31, April 1, 1995, 6, 1995, Manhattan College, Bronx, Baylor University, Waco, TX NY

FOCUS DECEMBER 1994 The Mathematical Association of America Second class postage paid at Washington, DC and 1529 Eighteenth Street. NW additional mailing offices Washington. DC 20036-1385