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FOCUS November 2004

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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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 © 2004 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

Inside4 Master of Recreational Mathematics—and Much More

An Interview with Martin GardnerBy Don Albers

8 Low Down Triple DealingBy Colm Mulcahy

10 Science Policy at the MAABy David Lutzer

12 New MathDLBy Lang Moore

13 MAA Around the World and in the ClassroomBy Joel Haack

14 The Changing Face of Calculus:First-and Second-Semester Calculus as College CoursesBy David M. Bressoud

17 First Annual Embry-Riddle Undergraduate Mathematics ConferenceBy Greg Spradlin

19 MathFest 2004

20 MathFest in Photos

22 The August 2004 Board of Governors Meeting:A Graduate Student’s PerspectiveBy Michael Lauzon

24 NSF BeatBy Sharon Cutler-Ross

25 Freshmen Can Offer Mathematical Solutions to Real-World IssuesBy Joseph Kirtland and Pau-San Hoh

26 ICME Study 16

27 Research Experiences for Minority Undergraduates:SUMMA’s National REU ProgramBy Robert E. Megginson

29 SAUM Offers On-line Guide for Assessment of Student Learning

30 Archives of American Mathematics Spotlight:The Mathematical Association of America’s RecordsBy Kristy Sorensen

31 Undergraduate Poster Session at the 2005 Joint Meetings

32 In Memoriam

34 Wisconsin’s NPrime ProjectBy Linda Thompson and Margaret Wilsman

35 Employment Opportunities

Volume 24 Issue 8

On the cover: Martin Gardner sitting on the Alice statue in Central Park. See pages 4-9 forour tribute to Gardner on the occasion of his 90th birthday. Photograph courtesy of JimGardner.

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November 2004

The National Science Foundation hasawarded the Mathematical Associationof America a Pathways Grant as part ofthe National STEM (STEM is NSF-speakfor Science, Technology, Engineering,and Mathematics) Digital Library(NSDL) Program. This four-year grantwill support the creation of a portal, TheMath Gateway, for undergraduate math-ematics materials within NSDL. Thisproject will bring together collectionswith significant mathematical contentand services of particular importance tothe delivery and use of mathematics onthe Web. The Association will use a newversion of the content management sys-tem currently supporting the Math-ematical Sciences Digital Library(MathDL) to support the portal to thesecollections and services.

The Math Gateway project is an out-growth of the Mathematical SciencesConference Group on Digital Educa-tional Resources. This group of individu-als with an interest in online mathemat-ics has met each year for the past fouryears at MAA headquarters. Many of theorganizations represented at these meet-ings will participate in the Math Gate-way. The initial participating organiza-tions/collections are listed below.

MERLOT(http://www.merlot.org) MERLOT pro-vides access toan extensivecollection ofresources andservices overmany different disciplines. FloraMcMartin of MERLOT is supervising theevaluation program for the GatewayProject.

Eisenhower National Clearinghouse(http://www.enc.org) The Eisenhower

National Clear-inghouse is ane x t e n s i v eonline resourcefor K-12 sci-ence and math

teachers. ENC is playing a central role inthe NSDL outreach to middle schools.

Math Forum(http://www.mathforum.org) The MathForum is one of the oldest online re-sources in mathematics with a particu-lar emphasis on K-12 mathematics.

iLumina(http://www.ilumina-dlib.org) TheiLumina site, hosted at the University ofNorth Carolina at Wilmington, is one ofthe oldest collections in the NSDL.

College Board(http://apcentral.collegeboard.com) Attheir AP Central site the College Boardhas a wealth of resources directed towardAP high school teachers. The Math Gate-way would link to their resources for cal-culus and statistics.

CAUSE(http://causeweb.org) The Consortiumfor the Advancement of UndergraduateStatistics Education is a project of theAmerican Statistical Association.

Demos with Positive Impact(http://mathdemos.gcsu.edu) This projectis managed by Lila Roberts of GeorgiaCollege and State University and DaveHill of Temple University. The site pro-vides teachers with demos and accom-panying information on how thesedemos might be used.

National Curve Bank(http://curvebank.calstatela.edu) This site,directed by Shirley Gray at Cal State LosAngeles, has a wide range of online math-ematical resources including an audio fileof Tom Lehrer singing New Math.

Virtual Laboratories in Probabilityand Statistics(http://www.math.uah.edu/stat)This sitewas developed by Kyle Siegrist at theUniversity of Alabama at Huntsville.

Ethnomathematics Digital Library(http://www.ethnomath.org) TheEthnomathematics Digital Library is aproject of Pacific Resources for Educa-tion and Learning. The Library has linksto relevant websites worldwide.

Duke ConnectedC u r r i c u l u mProject (http://www.math.duke.edu/educat ion/ccp)This site has online materials for lab ac-tivities for undergraduate mathematicscourses from precalculus through linearalgebra, differential equations, and en-gineering mathematics. Lang Moore andDavid Smith edit the site.

webODE ProjectThis project is just getting underwayunder the direction of Paul Blanchard atBoston University.

Eduworks(http://www.eduworks.com) The MAAand MathDL are cooperating with GeoffCollier and Robby Robson of Eduworkson their NSDL project to improveinteroperability and reusability.

WeBWork(http://webwork.math.rochester.edu)WeBWork, founded by Arnie Pizer andMike Gage of Rochester, is one of themost useful online homework systemsfor mathematics. MathDL will providesome services for WeBWork.

Some of these collections include mate-rials related to many disciplines. In thatcase, the Math Gateway will only link tothe mathematics items.

The new grant will support the publica-tion of a regular Math in the News col-umn on the Math Gateway portal. Inaddition to support of the portal, the newgrant will provide resources for the con-tinuing support of MathDL. Perhaps themost important of these will be funds toenable the hiring of a full-time web mas-ter to support both MathDL and theMath Gateway. The grant also will sup-port an extensive system of workshopsat the section meetings of the MAA toencourage the mathematical public toexplore the learning opportunities af-forded by The Math Gateway and, moregenerally, by the NSDL.

Math Gateway: An NSDL Pathway to Undergraduate Mathematics

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FOCUS November 2004

On October 21, Martin Gardner cel-ebrated his ninetieth birthday. For 25 ofhis 90 years, Gardner wrote the monthly“Mathematical Games “ column for Sci-entific American. His columns have in-spired thousands of readers to learnmore about the mathematics that heloved to explore and explain. Among hiscolumn correspondents were several dis-tinguished mathematicians and scien-tists, including John Horton Conway,Persi Diaconis, Ron Graham, DouglasHofstadter, Richard Guy, Don Knuth, SolGolomb, and Roger Penrose.

Gardner’s columns have earned him aplace of honor in the mathematical com-munity, which has given him manyawards. But he has always declined invi-

tations to accept awards in person, on thegrounds that he is not a mathematician.“I’m strictly a journalist,” he insists. “Ijust write about what other people aredoing in the field.” His modesty is admi-rable, but we insist that he is far morethan a journalist.

In addition to his massive contributionsto mathematics, Gardner has writtenabout magic, philosophy, literature, andpseudoscience. Over his first ninety years,

he has produced more than 60 books,most still in print; many have beenbestsellers. His Annotated Alice has soldover a million copies, and the 15 volumescollecting his “Mathematical Games”columns have gone through severalprintings. All 15 volumes have been digi-tized and will soon be published by theMAA on a single CD entitled MartinGardner’s Mathematical Games.

In his ninetieth year, he has returned toOklahoma, where he was born. He is ingood health and full of energy. We lookforward to more from him as he beginshis second 90 years. What follows is asmall portion of an interview done atGardner’s home in Hendersonville, NCin the fall of 1990 and spring of 1991.

Don Albers: As a high school student youwere already writing articles for TheSphinx, a magazine devoted to magic.Does your interest in magic go back toyour father?

Martin Gardner: Magic wasn’t a specialhobby of his, but he did show me somemagic tricks when I was a little boy. Ilearned my first tricks from him, in par-ticular one with a knife and little piecesof paper on it. I then got acquainted with

a few local magicians in Tulsa, LoganWaite and Wabash Hughes, who workedfor the Wabash Railroad.

DA: At what age did this occur?

MG: I was a high school student at thetime. I’ve never performed magic; it’s justbeen a hobby. The only time I got paidfor doing magic was when I was a stu-dent at The University of Chicago; I usedto work at the Marshall Field’s depart-ment store during the Christmas seasondemonstrating Gilbert magic sets. Ilearned a lot from the experience. Thatwas the first time I realized that you’rereally not doing a magic trick well untilyou’ve done it in front of an audience

about a hundred times. Then it becomessecond nature, and you know what to say.

DA: What are the elements of a success-ful magic trick?

MG: The most important thing is tostartle people, and have them wonderhow it’s done. Close-up magic that youdo on a table right in front of people isvery different from the stage illusionsthat David Copperfield does. It’s close-up magic that most intrigues me, espe-

Master of Recreational Mathematics — and Much More

An Interview with Martin Gardner

By Don Albers

Martin and his younger brotherJim, 1920.

Martin at age 10, 1925.Martin reading on his front porch at age15, 1929

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cially when it has a mathematical flavor.I did a book on mathematical tricks thathas, for example, a chapter on topologi-cal tricks. I did two massive books for themagic profession: The Encyclopedia ofImpromptu Magic and Martin GardnerPresents. The first book covers tricks thatdon’t require any special equipment. Alot of them are just jokes and gags of thetype ‘bet you can’t do this.’

DA: Your book Mathematics, Magic, andMystery has been a bestseller for manyyears.

MG: I waste a lot of time on magic. DaiVernon was one of the great inventors ofmagic. He was a great influence on PersiDiaconis. Persi traveled with Dai for along time. I knew Vernon very well. Iknew Persi when he was a student atNYU. You probably heard the story howhe got into Harvard.

DA: As I recall, he gave you some creditfor writing a letter of recommendationto Fred Mosteller, the Harvard statisti-cian.

MG: Mosteller is a magic buff. WhenPersi said he wanted to get into Harvard,I wrote to Fred and said that Persi cando the best bottom deal and second dealof anybody I know, and that got him intoHarvard. I talked to Fred on the phoneabout it and he said, “Is he willing tomajor in statistics?” And Persi said surehe’d major in statistics if that would gethim into Harvard. So he went up toHarvard, and they had a session together,maybe doing card tricks. Mosteller gothim into Harvard.

DA: What did your mother do?

MG: She was a kindergarten teacher be-fore marriage, but then became a house-wife, caring for three children. Her hobbywas painting, and I have a number of herpaintings hanging in the house. Both ofmy parents lived into their nineties. I hada brother and sister, both younger, whoare deceased.

I learned to read before I went to school.My mother read The Wizard of Oz to mewhen I was a little boy, and I looked overher shoulder as she read it. I learned how

to read that way. It was very embarrass-ing when I was in first grade, because theteacher would hold up cards that said ‘cat’and ‘dog’ and I was always the first to callout the word. She had to tell me to shut

up, to give the other children a chance tolearn how to read.

DA: As a kid, do you remember otherstrong interests in addition to magic?

MG: I was very good at math in highschool. In fact, it and physics were theonly subjects in which I got good grades.I was bored to death by the other classes.I flunked a class in Latin and had to takeit over. I just don’t have a good ear forlanguages.

DA: You got your B.A. in 1936, thenworked briefly for the Tulsa Tribune as areporter, and then came back to TheUniversity of Chicago to the PR officewriting news releases (primarily sciencereleases), and took a graduate coursefrom Carnap. What else did you do untilthe outbreak of World War II?

MG: I had various jobs. I worked as a caseworker for the Chicago Relief Adminis-tration, I had to visit 140 families regu-larly in what was called the Black Belt. Ialso had several odd jobs: waiter, sodajerk, etc. Remember, this was at theheight of the Great Depression.

DA: In December of 1941, the U.S. en-tered World War II and you enlisted inthe Navy.

MG: I ended up serving on DE 134, adestroyer escort, in the Atlantic. I wasmiserably seasick for about three days,and then I was never seasick again. Icouldn’t wait for the war to end, but laterI looked back at it as a rather pleasurabletime of my life. You’re on a ship, youmake friends with your shipmates, yougot liberties now and then, and you didn’thave to worry about anything.

I’ve had migraine headaches all my lifethat were fairly severe when I was in highschool. When I enlisted in the Navy, I didnot list my migraines because I was afraidthey wouldn’t take me. I feared that Imight develop migraine headaches dur-ing battle situations. We were part of aso-called “killer group” of six destroyerslooking for German submarines. Duringmy four years in the Navy, I never had amigraine headache. I’m convinced thatthey’re associated with periods of anxi-ety. When you’re in the Navy, you don’tworry about what you’re going to do to-morrow, what tie to put on, etc. You justfollow orders. In a way, you have a bigsense of freedom. Otherwise, I have noother explanation.

Martin Gardner with the Mad Hatter inCentral Park, New York City.

Gardner as a navy sailor, 1941.Gardner as a navy sailor, 1941.

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FOCUS November 2004

DA: At the end of the war, you promptlywent back to Chicago.

MG: Yes, I went back, and I could havehad my old job back in the public rela-tions office at The University of Chicagobecause there was an understanding thatif you enlisted in the service you couldget your old job back. But the one rea-son I didn’t go back to the PR office wasthat I sold a story, my first sale, to Es-quire. The title of the story, “The Horseon the Escalator,” came from a joke go-ing around at the time about a man whoentered Marshall Fields department storeon a horse, and the elevator operator toldhim he couldn’t take the horse on the el-evator. And he said, “But lady, he gets sickon the escalator!” It was a shaggy dog jokeabout a horse. The story is about a manwho collected horse jokes, and his wifedidn’t think any of them were funny, butshe laughed heartily every time he toldone to conceal the fact. So that was myfirst story. I decided that maybe I couldmake a living as a freelance writer, and Ivery quickly sold Esquire a second story,and that was the “No-Sided Professor,”about topology.

DA: That had to give you a lot of confi-dence, helping to convince you that youcould earn a living as a writer.

MG: That’s right, but Esquire changededitors after I had sold them several sto-ries. The new editor had a differentpolicy, and he didn’t care for the kind ofstories I was writing. So I moved to New

York City, because for writers that’swhere all the action is. I had a friend whoworked for Parents’ Institute, and whowas in charge of their periodicals for chil-dren. They were starting a new magazinecalled Humpty Dumpty, and were look-ing for activity features, where you foldthe page or stick something through thepage, or cut; where you destroy the page.So he hired me to do the activity featuresfor Humpty Dumpty, as well as a shortstory for every issue and a poem of moraladvice.

DA: Your work with children’s magazineswent up to about 1956. By 1957 you wereat Scientific American. So there was notmuch of a hiatus between HumptyDumpty and Scientific American.

MG: No, I stopped working for HumptyDumpty to start “Mathematical Games”at Scientific American. I couldn’t do both.It started with the sale in December 1956,of an article on Hexaflexagons. That wasnot a column, but that led to the column.When Gerry Piel, the publisher of Scien-tific American, called me and suggestedthe column. That was when I resignedfrom Parents.

DA: A lot of people are astonished thatanybody could turn out one of those col-umns on mathematical games and rec-reations every single month for ScientificAmerican.

MG: Perhaps they don’t realize I had noother job. I’m not a professional math-

ematician who has to teach a course inmathematics, and then write. To me, it’shard to imagine how a professionalmathematician would have time to evenwrite a book. I had nothing else to do,except research for those columns, andwrite them up.

DA: Most people that I’ve ever talked toabout your Scientific American columnsknow that it was your job, but they’re stillawed by the fact that you turned outsomething really sparkling every month.It’s one thing to write something everymonth, but that doesn’t mean that it’sgoing to be inspirational or great fun toread each time.

MG: I miss doing those columns, theywere a lot of fun, and I met many fasci-nating people while doing them. Oncethe column got started I began hearingfrom people like Sol Golomb and JohnConway, who were really doing creativework that had a recreational flavor. Thatkept the column going. It became muchmore interesting after I began gettingfeedback from people like Conway, RonGraham, Don Knuth, and many others.

Probably my most famous column wasthe one in which I introduced Conway’sgame of Life. Conway had no idea whenhe showed it to me that it was going totake off the way it did. He came out on avisit, and he asked me if I had a Go board.I did have one, and we played Life on theGo board. He had about 50 other thingsto talk about besides that. I thought that

Gardner with his wife Charlotte, andtheir two sons Jim, left, and Tom.

Martin and grandson Martin.Martin Gardner with his brother Jim andsister Judith.

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Life was wonderful — a fasci-nating computer game. When Idid the first column on Life, itreally took off. There was evenan article in Time magazineabout it.

DA: Can you tell me a little bitmore about how you actuallyapproach writing? You previ-ously said something about howyou did your monthly columnsover a long period of time. Youwrite about many other thingsas well. Do you have a differentstyle or a different mode whenyou write about pseudoscience?

MG: I don’t think so. I’ve neverworried about style. I just write asclearly as I can, and I suppose it’simproved over the years. I get in-terested in a topic, and I do asmuch research as I can on it. I havemy library of working tools, so Ican do a lot of research right here.I usually rough out the topic first,just list all the things that I have tosay, and then I sit down and try toput it together on the typewriter.It’s all kind of a sequence that ishard to explain. It comes easy forme, I enjoy writing and I don’t suf-fer from writer’s block, where I sitand wonder for an hour how I’mgoing to phrase the opening sen-tence.

DA: Which of your more than sixtybooks is in some sense a favorite?

MG: I think my Whys of a Philo-sophical Scrivener is my favorite be-cause it is a detailed account of ev-erything I believe.

DA: Let’s move back to math for aminute. You’ve lived long enough now tosee a lot of really interesting mathemati-cal ideas hit the scene, and there are alsosome really beautiful ideas that were herelong before you were on the scene. First,during your own lifetime, what ideas,what discoveries just kind of knockedyour socks off?

MG: Well, I think the most interesting de-velopments are mainly in mathematical

physics, and in particular the develop-ment of superstring theory. That cameas a complete surprise to me. It’s a beau-tiful theory of particles, and it may ormay not be true, but it’s the hottest thingin town now in particle physics. It opensup the possibility that higher dimensionsare not just artifacts but actually real.

DA: You’ve read a lot of contem-porary material, and you’ve reada lot by those who have beengone a long time. Are there anyof those departed people thatyou’d like to sit down with overdinner, or sit down here in yourlibrary and chat with them?

MG: I’d love to chat with Gödelfor example. He had somestrange cosmological views, andI’d like to talk to him about that,about time travel into the past. Inever could quite understandthat. And of course he was adedicated Platonist. He thoughtall of mathematics was outthere, including the transfinitenumbers. I’d enjoy talking tohim about that. Of course I’dlove to talk with Einstein andNeils Bohr. Among puzzle mak-ers, I’d most want to talk withHenry Dudeney and Sam Loyd.I also would enjoy talking toBertrand Russell. He’s one ofmy heroes.

DA: Here’s an equally easy ques-tion for you. Once you’ve de-parted this life, let’s suppose youhad an opportunity to comeback in a hundred years. Whatquestions would you most wantto know the answers to thatmight have been developedduring that time?

MG: I guess I’d be interested toknow if various famous un-solved problems had beensolved, such as the GoldbachConjecture. But I don’t have anygreat desire to come back andlearn what modern mathemat-ics is up to. You’re giving me

credit for being more of a mathemati-cian than I really am. I’m strictly a jour-nalist. I just write about what otherpeople are doing in the field.

Thanks to Jim Gardner for supplying thephotos that accompany this interview.

Gardner doing some table magic

Martin Gardner’s form letter, often sent as a response to re-quests he received from readers.

Martin Gardner regrets that it is impossible for him to:

1. Evaluate:

Angle trisections

Circle squarings

Proofs of Fermat’s last theorem

Proofs of the four-color theorem

Roulette systems

2. Give advice on, or supply references for,

high school science or math projects.

3. Inscribe books for strangers.

4. Give lectures, or appear on radio or TV shows.

5. Attend cocktail parties.

6. Make trips to Manhattan except under

extreme provocation.

7. Donate books to libraries.

8. Provide answers to old puzzles.

9. Prepare material on speculation for toy

companies or advertising agencies.

10. Put the reader in touch with Dr. Matrix.

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Consider the following three demon-strations of mathemagic:

1. A deck of cards is handed to a specta-tor, who is invited to shuffle freely. She isasked to call out her favourite ice-creamflavour; let’s suppose she says, “Choco-late.” Next, she is asked to cut off about aquarter of the deck and hold it ready fordealing. You take another quarter of thedeck and demonstrate a spelling deal,dealing cards into a pile, one for each let-ter in the word “chocolate,” before drop-ping the rest of your quarter deck on top.Set those cards aside and have the spec-tator perform this spelling routine threetimes with the cards in her hands. Youcorrectly name the top card in her pile atthe conclusion of her triple dealing.

2. A deck of cards is handed to two spec-tators, each of whom is invited to shuffleat will and then choose a card (of not toolow a value) and place it face up on thetable. Let’s suppose that 4♣ and 9❤ areselected and displayed. You run throughthe deck face up, tossing out all of theAces, 2s and 3s — saying, “Sorry, I shouldhave eliminated the low cards earlier.”Then riffle shuffle a few times. Remark,“Since a 9 was selected, let’s count outnine cards,” dealing into a pile on thetable. Shuffle overhand and continue,“We’ll need four more,” as you peel offthat many cards as a single unit, withoutchanging their order. Drop these on topof the other nine. (The rest of the deck isignored from now on.) Pick up this pileof thirteen cards and demonstrate a dealof the nine top cards into a pile, revers-ing their order, and then putting the re-maining four on top. Have the first spec-tator do this deal three more times, andhand the cards to the second spectator.Have the second volunteer deal eitherfour or nine cards into a pile, with theremainder placed beside this to form asecond pile. Recap: the two numbers (4and 9) being used were determined byfreely selected cards, and as a result a dealof nine cards was performed done (three

times) on a packet of thirteen cards,which was then split into two piles. Drawattention to the two cards originally se-lected. Say, “Wouldn’t it be surprising if,after all that triple dealing based on thevalues of two randomly selected cardsfrom a shuffled deck, there were cardsintimately related to the two you selectedat the bottoms of the two piles now onthe table?” Have the piles on the tableturned over: one of the cards exposed is9♣ and the other is 4❤. “A curious align-ment with the selected cards.”

3. Have each of three volunteers in turnpick a card at random, and then have thecards returned to anywhere in the deck.Shuffle with abandon. Ask a fourth per-son to name their favourite magician.Assume they say, “Harry Houdini.” Holdthe deck in the right hand, and peel cardsoff the bottom into a pile in the left hand,without altering their order, one for eachletter, as you spell out the whole name.Hand the stack of twelve cards to the firstvolunteer and ask him to spell outHOUDINI while dealing out seven cards,then dropping the other five on top. Nowgive the cards to the second volunteerand give the same directions, and finallyto the third volunteer for one last deal ofthe same type. Take the cards behindyour back and immediately producethree cards, handing one to each volun-teer face down. Have the chosen cardsnamed, as they are turned over, to revealthat you have correctly located each one.

The same purely mathematical principleunderlies each of these demonstrations,with a little more magic thrown in forgood effect as we progress to the secondand third tricks. We gradually reveal thisprinciple below, and discuss how each ofthe tricks is done as we go, before finallyexplaining why the principle works.

Let’s start with the first effect. There aretwo secrets working behind the scenes foryou here: an unadvertised but importantrelationship between the length of the

word being spelled out and the size ofthe “quarter deck” which the spectatorstarts with, and the fact that you mustsomehow know the identity of one cardin the spectator’s hand from the begin-ning! It should come as no surprise thatthe card in question is the bottom card:asking the spectator to hold the cards inher hand in preparation for the spellingis just to give you an added opportunityto peek at this card, if you haven’t alreadydone that as she completed her shuffling.You must do whatever it takes to discoverthat card’s identity!

This is the scoop on the ice cream trick:

Claim 1: Start with n cards, the bottomone of which is known. If k cards are dealtout into a pile, thus reversing their or-der, and the remaining n – k cards aredropped on top as a unit, and this typeof deal is repeated twice more, then theknown card rises like cream to the top— provided that n ≤ 2k.

In the case of the nine-letter wordCHOCOLATE, the trick works providedthat the portion of the deck selected bythe volunteer contains at most eighteencards. If MINT CHOCOLATE CHIP(seventeen letters) is named, you’ll askfor between a third and half of the deck.(If RUM is selected, try to force RUMRAISIN!)

The triple deal described is actually 75%of a rather interesting quadruple deal.This is the real scoop:

Claim 2: Start with n cards, and assumethat n ≤ 2k ≤ 2n. If k cards are dealt outinto a pile, thus reversing their order, andthe remaining n – k cards are droppedon top as a unit, and this deal is repeatedthree more times, the entire packet of ncards is restored to its original order.

Now consider the second effect above.Two cards (not Aces, 2s or 3s) are chosenand set aside face up. Let’s suppose they

Low Down Triple Dealing

By Colm Mulcahy

Dedicated to Martin Gardner on the occasion of his 90th birthday

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November 2004

are 4♣ and 9❤. As you run through thedeck face up, ostensibly to toss out thelow valued cards, what you really focuson doing is cutting the 9♣ and 4❤ to thetop and bottom respectively. They willstay there if you arecareful how youriffle shuffle. Con-tinue as describedearlier: reversingnine cards into a pileand then doingsome overhandshuffling whosepurpose is to bringthe bottom card tothe top. Peel fourmore off the topwithout reversingthem and drop ontop of the othernine. You now havethirteen cards withthe desired twocards at the top andbottom of thatpacket. Your subse-quent demonstra-tion of dealing nineand dropping four isjust the first of a series of four deals: thefirst spectator does the next three deals,thereby restoring the packet to its initialstate. The second spectator deals (eitherfour or nine) cards into a pile and thenthere are two piles on the table with oneof the desired cards at the bottom of eachpile. You are all set for the grand finale.

The third effect uses the fact that afterthree deals of the type described, not onlydoes the bottom card rise to the top, thenext to last card becomes the second cardfrom the top, the one above that becomesthe third card, and so on:

This is the real triple scoop:

Claim 3: If k cards from n cards are dealtout into a pile, reversing their order, andthe remaining n – k are dropped on topas a unit, and this process is repeatedtwice more, then provided that n ≥ k ≥n/2, the original k bottom cards becomethe top k cards, in reverse order.

To perform the third trick, ask each ofthree volunteers to pick a card at random.

Have these cards returned, one at a time,to the deck and then control them to thebottom — this means that you appear toallow free choice of where to put thecards, but you actually use elementary

magic techniques (e.g., double cuts) toget each card to the bottom. As a result,the third volunteer’s card is at the bot-tom of the deck, the second volunteer’scard is one up from the bottom, and thefirst volunteer’s card is two up from thebottom. Peel cards off the bottom of thedeck — without altering their order —one for each letter of the name of themagician called out, as you spell out bothwords in full. Hand the resulting packetof cards to the first volunteer and ask thatthe longer of the two names (HOUDINIin our example) be spelled out as cardsare dealt into a pile, before dropping theremainder on top. Now give the cards tothe second volunteer and finally to thethird volunteer for two more deals. Thethree chosen cards are now on the topof the packet of cards, with the order re-versed, and you are all set to conclude intriumph.

Why are all of the above claims valid forany n and k with n ≤ 2k ≤ 2n? It’s cer-tainly easy to see if n = k (reversing all ofthe cards each time), and almost as easyto see if n = 2k (reversing exactly half of

the cards). Actually, it’s easy to see in allcases: Suppose for the sake of concrete-ness that n = 13 and k = 8. Let’s agree torepresent a pile of thirteen cards in a par-ticular order by a sequence of gray-scale

panels in decreasingorder of brightness,from white for thetop card to black forthe bottom card, asdepicted in the im-age.

Then the results ofthe four deals — eachof eight cards into apile with the otherfive dropped on top— is given by the suc-cessive images in thepictures.

Since the last imageshows a fully restoredpile, the deal in ques-tion has period 4: af-ter four deals we arealways back to wherewe started. Afterthree such deals, the

original bottom card (black) has risen tothe top — in preparation for its finaljourney back to the bottom under onemore deal. Moreover, it is clear that theeight bottom cards become the eight topcards, suitably reversed, after three deals.There are just three portions of the packet— of sizes 5, 3 and 5 here — to keep trackof: and they move around intact, subjectat most to some internal reversals. Theonly relationship between 13 and 8 whichis needed to make this sequence of im-ages totally generalizable is the fact that8 ≥ 13/2.

Finally, we suggest that during all deal-ing the cards are held low, close to thetable, so as to justify fully the title of thisarticle.

Colm Mulcahy (colm@spelman.edu) hastaught at Spelman College since 1988. Heis currently the chair of the department ofmathematics there. The number of syl-lables in his first name is strictly between 1and 2. He is a member of the FOCUS edi-torial board and will be contributing aregular “Card Colm” to FOCUS Online.

Proof Without Words

10

FOCUS November 2004

Science Policy at the MAA

By David Lutzer

Many MAA members might not real-ize that MAA is involved in national sci-ence policy — but it is. Presenting adiscipline’s perspectives on researchfunding issues to national policy mak-ers has long been an activity of profes-sional organizations. See, for example,the governmental affairs sections of theweb pages of the American Institute ofPhysics, the American Chemical Society,the Society for Industrial and AppliedMathematics, and the American Math-ematical Society. But Washington deci-sions can also affect undergraduate math-ematics, which is among MAA’s mostcentral interests. Consequently the jobsof the MAA President and the MAA Ex-ecutive Director include presentingMAA policy perspectives on pendingfederal decisions with undergraduateramifications.

Where do MAA’s science policy positionscome from? According to the MAA by-laws, only the MAA President and Ex-ecutive Director may speak for MAA onscience policy issues. The Board of Gov-ernors can be influential in shaping MAAscience policy, and the MAA also has aScience Policy Committee (SPC) whosecharge is to assist the Association “inanticipating, responding to, and initiat-ing changes in the educational, the finan-cial, and the policy environments thatmay impact the work of the MAA andits members.” (To see some of what SPChas traditionally done, go to the MAAhome page at http://www.maa.org andthen choose “Science and ProfessionalPolicy” within the “Special Groups” pull-down menu.)

The MAA President and Executive Di-rector are both ex officio members of SPCand can seek committee advice wheneverthe need arises. For example, some yearsago the SPC formulated talking pointsthat the MAA President and ExecutiveDirector could use in case they wereasked for comment on what seemed tobe a controversial educational proposalfrom the White House. Perhaps the mostimportant SPC action in recent years was

to recommend that MAA engage the ser-vices of a professional government rela-tions firm. The Board of Governorsagreed, and the firm of Lewis-Burke As-sociates (LBA) was chosen.

Among LBA’s first activities on behalf ofMAA was to organize a two-day Wash-ington meeting of the Science PolicyCommittee on March 22 and 23 of thisyear. The purpose of the meeting was toget SPC members to meet with congres-sional and executive branch officials, topresent MAA’s positions on several sci-ence funding issues in person. On Mon-day, March 22, the SPC met senior staffmembers of the National Science Foun-dation (NSF) and the Office of Manage-ment and Budget (OMB), the goal wasto prepare committee members for meet-ings with congressional staffers, sched-uled on Tuesday.

Monday’s meetings included extendeddiscussions with David Radzanowskiwho is in charge of Science and SpacePrograms in the White House OMB; withRosemary Haggett, Director of the NSFDivision of Undergraduate Education;and with Bill Rundell, Director of theNSF Division of Mathematical Sciences.Both Joel Widder (of Lewis-Burke) andDavid Radzanowski (of OMB) made itclear that budget times will be very bleakin the near future. The NSF visitorsbriefed SPC on the programs in their di-rectorates that contribute to under-graduate mathematical education. BothNSF visitors agreed with Radzanowski’sprediction of lean budgets for the nextfew years and recently an important con-gressional appropriations subcommitteehas proposed a 2% budget cut for NSFin the 2005 fiscal year, confirmingRadzanowski’s gloomy predictions.

In addition, the SPC spent a consider-able amount of time trying to under-stand the intricacies of an administrationproposal to move NSF’s Mathematicsand Sciences Partnerships (MSP) pro-gram from NSF to the Department ofEducation, where it would be consoli-

dated with a second MSP program al-ready in the Education Department. Asexplained below, the MAA opposes thisproposed shift.

At the end of the day on Monday, SPCworked with Lewis-Burke Associatesstaff to formulate a page of talkingpoints. Themes were taken from sched-uled congressional testimony of MAAPresident Ron Graham (see pages 21–22in the May/June 2004 issue of FOCUS)and reflected the day’s conversationswith NSF and OMB officials. A copy ofthe talking points page was left with eachstaff member visited on Tuesday and isavailable on the SPC website, mentionedabove. The talking points focused onmathematics as a cornerstone of thenation’s technical workforce preparationprogram, currently a hot issue in Wash-ington. They urged Congress to reverseprevious years’ declines in the budget ofthe NSF Division of Undergraduate Edu-cation, one of two NSF divisions thatsupport undergraduate mathematics,and called for increased support for theVIGRE and REU programs in the NSFDivision of Mathematical Sciences be-cause of their importance to under-graduate mathematics. The talkingpoints also argued that the NSF Mathand Sciences Partnership Programshould not be shifted to the Departmentof Education, because, to quote PresidentGraham’s congressional testimony,

The MAA believes that if transferred to theDepartment [of Education], MSP fundswill likely be distributed via block grants,which could spread the money too thinlyto do any real good and which will, in alllikelihood, result in much of the fundingbeing redirected at the state level to pro-grams outside the scope of MSP’s originalintent.

On Tuesday, after some SPC membersvisited the offices of their own senatorsand representatives, SPC met as a groupwith Jeff Smith who is the senior adviserto Senate Minority Leader Daschle onscience policy; with Kara Haas and Jim

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November 2004

Wilson from the staff of the House Sci-ence Committee; with Tracy Locklin ofthe Senate Health and Labor committee;and with Jennifer Miller of the House VA,HUD and Independent Agencies Appro-priations Subcommittee. (In spite of itsname, the Senate Health and LaborCommittee is the authorizing commit-tee for both the NSF and for the Depart-ment of Education, and the House VA,HUD and Independent Agencies Com-mittee is the appropriations committeein charge of NSF.) With small variations,the message to each was (a) that, usingrelatively small expenditures, NSF hasbeen very effective in focusing nation-wide efforts of college and universitymathematicians on several importantundergraduate issues and in fosteringeducational improvement in the U.S.,and (b) that relatively small additionalallocations in the 2005 budget (now inthe planning stage) would yield a lot of

“bang for the buck” in terms of enhanc-ing the nation’s scientific and technicalworkforce preparation effort. We hadbeen warned that “Washington runs onanecdotes” and so we did our best towrap our messages in stories from ourpersonal experiences with undergradu-ates and undergraduate teaching.

Everyone with whom the SPC met wascourteous and many were enthusiasticabout the issues that we presented. Whilesome SPC members had never visited theoffices of a congressman or senator be-fore, by the end of the day, all of us feltthat presenting MAA’s perspectives “onthe Hill” was something we could confi-dently and comfortably do.

While members of SPC and the Lewis-Burke staff were pleased with the effortslaunched in March 2004, all agreed thatthis cannot be a one-time effort. The

multi-year task will be to build linkageswith congressional staffers and federalagency program officials who will cometo understand MAA’s science policy po-sitions, and to call upon MAA represen-tatives for advice on issues related to un-dergraduate mathematical education. Ifyou want to help in this effort, pleasecontact MAA Secretary Martha Siegel(msiegel@towson.edu) to volunteer forappointment to the SPC.

David Lutzer is Professor of Mathematicsat the College of William and Mary. Hechairs the MAA Science Policy Commit-tee, is a member of MAA’s Committee onthe Profession, and is a member of theJoint Policy Board for Mathematics(JPBM). He also headed the CBMS2000national survey of the undergraduatemathematical sciences. His website is athttp://www.math.wm.edu/~lutzer.

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FOCUS November 2004

By Lang Moore

New MathDL

The MAA’s Mathematical Sciences Digi-tal Library (MathDL) has a new home, anew look, new material, and many forth-coming new features. In August, theMAA began publishing the three com-ponents of MathDL, The Journal ofOnline Mathematics and its Applications(JOMA), Digital Classroom Resources(DCR), and Convergence, using a newcontent management system. The site isnow housed at MAA Headquarters andmaintained by the MAA. The web ad-dress has not changed: MathDL may stillbe accessed at http://www.mathdl.org.

Work on MathDL began in the Fall of2000 under a National Science Founda-tion grant in the National STEM(STEMstands for Science, Technology, Engineer-ing, and Mathematics) Digital Library(NSDL) Program (see http://www.nsdl.org). MathDL was one of thefirst of over 171 projects supported bythe NSDL program. MathDL debuted inJanuary 2001 with the first issue ofJOMA. It was hosted by the Math Forumuntil August of 2004.

All articles and other materials submit-ted to JOMA are peer-reviewed. Since thefirst year, JOMA has been published con-tinuously as accepted materials are readyto be posted. Each volume after Volume1 represents a calendar year without sub-division into issues.

JOMA takes full advantage of the Webas a publication medium. Its materialscontain dynamic, full-color graphics; in-ternal and external hyperlinks to relatedresources; applets in Java, Flash,Shockwave, or other languages; MathML,SVG, and other XML markups; audioand video clips; and other Web-basedfeatures. David Smith, founding editorof JOMA, will retire from the editorshipat the end of this calendar year. A searchis currently underway for his replace-ment.

The Digital Classroom Resources (DCR)library is an exemplary collection of free

online learning materials. All materialshave been classroom tested and peer re-viewed. DCR provides instructors witha set of tools ready for implementationin an existing curriculum as well as anongoing forum for discussion of the is-sues surrounding the materials and theiruses. Within this community, the libraryalso provides a snapshot of trends andthoughts on issues relevant to the use oftechnology in mathematics teaching andlearning. Learning materials in DCR in-clude (but are not limited to): interac-tive web pages; web pages enhanced withanimation or streaming video; down-loadable programs that run indepen-dently of the web or web browser; andmodules developed for commercial com-puter algebra systems. Doug Ensley, thefounding editor of DCR, continues as thecurrent editor.

Convergence, the newest component ofMathDL, first appeared last April. Thisonline magazine focuses on the use of thehistory of mathematics in teachingmathematics. The magazine, also fundedby an NSF grant, features articles, re-views, “Today’s Quotation,” a “problemfrom another time,” and “on this day.”Editors Victor Katz and Frank Swetz havecreated an online magazine that is bothenjoyable and instructive.

The next component of MathDL to comeonline will be OSSLETS — Open SourceSharable Mathlets. OSSLETS will featureshort interactive online materials that arescientifically and pedagogically soundand that can be easily reused orrepurposed. In addition, many of thesematerials can produce output that is eas-ily cut-and-pasted into a spreadsheet ora computer algebra system. The proto-type OSSLETS, called Lite Applets, wasdesigned by a group headed by FrankWattenberg and funded by a supplementto the MathDL grant. These first appletswere reported on in the article LiteApplets by Frank Wattenberg, BartStewart, and Suzanne Alejandre which

appeared in Volume 2 of JOMA.

The OSSLET site will feature mathletsthat satisfy the following criteria: themathlet and its source code are availablefor reuse; two examples of use of themathlet are given; a discussion of how

to work with the mathlet is included. Allmathlets published in OSSLETS, will bereviewed and approved by an editorialboard directed by OSSLETS Editor,Frank Wattenberg.

Early in 2005, two additional compo-nents, MAA Reviews and Online Class-room Capsules, will appear. MAA Reviewswill be the online successor to the Tele-graphic Reviews that, until recently, ap-peared in The American MathematicalMonthly. Fernando Gouvêa will edit thissection of MathDL. The reviews will besimilar to the ones that currently appearin the Briefly Noted section of Read This!,the MAA’s online book review column.In addition to brief reviews, the site willfeature longer reviews of selected books,a complete searchable database of booksreceived, and a regularly updated BasicLibrary List.

Classroom Capsules will bring togetherthe best of 111 years of the short class-room materials from the MAA printpublications. It will be easily searched bytopic, author, and student level. WayneRoberts, the editor of Classroom Cap-sules, is currently assembling an edito-rial board.

The Committee on Programs in Math-ematics is developing a successor to theircurrent Illustrative Resources site at http://www.maa.org/cupm/illres_refs.html. Thenew component of MathDL will replacethe current site and will continue to benamed Illustrative Resources. DavidBressoud and Susanna Epp will be co-editors. CUPM is currently seeking fund-

ing to support this site development.

In addition, MathDL has been develop-ing software to support online meetingsand workshops. Andrew Schretter ofDuke has done the development work.A preliminary version of the software wasused by Lang Moore, David Smith, andFrank Wattenberg to support their 2003online PREP workshop, AuthoringOnline Interactive Materials in Math-ematics. Information on how to use thissoftware for committee meetings, work-shops, and similar activities will be avail-able soon.

FOCUS

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November 2004

My academictraining was as aring theorist. Fol-lowing a stint inadministration, Ihave inherited thehistory of math-ematics courses atmy institution.Consequently, theprofessional devel-opment that I haveexperienced andenjoyed throughthe first two MAAmathematics studytours has been sig-nificant.

With respect to my teaching, I have beenable to use information learned on theGreece and England trips in my class-room in many ways that make the sub-ject more present for the students. Forjust a few examples, I have been able toshare photographs of Miletus and Samos,making Thales and Pythagoras comealive for the students. At the office of theEuropean Cultural Center of Delphi, wehad the opportunity to hear and play areconstruction of an ancient hydraulicorgan, discussed in one of Heron ofAlexandria’s works; the CD and accom-panying booklet have let me share someof this experience with my class as well.I can describe the reflecting telescope thatIsaac Newton presented to the Royal So-ciety, having had the chance to see a rep-lica at the Royal Society in London. Ourvisit to Bletchley Park will allow me toshare the story of Alan Turing’s life withan immediacy that would otherwise notbe possible.

Finally, I am now responsible for a courseentitled Science, Mathematics, and Tech-nology in the Americas. Next year’s MAAstudy tour to Mexico to study the Mayancivilization will be a significant learningopportunity for me. But, perhaps sur-prisingly, last year’s trip to England addsto this class as well, as we include a dis-cussion of “What is science?” that is made

tangible by information and photo-graphs about the development of sciencefrom the Royal Society and the BritishMuseum.

This year, I will make a number of pre-sentations that have been enriched by theMAA tours. Together with a colleaguefrom acoustics, I will make several pre-sentations describing the use of theHenrici harmonic analyzer, a hundred-year-old tool used to find Fourier coeffi-cients. While I first learned of this de-vice at the MAA’s pre-conference work-shop on Mathematical Technologies, Ihad the chance to view an early model inthe Science Museum of London, where Icould also see Lord Kelvin’s much moremassive harmonic analyzer. Anotherpresentation, to the secondary math-ematics teachers of Iowa, will be basedon what I learned about Thomas Harriotin a lecture Jackie Stedall delivered to ourgroup in London.

Space limitations here keep me from ex-tolling additional professional opportu-nities on the tours: discussing mathemat-ics education with Greek and Englishcolleagues, viewing an impressive math-ematics exhibit in Athens and an exhibitof JMW Turner’s lectures on perspectivein London, and developing professionalfriendships. The first two MAA tourshave been intellectually satisfying and

MAA Around the World and in the Classroom

By Joel Haack

reinvigorating; I look forward to the nextone!

Joel Haack is Professor of Mathematics atUniversity of Northern Iowa in CedarFalls, Iowa.

Joel and Linda Haack aboard the London Eye. Photocourtesy of Carol Dotseth.

Linda Haack studying the Thompson HarmonicAnalyser at the London Science Museum.Photograph courtesy of Joel Haack.

This is a new series that will featureoccasional articles by MAA Math-ematical Study Tour participants onhow they have incorporated the in-formation and educational experi-ence abroad into their classroomteaching, syllabi preparation, andcourse discussions.

Found Math

Florida Student: “What are the angleson a three-four-five-triangle?”

Governor Jeb Bush: “The angles wouldbe ... If I was going to guess ... Three-four-five. Three-four-five. I don’t know,125, 90 and whatever remains on 180?”

Florida Student: “It’s 30-60-90.”

Reported on WFTV, July 6, 2004 Onlineat http://www.wftv.com/education/3498203/detail.html.

14

FOCUS November 2004

By David M. Bressoud

There was a time when it made senseto teach single variable calculus as a year-long course. Most of the students whoenrolled for the first semester intendedto complete a full year. Nearly all the stu-dents who began the second semestercame from the first-semester course atthat institution. No more. The numberof students who take their first calculuscourse in high school is much higherthan the number who take calculus forthe first time in collegea. At many collegesand universities, the majority of studentsin Calculus II passed the first-semestercourse somewhere else, a trend that isaccelerating. Large and increasing num-bers of the students who take Calculus Ido so with no intention of continuing onto the second semester of the course.

In the CUPM Curriculum Guide 2004[6], the first and foundational recom-mendation for all departments is to “un-derstand the student population andevaluate courses and programs.” TheCUPM Guide encourages departmentsto “determine the extent to which goalsof courses and programs are aligned withthe needs of students” and “continuallystrengthen courses and programs to bet-ter align with student needs.” I will ar-gue that the traditional year-long singlevariable calculus course is badly out ofalignment with student needs at mostinstitutions.

The Need for a New Calculus II

At colleges and universities on semestersystems, the traditional Calculus I is dif-ferential calculus with the barest intro-duction to integration in the last fewweeks. Calculus II picks up where Cal-culus I left off, reintroducing and thendeveloping integral calculus for roughlyhalf a semester. It then moves on to se-quences and series and may touch onsome topics of several variable calculussuch as partial derivatives. Aside from thefact that the material on sequences andseries never seems to hang together withthe earlier work on differential and inte-

gral calculus, it is not a bad course. Theproblem is that few students take it asintended.

In the fall of 2000, 107,000 students tookmainstream Calculus II in a 2- or 4-yearcollege or university in the United States[4]. Spring enrollments were certainlyhigher. Enrollments in Calculus II havebeen flatb, so we can estimate that roughlya quarter million students take main-stream Calculus II in college each year.In the spring of 2004, over 150,000 highschool students earned a score of 3 orbetter on one of the Advanced PlacementCalculus Examsc. Many more high schoolstudents obtained International Bacca-laureate or community college credit forcalculus.

In many colleges and universities, it isalready the case that most of the studentswho take Calculus II come with credit forCalculus I taken in high school. Thesestudents are not well served by the tradi-tional approach to calculus in college.They have seen an entire course of dif-ferential and integral calculus and havealready studied many of the topics thatwill be covered in the first half of Calcu-lus II. It makes no sense to pretend thatthey are barely familiar with integration.

On the other hand, those who have takenthe AB syllabus have had the equivalentof a one-semester course, not a full col-lege year. There are significant gaps intheir knowledge. Most of these studentswill not have studied integration by parts,L’Hospital’s Rule, or parametrized mo-tion. Many of them would benefit frommore and deeper work on limits, implicitdifferentiation, differential equations,and the theorems of calculus. They needa Calculus II course, but not the one wetraditionally offer.

The need for revising Calculus II be-comes even more imperative when weremember that the students who cometo this course directly from a high schoolAP course are among our most math-ematically promising. The last thing weshould do is to put them into a course

that does not build directly on theirtraining and lead them into furthermathematics. Calculus II should be acourse that they find challenging andexciting, one that helps them see the po-tential of modern mathematics andmakes them want to pursue it. Thosecolleges and universities that find thatmany or most of their Calculus II stu-dents come with credit for calculus takenin high school should assess how welltheir curriculum meets the needs of thesestudents and entices them into continu-ing their study of mathematics.

The Need for a New Calculus I

The movement of first-semester calcu-lus into the high school curriculum alsohas profound implications for how weteach Calculus I in college. Students whobegin calculus in college are very differ-ent from those of a generation ago. Theyare far more likely to have weakness intheir mathematical preparation. They arealso far less likely to aspire to taking asecond semester of calculus. The tradi-tional Calculus I course was never de-signed to stand alone. Now it must.

There are many initiatives under way tosupplement Calculus I instruction with“just in time” refreshment or teaching ofpre-calculus topics. These are important,but I want to focus on a different side ofthe problem with Calculus I that is rel-evant to the needs of the students at myinstitution, Macalester College. The larg-est single group of students taking ourCalculus I consists of prospective majorsin the biological sciences. They are par-ticularly ill-served by the traditionalcourse.

As part of the preparation for the CUPMCurriculum Guide 2004, the subcommit-tee on Curriculum Renewal Across theFirst Two Years (CRAFTY) sponsored theCurriculum Foundations Project, a seriesof eleven workshops for faculty frompartner disciplines such as economics,engineering, and physics. These facultycame together to explain and elaborateupon what they want their students to

The Changing Face of Calculus:

First- and Second-Semester Calculus as College Courses

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November 2004

learn from their mathematics coursesd.The workshop for biologists, held atMacalester College in November, 2000,was personally enlightening.

Biology programs face constraints. Theyusually require two semesters of math-ematics. Some institutions require moreor less, but because there is so much tech-nical information that has to be taughtwithin four years, few feel they can af-ford to require more than two semestersof mathematics, and most feel that onesemester of mathematics is not sufficient.Many medical schools, a driving force inthe biology curriculum, require one se-mester of calculus. It is not uncommonfor biology departments to have a math-ematics requirement of Calculus I & II.When the biologists gathered atMacalester, they were unanimous andstrong in the opinion that Calculus I &II made no sense as the two mathemat-ics courses their majors should take. Intheir own words: “The current math-ematics curriculum for biology majorsdoes not provide biology students withappropriate quantitative skills. The fieldof biology is becoming much more quan-titative which will necessitate a changein the mathematics curriculum for biol-ogy majors” (p. 16). Biologists needmathematics, but not what we have beenteaching.

There are aspects of calculus that biolo-gists do need, though they need far lessthan we teach. The topics identified atthe workshop were “integration for thepurpose of calculating areas and averagevalue, rates of change, optimization, andgradients for the purpose of understand-ing contour maps.” The most importantmathematical tools for biologists lie indata analysis and statistics. Here the listof needed topics is far richer, “descrip-tive statistics, conditional probability,regression analysis, multivariate statis-tics, probability distributions, simula-tions, significance and error analysis” (p.16).

The kind of statistical analysis that thesestudents need to be able to do is deep. Ifthey are to understand the statistical toolsthat they will be using, then they needsome familiarity with the concepts ofgradients, linear transformations, and

eigenvectors. Can they learn all thiswithin the context of Calculus I?

Macalester is among a handful of collegesthat believes the answer is “yes.” We havedeveloped a substitute for Calculus I thatdoes not attempt to duplicate the cover-age of the traditional course. Its empha-sis is on geometric and conceptual un-derstanding, and its syllabus includes:

Functions and units: linear functions,power relations, polynomials, trigono-metric functions, exponential functions,logarithms.Dynamical systems: simple systems ofdiscrete difference equations and differ-ential equations.The derivative: graphically, numerically,algebraically; Taylor polynomials to sec-ond degree.The integral: as anti-derivative and asarea.Functions of two variables: contours,gradients, optimization via hill climbing.The linear algebra of Ax = b: vectors,projection, least-squares, subspace, span.Emphasis is on 3-dimensional space.

This is a course that stands on its ownmerits. Not only our biologists, but alsoour chemists and economists havepraised it for meeting the needs of theirstudents. We have been running it experi-mentally, a program made possible byfunding from the Hughes Foundation.That money is ending. We are too smallan institution to be able to afford to runtwo distinct Calculus I courses. In viewof the fact that Calculus II now draws sofew students from Calculus I, we havedecided that it is the traditional Calcu-lus I that will disappear. For us, CalculusI and Calculus II will become very dis-tinct courses.

These courses will still be connected. Partof the intention of the revised syllabus isto show students the importance andusefulness of mathematics and to en-courage them to continue their pursuitof it. But our two courses in single vari-able calculus will no longer be two halvesof a single course. Each is being rede-signed around the actual needs of thestudents who take it, moving them for-ward in their understanding of and abil-ity to use mathematics, preparing them

for and enticing them into the furtherstudy of mathematics. This should be thegoal of every mathematics course,whether taught in high school or college.

There are fundamental shifts now occur-ring in the needs of the students who takeour mathematics courses. Macalester’ssolution is built around the needs of thiscollege and its students. What is neededat your college or university will dependon your situation and your students.What you cannot expect is for the cur-ricular solutions that worked a genera-tion ago are still best for today.

Bibliography

[1] APCentral, AP Research and Data,http://apcentral.collegeboard.com/pro-gram/research/.

[2] Bressoud, David M., “The ChangingFace of Calculus: First-Semester Calcu-lus as a High School Course,” FOCUS,September 2004.

[3] Ganter, Susan and William Barker,Curriculum Foundations Project: Voices ofthe Partner Disciplines, MathematicalAssociation of America, 2004.

[4] Lutzer, David J., James W. Maxwell,and Stephen B. Rodi, Statistical Abstractof Undergraduate Programs in the Math-ematical Sciences in the United States: Fall2000 CBMS Survey, American Math-ematical Society, Providence, RI, 2002.

[5] Morgan, Rick and Len Ramist, Ad-vanced Placement Students in College: AnInvestigation of Course Grades at 21 Col-leges, Educational Testing Service ReportNo. SR-98-13, 1998.

[5] Pollatsek, Harriet et al, Undergradu-ate Programs and Courses in the Math-ematical Sciences: CUPM CurriculumGuide 2004, Mathematical Association ofAmerica, 2004.

Notes

a) As estimated in the first article of thisseries [2], there are probably between500,000 and 600,000 high schoolstudents taking calculus each year. Alsoas shown in that article, the numbers

16

FOCUS November 2004

taking first-semester calculus in collegeshave been flat or slightly declining for thepast twenty years. Total mainstream andnon-mainstream Calculus I enrollmentsin all 2- and 4-year institutions in the fallof 2000 was 384,000 [4]. If we estimatethat spring enrollments in Calculus I aretwo-thirds of fall enrollments, thenbetween 600,000 and 700,000 studentstake some form of Calculus I in collegeeach year. Roughly half of these, perhapsmore, will have taken calculus in highschool.

b) 111,000 in fall, 1990, 106,000 in fall,1995 [4].

c) Not all colleges or universities givecredit for a 3 on the AP Calculus exam,but a study [5] of students at 21universities including Boston College,Carnegie Mellon, William and Mary,Michigan State University, PennsylvaniaState University, Stanford, University ofVirginia, and Yale showed that those whoscored a 3 on the AP Calculus AB examand started at the university withCalculus II did better in that course thandid students who had completedCalculus I at that university.

d) The reports of these workshops,written by faculty in the partnerdisciplines, are available from the MAAas Curriculum Foundations [3]. Pagereferences that follow refer to thisedition.

David Bressoud is DeWitt Wallace Profes-sor of Mathematics at Macalester Collegein St. Paul, Minnesota. He serves both asChair of the MAA’s Committee on theUndergraduate Program in Mathematics(CUPM) and as Chair of The CollegeBoard’s AP Calculus Development Com-mittee. He has been involved with AP Cal-culus since 1990–91 when he had the privi-lege of teaching an AB course at the StateCollege Area High School and of learninghow to teach calculus from some greatteachers, especially Annalee Henderson.

Seventh Annual

February 4 - 6, 2005A national showcase for research

projects of undergraduate women

in the mathematical sciences.

Main ProgramTalks by undergraduate women

about their own research

Plenary SpeakersSusan Friedlander,

University of Illinois at Chicago

Margaret Wright,

New York University

For more information

or to register, request funding

or sign up to give a talk,visit us on the web at

www.math.unl.edu/∼∼∼∼∼ncuwmor write to us at

ncuwm@math.unl.edu

Department of Mathematics

University of Nebraska-Lincoln

203 Avery Hall

Lincoln, NE 68588-0130

Deadline for registrationJanuary 21, 2005

University of Nebraska-LincolnAn equal opportunity educator and employer with a comprehensive plan for diversity

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The first annualEmbry-Riddle Under-graduate MathematicsConference, funded byMAA NSF Grant DMS-0241090, was held onMarch 27, 2004 atEmbry-Riddle Aeronau-tical University. ERAU isa fairly small (with about4500 students at theDaytona Beach campus)university focusing onaviation and aerospace.ERAU has no mathemat-ics major, but does havea large and active studentMAA chapter, many ofwhose members partici-pated in the conference.The one-day programincluded student presen-tations and a keynote address. Approxi-mately 70 people attended, from severalFlorida universities.

A total number of 14 student presentersdelivered 10 talks. When registering forthe conference, the students were giventhe option of a 20-minute talk or a 50-minute talk. Two students chose the 50-minute option. Jay Lang of Embry-Riddle gave an enthusiastic talk about theGolden Ratio, its mathematical proper-ties, and its occurrence in art and nature.Uriah Tobey, also of Embry-Riddle, ex-plained how he programmed a TI-89calculator to compute rocket trajectoriesfrom Earth to Mars, given initial and ter-minal positions of the trajectory. Manyin the audience were awestruck by thecomplexity of the problem and the speedof the calculator in solving it.

Other highlights of the conference in-cluded an introduction by AmandaFountain (University of Western Florida)to hyperbolic geometry, ChristopherSubitch’s (University of Central Florida)simulation of propagating optical waves,and an Embry-Riddle team’s use ofSTELLA and Maple to design a landing

system for interplanetary travel. 8 of the10 student talks could be classified as “ap-plied” mathematics, and the other 2 as“pure,” reflecting the aerospace interestsof the Embry-Riddle students. Theagenda for the conference is still onlineat http://faculty.erau.edu/spradlig/erumc/agenda.htm .

The keynote address, by Erich Friedmanof Stetson University in Deland, Florida,was about unsolved problems in planegeometry. Professor Friedman presentedtwenty-five easily stated but unsolvedproblems. His talk was accessible to any-one with a high school background ingeometry, and drew many questionsfrom the audience.

Approximately 33 students attended theconference. It was difficult to count them,because these included many Embry-Riddle students who happened to be inthe same building, saw the signs for theconference, and dropped in to listen tosome talks. Although the students werenot polled about their affiliation, thenumber of unfamiliar faces suggestedthat at least half of them were from in-stitutions other than Embry-Riddle.

First Annual Embry-Riddle Undergraduate Mathematics Conference

By Greg Spradlin

The response of theattendees to the con-ference evaluationwas overwhelminglypositive. All respon-dents completing asurvey thought thatthe conference waswell organized, andindicated that theywould attend an-other conference.Some respondentswould have liked tohave more breaksbetween talks for in-troductions and so-cializing. Some re-spondents wouldhave liked a greatervariety of talks from

which to choose. Some complained (jus-tifiably) about an audiovisual snafu thatdelayed the last talk by 20 minutes. Wewill act on these suggestions at futureconferences.

The MAA and NSF have given Embry-Riddle another grant to hold a similarconference in spring 2005. This year, theConference Program Director will orga-nize a committee of ERAU mathematicsdepartment members to generate ideason how to improve on our promisingstart. Our primary challenge is to attractmore students to give talks, especiallyfrom other universities. In 2004 onlythree students from outside Embry-Riddle gave presentations. We will try toenlarge this number by speaking to areafaculty at MAA state and regional meet-ings, and more persistently remindingarea MAA liaisons and student chapterleaders about the 2005 conference.

Greg Spradlin is an Assistant Professor ofMathematics at Embry-Riddle Aeronau-tical University.

Jan Prokaj explaining “Multirate Numerical Techniques for Linear andNonlinear Diffusion Problems In One Spatial Dimension.”

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November 2004

MathFest 2004

The 2004 MathFest was held in Providence, RI on August 12 to 14. With over 1200 participants, it was one of the mostsuccessful MathFests ever. Peter Sarnak was the Hedrick Lecturer, giving three fascinating lectures on Ramanujan Graphs andtheir connections with automorphic forms and Ramanujan’s Conjecture. Alan Schoenfeld was the Leitzel Lecturer. Schoenfield’slecture, entitled Mathematics and the Schools, was a report on his attempt, as part of a group at the University of California atBerkeley, to do some work with the local schools. Other exciting speakers included Tony DeRose of Pixar Animation on “HowComputer Graphics is Changing Hollywood” and Steve Sigur on “The Mystery of the Missing Tangents.” There were manyspecial sessions, panels, and contributed paper sessions, and of course also many social activities. Even USA Today seemed to bein on the action, carrying a front-page story on how “Algebra’s for Everyone Now — Expectations are Rising” on August 21. The

following pages give a glimpse of some of what went on.

How to Get a Job at Pixar

Overheard at MathFest

Want to enter the high-flying world of computer animation? One way to getyourself a job at Pixar Animation is to figure out how to solve integral equationslike:

L x y B x y L x z R x y z V x z dzz Z

, , , , , ,( ) = ( ) + ( ) ( ) ( )∈∫

Or at least learn to approximate a solution quickly.

Tony DeRose described how animators handle lighting today by asking his audi-ence to imagine a photographer setting up his lighting equipment in the dark.Once everything was set up, the photographer would wait for two hours. At thatpoint, the lights would go on and he could assess the result. If he wasn’t satisfied,the lights would go out again, the equipment would be rearranged, and anothertwo hour wait would follow.

Figuring out the effect of lighting a scene in an animated film involves solvingthe integral equation above. This is done numerically on (essentially) asupercomputer, and it takes several hours. So if you can do it quickly, you’ll have

it made.

A full audience in a darkened room: Tony DeRoseexplains “How Computer Graphics is ChangingHollywood.”

I needed some exercise, so I rode the escalators up and down several times.

— Anonymous

Algebra is a 4000-year-old mathematical system that uses letters or other symbols to stand for relationships between numbers.

— USA Today

The USA Today forgot to mention that analysis is also useful.

— Peter Sarnak

The real macho guys do hard analysis; the clever guys do soft analysis. “Soft” means that you’ve understood it.

— Peter Sarnak

Photographs courtesy of Fernando Gouvêa.

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MathFest in Photos

The Board of Governor’s Meeting

Aparna Higgins

Joe Gallian, Richard Guy, and AparnaHiggins.

Darren Glass

Ron Graham at the MAABusiness Meeting.

Colm Mulcahy at the FOCUSEditorial Board Meeting.

Ron Bradley, fearlessleader of HOM-SIGMAA.

Ed Burger, winner ofthe Chauvenet Prize.

Ken Ross signs a copy of hislatest book.

The only person whoknew all that wasgoing on: Jim Tat-tersall, AssociateSecretary of the MAA.

An impossible object, an exhibit atthe “Glass and Geometry” booth.Baby pictures! Ina Lindemann and

Tom Grasso.

Francis Su, one of thefirst winners of theHenry Alder Award.

Books!

John Harvey, 50years with theMAA.

John Lutts at theSilver and GoldBanquet.

Dan Kalman speaking at theOpening Banquet.

Stan Seltzer celebrates25 years as a memberof the MAA.

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November 2004

More baby pictures! Jennifer Quinn,Doris Schattschneider, and MarthaSiegel.

Steve Kennedy looks closely at adodecahedron in the “Glass and Geometry”booth.

Placing the email center inside theexhibits area made it particularlypleasant to check on news from home.

Otto and Marlisa Bretscher promoteOtto’s Linear Algebra textbook.

Emma Breedlove Smithcelebrates 25 years as amember of MAA.

More books!

Richard K. Guy

Glass and Geometry

Douglas Duncan, winnerof the Trevor EvansAward.

Greg Frederickson,winner of the GeorgePólya Award.

Beverly Ruedi and Carol Baxtertending to the MAA booth.

Jim Smith, 50-yearmember.

Steve Sigur of thePaideia School, whogave one of the invitedaddresses.

“Dali is the one on the right.”–A slide from Tom Banchoff ’stalk at the Silver and GoldBanquet. Tom is the one onthe left.

Zvezdelina Stan-kova, one of the firstHenry Alder Awardwinners.

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A mathematician’s duties fall into threegeneral categories: research, teaching,and service. Most of us enjoy one or bothof the first two, and put up with the lat-ter because it is necessary to do someadministrative work to organize confer-ences, find new faculty or graduate stu-dents to keep our mathematics depart-ments thriving, and, in this case, to keepthe MAA running smoothly. The Boardof Governors, while a decision makingorganization, also serves as a vehicle fordifferent parts of the MAA to commu-nicate to each other what they are doingto further mathematics and mathemat-ics education. Governors fall into threebroad categories, sectional governors,who represent geographic regions, gov-ernors who represent specific interests,such as minorities, high school teachers,or certain MAA publications, and MAAofficers.

When I arrived at the Board of Gover-nors (BOG) meeting, I had a chance totalk with some of the governors beforethe meeting began. Some I knew fromeither my undergraduate or graduateinstitution; others I met for the first time.Everyone was friendly, but they allseemed to indicate we were in for a longday. The general opinion was that theagenda for this meeting had many re-ports and a few contentious issues thatmight lead to lively debates.

For the first two hours or so, the meet-ing consisted of dry but necessary re-ports. For example, we heard several re-ports related to the finances of the MAA,which can be summarized as follows:The MAA has enough money to carryout its programs, but of course moremoney would be nice. After these re-ports, the president issued a commentthat the BOG is responsible for all ac-tivities that take place in the MAA, andwe really should try to pay attention. Atthis point the governor sitting on my leftturned to me and said, “So what are yougoing to write?” Fortunately for this ar-

ticle, from here on the reports becamemore interesting.

The report about upcoming book pub-lications was the most enjoyable of themeeting. There were about a dozen newpublications this year, and we were givena summary of each book and copies ofthe new publications were passed aroundfor our perusal. We were also told aboutlast year’s bestsellers. Two books thatcaught my attention were Euler: Masterof Us All by Bill Dunham and Musings ofthe Masters, edited by Raymond Ayoub.Euler: Master of Us All is about Euler’slife and prolific works in mathematicsand has been on the MAA top tenbestseller list for five years. Musings of theMasters is a new book which presentsinformal writings of many mathemati-cal greats (Poincaré, von Neumann,Hardy, and many more).

Creating a conflict of interest policy wasthe most contentious issue of the meet-ing. While there was near universalagreement that some conflict of interestpolicy was necessary (for people onawards committees, for example), it wasnot clear what form the policy shouldtake. For example, the governors decidedthat a list of examples of conflict of in-terest as part of the MAA’s official writ-ten policy might turn into a laundry listof situations to avoid instead of servingas examples to suggest a general idea ofwhat conflict of interest means. It wasdecided that identifying when a conflictof interest arises should be left to thecommon sense of individuals, but thatthe MAA secretary should be contactedabout unclear cases. There was alsosome debate about what should be donein cases of suspected conflict of interest,and whether immediately recusing one-self should be part of official policy. Itwas decided that many discussions, suchas those conducted over e-mail, moveslowly enough for a conflict of interestto be resolved without someone neces-sarily having to recuse themselves, but

that a committee’s secretary should beinformed immediately about any pos-sible conflict of interest. Finally it wasdecided that the MAA secretary shouldtake these suggestions into account andwrite a policy that reflects them to bevoted on at the next board of governorsmeeting.

Another issue that involved some discus-sion was the formation of a steering com-mittee for the next strategic planningprocess. What was proposed was that afew section governors form a plan to puttogether a statement of long-term objec-tives for the MAA. The committee is notsupposed to suggest any particular long-term goals, but decide how such goalswill be decided upon. After some dis-cussion, the governors agreed that thecommittee should be kept small (and forthis reason would be unable to reflect toomany diverse opinions) and should bemade up of sectional Governors.

One interesting thing about attendingthe BOG meeting was that I heard aboutmany MAA activities that as a graduatestudent I would otherwise not knowabout. Some issues pertained to peoplewith much more money than I, such as apolicy requiring a minimum amount ofmoney to establish an endowed prize.Others were reports about programs forpeople with a different background fromme, such as the Report from the Officeof Minority Participation. Still otherswere programs targeted toward youngerpeople, such as a report about what goeson at the Math Olympiad Summer Pro-gram, and a report about mathematicalcontests in general. While there was littleexcitement or glamour in the BOG, I didcome away with a better idea of howmuch hard work is involved to keep thevarious parts of an organization as largeas the MAA working well together.

Michael Lauzon is a graduate student atBrown University.

The August 2004 Board of Governors Meeting:

A Graduate Student’s Perspective

By Michael Lauzon

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The Mentoring through Critical Tran-sition Points (MCTP) initiative of theNational Science Foundation made itsfirst awards this year. The program hassupport from the Division of Math-ematical Sciences, the Division of Under-graduate Education, and the MPS Officeof Multidisciplinary Activities. The tran-sition points of interest are those fromhigh school to college, undergraduateschool to graduate school, and fromgraduate school to a professional careerin mathematics.

The Statistics Undergraduate Mentoring(SUM) Project at St. Olaf College (JulieLegler, PI) is intended to increase thenumber of undergraduates from four-year colleges who concentrate on statis-tics in graduate school and to increasethe number of statistics PhDs whochoose to teach at four-year colleges. ACenter for Interdisciplinary Research willbe established where undergraduate stu-dents, post-doctoral assistants, and fac-ulty mentors can work collaborativelywith faculty and students in other de-partments on statistical aspects of pro-

fessional and undergraduate research.Other opportunities for undergraduatestudents will include working in smallteams with undergraduate summer re-searchers from other disciplines andhelping faculty mentors develop statis-tics modules for non-mathematicscourses. Post docs will help run the Cen-ter, teach undergraduate statisticscourses, aid the summer research teams,and continue their own research pro-grams.

The MCTP project at the University ofAlabama at Birmingham (Lex Overs-teegen, PI) addresses all three transitionpoints. Talented high school studentswill be able to go directly into an accel-erated program leading to a BS and anMS in four to five years. The transitionto graduate school will be smoothed byan increased focus on independent re-search in the undergraduate courses. Fi-nally, the mathematics doctoral programwill be supplemented with more empha-sis on the breadth of mathematics, ex-posure to another science, and develop-ment of interpersonal and communica-tion skills for career success.

The transitions from undergraduate tograduate school and from graduateschool to the early years of an academic

NSF Beat

By Sharon Cutler-Ross

career are the transition points addressedby the project at the University of Ne-braska (Judy Walker, PI). The centralpiece of the program is Nebraska Inten-sive Mathematics: a Mentoring, Educa-tion, and Research Experience which willbring together students about to entergraduate school, students who have justfinished the first year of graduate school,graduate students close to finishing thePhD, and faculty a few years out ofgraduate school who teach at predomi-nately undergraduate colleges. The keypiece of the various components of theproject is the focus on the relationshipbetween PhD- and non-PhD-grantinginstitutions.

The Institute for Advanced Study willsponsor a Program for Women in Math-ematics (Phillip Griffiths, PI) withMCTP funding. This annual ten-daymentoring program serves a mix of un-dergraduate and graduate students, andpost-doctoral researchers. Seniorwomen mathematicians organize andpresent the program on a specific topiceach year. The project goals are to en-hance the mathematical education of tal-ented women mathematicians and retainthese women in the field by establishingan extensive support network of otherwomen mathematicians.

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November 2004

Many first-semester freshmen viewtheir education as a process of master-ing a collection of unrelated skills froma variety of academic disciplines. The au-thors have found this to be particularlytrue of students who must take math-ematics and writing courses as part oftheir general requirements. Rather thanseeing the practical value of solid math-ematical and writing skills, these studentsare more apt to express relief at having“gotten through” these course require-ments because they perceive that theyhave gotten them “out of the way” of theircollege careers. To address this and otherconcerns, the authors have taught for thelast six years a mathematics-compositioncourse cluster (partially supported byNSF–DUE 9752632) to incoming unde-cided freshmen where the same studentsare enrolled in both an introductory-level mathematics and a freshman com-position class.

The cluster creates a unified learningenvironment where students developbasic skills and examine practical appli-cations of mathematics. As students writeformal papers on the mathematics, theyare compelled to demonstrate and assesstheir own understanding of the subject.By having them write at length, the in-structors can then identify those whohave a comprehensive understanding ofthe content, those who fall somewhatshort of that, and those who have simplyrelied on rote memorization. By the endof the semester, all cluster students dem-onstrate understanding of the math-ematics and its value in the real world bywriting a research paper. In this final pa-per, the students document their inves-tigation of a topic using the skills andknowledge presented in the mathemat-ics class. Whether drawing from a per-sonal experience or addressing a nationalor global problem, the project providesan avenue for students to explore thebroader impact of mathematics and tosee how mathematics can be used to ad-dress significant issues. The instructorsgive one-on-one guidance through allstages of research and writing, from de-fining the problem to formatting and

revising the paper. To complete theproject successfully, students must inves-tigate the history of their topic, be awareof current trends, and develop a solutionor describe the next step that should betaken. By doing this, they start to makelarger connections among different dis-ciplines.

Over the years, the students have tackleda variety of topics, including moderndance, environmental science, cryptog-raphy, criminal justice, and transporta-tion engineering. Some of the more in-teresting projects were those in whichstudent proposals anticipated or pre-dicted solutions suggested or imple-mented later. During the fall of 1998, forexample, one student decided to wadeinto the world of health care with its diz-zying array of care providers and benefitmanagement bureaucracies, coupledwith the constant movement of patientsthrough the system. In particular, hewanted to make it easier for patient in-formation to be maintained and insur-ance claims processed as a person growsand changes physicians and insurancecompanies. The student’s solution was todevelop a universal health care identifi-cation number system and accompany-ing check digit scheme.

The medical identification number hedesigned would be assigned to a personat birth and used by all health care pro-viders, insurance companies, and em-ployers throughout that person’s life.This involved creating a hashing processthat encoded the most relevant informa-tion that a doctor and an insurance com-pany would need to know about a pa-tient. The identifier was a 25-characteralphanumeric string. After all letters wereconverted into digits, the check digitscheme would apply the permutation s= (0)(1,2,4,8,7,5)(3,6)(9) to every otherdigit, add up all the resulting digits, andthen append the check digit so that thesum, with the check digit included, wasequal to 0 (mod 10). For example, theabbreviated number 186452 (here 2 is thecheck digit) would be a valid number ass(1)+8+s(6)+4+s(5)+2 = 2+8+3+4+1+2

= 20, which is congruent to 0 (mod 10).The abbreviated number 673494 (here 4is the check digit) would be an invalidnumber as s(6)+7+s(3)+4+s(9)+4 =3+7+6+4+9+4 = 33, which is not con-gruent to 0 (mod 10). Unknown to usuntil a year or so later was that the fed-eral Health Care Financing Administra-tion, an agency in the Department ofHealth and Human Services, had pro-posed creating a national standard iden-tifier in May of 1998.

Another student’s proposal in the fall of2003 similarly paralleled a real-worldinterest. To deal with the problem ofunderage drinking and fake IDs, a stu-dent developed an enhanced identifica-tion number system for all drivers in theU.S. The number would be associatedwith a person’s driver license and wouldbe unique to that person. In addition, thenumber included a check digit schemeso that all establishments that sell alco-hol could scan the card and verify its au-thenticity. This freshman’s proposal wasechoed in a September 2003 report by theAmerican Association of Motor VehicleAdministrators (AAMVA). While thestuden concentrated on a way to makethe identification number of a license amore secure and unique identifier of thelicense holder, the AAMVA report dis-cusses the progress that has been madewith regards to all aspects of driver’s li-cense security (issuing, forgeries, uniqueidentifiers, etc.).

In addition to predicting or parallelingcurrent efforts, a number of studentshave also tackled known problems. NewYork State, on August 16, 2000, and thestate of Washington, on April 19, 2001,passed laws stating that social securitynumbers could not be openly used bypublic or private colleges to identify stu-dents. A number of our cluster studentshave proposed new methods for creat-ing a student identification number sys-tem. These methods involved elaboratehashing functions that encode studentinformation in a sophisticated and secureway so that no two students get assignedthe same number (which is why schools

Freshmen Can Offer Mathematical Solutions to Real-World Issues

By Joseph Kirtland and Pau-San Hoh

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use social security numbers). In addition,many of the systems developed also in-cluded a check digit.

Although writing is often seen as the dis-cipline that serves mathematics in suchlinkages, the reverse effect is equallystrong in this particular cluster. The clus-ter students have said often that writingabout mathematics has forced them to

confront the demands of academic writ-ing, such as concision, precision, coher-ence, and logical order.

With careful guidance, even first-semes-ter freshmen produced results wheremathematics was used in a meaningfuland practical way. The key was to havethe students pick their own problems and

then to guide them so that they used themost appropriate data sources. While wenever pushed a student in one directionor another, we did impart on them theimportance of strong writing and goodmathematical skills. We also trained thestudents in basic research methodologyand encouraged them to not be afraid totackle large issues. Most importantly, theprojects gave the students the sense thatthey can do meaningful work on issuesthat have an impact on the world inwhich they live. Even at the initial stageof their projects when they were explor-ing topics to investigate, we could see thestudents’ excitement in considering theoptions where they thought mathemati-cal applications were possible: GPS, mo-lecular research, endangered species

tracking, ciphers based on natural lan-guage systems, etc. All of the studentsmentioned in this article were very proudof their work and felt a real sense of ac-complishment when they found out thattheir approaches paralleled or predictedwork done by others in the field. This factalone was the best reinforcement of theimportance of having solid mathemat-ics and writing skills.

Joseph Kirtland and Pau-San Hoh teachMathematics and English, respectively, atMarist College in Poughkeepsie, NY. Theywould like to express their gratitude to thestudents who participated in the clusterand especially to Rich Carlson, DavidChamberlain, Melissa Long, and ElizabethCamire.

The International Commission onMathematical Instruction (ICMI) hascommissioned a study on ChallengingMathematics in and beyond the Class-room, whose main event will be a StudyConference from June 27 to July 3, 2006at Trondheim, Norway with invited par-ticipants. The scope of this study will bewide. It will look at, for instance, theimpact of mathematical challenges bothinside and outside of the classroom, therole of mathematical challenges in sup-porting the curriculum for students ofall levels of ability, vehicles for propagat-ing mathematical challenges and assess-ment of their effectiveness. We would liketo emphasize that we are interested instudents and activities of all type, andwant to go far beyond contests for tal-ented students.

A discussion document has been pre-pared by an international committee

ICMI Study 16

chaired by Ed Barbeau of the Universityof Toronto (barbeau@math.utoronto.ca)and Peter Taylor of the University ofCanberra in Australia who is the execu-tive-director of the Australian Math-ematical Trust (pjt@olympiad.org). Thisdocument defines terms, describes is-sues, provides sample situations, andposes questions for discussion. Finally,it indicates how to become involved inthe Study Conference. Would-be partici-pants will be asked to submit a brief cur-riculum vita and a 6-10 page documentaddressing matters relevant to the studyno later than August 31, 2005. The com-mittee plans to send out invitations byJanuary 31, 2006. The Conference willbe followed by a publication. A copy ofthe discussion document can be ob-tained by going to the website http://www.amt.canberra.edu, clicking on“LINKS” and then on “ICMI Study 16.”

The History Of Mathematics SpecialInterest Group of the MAA is pleasedto announce its second annual StudentWriting Contest in the History ofMathematics.

The deadline for submissions is March30, 2005. Information and submissionguidelines can be found on the HOMSIGMAA website at http://www.maa.org/homsigmaa or by con-tacting Amy Shell-Gellasch atamy.shellgellasch@us.army.mil

HOMSIGMAA Contest

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November 2004

Research Experiences for Minority Undergraduates:

SUMMA’s National REU Program

By Robert E. Megginson

Though some progress hasbeen made in recent years onthe problem of the scarcity ofAfrican Americans, HispanicAmericans, and Native Ameri-cans (for brevity, these threegroups will hereinafter be re-ferred to collectively as minori-ties, with full recognition thatthere are many other minoritygroups in the U.S.) in the re-search mathematics commu-nity, much remains to be done.According to recent census fig-ures, these three groups to-gether now constitute about27% of the U.S. population (see[1]), but according to [2] theystill account for only about 6%of the mathematics Ph.D.sgiven to U.S. citizens and per-manent residents each year.

The under-representation of minoritiesin the ranks of Ph.D. mathematicians,and more generally in all of academe, isa well-known problem. Much of thedamage has already occurred by the timethe undergraduate years are reached. Forexample, minorities receive high schooldiplomas at rates substantially lower thanthe national average, and those minori-ties who do graduate from high schoolthen enroll in college at rates lower thantheir white counterparts with high schooldegrees (see http://nces.ed.gov/programs/digest/d02/tables/dt012.asp). Some mighttake this as evidence that “it’s not ourproblem here in college,” and that thematter needs to be addressed somewhereearlier in the educational pipeline. In fact,it makes it imperative that we, as collegemathematicians, encourage the minor-ity students who do make it into ourmathematics undergraduate programs topersist through to advanced degrees toprovide the next generation of mentorsand role models for students from simi-lar backgrounds.

There is much evidence that mathemat-ics REUs (research experiences for un-dergraduates) can excite minority stu-

dents about the prospect of a researchcareer in mathematics and persuadethem to continue their education intomathematics graduate school. A goodexample is provided by the Summer In-stitute in Mathematics for Undergradu-ates (SIMU) conducted at the Universityof Puerto Rico–Humacao from 1998 to2002 (see http://cuhwww.upr.clu.edu/~simu/). In each of its five summers thisprogram engaged about two dozen His-panic American and Native Americanstudents, all U.S. citizens or permanentresidents, in intensive six-week researchprojects designed and conducted by lead-ing mathematicians. Follow-up includedcontinuing in contact with research men-tors during the school year and presen-tations of research at the annual confer-ences of the Society for Advancement ofChicanos and Native Americans in Sci-ence as well as in the MAA’s undergradu-ate poster session at the January JointMathematics Meetings.

Students were not accepted into theSIMU program just on the basis of theirpromise for graduate school in the tra-ditional sense, but with much attentionpaid to their untapped potential and will-ingness to work as described by facultyrecommenders. As of January 2003,

twenty of the 47 studentswho participated in SIMUin its first two summershad been accepted intoPh.D. programs in themathematical sciences, andseventeen others had beenaccepted into other gradu-ate programs. With the to-tal annual output of U.S.Hispanic American andNative American math-ematics Ph.D.s averagingonly about fifteen in recentyears, this single programhas the potential of havinga significant impact on thatproduction.

One factor that almost cer-tainly contributed to

SIMU’s success is that participants inter-acted with a critical mass of studentsfrom backgrounds like their own, andsaw first hand that there were otherChicano, Latino, and Native Americanstudents who shared their interest inmathematics and could succeed in thefield. Without a direct focus on recruit-ing minority participants, it is difficultfor an REU to achieve such a criticalmass. Mathematics REU sites between1980 and 2000 that did not explicitly fo-cus on recruiting minorities averagedfewer than 4% minority participants,which clearly does not contribute to thesolution of the under-representationproblem in the Ph.D. ranks.

With all of this in mind, the MAA’sProject for Strengthening Under-repre-sented Minority Mathematics Achieve-ment (SUMMA) established a NationalResearch Experience for UndergraduatesProgram (NREUP) in 2003 to provideprimary or supplemental funding forsummer REUs of substantial length en-rolling enough minority students to havea presence in the program. It was decidedto require that the students be local tothe program, in part to stretch programfunds by eliminating travel costs but alsoto encourage program sites to develop

Student Researchers Ary Clemons, Francesca Duncan, MariamKonatè, and Jeremy Smith studied protein folding and DNAsequencing using graph-theoretic techniques with Debra Knisley atEast Tennessee State University.

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the talent at their own institutions ratherthan recruit from talent already devel-oped elsewhere.

With funding in handfrom the National Secu-rity Agency for a pilotproject, SUMMA con-ducted an e-mail solicita-tion of its members for“MAA Summer ResearchProgram” sites for sum-mer 2003. The two pri-mary sites selected fromthe seventeen applicationsreceived are programs atCalifornia State Universityat Chico and Texas South-ern University. Fundingwas also provided toGoshen College in Indianafor adding a student to anexisting REU. All threeprograms received con-tinuation funding fromNREUP for summer 2004after the pilot proved successful.

Quite a bit of thought is needed to beput into the initial selection process, sincemany more worthy proposals were re-ceived than could be funded, but the ex-cellence of the proposal pool showedfrom the beginning that a larger programwould be feasible with no loss in quality.A major criterion for selection was thatthe research in which the students wouldbe engaged had to be intellectually sub-stantial and require hard work on theirpart, with an excellent chance of devel-oping further directions of investigation,presentations that would interest re-search mathematicians, and, possibly,publications.

For example, in the program on knotpolynomials conducted by ThomasMattman at California State Universityat Chico, students investigated such mat-ters as the trip matrix of a knot and ageneralization from which the Jonespolynomial of the knot can be computedand the algebraic nature of some of theproperties of the Jones polynomial canbe deduced. There are several importantopen questions arising in this investiga-tion that lend themselves to student ex-ploration and for which the students can

produce interesting partial results. DavidHousman’s program at Goshen Collegefocuses on cooperative game theory andfair division, where, for example, known

allocation methods fail for partially de-fined cooperative games due to the diffi-culty or infeasibility of determining thecoalitional worth functions, but wherethere are several possible approachesopen to student investigation. In the pro-gram on geometric graph theory andgame theory directed by Nathaniel Deanand Tong Wu at Texas Southern Univer-sity, students work on problems such asfinding tight bounds for the size of thesmallest square integer lattice that willrealize a sphere-of-influence graph, a cer-tain type of graph important in patternrecognition and computer vision.

Though it is too early to know with cer-tainty how many of the students inNREUP’s 2003 pilot project will end upin graduate school, initial attitudinal sur-veys of the students are quite encourag-ing. For example, the four African Ameri-can students in the Texas Southern Uni-versity program, who were tentativeabout attending graduate school whenthe program began, reported at the endthat they had become determined to doso.

With this and much other evidence ofsuccess in hand, the MAA and SUMMAsought funding for expanding and con-

tinuing the project, and received an NSF/DMS grant for doing so along with con-tinued NSA funding. With this funding,it was possible to expand the number of

sites for summer 2004 to six, withEast Tennessee State University,Virginia State University, andCalifornia Lutheran Universityadded to the original sites. Eachof the six sites had at least fourminority undergraduates partici-pating, and initial indications arethat the students in them havedone exciting work that shouldwhet their appetites for a careeras a mathematician and pointthem toward graduate school inthe mathematical sciences.

Funding for NREUP will again beavailable for summer 2005, forwhich applications will be ac-cepted through January 31. Up tosix grants of up to $25,000 eachwill be given. Grants are intendedto provide some compensation

for a faculty researcher as well as stipends,room, and board for at least four under-graduates from minority groups under-represented in the mathematical sciences.Funding received through this programcan be for new projects, but can also beused to supplement existing projects pro-vided the student funds are used for un-dergraduates from underrepresented mi-nority groups. See http://www.maa.org/nreup for further details and applicationinstructions.

References

[1] U.S. census figures; http://www.census.gov/Press-Release/www/2003/cb03-100.html.[2] American Mathematical Society, An-nual Survey of the Mathematical Sciences,First Report, for 2000 through 2003;ht tp : / /www.ams.org /employment /surveyreports.html.

Robert E. Megginson is Professor and As-sociate Dean at the University of Michi-gan at Ann Arbor. The project describedin this article is being supported by theNational Science Foundation under GrantNo. 0353841, with other significant fund-ing received from the National SecurityAgency.

The Pebbling Team: Marlene Merchain, Modesty Briggs, JuanZuniga, and Victor Moreno did research on graph pebbling at theNREUP program at California Lutheran University.

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November 2004

Several factors continue to press forstronger assessment of student learning.In his recent article “The Four A’s: Ac-countability, Accreditation, Assessment,and Articulation,” Lynn Steen pointedout that “as higher education has be-come more important, more prevalent,and more costly, those who pay the bills— administrators, trustees, legislators,parents — are beginning to ask for evi-dence of value.” This summer, as Con-gress considers reauthorization of theHigher Education Act, connections be-tween accountability (and in particularoutcome assessment) and accreditationare some of the most contentious issues,raising concerns among many in highereducation of federal imposition of bur-densome and costly oversight. Unless theacademic community begins to take se-riously the need to use assessment as atool for both documenting and improv-ing our work, it is almost certain thatsuch requirements will be imposed fromthe outside, either from federal or stategovernments, traditional accreditationbodies, or (more likely) from a combi-nation of all three.

With support from the National ScienceFoundation, the MAA Supporting As-sessment in Undergraduate Mathemat-ics (SAUM) project aims to assist facultydevelop effective methods of assessingcourses, blocks of courses, or entire pro-grams within the mathematics depart-ment, not only to answer the externalcalls for accountability, but even moreimportantly, to assist faculty as they makecritical decisions about course and cur-ricular revision.

Over the past three years, a series ofworkshops have brought together teamsof faculty from mathematical sciencesdepartments with more experienced col-leagues from a variety of institutions toconstruct plans for assessment. Follow-up sessions have allowed the teams toreceive assistance at the implementationstage as well. A volume of case studies,Assessment Studies in UndergraduateMathematics (MAA Notes #49), pub-lished in 1999, was distributed to allmathematics departments and the fulltext is available on the SAUM web site,http://www.maa.org/saum. A second vol-ume is expected sometime next year.SAUM has also provided leaders for moreinformal “assessment forums” at sectionmeetings for seventeen of the 29 MAAsections.

Through both the forums and work-shops, we have found that there is a grow-ing interest in the mathematics commu-nity for information and support for de-velopment of assessment plans. In orderto reach a broader audience, a self-pacedon-line guide, “Designing and Imple-menting a Program for Assessing Learn-ing in the Major,” has now been postedon the SAUM website. Together with arange of other materials, including thefull text of the case studies volume,SAUM offers faculty an in-depth look atthe assessment process. Whether you arejust beginning to think about assessment,or trying to refine existing mechanisms,you can find the resources to help youunderstand and improve student learn-ing in your courses.

SAUM Offers On-line Guide for Assessment of Student Learning

SAUM Self Paced On Line Guideto Designing and Implementinga Program for AssessingLearning in the Major

Available through the SAUM website,http://www.maa.org/saum, this Guideprovides easy access to materials de-signed to assist faculty develop or en-hance assessment programs in their de-partments. The first section provides anoverview of assessment, including anintroduction to terminology, and pointsto recent recommendations from theMAA’s Committee on the Undergradu-ate Program in Mathematics on bothcurriculum and assessment.

In the second section, broader readingsare presented that expand on assess-ment by looking at it from an interna-tional perspective and in a larger arenaof program evaluation and accountabil-ity, where your assessment results maybe used.

Finally, a collection of representativecase studies are presented, together withpointers to ongoing projects that mayprovide points of contact for faculty in-terested in discussing their own effortswith others who are pursuing similargoals. A bibliography rounds out theGuide, offering those so inclined to con-tinue exploring the current researchand practice on assessment and ac-countability.

Tattoo Design Contest

Calling all aspiring artists! The MAA is looking for math-relateddesigns for its new temporary tattoo, to be made available to stu-dents, student chapters, and members. The first such tattoo, whichwas very popular at the Phoenix Joint Mathematics Meetings, isshown right. To enter, email a four-color design, two inches squareat 300 DPI, to the MAA at member@maa.org by Friday, Decem-ber 10th. Designs selected for printing will be notified by emailand receive 100 free tattoos. Winners will be announced in MathHorizons.The triaxial tritorus design was created by Paul Bourkeof Swinburne University.

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FOCUS November 2004

The Mathematical Association ofAmerica and the Archives of AmericanMathematics (AAM) at the Center forAmerican History have had a close rela-tionship for many years. Building on thepresence of the papers of R. L. Moore andsome of his colleagues and students, theAAM was established when the Math-ematical Association of America choseThe University of Texas at Austin as itsofficial archival repository in 1978. Sincethen, numerous deposits of papers, pho-tographs, and other records have comeinto the archives. The MAA records heldat the AAM now total more than 300 lin-ear feet.

We now have a strong foundation ofrecords in which mathematical histori-ans, mathematicians, and members andofficers of MAA can find valuable andunique information about the historyand work of this professional organiza-tion. I am working to develop a more fo-cused appraisal strategy that can bringin the most historically relevant materi-als from all areas of the MAA. Too oftenimportant records are inadvertently de-stroyed or relegated to unopened base-ment files. Alternatively, bulky day-to-day files can take up valuable space in of-fices or archives shelves. My goal is tocreate an appraisal strategy that will beflexible enough to allow for a variety ofhistorical records, without opening thefloodgates to unexamined materials.

In order to create an effective appraisalstrategy, I’ll need to hear from those ofyou who are creating potentially archi-val records. If you are an officer, a com-mittee chair, a section leader, an editor,or involved with any one of the many im-portant records-creating positions in the

Archives of American Mathematics Spotlight:

The Mathematical Association of America Records

By Kristy Sorensen

Annotated program from the SecondAnnual Meeting of the MathematicalAssociation of America, December 28–30, 1916. From the Mathematical As-sociation of America Records, Archiveof American Mathematics, Center forAmerican History, The University ofTexas at Austin.

MAA, I’d be happy to discuss yourrecords with you. To get an idea of whattypes of papers we currently hold, youmay be interested to learn that thesearching aid for the MAA Records wasrecently mounted on the Texas ArchivalResources Online (TARO) website. It canbe viewed at http://www.lib.utexas.edu/taro/utcah/00328/cah-00328.html.

As is the case with any growing collec-tion, the finding aid for the MAA Recordsis a work in progress. We expect it togrow, change, and become more refinedas new groups of papers are brought intothe archives, cataloged, and opened forresearch. The Mathematical Associationof America Records is one of the core col-lections at the AAM, and we look forwardto helping it grow and evolve to best helpour researchers in the future.

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. Our web site is located ath t t p : / / w w w . c a h . u t e x a s . e d u /collectioncomponents/math.html.

William Firey, Emeritus Professor atOregon State University, died on August15, 2004. Described by friends as a“mathematician of the old school,” Fireyhad been part of the Putnam QuestionsCommittee and a member of the edito-rial board for the MAA’s Spectrum se-ries. He was a member of MAA since1968.

John E. Freund, longtime member of theMAA and prolific author of textbooks onprobability and statistics, died on August14, 2004 at the age of 83. A passionateeducator, he was a member of the MAAsince 1949.

Joseph L. Doob, a pioneer in the studyof the mathematical foundations ofprobability theory, died on June 7, 2004

at the age of 94. Doob taught at the Uni-versity of Illinois at Urbana-Champaignfrom 1935 until his retirement in1978.He had been a member of the MAAsince 1963.

Brief death notices of interest to MAAmembers are posted online at http://www.maa.org/news/inmemoriam.htmland included in FOCUS. Send notices toCarol Baxter at cbaxter@maa.org.

In Memoriam

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November 2004

The 2005 Undergraduate StudentPoster Session will take place on FridayJanuary 7 in Atlanta, Georgia, at theJoint Annual Meeting of the AMS,MAA, and AWM. Professor MarioMartelli of Claremont McKenna Col-lege is the organizer. The MAA Com-mittee on Undergraduate Students Ac-tivities and Chapters (CUSAC) spon-sors the Session.

Please apply early, since the space is lim-ited! Posters are expected to present anew result, or a different proof of aknown theorem, or an innovative solu-tion of a Putnam problem, etc. Purely

expository posters cannot be accepted.To apply, students need to supply (1)the project title, (2) an abstract, nolonger than a half page, (3) names andaffiliations of all authors, (4) name,email, and telephone number of thestudent who will be the contact personfor the logistics of the presentation, (5)name(s) and affiliation(s) of theadvisor(s), and (6) sources of financialsupport. Send all the information toProfessor Mario Martelli, Mathemat-ics Department, Claremont McKennaCollege, Claremont, CA 91711 or byemail (PDF format, TeX, or Microsoft

Undergraduate Poster Session at the 2005 Joint Meetings

Word) to Mario Martelli atmmartelli@claremontmckenna.edu.

Each poster will be evaluated by at leastthree judges. Prizes will be awarded tothe best posters with money providedby the AMS, MAA, AWM, CUR, PME,and by the Moore Foundation. Theperson in charge of coordinating theaccomodations of students participat-ing in the Poster Session is Prof. DianaThomas of Montclair State University.Please get in touch with her atthomasdia@mail.montclair.edu if youare interested in this service.

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FOCUS November 2004

Howard W. Eves, 1911–2004By Cindy Eves-Thomasand Clayton W. Dodge

Howard W. Eves, well known authorand longtime professor at the Universityof Maine, died June 6, 2004, after a longillness. He was 93.

Eves received his Ph.D. in mathematicsfrom Oregon State University. He en-joyed a long and distinguished career asa teacher, geometer, writer, editor, andhistorian of mathematics. He served asassociate editor for several journals. Hismany awards included a DistinguishedTeaching Award from the State of Maine,honorary doctorates from the Universityof Maine and McDaniel College, and theGeorge Pólya Award for mathematicalwriting. Eves spent most of his career atthe University of Maine at Orono and atMachias, and more recently at CentralFlorida University. For 25 years he ed-ited the Elementary Problems section ofthe American Mathematical Monthly. Hewas a member of the MAA since 1942.

Eves was the author of numerous math-ematics articles and books, including In-troduction to the History of Mathematics,one of the most widely used texts in thesubject. His six volume MathematicalCircles series, collecting humorous andinteresting anecdotes about mathemati-cians, was recently reprinted by the MAA,who also published his two volumes ofGreat Moments in the History of Math-ematics and in 2001 his MathematicalReminiscences. In 1997 Dover reprintedhis Foundations and Fundamental Con-

cepts of Mathematics. His two volumeSurvey of Geometry was first publishedby Allyn & Bacon in 1963 and has beenreprinted in several abridged versions.

While at the Institute for Advanced Stud-ies in Princeton, he became a friend ofAlbert Einstein, who once pointed to anaster growing in a crack in the sidewalkand remarked, “Bloom where you areplanted.” His MMM (My MathematicalMuseum) contained a nickel thatEinstein had owned and a pencil OswaldVeblen had probably dropped, amonghundreds of other interesting curiosities.

Eves was a strong spokesman for theMAA and a founder of its Northeast Sec-tion, which made him the first recipient,in 1980, of its Howard Eves Award forservice to the Section and the Associa-tion. More importantly, he was a greathumanitarian. Quietly and without fan-fare or expectation of reward, he helpedmany people in need, going far beyondthe call of duty. His honorary degreefrom the University of Maine was there-fore a Doctorate of Humane Letters. Hiscomment on that degree was equallymodest: “They must have seen me pat-ting a dog.”

Murray Klamkin, 1921–2004By Steven R. Dunbar

Murray Klamkin, prolific mathemati-cal problem poser and solver, professorof mathematics, and member of theMAA since 1948, passed away on August6, 2004 at the age of 83. Murray Klamkinreceived a B. Ch. E. from the CooperSchool of Engineering in 1942, thenspent 4 years in the U.S. Army. After re-ceiving an M.S. in Physics at the Poly-technic Institute of Brooklyn in 1947, he

spent 1947–48 studying mathematics atCarnegie-Mellon. From there, he re-turned as an instructor to the Polytech-nic Institute, then held positions succes-sively at AVCO Research, SUNY-Buffalo,the University of Minnesota, Ford Mo-tor Company, the University of Water-loo, and the University of Alberta, wherehe was Chair of the Department of Math-ematics from 1976 to 1981. MurrayKlamkin is best known for editing theProblems columns of many journals:SIAM Review, the Pi Mu Epsilon Journal,School Science and Mathematics Journal,Crux Mathematicorum, the AmericanMathematical Monthly, MathematicsMagazine, and most recently, Math Ho-rizons. Klamkin is one of the three great-est contributors to the SIAM ReviewProblems and Solutions Section. Murrayalso served the MAA as a visiting lecturer,a committee member, and on the Boardof Governors,

Not surprisingly, he was also on thePutnam Competition Committee, andwas instrumental in starting the USAMathematical Olympiad. The standardshe set as the Chair of the USAMO Com-mittee from 1972–1985 and the Coachof the USA Team at the InternationalMathematical Olympiads from 1975–1984 were significant to the continuedsuccess of the program. Under his lead-ership, the USA team delightfully sur-prised the mathematics community bydoing well despite having to competeagainst countries that had been partici-pating in the IMO since its beginning in1959. In Steve Olson’s recent book CountDown, Klamkin is quoted as saying “A lotof people were dead set against it, theythought a US team would be crushed ...”In the 2001 IMO in Washington DC, hereturned as an Honorary Member of theProblem Selections Committee and aguest lecturer at the summer trainingprogram for the USA team.

Mathematicians and students of math-ematics will long appreciate his creationof brilliant problems and lucid solutionsand the standards that he set. “The bestproblems,” he said, “are elegant in state-ment, elegant in result, and elegant insolution. Such problems are not easy tocome by.” Murray found them consis-tently and shared them generouslythroughout his long and fruitful career.

In Memoriam

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November 2004

James E. White 1946–2004By Dan Kalman

James E. White, founder and director ofthe Mathwright Library at http://www.mathwright.com, as well as princi-pal creative force behind the Mathwrightsoftware family, died suddenly and un-expectedly July 18, 2004. He was 58 yearsold, and is survived by his wife, Sally, fourchildren, and two grandchildren. Whitereceived his Ph.D. at Yale University un-der William Massey in 1972 in AlgebraicTopology. He held permanent and visit-ing faculty positions at many institutions,including the University of California atSan Diego, Carleton College, Bates Col-lege, Kenyon College, Spelman College,California State University Monterey Bay,and Stetson University. His non-aca-demic experience included work at JetPropulsion Laboratory. Most of his workon the Mathwright project was done dur-ing his tenure at the Institute for Aca-demic Technology at the University ofNorth Carolina Chapel Hill.

White will best be remembered in themathematics education community forhis vision, creativity, and leadership inthe applications of technology. He rec-ognized early that computers offer aunique and powerful tool to inspire, cap-tivate, and entrance students, and for 30years devoted himself to innovative usesof computer technology. His philosophywas that students will learn best whenthey ask and answer their own questions,and he understood that computer soft-ware can create powerful environmentsin which students are empowered to doso. His dream and vision was to developa tool with which teachers and studentscould easily create these environments.The hundreds of activities housed in theMathwright Library, created by scores of

teachers and students from around theworld, bear witness to his successful re-alization of this vision.

White had a long and active involvementwith the Mathematical Association ofAmerica. He was co-director of theMAA’s Interactive Mathematical TextProject, which introduced dozens ofmathematicians to the development anduse of interactive instructional computeractivities. He was also Principal Investi-gator for another MAA project, the WebEducators Library Collection of Math-ematical Explorations (WELCOME).This project combined three areas ofMAA concern: educational technology,professional development, and increas-ing access to mathematics for under-rep-resented groups. The project, which wasincorporated into the MAA’s SUMMAProgram, worked to bring interactivecomputer activities to students of minor-ity serving institutions by offering pro-fessional development opportunities andmentoring to the faculty of these insti-tutions. His final project for the MAA,completed shortly before his death, in-volved incorporating materials from theWELCOME project in the MAA’sMathDL digital library.

James White had a life-long fascinationwith the world of ideas. He was first amathematician, with several books andscholarly papers to his credit. He waswidely read in mathematics, philosophy,and physics, studied differential geom-etry and its applications to relativity, andhad a particular interest in foundationalissues in quantum mechanics. At the timeof his death, he was deeply immersed inresearch in these areas, and had recentlycompleted a paper presenting an inno-vative new link between the geometricideas of ancient Greece and the modernsubject of special relativity. At the sametime, he was fascinated by the issues ofcognition and learning, and read widelyin this area.

White was also a prolific author of inter-active computer activities for students,and for their teachers. The MathwrightLibrary includes nearly a hundred of hiscontributions, displaying an amazingwealth of creative and inspiring lessons.There is a lunar lander that accurately

models the physics of rockets, an activ-ity that puts students in the driver’s seatof a space shuttle to achieve orbit, a beau-tifully rendered three dimensional ver-sion of tic-tac-toe, and a physically andgeometrically accurate simulation ofpocket billiards. Most impressive of all,perhaps, is his multimedia survey ofgravitation, in which the user navigatesa Myst-like virtual world, while retrac-ing the mathematical and physical evo-lution of our understanding of gravity.And this is just a small sample. He re-cently completed a calculus textbook,integrating both traditional text lecturesand interactive explorations.

Those who knew him well recognizedboth a powerful intellect and a gentle andgenerous spirit. There was poetry at theheart of his life and work, and he sawpoetry and beauty in mathematics. Whoelse would choose Monet’s Water Lilliesas the setting for an interactive explora-tion of buoyancy and boat construction?

Through his software and internet li-brary, James White inspired and influ-enced mathematics students and educa-tors from all over the world. He offeredgenerous encouragement to all who methim, and carried on correspondence witha host of collaborators, followers, andstudents. His memory will continue toinspire all who knew him. His energy,enthusiasm, creativity, and originalitywill be sadly missed. An invited papersession in his honor will take place at theJanuary Joint Mathematics Meetings inAtlanta. The title of the session is Worldsof Interactive Mathematics: The Legacy ofJames E. White. See http://www.ams.org/amsmtgs/2091_maainvited.html for moreinformation on this session.

The MAA makes it easy to changeyour address. Please inform theMAA Service Center about yourchange of address by using the elec-tronic combined membership list atMAA Online (www.maa.org) or call(800) 331-1622, fax (301) 206-9789,email: maaservice@maa.org, or mailto the MAA, PO Box 90973, Wash-ington, DC 20090.

Have You Moved?

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FOCUS November 2004

The Networking Project for Improve-ment in Mathematics Education(NPRIME) is currently in its sixth yearin Wisconsin. This highly successfulstatewide project has used the Internetand conferences to establish connectionsbetween faculty involved in mathemat-ics education at the state’s colleges anduniversities and PK-12 mathematicsteachers. The Project has been fundedby grants from the Eisenhower Profes-sional Development Program, the Wis-consin Education CommunicationsBoard, PBS Mathline, and the Wiscon-sin ESEA Improving Teacher QualityProgram. A summary of five ofNPRIME’s most successful programs fol-lows.

Through Student NPRIME, preserviceteachers from 10 Wisconsin colleges anduniversities have had the opportunitythrough an open forum to ask questionsonline of master mathematics teachersconcerning the teaching and learning ofmathematics. They are also encouragedto express their own views on questionsand concerns raised by other students.Over 250 students have participated todate.

The NPRIME Online Learning Commu-nity has brought some 50 mathematicseducators from state colleges and univer-sities online for discussions on such top-ics as Wisconsin’s new performance-based licensing, the NCTM 2000 Prin-ciples and Standards for School Math-ematics, mathematics education research,NSF Reform Curricula, and implicationsof the TIMSS study.

Two Book Talks have been organizedonline over the past couple of years.During the summer of 2002 participantsdiscussed Liping Ma’s Knowing andTeaching Elementary Mathematics. Dur-ing the fall of 2003 an online discussionof the National Research Council’s Add-ing It Up: Helping Children Learn Math-ematics was facilitated by LindaUselmann of Edgewood College.

In each year of the project two or threeFace-to-Face Meetings have been held atdifferent college and university sites.These conferences have featured presen-

Wisconsin’s NPRIME Project

By Linda Thompson and Margaret Wilsman

tations and discussion of current issuesin the field. Materials such as selectedMathline videos, information concern-ing NSF reform curricula, and the Wis-consin Department of Instruction’s Cur-riculum Planning in Mathematics Guidehave been distributed to those who at-tend or request these materials online.

In the past two years NPRIME has madesmall grants available for colleges or uni-versities for Connection Projects. Eightschools have received these grants forprojects that involve some or all of: col-lege faculty observations in PK-12 class-rooms; PK-12 students’ work used as casestudies in college courses; PK-12 teach-ers participation in college classrooms;preservice students connected onlinewith PK-12 mathematics teachers; col-lege faculty connected online with PK-12 mathematics teachers; staff in highneed school districts learning moreabout NPRIME and giving input intofuture directions of NPRIME.

An exciting new initiative for the groupin the coming year will be NPRIME’sparticipation in the Institutions ofHigher Education (IHE) Network of theMilwaukee Mathematics Partnership, aNational Science Foundation sponsoredaward of $20 million over 5 years target-ing the improvement of student learn-ing in mathematics. While the award ishoused at University of Wisconsin–Mil-waukee, the Milwaukee Public Schools,and Milwaukee Area Technical College,the IHE Network has been established toshare knowledge among those institu-tions of higher education in SoutheastWisconsin most likely to educate futureteachers of the Milwaukee PublicSchools. This connection with NPRIMEwill enable this effort to engage facultyfrom throughout the state. The work willbe centered on research efforts targetingteacher learning through multiple mea-sures and will be based on national re-search and professional recommenda-tions highlighted in The MathematicalEducation of Teachers (CBMS, 2001) andAdding It Up (NRC, 2001a).

Linda Uselmann of Edgewood College.

Marcia Weller Weinhold of PurdueUniversity presented the findings fromher dissertation.

Participants explored the use ofcalculators in teaching mathematics.

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November 2004

EMPLOYMENT OPPORTUNITIES

ALABAMA

UNIVERSITY OF ALABAMAIN HUNTSVILLEDepartment of Mathematical SciencesThe Department of Mathematical Sciencesat the University of Alabama in Huntsvilleinvites applications for a tenure track posi-tion at the rank of assistant professor, begin-ning spring semester 2005 or fall semester2005. In exceptional cases, more advancedappointments may be considered. A Ph.D.degree in mathematics or applied mathemat-ics is required. Applicants must have a strongcommitment to teaching and show evidenceof excellent teaching ability. Applicantsshould also show evidence of outstandingresearch potential in an area that matches theinterests of the department. Preference willbe given to applicants whose research areasare probability/stochastic processes or nu-merical analysis.

Applicants should send a curriculum vitawith the AMS standard cover sheet, tran-scripts, and three letters of recommendation(with at least one letter addressing teaching)to

ChairmanDepartment of Mathematical SciencesUniversity of Alabama in HuntsvilleHuntsville, AL 35899.

For more information about the department,visit our web site at:

http://www.math.uah.edu.

To ensure full consideration, all materialsshould be received by November 1, 2004. Lateapplications will be reviewed until the posi-tion is closed. Women and minorities areencouraged to apply. The University of Ala-bama in Huntsville is an Affirmative Action,Equal Opportunity Institution.

ARIZONA

THE UNIVERSITY OF ARIZONADepartment of MathematicsTucson, AZThe Department of Mathematics is seekingapplications for tenure-track positions at ei-ther the Assistant, Associate or Full Profes-sor level, which will begin in Fall 2005. Bythe time of appointment, candidates are ex-pected to have a Ph.D. and excellent researchrecord or potential, as well as a strong com-mitment to teaching. Rank and salary de-pend on the qualifications of the selectedcandidate(s).

The Department may also have postdoctoralor visiting positions for the 2005-2006 aca-demic year (Ph.D. required).

Further information about the full range ofthe Department’s research and educationalactivities may be found at http://www.math.arizona.edu.

Application review begins October 1, 2004and continues as long as positions remainunfilled. Applications received before Octo-ber 1, 2004 will receive the fullest consider-ation; applications received after January 2,2005 are unlikely to be considered.

Please send a letter of interest (specifyingposition(s) applied for), an AMS Cover Sheet(which can be downloaded from http://www.ams.org/coversheet), a curriculum vi-tae with a list of publications, a statement ofresearch interests, a statement of teachingexperiences/philosophy and a minimum ofthree (3) letters of recommendation (encloseor arrange to be sent) to:

Personnel CommitteeDepartment of MathematicsUniversity of ArizonaP.O. BOX 210089Tucson, Arizona 85721-0089

The University of Arizona is an EEO/AAEmployer-M/W/D/V

CALIFORNIA

CALIFORNIA STATE POLYTECHNICUNIVERSITY, POMONAThe Mathematics Department invites appli-cations for two tenure track positions, onein Mathematics Education and one in Sta-tistics, both at the Assistant or Associate Pro-fessor, beginning September 2005. To be con-sidered in the initial review, complete appli-cations are due by 12/8/04 for MathematicsEducation and 1/20/05 for Statistics. Thesearch continues until closed. For informa-tion about qualifications or the applicationprocedure, visit www.csupomona.edu/~math/position, or contact the FacultySearch Committee, Mathematics Depart-ment, Cal Poly Pomona, 3801 W. Temple Ave.,Pomona, CA 91768-4007; 909-869-4008; Fax:909-869-4904; math@csupomona.edu. AA/EEO.

GEORGIA

COLUMBUS STATE UNIVERSITYThe Mathematics Department at ColumbusState University invites applications for a ten-ure track position beginning August 2005.Responsibilities include teaching four coursesper semester, academic advising, service for

the department and for the university, andscholarship. Required: excellent communica-tion skills and a Ph.D. in math/statistics bythe time of appointment. Preferred: teach-ing experience, potential for continued re-search, and ability to contribute to our newlydesigned applied math program with tracksin actuarial science and statistics. Informa-tion about the position and the university canbe found on the web at http:/math.colstate.edu. Review of applicationsbegins November 329, 2004. As an AA/EEOemployer, CSU is committed to diversity andequality in education and employment.

GEORGIA COLLEGE& STATE UNIVERSITYThe Mathematics/Computer Science Depart-ment of Georgia College & State Universityinvites applications for a tenure track Assis-tant/Associate Professor position in math-ematics education. Employment would be-gin August 2005. For details seewww.gcsu.edu/facultyjobs. Application re-view begins December 8, 2004 and contin-ues until position is filled. GC&SU is anEqual Opportunity/Affirmative Action Em-ployer.

INDIANA

UNIVERSITY OF NOTRE DAMEDepartment of Mathematics, University ofNotre Dame, Notre Dame, IN46556 Special ProfessionalFaculty PositionsThe Department of Mathematics of the Uni-versity of Notre Dame invites applications fortwo Special Professional Faculty positions.Candidates should have a doctorate in Math-ematics or Mathematics Education, a passionfor undergraduate teaching, and a record ofexcellence in the classroom. The starting datefor these positions is August 22, 2005. Can-didates at any rank will be considered. Theteaching load can vary between two and threecourses a semester, depending on class sizeand other duties. These are not tenure trackpositions, but they provide all usual facultybenefits, and have the possibility of beingrenewed indefinitely. The salary is competi-tive. Applications, including a curriculumvitae, a letter of application, and a completedAMS standard cover sheet, should be sent to:William G. Dwyer, Chair, at the above ad-dress. Applicants should arrange for at leastthree letters of recommendation to be sentto the chair. These letters should documentthe applicant’s ability as a creative and effec-tive teacher of undergraduate mathematics.Notre Dame is an equal opportunity em-ployer. Women and minorities are urged toapply. The evaluation of candidates will be-gin December 1, 2004. Information about thedepartment is available at http://www.math.nd.edu/.

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MARYLAND

GOUCHER COLLEGEAssistant ProfessorDepartment of Mathematicsand Computer ScienceA tenure track position is available at the as-sistant professor level for Fall 2005, pendingfinal approval in October 2004. Ph.D. re-quired in mathematics, with a specializationin the fields of applied mathematics or prob-ability preferred. Additional requirements:a commitment to excellence in teaching; theability to teach a wide variety of courses andconduct a research program; a commitmentto fostering research by undergraduates. Theposition also includes opportunities to de-velop courses for the college’s first year pro-gram and courses with interdisciplinary andinternational emphases. Preference will begiven to qualified candidates who are inter-ested in participating in such programs. Theability to teach introductory level computerscience courses is a plus. Deadline for appli-cations: January 7, 2005. Informal interviewswill be conducted at the AMS/MAA meet-ings in January. Submit vitae, transcripts ofgraduate work, three letters of recommenda-tion (two of which must address teachingexperience or potential), and a personal state-ment describing your interest in teaching ata small liberal arts college and also brieflydescribing your research to: Human Re-sources, Goucher College, 1021 Dulaney Val-ley Road, Baltimore, MD 21204. GoucherCollege is an Equal Opportunity Employer.

U.S. NAVAL ACADEMYThe USNA Mathematics Department antici-pates at least one tenure-track position (sub-ject to approval and funding) at the Assis-tant Professor level to start in August 2005.See web site http://www.usna.edu/MathDept/website/Hire.htm for full infor-mation. Tel: 410-293-6701; Fax: 410-293-4883; Email: amg@usna.edu . The UnitedStates Naval Academy is an Affirmative Ac-tion/Equal Employment Opportunity Em-ployer and provides reasonable accommoda-tions to applicants with disabilities.

MASSACHUSETTS

WILLIAMS COLLEGEThe Williams College Department of Math-ematics and Statistics invites applications forone tenure track position in mathematics, be-ginning fall 2005, at the rank of assistant pro-fessor (in an exceptional case, a more ad-vanced appointment may be considered). Weare seeking a highly qualified candidate whohas demonstrated excellence in teaching andresearch, and who will have a Ph.D. by thetime of appointment.

Williams College is a private, residential,highly selective liberal arts college with anundergraduate enrollment of approximately2,000 students. The teaching load is twocourses per 12-week semester and a winterterm course every other January. In additionto excellence in teaching, an active and suc-cessful research program is expected.

To apply, please send a vita and have threeletters of recommendation on teaching andresearch sent to the Hiring Committee, De-partment of Mathematics and Statistics, Wil-liams College, Williamstown, MA 01267.Teaching and research statements are alsowelcome. Evaluations of applications willbegin on or after November 15 and will con-tinue until the position is filled. WilliamsCollege is dedicated to providing a welcom-ing intellectual environment for all of its fac-ulty, staff and students; as an EEO/AA em-ployer, Williams especially encourages appli-cations from women and minorities. Formore information on the Department ofMathematics and Statistics, visit http://www.williams.edu/Mathematics.

WILLIAMS COLLEGEThe Williams College Department of Math-ematics and Statistics invites applications forone tenure track position in statistics, begin-ning fall 2005, at the rank of assistant pro-fessor (in an exceptional case, a more ad-vanced appointment may be considered). Weare seeking a highly qualified candidate whohas demonstrated excellence in teaching andresearch, and who will have a Ph.D. by thetime of appointment.

Williams College is a private, residential,highly selective liberal arts college with anundergraduate enrollment of approximately2,000 students. The teaching load is twocourses per 12-week semester and a winterterm course every other January. In additionto excellence in teaching, an active and suc-cessful research program is expected.

To apply, please send a vita and have threeletters of recommendation on teaching andresearch sent to the Hiring Committee, De-partment of Mathematics and Statistics, Wil-liams College, Williamstown, MA 01267.Teaching and research statements are alsowelcome. Evaluations of applications willbegin on or after November 15 and will con-tinue until the position is filled. WilliamsCollege is dedicated to providing a welcom-ing intellectual environment for all of its fac-ulty, staff and students; as an EEO/AA em-ployer, Williams especially encourages appli-cations from women and minorities. Formore information on the Department of

Mathematics and Statistics, visit http://www.williams.edu/Mathematics.

NEW HAMPSHIRE

DARTMOUTH COLLEGEJohn Wesley YoungResearch InstructorshipThe John Wesley Young Instructorship is apost-doctoral two-year appointment in-tended for promising Ph.D. graduates withstrong interests in both research and teach-ing and whose research interests overlap adepartment member’s. Current research ar-eas include applied mathematics, combina-torics, geometry, logic, non-commutativegeometry, number theory, operator algebras,probability, set theory and topology. Instruc-tors teach four ten-week courses distributedover three terms, though one of these termsin residence may be free of teaching. The as-signments normally include introductory,advanced undergraduate, and graduatecourses. Instructors usually teach at least onecourse in their own specialty. This appoint-ment is for 26 months with a monthly salaryof $4,350.00, and is not renewable. Salary in-cludes two-month research stipend for In-structors in residence during two of the threesummer months in 2006 and 2007. To be eli-gible for a 2005-2007 Instructorship, candi-date must be able to complete all require-ments for the Ph.D. degree before Septem-ber, 2005. Applications may be obtained athttp://www.math.dartmouth.edu/recruiting/. Or, submit a letter of application, curricu-lum vitae, graduate school transcript, thesisabstract, statement of research plans and in-terests, and at least three, preferably four, let-ters of recommendation to Donna Black,Department of Mathematics, DartmouthCollege, 6188 Bradley Hall, Hanover, NewHampshire 03755-3551. At least one refereeshould comment on applicant’s teaching abil-ity; at least two referees should write aboutapplicant’s research ability. Applications re-ceived by January 5, 2005 receive first con-sideration; applications will be accepted un-til position is filled. Dartmouth College iscommitted to diversity and strongly encour-ages applications from women and minori-ties.

DARTMOUTH COLLEGEThe Department of Mathematics anticipatesa tenure-track opening with initial appoint-ment in the 2005-2006 academic year. Theposition is for an applied mathematician atthe rank of Assistant Professor. In extraordi-nary cases, an appointment at a higher rankis possible. Successful candidate should havedemonstrated ability to work across disci-plines; particularly, it is expected that he orshe seek out and strike up collaborations

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across campus with departments such as bi-ology, physics, computer science; he/sheshould also aggressively seek funding in his/her area of research. Current applied inter-ests include (but not limited to) imaging, sig-nal processing, computational numbertheory, statistical physics, stochastic pro-cesses, quantum computing and computa-tional biology and are receiving funding fromvarious sources including NSF and NIH.Candidates for the position must be commit-ted to outstanding teaching and interactionwith students at all levels of undergraduateand graduate study.

To create an atmosphere supportive of re-search, Dartmouth offers new faculty mem-bers grants for research-related expenses, aquarter of sabbatical leave for each three aca-demic years in residence and flexible sched-uling of teaching responsibilities. The teach-ing responsibility in mathematics is threecourses spread over three of four ten-weekterms.

To apply for the position, applications maybe obtained at the math department website:http://www.math.dartmouth.edu/recruiting/. Or, send a letter of application, curriculumvitae, and a brief statement of research re-sults and interests, and arrange for four let-ters of reference, at least one of which spe-cifically addresses teaching, to be sent toDonna Black, Recruiting Secretary, Depart-ment of Mathematics, Dartmouth College,6188 Bradley Hall, Hanover, New Hampshire03755-3551. Applications received by De-cember 15, 2004 will receive first consider-ation.

Dartmouth College is committed to diversityand strongly encourages applications fromwomen and minorities. Inquiries about theprogress of the selection process may be di-rected to Dan Rockmore, Recruiting Chair.

DARTMOUTH COLLEGEThe Department of Mathematics anticipatesa tenure-track opening with initial appoint-ment in the 2005-2006 academic year. In ex-traordinary cases, an appointment at a higherrank is possible. Preference given to candi-dates working in either set theory/logic orareas of algebra with connections to existingresearch interests in the department includ-ing computational algebra, algebraic andarithmetic geometry, representation theory,coding theory and algebraic combinatorics.Candidates for the position must also becommitted to outstanding teaching and in-teraction with students at all levels of under-graduate and graduate study.

To create an atmosphere supportive of re-search, Dartmouth offers new faculty mem-bers grants for research-related expenses, aquarter of sabbatical leave for each three aca-demic years in residence and flexible sched-uling of teaching responsibilities. The teach-ing responsibility in mathematics is threecourses spread over three of four ten-weekterms.

To apply for the position, applications maybe obtained at the math department website:http://www.math.dartmouth.edu/recruiting/. Or, send a letter of application, curriculumvitae, and a brief statement of research re-sults and interests, and arrange for four let-ters of reference, at least one of which spe-cifically addresses teaching, to be sent toDonna Black, Recruiting Secretary, Depart-ment of Mathematics, Dartmouth College,6188 Bradley Hall, Hanover, New Hampshire03755-3551. Applications received by De-cember 15, 2004 will receive first consider-ation.

Dartmouth College is committed to diversityand strongly encourages applications fromwomen and minorities. Inquiries about theprogress of the selection process may be di-rected to Dan Rockmore, Recruiting Chair.

NEW YORK

BUFFALO STATE COLLEGEMathematicsAssistant/Associate ProfessorBuffalo State will receive applications for atenure-track assistant/associate professor,Mathematics Department, to begin spring orfall 2005 semester. Salary is competitive.

Responsibilities: Effectively teach variety ofundergraduate and graduate courses inmathematics and applied mathematics; growprofessionally through scholarly activities;participate in department and college com-mittee work; advise students. Provide lead-ership in developing new concentration inapplied mathematics. Teaching load 9 hours/semester. Successful graduate must havegenuine interest in teaching undergraduates.

Required Qualifications: Ph.D. in appliedmathematics or mathematics with concen-tration in applied field; potential for schol-arly activity; effective teaching; strong com-munication skills; knowledge of computeralgebra systems and/or graphing calculators.

Preferred Qualifications: Operations research,modeling, computational mathematics, ap-plied statistics, actualrial science, biomedi-cal mathematics, or other applications tonatural sciences.

Review of applications will begin November15, 2004 and continue until the position isfilled. Send letter of application, vita, tran-scripts, and 3 letters of recommendation (atleast one addressing teaching potential orability) to: Dr. Robin Sue Sanders, Chair,Mathematics Dept., Buffalo State College,Bishop 317, 1300 Elmwood Ave., Buffalo, NY14222-1095. For more information about thecollege, visit www.buffalostate.edu.

Buffalo State is the largest four-year compre-hensive college in the State University of NewYork (SUNY) system. The campus is locatedin the museum district of Buffalo, the sec-ond largest city in New York State. The areaoffers a variety of cultural and recreationalactivities.

Buffalo State is an affirmative action/equalopportunity employer.

NAZARETH COLLEGETenure-track position in mathematics, begin-ning Fall 2005. Ph.D. in mathematical sci-ences, demonstrated teaching excellence,commitment to innovative teaching in a col-laborative environment, and use of technol-ogy in teaching required. Responsibilities in-clude: 4 courses per semester (majors andnon-majors), scholarship and service. Pref-erence will be given to qualified candidateswith an interest in teaching applied math-ematics, in particular, statistics, mathemat-ics education, and/or directing student re-search.

Nazareth College, a thriving, independent,co-educational, liberal arts college with 2000undergraduates and 1200 graduate students,is minutes from downtown Rochester, notedfor its internationally recognized industriesand museums, and for its cultural diversity.Nazareth College seeks individuals with anunderstanding of the benefits and impor-tance of ethnic and racial diversity on cam-pus and demonstrated commitment to thepromotion of such diversity.Send letter of application, philosophy ofteaching, curriculum vitae, transcripts, andthree letters of reference at least two of whichaddress teaching history/potential to: Profes-sor Susan Riegle, Search Committee,Nazareth College, 4245 East Avenue, Roch-ester, NY 14618. E-mail: smriegle@naz.edu.

See: http://www.naz.edu/dept/hr/postings/faculty.html EOE/AA.

OHIO

BALDWIN-WALLACE COLLEGEMathematics and Computer Science Depart-ment, Tenure-track Assistant Professor, be-ginning August 2005. Teaching introductorymathematics courses for education majors.

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Qualifications include a Ph.D. in Mathemat-ics Education with master’s level work inmathematics and K-12 teaching experience.Candidates with a Ph.D. in Mathematics orthose who have entered a Ph.D. program inMathematics Education will be considered.B-W is an equal opportunity employer, com-mitted to a diverse faculty, staff and studentbody. For position information and appli-cation instructions, see www.bw.edu/re-sources/hr/jobs.

THE OHIO STATE UNIVERSITYAT NEWARKAssistant Professor of Mathematics(Two Positions)The Ohio State University at Newark seeksto fill two positions in mathematics at thelevel of assistant professor. Applicants shouldpossess a Ph.D in Mathmatics, excellentteaching documentation and an active re-search program. Duties include an annualteaching load of six courses on a quarterlysystem and service to the department andcampus. Preference will be given to thoseapplicants with a research area compatiblewith current OSUN math faculty. These ar-eas include Algebraic Topology, Commuta-tive Ring Theory, Differential Geometry andAnalysis.

OSUN is located 35 miles east of downtownColumbus on a lovely campus in the scenicrolling hills of central Ohio. It enjoys closeties with the Columbus campus and area.OSUN faculty members have their primaryteaching responsibilities in Newark but areregular faculty members of their respectivedepartments in Columbus. Instruction takesplace in small classes which facilitates care-ful attention to student needs.

To apply please send a cover letter, detailedCV and three letters of reference to The OhioState University Newark, 1179 UniversityDrive, Newark, OH 43055. The Ohio StateUniversity is a regional campus of The OhioState University. To build a diverse workforceOhio State University encourages applica-tions from individuals with disabilities, mi-norities, veterans, and women. “EEO/AAemployer”.

PENNSYLVANIA

CLARION UNIVERSITYTenure track Assistant Professor of Math-ematics beginning August 2005. We seek anoutstanding teacher, who is an active scholarand an excellent colleague. Doctorate inmathematics or a related field preferred: ABDconsidered. For complete details see our webpage: http://math.clarion.edu. Send to Math-ematics Search Committee, Department of

Mathematics, Clarion University, Clarion, PA16214 or e-mail to mathsearch@clarion.edu.Applications completed by December 10,2004 will receive full consideration. ClarionUniversity is an EOE Empolyer.

INDIANA UNIVERSITYOF PENNSYLVANIAMathematics Faculty PositionsIndiana University of Pennsylvania’s Math-ematics Department invites applications fortenure track faculty positions in Mathemat-ics, Statistics, and Research in undergradu-ate mathematics education to begin in fall of2005. A Ph. D. in the appropriate field is re-quired. Review of applications begins De-cember 1, 2004 and continues until positionsare filled or closed. All applicants must bework eligible. For job descriptions, require-ments, and application procedures, log on tohttp://www.math.iup.edu/jobs, e-mailGary.Stoudt@iup.edu or call 724-357-2608.Indiana University of Pennsylvania, a mem-ber of the State System of Higher Education,is an equal opportunity employer M/F/H/V.

MESSIAH COLLEGEMathematics - Tenure-TrackFaculty PositionApplications are invited for a full time, termtenure-track position in the MathematicalSciences Department to begin August 2005.The position requires a doctorate in Math-ematics and a commitment to teaching a fullrange of undergraduate courses in a Chris-tian College environment.

For more information on Messiah Collegeand the Department visit: www.messiah.edu/acdept/depthome/mathsci/home.htm

Send letters of interest, a statement of teach-ing philosophy, and a résumé to:

J. Barry DeRoos, ChairMessiah CollegeDepartment of Mathematical SciencesPO Box 3041One College AvenueGrantham, PA 17027EOE

SHIPPENSBURG UNIVERSITYMathematics DepartmentThe Mathematics Department seeks candi-dates having a primary interest in mathemat-ics teacher preparation. Responsibilities:Teaching undergraduate mathematics educa-tion or mathematics courses, advising stu-dents, supervising student teachers, conduct-ing research, and contributing to the aca-demic climate of the department throughwriting grants, reviewing the curriculum,serving on committees, and interacting with

regional mathematics teachers. Qualifica-tions and requirements: Doctorate in Math-ematics or Mathematics Education (ABDupon hire may be considered). A terminaldegree from an accredited institution is re-quired for tenure. The position requires ex-cellence in teaching, as well as experience orpotential in research and academic service.A demonstration of teaching effectivenesswill be required as part of the interview. Can-didates will be judged on potential for teach-ing, research and university service. Prefer-ence will be given to candidates with twoyears of K 12 teaching experience or theequivalent in knowledge and experience. Allcandidates must furnish proof of eligibilityto work in the U.S. upon appointment.Shippensburg University is an Equal Oppor-tunity Employer. Review of applications be-gins November 15, 2004, and will continueuntil the position is filled. Applicants mustsend a letter of application, current curricu-lum vitae, official undergraduate and gradu-ate transcripts, three letters of recommenda-tion, and copies of course outlines: SearchCommittee, Department of Mathematics,1871 Old Main Drive, Shippensburg Univer-sity, Shippensburg, PA 17257. At least one rec-ommendation letter must address thecandidate’s teaching ability, and the letter ofapplication should address how the candi-date will contribute to this department. In-complete applications and applications sentby e mail will not be considered. For addi-tional information see http://www.ship.edu/~math. Contact: Pamela A. McLaughlin, EMail: mathcs@ship.edu, Phone: 717-477-1431, Fax: 717-477 4009

TEXAS

TEXAS LUTHERAN UNIVERSITYDepartment of Mathematics invites applica-tions for a tenure-track assistant professor-ship beginning August 2005. Requirementsinclude Ph.D. in mathematics by appoint-ment date, ability to teach a wide range ofintroductory and advanced undergraduatecourses, and a commitment to mentor stu-dents in an undergraduate research program.Submit letter of application, cv, statement ofteaching philosophy, and five references(names, addresses including email, tele-phone) to: Dean John T. Sieben - College ofNatural Science and Mathematics, TexasLutheran University, 1000 W. Court St.,Seguin, TX 78155; fax (830) 372-6095, phone(830) 372-6007, e-mail jsieben@tlu.edu.mailto:jsieben@tlu.edu. Review of applica-tions begin November 8 and continue untilthe position is filled. Texas Lutheran Univer-sity is an equal opportunity employer andencourages women and minorities to apply.Full position description is available atwww.tlu.edu http://www.tlu.edu.

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