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FOCUS is published by theMathematical Association of America inJanuary, February, March, April, May/June,August/September, October, November, andDecember.

Editor: Fernando Gouvêa, Colby College;fqgouvea@colby.edu

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Executive Director: Tina H. Straley

Associate Executive Director and Directorof Publications: Donald J. Albers

FOCUS Editorial Board: Rob Bradley; J.Kevin Colligan; Sharon Cutler Ross; JoeGallian; Jackie Giles; Maeve McCarthy; ColmMulcahy; Peter Renz; Annie Selden;Hortensia Soto-Johnson; Ravi Vakil.

Letters to the editor should be addressed toFernando Gouvêa, Colby College, Dept. ofMathematics, Waterville, ME 04901, or byemail to fqgouvea@colby.edu.

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Copyright © 2005 by the MathematicalAssociation of America (Incorporated).Educational institutions may reproducearticles for their own use, but not for sale,provided that the following citation is used:“Reprinted with permission of FOCUS, thenewsletter of the Mathematical Associationof America (Incorporated).”

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ISSN: 0731-2040; Printed in the United Statesof America.

FOCUS

Inside

4 Peter Lax: Pure and Applied

10 Groups in the Household

12 Building Bridges for QL Education:National Numeracy Network and SIGMAA QL

14 Archives of American Mathematics Spotlight:The Max Dehn Papers

15 American Mathematical Monthly Editor Search

15 Women Excel in the 2004 Putnam Competition

16 A Century Celebration: Former MAA President G. Baley Price Turns 100

18 Looking for Stat(isticians) in All the Wrong Places

19 NSF BeatCourse, Curriculum, and Laboratory Improvement (CCLI) Program

20 How to Design a Mathematics Building

22 In Memoriam

24 What I Learned...Working in a ProfessionalLearning Community

26 Short Takes

28 MAA Establishes a Prize in Honor of David P. Robbins

30 The Preparation of Mathematics Teachers: A British View, Part I

32 NSF Budget: Not Far Away From Us

33 Joel Cohen Interviewed Online at NAS Site

34 They Chose Mathematics

36 Spatial Visualization: Is There a Gender Differentiation?

39 What Will They Do This Summer?

40 MAA Contributed Paper SessionsSan Antonio Joint Mathematics Meeting, January 12-15, 2006

Volume 25 Issue 5

Cover image of Peter Lax courtesy of the NYU Office of Public Relations.

FOCUS Deadlines

August/September October NovemberEditorial Copy June 8 September 16Display Ads July 10 August 20 September 24Employment Ads June 11 August 13 September 10

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The MAA has received a grant for$144,000 from The Moody’s Foundationof New York to support the expansionof SUMMA’s National Research Experi-ences for Undergraduates Program. TheNational REU Program, which was de-scribed in the November issue of FOCUS(pages 27–28), is conducted by the MAAOffice of Minority Participation to en-courage mathematical sciences faculty tooversee research by small groups of mi-nority students. The grant will supportstudent research at up to five sites.

“Mathematics education is a key focusof The Moody’s Foundation,” saidFrances G. Laserson, the foundation’spresident. “We have a keen interest inprograms that may encourage womenand minorities to pursue careers in fi-nancial services. We believe thatpartnering with MAA’s National Re-search Experiences for UndergraduatesProgram will further that goal.”

“The need for increased participation ofU.S. citizens in the mathematical sciences

requires that students from under-rep-resented groups be identified and nur-tured, both to serve as professional math-ematicians and to serve as role modelsand mentors for future generations,” saidMichael Pearson of the MAA. “The grantfrom The Moody’s Foundation enablesMAA to support faculty mentors and thefocused peer-group experience shared bythe student researchers, thus encourag-ing broadened participation of these stu-dents in graduate studies and careers inmathematics.”

By supporting faculty at a diverse groupof institutions to direct undergraduatesummer research, the National ResearchExperience for Undergraduates Programsimultaneously supports the develop-ment of a community of skilled facultymentors expected to lead to ever-increas-ing opportunities for undergraduate re-search by all mathematics students.Grants for partial support of this pro-gram have also been received from theNational Security Agency and the Divi-

Moody’s Foundation Will Support the MAA’s National REU

sion of Mathematical Sciences of theNational Science Foundation.

The Moody’s Foundation is a charitablefoundation established by Moody’s Cor-poration (NYSE: MCO), the parent com-pany of Moody’s Investors Service (aleading provider of credit ratings, re-search and analysis covering debt instru-ments and securities in the global capi-tal markets) and Moody’s KMV (theleading provider of market-based quan-titative services for banks and investorsin credit-sensitive assets serving theworld’s largest financial institutions).The corporation, which reported rev-enue of $1.4 billion in 2004, employsapproximately 2,500 people worldwideand maintains offices in 18 countries.Further information is available at http://www.moodys.com.

The Norwegian Academy of Scienceand Letters announced that the AbelPrize for 2005 will go to Peter D. Lax ofthe Courant Institute of MathematicalSciences, New York University. The AbelCommittee said that it was awarding Laxthe prize “for his groundbreaking con-tributions to the theory and applicationof partial differential equations and tothe computation of their solutions.”

The official biography released by theAbel Committee describes Lax as “themost versatile mathematician of his gen-eration.” It highlights his ability to workin both pure and applied mathematics,combining a deep understanding ofanalysis and a talent for finding unify-ing concepts with the ability to identifyproblems that are of direct interest inapplied mathematics and contribute to-wards their solution. They also note hispersonal influence, both as a teacher andas an author.

Lax’s writing has been twice been hon-ored by the MAA with a Lester R. Fordaward: in 1966 for “Numerical Solutionsof Partial Differential Equations”(American Mathematical Monthly 72[1965], Part II, 78–84) and in 1973 for“The Formation and Decay of ShockWaves” (American MathematicalMonthly 79 [1972], 227–241). The latteralso won him the Chauvenet Prize in1974. His skills as a speaker were recog-nized when he was invited to be theHedrick Lecturer at the MAA summermeeting in 1972.

Lax’s work has been recognized by manyother honors and awards, including theNational Medal of Science in 1986, theWolf Prize in 1987, and the AmericanMathematical Society’s Steele Prize in1992.

See page 4 for more on Lax and the AbelPrize.

Peter Lax Wins the 2005 Abel PrizeTwo mathematicians appear among thefour American scientists honored onstamps released in May by the UnitedStates Post Office — though one of themmight be claimed by physics as well. Johnvon Neumann is described as a ‘math-ematician’ and Josiah Willard Gibbs as a‘thermodynamicist.’ The other two sci-entists are physicist Richard Feynmanand geneticist Barbara McClintock. Onthe back of the stamps are short descrip-tions of each scientist’s work. John vonNeumann is said to have made “signifi-cant contributions in both pure and ap-plied mathematics, especially in the ar-eas of quantum mechanics, game theory,computer theory and design.” AboutGibbs, the text says only that he” formu-lated the modern system of thermody-namic analysis.” Mathematicians, ofcourse, remember Gibbs for his creationof the modern form of vector calculusand for his work on statistical mechan-ics. More about the stamps, includingimages, can be found at http://www.usps.com/communications/news/stamps/2004/sr04_076.htm.

Gibbs & von Neumann

on Postage Stamps

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Peter D. Lax of the Courant Instituteof Mathematical Sciences, New York Uni-versity, has been awarded the Abel Prizefor 2005 in recognition of “hisgroundbreaking contributions to thetheory and applications of partial differ-ential equations and to the computationof their solutions.”

Fifteen-year old Lax, a child prodigy inHungary, sailed from Lisbon with his fa-ther, mother, and brother on the fifth ofDecember, 1941, two days before theJapanese attacked Pearl Harbor thatbrought the United States into WorldWar II. Upon the advice of John vonNeumann, he enrolled at StuyvesantHigh School in New York for a year toimprove his English and then enteredNYU, where he immediately started tak-ing graduate courses. In a course on com-plex variables, he met Anneli. A few yearslater, they were married. Anneli, after fin-ishing her doctorate under Richard Cou-rant, spent the rest of her career at NYU.For thirty-eight years, until her death in1999, she served as Editor of the MAA’sNew Mathematical Library.

In 1944, Lax was drafted into the Army;in 1945, he was sent to Los Alamos, wherework on the first atomic bomb was mov-ing into the testing phase. In the fall of1946, he returned to NYU, and earnedhis Ph.D. in 1949. He has been a mem-ber of the NYU faculty ever since, andspent ten summers consulting at LosAlamos.

Lax insists that he is both pure and ap-plied. In an earlier interview, he said “Inapplied mathematics you are very muchaware of where the question comes fromand also where the answer is going. Af-ter all, when a mathematician says he hassolved a problem, that doesn’t have adefinite meaning — rather it means usu-ally that he has understood somethingabout the problem. So the kind of un-derstanding that you need to be able tosay you have solved the problem as anapplied problem is different from thekind of understanding you need to be

able to make the same statement about aproblem in pure mathematics.” In theend pure and applied are labels, andprobably not too important.

The following interview took place inNew York City on April 8, 2005.

Don Albers: Peter, you recently won theAbel Prize. What was your reaction towinning it?

Peter Lax: It was a bit dream-like, butcertainly very nice. It won’t make muchdifference in my life.

DA: Was it a big surprise?

PL: Well, certainly not a thing I countedon. I knew that I had been nominated,but I put it out of my mind so the an-nouncement came as a big surprise.

DA: How were you informed?

PL: I was called at 5:30 in the morning.

DA: That’s not a good time to call people.

PL: It depends on the message.

DA: But generally one would think it’sbad news at that time of day.

PL: To me it was a complete surprise,but my son Jim knew about it in advance.The Abel committee wanted to make surethat they would catch me on the day sothey contacted Jim a few days earlier. Jimhad a dinner party the night before theycalled to make sure I would be home andsaid he would come over the next morn-ing to take a blood sample. (Jim is a phy-sician.)

DA: So your son knew before you did?It must have been hard for him to keephis mouth shut.

PL: He kept it completely secret.

DA: Some mathematicians used to ar-gue that it was good in some sense thatthere is no Nobel Prize in mathematics.There may have been a bit of sour grapesin such statements. Now they have theAbel, which carries a monetary awardthat is comparable to the Nobel. Whatdo they say now?

PL: Certainly it’s a very nice thing formathematics, and I think it should bejudged from that point of view. The NewYork Times did not carry it as a news item,but I think from now on they will. I hopeto convince the Times to carry a state-ment from the International Mathemati-cal Union about the Abel Prize each year.

Peter Lax: Pure and Applied

By Don Albers

Lax does not always lecture in a tuxedo.

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They did print an interview with me inthe Tuesday Science Section [March 29,2005].

DA: Well, if the Times covers the AbelPrize each year, you can be assured thatother newspapers will do the same, andthat’s good for mathematics.

PL: Yes.

DA: The Bolyai Prize was established byHungary very early in the 20th centuryto honor mathematics.

PL: That’s right. Bolyai and Abel wereborn in the same year, 1802. The BolyaiPrize was established in 1902, the cente-nary of Bolyai’s birth. The Abel Prize alsowas first proposed in 1902 by King Os-car II of Norway and Sweden. But theplan was dropped when Norway brokeaway from Sweden in 1905. The firstBolyai Prize wasn’t awarded until 1905,four years after the first Nobel Prizes wereawarded. The Bolyai Prize was given ev-ery five years and had a very distin-guished record. The first recipient wasPoincaré in 1905 and the second wasHilbert in 1910, and then came the WorldWar.

DA: It’s interesting to contemplate whatmight have been if the Bolyai Prize hadcontinued.

PL: It’s also interesting to contemplatewhat might have happened had therebeen no First World War! There was ajoke among journalists at the end of theFirst World War in Hungary. Everythingwas destroyed and there was misery allaround. Hungarian journalists were play-ing various games and one of the gameswas to construct the most sensationalheadline. And the winner was “FranzFerdinand Found Alive – World WarFought in Error.”

DA: You have previously won manyother prizes that are regarded as very dis-tinguished. Among them are the WolfPrize, the Wiener Prize, and the NationalMedal of Science. It’s quite a list. Does itfeel any different winning this one — theAbel?

PL: The public recognizes only a NobelPrize. If you introduce anyone to a per-

son who is a Nobel Prize winner, that’s abig deal. The Abel has half the aura ofthe Nobel. I’m not sure how Anneliwould have reacted to the Abel Prize. Shewas puritanical. She thought all math-ematicians are foot soldiers in the armyof mathematics.

DA: But they’re pretty competitive footsoldiers aren’t they?

PL: True. This is an ideal. Inside math-ematics these prizes don’t matter thatmuch. I think it’s public relations stufffor the outside world.

DA: I think it’s more than that. I thinkthe recognition, not just of the individu-als, but of the field, is good.

PL: Yes, I think this was a boost for ap-plications of mathematics.

DA: You mentioned that your sonJohnny would have been happy to seeyou win the Abel Prize.

PL: He would have been tickled.

DA: I’ve never asked about him — Iguess for obvious reasons. [Johnny waskilled in an automobile accident when hewas a graduate student.]

PL: It’s not a painful subject to me re-ally. He was lovely. He was a historian.He would go to universities to visit librar-ies and special collections. He lookedvery much like me and he would drop

into the Math Department and ask:Whose son am I?

DA: There are stories about why Nobeldid not choose to recognize mathemat-ics. Most of the stories are false andthe most notorious is the one about thewell-known mathematician Mittag-Leffler romancing Nobel’s wife, andthat Nobel was afraid that Mittag-Leffler might win a mathematics Nobelif it were to be established.

PL: But Nobel wasn’t married.

DA: Yes, so that’s a real complicationfor that story.

PL: Do you know why Alfred Nobel es-tablished the prize? Robert, one of hisbrothers, died while Alfred was stillalive, and one of the newspapers madea mistake and thought it was Alfred. Ablistering editorial said that Alfred, whohad invented dynamite, was a man whodevoted his life to death and destruc-tion. It took Nobel several years tomake dynamite safe for transport, andduring the first years, there were manyaccidents. So Alfred decided to dosomething to enhance his reputation.By establishing the Nobel Prizes, he

succeeded.

DA: Others have defended Nobel’s deci-sion to not recognize mathematics bynoting that biology is not recognized ei-ther.

PL: That’s true, but medicine is.

DA: Essentially the argument that’s of-fered is that biology is not recognizedbecause it was regarded as one of thetools for medicine. And mathematicswas not recognized for essentially thesame reason — that it’s a tool for phys-ics, chemistry, and other sciences.

Peter Lax and his wife Anneli, who also spenther career at NYU. She edited the MAA’s NewMathematical Library (NML) book series for 38years until her death in 1999. In her honor, theNML was renamed the Anneli Lax New Math-ematical Library.

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One of the things that I like about theAbel Prize a lot is that it really seems toclose the “prize gap” between accom-plished mathematicians under 40 (theFields Medal) and those over 40. You’vepreviously said that it’s a myth that math-ematics is a young person’s sport.

PL: I’ll stick to that. I can give some ex-amples. For instance, Haar wrote his lastpaper, on Haar measure, when he was 53,and he died soon thereafter. WhenOnsager did his work on change of phase,for which he received a Nobel Prize in1968. He needed a mathematical theo-rem on the asymptotics of the determi-nant of Toeplitz matrices. Onsager wastold that if anyone can prove it, it wouldbe Szegö; Szegö did. He was 58 at thetime.

DA: Of the first four winners of the Abel,Serre, Atiyah, Singer, and you, three havemade substantial contributions to ap-plied mathematics.

PL: The index theorem of Atiyah andSinger is of great importance in physics,although that was not their motivation.

DA: Do you expect future Abel winnersto be recognized for work within appli-cations based on the winners so far?

PL: That depends on how the criteriafor the Abel prize are specified.

DA: Here’s the official statement: “Theprize is to recognize contributions tomathematics and its applications of ex-traordinary depth and influence. Suchwork may have resolved fundamentalproblems, created powerful new tech-niques, introduced unifying principles oropened up new areas. The intent is toaward prizes over the course of time in awide range of areas of mathematics andits applications.”

PL: That’s a very broad statement. I’msure that was taken into account when Iwas chosen.

DA: In 1989 you wrote the “Floweringof Applied Mathematics in America.” Itwas one of the AMS Centennial ad-dresses. You said that “today most math-ematicians are keenly aware that math-ematics does not trickle down to the ap-

plications, but that mathematics and thesciences, mainly but by no means onlyphysics, are equal partners feeding ideas,concepts, problems and solutions to eachother.” That may be true, Peter, when youlook at specialized graduate programs.But it seems to me that most new gradu-ates at all levels are woefully ignorant of

applications. Take physics, for example,which used to be required virtually uni-versally of undergraduate majors andhasn’t been for twenty years. Today, mostundergraduate mathematics majors cantake one year of science survey courses,which can be a term of rocks, a term ofstars, or a little bit of human biology, andthat’s it. I think that really gets in theway of developing an appreciation forapplications among the students if themajority of faculty themselves do notknow any applications. I think that ex-tends through graduate education, too.

PL: I’d like to quote a distinguished pre-decessor, Poincaré, who said: “Nature notonly suggests to us problems but alsosuggests a solution.” I think that math-ematics education is changing, partlybecause of the decrease in the numberof academic jobs; and because of thatmathematicians spend more time as

post-docs than they used to, usually atthe leading universities.

DA: So those universities can influencethe shape of graduate education andundergraduate education.

PL: Yes, the good universities have verygood science departments. Now, new ar-eas in biology are becoming important;the biologists themselves are very eagerto work with mathematicians. At the lasttwo Joint Meetings in Phoenix and At-lanta, there were some excellent talks onbiology.

DA: You may be interested to know thatNIH, MAA, NSF, and several other or-ganizations have developed Math andBio 2010 with the goal of linking under-graduate mathematics and biology.

PL: At NYU we have a NeurosciencesInstitute that Courant collaborates with.And we have Charlie Beskin, who worksin mathematical biology. If you look atour weekly bulletin, you will find lots ofbiological talks.

DA: Courant is an unusual institution.In terms of applications, it has alwaysbeen well ahead of the curve in theUnited States, thanks in large part to theman for whom the institution is named.Certainly Richard Courant’s forced de-parture from Göttingen by the Nazis andhis subsequent arrival at NYU in 1934was a watershed event in Americanmathematics, partly because he was achampion of applied mathematics.

You’ve cited the positive impact of WorldWar II on American mathematics. Howdo you view the recent decision by theDefense Advanced Research ProjectAgency (DARPA) — which has long un-derwritten open-ended “blue sky” re-search by our best computer scientists inuniversities—in favor of financing moreclassified works and narrowly definedprojects that promise more immediateresults?

PL: I think it’s very shortsighted. One ofthe strengths of funding in America isthat financial support for science, andmathematics has come from multiplesources. So if DARPA cuts down, thenhopefully NSF will increase. Of course

With son Johnny.

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classified research would be incompat-ible with university research. At the endof the Second World War the Americanmilitary was very much shaken by theirexperience. When scientists first broughtup the possibility of nuclear weapons, themilitary refused to support it, but in theend they realized it could make a differ-ence between winning or losing. Theywere determined never again tobe caught flat-footed like that.Sputnik appeared in 1957 —that was 12 years after the war—and that produced another waveof anxiety. In short order the“new math” and the New Math-ematical Library came into ex-istence. Today the realizationthat there is a connection be-tween vigorous pursuit of sci-ence and national readiness isbeginning to fade.

DA: The National ScienceFoundation really began to de-velop at that time, too.

PL: The Office of Naval Re-search was the first agency tosystematically support math-ematics and science. NSF cameafter it. It became clear thatfrom theoretical investigationscome concrete applications.

DA: You’re something of a champion ofcomputers and their importance tomathematics. You have said that theirrole in mathematics is comparable to thatof telescopes in astronomy and micro-scopes in biology.

PL: I don’t think I’m alone in extollingthe importance of computers in math-ematics.

DA: You’ve been saying that for a prettylong time.

PL: Well, I had the good fortune to getin on the ground floor of computing atLos Alamos in the 50s. I started workingthere during summers and continued todo so in the summers for the next 10years. While I was there I was able to workwith sophisticated computers.

DA: You had a good time during yourLos Alamos years.

PL: Oh, yes, it was very exciting. Therewere many great people there — vonNeumann, Feynman, Bethe, and manymore.

DA: And that’s where you really came toappreciate the value of computing.

PL: Absolutely; it was vital to the work.Each year’s computer was a tremendousimprovement over the previous one, solast year’s difficult problem was now easy.

DA: Von Neumann entered your lifewhen you were only 15, and his influenceon you has been considerable. In your re-cent SIAM Review article about him(“John Von Neumann: The Early Years,The Years at Los Alamos and The Roadto Computing”), you wrote: “Nuclearweapons cannot be designed by trial anderror; each proposed design has to betested theoretically. This requires solvingthe equations of compressible flows, gov-erned by nonlinear equations. VonNeumann came to the conclusion thatanalytical methods were inadequate forthe task, and that the only way to dealwith equations of continuum mechan-ics is to discretize them and solve the re-sulting system of equations numerically.The tools needed to carry out such cal-

culations effectively are high speed, pro-grammable electronic computers, largecapacity storage devices, programminglanguages, a theory of stable dis-cretization of differential equations, anda variety of algorithms for solving rap-idly the discretized equations. It is tothese tasks that von Neumann devoted alarge part of his energies after the war.

He was keenly awarethat computationalmethodogy is crucialnot only for designingweapons, but also foran enormous varietyof scientific and engi-neering problems; un-derstanding theweather and climateparticularly intriguedhim. But he also real-ized that computingcan do more thangrind out by bruteforce the answer to aconcrete question.”

Von Neumann onlylived to be 53. His ac-complishments weretruly extraordinary.Suppose he had had anormal life span?

PL: In my SIAM article, I give an an-swer: “Had von Neumann lived his nor-mal span of years, he would have cer-tainly been honored by a Nobel Prize inEconomics, created only after his death.And had he lived an abnormal span, hewould certainly be honored by a NobelPrize in Computer Science and anotherone in Mathematics; these Prizes do notexist yet, but they are bound to be estab-lished eventually. So we are talking abouta triple, possibly 3 1/2 fold Nobelist, ifwe take into account his contributionsto the foundation of quantum mechan-ics.”

DA: Apart from his powerful intellect,what aspect stands out about him mostvividly in your mind?

PL: His interests were so very broad. Itwas easy to explain things to him becausehe had such a powerful mind. Mostthings he figured out himself. In a way itwas a curse because he was easily bored.

With son Jimmy, who now practices medicine in his grandfather’s oldoffice.

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In a way he extended the boundaries ofthinking and intellectual analysis.There’s a quote from Wigner. He visitedHungary in the 70s, and they made muchof him on television. One of the ques-tions put to him was: “Is it true that inthe late ‘40s and early ‘50s the policy ofthe Defense Department was determinedby von Neumann?” He replied: “Well, thiswas not exactly true. But once vonNeumann analyzed a problem it wasclear what was to be done.”

DA: A few years ago you said some prettystrong stuff about the teaching of calcu-lus. You said, among other things, that“we should abolish the calculus commit-tees. The teaching of calculus is com-pletely diverted from the way in whichcalculus is thought about and used byprofessionals.” And then I love your nextone: “If we taught music like we taughtcalculus we’d just be teaching scales.” Youalso wrote, “I strongly believe that cal-culus is a natural vehicle for introducingapplications and that it is applicationsthat give proper shape to calculus, show-ing how and to what end calculus isused.” The Tulane Conference occurredin 1989 and that basically kicked off thecalculus reform movement, and thenNSF supported calculus reform through-out the 90s.

PL: Calculus books have improved, butI still worry about their treatment of ap-plications; it is often superficial. I like ourbook, Calculus with Applications andComputing, published in 1976. There arelots of good ideas in it, but they’re notpolished. A calculus book has to behighly polished. I still dream of findinga good co-author and writing a revisedversion.

Something that’s never asked in a calcu-lus book is how come the laws of physicsare in the form of differential equations.Is there a calculus Mafia? The answer isvery simple. In nature there is no, or verylittle, influence at a distance except forgravity. Usually two objects have to be incontact in order to influence each other.The laws of science express the relationsbetween physical (or chemical) quanti-ties at a point of contact. The physicalquantities can be expressed in terms offunctions and their derivatives.

DA: You’re right. That brings me backto a previous concern — I was going tosay complaint, but I’ll be milder and call

it a concern. I still think that most un-dergraduate calculus classes are taught by

people who really know very little aboutphysics, and that’s a real impediment.

PL: You’re right.

DA: Some have said, particularly peoplein computer science, that discrete math-ematics is more important than calcu-lus. And that it might be a better foun-dation than calculus for students. Whatdo you think?

PL: I think that’s an exaggeration and Idon’t agree with it. In particular, discretemathematics is more difficult than con-tinuous mathematics. If you look at for-mulas for derivatives of reciprocals andthen finite differences for reciprocals, yousee how things are more complicated inthe discrete case. In fact, I’m just finish-ing a revision of some very old notes onhyperbolic equations. I have written anadditional long chapter on differenceapproximations for solving hyperbolicequations. The main point in the theoryof difference approximations is to provestability. To prove stability is like gettingan a priori estimate for the solution ofthe equation. But to get those estimatesfor difference approximations is muchmore sophisticated than to get them fora differential equation. My wife Anneli,however, made the point that a highschool course along the lines of “FiniteMathematics” would be good.

DA: Finite Mathematics, by Kemeny,Shell, and Thompson.

PL: Yes. That was a wonderful book.Something like that on the high schoollevel could be very good.

DA: I think you’re right. But a big diffi-culty for high schools is the pressure totake calculus because having calculus onyour record will enhance your chancesof getting into the college that you want.

PL: That’s fine, if it does enhance yourchances. It puts you ahead in studyingphysics, and chemistry, so there’s noth-ing wrong with that. I’m not saying re-place calculus. The thrust of today’s edu-cational reform, No Child Left Behind,concentrates on the weaker student. Thatis very important, but it is equally im-portant to not forget about the strongstudent.

Lax was only 15 when he first met Johnvon Neumann,. According to Lax, “Mostthings he figured out himself. In a way itwas a curse because he was easily bored.”

Dismissed by the Nazis as director of themathematics institute in Göttingen, Ri-chard Courant, came to the UnitedStates and created the mathematicsinsitute (now the Courant Institute) atNew York University. Anneli earned herdoctorate under Courant’s direction.

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Shock Waves: All of us are familiar withshock waves coming from airplanes mov-ing at supersonic speeds, but shocks alsooccur in the interface of oil and water asfound in petroleum reservoirs. Shockwaves also occur in traffic congestion.

Lax clarified shock wave theory by solv-ing the Riemann problem and then de-veloped practical numerical methods forcalculating flows associated with shockwaves.

Scattering Theory: In scattering, light orsound that is intercepted by an object,such as a molecule, is sent off in many,perhaps random, directions. For ex-ample, the scattering of sunlight by mol-ecules in the atmosphere gives the sky itsgeneral glow. Radar is based on scatter-ing of electromagnetic waves.

Lax and Ralph Phillips developed theLax-Phillips semigroup, which led to animproved understanding of scattering.Curiously, this has applications to thetheory of automorphic functions.

Solitons: Solitons are solitary waves, firstdiscovered in 1834, when the Scottishengineer, John Scott Russell, while ridinghis horse along a channel, observed aboat that was being pulled by horsesalong the channel. When the boat cameto a halt, an isolated wave emanated fromthe bow, and Scott Russell followed it formore than a half mile. The wave did notdisperse and its shape remained un-changed.

Solitons were studied by Korteweg anddeVries in 1895. The model they derivedis now called the KdV equation. Lax pro-vided great insights into the KdV by cre-ating Lax pairs. Recent experiments haveused solitons for high-speed communi-cation in optical fibers. The digital sig-nal is coded using “ones” and “zeroes,”and we let “ones” he represented by soli-tons. Since solitons are highly stable overlong distances, this offers the potentialof considerably higher capacity in opti-cal fiber communication networks.

Some of Peter Lax’s

Major Contributions

DA: Over the years you have worked onseveral big problems. Where do the bestproblems come from?

PL: It helps to be at a center of math-ematics like Courant because then youkeep your finger on the pulse of math-ematics. It’s a tremendous advantage andit’s really unfair to guys at smallerschools. The Internet helps a little bit,but personal contact is best. So I havehad an unfair advantage.

DA: You’ve previously stated that youreally like to find your own problems andthat for you those problems have typi-cally been rooted in a natural phenom-enon. The more striking the phenom-enon the more interested you become init, and then in trying to explain it.

PL: Yes, yes. Mathematics is certainlyvery strongly rooted in understandinginteresting phenomena.

DA: You have worked in many areas.What’s particularly striking are all of theterms and theorems that bear your name:Lax-Phillips scattering theory, the Lax en-tropy condition, the Lax theorem, the Lax-Milgram theorem, the Lax equivalenceprinciple, the Lax-Friedrichs scheme, theLax-Wendroff scheme, Lax shocks, the Laxrelation, and Lax pairs. Your name willlive on. Have some of the areas given youmore joy or satisfaction than others?

PL: No, I loved all of them.

DA: You loved them all. Like your chil-dren.

PL: Yes, yes, like children.

DA: What’s the toughest problem youever worked on and solved?

PL: Two things come to mind. One is avery tricky result — I called it an abstractPhragmen–Lindelöf principle. It’s a verydifficult result. I had carelessly an-nounced it as a theorem and then I hadto prove it. And it takes 12 lemmas.

DA: That’s a lot of lemmas.

PL: And the other tricky result is the zerodispersion limit for the KdV equationwhich I did with a student, Dave

Levermore. That was technically very dif-ficult.

DA: You have said that mathematics islike painting.

PL: Yes, yes, I’m very proud of that meta-phor. I think it is original. I love paint-ing. And I gave the reason for it. “In maththere is a creative tension between de-scribing and understanding and solvingthe laws governing nature, on the onehand, and making pleasing logical pat-terns on the other.” And in painting it’sthe same way. There is a creative tensionbetween rendering the shapes, colors,and textures of nature, and making pleas-ing abstract patterns. I have little talentfor it. Finishing a painting was like solv-ing a problem. If I were doing it again, Iwould work on several paintings at once.Certainly in mathematics I always toldmy students to work on several problemsat the same time. You’ll usually be sty-mied on most of them.

References

P.D. Lax in More Mathematical People(eds. D.J. Albers, G.L. Alexanderson, andC. Reid) Harcourt Brace Jovanovich,Boston, 1990, pp 139-158.

P.D. Lax, The flowering of applied math-ematics in America, SIAM Review 31(1989), pp. 533-541.

P.D. Lax, John von Neumann: The earlyyears, the years at Los Alamos and theroad to computing, SIAM Review, to ap-pear..

D.J. Albers, Once upon a time: Anneli Laxand the New Mathematical Library, FO-CUS, Mathematical Association ofAmerica,June 1992, pp. 30-32.

N. Hungerbühler, The Abel Prize—thenew coronation of careers, Elemente derMathematik 50 (2003), pp. 45-48.

www.abelprisan.no — the official AbelPrize web site.

Don Albers is the MAA’s Director of Pub-lications. He was one of the authors ofMathematical People, and More Math-ematical People.

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“The more math you know, the more mathyou see…” Jason Fox, Foxtrot

Although a typical undergraduate stu-dent taking abstract algebra views grouptheory as something having little connec-tion with everyday affairs, an instructorcan counter this impression by callingattention to the fact that groups arisenaturally in many ordinary contexts. Inthis note we describe instances of groupsthat are commonplace but often over-looked.

An instance of groups that ones sees ev-eryday is automobile wheel designs.These are appealing examples of cyclicand dihedral symmetry groups. Eventhough wheel patterns appear highlysymmetrical and attractive their symme-try groups may be the trivial group. Thisis usually the case for wheels that haveone symmetry pattern around the outeredge and another one in the middle. Ihave seen examples of wheels with 12-fold, 9-fold, and 8-fold rotation symme-tries around the outer edges and 5-foldrotational symmetry in the middle (be-cause of the lug nuts). Since the groupof symmetries of the entire wheel is theintersection of the groups of the two pat-terns, it follows from Lagrange’s theoremthat in these cases the trivial symmetryis the only symmetry of the entire wheel.

The symmetry group of a bicycle wheelis another case where the symmetrygroup is not immediately obvious. Forexample, the wheels on my bicycle have36 spokes but only 9-fold rotational sym-metry since the spokes are staggered fourat a time.

Direct products of cyclic groups can befound in your home. In a bedroom the

group Z Z2 2⊕ , which one can also think

of as the dihedral group D2, arises when

one rotates a mattress all possible ways.This group consists of R

0, a rotation of 0

degrees; R180

, a rotation of 180 degreesabout an axis perpendicular to the top;H, a rotation about an axis perpendicu-lar to a side (thereby interchanging the“up” and “down” sides and the head andfoot of the mattress); and V, a rotationabout an axis perpendicular to the foot(thereby interchanging the left and rightsides and “up” and “down” sides but leav-ing the head side at the head). Since thisgroup is not cyclic there is not a singlemotion that one can repeat monthly toensure even wear. However, by monthlyalternating the motions R

180 and V (the

easiest two non-trivial motions to per-form) all four possible positions of amattress are realized over the course offour months.

Hallways and stairways often have lightsthat are operated by two or more

switches so that when any one switch isthrown the light changes its status fromon to off or vice versa. The group

Z Z2 2⊕ models the case where there are

two of these switches. If the wiring isdone so that the lights are on when bothswitches are up or both switches aredown then we can conveniently think ofthe states of the two switches as being

matched with the elements of Z Z2 2⊕

with the two switches in the up positioncorresponding to (0,0) and the twoswitches in the down position as corre-sponding to (1,1). Each time a switch isthrown we add 1 to the corresponding

component of Z Z2 2⊕ . It follows that

the lights are on when the switches cor-respond to the elements of the subgroup〈 )( 〉1 1, (the subgroup generated by(1,1)), and are off when the switches cor-respond to the elements in the coset (1,0)+ 〈 )( 〉1 1, . The case of three switches ismodeled by the group Z Z Z2 2 2⊕ ⊕

Groups in the Household

By Joseph A. Gallian

Broken symmetries in a car wheel.

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with the subgroup〈 )( ( )1 1 0 0 1 1, , , , , 〉 correspond-ing to the situation where thelights are on.

Items in kitchen cupboardsgive rise to interesting groups.The symmetry group of a spa-ghetti box (nonsquare ends) is

Z Z Z2 2 2⊕ ⊕ . The rotation

group of a box of crackers(with square ends) is D

4 and

the full symmetry group con-sists of the semidirect productof D

4 and Z

2 (the identity and

a reflection). The full group isa semidirect product ratherthan a direct product since thereflection that interchangesthe opposite ends of the boxdoes not commute with therotations.

Games found around thehouse occasionally involvegroups. The 15-puzzle that hassliding blocks numbered 1 to15 and a empty space in thelower right hand corner permits rear-rangements corresponding to the ele-ments of A

15, the alternating group on

{1,2,... ,15}. The group of motions of aRubik’s cube has order 43252-003274489856000. The 15-puzzle andthe Rubik’s cube are good examples ofinstances where the theory of groupsprovides insight into the solutions of thepuzzles. Without group theory it wouldbe quite difficult to determine exactlywhich rearrangements of the 15-puzzleare obtainable.

One of the most striking facts about theworld we live in is that there are only fivekinds of finite groups of rotational sym-metry in three dimensions: cyclic, dihe-

dral, A4, S

4, and A

5. All five are realized

by common objects. Indeed, the groupof rotations of a volleyball, a cube, and asoccer ball have the rotation groups A

4,

S4, and A

5, respectively. In each case the

full symmetry group is the semidirectproduct of the rotation group and Z

2.

Two interesting infinite groups of rota-tional symmetry are those of a beach ball(sphere) and of a smooth drinking glass.The first is isomorphic to the group of3x3 matrices of determinant 1 that havethe property that the transpose of a ma-trix is its inverse (the special orthogonalgroup SO

3) The second group is the

group of rotations around a central axis,

which can be thought of ei-ther as SO

2 or as the factor

group R/2πZ, where R is thegroup of real numbers un-der addition and 2πZ is thesubgroup of integral mul-tiples of 2π.

One can even find an ex-ample of a group when wa-gering on horse racesonline! There is a wagercalled the “trifecta box”where a bettor selects threehorses that he believes willfinish first, second, andthird in any order. Ofcourse, this is an instance ofS

3. The person who ex-

plained this wager to mecommented, “Someone fig-ured out that are 9 possi-bilities.” Even though thisperson is quite intelligent,he accepted this statementas fact.

It is worth pointing out thatthe connection between

groups and commonplace objects is two-way. Sometimes the groups provide in-teresting information about the objects,as in the case, of the 15-puzzle, and some-times the objects provide an interestingway to think about the group, as in thecase of the rotations of a soccer ball.

Editor’s note. This article was the substanceof a talk given at the Joint MathematicsMeetings in Atlanta in a special session,organized by the CUPM 2004 Committee,on the topic of introducing contemporaryconcepts into mathematics courses.

A drinking glass whose symmetry is not R/2πZ

Due to the size of this issue, we have had to save our letters section for the next issue.

Letters to the Editor

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In response to the increasing need forcollegiate education that helps studentsachieve quantitative literacy (QL) and thecomplexities of providing that education,two new complementary organizationshave emerged. One is the MAA’s specialinterest group SIGMAA QL, and theother is an interdisciplinary membershiporganization, the National NumeracyNetwork (NNN). These organizationshave missions that are integral parts of agrowing national effort to make Ameri-cans more able to deal with the multi-tude of quantitative issues that confrontthem in their daily lives as citizens, con-sumers, and workers.

Different terms are used around theworld with meanings closely related toor interchangeable with QL. “Numeracy”is used in many countries outside the US.Other closely related terms are “quanti-tative reasoning,” “mathematical literacy,”“statistical literacy,” and “financial lit-eracy.”

SIGMAA QL was formed by action of theMAA Board of Governors in January2004 and aims to provide a structurewithin the mathematics community toidentify the prerequisite mathematicalskills for QL and find innovative ways ofdeveloping and implementing QL cur-ricula. The 2004 Chair of SIGMAA QLwas Judy Moran (Trinity College) andthe 2005 Chair is Caren Diefenderfer(Hollins University). Rick Gillman(Valparaiso University) was a drivingforce in organizing SIGMAA QL.

The National Numeracy Network(NNN) was formally established as amembership organization at a meetingheld at Moose Mountain Lodge nearDartmouth College (NH) in June 2004.As stated in its vision statement, NNNaims toward a society in which all citi-zens possess the power and habit of mindto search out quantitative information,critique it, reflect upon it, and apply it intheir public, personal, and professionallives.

NNN is incorporated in the State ofWashington, and of the five members ofthe NNN Board of Directors, two are inmathematics, and one each in physics,geology, and education. Bernard L Madi-son (University of Arkansas) is NNNPresident, and Rebecca Hartzler (SeattleCommunity College) is Secretary-Trea-surer. The other directors are KimRheinlander (Dartmouth College),Henry L. Vacher (University of SouthFlorida), and Dorothy Wallace(Dartmouth College). The first meetingof NNN will be held at Macalester Col-lege in St. Paul (MN) June 18-19, 2005.

Common Goals

Both NNN and SIGMAA QL recognizethat education for QL involves disciplinesother than mathematics, but that math-ematics has a major contribution tomake. As stated in its purpose, beyondits work within the mathematics com-munity, SIGMAA QL also intends to as-sist colleagues in other disciplines to in-fuse appropriate QL experiences intotheir courses. NNN is an interdiscipli-nary organization and is dedicated topromoting education that integratesquantitative skills across all disciplinesand at all levels. To this end NNN sup-ports and promotes collaborationsamong students, educators, academiccenters, educational institutions, profes-sional societies, and corporate partners.Both SIGMAA QL and NNN strive tokeep issues of quantitative literacy at theforefront of national and internationalconversations about educational priori-ties.

NNN Background

For about three years prior to its officialorganization, NNN had been a looseconfederation of QL centers on collegecampuses and was part of the initiativein QL sponsored by the National Coun-cil on Education and the Disciplines(NCED) located at the Woodrow WilsonFoundation. NCED, led by Robert Orrill,

was the lead sponsor of the 2001 nationalforum, Quantitative Literacy: WhyNumeracy Matters for Schools and Col-leges, held at the National Academy ofSciences. MAA was a cooperating spon-sor of the forum, which was hosted bythe Mathematical Sciences EducationBoard of the National Research Coun-cil.

The NCED QL initiative also resulted inthe publishing of Mathematics and De-mocracy (edited by Lynn Arthur Steen)and the proceedings of the national fo-rum, Quantitative Literacy: WhyNumeracy Matters for Schools and Col-leges (edited by Bernard L. Madison andLynn Arthur Steen). A third book,Achieving Quantitative Literacy: An Ur-gent Challenge for Higher Education, writ-ten by Lynn Steen and published byMAA, is based on the proceedings andrecommendations from the national fo-rum. All three of these books are avail-able from the MAA Bookstore.

NNN offers memberships for individu-als, institutions, and corporations. Mem-bership benefits highlight interdiscipli-nary communication and cooperationfacilitated by NNN publications andmeetings.

SIGMAA QL Background

Although mathematics for general edu-cation always has been a part of the UScollege curriculum, expectations in QLas a part of an undergraduate degree havebeen becoming more prominent in thepast few decades. In 1989 the MAA,partly in conjunction with the appear-ance of the National Council of Teach-ers of Mathematics (NCTM) Curriculumand Evaluation Standards for SchoolMathematics, appointed a Subcommitteeon Quantitative Literacy Requirements(QL Subcommittee) of the Committeeon the Undergraduate Program in Math-ematics (CUPM). This subcommitteebegan by considering the question: Whatquantitative literacy requirements shouldbe established for all students who receivea bachelor’s degree?

In 1994, the QL Subcommittee issued areport, “Quantitative Reasoning for Col-lege Graduates: A Complement to the

Building Bridges for QL Education:

National Numeracy Network and SIGMAA QL

By Bernard L. Madison

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Standards,” which highlighted four con-clusions:

Colleges and universities should treatquantitative literacy as a thoroughly legiti-mate and even necessary goal for bacca-laureate graduates.

Colleges and universities should expectevery college graduate to be able to applysimple mathematical methods to the solu-tion of real-world problems.

Colleges and universities should devise andestablish quantitative literacy programseach consisting of foundation experienceand a continuation experience, and math-ematics departments should provide lead-ership in the development of such pro-grams.

Colleges and Universities should acceptresponsibility for overseeing their quanti-tative literacy programs through regularassessments.

These conclusions emphasize the colle-giate responsibility for QL education, butthe report did not have much immedi-ate effect on collegiate mathematics, andQL continued to be poorly understoodand largely ignored in college mathemat-ics curricula. The QL Subcommittee con-tinued to work after 1994, but the needfor a more substantial presence of QL inMAA activities was evident from thework produced by the NCED initiativeand the substantial attention to generaleducation issues in the CUPM Curricu-lum Guide 2004. This need led to creationof the SIGMAA QL.

Other Organizations

MAA, NCED, and NNN are not the onlyorganizations that have recognized thegrowing issue of education for QL. Overthe past 20 years the American Statisti-cal Association and NCTM developedcurricular descriptions and materialsthat formed the basis of the NCTM’s dataanalysis and probability strand in theNCTM Standards. These developmentswere made under the heading of quanti-tative literacy and are critical compo-nents of the existing efforts in QL edu-cation.

Len Vacher, NNN Director, has for sometime written a column for the Journal ofGeoscience Education about QL for geo-scientists. Project Kaleidoscope, an inter-disciplinary science and mathematicsproject that promotes reform, has orga-nized several sessions and workshops onQL. The Association of American Col-leges and Universities (AAC&U) hashosted several major conferences on re-form of general education with QL (orquantitative reasoning) as one of themajor topics.

The momentum of the QL movementwas affirmed and increased with the pub-lication of the Summer 2004 issue ofAAC&U’s Peer Review dedicated to QL.Peer Review’s headline mission is to ad-dress ‘emerging trends and key debatesin undergraduate education.’ The PeerReview QL issue contains two analyticalessays by Lynn Steen and Bernard Madi-son along with descriptions of QL pro-grams at Hollins University, AugsburgCollege, and James Madison University.

Colleges and QL

One of the driving forces behind theNCED initiatives and the missions ofNNN and the SIGMAA QL is the real-ization that education for QL is a collegeissue, as made clear in the 1994 MAAreport. Lynn Steen makes this point co-gently in his Peer Review article. Using

several examples of percentages and av-erages, Steen concludes, “… QL is suffi-ciently sophisticated to warrant inclusionin college study and, more important,that without it students cannot intelli-gently achieve major goals of college edu-cation. Quantitative literacy is not just aset of precollege skills. It is as important,as complex, and as fundamental as themore traditional branches of mathemat-ics. Indeed, QL interacts with the coresubstance of liberal education every bitas much as the other two R’s, reading andwriting.”

Along with Steen, in his Peer Reviewanalysis Bernard Madison emphasizesthat education for QL requires interdis-ciplinary cooperation far beyond what isnow the norm in colleges and universi-ties. Madison’s analysis focuses onchanges in collegiate mathematics thatwill promote this interdisciplinary coop-eration and stronger QL education. In-terdisciplinary cooperation is at the verycore of the motivation for creating NNN,and the fact that there are strong con-nections to SIGMAA QL offers oppor-tunities to simultaneously strengthencollegiate mathematics and QL.

Bernard L. Madison is professor of math-ematics at the University of Arkansas,member of the SIGMAA QL, and Presi-dent of NNN.

MAAQLhttp://www.maa.org/QL/index.html

National Numeracy Networkhttp://www.math.dartmouth.edu/~nnn/index.html

SIGMAA QLhttp://pc75666.math.cwu.edu/~montgomery/sigmaaql/

National Numeracy Network MeetingJune 18-19, 2005

Immediately followingPREP Workshop: Creating and Strengthening Interdisciplinary Programs inQuantitative LiteracyJune 14-17, 2005http://www.macalester.edu/qm4pp/workshops/prep.html#wlMacalester CollegeSt. Paul, MN

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The Max Dehn Papers at the Centerfor American History’s Archives ofAmerican Mathematics tell the story ofan established Jewish mathematicianfrom Germany leaving his homelandunder pressure from the Nazis and fin-ishing his career in the United States,moving from one mathematically low-profile position to another. It is not aunique story, but the breadth and detailof the papers collected at the AAM makeit an important part of the history ofAmerican mathematics.

Dehn (1878-1952) earned his doctorateat Göttingen in 1900 under the direc-tion of David Hilbert. He spent the ma-jority of his career in Germany at Frank-furt University, where he served as thechair of Pure and Applied Mathematicsfrom 1921-1935. In Germany he wroteone of the first systematic expositionsof topology and developed importantproblems on group presentations. Hisscope of research included geometry, to-pology, group theory, and the history ofmathematics. In 1938 he was forced toleave the university by the Nazis. He firsttook a position in Scandinavia, and in1940 came to the United States by anEastern route through Russia and Japan.

After arriving in the United States, Dehnheld several temporary appointmentsincluding positions at the University ofIdaho in Pocatello, the Illinois Instituteof Technology, and St John’s College inAnnapolis, Maryland, before becomingthe first mathematician on the staff ofBlack Mountain College, an un-accred-ited creative arts college in North Caro-lina. Dehn remained in North Carolinauntil his death in 1952.

The Max Dehn Papers at the AAM in-clude lecture notes by E. Hellinger; andcorrespondence, notebooks, manu-scripts of publications, reprints, and lec-ture and course notes by Dehn. Corre-spondents include E. Artin, O.Blumenthal, H. Bohr, S. Breuer, C.Caratheodory, M. Kneser, E. Noether, M.

Archives of American Mathematics Spotlight:

The Max Dehn Papers

By Kristy Sorensen

C.L. Siegel article with caricature for 1928 Festschrift in honor of Arthur M. Schoenflies,6 November 1927.

Mathematician C. L. Siegel wrote this article, “Über Riemann’s arithmetischer Nachlass”(“On Riemann’s arithmetical Nachlass”), as part of a tribute to Arthur Schoenflies, whomSiegel had replaced as professor of mathematics at Frankfurt University six years earlier.His colleague Max Dehn, a former assistant of David Hilbert, organized the compilationof the manuscript. From the Max Dehn Papers, Archives of American Mathematics, Cen-ter for American History The University of Texas at Austin.

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Pasch, O. Toeplitz, and E. Zermelo. Themajority of the materials are written inGerman, with some English and French.

The finding aid for the Max Dehn Pa-pers is available online at: http://www.lib.utexas.edu/taro/utcah/00192/cah-00192.html.

The Archives of American Mathematicsis located at the Research and Collectionsdivision of the Center for American His-tory on the University of Texas at Austincampus. Persons interested in conduct-ing research or donating materials orwho have general questions about theArchives of American Mathematicsshould contact Kristy Sorensen, Archi-vist, k.sorensen@mail.utexas.edu, (512)495-4539. The Archives web page: http:// w w w . c a h . u t e x a s . e d u /collectioncomponents/math.html.

American Mathematical Monthly

Editor Search

The Mathematical Association ofAmerica seeks to identify candidates tosucceed Bruce Palka as editor of theAmerican Mathematical Monthly whenhis term expires in December 2006. TheSearch Committee plans to make a rec-ommendation during the summer of2005 so that the new editor can be ap-proved by the Board of Governors andbegin handling all new manuscript sub-missions in January, 2006. The new edi-tor would be Editor-Elect during 2006and would serve as Editor for the fiveyears 2007-2011.

Questions about the position and itsworkload can be addressed to: G. L.Alexanderson (galexand@math.scu.edu),or Don Albers, Director of Publicationsat the MAA (dalbers@maa.org). Ques-tions about MAA support for the editor’swork can be addressed to Albers. Each

applicant should submit a resumé, namesof references, and a statement of interestcontaining his or her ideas about thejournal. These can be emailed as attach-ments in Word or pdf format to the chairof the Search Committee, Gerald L.Alexanderson (galexand@math.scu.edu),or mailed to:

Gerald L. AlexandersonDepartment of Mathematics& Computer ScienceSanta Clara University500 El Camino RealSanta Clara, CA 95053-0290

A candidate who would be an outstand-ing editor may be nominated by some-one else. Applications and nominationswill be accepted until the position isfilled, although preference will be givento applications received by late May.

In 2004, women made their best show-ing ever on the Putnam Competition.Sophomore Ana Caraiani of PrincetonUniversity became the first woman to beone of the five winners of the competi-tion for a second time. Caraiani and herteammate Suehyun Kwon helpedPrinceton’s team place second among the411 teams (each with three students)entered in the competition. This marksthe first time since 1939 that a team witha majority of women placed among thetop five teams. In addition, two womenwere among Harvard’s top three per-formers: Alison Miller, a freshman, andInna Zaharevich. Miller, Zaharevich, andOlena Bormashenko of Waterloo fin-ished in the 6–15 category. Women whoreceived honorable mention were Kwon,Yuliya Gorlina of Caltech, KarolaMeszaros of MIT, and Shubhangi Sarafof MIT. Eleven more women wereranked in the top 200.

Melanie Wood, who co-coached the 2004 PrincetonPutnam problem solvingclass, attributes the women’ssuccess to their high schoolOlympiad training. Ana,Suehyun, and Alison allagree, citing the great coach-ing they had for the Interna-tional Math Olympiad. Anawon a silver and two goldmedals as a member of theRomanian IMO team.Suehyun won a gold medalfor the South Korean IMOteam. Alison was a gold med-alist on the US IMO team in 2004. Olenawon silver and gold medals as a memberof the Canadian IMO team. The inten-sive training they received in high schoolfor math competitions continues to payoff in the Putnam.

A record number 3733 students from 515schools participated in the Putnam. ReidBarton of MIT became the sixth personto win the competition for a fourth time.Along with Barton and Caraiani, sopho-more Daniel Kane of MIT was a repeatwinner in 2004.

Women Excel in the 2004 Putnam Competition

By Joseph A. Gallian

Princeton students Suehyun Kwon and Ana Caraiani.

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Along the multi-story, upward-spiral-ing staircase in the Vaughn Building atMAA Headquarters hang photographs ofthe presidents of the MAA. The tenthpicture above the second floor is labeledsimply “G. B. Price, President 1957–1958,” and it shows a man of humbleappearance who was in his early fifties atthe time it was taken. It was with greatpleasure that on March 14th the MAA— along with his family and manyfriends and colleagues world-wide —celebrated Griffith Baley Price’s 100thbirthday. This centennial observance for“Baley,” as he is known by many, has beenan occasion to celebrate the life of a veryspecial mathematician and teacher.

Baley Price graduated from MississippiCollege in 1925, received his Ph.D. atHarvard in 1932 under the direction ofG. D. Birkhoff, and joined the faculty ofthe Department of Mathematics at theUniversity of Kansas in 1937. His pro-fessional service contributions began in1935, serving on the AMS PublicityCommittee, followed by several years ofwork to help launch Mathematical Re-views. Among his early contributions tothe MAA was a 1938 proposal that led tothe establishment of the “HerbertSlaught Memorial Publications” andlater, in 1952, the “Earle RaymondHedrick Lectures.” During the 1950sPrice proposed and sought NSF fundingfor the Association’s Visiting LecturersProgram, and he influenced — throughhis involvement with the National Re-search Council — the creation of boththe program of Summer Institutes forteachers and the Committee on the Un-dergraduate Program. As MAA Presidenthe guided the Association’s involvementwith the “New Math” program of theSchool Mathematics Study Group(SMSG). His work between 1959 and1962 on behalf of the Conference Boardof the Mathematical Sciences (CBMS)was crucial, including service during theplanning stages, as Chairman, and asExecutive Secretary.

A Century Celebration:

Former MAA President G. Baley Price Turns 100

By Steve Carlson

G. Baley Price with former student Joan Kirkham. She was in his statistics class in 1944.Taken at a March 12, 2005 private celebration at his church.

G. Baley Price with K.U. Professor Jack Porter, current chair of the K.U. MathematicsDepartment. Taken at the March 18, 2005 reception honoring Price during the KansasMAA Section meeting held on the K.U. campus.

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In addition to serving themathematical community,Price answered the call toserve the nation duringWorld War II, accepting anappointment within theOperations Research Sec-tion of the Eighth AirForce in England. His workon behalf of the war effortand the mathematics in-volved remain todayamong Baley’s favorite dis-cussion topics and werehighlighted in a special lec-ture he presented at theK.U. Dole Institute of Poli-tics in April 2004. He alsocontributed a section onthis topic in Volume 4 of ACentury of Mathematics.

Baley chaired the Math-ematics Department atK.U. from 1959 through1970, the year in which hereceived the MAA’s Awardfor Distinguished Serviceand also was named as thefirst E. B. Stouffer Distin-guished Professor ofMathematics at Kansas. Under his lead-ership the K.U. math department hadflourished, and with his unassuming ap-proach and genuine kindliness he easilywon the respect of colleagues and stu-dents. Baley officially retired in 1975, andthat year the K.U. Mathematics Gradu-ate Student Association honored him bynaming its annual faculty teaching awardthe G. Baley Price Award for Excellencein Teaching. In 2004 a trust was fundedby K.U. alumnus Balfour McMillen andhis wife to honor Price’s career achieve-ments at the university with the creationof the G. Baley Price Professorship inMathematics.

Baley and his wife Cora Lee Beers Price,who retired in 1979 from K.U. where shetaught in both the English and classicsdepartments, raised six children — fivedaughters and one son. Cora Lee died inDecember of 2004, but will long be re-membered on the K.U. campus. Baleyrecently endowed the Cora Lee BeersPrice Professorship in International Cul-

G. Baley Price with K.U. Professor Charlie Himmelberg, who chaired theMathematics Department at Kansas from 1978 through 1999. Taken at theMarch 12, 2005 celebration.

tural Understandingat K.U. to honor herdedication to teach-ing.

In addition to privatebirthday gatherings,Baley’s 100th birthdaywas celebrated at themeeting of the KansasMAA Section that washeld on the K.U. cam-pus March 18th. Thespecial reception hon-oring his “One Hun-dred Years of Life and70 Years of Mathemat-ics” included a slideshow of images span-ning Baley’s career atK.U. Price served asKansas Section Chair1940–1941 and asKansas Section Gover-nor 1952-1955 — justthe first three years ofa continuous presencein various capacitieson the Board of Gov-ernors through 1964.He also later returned

to the Board as a member of the MAAFinance Committee in the late 1970s andearly 1980s, establishing a truly incred-ible record of Board service.

During one of his birthday events, usingnotes he typed on his computer, Baleytalked briefly about his life. He startedwith one question: “Can you hear me?”Then he said, “When I talk, I want to beheard!” We have heard your wise wordsfor many years, Professor Price, and lookforward to hearing you for many yearsto come.

The author, who teaches at the Rose-Hulman Institute of Technology but re-ceived all three of his degrees from theUniversity of Kansas, is currently a Visit-ing Mathematician with the MAA.

February 1970 Monthly photo:Photograph of G. Baley Price, 1970.From the article “Award forDistinguished Service to ProfessorGriffith Baley Price” by W. L. Duren,Jr. (The American MathematicalMonthly, Volume 77, No. 2, Feb. 1970,pp. 115-117)

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Are you in a mathematics departmentthat has been searching for an academicstatistician but having a hard time find-ing one? Do you anticipate an openingfor a statistician in 2006? You aren’t alone.Anecdotal evidence suggests that manymathematics departments are havingtrouble hiring statisticians. The statisticscommunity has taken notice of the situ-ation and is attempting to help.

In the fall of 2004, fifteen statisticians,representing both liberal arts collegesand institutions with graduate depart-ments of statistics, got together to dis-cuss ways to improve the (two-direc-tional) pipeline between these two typesof institutions. Graduate institutions areconcerned about declining numbers ofdomestic graduate students. Liberal artscolleges want to attract faculty memberswith degrees in statistics. This article isone of the results of this conversation.

With respect to the issue of mathemat-ics departments wishing to recruit stat-isticians, one of the things we noted wasthat frequently mathematics depart-ments advertise positions in places thatare not the ones where academic statis-ticians tend to look. This article offerssuggestions for where to advertise whenrecruiting academic statisticians. Withineach category, we have ordered the list-ings starting with those mostly likely tobe referenced by a graduate statistics stu-dent looking for an academic position.

Advertising in print (not free)

1. AmStat News, a monthly magazinepublished by the American StatisticalAssociation and similar to FOCUS. Thebasic ad listing may not exceed 65 words,not counting equal opportunity infor-mation, and the cost for this basic ad is$290 for nonprofit organizations. (Largerads for greater fees are also available.) Adsmust be received (electronically or inhard copy) by the first of the precedingmonth to ensure appearance in the nextissue (for example, September 1 for theOctober issue). A paid AmStat News adalso appears for free during the same

month on the ASA job web site at http://www.amstat.org/opportunities/. The con-tact email address for more informationis advertise@amstat.org.

2. IMS Bulletin, a bimonthly magazinepublished by the Institute of Mathemati-cal Statistics. It reaches a much smalleraudience than the AmStat News, but isstill a search source for students in someof the graduate programs in statisticshoused within mathematics depart-ments. The deadline for the October is-sue is September 1 and there will be asimilar deadline each year. The cost for abasic ad (up to 100 words) is $100, butthey also accept longer ads for a higherfee. For more information about this ad-vertisement option, see http://www.imstat.org/advertising.htm. A posi-tion advertisement published in any is-sue of the IMS Bulletin is also posted atthe web site without additional cost forthe two month period corresponding tothat issue.

3. Newsletter of the Caucus for Women inStatistics: Job notices must be submittedby December 30, 2005 for inclusion inthe Winter 2005 Newsletter. The fee forpublishing a job notice for a half-pagead or less is $55, if prepaid, and $80 ifbilled. Longer ads are $75 prepaid and$100 billed. Please send the job noticeand a check payable to the Caucus forWomen in Statistics to MargaretMinkwitz. For more information, visithttp://www.forestsoils.org/wcaucus/.

4. Ranked below the above sources aretwo mathematics department mainstays:Employment Information in the Math-ematical Sciences and The Chronicle ofHigher Education. Of note to potentialemployers, none of the statisticians at themeeting realized that mathematics de-partments at liberal arts colleges regu-larly advertise in the Chronicle.

Direct Advertising

Hard copy notices can be sent to thechairs of statistics departments in theUnited States. The addresses are available

from the ASA web site http://www.amstat.org. Job notices sent directlyto departments typically get posted in anarea available to graduate students.

Electronic Advertising

Graduate students have become quitesavvy about searching the web for jobopening advertisements from schoolswhich might be of interest. Put your bestfoot forward and make yourself appeal-ing to a statistician.

1. The Department of Statistics at theUniversity of Florida maintains a job list-ing web site http://www.stat.ufl.edu/vlib/jobs.html) where any Statistics positioncan be posted free of charge. The jobposition description should be sent as aplain text attachment to the email ad-dress jobs@stat.ufl.edu with a request topost it to their job listing web site. Ques-tions regarding the web page may be sentto the same email. Many statistics gradu-ate students search this web site everyyear, looking for positions. Once the jobis posted, the electronic advertisementstays on the site for 6 months or when arequest is made to have it removed.

2. The American Statistical Associationmaintains an email alias for chairs ofboth statistics and mathematics depart-ments that have Ph.D. programs in sta-tistics. Job position advertisements canbe emailed electronically to all suchgraduate programs through this emailalias. You will not be able to send theemail directly to this list as only peoplewho belong to this group can do that.However, you can send a job positionnotice to the American StatisticalAssociation’s office with a request thatthe job position be sent out to the chairsvia this email alias. For this purpose, youneed to send your job position (either asan attachment or entirely containedwithin your email message) to CaroleSutton, at this email address:Carole@amstat.org, along with the re-quest that she send this job notice out tothe “stat academic representatives” list.

Looking for Stat(istician)s in All the Wrong Places

By Ann Cannon and Carolyn Cuff

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Many mathematics departments rou-tinely plan to conduct interviews at theJoint Mathematics Meetings in January.Most statisticians are not particularlyinterested in (or even aware of) thesemeetings and hence their graduate stu-dents are typically unaware of them. Ifyour position is primarily aimed at hir-ing a statistician, interviews conductedat these meetings will be frustrating atbest.

Statisticians can be extremely happy inmathematics departments. The statisticscommunity has strong support systems

for those individuals who serve as thesole statistician at a college (see http://www.isostat.org). The MAA also has aspecial interest group devoted to theteaching of statistics (see http://www.pasles.com/sigmaastat). Reachingstatisticians who may eventually considera mathematics department as their homeis quite possible, but it’s important toplace the information where it is likelyto be seen.

Ann Cannon is associate professor of sta-tistics and mathematics at Cornell College(Mt. Vernon, IA). She is the current mod-

erator of the Isolated Statisticians (a groupof self-defined isolated academic statisti-cians), past chair of the Iowa Chapter ofthe ASA and is active in the ASA’s Sectionon Statistical Education.

Carolyn Cuff is a professor of mathemat-ics at Westminster College (PA). She is apast-chair of SIGMAA Stat-Ed and is ac-tive in the ASA’s Section on Statistical Edu-cation.

The CCLI program of the Division ofUndergraduate Education has been sub-stantially rewritten to reflect the matu-ration of the program, increased knowl-edge about the teaching and learning ofscience, technology, engineering, andmathematics (STEM) subjects, new chal-lenges for STEM education, and changesin the NSF budget. Five components ofa cyclic model of knowledge productionand improvement of practices have beenidentified and form the basis for CCLIgrant proposals. Briefly, these are re-search on undergraduate STEM teachingand learning; creation of materials andteaching strategies; faculty development;implementation of educational innova-tions; and assessment of learning andevaluation of innovations.

The revised CCLI program will acceptthree types of proposals. Phase 1 projectsare exploratory in nature, likely to be fo-cused on one curriculum component,and involve a limited number of studentsand faculty at one institution. Broaderscope projects are possible if within bud-get limitations. An incentive of addi-tional funding is offered to projects inwhich two- and four-year institutions

collaborate. Depending on suitable ap-plications, between 55 and 70 Phase 1awards are planned. Grants for one- tothree-year projects can be up to $150, 000(or $200,000 for joint two- and four-yearinstitution proposals).

Phase 2 expansion projects are expectedto include at least two of the five com-ponents of the cyclic model and to spellout carefully the connections betweeneach part. A Phase 2 project will buildon smaller-scale innovations or imple-mentations to refine and test these in sev-eral settings. This type of project shouldaim to develop products or processes tothe point where they can be distributedwidely or commercialized, if appropri-ate. Again, depending on the proposalssubmitted, DUE anticipates funding 15to 25 Phase 2 awards, each with a totalbudget of up to $500,000 for 2 to 4 years.

The third category of new CCLI projectsis comprehensive projects that combineestablished results and mature productsfrom several components of the cyclicmodel. Evaluation activities should bedeep and broad based and demonstratethe project’s impact on many students

and faculty at a wide range of institu-tions. Dissemination and outreach withnational impact are a particularly impor-tant element of Phase 3 projects. Fund-ing is available for one to four Phase 3awards of up to $2,000,000 for 3 to 5years each.

Important features of successful propos-als include: quality, relevance, and im-pact; student focus; use and contributionto STEM education knowledge; STEMcommunity building; measurable ex-pected outcomes; and a strong evalua-tion plan.

The former CCLI program was very suc-cessful in promoting the development,implementation, dissemination, andevaluation of innovative course and cur-ricular materials and in assisting STEMeducators to support these activities withappropriate technology. The kinds ofprojects supported in the earlier programcan be part of these revised categories.The emphasis in the new CCLI programis on greater integration of efforts fromall three types of projects to maximizethe effectiveness of improving under-graduate STEM education.

NSF Beat

Course, Curriculum, and Laboratory Improvement (CCLI) Program

By Sharon Cutler Ross

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At Wartburg College, we recently un-derwent an expansion and renovation ofour science building. The Becker Hall ofScience was built in 1967 and housed theBiology, Chemistry, Physics, ComputerScience, and Mathematics departments.Throughout the renovation process thefaculty worked with the architects andconsultants to help design optimal teach-ing and research space. However, whenpreparing for discussions with the archi-tects, we found very little literature spe-cifically addressing designing a math-ematics building.

Often mathematics gets included in thescience building, but the unique de-mands of a mathematics department arefrequently overlooked by consultants.While many of the other sciences requireexpensive laboratory equipment, themathematics department is cheap bycomparison and gets less attention dur-ing the design phase. The purpose of thisarticle is to address the characteristics ofa well designed math building for facultyfaced with this task in the future.

Study Space

Fundamental to a mathematics depart-ment is the existence of places for stu-dents to congregate and study. Math-ematics thrives on an exchange of ideas,and there must be places available forstudents to meet and work. Furthermore,the lounge needs to be centrally locatedto increase the likelihood of random en-counters. In this setting faculty are morelikely to happen upon students workingand offer a word or two of direction orencouragement. Students are more likelyto recognize colleagues from class work-ing on assignments and join in.

A well equipped lounge will have chalk-boards or whiteboards on which studentscan do their work. This allows multiplestudents to work together and also en-courages students to separate the processof solving a problem from that of writ-ing up the solution. An open space willhelp bring more people into the loungeby removing barriers to entry. This also

decreases the chance that the lounge willbe converted into a classroom or officeat some later date.

In addition to a central lounge, havingmany other spots where small groups cangather for a quick discussion is benefi-cial. At Rockhurst University, for ex-ample, the hallways are lined withbenches; students waiting for classes tostart have a place to sit and read beforeclass, and teachers have a place to con-tinue a conversation with a student afterclass. During the design phase, keep inmind that to increase the amount ofmathematics done, one must increase theamount of interaction among its practi-tioners.

Office Space

There are a variety ofways in which mathema-ticians use their offices,which results in a varietyof opinions of how officesshould be designed. Forsome the focus is to bringstudents into faculty of-fices, while for others thegoal is to get professorsout of their offices work-ing together in a commonarea. Still others wanttheir office to be a placeof quiet repose wherework can be done. Onemust try to find a designthat can serve all of theseneeds.

Common to all is theneed for offices to be cen-trally located, ideallyaround a common studylounge. When offices areclose together, there is in-creased interactionamong faculty and moremathematics is done. Atinstitutions with a gradu-ate program, graduatestudent offices should bemixed together with fac-ulty offices. At the Univer-

sity of Michigan, offices are in clustersof five with faculty in three of the officesand graduate students filling the othertwo. This facilitates the finding of an ad-visor, increases the interaction betweenstudent and advisor, reminds advisors ofthe teaching demands on graduate stu-dents, and produces other beneficial sideeffects.

It is also important that future growthbe taken into account when planningoffice space. If the offices are centrallylocated except for one or two which wereadded later, there is a danger of depart-mental fragmentation, isolating the fac-ulty away from the central hub. (This is

How to Design a Mathematics Building

By Brian Birgen

The classroom with a group work arrangement.

The central study area at the Wartburg College Departmentof Mathematics

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particularly likely if those faculty mem-bers are shy or have the tendency to fo-cus only on their own work.) For thisreason it is a good idea to include a smallclassroom or seminar room among theoffices which could be converted into anoffice in the future.

Ideally the offices should be places whichenable both research and teaching. Thereshould be space for individual academicadvising and small group interaction, butthere also needs to be room for facultyto work on their own research topics. AtKenyon College the offices were designedwith a partition in the middle of theroom, dividing the space into a researcharea and a teaching area. This enablesfaculty to have projects in various stagesof completion and to meet with studentsin a separate area. No matter how it isaccomplished there needs to be enoughroom in the office for advising studentswithout first putting away existing re-search projects.

Classrooms

The most important factor to considerwhen designing a classroom is flexibilityof the teaching environment. The sameclassroom should work equally well fora lecture as it does for working in smallgroups. Teaching techniques are continu-ally being refined and revisited, so thisflexibility is crucial. It is best accom-plished through appropriate choice offurniture. At Wartburg College the class-rooms are equipped with small two-per-son tables which can be moved to formsquares for groups of four or can beplaced in rows for a traditional lecture.This gives faculty much more controlover the learning environment and theability to adapt the room to the needs ofthe students.

Technology should be built into theroom, yet unobtrusive. There should bea built-in projector and the ability to eas-ily connect a laptop computer to the sys-tem. Technology can add a great deal tothe teaching process, both for demon-stration and as a computation tool. How-ever, if the process for using the technol-ogy is unnecessarily complicated, facultywill be discouraged from trying newthings. The computer system in a class-

room should be quick and easy to startup and use. USB ports for easy plug-inand internet connectivity to appropriatewebsites are a must for classroom tech-nology.

Perhaps the greatest source of contro-versy for mathematicians is the split overchalkboards and markerboards. Mostmath faculty are used to teaching withchalkboards and the cost of chalk is sig-nificantly less than the cost of markers.It is much easier to use color on amarkerboard and the amount of dustproduced is significantly less. AtWartburg, we decided to create roomsthat have both: markerboards at each endand a chalkboard at the front. Due to theflexible seating, faculty can chose whichthey use by having the students turn theirtables to face one wall or another.

There are other issues which one mustattend to in order to effectively incorpo-rate technology into the classroom. Forexample, rather than center the projec-tor on the wall, it can be offset to oneside, so there is room to use a chalkboardnext to the projector screen. Even better,the projector can be aimed at amarkerboard so that the instructor candraw on what is being projected — thisis especially good for drawing flow lineson a vector field. This is an area wherecreativity and vision will continue to findnew ideas for the classroom.

Computer Labs

Even with an increased emphasis onwireless technology and laptop comput-ers, there continues to be a need for com-puter labs. They can serve as a placewhere students can access specialty soft-ware like Mathematica, Maple or Minitabor as a classroom where a professor willlead students through hands-on activi-ties; either way, they are essential. Theserooms will not have the same level offlexibility as a classroom — completerearrangement of the tables is hard withall the computers and cables in the way— but should still be capable of support-ing group work as well as lecture asneeded. Group work can be facilitated byproviding plentiful desk space for eachcomputer and raising the computermonitor so that more students can view

it at a time. Additional table space awayfrom the computer is helpful for sup-porting lectures.

At Wartburg the computer labs are fre-quently used during only a portion ofclass time. An instructor might relocateall of the students into the computer labfor the second half of the class period.For this reason each of the computer labshas a classroom next to it, with the doorsonly a few feet apart. This allows for aquick move from one room to the other,without any students getting “lost” alongthe way.

The WOW Factor

Finally, a math building needs someidentifying characteristic so that anyoneentering will immediately know that thisis not the English department. There aremany examples of details that can beadded to make for a special space thatmathematicians can call home. Mostmathematicians are familiar with thesculptures of Helaman Ferguson whichdisplay the inherent beauty of math-ematics. At Meredith College the floor ofthe atrium has a Penrose tiling which wasdesigned by two students and a facultymember. At Central College the floor hasa large sine wave down the hallway.Carleton College boasts an outdoorchalkboard where professors can relocateclass outside on especially nice days.There should be some way to identifyyour building where the mathematicianscan be found.

In summary, when designing a mathbuilding the focus should be on enablingits inhabitants to interact more readilywith each other. Learning space shouldbe flexible and technology should fit innaturally. And finally, a math buildingshould showcase the beauty and unique-ness of mathematics for the entire worldto behold.

Brian Birgen teaches at Wartburg College.He thanks Russell Goodman, Ruth Gornet,Jill Guerra, Jennifer Hontz, Thomas Hull,Sarah Merz, Gail Ratcliff, CarolSchumacher and others for their contri-butions.

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Kenneth P. Bogart, Professor of Math-ematics at Dartmouth College, died in abiking accident. He was 62. He was amember of the MAA for 40 years.Thefollowing is excerpted from the Dart-mouth College Department of Math-ematics website.

Bogart graduated from Marietta Collegein Ohio in 1965, and earned his Ph.D. inmathematics from the California Insti-tute of Techn