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FOCUS March 2003

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

Managing Editor: Carol Baxter, MAAcbaxter@maa.org

Senior Writer: Harry Waldman, MAAhwaldman@maa.org

Please address advertising inquiries to:Carol Baxter, MAA; cbaxter@maa.org

President: Ronald L. Graham

First Vice-President: Carl C. Cowen, SecondVice-President: Joseph A. Gallian, Secretary:Martha J. Siegel, Associate Secretary: JamesJ. Tattersall, Treasurer: John W. Kenelly

Executive Director: Tina H. Straley

Associate Executive Director and Directorof Publications and Electronic Services:Donald J. Albers

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

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

Subscription and membership questionsshould be directed to the MAA CustomerService Center, 800-331-1622; e-mail:maahq@maa.org; (301) 617-7800 (outsideU.S. and Canada); fax: (301) 206-9789.

Copyright © 2003 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).”

Periodicals postage paid at Washington, DCand additional mailing offices. Postmaster:Send address changes to FOCUS,Mathematical Association of America, P.O.Box 90973, Washington, DC 20090-0973.

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

FOCUS

4 Mathematical LEGO SculpturesBy Andrew Lipson

6 NSF BeatBy Sharon Cutler Ross

7 Mathematics Awareness Month 2003: Mathematics and ArtBy Joseph Gallian

9 Mathematics and Art—So Many ConnectionsBy Doris Schattschneider

12 IN FOCUS: The January 2003 Joint Mathematics Meetings

14 Report on the Undergraduate Student Poster Session in BaltimoreBy Mario Martelli

16 MAA Prizes and Awards at the Baltimore Joint Meetings

17 Secretary’s Report on the Joint MeetingsBy Martha J. Siegel

21 Benoit Mandelbrot and James Yorke Win Japan Prize

22 PMET: Preparing Mathematicians to Educate TeachersBy Victor J. Katz and Alan Tucker

24 MAA National Elections Coming Up in April

25 The Curriculum Foundations Workshop in BiologyBy Anita Salem and Judith Dilts

26 Short TakesBy Fernando Q. Gouvêa

29 Employment Opportunities

FOCUS Deadlines

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

March 2003Volume 23, Issue 3

On the cover: A Costa Surface made out of Legos. Article begins on page 4.

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March 2003

A New President for the MAA

At the close of the Joint MAA-AMSmeeting in Baltimore in January 2003,Ron Graham became the fiftieth Presi-dent of the MAA. It was an eventful meet-ing for Graham, since he also received theSteele Prize for lifetime achievement as aresearch mathematician (see page 16).

Graham did his undergraduate work atthe University of Chicago, the Universityof California at Berkeley, and (courtesyof the U.S. Air Force) at the University ofAlaska. He earned his Ph.D. at the Uni-versity of California at Berkeley in 1962.He worked at Bell Labs for 37 years, even-tually becoming Chief Scientist at whatwas then the AT&T Bell Laboratories. Heis now at the University of California atSan Diego.

Ron Graham has served the MAA onmany committees and was First Vice-President of the MAA in 1982-1983. in1972 he was awarded the Pólya Prize inCombinatorics by the Society for Indus-trial and Applied Mathematics. The MAA

awarded him the Carl B. AllendoerferAward in 1990, the Lester R. Ford Awardin 1991, and he was an Earle RaymondHedrick Lecturer in 1994. In 1996, he was

Ron Graham took over as President ofthe MAA at the end of the JanuaryJoint Meetings. His term will extenduntil the end of the January 2005 JointMeetings.

Full text versions of Mathematics Maga-zine and The College Mathematics Maga-zine are now available online at JSTOR,joining The American MathematicalMonthly in that important online archiveof scholarly journals. JSTOR can be ac-cessed at http://www.jstor.org.

JSTOR (short for Journal Storage) is anelectronic archive of scholarly journalsin many fields. It contains both search-able text and high-quality images of thejournal pages. Articles can be viewedonline, downloaded, or printed.

The Mathematics Magazine archive con-tains every issue published between l927(volume 1) and l997. The College Math-ematics Journal archive contains all issuespublished since its inception in 1970 (asvolume 1 of The Two Year College Math-

ematics Journal) through l997. Each year,one more volume will be added to eacharchive, so that all but the most recentfive years of each of the MAA’s journalswill be accessible.

Access to JSTOR requires a subscription,usually on an institutional basis. Insti-tutions can subscribe to various differ-ent collections of journals. MathematicsMagazine and The College MathematicsJournal are part of JSTOR’s Arts and Sci-ences II Collection. (The Monthly is partof Arts and Sciences I.) Each collectionrequires a separate institutional sub-scription. Both collections include manyother journals.

As it has done for the Monthly, the MAAhopes to offer access to individual mem-bers soon.

Mathematics Magazine and The College

Mathematics Journal Now on JSTOR Before his recent death, Henry Alderendowed a new MAA teaching award, tobe known as the Henry Alder Award forDistinguished Teaching by BeginningCollege or University MathematicsFaculty. The awards “are to be made tocollege or university faculty who havetaught full time in a mathematicalscience in the United States or Canadafor at least two but not more than sevenyears since receiving their Ph.D. andwhose teaching has been extraordinarilysuccessful. Their effectiveness in teachingundergraduate mathematics must bedocumented and shown to haveinfluence beyond their own classroom.”

The awards will be given every year at oneof the national meetings of theAssociation. Linda Sons will be chairingthe committee that will recommend theprocedures for nomination and selectionof winners.

Alder Awards Will

Recognize Talented

Young Teachers

featured on the cover of Math Horizons.That article highlighted his activity as ajuggler; he has, in fact, been the presidentof the International Jugglers Association.

At the MAA Business Meeting, Grahamexplained that “Everything I’ve done upto now is preparation for this job.” Thatincludes serving as President of theAmerican Mathematical Society from1993-1994. Graham is the sixth person tobe president of both the MAA and theAMS. The first, E.R. Hedrick, was theMAA president in 1916 and AMS presi-dent in 1929-1930. E.J. McShane wasMAA president in 1953-1954 and AMSpresident in 1959-1960. R.L. Wilder wasAMS President in 1955-1956 and MAAPresident in 1965-1966. Saunders MacLane was President of the MAA in 1951-1952 and the AMS in 1973-1974. R.H.Bing was President of the MAA in 1963-1964 and the AMS in 1977-1978. OnlyWilder and Graham were President of theAMS before being president of the MAA.

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I’m not quite sure how it first occurred to me to build a Möbiusband out of LEGO bricks, but the thought was irresistible.

There is a large and active adult LEGO community on theinternet. (If you’re interested, http://www.lugnet.com, the un-official “LEGO Central” for fans, is a good place to start look-ing.) Like many others among its members, I had played withLEGO as a child and forgotten about it. Decades later, and withchildren of my own, it slowly dawned on me that first, the littleDanish bricks are still fun to play around with, and second, Icould afford to buy a lot more of them than I ever had before.

There are some extremely impressive LEGO constructions onthe web. There are people who build elaborate castles, peoplewho make huge train layouts, people who make vehicle repro-ductions, and a few who specialize in large sculptures. EricHarshbarger (http:/www.ericharshbarger.com) is the undisputedchampion of this subgenre and has made life-size figures, agrandfather clock, and even a desk out of LEGO. Henry Lim(http://www.henrylim.org/LEGOSculptures.html) has made,among other things, a 14-foot stegosaurus and a full-size work-ing harpsichord from LEGO bricks. Clearly, I could not com-pete with these masters, but for some reason it didn’t seem tohave occurred to anyone to make abstract sculptures from LEGO,let alone anything mathematical.

I didn’t trust my artistic abilities enough to try building theMöbius band by eye. While I wasn’t in any doubt that I’d be

able to make one, I wanted something that would be aestheti-cally and mathematically pleasing. I decided to write a com-puter program to generate the outline of the model. The pro-gram would subdivide space into cells the shape of a 1x1 LEGO

brick (the height of a brick is exactly 6/5 times the horizontaldistance between studs), and produce output telling me whichcells should be occupied. Of course a model built entirely of1x1 LEGO bricks would not hold together without gluing (her-esy!) so this would leave me the challenge of actually construct-ing it out of larger bricks in such a way that the structure wouldbe reasonably robust. In order to make the problem more in-teresting, I chose a parameterization of the surface that meantthat the model would balance on a single short section of theedge.

My first attempt was just over 5 inches high, and I was suffi-ciently pleased with it to attempt some larger versions, culmi-nating in the model shown in Figure 1, which is about 14 incheshigh. There were several challenges along the way. While themakers of LEGO produce a great variety of pieces, includingplates that are 1/3 of the height of a brick, I wanted to make theMöbius band using only standard rectangular bricks. The mostcommonly available sizes are 1xn and 2xn bricks, for n=1,2,3,4,6and 8, with n=3,6 and 8 being significantly rarer than the oth-ers. Unfortunately I discovered that in building a curving wallwhich is essentially one brick thick throughout (another de-sign goal), I kept having to dive into my stock of 1x3 bricks,which dwindled alarmingly. The overhanging “roof” of thestructure, which is horizontal at the top, also constrained myoptions (I admit it — I cheated a bit by deviating from mycomputer instructions to allow the top to hold together).

Mathematical LEGO® Sculptures

Figure 1: A LEGO Möbius band. Figure 2: The figure-eight knot 41

By Andrew Lipson

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March 2003

If a surface, why not a knot? Shortly after completing theMöbius strips, I decided to attempt the trefoil knot 3

1, the sim-

plest non-trivial embedding of the unit circle in Euclidean 3-space [1]. I was rather less sure of myself this time. I decided toparameterize the knot as a curve on the surface of a torus, thick-ening it to a diameter of about three LEGO studs. The result wasonly moderately successful, but encouraged me to attempt amore ambitious structure — the figure-eight knot 4

1. This time

I chose a parameterization that shows off the rather nice tetra-hedral skew-symmetry of this knot. Building this model wasquite challenging. My experience with the trefoil indicated thatI needed to thicken the curve by slightly more than the threestuds I had previously used to have any hope of the structurebeing self-supporting. In fact, the long curving arches of thestructure shown in Figure 2 required repeated backtracking asit was built. It did not become evident until close to the top ofthe structure which parts lower down were suffering the most

stress and were likely to fall apart under the weight. The finalresult, however, was very satisfying .

And there it would have stopped, were it not for the involve-ment of a colleague. Knowing that it would provoke me to provehim wrong, he commented that most of the interesting mini-mal surfaces would probably be too difficult to construct inthis way. How could anyone ignore such a challenge?

A minimal surface is one with mean curvature zero [2]. Lo-cally, a small patch of such a surface has minimal area amongall surfaces sharing the same boundary. They have been widelypopularized as the shapes formed by bounded soap bubbles.For my purposes, of course, the interest of minimal surfaces isthat they provide a small library of mathematically interestingand pleasing shapes to build, with a variety of associated con-

struction challenges. The study of minimal surfaces has beenintertwined with computation; the ability to use computers tovisualize has led to new insights, and this added a small frissongiven my intention to use computer programs to aid my LEGO

constructions.

But which minimal surface to try? I daydreamed about pro-ducing a Costa surface — the beautiful new complete minimalembeddable surface discovered by Costa in 1984 [3]— but re-luctantly decided that this would be too ambitious, at least forthe time being. I settled for Enneper’s surface and the Catalansurface, both of which looked easy enough to attempt.

Although I no longer claim the title, I was once a topologist.Naturally I would have to build a Klein bottle! The major diffi-culty here was a new one; what parameterization should I use?There were several constraints. I wanted something that wouldlook recognizably like the classic bottle shape, with the tube

feeding in through the outer wall of the bottle. I wanted theoverall shape to be aesthetically pleasing, and I wanted, despitethe constraints of working with LEGO bricks, for a gap genu-inely to run around between the inner and outer tubes nearthe mouth of the bottle. I played around with Mathematica fora couple of days before coming up with something I foundacceptable. When I built the bottle, I broke my usual “bricksonly” rule and allowed myself a couple of LEGO hinges so thatthe model could be opened up. It is well known that a Kleinbottle can be obtained by gluing together the edges of twoMöbius strips, and the model shows this!

Well, you get the idea. One thing led to another and an initialwhim turned into a hobby. Many of us have at some point en-joyed painstakingly building polyhedra or other mathematicalmodels from paper or card. Certain areas of mathematics have

Figure 3: A hinged Klein bottle Figure 4: A Costa surface.

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a distinctly tactile pleasure in addition to their abstractly math-ematical aesthetic qualities. In fact, one of the nice things aboutthese LEGO constructions is just how accessible they seem to beto non-mathematicians.

But why LEGO? One would have thought that small rectangularbricks would be the very last thing from which one might buildmodels of smooth surfaces! But, of course, that’s part of thepoint. There is a very obvious contrast between the mediumand the content in these models. The fun is in producing some-thing that lets the eye shift back and forth between seeing some-thing angular and bricky, and seeing something smooth. Thisis one of the reasons why I have never attempted to build amathematical LEGO sculpture bigger that about 15 inches high;too large, and the resolution becomes too good! The fun is inpicking a scale just the right size so that the intended shape canbe conveyed without losing the detail of what it’s made of.

There are other aspects of LEGO that pique my mathematicalinterest as well. I mentioned that my programs produce as out-put a description of which cells in a rectangular grid need tobe filled. It takes very little experience to discover that filling ina specified set of cells with a given selection of LEGO bricks isdistinctly non-trivial — especially when one is working underthe constraint that the entire structure needs to hold togetherand that the only solid connections are, as with LEGO, thosebetween vertically adjacent bricks. I have very nearly convinced

myself that connected LEGO space-filling is in general an NP-hard problem, although in practice I have hardly ever found Ihad to backtrack by more than two or three layers while build-ing. Of course, I’d be delighted to be shown that the problem isin fact easy. Constructive proofs preferred!

Oh, yes. And I can’t end without bragging that I did eventuallyproduce the Costa surface I had hoped for. How do you likethem apples, Fred? (Figure 4)

[1] Lickorish, W.B.R. An Introduction to Knot Theory. Springer1997[2] Osserman, Robert. A Survey of Minimal Surfaces. Dover,1986[3] Costa, A. “Examples of a Complete Minimal Immersion in

of Genus One and Three Embedded Ends.” Bol. Soc. Bras.Mat. 15, 47-54, 1984.

Andrew Lipson trained as a knot theorist and now works as acomputer programmer, specializing in algorithmic optimization.His various LEGO constructions can be seen at http://www.lipsons.pwp.blueyonder.co.uk/lego.htm and he can be con-tacted by email at andrewlipson@blueyonder.co.uk.

LEGO® is a trademark of The Lego Group, which did not spon-sor or authorize this work and with whom the author has no con-nection.

One of the changes that the mathematics community hasexperienced in the last few years is an increased dialog and co-operation between those who train teachers of mathematicsand those who train mathematicians. Currents from the chang-ing job market, from reform efforts in undergraduate math-ematics education, and from the increasing challenges facingK-12 education have all contributed to a heightened aware-ness of the necessity and the benefits of dealing with pre-ser-vice and in-service teacher training as a joint effort of math-ematics and mathematics education faculty. In order to sup-port these trends, the National Science Foundation is revamp-ing the Division of Undergraduate Education (DUE) FacultyEnhancement program; and the Division of Elementary, Sec-ondary, and Informal Science Education (ESIS) Science, Tech-nology, Engineering, and Mathematics Teacher Preparationprogram. These two programs will be replaced by the TeacherProfessional Continuum (TPC) program administered jointlyby DUE and ESIS.

The Teacher Professional Continuum program will not be amerging of the old programs, but a fresh approach to the is-sues and needs of teacher recruitment, preparation, retention,and further professional training. The emphasis will be onbuilding research-based knowledge in the area of preparing and

educating teachers. The intent is to produce studies on teacherlearning and on teaching practices. Of particular interest arethe transition period as new teachers become practicing pro-fessionals and strategies to strengthen and diversify the K-12teacher group. The Foundation hopes to see materials and toolsdeveloped that will be of use through the continuum of teachertraining from pre-service to in-service.

A related program that is also designed to strengthen and di-versify the pool of K-12 teachers of science and mathematics isthe Noyce Scholarship program. These scholarships may makeK-12 teaching an attractive option for science, technology, en-gineering, and mathematics majors or practitioners who areinterested in becoming teachers.

At the time this article was written (January 2003), the finalbudget had not been approved for the NSF, so more detailsabout the TPC program were not available, but grants are likelyto be for multi-year projects involving collaboration of math-ematics, science, mathematic education, and science educationfaculty. Preliminary proposals will likely be required. By thetime of publication the full solicitation for TPC is available onthe NSF website. (See page 28.–Ed.)

NSF Beat March 2003

By Sharon Cutler Ross

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March 2003

April is Math Awareness Month! Thetheme for this year is Mathematics andArt. Each MAM theme has an accompa-nying poster that depicts the theme in asignificant way. The 2003 poster featuresa computer generated Escher-like imagein the Poincaré model of the hyperbolicplane designed by Douglas Dunham.

The connection between Mathematicsand Art dates back thousands of years.From the geometry in the buildings inancient Greece to the topology in mod-ern sculptures, artists have been inspiredby mathematical shapes and forms. TheMathematics Awareness Month websiteat http://www.mathforum.org/mam/03lists many resources that can help explorethis theme, including the poster, essays,and links. To get you started, here are justa few of them.

Web Sites

Jill Britton’s spectacular web site on sym-metry and tessellations at http://c c i n s . c a m o s u n . b c . c a / ~ j b r i t t o n /jbsymteslk.htm has numerous activitiesand links to many other sites on relatedtopics.

A truly outstanding site at http://w w w. g e o r g e h a r t . c o m / s c u l p t u r e /sculpture.html features the work ofGeorge W. Hart, a computer scientist andaward winning sculptor of constructivegeometric forms who deals with patternsand relationships derived from classicalideals of balance and symmetry. Articlesabout Hart’s sculptures have appeared inthe New York Times, Science News andNatural History. The site has articles writ-ten by Hart and interviews with Hart.

You can find mathematically inspiredsculptures, puzzles and jewelry by theartist Charles O. Perry at http://www.charlesperry.com. Perry’s work is ondisplay at the offices of the Mathemati-cal Association of America, the Ameri-can Mathematical Society, the NationalCouncil of Teachers of Mathematics andthe American Center for Physics. He hasreceived numerous awards.

The mathematically inspired sculpture ofHelaman Ferguson is featured at http://www.helasculpt.com. Articles about hiswork have appeared in Science, ScienceNews, SIAM News and The Mathemati-cal Intelligencer. A photograph of his Fi-bonacci Fountain was on the cover of theJanuary issue of FOCUS. The site in-cludes a statement from the artist aboutwhat motivated him to become a sculp-tor. Helaman and Claire Ferguson wonthe Joint Policy Board for MathematicsCommunications Award in 2002.

Courses

Paul Calter teaches a survey course onmathematics in art and architecture atDartmouth College. The course web siteis http://www.dartmouth.edu/~matc/math5.geometry. The course explores themany places where the fields of art andmathematics overlap. Topics include:sculpture in ancient Greece, use of pro-portion in art, perspective, perspectivemachines and cameras, the golden sec-tion, knots, and symmetry, twentieth-century geometric art, chaos, andfractals.

Helmer Askalan teaches a course onMathematics in Art at the National Uni-versity of Singapore. The web site is http://www.math.nus.edu.sg/aslaksen/teaching/math-art-arch.shtml. Topics include thegolden ratio, Platonic solids, kaleido-scopes, symmetry, tilings, polyhedra, andperspective.

Books

Mathematics and Art by Claude P. Bruter,Springer, 2002. This book illustrates howpolyhedra, group theory, dynamical sys-tems, and topology have provided inspi-ration for artists.

M. C. Escher’s Legacy, edited by D.Schattschneider and M. Emmer,Springer, 2003. This book, which comeswith a CD-ROM, grew out of a 1998 cen-tennial celebration of the birth of the art-ist M.C. Escher. It contains 40 articles byartists and scientists whose work hasbeen directly inspired by Escher.

About Math Awareness Month

Math Awareness Month, held in Aprileach year, first began in 1986 with a man-date to increase public understanding ofand appreciation for mathematics. Aproclamation by President RonaldReagan said in part:

Despite the increasing importance ofmathematics to the progress of oureconomy and society, enrollment in math-ematics programs has been declining at alllevels of the American educational system.Yet the application of mathematics is in-dispensable in such diverse fields as medi-cine, computer sciences, space exploration,the skilled trades, business, defense, andgovernment. To help encourage the studyand utilization of mathematics, it is ap-propriate that all Americans be remindedof the importance of this basic branch ofscience to our daily lives.

During that first Mathematics AwarenessWeek, expanded in 1991 to be Math-ematics Awareness Month (MAM), ac-tivities were concentrated in Washington,D.C. with a Capitol Hill reception andexhibit at the Smithsonian Institution.Since then participation and support hasincreased to include many thousands ofstudents and teachers, in high schools,colleges, and universities across the na-tion. The Mathematical Association ofAmerica, the American MathematicalSociety, and the Society for Industrialand Applied Mathematics—three of thelargest mathematical organizations in thecountry—coordinate efforts to publicizethis event to reflect the wide and com-prehensive world of mathematics andhow it affects each and every one of us.

Among the themes from previous yearsare Mathematics and the Environment,Mathematics and Manufacturing, Math-ematics and Medicine, Mathematics andSymmetry, Mathematics and theInternet, Mathematics and Imaging,Mathematics and Biology, Mathematicsand the Ocean, and Mathematics and theHuman Genome.

Math Awareness Month 2003: Mathematics and Art

By Joseph Gallian

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The theme Mathematics AND Art mayseem strange to those who are more usedto thinking Mathematics OR Art, but, infact, there are many connectors to fill theblank in Mathematics ___ Art and itstwin Art ___ Mathematics. The manyinterconnections between mathematicsand art provide a wealth of material fromwhich organizers of Math AwarenessMonth events can select. In this brief es-say, I’ll highlight a few of the possibleways to fill in the blanks above. Ihope that this will stimulate youto explore many others.

Mathematics produces art

At the most practical level, math-ematical tools have always beenused in an essential way in the cre-ation of art. Since ancient times,the lowly compass and straight-edge, augmented by other simpledraftsmen’s and craftsmen’s tools,have been used to create beauti-ful designs realized in the archi-tecture and decoration of palaces,cathedrals, and mosques. The in-tricate Moorish tessellations intile, brick, and stucco that adorntheir buildings and the equally intricatetracery of Gothic windows and interiorsare a testament to the imaginative use ofancient geometric knowledge.

During the Renaissance, several artistsused simple grids and mathematicallybased devices to accurately portrayscenes on a flat surface, according to theprinciples of linear perspective. Severalof Dürer’s engravings give a glimpse ofthese techniques. The symbiosis of artand mathematics during these times aslinear perspective and projective geom-etry were developing is one of the moststriking examples of art and mathemat-ics evolving almost simultaneously innew directions.

Today’s mathematical tools are more so-phisticated, with digital technology fastbecoming a primary choice. In the handsof an artist, computers can produce art,

powered by unseen complex internalmathematical processes that providetheir magical abilities. Mathematicaltransformations provide the means bywhich an image or form in one surfaceor space is represented in another. Art isillusion, and transformations are impor-tant in creating illusion. Isometries, simi-larities, and affine transformations cantransform images exactly or with pur-poseful distortion, projections can rep-

resent three (and higher)-dimensionalforms on two-dimensional picture sur-faces, even curved ones. Special transfor-mations can distort or unscramble a dis-torted image, producing anamorphic art.All these transformations can be math-ematically described, and the use of guid-ing grids to assist in performing thesetransformations has been replaced todaylargely by computer software. Com-passes, rulers, grids, mechanical devices,keyboard, and mouse are physical toolsfor the creation of art, but without thepower of mathematical relationships andprocesses these tools would have littlecreative power.

Mathematics generates art

Pattern is a fundamental concept in bothmathematics and art. Mathematical pat-terns can generate artistic patterns. Of-ten a coloring algorithm can produce

“automatic art” that may be as surpris-ing or aesthetically pleasing as that pro-duced by a human hand. Colored ver-sions of the Mandelbrot set and Julia setsare striking examples of this: each isgenerated by iterating the function f(z)= z2 + C. In the case of the Mandelbrotset we start from z = 0 and set z

n+1 = f(z

n)

for each point C in the complex plane,and the point C is colored according torules based on whether the absolute valueof z

n eventually exceeds 2 and the num-

ber of iterations after which this occurs.Other fractals, as well as images based onattractors, are also produced by iterationand coloring according to rules. The in-

tricacy of these images,their symmetries, and theendless (in theory) con-tinuance of the designs onever-smaller scales, makesthem spellbinding.

Much more mundanemathematical patterns canalso provide surprising art.For example, begin with anarray of numbers (such asa large data set, a sequence,a modular operation table,or Pascal’s triangle) andcolor the numbers in the ar-ray according to some rule.Often surprising patterns

— even art — emerge. Recursive algo-rithms applied to geometric figures cangenerate attractive self-similar patterns.Begin with a curve, a closed figure, or asimple spatial form, apply an algorithmto alter that figure by adding to (or sub-tracting from) specified parts of that fig-ure, then repeat the algorithm recur-sively. Many nonperiodic tilings (such asthe Penrose tilings) can also be generatedautomatically, beginning with a smallpatch of tiles and then applying a recur-sive “inflation” algorithm.

Transformations and symmetry are alsofundamental concepts in both math-ematics and art. Mathematicians actuallydefine symmetry of objects (functions,matrices, designs or forms on surfaces orin space) by their invariance under agroup of transformations. Conversely,the application of a group of transfor-mations to simple designs or spatial ob-

Mathematics and Art—So Many Connections

By Doris Schattschneider

Escher II: Infinite Reflection, by Kelly M. Houle. Charcoal on il-lustration board. The drawing is a 360-degree distorted imagewhich the cylindrical mirror transforms into a famous photo ofEscher.

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jects automatically generates beautifullysymmetric patterns and forms. In 1816,Brewster’s newly invented kaleidoscopedemonstrated the power of the laws ofreflection in automatically generatingeye-catching rosettes from jumbles ofcolored shards between two mirrors. To-day computer programs use symmetrygroups to generate rosettes, borders,wallpaper designs, and Escher-like circle-limit designs such as featured on the 2003Math Awareness Month poster.Each of these designs beginswith a small fragment or mo-tif (chosen judiciously or ran-domly) whose transformedimages fill out the full design.Periodic tessellations, whethergeometric or Escher-like, canbe automatically generated bycomputer programs or byhand, following recipes thatemploy isometries.

Art illuminates mathematics

When mathematical patternsor processes automatically gen-erate art, a surprising reverseeffect can occur: the art oftenilluminates the mathematics.Who could have guessed themathematical nuggets thatmight otherwise be hidden ina torrent of symbolic or nu-merical information? The pro-cess of coloring allows the in-formation to take on a visualshape that provides identity and recog-nition. Who could guess the limitingshape or the symmetry of analgorithmically produced fractal? Withvisual representation, the mathematiciancan exclaim, “now I see!”

Since periodic tessellations can be gen-erated by groups of isometries, they canbe used to illuminate abstract math-ematical concepts in group theory thatmany find difficult to grasp in symbolicform: generators, cosets, stabilizer sub-groups, normal subgroups, conjugates,orbits, and group extensions, to name afew.

In the examples above, illumination ofmathematics is a serendipitous outcomeof art created for other reasons. But there

are examples in which the artist’s mainpurpose is to express, even embody math-ematics. Several prints by M.C. Escher arethe result of his attempts to visually ex-press such mathematical concepts as in-finity, duality, dimension, recursion, to-pological morphing, and self-similarity.Perhaps the most striking examples of artilluminating mathematics are providedby the paintings of Crockett Johnson andthe sculptures of Helaman Ferguson.

From 1965 to 1975, Johnson producedover 100 abstract oil paintings, each arepresentation of a mathematical theo-rem. Ferguson’s sculptures celebratemathematical form, and have beentermed “theorems in bronze and stone.”Each begins with the idea of capturingthe essence of a mathematical theoremor relationship, and is executed by har-nessing the full power of mathematically-driven and hand-guided tools.

Mathematics inspires art

Patterns, designs, and forms that are the“automatic” product of purely math-ematical processes (such as those de-scribed in “Mathematics generates art”)are usually too precise, too symmetrical,too mechanical, or too repetitive to hold

the art viewer’s attention. They can bepleasing and interesting, and are fun tocreate (and provide much “hobby-art”)but are mostly devoid of the subtlety,spontaneity, and deviation from preci-sion that artistic intuition and creativityprovide. In the hands of an artist, math-ematically-produced art is only a begin-ning, a skeleton or a template to whichthe artist brings imagination, training,and a personal vision that can transform

the mathematically perfect toan image or form that is trulyinspired.

Wallpaper patterns and tes-sellations can be pleasingfrom a decorative point ofview; few would be viewed asart. Escher did not view histessellations as art, but asfragments to be an integralpart of his complex prints.Makoto Nakamura’s art alsoemploys this technique. JinnyBeyer, a designer and quiltartist, uses her artistic intu-ition and color sense to turntessellations into art. Kaleido-scopic designs are the inspi-ration for quilted art by PaulaNadelstern; her use of colorand composition subtly breakmathematical rules.

Dick Termes uses photogra-phy and grids to guide hisprojections of images onto

the surface of a sphere, but his“Termespheres” bear his personal inter-pretation. Anamorphic artists IstvánOrosz and Kelly Houle are guided bymathematical rules of transformation asthey create mysterious distortions ofimages on the picture plane, but also usetheir intuition and imagination, check-ing with a mirrored cylinder as the workdevelops.

Pure mathematical form, often with highsymmetry, is the inspiration for severalsculptors who create lyrical, breathtak-ing works. With practiced eye and hand,relying on their experience with wood,stone, bronze, and other tactile materi-als, the artists deviate, exaggerate, sub-tract, overlay, surround, or otherwisechange the form into something new,

Whoville, a 35-inch aluminum sculpture by George Hart. see theApril issue of Math Horizons for more on Hart’s sculpture.

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often dazzlingly beautiful. With the ad-vent of digital tools to create sculpturalimages, the possibilities of experimen-tation without destruction of material orof producing otherwise impossibleforms infinitely extends the sculptor’sabilities.

Mathematics constrains art

We often hear of “artistic freedom” or“artistic license”, which imply the rejec-tion of rules in order to have freedom ofexpression. Yet many mathematical con-straints cannot be rejected; artists igno-rant of these constraints may labor torealize an idea only to find that its real-ization is, indeed, impossible. Euler’stheorem (v + f = e + 2) and Descartes’theorem (the sum of the vertex defectsof every convex polyhedron is 720˚) gov-ern the geometry of polyhedra. Othertheorems govern the topology of knotsand surfaces, aspects of symmetry andperiodicity on surfaces and in space, factsof ratio, proportion, and similarity, thenecessity for convergence of parallel linesto a point, and so on. Rather than con-fining art or requiring art to conform toa narrow set of rules, an understandingof essential mathematical constraintsfrees artists to use their full intuition andcreativity within the constraints, even topush the boundaries of those con-straints. Constraints need not be nega-tive—they can show the often limitlessrealm of the possible.

Voluntary mathematical constraints canserve to guide artistic creation. Propor-tion has always been fundamental in theaesthetic of art, guiding composition,design, and form. Mathematically, thistranslates into the observance of ratios.Whether these be canons of human pro-portion, architectural design, or evensymbols and letter fonts, ratios connectparts of a design to the whole, and toeach other. Repeated ratios imply self-similarity, hardly a new topic despite itsrecent mathematical attention. One ofthe earliest recorded notices of it is inEuclid’s Prop. 30, Book VI, the divisionof a segment in extreme and mean ratio(also known as the golden cut, or goldensection). A segment AB is to be dividedinternally by point E so that the ratio ofthe whole AB to the part AE equals the

ratio of the (larger) part AE to the(smaller) part EB. This geometric taskproduces the common ratio AB/AE = (1+ √5)/2, known as the golden ratio, de-noted as φ (or τ). The ratio has manyunique, almost magical mathematicalproperties (for example, φ2 = φ + 1, and1/φ = φ – 1), and it is these properties, aswell as connections to the Fibonacci se-quence, that have fascinated artists andarchitects, enabling them to produce de-signs and compositions with specialproperties. Other ratios and special geo-metric constructions (root rectangles,reciprocal rectangles, and grids of simi-lar figures) also guide composition anddesign.

Art engenders mathematics

It is to be expected that in the executionof an artwork, mathematical questionswill arise that the artist (or fabricator)must answer. This goes with the territory.In many instances, artists will struggle toanswer the questions on their own inorder to reach the answer in a way thatmakes sense to them. Escher did this inseeking to answer the question “How canI create a shape that will tile the plane insuch a way that every tile is surroundedin the same way?” Sometimes these ques-tions need the attention of trained math-ematicians, engineers, or software de-signers and provide interesting practicalproblems to solve. The intricate textilepatterns of designer Jhane Barnes resultfrom close collaboration with mathema-tician Bill Jones and computer softwaredesigner Dana Cartwright of DesignerSoftware.

There are also frequent instances wherefinished works of art suggest purelymathematical questions, ones that theartist never imagined, nor needed to con-sider. Folk art from other times and othercultures is a rich source for mathemati-cal questions. Celtic knots and art fromAfrican cultures are two examples. Mod-ern sculptures can also lead to math-ematical questions. Escher’s tessellationsand some prints have been the source ofseveral mathematical challenges, mostnot yet settled. Two of these mathemati-cal questions seek to understand the re-lationships between local and globalsymmetry.

A most mathematical artist

I want to end this essay with a bit moreabout the work of the Dutch graphic art-ist M.C. Escher (1898-1972), who is per-haps the most astonishing recent ex-ample of an artist whose work containsa multitude of connections betweenmathematics and art. Escher was notmathematically trained, and evenstruggled with mathematics as a schoolstudent. Yet he did not reject mathemat-ics, but instead figured out in his ownway, using various (mostly pictorial)sources, the mathematics that he neededin order to realize his ideas and visions.Escher celebrated mathematical forms:polyhedra as decoration, stars, or livingstructures, Möbius bands, knots, andspatial grids. He used (and sometimesfused) various geometries in his work—Euclidean in his tessellations, hyperbolicin his Circle Limit series, projective in de-picting scenes in linear perspective,spherical in prints and his carved spheres.He employed topological distortions andtransformations, strange or multiple per-spectives, and visual recursion. He ex-plored the topic of symmetry and tessel-lation in the plane, on the sphere, and inthe Poincaré disk, developing his own“layman’s theory” of classification oftypes of planar periodic tilings and sym-metric coloring of them, anticipatingmathematician’s and crystallographer’slater studies of these topics. He asked andanswered, in his own way, combinatorialgeometric questions. He depicted ab-stract mathematical concepts in visualmetaphors. And though Escher’s workgained him the admiration of mathema-ticians and scientists, he felt isolated asan artist. Today there are many artistswhose work is directly or indirectly in-spired by Escher’s work. While he has leftus his own legacy, others are continuingto explore some of the paths he blazedand also are striking out on new pathsfrom these.

This essay is a shorter version of DorisSchattschneider’s contribution to theMAM 2003 web site. The online versionat http://www.mathforum.org/mam/03includes full references (and links) for eachof the topics and artists mentioned.

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I usually arrive a day early for nationalmeetings of the MAA, because as editorof FOCUS and MAA Online I need toattend the meeting of the Board of Gov-ernors, which typically happens the daybefore the meeting begins. Thistime, though, I arrived even ear-lier, and only made a short ap-pearance at the Board. Instead, Ispent two days attending theMAA Short Course on ancientmathematics. That also meantthat I was already there Sundaynight when there was a small fireat the Sheraton. After some ex-citement we were all moved toanother hotel for what turnedout to be a two-day stay. Becauseof all this, I was late for EleanorRobson’s talk on MesopotamianMathematics. The part I did getto listen to was very nice. Robsonencouraged interested partici-pants to learn cuneiform and getinto the game themselves; per-haps one or two will!

The talks that followed, that dayand the next, were all very useful and in-teresting. I particularly enjoyed RevielNetz’s discussion of Archimedes and KimPlofker’s overview of Indian Mathemat-ics. On the Tuesday, the speakers held ajoint question session. That afternoon,the short course group went to theWalters Art Museum to see theArchimedes Palimpsest and learn abouthow it is being studied.

On Wednesday things began in earnest.The first event for me was a panel dis-cussion on “Truth in Using History ofMathematics in Teaching Mathematics.”I was one of the panelists, perhaps rep-

resenting non-historians who make se-rious use of history in their classes. Thepanel was organized by HOMSIGMAA,the MAA special interest group on thehistory of mathematics. To some extent,we were preaching to the choir, sincemany of those present were historians orat least part-time historians. But the topicgenerated some useful and interestingdiscussion, and I enjoyed myself.

I ended up going to far fewer of the ple-nary talks than I had hoped to, and neverdid make it to any of the special sessions.Partly this was because of having to be atso many committee meetings, but the

other reason was the sheer abun-dance of things to do and peopleto talk to. I did go to talks by EdScheinerman, Joe Silverman,Noam Elkies, Robin Wilson, andIvor Grattan-Guinness. I particu-larly enjoyed Robin Wilson’s talkon the four-color theorem.

I always attend the prize sessionand the MAA business meeting.This is in part because of my re-sponsibilities as a “member of thepress.” (Does FOCUS count as“the press”?) But the prize ses-sion is also an opportunity tohonor people who have madesignificant contributions tomathematics and to our profes-sional organizations. We listenedto the MAA and AMS presidentsannouncing the winners andreading from their citations,

squinted a little to try to see the winner’sfaces from a distance, and applauded. Itwas a happy moment.

Though there wasn’t all that much busi-ness to transact, the MAA business meet-ing was enjoyable. Ann Watkins gave RonGraham a gavel to use when presidingover MAA meetings, and then gave allmembers in attendance a “dot.” It seemsthat some members have expressed envy

My Adventures in Baltimore

By Fernando Q. Gouvêa

IN FOCUS: The January 2003 Joint Mathematics Meetings

My badge, sporting the MAA Business Meeting “dot” andmy own additions identifying me as editor of FOCUS andMAA Online. I forgot to add the circumflex in Gouvêa.

More than five thousand mathemati-cians came to the Joint Meetings of theAMS and MAA in Baltimore this Janu-ary. As always, the meetings were a diz-zying affair, with plenary talks, panel dis-cussions, special sessions, and commit-

tee meetings all happening simulta-neously while the book exhibits temptedparticipants to leave all that behind andspend their hard-earned money. Sincethe MAA has about 25,000 members, atleast 20,000 of you weren’t there. While

we can’t bring you anything like a realsummary of all that went on, the follow-ing pages are a sampler. Perhaps nexttime you will be there!

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of the colorful dots worn by NExT fel-lows (a different color each year), andeven more so of the large collection ofdots that those who have worked withseveral generations of NExT fellows haveon their badges. So we all got dots forattending the business meeting. Theysaid “I survived the MAA business meet-ing.” Which is true. Not that it was all thathard to survive.

People who know me know that I’mcrazy about books. So they wouldn’t besurprised to hear that I spent a lot of timeat the exhibits. I talked to publishersabout sending review copies of theirbooks to MAA Online, asked them about

what was new, bought a few books, an-noyed the folks at the MAA booth,bought a icosahedral stress reliever, hadJohn di Pillis make a caricature of me(sitting on a pile of books, of course) andeven spent some time signing books. BillBerlinghoff and I signed copies of our“gentle history,” Math through the Ages,at the MAA booth. It was fun to do, andgave us a chance to talk to lots of people.

People think of the exhibits as beingabout books. That’s partly true, butthere’s other stuff, too. I was particularlyhappy to see Helaman Ferguson and hissculptures.

I don’t know whether the residents ofBaltimore noticed the 5,000 mathemati-cians in their midst. Perhaps they weretoo distracted by the cold. I had a goodtime, learned some things, got to seepeople I like, met new people, went tosome great restaurants and to some thatwere not-so-great, and even bought a fewbooks.

Fernando Gouvêa (and yes, the circumflexis required) is Professor of Mathematics atColby College in Waterville, ME. Despitehaving been born in Brazil, he likes coldweather and thought the temperature inBaltimore was quite nice. He is the authoror co-author of four books.

One of the highlights of the JanuaryJoint Meetings is the Morgan PrizeLecture, in which the winner of theMorgan Prize for Outstanding Researchby an Undergraduate gives a talk on hisor her work. The 2002 Morgan Prizewent to Josh Greene of Harvey MuddCollege. Greene’s work is incombinatorics, dealing specifically withKneser’s Conjecture (proved by Lovászin 1978) which states that if the k-element subsets of a n-element set arepartitioned into n-2k+1 classes then oneof the classes must contain a pair ofdisjoint subsets.

Greene’s beautiful new short proof of thistheorem is explained in his paper “A newshort proof of Kneser’s conjecture,”which appeared in the December issueof the American Mathematical Monthly.The citation for the prize points out that“In his senior thesis, Greene addressesfurther associated combinatorialquestions and has already provided twonew simplified proofs of Schrijver’stheorem on chromatic-critical subgraphsof Kneser graphs. His insight intopological combinatorics bypassestraditional technical difficulties in thisarea, and experts predict that his methodwill become the standard approach inthis rapidly developing area ofmathematics.”

Josh Greene was born and raised in the

sprawling suburbs of Columbia,Maryland. After early unsuccessfulattempts to become an artist and prohockey player, Josh took up an interestin science and mathematics during high

school. Beginning in his junior year, hestudied astrophysics under the guidanceof Dr. Jay Norris at NASA / GoddardSpace Flight Center, and was named aFinalist in the 1998 WestinghouseScience Talent Search for his work there.In the summer of 1998, Josh was astudent at the Hampshire CollegeSummer Studies in Mathematics, whichsparked his interest in combinatorics,and he returned to teach at the programin 1999 and 2002. He matriculated atHarvey Mudd College in 1998, where heenjoyed a broad education and learningfrom a dedicated, enthusiastic faculty,graduated with distinction inmathematics in 2002. During college,Josh also participated in the BudapestSemesters in Mathematics, JosephGallian’s Research Experience forUndergraduates in Duluth, Minnesota,and the Director’s Summer Program.Each program uniquely shaped hisresearch experience and current interests,which include discrete mathematics,number theory, and topology.

Josh is currently building houses withHabitat for Humanity in Appalachiathrough the Americorps serviceprogram, and he plans to enter theUniversity of Chicago next fall to pursuea doctorate in mathematics. When he isnot studying or communicatingmathematics, Josh enjoys hockey,Frisbee, nature, and trying to determinethe meaning of life.

Josh Greene Wins the 2002 Morgan Prize

Josh Greene giving his MorganPrize lecture.

The winner: Josh Greene receivesthe Morgan Prize.

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Report on the Undergraduate Student Poster Session in Baltimore

By Mario Martelli

The 2003 Undergraduate StudentPoster Session was a resounding suc-cess. I received 108 applications. Theroom of the Baltimore ConventionCenter reserved for the event could ac-commodate only 80 and I had to say“no” to many interesting researchprojects. Fortunately, thanks to an un-predictable sequence of events, JimTattersall, Associate Secretary of theMAA, was able to offer the same roomfor a morning session that was at-tended by 23 teams. Although I couldnot organize an evaluation for theposters displayed at this additional ses-sion, I received three books from Cam-bridge University Press and we had a ran-dom drawing among the participants.Thanks to my recommendation quite afew people, including Ron Graham, thenew President of the MAA, came to seethe morning posters.

The afternoon session was a sight to beseen. The 42' x 80' room was packed with192 undergraduates presenting theirposters, 115 judges evaluating them, andmany visitors and friends. Those whoattended the session for the first timecould not believe their eyes. Those whohad attended previous sessions told merepeatedly that the posters are gettingbetter every year. Among the judges of-fering their help there was a large groupof Project NExT fellows and consultants.I cannot thank them enough for pro-viding crucial support. Part of the creditgoes to Joe Gallian, who sent an e-mailto the entire Project NExT family askingthem to get in touch with me to offerhelp. I used 43 judges from this group. Ialso asked 6 of them to be my “standbyjudges,” necessary to solve all last min-utes emergencies. (There were a few.) Iwant to recognize the contribution of 12faculty members from the CaliforniaState University system. I will not men-tion their names here, but I was movedby their presence.

Sixteen posters were recognized as stand-ing out among equals. The prize: $100each. The money was offered by the

MAA, AMS, AWM, CUR and by someanonymous donors. The posters recog-nized are listed in alphabetical order.

Poster # 5 on Semiregular relative differ-ence sets authored by Christine Berkesh(Butler University), Jeff Ginn and ErinMilitzer (Central Michigan University),and Erin Haller (University of Missouri,Rolla). The research was done at CentralMichigan University (NSF-REU pro-gram). The supervisor was Ken Smith.

Poster # 6 on Analysis of a food chain withan added competitor authored by BrianBockelman (State University of WestGeorgia), Elisabeth Green (University ofNebraska-Lincoln), Leslie Lippitt (IowaState University), Jason Sherman (KentState University). The research was doneat the University of Nebraska-Lincoln(NSF-REU). The supervisors were BoDeng and Wendy Hines.

Poster # 7 on Canards in the forced Vander Pol equation authored by KatherineBold (University of Texas at Austin). Theresearch was done at Cornell University(NSF-REU). The supervisor was JohnGuckeneimer.

Poster # 16 on Biquaternionic projectivespace authored by Scot Childress (Cali-fornia State, University Fullerton). Theresearch was done at California StateUniversity, Fullerton (Sally-Casanova

Predoctoral Fellowship). The super-visor was Alfonso Agnew.

Poster # 19 on Asymptotic analysis offinite deformation in a nonlineartransversely isotropic incompressiblehyperelastic half-space subjected to atensile point load authored by EthanCoon (University of Rochester). Theresearch was done at James MadisonUniversity (NSF-REU). The supervi-sors were Debra and Paul Warne.

Poster # 22 on A computational modelfor the motion of flagella authored byOscar Del Valle (University of Cali-

fornia, San Diego), Heather Flores (Uni-versity of Nebraska-Lincoln), and StefanMendez-Diaz (University of Chicago).The research was done at the Universityof Puerto Rico Humacao (NSF-REU andNSA). The supervisor was Victor Moll.

Poster # 34 on The rigidity of plane gridsand some new extensions authored bySandra Gregov and Joe Aiken (York Uni-versity). The research was done at YorkUniversity (NSERC Canada). The super-visor was Walter Whiteley.

Poster # 48 on How hard is the knighttour? authored by Ananda Leininger(MIT), and Kevin McGown (OregonState University, Corvallis). The researchwas done at Oregon State University,Corvallis (NSF-REU). The supervisorwas Paul Cull.

Poster # 50 on Mixed vs. independent pre-dation terms in one predator, two prey sys-tem authored by Leslie Lippitt (IowaState University), Elisabeth Green (Uni-versity of Nebraska-Lincoln), and JasonSherman (Kent State University). Thework was done at the University of Ne-braska-Lincoln (NSF-REU). The super-visors were Bo Deng and Wendy Hines.

Poster # 56 on A mathematical model foran electro-pneumatic pulsed jet actuatorauthored by Borislav Mezericher(Queens College) and Matthew Willyard(University of Rochester). The research

The afternoon poster session drew a large crowd.

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Aparna Higgins, flanked by MarioMartelli and Colin Adams, announcesthe winning posters.

The winners, with Mario Martelli and ColinAdams.

was done at the Worcester PolytechnicInstitute (support from the Center forIndustrial Mathematics and Statistics).The supervisor was Bogdan Vernescu.

Poster # 59 on Polynomials and powerseries in the Sierpinski gasket authored byJonathan Needleman (Oberlin College).The work was done at Cornell Univer-sity (NSF-REU). The supervisor was BobStrichartz.

Poster # 65 on K*-ultrahomogeneousgraphs authored by Stephanie Proctor(California State University, Fullerton),and Chris Jankowski (Notre Dame). Thework was done at the University of NotreDame (NSF-REU). The supervisor wasDan Isaksen.

Poster # 68 on The effects of mass trans-portation during the deliberate release ofsmallpox authored by Karen Rios-Soto(Cornell University), Emilia Huerta-Sanchez (Cornell University), andGuarionex Jordan-Salivia (University ofIowa). The work was done at CornellUniversity (supported by the Mathemati-cal and Theoretical Biology Institute).The supervisor was Carlos Castillo-Chavez.

Poster # 69 on Cyclotomic factoriza-tion authored by Jeremy Rouse(Harvey Mudd College). The re-search was done at Harvey MuddCollege. The supervisor was ArthurBenjamin.

Poster # 78 on Optimal control andcoupled solid-state lasers authored byJohn Workman (University of Ten-nessee, Knoxville). The research wasdone at the University of Tennessee,Knoxville (NSF-REU). The supervi-sor was Suzanne Lenhart.

Poster # 82 on Constructing the modulispaces of Riemann surfaces with aG(k,l,m,n) action authored by KathrynZurh (Mount Holyoke College). The re-search was done at Rose-Hulman Insti-tute of Technology (NSF-REU). The su-pervisor was Allen Broughton.

All students attending the poster sessionand everybody reading this report shouldregard every presenter as a winner. Just

to be there after being selected by a pro-fessional mathematician, and after theposter was accepted among others setaside is the recognition of a great accom-plishment. The prizes are given ex-equo,that is, among equals. Many posters wereranked by the judges only one or twopoints lower than the posters recognized.

Everyone should also keep in mind thatalthough all judges are committed to afair evaluation, they bring to it personalpreferences and different evaluatingstyles. This year I was very pleased to beable to award prizes to some young un-dergraduates who had attended theposter session before and did not receivea prize the first time. Students, please do

not give up. You will find a set of judgeswho really appreciate your work.

I wish I could describe all posters, butthe editor of FOCUS is not going to giveme the space I would need. (Indeed! –Ed.)I want to say, however, that a great num-ber of students did their work in connec-tion to NSF-REU programs. I received 8posters from the program organized byHerbert Medina and Ivelisse Rubio at theUniversity of Puerto Rico Humacao.Cornell came in strong at 11 posters,some from the NSF-REU program and alarger number from the Mathematicaland Theoretical Biology Institute di-rected by Carlos Castillo-Chavez. Fourposters came from the NSA NSF-REUprogram at Miami University, and an-other four from the NSF-REU programat California State University, San Ber-nardino. Three posters came from theNSF-REU program at Central MichiganUniversity, and another three from theNSF-REU program at the University ofNebraska-Lincoln.

Of course, all the institutions that spon-sored (and funded!) students are close tomy heart. I count on your full participa-

tion next year in Phoenix. I have aformal promise from Jim Tattersall,Associate Secretary of the MAA thatwe will get a bigger room. We willinvite the press to see how energetic,enthusiastic, and well informed ourundergraduates are.

Congratulations to all students! Myheartfelt thanks to the Advisors, tothe Judges, to Colin Adams for find-ing the prize money, and to AparnaHiggins for standing on an unstableplatform to announce the winnerswith a lot of humor and many ap-propriate comments. I would be de-lighted to see all of you at the 2004

Winter Meeting in Phoenix.

Mario Martelli teaches at ClaremontMcKenna College. He has been organiz-ing student poster sessions at the JointMathematics Meetings for many years.

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Yueh-Gin Gung and Dr. Charles Y. Hu Award forDistinguished Service to Mathematics

Clarence F. Stephens

Certificates of Meritorious Service

Larry J. Morley, Illinois Section (ISMMA)Karin Chess, Kentucky SectionAlvin R. Tinsley, Missouri SectionLester H. Lange, Northern California SectionLuise-Charlotte Kappe, Seaway SectionFredric Tufte, Wisconsin Section

Deborah and Franklin Tepper Haimo Awards forDistinguished College or University Teaching ofMathematics

Judith Victor Grabiner, Pitzer CollegeRanjan Roy, Beloit CollegePaul Zeitz, University of San Francisco

Chauvenet Prize

Thomas C. Hales“Cannonballs and Honeycombs”Notices of AMS, April 2000, vol. 47, no. 4, 440-449.

Frank and Brennie Morgan Prize for OutstandingResearch in Mathematics by an Undergraduate

Joshua Greene“A new short proof of Kneser’s conjecture”

MAA Prizes and Awards at the Baltimore Joint Meetings

Prizes and Awards from the American MathematicalSociety:

Leroy P. Steele Prize for Mathematical Exposition:John B. Garnett

Leroy P. Steele Prize for Seminal Contribution toResearch:Michael Morley and Ronald Jensen

Leroy P. Steele Prize for Lifetime Achievement:Ronald L. Graham and Victor W. Guillemin

George David Birkhoff Prize in Applied Mathematics:Charles Samuel Peskin and John Norman Mather

Frank Nelson Cole Prize in Algebra:Hiraku Nakajima

Levi L. Conant Prize:Nicholas Katz and Peter Sarnak

Ruth Lyttle Satter Prize:Abigail Thompson

Prizes and Awards from the Association for Women inMathematics

Alice T. Schafer Prize for Excellence in Mathematics byan Undergraduate Woman:Kate Gruher

Louise Hay Award for Contributions to MathematicsEducation:Katherine Puckett Layton

Joint Policy Board for Mathematics CommunicationsAward

Robert Osserman

For more information on the prizes and awards see the Februaryissue of FOCUS or visit http://www.maa.org/news/awards_jan03.html and the links therein.

All of the prize winners sitting patiently on the stagewaiting for their moment of glory.

Other Prizes and Awards Announced in Baltimore

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President Ann E. Watkins opened theBusiness Meeting of the MAA with atribute to Henry L. Alder. She also de-voted some time at the Board of Gover-nors meeting to recalling Alder’s out-standing contributions as a wonderfuland caring leader within the MAA. Aformer Secretary and President of theAssociation, Henry led the organizationin a variety of areas. One of the mostnotable contributions was his meticulouswork with the first Haimo Awards Com-mittee. In his careful way, Henry pro-vided for the MAA as he accepted his re-cent illness. At its meeting in November2002, the Executive Committee approvedthe regulations for another teachingaward—this time for people at the be-ginning of their careers—from an anony-mous donor. Unbeknownst to the Execu-tive Committee, Henry (the benefactor)had died the day before its meeting. Atthese January meetings, the Board ofGovernors approved the new Henry L.Alder Awards for Distinguished Teach-ing by Beginning College or UniversityMathematics Faculty. We will appoint acommittee to administer the award.

One of the most significant items to re-port is the recent gift of more than$3,000,000 from Virginia and PaulHalmos for the establishment of theMAA Conference Center. (See the Feb-ruary issue of FOCUS for details.) Thehistoric Carriage House adjacent to theMAA Headquarters building will berenovated to accommodate a small Con-ference Center, which will be used formeetings and seminars to advance theactivities of the MAA in professional de-velopment and in the study of math-ematics. I want to offer special thanks toJerry Alexanderson who helped to makethe idea of the gift a reality and to JerryPorter, who was a masterful manager ofthe stock transfer. Members of the Advi-sory Board for the new Conference Cen-ter are Gerald Alexanderson (chair), ArtBenjamin, Sr. Helen Christensen,Hortensia Soto-Johnson, CarlPomerance, Kenneth Ross, David Scott,and Larry Wallen. Jerry Alexanderson

also heads the Building Committee forthe Center.

The newest members of the IcosahedronSociety are the Mary P. Dolciani HalloranFoundation and, of course, Virginia andPaul Halmos.

The new software system installed overthe past year has reduced our reliance onoutsourcing and has resulted in our com-plete ownership of our own database. Wewill be launching e-commerce veryshortly and we intend to increase ourstaff in the information systems area tosupport the many member and non-member services that we hope to offer.The non-member services are meant toserve the community, increase revenue,and attract members.

Project NExT continues to be one of ourpremier programs, but it is in continualneed of our financial support. Pleaseconsider making a gift (or urging othersto make a gift) that would support oneor more Fellows annually. We are happyto announce that some of the CBMSmember organizations such as AMS andNCTM have agreed to sponsor one ormore Fellows. Contact the office if youknow of someone who might be inter-ested in providing such support.

The major actions of the Board of Gov-ernors at its meeting on January 14 aresummarized below. The Board has ap-proved the following meetings of theAssociation:

July 31-August 2, 2003, in Boulder COJanuary 7-10, 2004, Phoenix, AZAugust 12-14, 2004, in Providence, RIJanuary 5-8, 2005, in Atlanta, GAAugust 4-6, 2005, in Albuquerque, NMJanuary 12-15, 2006, in San Antonio, TXJanuary 4-7, 2007, in New Orleans, LAJanuary 6-9, 2008, in San Diego, CAJanuary 7-10, 2009, in Washington, DC

The Board approved the Dues Matrix for2004, including $1 to $5 increases over

2003 dues inthe primarymembershipcategories.

R e t i r e dpeople whoqualify mayretain mem-bership at nocost, receiv-ing FOCUSand memberprivileges such as reduced rates for meet-ing registrations and book discounts.Such Retired Members may subscribe toa journal by paying a fee. The Board ofGovernors has approved a Bylaws changeto the effect that Retired Member’s jour-nal fees should not be stipulated in theBylaws of the Association. This will cometo a vote of the membership at the nextBusiness Meeting. Details on the pro-posed Bylaws changes will appear in theMay issue of FOCUS.

Membership Director Jim Gandorf re-ported that membership is holding fairlysteady. We have six SIGMAAs now andmore than 1500 paid SIGMAA member-ships to date.

The Board has approved electronic vot-ing as an option for national elections. Acommercial firm will run the electionfrom its website. Ballots will be sent bymail, and also will appear on the web site.Members are encouraged to vote online(very secure and simple) but they maycontinue to choose to use the US mail.Ballots will be mailed by April 1. I wantto thank Julie Kraman in the MAA of-fice for having carefully arranged andprepared for this innovation.

The State of Illinois in which we are in-corporated has ruled that electronic vot-ing may replace mail ballots. In order tobe sure that there is no confusion, theBoard of Governors approved severalsmall changes in the Bylaws. These willalso appear in the May issue of FOCUS

Secretary’s Report on the Joint Meetings

By Martha J. Siegel

Martha Siegel

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FOCUS March 2003

and will be voted on at the next BusinessMeeting.

The Board approved Section Bylawchanges for the California Sections, andthe Indiana, MD-DC-VA, Michigan, andthe Pacific Northwest Sections. Therewere some boundary changes in theSouthern and Northern California Sec-tions and the name of the Northern Cali-fornia Section will be changed to theNorthern California, Nevada, and HawaiiSection.

The Board voted to reorganize the Com-mittee on the American MathematicsCompetitions (CAMC). CAMC will bea small executive-type committee. ElginJohnston is the chairperson. There willalso be a large Advisory Board compris-ing representatives appointed by theMAA President on the advice of support-ing organizations. Titu Andreescu is fin-ishing his Ph.D. and is preparing to leavehis position as Director of Competitions.We have begun our search for a Directorof the Mathematical Olympiad SummerProgram. The Board voted to formallythank Titu for his dedication and hardwork on behalf of the AMC.

A revision of the Guidelines for Programsand Departments in the MathematicalSciences was recently approved by theBoard and can be found on MAA Online(see http://www.maa.org/guidelines/guidelines.html). I urge you to make useof this excellent document — a credit toJohn Fulton’s skill and persistence. TheseGuidelines have received the endorse-ment in principle by both the AmericanStatistical Association and the Council ofthe American Mathematical Society.

The Board elected Lowell Beineke Edi-tor-elect of the College Mathematics Jour-nal and Jennifer Quinn and Arthur Ben-jamin Editors-Elect of Math Horizons.Their five-year editorial terms beginJanuary 2004.

April is Mathematics Awareness Month.This is a project of the Joint Policy Boardon Mathematics. The theme this year willbe Mathematics and Art. We are lucky tohave MAA Second Vice-President JoeGallian heading up the effort. I urge you

to check the website at http://mathforum.org/mam/03. See also the ar-ticle on page 7.

The President appointed three new Co-ordinating Council Chairs. BarbaraFaires will chair the Council on Awards,Richard Gibbs will chair the Council onCompetitions, and Anita Solow will headup the Council on Human Resources. Weacknowledge the outstanding service ofthe outgoing chairs: Linda Sons atAwards, Frank Giordano at Competi-tions, and Robert Megginson at HumanResources. Let me formally thank theother chairs, Jim Lewis at Education, KenRoss at Meetings, and Jerry Alexandersonat Publications. They keep the organiza-tion running!

The Board elected Joan Ferrini-Mundyas Governor-at-Large for Teacher Edu-cation for a three-year term. We aregrateful to M. Kathy Heid, who servedin that role for three years. The Board willalso miss Walter Stromquist, Governor-at-Large for Mathematicians OutsideAcademia. The Board elected CarlPomerance to replace Walter as Gover-nor-at-Large representing that constitu-ency. We welcome him. Claudia Carter,Governor-at-Large for High SchoolTeachers, has resigned from the Board;Daniel Teague of the North CarolinaSchool for Science and Mathematics waselected to fill the remaining two years ofher term on the Board.

We acknowledge, with gratitude, the con-tributions of several Governors who areleaving the Board at this time. KennethA. Ross, Former President; David Stone,Chair of the Committee on Sections;Walter Stromquist, Governor-at-LargeMathematicians Outside Academia; andM. Kathy Heid, Governor-at-Large forTeacher Education.

David Stone of Georgia Southern Uni-versity has provided exemplary serviceand leadership for the MAA for six yearsas chair of the Committee on Sections,member of the Executive Committee,and member of the Board of Governors.In July, the Board elected Nancy L.Hagelgans, of Ursinus College and theEPADEL Section, to chair the Commit-

tee on Sections, and we welcome her tothe Executive Committee and to theBoard. We thank David for all his hardwork.

When Former Presidents leave the Board,it is always difficult to say goodbye. KenRoss has been on the Board for 19 yearsand he has served as Section Governor,Secretary, Associate Secretary, President,chair of numerous committees, and iscurrently chair of the CoordinatingCouncil on Meetings. He is a wise anddedicated leader of the MAA. We thankhim for all he has done so far and expectmany more years of his contributionsand counsel.

We say goodbye to Ann Watkins as Presi-dent and congratulate her on a very ac-tive and inspirational presidency. She hasled the Association with great attentionto our mission and our membership.And she will wear the mantle of PastPresident with great aplomb. We expectthat she will have many invitations toemcee as her sense of humor and abilityin this role is now no secret! She will con-tinue as a member of the Executive Com-mittee through 2003 and will remain onthe Board for several years more.

And we welcome Ronald L. Graham,President. We congratulate him on win-ning the American MathematicalSociety’s Steele Prize for LifetimeAchievement. The MAA believes that youain’t seen nuthin’ yet! The best of hisachievements are yet to come!

As you can imagine, meetings do not justhappen. They take careful and imagina-tive planning. I wish to express appre-ciation for the fine work of the membersof the Program and Local ArrangementsCommittees for the Baltimore JointMathematics Meetings, with a specialthank you to (new Grandpa) AssociateSecretary Jim Tattersall. It was a wonder-ful meeting, with record attendance. Ihope the Joint Meetings will come backto Baltimore soon.

Martha J. Siegel is MAA Secretary andteaches at Towson University, just outsideof Baltimore.

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March 2003

Ann Watkins, MAA President.

Paul Sally, InvitedSpeaker.

Fred Rickey gives instructions to shortcourse participants on how to get to the

Walters Art Museum.

Where everyone wanted to be: partici-pants entering the book exhibits.

Ready to go: the MAA Book Exhibit at thebeginning of the meeting.

Message board and meeting area at theBaltimore Convention Center.

Demo on ecommerce at the MAABoard of Governor’s meeting.

Martha Siegel, MAASecretary

An unusual concentration of historicalexpertise: Joe Dauben, Eleanor Robson,and Reviel Netz listen to a talk at theshort course on ancient mathematics.

John de Pillis does carictures ofparticipants at the MAA booksale.

The managing editor of FO-CUS struts her stuff beforethe Board of Governors.

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FOCUS March 2003

The other place everyone wanted to be: the long-est line at the meetings was the line for the emaillab.

Robin Wilson explains the four-color theo-rem.

Ron Graham, incomingMAA President.

Participants gathered in the Baltimore Conven-tion Center to catch up with colleagues.

Robin Wilson in a four-color shirtjust before his talk on the four-color theorem.

Poster session on NSF-funded projects in Math-ematics Education.

Almost all gone: the MAA booksale at the end ofthe meeting.

FOCUS

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March 2003

Benoit B. Mandelbrot, 78, Sterling Pro-fessor of Mathematical Sciences, YaleUniversity; and James A. Yorke, 61, Dis-tinguished University Professor of Math-ematics and Physics, University of Mary-land, have won the Japan Prize. They willshare the $412,000 prize money from theScience and Technology Foundation ofJapan.

The Japan Prize recognizes “original andoutstanding achievements that contrib-ute to the progress of science and tech-nology and the promotion of peace andprosperity of mankind.”

Mandelbrot hasbeen called the“father offractals.” In l993,when he won theWolf Prize forP h y s i c s ,Mandelbrot wascited for “havingchanged our viewof nature.” Physi-cist Michael V.Berry has writtenthat”“fractal geometry is one of thoseconcepts which at first sight invites dis-belief but on second thought becomesnatural that one wonders why it has onlyrecently been developed.” John Wheeler(the Princeton physicist) wrote that “no

one will be considered scientifically lit-erate tomorrow who is not familiar withfractals.”

“Fifty years ago” said Mandelbrot, “whenI began to study complexity for its ownsake, I was very lonely,” Mandelbrot said.“Today, it is the theme of this great prizeand I am utterly delighted to be chosenas a recipient. Early on, I became a wan-derer-by-choice between the disciplines,and between theory and applications.Electing to live as a constant maverick, Iallowed my interests to move in and outof mathematics, in and out of physics,of economics, or diverse other fields ofphysical and social sciences, and evenmusic and art. I showed that very simpleformulas can generate objects that ex-hibit an extraordinary wealth of struc-ture. Lately, I have also been very activein college and high school education. Ifeel extraordinarily privileged that myprofessional life has continued longenough to allow me to merge every oneof my activities into a reasonable begin-ning of a science of roughness.”

James Yorke has been called “Dr. Chaos,”that is, the one who found the universalmechanism underlying nonlinear phe-nomena, naming it chaos.

Early in his academic career, James Yorkequickly earned a reputation as a man

Benoit Mandelbrot and James Yorke Win Japan Prize

with an unpredict-able mind. “Hethinks very uncon-ventionally,” saysEdward Ott, a pro-fessor of physicsand electrical engi-neering at the Uni-versity of Mary-land, who has col-laborated withYorke. “When I’m talking to him in thehall sometimes, he’ll say something thatseems completely bizarre to me. Then I’llgo away and I’ll think, ‘Hey, that was verygood.’’

In 1975, Yorke published the math pa-per that made him famous. It was called“Period Three Implies Chaos,” and it gavea name to the emerging new field thatwas thereafter known as chaos theory.

In his best-selling 1987 book, Chaos:Making a New Science, author JamesGleick summed up the revolutionary ef-fect of Yorke’s paper: “Yorke had offeredmore than mathematical result. He hadsent a message to physicists: Chaos isubiquitous; it is stable; it is structured.”

More information about the award andthis year’s winners can be found athttp://www.japanprize.jp/English.htm.

James Yorke

MAA CP L1 Innovations in TeachingUpper Level Mathematics CoursesSaturday afternoon

This session offers a forum for faculty todisseminate innovative teaching tech-niques they have employed in upper levelundergraduate courses —typically thosebeyond the calculus and differentialequations sequences. Such techniques asstudent journals, guided reading assign-ments, and creative projects can poten-tially benefit mathematics teachers seek-ing to improve student learning in tra-ditionally difficult classes. The calculusreform and statistics reform movements,together, have initiated a lively and con-

tinuing discussion about teaching ap-proaches to freshman and sophomorelevel mathematics courses. While math-ematicians disagree about specifics, mostagree that the discussion has either ledto experimenting with new techniques orelse re-evaluating a time-tested ap-proach. This level of innovation and dis-cussion is just as needed in upper divi-sion mathematics courses. Many math-ematics majors have little difficulty intheir mathematics courses until theyreach the junior and senior year. Proofcourses, such as algebra and analysis, of-ten provide difficult hurdles. Manymathematics teachers have made a greatdeal of progress in incorporating inno-

vative techniques in such classes withoutsacrificing rigor. Now is an especiallyopportune time to share such techniques.

David Mazur (*)Department of MathematicsWestern New England CollegeSpringfield, MA 01119Phone: (413) 782-1696Fax: (413) 782-1746Email: dmazur@wnec.edu

Michael Axtell, Wabash CollegeCrista Coles, Elon University

Other special sessions were listed in theFebruary issue of FOCUS.

MathFest 2003: Call For Papers

Benoit B. Mandelbrot

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FOCUS March 2003

The MAA has received funding to ini-tiate a multifaceted project entitled Pre-paring Mathematicians to EducateTeachers (PMET) in response to numer-ous national reports calling for betterpreparation of the nation’s mathematicsteachers. These reports are sparkinggrowing interest among college and uni-versity mathematicians to do more tohelp improve school mathematics teach-ing. The PMET project, directed by AlanTucker and Bernie Madison, will helpnurture and support this interest by pro-viding a broad array of educational, or-ganizational, and financial assistance tomathematicians.

The major report stimulating action forimproving school mathematics teachingwas Before It’s Too Late: A Report to theNation from the National Commission onMathematics and Science Teaching for the21st Century, more commonly known asthe Glenn report, after the chairman ofthe commission, former Senator JohnGlenn. (The report is online at http://www.ed.gov/americacounts/glenn/report.pdf). The Comission, which wasappointed by then Secretary of Educa-tion Richard Riley on July 20, 1999, is-sued this report on September 27, 2000.Among the representatives of the math-ematics community on the commissionwere Deborah Ball, Professor of Math-ematics Education at the University ofMichigan; Diane Briars, MathematicsDirector of the Pittsburgh PublicSchools; and Javier Gonzalez, a math-ematics teacher from Pioneer HighSchool in California. The commission’sExecutive Director was Linda Rosen, for-merly the Executive Director of the Na-tional Council of Teachers of Mathemat-ics.

The Glenn Report made only a fewstraightforward points, but it made themurgently and insistently. In particular, thereport concluded that “the most power-ful instrument for change, and thereforethe place to begin, lies at the very core ofeducation — with teaching itself.” It sug-gested three specific goals, each accom-

panied by several strategies to accom-plish the goal.

Goal 1: Establish an ongoing system toimprove the quality of mathematicsand science teaching in grades K-12.

1. Each state must undertake a needsassessment.

2. Summer Institutes must be establishedfor professional development.

3. Inquiry groups should be established,both building-wide and district-wide.

4. Leadership training must be madeavailable for facilitators for SummerInstitutes and Inquiry groups.

5. There should be a Dedicated InternetPortal for teachers.

6. A Nongovernmental CoordinatingCouncil must be established to bringtogether the above.

7. Reward and incentive programsshould be set up in each state andlocal district.

Goal 2: Increase significantly the num-ber of mathematics and science teach-ers and improve the quality of theirpreparation.

1. Identify exemplary models of teacherpreparation whose success can bewidely replicated.

2. Find ways to attract additionalqualified candidates into teaching.

3. Create 15 competitively selectedMathematics and Science TeachingAcademies to train annually 3000Academy Fellows on effective teachingmethods in science and mathematics.

Goal 3: Improve the working environ-ment and make the teaching professionmore attractive for K-12 mathematicsand science teachers.

1. Establish focused induction programsto help acclimate beginning teachers.

2. Develop district/business partnershipsto provide support for a broad rangeof efforts to help create professionalworking environments for teachers.

3. Establish incentives to encourage

deserving mathematics and scienceteachers to remain in teaching andimprove their skills.

4. Make salaries of all teachers morecompetitive, especially formathematics and science teachers.

Certainly, the achievement of these goalsrequires political leadership from Con-gress and the President, not to mentionthe state governments and the localboards of education, but the MAA,through the PMET program, is attempt-ing to play a significant role toward theachievement of goal 2. This goal is alsothe focus of the 2001 report from theConference Board of the MathematicalSciences (CBMS) on The MathematicalEducation of Teachers (usually called theMET report; it can be found online ath t t p : / / w w w . c b m s w e b . o r g /MET_Document/index.htm). That reportstresses two general themes: the intellec-tual substance in school mathematicsand the special nature of the mathemati-cal knowledge needed for teaching.Mathematicians often assume, the reportpoints out, that because the topics cov-ered in school mathematics are so basic,they must be easy to teach. But recentmathematics education research hasshown that substantial mathematicalunderstanding is necessary even to teachwhole number arithmetic well. LipingMa’s widely read 1999 book, Knowingand Teaching Elementary Mathematicshas numerous examples of the differ-ences between a group of Americanteachers and a group of Chinese teach-ers in their understanding of certain “el-ementary” concepts and how those dif-ferences impact on the teaching of theseconcepts.

The authors of the MET report madenine basic recommendations, some ofwhich form the basis for the PMETproject. Among these recommendationsare:

1. Prospective teachers needmathematics courses that develop adeep understanding of themathematics they will teach.

PMET: Preparing Mathematicians to Educate Teachers

By Victor J. Katz and Alan Tucker

FOCUS

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March 2003

2. Mathematics courses for prospectiveteachers should develop the habits ofmind of a mathematical thinker anddemonstrate flexible, interactive stylesof teaching.

3. Teacher education must be recognizedas an important part of themathematics department’s mission atinstitutions that educate teachers.More mathematicians should considerbecoming deeply involved in K-12mathematics education.

4. Teachers need the opportunity todevelop their understanding ofmathematics and its teachingthroughout their careers.

One major thrust of the recommenda-tions in the Glenn Report and the METreport, at least insofar as the MAA is con-cerned, is that mathematics departmentsneed to be more involved in K-12 edu-cation. Although, historically, the collegeand university mathematics communitywas always deeply involved in schoolmathematics and teacher preparation, inrecent years this interest has been in de-cline. As the 1999 AMS report TowardsExcellence (available online at http://www.ams.org/towardsexcellence) notes,“If K-12 mathematics education in theU.S. deserves criticism (and it surely hasreceived a lot of criticism in the wake ofthe TIMSS reports), then a share of theblame falls to those university mathema-ticians who should be playing an impor-tant role in the preparation of teachersbut are not.” The report further notesthat in many institutions, a department’sincreased attention to this part of theuniversity’s mission will provide benefitsfor all aspects of departmental life.

Some universities, of course, already havea substantial involvement in K-12 math-ematics education. Among these is theUniversity of Chicago, where Paul Sally,the director of undergraduate studies,has for years insisted that the departmentcommit itself to work with school math-ematics teachers and even with their stu-dents. In his address at the Joint Math-ematics Meetings in January, Sally reit-erated that mathematicians must workseriously with educators and teachers atevery level by, for example, creating prob-lems that could span the grades from kin-dergarten to graduate school. Similarly,

at Oklahoma State University, the math-ematics department faculty is signifi-cantly involved in instructional pro-grams, centered in the College of Edu-cation, in the preparation of elementaryand high school teachers. Interestingly,undergraduates majoring in mathemat-ics education consider the Departmentof Mathematics their “home,” not theCollege of Education, and look to math-ematics faculty as mentors and advisors.

Although there are numerous other ex-amples of university and college math-ematics departments being heavily in-volved in the preparation of K-12 teach-ers, the majority of college and univer-sity mathematicians still need assistancein finding appropriate instructionalstrategies for helping future teachers con-nect their college mathematics to themathematics they will teach and alsoneed better information about the math-ematical issues that arise in K-12 class-room lessons. It is the goal of the PMETproject to provide that assistance andinformation.

The PMET project will have three majorcomponents:

1. Faculty Training: Summer workshopsof various lengths and mini-courses atprofessional meetings.

2. Information and Resources: Articles inprofessional journals, panels atmeetings, multi-media websites, andhard-copy material dissemination tosupport faculty instruction forteachers.

3. Mini-grants and Regional Networks: tonurture and support grassrootsinnovation in teacher education onindividual campuses. These grants andnetworks will be concentrated in fivestates: New York, California, Ohio,Nebraska, and North Carolina.

Component 1 will begin this summerwith three faculty workshops on teach-ing elementary school teachers and oneworkshop for teaching high school teach-ers. In 2004 and 2005, the number ofworkshops will increase; some of theworkshops will extend over two summerswith activities in the intervening aca-

demic year. Workshop activities will in-clude (1) connecting content of collegemathematics courses to school math-ematics and discussing how those collegecourses should be taught; (2) demonstra-tion college classes by master teachers,both live and video; (3) discussions ofdemonstration classes; (4) discussions ofschool standards, both state and those ofthe National Council of Teachers ofMathematics (NCTM); (5) individualcourse development projects by partici-pants: (6) guest lectures by visiting ex-perts, including learning theory research-ers; (7) discussion of curricular materi-als; (8) discussion of reports such as theMET report; (9) use of technology; and(10) networking with others. Each work-shop will be led by a team including amathematician and a mathematics edu-cator, with at least one member (or pos-sibly a third person) having had severalyears of experience teaching school.There will also be introductoryminicourses at national and sectionalmeetings, whose aim is to get more fac-ulty interested in teaching prospectiveteachers.

As part of component 2, PMET will or-ganize talks and panel discussions aboutthe mathematical education of teachersat national and regional meetings of theMAA, the American Mathematical Asso-ciation of Two Year Colleges (AMATYC),the American Statistical Association(ASA), and the NCTM. Presentationswill be made to national education or-ganizations in order to coordinatePMET’s agenda with their goals. Further-more, PMET will encourage articles onways to support school mathematics insuch publications as FOCUS, the AMSNotices, and ASA’s Amstat News. Finally,PMET intends to develop a website withinformation and resources about themathematical education of teachers. Thissite will offer extensive guidance for get-ting started in various situations; for ex-ample, it will provide a discussion of dif-fering ways to teach a geometry coursefor teachers using available technologysuch as Cabri or Geometer’s Sketchpad.

As part of component 3, PMET will pro-vide mini-grants of approximately $3000to help faculty at individual campusesrework mathematics courses for teach-

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FOCUS March 2003

ers, bring speakers into their departmentto raise faculty consciousness aboutteacher education, and send proposals tofunding agencies for more extensivecourse and materials development.PMET will also support networking ofthose receiving these minigrants.

Most of the workshops, mini-grants, andnetworks will be concentrated in fivestates: California, Nebraska, New York,North Carolina, and Ohio. This focus willhelp the project develop a critical massof activities in a given area for maximumimpact. It will also help PMET securelocal funding of further projects. The

networks in each of the five selectedstates will connect the faculty involvedin PMET with various state educationinitiatives and help them participate inlocal and state policy-making aboutteacher education and K-12 mathemat-ics. For example, the PMET project di-rectors have already been in touch withleaders of the State of California’s Math-ematics Professional Development Insti-tutes who look to the PMET initiative totrain more California mathematics fac-ulty to teach in their institutes.

For the long-term health of K-12 math-ematics education, it is essential that col-

legiate mathematics faculty reclaim acentral role in the training and supportof classroom teachers. Through PMET,the MAA’s members have an opportunityto contribute to this process.

For more information on PMET and onhow to participate, follow the links to thePMET project on MAA Online.

Victor Katz is Professor of Mathematics atthe University of the District of Columbia.He is the author of an introductory text-book and many other books and papers onthe history of mathematics. He is currentlya visiting mathematician at the MAA.

The Board of Governors has voted toallow electronic voting in the upcomingnational election of officers of the MAA.In the spring 2003 election, memberswill elect the President-Elect, and theFirst and Second Vice Presidents. Paperinformational brochures will be sent toevery member of the Association on

MAA to Use Electronic Voting in National Election

April 1, as required by the Bylaws. Thiswill contain information on all the can-didates and a paper ballot for those whoopt to use the U.S. mail instead of theweb to cast their vote. Voting online willbe easy, secure, and fun! There will be alink on the MAA website to Intelliscan,Inc. for a replica of the paper brochure

MAA National Elections Coming Up in April

and specific instructions on how to voteonline. You simply click on your choicesas you would in any approval voting pro-cedure and hit a button to register yourvote. That’s all there is to it!

A new MAA President has just takenoffice; how can it be time for electionsagain? The reason is the MAA’s systemof allowing future Presidents a full yearof President-Elect status, during whichthey participate in the governance of theAssociation and get ready for their twoyears as President. So it’s time to electthe person who will serve as President-Elect in 2004 and then as President in2005 and 2006. It’s also time to choosenew MAA Vice-Presidents who will servein 2004 and 2005.

Election booklets and ballots will be sentout in April. Members will be able to voteeither electronically or using paperballots. See above for information onelectronic voting.

The candidates for the MAA nationalelections are:

President:

Carl C. CowenPurdue University, West Lafayette, IN

Wade Ellis, Jr.West Valley College, Saratoga, CA

Doris SchattschneiderMoravian College, Bethlehem, PA

First Vice-President

Amy CohenRutgers University, Piscataway, NJ

Barbara T. FairesWestminister CollegeNew Wilmington, PA

William Yslas VelezUniversity of Arizona, Tucson, AZ

Second Vice-President

Charles C. AlexanderUniversity of MississippiUniversity, MS

Jean Bee ChanSonoma State UniversityRohnert Park, CA

William A. Hawkins, Jr.Univeristy of the District of ColumbiaWashington, DC

FOCUS

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March 2003

Ten biologists met at Macalester Col-lege November 2-5, 2000 for the MAACurriculum Foundations Workshop inBiology. Among the biologists were LouGross from the University of Tennessee,who holds a joint appointment in ecol-ogy and mathematics, and John Jungck,who was the original developer ofBioQUEST, a reform undergraduate cur-riculum in biology. The biologists’ chargewas to provide advice for the planningand teaching of the mathematics cur-riculum as it affects biology majors. Ninemathematicians were present to answerquestions and probe for clarification.Five of the mathematicians (Fred Adler,Danny Kaplan, Eric Marland, ClaudiaNeuhauser, and Dan Tranchina) have re-search interests in the biological sciences.This article highlights the major findingsof the workshop participants. The sum-mary report is available at the Bowdoinwebsite at http://academic.bowdoin.edu/f a c u l t y / B / b a r k e r / d i s s e m i n a t i o n /Curriculum_Foundations/CF_Biology.doc.

Understanding and Content

Surveys of quantitative skills needed forbiologists frequently include college al-gebra, introductory calculus and statis-tics. Among these three areas of math-ematics, statistics is the most commonlymentioned and the most extensivelyused. Other content areas that are men-tioned include mathematical modeling,discrete mathematics, and matrix alge-bra. What follows are topics, organizedby course, that the workshop participantsidentified as important in the study ofbiology.

College Algebra or Precalculus: Biologystudents need to understand the mean-ing and use of variables, parameters,functions and relations. They need toknow how to formulate linear, exponen-tial, and logarithmic functions from dataor from general principles. They mustalso understand the basic periodic natureof the sine and cosine functions. It is fun-damentally important that students arefamiliar with the graphical representa-tion of data in a variety of formats (his-

tograms, scatter plots, pie charts, log-log,and semi-log graphs.)

Introductory Calculus: The topics fromintroductory calculus that were men-tioned at the workshop included integra-tion for the purpose of calculating areasand average value, rates of change, opti-mization, and gradients for the purposeof understanding contour maps.

Statistics: It is here where the list of nec-essary topics is the longest and encom-passed descriptive statistics, conditionalprobability, regression analysis, multi-variate statistics, probability distribu-tions, simulations, significance, and er-ror analysis.

Discrete Mathematics and Matrix Alge-bra: The topics most frequently men-tioned were qualitative graphs (trees,networks, flowcharts, digraphs), matri-ces (Leslie, Markov chains), and discretetime difference equations. Other topicsincluded equilibria, stability and count-ing techniques.

Technology

The pervasive presence of computers,together with their ever-increasing com-putational power, encourages biologiststo apply statistical methods to analyzedata that is collected in the laboratory orthe field. One important software appli-cation used by biologists is the spread-sheet. Increasingly, spreadsheet applica-tions contain sophisticated statisticaltools sufficient for use with undergradu-ate biology majors. The panelists wereunanimous in their observation that thegraphing calculator is not the tool of choicefor biology students. Technological toolsmust be capable of producing graphs thatcan be incorporated into printed andpresentation documents. They must al-low students to apply modeling tech-niques to large data sets and they mustalso support simulation of models thatare stochastic, discrete or continuous.

Implementation

The biologists generally agreed that cur-rent research areas in biology are more

quantitatively oriented. At the same time,they also recognized that the quantita-tive needs of undergraduate studentsenrolled in biology courses are diverseand depend largely upon the studentaudience (e.g., majors versus non-ma-jors) and the variety of disciplinarytracks, ranging from molecular biologyto ecology, that students choose to ex-plore. In an already crowded biology cur-riculum, the biologists agreed that theissue of increasing quantitative empha-sis would call for innovative solutions.They suggested solutions ranging fromthe creation of mathematical coursesdesigned specifically for biology majorsto the creation of mathematical modulesthat could be incorporated into existingbiology courses.

One particular challenge facing biologyeducators is the range of mathematicalbackgrounds of professors of biology.Many biology educators have completedonly calculus and one course in statis-tics. The limited mathematical back-ground of most biologists is clearly re-flected in the correspondingly limitedquantitative components of both biologytextbooks and curricula. As we begin toexpand the quantitative backgrounds ofbiology students we will also have to pro-vide opportunities for the biology fac-ulty to increase their own facility withmathematics.

To build and require more quantitativelyoriented biology courses would be amajor, but important, undertaking andwould necessitate increased cooperationamong biologists and mathematicians.The biologists viewed the proposed ac-tions of the MAA in assisting their part-ner colleagues with possible changes andemphasis in the mathematics curriculumas a catalyst for needed changes in theundergraduate biology curriculum.

Anita Salem is Professor of Mathematicsand Interim Dean, College of Arts & Sci-ences at Rockhurst University. Judith Diltsis the Dr. Burnell Landers Chair in Biol-ogy and Department Chair of Biology atWilliam Jewell College.

The Curriculum Foundations Workshop in Biology

By Anita Salem and Judith Dilts

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FOCUS March 2003

What Actually Happens in Classrooms

The Manhattan Institute for Policy Re-search recently released a report, writtenby Christopher Barnes of the Universityof Connecticut, entitled What Do Teach-ers Teach? The report is based on a sur-vey of 4th-grade and 8th-grade teachersand tries to describe their actual class-room practice. The report focuses espe-cially on assessment issues. The overallthrust is that teachers aren’t holding theirstudents to a high enough standard. Thefull report can be found online at http://www.manhattan-institute.org/html/cr_28.htm.

American Institute of MathematicsResearch Conference Center

The American Institute of Mathematics(AIM) Research Conference Center will behosting focused workshops in all areasof the mathematical sciences. The work-shops are intended to focus on a specificmathematical goal by bringing togetheractive researchers in a particular area. Seehttp://www.aimath.org/ARCC/ for theworkshops that are already scheduled,and also for information on how to or-ganize workshops. For more about AIMitself, check http://www.aimath.org.

Studying the Mathematical ReviewsDatabase

In an article published in the November2002 issue of SIAM News, MAA gover-nor Jerrold W. Grossman reports on astatistical analysis of the MathematicalReviews database. It turns out that 42.7%of the authors represented in the data-base have written only one paper. About16% have written ten or more papers.The mean number of papers per authoris 6.87, with a standard deviation of15.34.

Grossman highlights the growth in thenumber of collaborations over the lastfew decades. In the 1960s, 81% of thepapers had only one author, as comparedwith only 54% in the 1990s. Papers withthree or more authors represented only

3% of the papers reviewed in the 1960s,as compared with 13% in the 1990s.

Grossman includes a careful study of thecollaboration graph, with vertices corre-sponding to the 337,454 mathematiciansin the database and edges correspond-ing to joint papers. There are 84,115 iso-lated vertices, 16,883 small componentshaving between 2 and 39 vertices, andone giant component representing every-one else. The average distance betweentwo vertices in this component is be-tween 7 and 8, and Grossman suggeststhat “the appropriate buzz phrase formathematicians should be ‘eight degreesof separation’. See http://www.siam.org/siamnews/11-02/collaboration.pdf or theNovember 2002 issue of SIAM News forthe details.

National Academy Announces Honors

In January, the National Academy of Sci-ences announced several awards for sig-nificant contributions to research.Among those honored were David A.Freedman of the Berkeley Department ofStatistics, who received the John J. CartyAward for the Advancement of Science,and David R. Karger of the Massachu-setts Institute of Technology, who re-ceived the NAS Award for Initiatives inResearch for his work on algorithms fornetwork flow, graph coloring, minimumtrees and minimum cuts. For a completelist of those honored, see http://www4.nationalacademies.org/news.nsf/isbn/01102003?OpenDocument.

A Matched Pair of Teaching Awards

Barbara Faires was the winner of the2002 Distinguished Teaching Awardfrom the Allegheny Section of the MAA.Her husband, Douglas Faires, won thesame award from the Ohio Section in1996. It seems likely that this makes themthe only couple with a matched pair ofteaching awards.

Education Schools Under Pressure

According to the Washington Post, tradi-tional schools of education “are under

increasing pressure to change the waythey train teachers.” The article gives sev-eral examples of schools that are chang-ing their programs in response to the NoChild Left Behind Act. See http://www.washingtonpost.com/wp-dyn/ar-ticles/A52358-2003Jan13.html for thearticle.

CUPM Curriculum Guide DraftAvailable

Look for draft 4.0 of “UndergraduatePrograms and Courses in the Math-ematical Sciences: A CUPM CurriculumGuide” to appear on MAA Online earlyin March. CUPM is looking for sugges-tions and comments. Send suggestionsof additional examples for the “Illustra-tive Resources” section to Kathi Snookat kathleen.snook@verizon.net. All othercomments on this draft should go toHarriet Pollatsek, the chair of CUPM, athpollats@mtholyoke.edu. Comments willbe most helpful if received before May 1,2003. CUPM plans to have a final draftready for approval at MathFest 2003,with publication in time for the January2004 meetings.

The Decidable and the Undecidable inMathematics Education

The Mathematics Education into the 21stCentury project will be holding its nextconference in Brno, Czech Republic,from September 19-25, 2003. The title ofthe conference is “The Decidable and theUndecidable in Mathematics Education,”a tribute to Kurt Godel who was bornand educated in Brno. Plenary Speakerswill include Nicolina Malara and FilippoSpagnolo. Contact arogerson@vsg.edu.aufor more information.

Board of Governors Decides on Substi-tution Policy

After much discussion, the MAA Boardof Governors has settled on a policyabout how to handle cases in which gov-ernors are unable to attend meetings. TheBoard approved a bylaws change thatwould allow designated substitutes to be

Short Takes

By Fernando Q. Gouvêa

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March 2003

seated and to have the right to vote. Sub-stitutes must be selected among past gov-ernors for the section (or for the con-stituency) represented by the absent gov-ernors. See the May issue of FOCUS fordetails on this and other bylaws changes.

Courts Recognize “Math Phobia”

According to a news item in USA Today,an Italian court has ruled that a teenagegirl should be excused from her highschool mathematics requirements be-cause she has an “irreversible psychologi-cal pathology,” namely math phobia. Thecourt asked the school to allow the stu-dent to be promoted to a higher gradedespite having failed her mathematicscourse. According to the article, JohnnyLott, president of the National Councilof Teachers of Mathematics, suggestedthat the school “should have tried put-ting Viviana in a substitute course suchas economics, computer science or phys-ics that might have been easier for herwhile still maintaining what he called the‘intellectual honesty’ of the curriculum.”

The article goes on to quote Lott as say-ing that “Students should be taking moremath classes, not fewer. If a student hassome kind of block against math, thatmeans the school should try harder toreach that student; simply allowing thestudent to pass without a sufficient scorein math is not an alternative I can rec-ommend. We all need a certain amountof math literacy to function in the world,and that must come from the schools.”See http://www.usatoday.com/usatonline/20030121/4795963s.htm for the article.

More and More SIGMAAs

There are now six SIGMAAs (SpecialInterest Groups within the MAA), fo-cused on Philosophy of Mathematics,Environmental Mathematics, StatisticsEducation, History of Mathematics, Re-search on Undergraduate MathematicsEducation, and Mathematics in Business,Industry and Government. The SIGMAAon RUME is the largest, with 1264 mem-bers. Some of the older SIGMAAs arevery active, sponsoring special sessionsat MAA meetings and other activities.Others are just starting out. MAA mem-bers can become members of a SIGMAA

by calling up the MAA Service Centerand making the request. See http://www.maa.org/sigmaa/sigmaa.html formore information and links to the homepages of the various SIGMAAs.

Cora and Baley Price Donate Papers toArchive

G. Baley Price, professor emeritus ofmathematics at the University of Kansas,and Cora Lee Beers Price, retired assis-tant professor of classics at KU, have do-nated their professional papers to theUniversity Archives. Baley Price playedan important role in the development ofthe “new math” in the 1960s. The couplewas honored at a reception at the Uni-versity of Kansas Kenneth Spencer Re-search Library on the eve of Baley Price’s97th birthday. More information, andsome interesting samples from the col-lection, can be found online at http://www2.lib.ukans.edu/~public/spencerlib/exhibits/price/index.htm.

MET Summit II

The Benjamin Banneker Association andthe National Association of Mathemati-cians, in cooperation with other mem-ber societies of the Conference Board ofthe Mathematical Sciences, will be spon-soring a national conference on themathematical education of teachers,MET Summit II. The meeting will beheld October 11 and 12, 2003, in theWashington, D.C. area. The conferencewill emphasize the participation of his-torically black colleges and universitiesand other institutions serving minoritiesthat are involved in the mathematicaleducation of teachers. For more informa-tion, visit the BBA website at http://www.math.msu.edu/banneker or theNAM web site at http://jewel.morgan.edu/~nam.

Baltimore Talk Gets Press Attention

One of the plenary talks at the Baltimorejoint meetings got the attention of thepress even before it was given. The Uni-versity of Chicago distributed in advancea press release on Paul Sally’s talk, whichdiscussed the trend towards offering lib-eral arts students “courses about math-ematics” instead of mathematics courses.

Sally described such courses as full of“beautiful pictures and imprecise ideas,”and argued that we should be offeringthese students some real mathematics.The story was picked up by UPI( s e e ” h t t p : / / w w w . u p i . c o m /view.cfm?StoryID=20030116-012039-1511r) and the Chicago Sun-Times.

Robert Lewand Presents Ohio SectionSummer Short Course

Robert Lewand of Goucher College willpresent the Ohio Section’s summer shortcourse, entitled “Cryptography,” on July16-18. This course, designed for thosewith no experience in the subject, willinvestigate techniques of encryption anddecipherment along with the mathemati-cal underpinnings of these systems. Any-one with a background in elementarynumber theory and at least a rudimen-tary familiarity with computing (a pro-gramming language, or Maple, or evenExcel) will be sufficiently prepared tounderstand the material in this course.The course will be held at Capital Uni-versity in Columbus, Ohio. Details canbe found at the section’s web site http://www.maa.org/Ohio.

Sources. What actually happens: Wash-ington Post, December 17, 2002, Manhat-tan Institute website. AIM Research Con-ference Center: AIM web page. Patternsof collaboration: Ann Watkins, SIAMNews (November 2002). NAS honors:NAS website. Matched pair: LeoSchneider, section web pages. Educationschools: Washington Post, January 14,2003, and NASSMC Briefing Service.Missing governors: Martha Siegel. Mathphobia: USA Today, January 21, 2003,NASSMC Briefing Service. SIGMAAs:president’s report to the Board. Pricepapers: KU alumni magazine, KUwebsite. MET Summit: BBA press release.Paul Sally’s talk: University of Chicagopress release, UPI website, Chicago Sun-Times. Ohio section: email communica-tion.

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Still on Heron

It may be of interest to note that Hersh’sproof of Heron’s formula (FOCUS, Nov.2002, pg. 22) exactly works forBrahmagupta’s formula for the area ofcyclic quadrilaterals.

Pete GilmoreNortheastern University

Textbook Reviews

Congratulations to the MAA on thereviews project outlined on p. 3 of thelatest issue of FOCUS. When I get backto teaching, I’ll be glad to both use andcontribute to it.

Robert ThomasEditor, Philosophia MathematicaUniversity of Manitoba

I agree that this has the potential to be anextremely useful resource. In order to getthere, we need to get more reviews of morebooks. Please visit MathDL at http://www.mathdl.org and click on theCommercial Products link to see the listingand to contribute your own reviews.

Past-Presidential Correction

I made a mistake in cutting and pastingin “A Year in the Life of the MAA” in theJanuary issue of FOCUS. The number offull-time graduate students inmathematics is not 26,168 as reportedthere. That is the number of four-yearcollege mathematics faculty from the2000 CBMS survey. The number ofgraduate students in mathematics is12,127, according to the latest AnnualSurvey of the Mathematical Sciences,published in the Notices in September2002. Thanks to Jim Maxwell forpointing this out.

Ann WatkinsMAA Past President

California State University Northridge

Letters to the Editor

The Teacher Professional Continuum(TPC) program at the National ScienceFoundation (NSF) announces new fund-ing opportunities to conduct researchstudies, as well as research and develop-ment projects for K-12 science, technol-ogy, and mathematics (STM) education.This professional continuum includes K-12 experiences, teacher preparation pro-grams, instructional practice, profes-sional development, leadership develop-ment, and other life and professional ex-periences.

The principal mission of the TPC pro-gram is to promote quality K-12 STMteaching through (1) the production ofresources, (2) the development of infra-structure, and (3) the advancement ofknowledge. To fulfill its mission, the TPCprogram set the following goals to:

• Improve the quality and coherence ofthe learning experiences that prepareand enhance STM teachers;

• Develop innovative curricula, mate-rials, tools, ideas, and informationresources that prepare and supportSTM teachers and administrators;

• Research, develop, and identifymodels, organizational structures,and systems that support the teacherprofessional continuum;

• Research teacher learning throughoutthe teacher professional continuumand its impact on teaching practiceusing scientifically-basedinvestigations;

• Advance the knowledge base on thepreparation, enhancement, andretention of STM teachers, and on thestrategies that strengthen anddiversify the STM teaching profession;and

• Disseminate this knowledge andresearch, as well as innovativemodels and resources, to a nationalaudience.

Research studies from first-time Princi-pal Investigators are especially encour-aged. The deadline for required prelimi-nary proposals is May 19, 2003. Formore information and the TPC programsolicitation visit the NSF website at:www.ehr.nsf.gov/esie/programs/te/te.asp.

Other programs in the Division of El-ementary, Secondary and Informal Edu-cation (ESIE) include the following.

Centers for Learning and Teaching -www.ehr.nsf.gov/esie/programs/clt/clt.asp

Informal Science Education -www.ehr.nsf.gov/esie/programs/ise/ise.asp

Instructional Materials Development -www.ehr.nsf.gov/esie/programs/imd/imd.asp

Presidential Awards – www.ehr.nsf.gov/pres_awards.

NSF Announces New Solicitation

Tensor Grants for Women and Mathematics Projects

The MAA plans to award grants for projects designed to encourage collegeand university women or high school and middle school girls to study math-ematics. The Tensor Foundation, working through the MAA, is solicitingcollege, university and secondary mathematics faculty (in conjunction withcollege or university faculty) and their departments and institutions to sub-mit proposals. Projects may replicate existing successful projects, adapt com-ponents of such projects, or be innovative. The deadline for proposals isMarch 3, 2003. For more information on these grants go to: http://www.maa.org/projects/solic_99.html.

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March 2003

INDIANA

INDIANA UNIVERSITY PURDUE UNIVER-SITY INDIANAPOLISEndowed Chair in Mathematics EducationThe Department of Mathematical Sciences atIndiana University Purdue University India-napolis, invites applications and nominationsfor the Marvin L. Bittinger Endowed Chair Pro-fessorship in the area of Mathematics Educa-tion.

Located in the heart of Indianapolis, IUPUI isan urban doctoral/research intensive universitywith 29,000 students. The Department of Math-ematical Sciences, with a faculty of 42 mem-bers, houses the mathematics and statistics dis-ciplines and offers a range of undergraduate andgraduate programs, leading to Purdue Univer-sity B.S, M.S., and Ph.D. degrees in mathemat-ics and applied mathematics as well as Mastersdegrees in applied statistics and mathematicseducation.

We seek a well-established colleague with na-tional/international recognition and withstrong interests in mathematics education at theuniversity level. The person holding this posi-tion is expected to be a leader in the Depart-ment, in terms of teaching, scholarship andcurricular development. In particular, the per-son will have demonstrated a commitment toworking on the forefront of efforts to advancethe teaching and learning of developmental anduniversity-level undergraduate mathematics.

Applicants must have a Ph.D. degree in themathematical sciences with academic andscholarly accomplishments adequate for ap-pointment to Full Professor. The successful can-didate must have record of teaching excellence.The Bittinger Chair offers a competitive salarycommensurate with background, experience,and record of professional achievements, andan excellent fringe benefit package.

All application materials, including a letter ofinterest, a detailed curriculum vita and thenames and contact information of at least fourreferences should be mailed to:

The Bittinger Chair SearchCommitteeDepartment of MathematicalSciencesIndiana University Purdue UniversityIndianapolis402 N. Blackford St., LD Suite270 Indianapolis, IN 46202-3216

Screening of applications will begin on March1, 2003, and will continue until the position isfilled.

IUPUI is an Equal Opportunity/AffirmativeAction Employer and strongly encourages ap-plications from women and underrepresentedminorities. Additional information aboutIUPUI and the Department is available atwww.iupui.edu and www.math.iupui.edu.

NEW YORK

BRONX COMMUNITY COLLEGE OF CUNYThe Department of Mathematics & ComputerScience invites applications for one anticipatedtenure track position starting in September2003. A Ph.D. in mathematics or computer sci-ence is preferred; enrollment in a doctoral pro-gram is desirable in its absence. Candidatesmust have a record of and commitment to ex-cellence in teaching and continued scholarlyactivity. The department has 23 full-time and55 part-time faculty members. Courses offeredrange from developmental to upper level math-ematics and computer science. Bronx Commu-nity College encourages applications fromwomen and minority candidates and is an AA/EOE. Send a letter of application, a statementof teaching philosophy, resume, graduatetranscript(s) and three recent letters of refer-ence, (at least one should address teaching), nolater than March 15, 2003, to: Prof. GermanaGlier, Chair Department of Mathematics &Computer Science, Bronx Community College/CUNY, University Avenue & West 181 Street,Bronx, NY 10453.

OHIO

THE OHIO STATE UNIVERSITYVISITING ASSISTANT PROFESSOR INMATHEMATICSThe Ohio State University at Newark is seekinga one-year Visiting Assistant Professor in Math-ematics to begin Autumn Quarter 2003. TheNewark Campus is an extended campus in TheOhio State University system that serves around1800 students and is located 30 miles east ofthe central Columbus campus.

DUTIES:Teaching load is negotiable and will consist offirst-year and second-year undergraduatecourses.

QUALIFICATIONS: Ph.D. in mathematics re-quired by start date, with research interests incommutative rings, differential geometry,

homotopy theory, optimization, and represen-tation theory preferred. Applicants should havean active research program, be able to demon-strate the ability to communicate effectively inthe classroom, and have a record of outstand-ing college teaching.

TERMS: Full-time, non-tenure track one-yearappointment.

SALARY:$38,000 - $42,000 per year.

APPLICATION PROCEDURE: To assure con-sideration, submit a research description, cur-riculum vitae and three letters of professionalreference to The Ohio State University at New-ark, Search #02-83, 1179 University Drive, New-ark, Ohio 43055 by March 28, 2003. The OhioState University at Newark is an Equal Oppor-tunity/Affirmative Action employer. Women,minorities, veterans, and individuals with dis-abilities are encouraged to apply.

UNIVERSITY OF CINCINNATIOMI College of Applied Science,Assistant Professor of MathematicsThe OMI College of Applied Science at theUniversity of Cincinnati invites applications fora full-time tenure-track Faculty position inMathematics to begin in September, 2003. TheOMI College of Applied Science is a fully ac-credited baccalaureate college with an interna-tional reputation in delivering innovative edu-cation in science and technology. The Depart-ment of Mathematics, Physics and ComputingTechnology presently has twelve full-time Fac-ulty, offers BS and AS degrees in Computer Sci-ence Technology, Information EngineeringTechnology, and Information Technology aswell as support courses in Mathematics, Phys-ics and Computing Technology. This positionis contingent on availability of funding.

This is a nine-month appointment with pos-sible opportunity to teach during alternate sum-mers. The position requires a minimum of amaster’s degree in Mathematics and experiencein teaching Mathematics in higher education.The candidate must be able to teach a full rangeof undergraduate mathematics offerings fromalgebra through differential equations and dis-crete mathematics. The candidate should befamiliar with the use of modern technology inthe classroom. The candidate must be willingto teach classes in both day and evening as partof the regular load. Since this is a full-timeteaching position, an ability to demonstrateteaching excellence will be required. Ability towork with other Faculty Members in offeringcommon courses is necessary. Excellent oral and

EMPLOYMENT OPPORTUNITIES

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FOCUS March 2003

written communication skills are required. In-terpersonal skills necessary to deal profession-ally, effectively, and courteously with faculty,students, staff, administrators, and the publicare required. Other duties will include advising/ counseling students, participating in scholarlyactivities, serving on department, college anduniversity committees.

Salary will be commensurate with expertise andexperience. Excellent benefits are included.Review of applications will begin mid Febru-ary and continue until the position is filled.Send letter of application, resume, official cop-ies of all undergraduate and graduate tran-scripts, and three (3) letters of recommenda-tion to melinda.stout@uc.edu. or by mail to :Melinda Stout; OMI College of Applied Science;University of Cincinnati; 2220 Victory Parkway;Cincinnati, OH 45206.

To learn more about the OMI College of Ap-plied Science visit our home page at http://www.uc.edu/cas. The University of Cincinnatiis an affirmative action / equal opportunityemployer. Women, minorities, disabled per-sons, Vietnam-era and disabled veterans areencouraged to apply. UC is a smoke-free envi-ronment.

OMI College of Applied Science, University ofCincinnatiAssistant Professor of Mathematics or Physics

The OMI College of Applied Science at theUniversity of Cincinnati invites applications fora full-time tenure-track Faculty position inMathematics or Physics to begin in September,2003. The OMI College of Applied Science is afully accredited baccalaureate college with aninternational reputation in delivering innova-tive education in science and technology. TheDepartment of Mathematics, Physics and Com-puting Technology presently has twelve full-time Faculty, offers BS and AS degrees in Com-puter Science Technology, Information Engi-neering Technology, and Information Technol-ogy as well as support courses in Mathematics,Physics and Computing Technology. This po-sition is contingent on availability of funding.

This is a nine-month appointment with pos-sible opportunity to teach during alternate sum-mers. The position requires a minimum of amaster’s degree in either Mathematics or Phys-ics and experience in teaching in higher educa-tion within these disciplines. The candidatemust be willing to teach both Mathematics andPhysics Courses and must be willing to teachclasses in both day and evening as part of theregular load. Since this is a full-time teachingposition, an ability to demonstrate teachingexcellence will be required. Ability to cooper-ate with other Faculty Members in offering sec-tions of common courses is necessary. Excel-lent oral and written communication skills arerequired. Interpersonal skills necessary to deal

professionally, effectively, and courteously withfaculty, students, staff, administrators, and thepublic are required. Other duties will includeadvising / counseling students, participating inscholarly activities, serving on department, col-lege and university committees.

Salary will be commensurate with expertise andexperience. Excellent benefits are included.Review of applications will begin mid Febru-ary and continue until the position is filled.Send letter of application, resume, official cop-ies of all undergraduate and graduate tran-scripts, and three (3) letters of recommenda-tion to melinda.stout@uc.edu. or by mail to :Melinda Stout; OMI College of Applied Science;University of Cincinnati; 2220 Victory Parkway;Cincinnati, OH 45206.

To learn more about the OMI College of Ap-plied Science visit our home page at http://www.uc.edu/cas. The University of Cincinnatiis an affirmative action / equal opportunityemployer. Women, minorities, disabled per-sons, Vietnam-era and disabled veterans areencouraged to apply. UC is a smoke-free envi-ronment.

Guaranteed Special Positions10% additional charge; first-come, first-served basis.

Inserts/Business Reply CardsPlease contact The Mathematical Asso-ciation of America for prices and speci-fications.

Mechanical SpecificationsTrim Size: 8 1/2 " wide x 10 3/8 " highScreen: 150-line halftone Full page bleed8 3/4" x 11 1/4", (10% extra charge)Color: FOCUS standard second coloravailable (15% extra charge). Columnwidth: 2 5/16", 4 13/16", 7 3/8"Printing: Offset, saddle-stitched

How to send your Materials:

Electronic files: Laser output should ac-company your electronic files. PC andMAC based files must be sent as Post-script files (please subset and embed allfonts). PDF files are also acceptable.

Camera-ready art: Should be preparedaccording to the mechanical specifica-tions Please call for rates and specifica-tions.Classified Rates (includes a a free list-ing in MAA Online to appear the samemonth as the print ad): $2.25 per word.

Contact the MAA Advertising Depart-ment toll free at 1-866-821-1221, fax:(703) 528-0019. Ads may be sent viaemail to ads@catalystcom.com.

Advertising Information for Display & Classified Ads Nominations are now being acceptedfor the 2004 Yueh-Gin Gung and Dr.Charles Y. Hu Award for DistinguishedService to Mathematics, the mostprestigious award given by theAssociation. It is to be made for serviceto mathematics that has been widelyrecognized as extraordinarily successful.The period of service may be long orshort, and the award may be made on thebasis of one or several activities. Thecontribution should be such as toinfluence the field of mathematics ormathematics education in a significantand positive way on a national scale.Nominations should be sent to RobertMegginson, Deputy Director,Mathematical Sciences ResearchInstitute, 17 Gauss Way, Berkeley CA94720-5070, or via emailmeggin@msri.org, to arrive no later thanApril 1.

Nominations Sought for

2004 Gung-Hu Award

FOCUS

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March 2003

ALLEGHENY MOUNTAIN

April 4-5, 2003-Penn State UniversityDuBois, PA

EASTERN PA & DELAWARE

April 12, 2003-Wilkes UniversityWilkes-Barre, PA

FLORIDA

February 21-22, 2003-JacksonvilleUniversity, Jacksonville, Florida

ILLINOIS

March 28-29, 2003-Illinois CollegeJacksonville, IL

INDIANA

March 28-29, 2003-Butler UniversityIndianapolis, IN

INTERMOUNTAIN

March 19-20, 2003, Weber StateUniversity, Ogden, UT

IOWA

April 4-5, 2003-University ofNorthern Iowa, Cedar Falls, IA

KANSASApril 4-5, 2003-Hays, KS

KENTUCKY

April 4-5, 2003-Bellarmine UniversityLouisville, KY

LOUISIANA-MISSISSIPPI

February 21-22, 2003-MississippiCollege, Clinton, MS

MD-DC-VA

April 11-12, 2003-Norfolk StateUniversity, Norfolk, VA

METRO. NEW YORK

May 3, 2003-La Guardia CommunityCollege (CUNY)

MICHIGAN

May 2-3, 2003-Saginaw Valley StateUniversity, University Center, MI

MISSOURI

April 4-5, 2003-Washington UniversitySt. Louis, MO

NEBRASKA-SOUTHEAST SOUTHDAKOTA

March 28-29, 2003-University of SouthDakota at Vermillion, Vermillion, SD

NEW JERSEY

April 5, 2003-Kean University, Union, NJ

November 8, 2003-Raritan ValleyCommunity College, North Branch, NJ

NORTH CENTRAL

April 25-26, 2003- Malcalester CollegeSt. Paul, MN

Fall 2003-University of Sioux FallsSioux Falls, SD

NORTHEASTERN

June 13-14, 2003-Massachusetts Collegeof the Liberal Arts, North Adams, MA

NORTHERN CALIFORNIA, NEVADA,HAWAII

February 22, 2003-College of MarinKentfield Campus, Kentfield, CA

OHIO

April 4-5, 2003-Ohio State UniversityColumbus, OH

October 17-18, 2003- Ohio NorthernUniversity, Ada, OH

OKLAHOMA-ARKANSAS

March 28-29, 2003-The University ofTulsa, Tulsa, OK

PACIFIC NORTHWEST

June 20-21, 2003-Whitman College

ROCKY MOUNTAIN

April 2003-United States Air ForceAcademy, Colorado Springs, CO

SOUTHEASTERN

March 21-22, 2003-Joint Meeting withAtlantic Section of SIAM, Clemson, SC

SOUTHERN CALIFORNIA

March 8, 2003-Harvey Mudd CollegeClaremont, CA

SOUTHWESTERN

April 5-6, 2003-New Mexico Institute ofMining and Technology, Socorro, NM

SEAWAY

April 4-5, 2003 Alfred UniversityAlfred, NY.

November 7-8, 2003-Rochester Instituteof Technology, Rochester, NY

TEXAS

April 3-5, 2003-Sam Houston StateUniversity, Huntsville, TX

WISCONSIN

April 25-26, 2003-University ofWisconsin-Marathon CountyWausau, WI

September 26-28, 2003 (Meeting forProject NExT Wisconsin) Bundy HallConference Center, Menomonie, WI

MAA Section Meeting Schedule 2003