FOCUS August/September 2003

FOCUS is published by the Mathematical Association of America in FOCUS January, February, March, April, May/June, August/September, October, November, and December. August/September 2003 Editor: Fernando Gouvêa, Colby College; Volume 23 Issue 6 [email protected] Managing Editor: Carol Baxter, MAA [email protected] Inside Senior Writer: Harry Waldman, MAA [email protected] 4Elvis: Optimizing My Opportunities By Tim Pennings Please address advertising inquiries to: Carol Baxter, MAA; [email protected] 5Alder Awards Will Recognize Talented Beginning Teachers President: Ronald L. Graham First Vice-President: Carl C. Cowen, Second 6 One Day as Washington Lobbyists Vice-President: Joseph A. Gallian, Secretary: By Jason L. Haun, Kelly A. Peck, and Richard B. Thompson Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: John W. Kenelly 8MAA Tour of Greece Executive Director: Tina H. Straley Associate Executive Director and Director 10 Mathematics and Art of Publications and Electronic Services: Donald J. Albers By Alexander Bogomolny FOCUS Editorial Board: Rob Bradley; J. Kevin Colligan; Sharon Cutler Ross; Joe 12 Manjul Bhargava Receives Hasse Prize at MathFest Gallian; Jackie Giles; Maeve McCarthy; Colm Mulcahy; Peter Renz; Annie Selden; 13 MAA Writing Prizes Announced at MathFest Hortensia Soto-Johnson; Ravi Vakil. Letters to the editor should be addressed to 14 2003 Award Winners for Distinguished Teaching Fernando Gouvêa, Colby College, Dept. of Mathematics, Waterville, ME 04901, or by email to [email protected]. 16 The Mathematical Olympiad Summer Program Brings Together Talented High School Students Subscription and membership questions should be directed to the MAA Customer By Steven R. Dunbar Service Center, 800-331-1622; e-mail: [email protected]; (301) 617-7800 (outside 17 A Problem-Solving Dynasty U.S. and Canada); fax: (301) 206-9789. By Steve Olson Copyright © 2003 by the Mathematical Association of America (Incorporated). 18 NSF Beat Educational institutions may reproduce articles for their own use, but not for sale, provided that the following citation is used: 19 MAA Election Results Are In “Reprinted with permission of FOCUS, the newsletter of the Mathematical Association 20 Short Takes of America (Incorporated).” Periodicals postage paid at Washington, DC 28 What’s the Best Textbook?—Elementary Number Theory and additional mailing offices. Postmaster: By Fernando Q. Gouvêa Send address changes to FOCUS, Mathematical Association of America, P.O. Box 90973, Washington, DC 20090-0973. On the cover: Elvis working on his math paper. Photo courtesy of Tim Pennings. ISSN: 0731-2040; Printed in the United States of America. FOCUS Deadlines November December January Editorial Copy September 16 October 16 November 14 Display Ads September 24 October 29 November 26

2 August/September 2003 FOCUS Jean-Pierre Serre Is First Abel Laureate

The first Abel Prize in Mathematics The Abel Prize, which was established was awarded to French mathematician in January 2002 and is awarded annu- Jean-Pierre Serre. At a formal ceremony ally to recognize outstanding achieve- on June 3, King Harald of Norway pre- ment in mathematics, carries a cash sented the award, honoring Serre “for award of 6 million Norwegian kroner, playing a key role in shaping the mod- which comes out to about $800,000. The ern form of many parts of mathemat- prize is named for Niels Henrik Abel, ics, including topology, algebraic geom- who lived in Norway in the early 19th etry, and number theory.” The awards century and is recognized as one of the ceremony was part of a week full of spe- most brilliant mathematicians of his cial events related to mathematics. time. The Abel Prize is administered by Events included the laying of a wreath Jean-Pierre Serre receiving the Abel Prize from the Norwegian Academy of Science and at the monument in honor of Niels King Harald of Norway. Letters, which has appointed an Abel Henrik Abel, the Abel Lecture by Serre Committee consisting of five mathema- (“Prime Numbers, Equations and Modu- ticians to review the nominated candi- lar Forms”), and the Abel symposium, Jean-Pierre Serre, who is Emeritus Pro- dates and submit a recommendation for which included lectures by several math- fessor at the Collège de France, in Paris, a worthy Abel laureate. ematicians, including Barry Mazur and is noted both for his mathematics and Peter Sarnak. A “Math Carnival” was held for his expository skills. He has made For more about the Abel Prize and about at the Universitetsplassen, in Central fundamental contributions to topology, Jean-Pierre Serre, visit the Abel Prize Oslo, with the participation of many chil- number theory, and algebraic geometry. website at http://www.abelprisen.no/ dren aged 10 to 12. Serre was present to He has also written many books and is index_english.html. Among other things, hand out prizes to the winners of math- famous for the clarity and penetration the site includes a well-written exposi- ematical competitions. of his writing. tory account of Serre’s work. About Jean-Pierre Serre By Fernando Q. Gouvêa Most good college and university li- GAGA (“Geométrie Algébrique et dent there. It braries own many volumes of collected Geométrie Analytique”), FAC was then com- papers by various mathematicians, but (“Faisceaux Algébriques Coherents”), mon knowl- few of these volumes ever make it into and “Serre’s Duke paper” (“Sur les edge among private book collections. Buying what is représentations modulaires de degré 2 de the graduate usually an expensive set of books is Gal(Q/Q),” published in the Duke Math- students that something one only does if the works in ematical Journal). The last is particularly Serre’s pres- question are so useful that one knows famous; in it, Serre formulated a far- ence had a they will be opened and read again and reaching conjecture connecting modu- positive effect again. Thus, it is an indication of how lar forms and Galois representations, a on the depart- valuable Serre’s work is to note that all small part of which was the core of Wiles’ ment: his four volumes of his collected works are proof of Fermat’s Last Theorem. Serre courses were Jean-Pierre Serre on my shelves—the only living math- calls it his paper pour optimistes. exciting, his ematician whose collected works I have ping-pong was top-notch, and the wine felt I absolutely needed to buy. Next to In addition to his research work, Serre at the Friday afternoon wine-and-cheese them are a volume of summaries of semi- has written many books, some at an ad- parties was noticeably better. nars, a volume of correspondence, and vanced level, others more accessible. His at least eight other books, several of writing is famous for being clean, effi- Asked by a French news magazine which I have studied in detail. cient, and easy to understand. This side whether being a great mathematician of his work was recognized by the AMS required genius, Serre replied that it was Serre’s work focuses mostly on three ar- a few years ago, when it awarded him a above all a question of taste: a taste for eas: topology, algebraic geometry, and Steele prize for exposition. mathematics itself, and good taste in number theory. In all three fields, he has choosing the right mathematical prob- had a formative impact, changing the In addition to his work at the Collège de lems. In fact, the first Abel Laureate has very shape of the subject. Some of his France, Serre was a frequent visitor to both taste and genius. papers are cited so often that they are American universities. He spent a semes- known by nicknames: for example, ter at Harvard while I was a graduate stu- Photos courtesy of: The Abel Prize website: http://www.abelprisen.no/presse/ 3 FOCUS August/September 2003 Elvis: Optimizing My Opportunities As told to Tim Pennings

Hi. I’m Elvis. I got my name because as a nursing puppy I gyrated my back legs in a motion similar to my namesake, the King of Rock and Roll. As with Presley, I love the spotlight, from pos- ing for a camera to diving into an eager crowd of high school students.

I knew that I was destined for fame, but when I went to live with mathematics professor, Tim Pennings, two years ago, I could see that my opportunities were limited. Nice guy, but not star quality, if you know what I mean. Then one fine day playing fetch at the beach, I had an inspiration: Show him that I have an in- stinctual knack for calculus by choosing the quickest path to the ball. (I have Elvis relaxing at home in between interviews and persona l appearances. trouble with symbolic manipulation, but Photo courtesy of Tim Pennings. max-min problems come naturally to me.) It took him a few weeks to catch on, but when he did we researched and The BBC found out about me and called ward to us giving our talk in various high wrote the paper and I knew that I was for a live on-the-air interview, as did our schools and colleges next fall. Those stu- on my way to the top. own country’s NPR radio. Finally, we had dents are just suckers for my handsome an offer to go to Los Angeles for a spot face. With my smile gracing the front cover on an NBC daytime talk show in August. of the May issue of The College Math- (I was all for it, but my co-author would Tim Pennings is an Associate Professor of ematics Journal, what would come next? rather go camping.) All together we gave Mathematics at Hope College in Holland, Well, first several local papers wrote sto- nine interviews and appeared in 28 news Michigan. His research, done col- ries, including two with headlines and stories of various types. laboratively with undergraduate students, front page pictures. Then The Chicago is in dynamical systems and modeling. He Tribune and The Baltimore Sun followed All of this press led to some fine letters also directs the Hope College NSF-REU suit. ABCNEWS.com called for an inter- from dog lovers including one from a sin- Mathematics Summer Research Program. view and ran me as their top story, just cere elderly woman who described her Other reasons for living include ultimate ahead of the Microsoft-AOL merger. Rottweiler’s ability to solve algebraic for- frisbee, racquetball, nature photography, (And Bill Gates thought that HE was top mulas and do square roots. As for my- choral music, folk song guitar gigs, and dog!) self, I’ll stick to calculus, and look for- playing with Elvis at the beach.

Don Albers, the MAA’s Associate Executive Di- rector, John dePillis, author of 777 Mathemati- cal Conversation Starters, and Lisette dePillis met Jay Leno after the Tonight Show aired on April 21, 2003. Leno likes mathematics and Albers and dePillis talked with him about Elvis and getting more math on the Tonight Show. Photo courtesy of The Tonight Show.

4 August/September 2003 FOCUS

Alder Awards Will Recognize Talented Beginning Teachers

Before his recent death, Henry Alder Nominations for the award may be made endowed a new MAA teaching award, to by any member of the MAA or by any be known as the Henry L. Alder Award section of the MAA. for Distinguished Teaching by Beginning College or University Mathematics Fac- Alder Award Eligibility and Guidelines ulty. The awards “are to be made to col- for Nomination lege or university faculty who have taught full time in a mathematical science in the Eligibility United States or Canada for at least two but not more than seven years since re- Nominees must: ceiving their Ph.D. and whose teaching has been extraordinarily successful. Their Hold the Ph.D. degree effectiveness in teaching undergraduate mathematics must be documented and Be college or university teachers who shown to have influence beyond their have taught full time in a mathematical own classroom.” science in the United States or Canada for at least two, but not more than seven, Nominations for the first Alder Awards years since receiving the Ph.D. should be sent to Martha Siegel at the Henry Alder Department of Mathematics, Towson Hold membership in the Mathematical for mathematical competitions, directing University, 8000 York Rd., Towson, MD Association of America undergraduate students in research in 21252-0001 by December 15, 2003. Con- mathematics, directing students in the tact Linda Sons, chair of the Alder Guidelines for nomination preparation of honors theses, preparing Awards Committee, with any other ques- teaching materials used by others, etc. tions. Sons can be reached at the Depart- Nominees for the award may be made by ment of Mathematical Sciences, North- any member of the MAA or by any sec- Nominations must be submitted accord- ern Illinois University, DeKalb, IL 60115, tion of the MAA ing to the Nomination Form. Instruc- by phone at 815-753-6760, or by email tions for that form should be followed at . Nominees should: [email protected] precisely to assure uniformity in the se- lection process. Alder Award Description Be recognized as extraordinarily success- ful in their teaching The Nomination Form and a Nomina- In January 2003 the MAA established the tion Packet that provides evidence docu- Henry L. Alder Award for Distinguished Have effectiveness in teaching under- menting extraordinary success in teach- Teaching by a Beginning College or Uni- graduate mathematics that can be docu- ing should be submitted to the Secretary versity Mathematics Faculty Member to mented of the MAA by December 15 of the aca- honor beginning college or university demic year in which the nomination is faculty whose teaching has been extra or- Have had influence in their teaching be- to be considered. Directions for the dinarily successful and whose effective- yond their own classrooms nomination packet should be followed ness in teaching undergraduate math- with precision to assure uniformity in the ematics is shown to have influence be- Interpretive notes selection process. Nomination forms and yond their own classrooms. An awardee further information can be found online must have taught full time in a math- In determining eligibility, we do not at http://www.maa.org/news/ ematical science in the United States or count time spent in a postdoctoral posi- 062703alder.html. Canada for at least two, but not more tion where nearly all the nominee’s time than seven, years since receiving the was spent on research, and the nominee Ph.D. Each year at most three college or did very little or no teaching (e.g. three university teachers are to be honored semester courses a year or less). with this national award and are to re- ceive $1,000 and a certificate of recogni- Teaching is intended to include class- tion from the MAA. Award recipients will room instruction as well as activities be expected to make a presentation at outside the classroom, such as working one of the national meetings of the MAA. with student groups, preparing students

5 FOCUS August/September 2003 One Day as Washington Lobbyists sentations that were viewed by over 270 attendees from House, Senate, and White By Jason L. Haun, Kelly A. Peck and Richard B. Thompson House offices. The MAA exhibit at- tracted one of the most important guests to the exhibit: Congressman Jim This year the MAA sponsored the Kolbe (R, Tucson), who is a University of Arizona’s Mathemat- member of the House Appro- ics for Business Decisions project on priations Committee. Represen- a tour of congressional offices and tative Kolbe came especially to at the CNSF Exhibition and Recep- meet with us, as he had promised tion. On June 17, 2003 we spent a he would. fascinating day as Washington lob- byists for the mathematical commu- As a mathematician and co-au- nity for both research and educa- thor of Mathematics for Business tion. Those of us participating Decisions, I prepared materials found it to be a surprisingly reward- for our exhibit and invited two ing day. More than lobbying, we Thompson, Kolbe, Haun, & Peck of our students, Kelly Peck and were sharing very important infor- Jason Haun, to join me on the mation with members of Congress. to join me on this trip to Washington, trip. And yes, seeing how government D.C. works was fascinating. Our prepa- We wanted our exhibit to make a good ration for promoting National Sci- Mathematics for Business Decisions is a impression. The MAA supported travel ence Foundation funding and our two-semester sequence of mathematics and the distribution of CD’s and color observations from Washington may courses for undergraduate business ma- brochures, and The University of Ari- offer some insights into the mechan- jors that has been developed at the Uni- zona supported the production of a 4′ x ics of gaining support for math- versity of Arizona, with partial support 6′ laminated color display poster. The ematics. from the NSF. It is now published and MAA rented a 37″ plasma video moni- distributed by the MAA as self-contained tor as part of their exhibit space. In the The Coalition for National Science electronic texts. The MAA chose this intense competition for Washington dol- Funding (CNSF) is an alliance of lars, a low quality presentation is per- universities and major professional ceived as reflecting the value of the societies from many areas of science, cause that it promotes. People were mathematics, and engineering. Its notably impressed with the profes- purpose is to encourage funding for sional appearance of our materials. the National Science Foundation. A major part of this endeavor is an Congressmen and their staffers re- annual exhibition and reception for ally do care about young people members of Congress and their staff. and students. Comments by Jason Each coalition member may present and Kelly held people’s attention a project that has received NSF sup- during both the office visits and at port. Each year the MAA sponsors a the exhibition. A copy of a course project that highlights funding for project report by Kelly commanded undergraduate mathematics educa- more interest than did some of our tion and provides additional sup- Albers, Straley, Thompson, Haun, & Peck descriptive material. In fact, our port for the reception. only copy of the report went home project for its innovation in both con- with Representative Kolbe since we did This year the MAA chose us and the tent and delivery and its ready appeal to not really want to ask him to give it back. Mathematics for Business Decisions the public. The follow-up e-mails that I have re- course to be their exhibitors. The ceived all mention the outstanding qual- course was developed by myself, Ri- In Washington, we were escorted by Tina ity of our students. It is, of course, pos- chard Thompson, of the University Straley, Executive Director of the MAA, sible that this favorable impression is of Arizona Department of Math, on half-hour visits to the offices of five related to the fact that I managed to in- along with my colleague Chris congressmen from the Arizona delega- vite two outstanding, articulate young Lamoureux of the University of Ari- tion. In the evening the MAA’s Associ- people! zona Department of Finance. Jason ate Executive Director, Don Albers, Haun and Kelly Peck are students helped us set up a display booth at an Our scheduled office visits all had the who have been through the course. exhibition and reception in the Rayburn same format. Tina Straley would thank Each was very excited to be invited Office Building. It was one of 30 pre- the congressman for past NSF support

6 August/September 2003 FOCUS and ask for continued support, es- connection is made, change and in- pecially for the effort to double novation can take place. I want to NSF’s budget over a five-year pe- thank everyone at the MAA as well riod. She explained that The Univer- as everyone who has worked with the sity of Arizona project that the MAA Mathematics for Business Decisions was presenting represented one type program. of work that had received funding. She suggested that Congress might Kelly Peck: It is not every day that not be as familiar with funding for you get an invitation to go to Wash- undergraduate education as it is ington, D.C. with an agenda that in- with research dollars. I would then cludes meeting personally with Ari- give a brief explanation of the e- zona Congressmen. Yet, here I am, a texts, and ask the students for their Haun, Thompson, & Ehlers 20-year-old college student who is reactions to the program. able to say that I have “been there, sary to implement the agenda. These done that.” The whole experience On most occasions when I discuss our ideas brought us back to the need for went by in a flash, but I walked away from project I am talking to other mathema- continued NSF support and funding. it with some treasured memories. ticians who share my background in, and appreciation of, mathematics. In short, Our display at the evening exhibition Having virtually no knowledge of politi- I am usually preaching to the choir. Pub- drew attention from quite a few people, cal procedures, I was quite surprised to lic officials cannot be assumed to share leading to discussions of NSF funding see how things ran at the congressional our views of mathematics. and of our project. We had a nice visit offices. When speaking with congress- with Congressman Vernon Ehlers (R, men, whose days are packed, you imme- My approach to congressmen was based Grand Rapids). He is a member of the diately learn how to get your point across on the assumptions that they care about House Committee on Science who also as concisely as possible. I had to learn to students in their home districts, that they holds a Ph.D. in physics. Representative condense two semester’s worth of Math- want a work force which is competitive Ehlers has been a strong supporter of the ematics for Business Decisions into a few in the world market, and that they see National Science Foundation. minutes, and hope that I could maintain technology as a key to the future. Re- the representative’s attention. It was defi- flecting these, I mentioned that Math- Jason Haun: One needs to make contact nitely a learning experience, to say the ematics for Business Decisions is built with several congressional offices in or- least. around the topics, project structure, der to be heard. I constantly encounter teamwork, and computer skills that are ideas and complaints from people The beautiful Washington cityscape also actually used in business. I was careful around me. However, in most cases their left a lasting impression. I was awed by to work in the name of a local commu- words are never heard by Congress. Due the grand historic buildings and their nity college or university in the to this incredible opportunity offered by classical features. Perhaps even more representative’s home district and to note Professor Thompson and the Math- impressive was the fact that the entire city that students who can use mathematics ematical Association of America I was is surrounded by, and engulfed in, lus- effectively will be the ones who create able to be heard and show my support cious greenery—something considered a jobs and expand the local tax base. These for something in which I truly believe, luxury by Arizonans. ideas resonated well with most of the “the future of education.” Education is congressmen, eliciting some very percep- constantly changing and it is our duty, In addition to the experience and the tive responses. as citizens, to make sure that these scenery, I will forever remember the changes propel the system in the right people. Tina Straley, Don Albers, and the Several representatives mentioned the direction. Laws go through the govern- other MAA members I met were ex- specific courses (ranging from Algebra mental structure. However, “officials” act tremely friendly and accommodating. II to Calculus) where mathematics had as liaisons to voice the views of citizens They became familiar faces in an unfa- disconnected from the real world and within their communities. It is the citi- miliar place. Unfortunately, the trip stopped having meaning to them. Our zens’ ultimate duty to make sure that went by way too fast. Upon leaving program’s continual contact with stu- their words are heard. In the world to- Washington, there was one thing I knew dents’ goals and interests was seen as day, this may mean building a team of for certain: I would be back. highly desirable. In some cases, congress- people who share common beliefs and men actually suggested ideas, such as then going to Washington. Photographs by Sharon L. Thompson. In- extending our program to areas other formation on the CNSF can be found at than business and implementing our This is only the beginning. The next step http://www.cnsfweb.org. Information on approach in high schools, for further ex- lies in making a direct connection with Mathematics for Business Decisions can be ploration. They recognized that a major the person to whom you are speaking. found at http://www.maa.org and http:// effort would be required and that much He or she must begin to feel and believe business.math.arizona.edu/MBD/ instructor preparation would be neces- in the same way that you do. Once this mbd.html. 7 FOCUS August/September 2003 MAA Tour of Greece

Thirty members (and guests) of the interest in Epidauros and the Eupalinos MAA traveled to Greece in late May to Tunnel. The mathematical presentations participate in the first MAA Study Tour that were arranged at various sites in abroad. There was a wide variety of par- Greece were a pleasure. We were treated ticipants, from high school teachers to as mathematical ambassadors from the retired professors, including two former USA at several receptions, and in fact we presidents of the MAA as well as the cur- did carry out those responsibilities rent and former executive directors. All throughout our trip. Talking with col- agreed that the trip met, and even ex- leagues from Greece was enlightening. ceeded, their expectations. Five of them Because of the special interests of our agreed to write brief comments for FO- group, the aegis of the MAA, the hard CUS about their experiences. work of those putting the trip together, and some serendipity, we had the chance Victor Katz and Lisa Kolbe, tour organiz- From Joel and Linda Haack to visit the Academy of Athens and three ers, at the Acropolis. University of Northern Iowa, Greek universities, see and hear the Cedar Falls, IA: model of the ancient Greek harmonium, sons I was excited to participate. The attend a special museum exhibit entitled chance to see where Thales walked and There were quite a few reasons that we “Is There a Solution for Everything? A created what are regarded as the first were eager to participate on the MAA Journey to the World of Greek Math- proofs in mathematics, the creation of Study Tour of Greece. First, of course, ematics,” receive guided tours of sites in the theoretical mathematics that we as I have been teaching the history of Athens and on Samos by archaeologists claim as ours, was an opportunity that mathematics for parts of the past 15 from the region, and visit Miletus. All I’d likely have on no other tour. Thank years, I was very eager to see Athens, those on the trip were pleasant and re- you for including it!) Delphi, Miletus, and Samos. Second, sponsible, creating an atmosphere of there are a few places in the world that general good will that was a delight. And, Finally, an insight from Linda: this trip my wife Linda and I have always wanted the fellow travelers included previous was of such great interest to even the to see. Greece has been one of those, ever acquaintances and new friends that we non-mathematicians because so much of since learning about it in our ancient his- can expect to see again in the future. the focus was on mathematics and its tory class way back in ninth grade. Fi- relation to other disciplines: architecture, nally, this trip provided us the perfect One of the special treats for me on this art, music, philosophy, mythology, his- occasion to celebrate our thirtieth wed- trip was the chance to see and experience tory, astronomy, etc. ding anniversary. sites that would not normally be included in a tour of Greece, in particular the an- The focus on mathematics and the spon- cient harmonium, the visit to Miletus, sorship by the MAA set this trip apart and the time spent on Samos. (Paren- from other tours we’ve taken. The pre- thetically, a word about Miletus: its in- travel readings and videos increased my clusion on our trip was one of the rea-

The Academy of Athens Temple at Delphi

8 August/September 2003 FOCUS

From Julius Barbanel From Marcia Sward Union College, Executive Director Emeritus, Schenectady, NY: MAA, Rockville, MD:

Over the past few years, I When I tell my non-math- have become quite fasci- ematical friends that I went on nated with ancient Greek a “mathematical tour of mathematics. When I heard Greece,” they invariably look about the MAA trip to puzzled, seeing no connection Greece, I knew this was for between mathematics and me. It was a great trip, com- Greece. But mathematicians bining lectures on ancient know immediately about the Greek mathematics and deep roots that modern math- travel to some marvelous ematics has in ancient Greece sites. and are curious about what we learned. Some of our learning My favorite three lectures came from lectures by Greek were on ancient Greek as- mathematicians and astrono- tronomy, the mathematics mers, some through dialogue of Plato’s Academy, and the with them. One particular Method of Archimedes. The special occasion was a visit to Greek mathematicians that the Academy of Athens. we met were very welcom- ing and kind. They all But the deepest insights came seemed delighted to host a from just being in places where group of visiting mathema- ancient Greeks lived and wor- ticians from the United shiped. A picture may be States. worth a thousand words, but actually being there is worth a We saw some marvelous thousand pictures. Although Tour participants at the Statue of Pythagoras in Pythagoreion, sites. Some of the high the ancient temples, fortresses, Samos. points for me were: Delphi, towns, and homes lie in ruins, where the ancient oracle used to dispense it is still possible to imagine her wisdom; Olympia, site of the origi- The tours across Greece and lectures at traveling back in time and seeing them nal Olympic Games; and the ancient city the university level were excellent. I felt as they must have been so long ago. At of Mycenae, the oldest site of all, home comfortable participating in the formal the archaeological sites we visited, we of the civilization about which Homer and informal discussions. The guides were surrounded by the ancient Greeks’ wrote in the Iliad. and bus drivers were knowledgeable records of commerce, their tributes to about all aspects of Greek life and cul- winning athletes, and the many tales of Greece is a beautiful country. I’ll always ture. And I feel that my presence en- the lives and loves of the gods and god- remember the gorgeous mountains, the riched the impression that our Greek col- desses, all meticulously carved in stone. beautiful sea, the vibrant people, and, of leagues had of American mathemati- We were awed by the engineering feats course, the great food. I wish I could do cians. required to construct elaborate temples it all over again. What a joy this was! and fortresses, and most particularly by Special thanks to a host of MAA friends the immense stone arches, still firmly in From Genevieve Knight who assisted those of us who needed an place after thousands of years. Coppin State University, extra arm. That’s what friends are for! Baltimore, MD: Day after day, for fourteen days, we were The MAA should organize other similar treated to a bounteous feast of ideas and My trip to Greece was one of the most activities for the membership. Reading images. Meal after meal we were also rewarding activities that I have experi- a book or surfing the Internet provides treated to the delights of Greek cuisine. enced in both my personal and profes- information, but walking among the re- And sharing all this with friends and col- sional life. The planners carefully ar- mains of ancient Greece is a once-in-a- leagues made those two weeks even more ranged an exceptional mix of mathemat- lifetime experience! special. This was definitely a trip to re- ics, Greek history, mythology, entertain- member. ment, culture, food, and the list could go on. Photographs courtesy of: Julius Barbanel Lisa Kolbe, and Liz Teles.

9 FOCUS August/September 2003 Mathematics and Art By Alexander Bogomolny

Who will wish to paint you, when no good at. But even very abstract math- hensive even if the latter were selected as one wishes to see you? Gotthold Ephraim ematical ideas may have practical appli- the MAM theme. Lessing Laocoön, Everyman’s Library, cations. 1970, p. 10 Why? Because art is an active pursuit of Mathematics and Biology (1999). Even beauty. The concept of beauty, however, Mathematics and Art was the theme of without a definition everything is very and the expressive means of achieving it, this year’s Mathematics Awareness clear: epidemics is in the domain of bi- differ between various arts. G. E. Lessing, Month. I believe that the theme selection ology, epidemics modelling is in the pur- whose Laocoön: An Essay on the Limits of was unfortunate on several counts. First, view of mathematics as is the solution Painting and Poetry is considered the ori- we tend to forget that in common lan- of the resulting equations. This is what gin of modern esthetics, alluded in pass- guage words may have meanings differ- mathematicians do after all—solve equa- ing to the difference between painting ent from their conventional meanings in tions. Biology is biology. Mathematics is and sculpture, the most congenial of any mathematics. As an example: something else. two arts:

Mother: Would you like to have a cookie Mathematics and Art (2003). There are The mere wide opening of the mouth or ice cream for dessert? plenty of connections. But by juxtaposi- —apart from the fact that the other tion or by inductive reasoning, if you will, parts of the face are thereby violently Kiddie: But, Mommy, I want a cookie art is art, whereas mathematics is some- and unpleasantly distorted—is a blot and ice cream. thing else. in painting and a fault in sculpture which has the most untoward effect Regardless of which connective is used, I am sure that the message that math- possible. these two treats are perceived as indi- ematics is not art was not the intended vidual, independent desserts. A similar purpose of the MAM/2003. No, of course The Mandelbrot set is beautiful even if it impression is left by the combination not. Mathematics is multifaceted, and its is the monochromatic blot in the middle Mathematics and Art. For additional ex- artistic nature is hard to deny. In their of the colorful depiction of equipoten- amples, let’s have a look at past MAM well-known book, Kasner and Newman tial lines. Just to think of the infinite in- themes. There is never doubt as to what wrote: tricacy of the whirl patterns produced by mathematics is not. a mere quadratic formula takes one’s Mathematics is an activity governed by breath away. Add to that the fact that the Mathematics and Decision Making the same rules imposed upon the sym- set serves as an index into the variety of (1996). Democracy is a human inven- phonies of Beethoven, the paintings of Julia sets which, in turn, are classified tion. Vote counting and power indices are Da Vinci, and the poetry of Homer. according to the location of a single pa- mathematics. He who loves number rameter inside the Mandelbrot set. counting is bound to be a mathemati- In the Middle Ages and during the Re- cian. Democracy is one thing. The im- naissance, mathematics constituted a Certainly, the now common colorful pic- possibility to satisfy everyone’s political major part of the Liberal Arts. This is why tures of the Mandelbrot set have great preferences is a proven mathematical math departments usually belong to Lib- visual appeal. But then it is so much truth. eral Arts colleges. To be sure, mathemat- easier to substitute one for the other: “Ah, ics has changed fundamentally since. But this is beautiful; and there’s mathemat- Mathematics and the Internet (1997). it became more of an art, not less. ics behind all that! Hence mathematics First engineers invented the ethernet, is beautiful!” I believe such misrepresen- then the internet. Computer scientists Therefore I feel apprehensive that the tations are popular and I deplore the dis- then came up with the web and eventu- intention of the theme Mathematics and service they might be doing to math- ally a browser. Mathematicians made the Art might have been misconstrued. In- ematics education. Here’s an episode internet secure with very, very big prime deed, I think it is highly probable that it from my personal experience. numbers. was. “Sculpture and Art” or “Music and Art” look and sound incongruous, right? The incident occurred several years ago, Mathematics and Imaging (1998). Well, Why doesn’t “Mathematics and Art”? I when my older son took Geometry I in getting an image is imaging. Multi-reso- would be more comfortable with the cap- junior high. The boy was given an assign- lution image compression is mathemat- tion “Mathematics and the Visual Arts” ment. The basic idea was to take two line ics. Just think of the abstraction of an that was probably the intention to start segments and divide them both into an expanding hierarchy of vector spaces and with. However, I would remain appre- equal number of subintervals. The divi- their wavelet bases. Incomprehensible sion points then had to be connected to abstractions is what mathematicians are

10 August/September 2003 FOCUS form a pretty web of straight lines. It was sake, like a scientist (let alone a math- No one knows better than mathemati- left to the student’s imagination to com- ematician!)? cians themselves where the real beauty bine the webs into more intricate pat- of mathematics lies. I believe it would terns. The assignment did not follow, nor A common argument leaves me cold. enrich both mathematics education and was it preceded by, any discussion of We are often attracted to a book by its public awareness of mathematical beauty mathematical relevance. Division of a cover and may even purchase a book were it pursued regularly and consis- line segment into a number of equal without first tasting a page or two. Yes, tently. The other arts could take care of parts with straightedge and compass — we may. But would it not be a disappoint- themselves. no. The standard ruler with tick marks ment to uncover at home a construction was sufficient to complete the assign- set where we thought to find a book? And ment. The idea of an envelope of a fam- what about shoes? Do we buy shoes solely The first paragraph makes an allusion to ily of lines had not been mentioned ei- by appearance? D. Schattschneider’s note in the March ther. The assignment lacked any math- 2003 issue of FOCUS. Other references can ematical content whatsoever. I suggested True, it often pays to introduce math- be found in Alex’s MAA Online April col- that he program QuickBasic to automati- ematics gently with story telling or col- umn. This note is in fact a mutilated (but cally generate various patterns. My son orful illustrations. The best teachers do also somewhat improved) version of the insisted that programming was strictly that all the time. I could not possibly have latter. and specifically forbidden. The assign- an issue with that. So what is it about? ment had to be completed by hand. This sound byte, which is the theme Alex Bogomolny is a former Associate Pro- After a couple of unsuccessful attempts Mathematics and Art, draws a line be- fessor of Mathematics at the University of to engage the teacher, I was granted a tween mathematics and art. It pulls the Iowa. One of the greatest pleasures he en- meeting with the principal. In the school, two apart more than it invokes any pos- joys nowadays is watching his 4-and 23- the web patterns were proudly decorat- sible connections. And the fact is that the year old sons play together. Alex also spends ing all the available wall space. There first impression, however false, is often much time working on his website, Inter- were lace masterpieces by girls and in- hard to get rid of. The theme, taken by active Mathematics Miscellany and tricate woodwork by boys—all for the itself, suggests at best that mathematics Puzzles (http://www.cut-the-knot.org), sake of extra credit. The assignment ap- has found yet another application, now that has been recently recognized with the peared to be a yearly milestone for Ge- in art. Big deal! Most artists hate math- 2003 Sci/Tech Web Award from the edi- ometry I. ematics just like anyone else. Who do we tors of Scientific American. want to cheat? Besides, since the appli- The principal readily admitted the shal- cability of mathematics is talked about lowness of this exercise. The district math all the year round, would it not make supervisor who was also present re- more sense to emphasize its (specifically IASE 2004 Roundtable mained unmoved. After a short exchange mathematical) beauty at least once a year, I left utterly disappointed. What a waste during this special event—Mathematics of time! And zero knowledge acquisition. Awareness Month? The International Association for Sta- As far as I know, the assignment is still tistics Education (IASE) will hold a being offered as a mathematical attrac- Perhaps it’s fitting to relay a story told “Roundtable” at Lund University in Swe- tion. by Raymond Smullyan in one of his den on June 28 to July 3, 2004. Lund books. A friend invited him for dinner. University is close to the ICME-10 loca- I am not building a critical edifice based He told Smullyan that his teenage son tion, so this will act as a kind of “satellite on a single personal experience. There is was crazy about Smullyan’s logic puzzle conference.” The Roundtable will bring definitely an unfortunate trend in math- books and could not wait to meet him. together a small number of experts, rep- ematics education that seeks to endear The friend warned Smullyan not to men- resenting as many different countries as mathematics to students with no attempt tion that he is a mathematician and that possible, to discuss Curricular Develop- at transferring any significant mathemat- logic is a part of mathematics because the ment in Statistics Education. Papers pre- ics. D. Hofstadter asks this question: young fellow hated mathematics. sented and discussed during the confer- ence will be published in a proceedings Why does mathematics today have to Branko Grünbaum wondered: volume that will present a global over- be ‘relevant’ and ‘fun’, have to prove its view of Statistics Education. For more worth by chewing gum like a sports star, ... it is very likely that Escher did not information, contact Gail Burrill at acting sexy like a movie star, spouting wish to learn any of the mathematics [email protected] or visit http:// cutesy sound-bytes like a with-it jour- we think might have helped him, and hobbes.lite.msu.edu/ nalist, displaying itself as eye candy like that we are much richer for it. ~IASE_2004_Roundtable. a top model—but, heaven forbid, not by exploring unsuspected symmetries and subtle patterns purely for their own

11 FOCUS August/September 2003 Manjul Bhargava Receives Hasse Prize at MathFest

By Joseph Gallian

At the August 2003 MathFest in Boul- der Manjul Bhargava received the MAA’s Hasse Prize for exposition. It has been quite a year for Manjul. In November 2002 he was the only mathematician among Popular Science’s “Brilliant 10”, the publication’s first annual celebration of ten scientists who are shaking up their fields. (The article is available online at http://www.popsci.com/science/article/ 0,12543,364881,00.html) In January 2003 he was selected to be one of the AMS/MAA one hour invited speakers at the January 2004 Joint Meetings in Phoe- nix. Then came offers of tenured Associ- ate Professorships from the top Ivy League schools. Shortly thereafter, these offers were increased to full professor- ships. It is believed that the two years from thesis to full professorship offers is the shortest period ever for an Ivy League school. In June he accepted the profes- sorship from Princeton and also was ap- pointed to the editorial board of the Journal of Number Theory. Manjul Bhargava lecturing on the Fifteen Theorem.

Awards are not new to the 29-year-old plified the Conway-Schneeberger proof, Bhargava, who is the son of a chemist Manjul’s research interests include alge- but also generalized the result in several father and mathematician mother, Mira braic number theory, combinatorics, and beautiful ways. Another of Bhargava’s Bhargava, a professor at Hofstra Univer- representation theory. The paper for achievements, which was the basis for his sity. In high school Manjul was the win- which he won the Hasse Prize, “The fac- thesis, is a generalization of Gauss’s 1801 ner of the First Annual New York State torial function and generalizations,” pub- law of composition of binary forms. Science Talent Search. As an undergradu- lished in the American Mathematical Manjul showed that Gauss’s composition ate at Harvard he won the Hoopes Prize Monthly (November 2000), explains his is only one of at least 14 such composi- for his outstanding senior thesis and new generalization of the factorial func- tion laws. (three times!) the Derek Bok Award for tion and its connections with some clas- Excellence in Teaching. He was selected sical problems in number theory, ring Andrew Wiles, Manjul’s Ph.D. advisor, is to lead the commencement of the 1600 theory, and combinatorics. His work on quoted in the Popular Science article as Harvard graduates of the class of 1996. the factorial function unifies and gener- saying Bhargava’s thesis was one of the alizes the results of about 20 previous strongest he’s seen in 20 years. Also Also in 1996 Bhargava received the AMS- papers, many by well-known mathema- quoted in the article is Princeton profes- MAA-SIAM Frank and Brennie Morgan ticians. sor Peter Sarnak: “We are watching him Prize for Outstanding Research in Math- very closely. He is going to be a super- ematics by an Undergraduate Student for One of Bhargava’s recent accomplish- star. He’s amazingly mature mathemati- work he began at the Duluth REU and ments has to do with the so-called “Fif- cally. He is changing the subject in a fun- expanded on in his senior thesis. A year teen Theorem”, which was originally damental way.” before he obtained his Ph.D. from proved by Conway and Schneeberger in Princeton on a Hertz Fellowship, Manjul 1993. It states that if a positive definite In addition to doing mathematics, was also appointed as the first Clay Math- quadratic form whose associated sym- Manjul is also an accomplished tabla ematics Institute Long-Term Prize Fel- metric matrix has integer values repre- player, and performs extensively in the low and a Visiting Fellow at Princeton sents all positive integers up to 15, then New York and Boston areas. He also en- University. This past year he was a visit- it is “universal,” that is, it represents all joys nature hiking, running, tennis, and ing professor at Harvard. positive integers. Bhargava not only sim- spending time with friends.

12 August/September 2003 FOCUS

MAA Writing Prizes Announced at MathFest 2003

Carl B. Allendoerfer Awards Lester R. Ford Awards Merten M. Hasse Prize

Ezra Brown Leonard Gillman Manjul Bhargava “The Many Names of (7, 3, 1),” “Two Classical Surprises Concerning “The Factorial Function and Mathematics Magazine, the Axiom of Choice and the Generalizations,” The American April 2002, pp. 83-94. Continuum Hypothesis,” Mathematical Monthly, The American Mathematical November 2000, pp. 783-799. Dan Kalman Monthly, June-July 2002, pp. 544-553. “Doubly Recursive Multivariate In 1986 an anonymous donor gave the Automatic Differentiation,” Warren P. Johnson Mathematical Association of America Mathematics Magazine, “The Curious History of Faà du funds sufficient to support a prize hon- June 2002, pp. 187-202. Bruno’s Formula,” The American oring inspiring and dedicated teachers. Mathematical Monthly, March 2002, The price is named after Merten M. The Carl B. Allendoerfer Awards, estab- pp. 217-234. Hasse, who was a former teacher of the lished in 1976, are made to authors of donor, and who exemplified the quali- expository articles published in Math- Sam Northshield ties of a fine teacher. The Merten M. ematics Magazine. The Awards are named “Associativity of the Secant Method,” Hasse Prize is given for a noteworthy ex- for Carl B. Allendoerfer, a distinguished The American Mathematical Monthly, pository paper appearing in an Associa- mathematician at the University of March 2002, pp. 246-257. tion publication, at least one of whose Washington and President of the Math- authors is a younger mathematician. The ematical Association of America, 1959- Eleanor Robson prize is designed to be an encouragement 60. “Words and Pictures: New Light on to younger mathematicians to take up Plimpton 322,” The American the challenge of exposition and commu- Mathematical Monthly, nication. Trevor Evans Awards February 2002, pp. 105-120.

Laura Taalman and Eugenie Hunsicker Sérgio B. Volchan George Pólya Awards “Simplicity is not Simple,” “What Is a Random Sequence?,” The Math Horizons, September, 2002. American Mathematical Monthly, David L. Finn January 2002, pp. 46-63. “Can A Bicycle Create a Unicycle Philip D. Straffin, Jr. Track?,” College Mathematics Journal, “The Instability of The Lester R. Ford Awards, established September 2002, pp. 283-292. Democratic Decisions,” in 1964, are made to authors of exposi- Math Horizons, April 2002. tory articles published in The American Dan Kalman Mathematical Monthly. The Awards are “An Undetermined Linear System for The Trevor Evans Awards, established by named for Lester R. Ford, Sr., a distin- GPS,” College Mathematics Journal, the Board of Governors in 1992 and first guished mathematician, editor of The November 2002, pp. 384-390. awarded in 1996, are made to authors of American Mathematical Monthly, 1942- expository articles accessible to 46, and President of the Mathematical The George Pólya Awards, established in undergraduates that are published in Association of America, 1947-48. 1976, are made to authors of expository Math Horizons. The Awards are named articles published in the College Math- for Trevor Evans, a distinguished ematics Journal. The Awards are named mathematician, teacher, and writer at for George Pólya, a distinguished math- Emory University. ematician, well-known author, and pro- fessor at Stanford University.

13 FOCUS August/September 2003 2003 Award Winners for

PACIFIC NORTHWEST

NORTH CENTRAL

IOWA

Steven A. Bleiler Portland State University Tom Sibley St. John’s University Alexander F Kleiner Drake University

NORTHERN CALIFORNIA NEBRASKA-SE SD

ROCKY MOUNTAIN

Peter Tannenbaum California State University, Fresno Judy L. Walker University of Nebraska-Lincoln KANSAS Hugh King Colorado School of Mines SOUTHERN CALIFORNIA

SOUTHWESTERN

Frank S. Brenneman Tabor College

Mark Finkelstein University of California, Irvine TEXAS

Janet M. McShane Northern Arizona University

Gregory B. Passty Southwest Texas State University

14 August/September 2003 FOCUS Distinguished Teaching

NORTHEASTERN

SEAWAY

Emma Previato Boston University

Olympia Nicodemi SUNY Geneseo

NEW JERSEY

INDIANA OHIO

Steve Greenfield Rutgers, the State University of New Jersey Johnny E. Brown Thomas P. Dence Purdue University Ashland University MD-DC-VA MISSOURI

KENTUCKY SOUTHEASTERN

Rebecca Berg Tom Ingram Bowie State University University of Missouri-Rolla Ted J. Suffridge University of Kentucky Sue Goodman University of North Carolina at Chapel Hill

Not pictured: Florida Section: Athanassios Kartsatos Michigan Section: Steven Kahn

The following sections did not make awards this year: Allegheny Mountain, EPADEL, Illinois, Intermountain, Louisiana-Mississippi, Metro New York, Oklahoma-Arkansas, and Wisconsin.

15 FOCUS August/September 2003 The Mathematical Olympiad Summer Program Brings Together Talented High School Students

By Steven R. Dunbar

In late June and early IMO attracts 500 of the July, 30 of the best most talented mathemat- high school math- ics students from more ematics students in than 80 countries. The the nation grappled USA team consists of with challenging Daniel Kane, Anders mathematical prob- Kaseorg, Mark Lipson, lem solving at the an- Po-Ru Loh, Aaron nual Mathematical Pixton, and Yan Zhang. Olympiad Summer Zuming Feng of Phillips Program (MOSP) Exeter Academy is the held on the campus Head Coach and Gregory of the University of Galperin of Eastern Illi- Nebraska-Lincoln in nois University is the As- Lincoln, NE. The sistant Coach. MOSP is sponsored by the Mathematical MOSP, which covers the Association of subjects which appear on America through the the USA and Interna- American Mathemat- tional Mathematical ics Competitions pro- Clockwise from lower left seated individual: Jae Min Bae, Tiankai Liu, Boris Olympiads, is deep and gram. This extraordi- Alexeev, Daniel Kane, Mark Lipson, Aaron Pixton, Anders Kaseorg, Ron Gra- sophisticated. It includes nary group of young ham, MAA President, Tony Zhang, Yan Zhang, Zwok Fung Tang, Po-Ling Loh, number theory, advanced mathematicians spent Po-Ru Loh, and Tina Straley, MAA Executive Director. Photo by Robert A. Euclidean geometry, po- 8 to 9 hours each day Strawn. lynomial theory, in- in classes and study sessions learning in Exeter, NH, Po-Ling Loh of James equalities, invariants, combinatorics, problem solving techniques and solving Madison Memorial High School in and counting methods. Students prac- Olympiad-caliber problems in both team Madison WI, Po-Ru Loh of James Madi- ticed their skills frequently with home- and individual contests. All of the stu- son Memorial High School in Madison work sets and contests which were dents were top scorers from the 32nd WI, Aaron Pixton of Vestal Senior High graded and discussed daily. A typical USA Mathematical Olympiad (USAMO) School in Vestal NY, Kwok Fung Tang of problem is Problem 2 from the 2003 exam in May. Each USAMO participant Phillips Exeter Academy in Exeter, NH, USAMO: A convex polygon P is dis- had already survived two challenging Tony Zhang of Phillips Exeter Academy sected into smaller convex polygons by preliminary examinations: the American in Exeter, NH and Yan Zhang of Thomas drawing all of its diagonals. The lengths Mathematics Competition held in Feb- Jefferson High School of Science and of all sides and all diagonals of the poly- ruary 2003 and the American Invita- Technology in Alexandria,VA. The win- gon P are rational numbers. Prove that tional Mathematics Exam held in March ners were celebrated on June 22-23 with the lengths of all sides of all polygons in and April. a reception at the MAA Headquarters in the dissection are also rational numbers. Washington D.C., a tour of the National Among the participants at the MOSP Science Foundation, a reception at the The 12 USAMO Winners, along with were the top twelve named as the National Academy of Sciences with a talk their hometowns and schools, the Hon- USAMO Winners. They are Boris by Dr. Peter Winkler of Bell Labs (Lu- orable Mentions, and the questions on Alexeev of Cedar Shoals High School in cent Technologies), and a gala dinner the USAMO as well as the answers can Athens GA, Jae Min Bae of the Academy with the mathematical sciences commu- all be found at www.unl.edu/amc/. More for Advancement of Science and Tech- nity in the U.S. Department of State Dip- pictures and information about the nology in Hackensack NJ, Daniel Kane lomatic Reception Rooms. American Mathematics Competitions, of Madison West High School in Madi- the USAMO, the IMO and the MOSP are son WI, Anders Kaseorg of the Char- After taking yet another rigorous two- also available on the website. lotte Home Educators Association in day Team Selection Contest six students Charlotte NC, Mark Lipson of Lexing- were named as the USA team for the 44th On MOSP, see also the advertisement on ton High School in Lexington MA, International Mathematical Olympiad to page 22 of this issue. Steven R. Dunbar is Tiankai Liu of Phillips Exeter Academy be in Tokyo, Japan, on July 11-19. The the Director of the American Mathematics Competitions. 16 August/September 2003 FOCUS A Problem-Solving Dynasty

By Steve Olson

Tennis stars Venus and Serena tion (which has since been Williams may be better known, split into the AMC 10 and but the three children of Wei- AMC 12). In his junior year Yin and Theresa Loh are no less he did so well that he quali- accomplished. fied first for the American In- vitational Mathematics Ex- Po-Shen Loh, a senior at the amination and then for the California Institute of Technol- United States of America ogy, Po-Ru, a Caltech freshman, Mathematical Olympiad and their sister Po-Ling, a jun- (USAMO). He finished ior at James Madison Memorial among the top 12 in the na- High School in Madison, Wis- tion on the USAMO, earning consin, are the most decorated a trip to Washington, D.C., to set of siblings in the history of be honored at a black tie din- U.S. competitive mathematics. ner at the State Department. All three have scored at the high- And he qualified for the U.S. est levels of national competi- Po-Ru Loh, MAA President Ron Graham, and Po-Ling Loh at International Mathematical tions, and the two older boys are the USAMO Award Ceremony at the US Department of Olympiad team that year, the first set of siblings ever to State.Photo by Robert A. Strawn. where as one of six team qualify for U.S. International members he earned a bronze Mathematical Olympiad teams. “Their (The Lohs have observed a Chinese tra- medal at the 1999 Olympiad in Roma- achievement is unprecedented,” says Titu dition of giving their children the same nia. Andreescu, who formerly served as di- name; one meaning of “po,” in Chinese, rector of the MAA’s American Math- is “breadth.”) “Everybody told Po-Ru he The next year Po-Shen and Po-Ru, then ematics Competitions and leader of the had to do better than his brother, and I a freshman, finished among the top 12 U.S. IMO team. thought there was no way he could do on the USAMO — the first time two sib- that,” says Loh, but he was wrong. In the lings ever had achieved that feat. Po- As is the case with many mathematically seventh grade, Po-Ru finished second in Shen opted to do a fellowship at Caltech talented U.S. students, the Lohs learned the nation in Mathcounts, and he fin- that summer, but Po-Ru was on the about competitive mathematics through ished first in the eighth grade. Olympiad team that went to Korea in Mathcounts, the middle school problem- 2000, where he earned a silver medal. Po- solving program. “In the sixth grade, a “That got the eye of his sister, Po-Ling,” Ru also was on the Olympiad teams that teacher called Po-Shen and said that he says Loh. Two years younger than Po- competed in Scotland in 2002 and Japan should take the selection test for the Ru, Po-Ling was not sure at first that she in 2003, earning gold medals both times. school team,” says Wei-Yin, a professor liked competitive mathematics. “It’s tra- And in 2003, the second set of siblings of statistics at the University of Wiscon- ditionally been more of a boys’ subject,” ever to finish together in the top 12 on sin. “We had no idea what to expect. We she says. But in the seventh grade she, the USAMO came to the State Depart- just thought it was a local event.” too, advanced to the national level in ment dinner in Washington, when Po- Mathcounts, where she did even better Ru was joined by his sister Po-Ling. The following year, Po-Shen did so well than her eldest brother had done. The at the local and state levels of Mathcounts following year, in the eighth grade, she With such accomplished children, Wei- that he was one of four people selected was second in the nation. No other girl Yin and Theresa Loh often are asked for to the Wisconsin state team. He went to has ever done as well in the national their secret. But they say that the credit Washington to compete at the national Mathcounts competition. belongs entirely to their children. “We level against 227 other middle schoolers haven’t done anything special with and finished in the top 30. “I was When Po-Shen began high school, “we them,” says Wei-Yin. “They got each shocked,” says Po-Shen, “I thought for thought that was the end of the compe- other interested in it.” sure that I would be in the lower half.” titions,” says Wei-Yin. But then the Lohs discovered the American Mathematics Steve Olson is the author of “Mapping The following year, in eighth grade, Po- Competitions (AMC) examinations Human History: Genes, Race, and Our Shen placed third in the nation in sponsored by the MAA. Beginning his Common Origins” and the forthcoming Mathcounts. According to his father, freshman year, Po-Shen took the Ameri- “Brainstorms: Six Kids Vie for Glory at “That got the attention of his brother, Po- can High School Mathematics Examina- the World’s Toughest Math Competition.” Ru,” who was then in the fifth grade. 17 FOCUS August/September 2003 NSF Beat September 2003 By Sharon Cutler Ross

The NSF has announced a new pro- Undergraduates in a VIGRE project will MCTP gram to complement the VIGRE (Verti- gain research experience through activi- cal Integration of Research and Educa- ties such as faculty-directed projects, in- The Mentoring through Critical Transi- tion) initiative that is already underway. ternships, or participation in interdisci- tion Points program solicits proposals VIGRE will become part of a three- plinary research. Mentoring of these stu- that deal with any of the following or pronged effort to increase the number of dents should aim to stimulate further similar career transitions: from under- U.S. citizens, nationals, and permanent interest in the mathematical sciences and graduate to graduate school; from course residents who are well prepared and pur- to develop enhanced mathematical com- work to original research; from gradu- sue careers in the mathematical sciences. munication skills. ate school to a postdoctoral appoint- The new program, Enhancing the Math- ment, to a teaching position at an un- ematical Sciences in the 21st Century A VIGRE project is intended to offer dergraduate institution, or to a position (EMSW21), is comprised of VIGRE, Re- postdoctoral associates opportunities in industry. Proposers should describe search Training Groups in the Math- outside the usual mathematical sciences plans for addressing the issues related to ematical Sciences (RTG), and Mentoring education and training through interdis- a specific transition point or set of points, through Critical Transition Points in the ciplinary research experiences, external for the recruitment of participants with Mathematical Sciences (MCTP). A broad internships, and participation in research particular attention to those from stroke description of each component institute programs. A critical element is underrepresented groups, and for care- follows. A complete description may be mentoring as it is for the undergraduate ful mentoring of the participants. The found at the NSF website. All three com- and graduate students. For the NSF hopes to make awards of up to ponents have the same proposal dead- postdoctoral associates, mentors should $500,000 per year for one to five years to line: 16 September 2003. help develop successful researchers, com- fund six MCTP projects. municators, and mentors. VIGRE The NSF anticipates making up to seven VIGRE projects must be designed to pro- VIGRE awards based on a budget of mote interaction among undergraduates, $10,000,000. Grants will be $400,000 to graduate students, postdoctoral associ- $1,000,000 per year for three years with ates, and faculty members in a depart- the possibility of an extension for two ment (or departments). A team approach more years. A VIGRE proposal should based on broad support by faculty should describe a five-year plan. integrate research and education for graduate students and involve under- RTG NSF to Fund “Science graduates in learning by discovery. A new of Learning” Centers feature of the revised VIGRE program is A Research Training Group will be a the possibility of support for interna- group of researchers focused on a major The National Science Foundation plans tional research and education activities. research theme. Members may come to fund several Science of Learning Cen- All VIGRE proposals are required to in- from different departments or institu- ters that focus on studying how people clude an extensive curriculum review tions, but the research and education learn and transform the knowledge into supported by five years of data. activities must be based in the math- practical ways of improving teaching. ematical sciences and in a mathematical The Centers are to be interdisciplinary Goals for graduate students in a VIGRE sciences department. Support requests and are expected to develop “appropri- project include significant teaching ex- for advanced undergraduates, graduate ate partnerships with academia, indus- perience, involvement with research ac- students, postdoctoral investigators, and try, all levels of education, and other pub- tivities involving the full range of par- visitors may be included in a RTG pro- lic and private entities.” For more infor- ticipants, broad and deep graduate edu- posal. A significant collective mentoring mation, see http://www.nsf.gov/home/ cation, and the development of strong component is required to help ensure crssprgm/slc/summary.htm. communication skills. In contrast to tra- that all participants benefit from new or ditional graduate support, VIGRE par- enhanced research-based training and ticipants should have significant time for education. Funding of $4,000,000 will course work, research, and other activi- support up to nine RTG awards. A pro- ties as well as at least one year of super- gram may receive up to $500,000 per year vised teaching. for one to five years.

18 August/September 2003 FOCUS

MAA Election Results Are In: Carl Cowen Will Former FOCUS Editor Become the Association’s 51st President Keith Devlin Wins Italian Literature Prize Carl C. Co- winner, is a long-standing member of the MAA Online wen of Purdue MAA who has served as Chair of the columnist Keith University will Committee on Sections and on a host of Devlin has been be the MAA’s committees, including Audit and Budget, awarded the next President. Finance, Executive, Strategic Planning, Italian Peano He will serve as Gung Hu Award, and others. She is Prize for 2002. President-Elect currently the Chair of the Coordinating The prize is in 2004 and Council on Awards. awarded to the begin a two- author of a book year term as One im- of “readable Carl C. Cowen Keith Devlin President in portant goal mathematics” January 2005, when he will succeed of the MAA “is published in Italian during the year of Ronald Graham. That year will also to expand attribution, and is the only award in Italy mark the MAA’s 90th anniversary. membership dedicated to this subject. Devlin was to include a chosen to receive the award for his books Barbara T. Faires of Westminster College larger per- The Math Gene and The Language of (New Wilmington, PA) was elected the centage of Mathematics, both of which have been Association’s next First Vice-President those in- reviewed in the Read This! section of for the term 2004-2005. terested in MAA Online. undergraduate And for the position of Second Vice- mathematics Barbara T. Faires Previous winners are Apostolos Doxiadis President, Jean Bee Chan of Sonoma education,” of Greece and Alaine Connes of France. State University (Rohnert Park, CA) won said Professor Faires. “I will work to Other authors whose books were the two-year term 2004-2005. ensure continued success of Project considered for the 2002 prize included NExT and other such projects from Amir Aczel, Freeman Dyson, Michele Professor Cowen is at present the MAA’s which future leaders will come.” Emmer, Stephen Hawking, Roger First Vice-President. He is former Head Penrose, Charles Seife, and Ian Stewart. of the Mathematics Department of Jean Bee Chan served on the MAA Board Purdue University, and is coauthor of of Governors (l999-2002) and as Vice- Devlin will travel to Turin in the fall to Composition Operators on Spaces of Chair of the Northern California Section be awarded the prize and to give an Analytic Functions (1995). (l996-97). She has also served on the invited public lecture. Association’s Membership Committee, He won the Haimo Award for Development Committee, and Distinguished Teaching in l997 and has Committee on Undergraduate Student Distance Learning over the past decade served the Activities and Chapters. Association as a representative and Program Sought consultant to numerous committees, Prof. Chan councils, and boards, and been a member stated “I will Community College mathematics profes- of the Joint Advisory Board for FOCUS devote my sor is seeking a doctoral program in math- and MAA Online. energy to in- ematics that would offer some courses via crease public distance learning. His plans are to com- “I will work within the MAA and with appreciation plete the degree (on location) during a other organizations to connect our of math- two/three year leave of absence from full students with the phenomenal ematics, work time employment. opportunities in the mathematical for student sciences,” he said, “and to build better programs, Contact Information: mathematical futures for us all.” and generate Jean Bee Chan financial S. Kaczkowski Barbara T. Faires, a 2002 Allegheny support for S.U.N.Y. Orange Mountain Section Teaching Award the MAA.” 115 South Street Middletown, NY 10940 Email: [email protected]

19 FOCUS August/September 2003 Short Takes Compiled by Fernando Q. Gouvêa

MAA Online on the Radio geometric group theory. Meier, who is a in mathematics education aimed at fig- member of the Association, is one of the uring out what actually will help attain We understand that Michael Krazny, few Centennial Fellows to work at a small the goal of proficiency for all. The report in a program called Forum that can be college. can be ordered in book form or viewed heard on KQED (the NPR station in the online at http://www.rand.org/publica- San Francisco area) recently recom- Kaplan Plans Move Into Teacher tions/MR/MR1643/. mended that viewers visit MAA Online’s Education Read This! section. He also recom- MAA Member George Andrews Elected mended John dePillis’s book, 777 Math- Kaplan Inc. is the latest institution to to National Academy of Sciences ematical Conversation Starters. We are, of open a school of education, hiring course, in full agreement with both of Harold O. Levy, the former New York The National Academy of Sciences an- Krazny’s recommendations. City schools chancellor, to run its school, nounced the election of 72 new mem- which will target working adults who bers and 18 foreign associates from 11 This Just In want to switch careers. When he was countries in recognition of their distin- chancellor in New York, Levy developed guished and continuing achievements in Patricia A. McKillip’s new book, In the a Teaching Fellows program that catered original research. Six of the new mem- Forests of Serre, was recently offered by to those who sought to change careers. bers are mathematicians, statisticians, or the Science Fiction Book Club with the Levy envisions “a full-service school of computer scientists and one—George blurb “Whoever walks the forests of Serre education” that would award associate, Andrews —is also a member of the MAA. may never find his way home.” We are bachelor’s and master’s degrees. Kaplan Election to membership in the Academy reliably informed, however, that the book will seek accreditation for the school is considered one of the highest honors is not about being lost in the mathemati- from the North Central Association of that can be accorded a scientist or engi- cal work of the recent Abel laureate. His Colleges and Schools. neer. many papers, after all, are more like mountaintops than they are like forests. National Research Council Suggests The new members in the mathematical States Fund Educational Research sciences are: George E. Andrews of Penn- Commemorations sylvania State University, James O. Berger A report by the National Research Coun- of Duke University, Yakov Eliashberg of This year marks the 400th anniversary of cil calls upon states to band together and Stanford University, Solomon W. the death of French mathematician invest in educational research. The NRC Golomb of the University of Southern François Viète (1540-1603), who made report proposes the creation of a “stra- California, Karl Hess of the University of contributions to algebra and other tegic education research partnership” Illinois, and Haim Brezis of the branches of mathematics. It is also the that would bring together scientists and Universitè Pierre et Marie Curie, elected centenary of the birth of Andrei partnerships to conduct research in as a foreign associate. Nikolaevich Kolmogorov, famous among school and district settings. The report, other things for proposing a mathemati- “Strategic Education Research Partner- cal foundation for the theory of prob- ship,” can be viewed online at http:// Sources. Krazny: Jerry Alexanderson, ability. Both anniversaries will be marked books.nap.edu/books/0309088798/html/ Frank Farris. Forests of Serre: SFBC flyer. by conferences and other special events. index.html. Commemorations: email communica- Also worthy of note is the 25th anniver- tions, http://tug.org. Centennial Fellow- sary of TEX, celebrated this July at the RAND Report Released ships: email communication, Chronicle TUG (TEX Users Group) meeting in Ha- of Higher Education, AMS website. waii. The RAND Corporation has released a Kaplan: Chronicle of Higher Education, report entitled Mathematical Proficiency http://www.kaplan.com/about/f1b.html. AMS Centennial Fellowships for All Students. Prepared by a panel of NRC: Education Week, 09 April 2003, mathematicians and mathematics edu- National Academy of Sciences website. The AMS announced that it has awarded cators chaired by Deborah L. Ball, the RAND report: Education Week, 30 April Centennial Fellowships to two outstand- report concludes that the many attempts 2003, RAND website. New NAS mem- ing research mathematicians: Henry H. to create the conditions for all students bers: NAS website. Kim of the University of Toronto, who to attain a reasonable level of mathemati- works on the theory of automorphic cal proficiency suffer from an inadequate forms and L-functions, and John E. empirical research base. It, therefore, pro- Meier of Lafayette College, who works on poses a wide-ranging research program

20 August/September 2003 FOCUS American Institute of Mathematics Research Conference Center Call for Proposals

Proposals are now being solicited by specific mathematical goal. Special atten- of the proposal. The inclusion of women, the American Institute of Mathematics tion is paid to facilitating collaborations members of underrepresented ethnic/ (AIM) Research Conference Center that include women, underrepresented racial groups, junior researchers, and re- (ARCC), for small, focused workshops minorities, and researchers at primarily searchers from primarily undergraduate to be held between summer 2004 and undergraduate institutions. To aid in col- institutions is a plus. summer 2005. These workshops are laboration before and after the work- sponsored by AIM and the National shops, each workshop has an accessible AIM is a nonprofit mathematics institute Science Foundation, which jointly fund website which includes open problems based in Palo Alto, California, and has ARCC. It is anticipated that there will and progress updates. been in existence since 1994. AIM was be eighteen focused workshops in 2004- founded by Silicon Valley businessmen 2005, at AIM in Palo Alto, California. Proposals will be accepted until Novem- John Fry and Steve Sorenson, to support Each workshop will last approximately ber 1, 2003. Typically one to two pages research mathematics. John Fry received one week and involve up to 32 partici- in length, proposals should describe the an undergraduate degree in mathemat- pants, allowing for close collaboration specific mathematical goal comprising ics at Santa Clara University, and was in- between scholars. All participants re- the focus of the workshop. Also included spired by his professor and former MAA ceive full funding to attend. should be an outline of how this goal president, Gerald Alexanderson, who is would be accomplished during the week, chair of the board of trustees of AIM. Whereas fifty years ago mathematical as well as anticipated workshop out- AIM also sponsors conferences, small collaboration was relatively rare, today comes. Proposals will be judged for their focused research groups, REUs, public approximately half of all mathematical scientific merit and timeliness, as well math lectures, and math activities for papers are written by multiple authors. upon their appropriateness for a small, local high school students. ARCC helps to develop and support intensive workshop format. The overall such collaborations by holding small, quality of the workshop plan and the See http://www.aimath.org/ARCC/ for focused research workshops that allow likelihood that the proposed goals would more information. entire groups of attendees to devote be achieved are also considered. A list of their efforts toward accomplishing a expected participants is required as part

Final Report on Project to Assist Mathematics Departments to Monitor Their Undergraduate Programs

An NSF-funded project to develop sta- marizing the major findings is now search articles on teaching and learning tistical indicators to help college math- available online or on CD at the website, undergraduate mathematics. The docu- ematics departments to monitor the http://www.mste.uiuc.edu. ments are provided in a database that is quality of their lower division (first two searchable by topic, statistical indicator, years) undergraduate mathematics pro- The final report also provides back- author, and title. For further information grams was announced in a prior issue of ground for the project. Student outcomes contact Kenneth J. Travers at FOCUS (August/September, 2001). The and assessment, by John A. Dossey and [email protected]. project, carried out under the direction Alan H. Schoenfeld, is a comprehensive of a national advisory panel, collected paper, that outlines strategies, together data from the mathematics departments with abundant sample assessment on three campuses: a community college; items, for monitoring student achieve- a comprehensive state university, and a ment in mathematics. Also included is research university. A final report sum- a collection of abstracts of over 100 re-

21 FOCUS August/September 2003

The Tenth International Congress on MAA American Mathematical Education (ICME-10) Mathematics Competitions Under the auspices of ICMI (Interna- •Learn and benefit from recent ad- Program Seeks tional Commission on Mathematical In- vances in mathematics as a discipline struction) the 10th International Con- MOSP-IMO Leader gress on Mathematical Education, ICME-10 hopes to attract between three ICME-10, will be held in Copenhagen, and four thousand researchers in math- Denmark, July 4-11, 2004. The aim of ematics education, mathematics educa- The MAA seeks a mathematician to be the ICME congresses is to: tors, including teachers, and others work- Academic Director of the Mathematical ing within the educational system, from Olympiad Summer Program June-July, • Show what is happening in math- around 100 countries. Applications to 2004 in Lincoln, NE and Leader of the ematics education worldwide, in attend can be found at the ICME-10 US delegation to the International Math- ematical Olympiad in Athens, Greece terms of research as well as teaching website at http://www.icme-10.dk. Travel practices grants are available through NCTM. For July 6-18, 2004. Must be excellent math- more information and grant applica- ematical problem solver, have excellent teaching skills and be able to work with •Exchange information on the prob- tions, visit the NCTM website at http:// exceptionally talented high schools stu- lems of mathematics education www.nctm.org/icme10/. around the world dents, and be able to represent the USA and the MAA. Experience with AMC and Olympiad style math competitions is desired. The position is renewable for succeeding summer programs in 2005 Data on Gender For 2002 and 2006. Please send letter of applica- tion and resume by November 1, 2003, Below is the information collected for the year 2002. to Prof. Steve Dunbar, MAA American Mathematics Competitions, 1740 Vine MAA Awards Committee Chairs Street, Lincoln, NE. Please direct your inquiries about the position to Profes- Total Awards 22 This list includes chairs of committees, sor Dunbar at 1-402-472-6206 or Female Awardees 3 including joint committees, representa- [email protected]. Male Awardees 19 tives, and editors.

Percentage of Female Participation: 14% Total Chairs 96 Female Chairs 31 Board of Governors Male Chairs 65

Total Board Members 51 Percentage of Female Chairs: 32% Have You Moved? Female Board Members 17 Male Board Members 34 Speakers at National Meetings The MAA makes it easy to change your address. Please inform the Percentage of Female Board Members: This list includes MAA Invited Addresses, MAA Service Center about your 33% Minicourses and Short Course Instruc- change of address by using the elec- tors, and Organizers of Contributed Pa- tronic combined membership list at Nominees to the Board of Governors per Sessions. MAA Online (www.maa.org) or call (800) 331-1622, fax (301) 206-9789, This list includes nominees for section Total Speakers 110 email: [email protected], or mail governors elected in 2002 as well as Female Speakers 44 to the MAA, PO Box 90973, Wash- nominees for other governor slots in- Male Speakers 66 ington, DC 20090. cluded in Board agendas. Percentage of Female Participation: 40% Total Nominees 26 Female Nominees 5 Male Nominees 21

Percentage of Female Nominees: 19%

22 August/September 2003 FOCUS Career Brochure Order Form

The new MAA career brochure We Do Math! highlights eleven profiles from 101 Careers in Mathematics. These vignettes describe a variety of non-academic careers for which a background in the mathematical sciences is useful. Each of the jobs presented shows real people in real jobs.

The eight-panel brochure is 4’’ by 9’’ (folded) and can be mailed in a standard envelope or distributed in the classroom or at career fairs or recruiting events.

When students want to know how a mathematics degree can benefit them, be prepared to answer with We Do Math!

A Special Offer Your school logo and/or contact information can be printed on the brochure Schools ordering brochures in time have the option of including the school logo and/or contact information on the front of the brochure. PRE-ORDERS + LOGO (black or one-color version only) must be received by MAA headquarters by September 12, 2003.

Brochure Pricing Yes! I want to preorder brochures with my school logo Copies of We Do Math! are available in bulk in multiples of 1000. If and/or contact information on you add your institutional information on the brochure, there is a the brochure. one-time set up fee of $150.00. I want to order brochures without my school logo on the front.

Quantity:______at $175/1000 = ______Questions? Setup: $150.00 Contact Chris Proesel Total: ______(202) 319-8469 [email protected]

We're looking for more career profiles. If you would like to contribute profiles featuring your students for possible use in future brochures, please contact us.

Contact Name

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Fax Number Email

23 FOCUS August/September 2003 I. Bernard Cohen (1914–2003) By Judith V. Grabiner

I. Bernard Cohen, the thesis director for exhibiting the inertial motion of projec- many of the first generation of profes- tiles and the stroboscopic photographs sionally trained American historians of of parabolic motion remained in stu- mathematics and the first American to dents’ minds many years later. I have a receive a Ph.D. in the History of Science vivid memory of Cohen demonstrating in the United States, died at his home in Copernicus’s three motions of the earth Waltham, Massachusetts on June 20. Best by walking around a table and twirling a known to the mathematical community well-aimed yardstick. as America’s most prominent Newtonian scholar, Cohen was the author of many Arising from his courses was his wonder- books, including his monumental criti- ful little book, historically sophisticated cal edition (1972) and the definitive but also highly readable, The Birth of a modern translation (1999, with Latinist New Physics (1960, updated 1985), which Anne Whitman) of Newton’s Principia. I. Bernard Cohen clearly and succinctly describes the his- Also notable are The Newtonian Revolu- tory of physics and astronomy from tion (1980), analyzing Newton’s math- scholars, whoever and wherever they Aristotle through Copernicus, Tycho, ematical physics, and Newton: Text, Back- might be, independently of their conven- Galileo, and Kepler, culminating in the ground, Commentaries (1995), a compre- tional academic stature. Without fanfare achievements of Newton. Yet another of hensive collection of primary sources or ideology, he was a champion of equal his books, Revolution in Science (1985), and recent scholarship, co-edited with treatment for women at a time when it covering developments from Renaissance Richard S. Westfall. was far from universal at Harvard. astronomy and anatomy to Einstein and Continental Drift, won the 1986 Pfizer Educated at Harvard, Cohen received his He taught his students, many of whom award of the History of Science Society. B.S. in Mathematics in 1937, and his were trained in the sciences, how to think His interest in the history of computers Ph.D. in the History of Science in 1947. like historians. One of his maxims was resulted in another book, Howard Aiken: He taught history of science at Harvard “Remember that scientists of the past Portrait of a Computing Pioneer (1999). from 1946 until 1984, and later taught at were just as intelligent as we are, so that, Among his many articles on subjects of Brandeis and at Boston College. Al- if we had lived when they did, what interest to mathematicians, I would es- though the history of mathematics was puzzled them would puzzle us too.” An- pecially highlight three in the Scientific not Cohen’s primary field, his knowledge other maxim, a call to ethical scholarship American: on Florence Nightingale as a of it was amazing, and it was he who in- and the excitement of research, was statistician, on Newton’s discovery of troduced many future historians of “Truth is more interesting than fiction.” gravity, and an interview with Albert mathematics to topics as diverse as alge- Above all, Cohen had an unerring abil- Einstein shortly before the latter’s death. bra in Islamic civilization, the statistical ity to pick out what was important and The manuscript of Cohen’s last book, revolution of the nineteenth century, and to discourage what was lazy, superficial, The Triumph of Numbers, a history of Kepler’s anticipations of the integral cal- or trivial—and to do this in a way that numbers and their impact on society and culus. Among his Ph.D. students at empowered, rather than discouraged. He culture, was mailed to the publisher one Harvard were the historians of math- was always delighted when somebody week before he died. ematics Uta Merzbach, Victor Hilts, could teach him something new. “That’s Bruce Collier, Joseph Dauben, Kenneth very interesting!” was one of his charac- Cohen leaves his wife of nineteen years, Manning, Lorraine Daston, Joan teristic responses. He understood the Susan Johnson, a daughter, Dr. Frances Livingston Richards, and the present exigencies of academic life thoroughly Cohen, and granddaughter Angelica writer. Other notable historians of math- and got them across to his students. I am Koch of New York, and two stepsons, ematics, including Wilbur Knorr, took fond of quoting what he said when I was David Johnson of St. Louis and Benjamin Cohen’s courses while at Harvard. trying to finish my dissertation by the Johnson of New York. A memorial ser- deadline: “Don’t get it perfect; get it vice is being planned for November 19, Cohen was a wonderful mentor. He and done.” 2003; see http://www.fas.harvard.edu/ his wife often had graduate students over ~hsdept/ for information. His many to their home, bringing students together Generations of Harvard students were graduate students, colleagues, and with visiting scholars. He made it seem introduced to the physical sciences friends will miss him beyond what words as though this was the natural way to through Cohen’s general-education can convey. treat graduate students. He always courses. His lectures were intellectually worked to help young—and older— and physically dramatic: The model train

24 August/September 2003 FOCUS Etta Zuber Falconer (1933-2002) By Sylvia T. Bozeman

Etta Z. Falconer passed away on Sep- Falconer’s research in algebra and sub- tion of tember 19, 2002. She had retired in May sequent publications were highly re- Mathema- 2002 as Fuller E. Callaway Professor of garded, yet she chose to devote her ex- ticians; and Mathematics at Spelman College where ceptional creativity to the design of the Louise she spent 37 years on the faculty. Falconer highly effective academic structures that Hay Award was a transforming force at the College would increase access to education in for Contri- while holding positions as Chair of the science and mathematics for generations butions to Mathematics Department, Chair of the of black women. It was her greater vi- Mathemat- Division of Natural Sciences and Math- sion to increase the diversity of the U.S. ics Educa- ematics, Associate Provost for Science scientific community. Under Falconer’s tion from Programs and Policy, Senior Advisor to leadership, the College added majors and the Asso- the President and Acting Provost. In these departments in Computer Science and ciation for Etta Z. Falconer and her many roles beyond Spelman Physics and a concentration in Environ- Women in Mathematics. In April 2002, College, she committed herself to excel- mental Science, and worked with the Spelman College gave recognition to the lence and left a rich legacy that forever National Aeronautics and Space Admin- magnitude and importance of Etta’s con- places her at the national forefront in ef- istration to launch the Women in Science tributions when it opened a state-of-the- forts to increase the presence of minori- and Engineering Program, an initiative art science center that bears the Falconer ties and women in mathematics and sci- that has contributed scores of extremely name. ence. talented women to the scientific commu- nity over the past decade. In addition, she Falconer’s impact on the development of Etta was one of two daughters born to was an inspiring mentor for hundreds of minorities in science is profoundly re- Walter A. Zuber and Zadie L. Montgom- students, faculty and staff, including this flected in her own family. She, with her ery in Tupelo, Mississippi. At age 15, she writer. loving husband Dolan, nurtured the de- entered Fisk University where she earned velopment of their children: Dolan, Jr., a the B.A. degree in mathematics in 1953. Several honors and awards indicate the nuclear engineer; Alice, a pediatrician; A year later she would earn the M.S. de- extent of Etta’s impact, the breadth of her and Walter, an urologist. Following in gree in mathematics from the University service and the depth of her commitment Etta’s footsteps is granddaughter, Shelby, of Wisconsin and begin a teaching career to the advancement of students in math- a sophomore at Spelman College. at Okolona Junior College (MS). She re- ematics and science. Recognitions in- turned to graduate school at Emory Uni- clude the Giants in Science Award from We will miss Etta Falconer—miss her versity where she earned the Ph.D. de- the Quality Education for Minorities wise counsel, her warm and gentle spirit, gree in 1969 with a dissertation entitled Network; an honorary doctorate degree and her strong voice of advocacy in the Quasigroup Identities Invariant Under from the University of Wisconsin at scientific community. Isotopy, written under advisor Trevor Madison; a Lifetime Mentor Award from Evans. Prior to that time, there were the American Association for the Ad- Sylvia T. Bozeman is Professor of Math- fewer than 15 African-American women vancement of Science; a Distinguished ematics at Spelman College. in the U.S. who had earned the doctor- Service Award and a Lifetime Achieve- ate in mathematics. ment Award from the National Associa-

PREP Workshop–Integrating Technology into Math Instruction On May 26-30, 2003 a culturally diverse group of math- ematics professors participated in an MAA PREP Work- shop entitled “Integrating Technology into Mathematics Instruction.” The focus was on the use of technology in precalculus and calculus classes. Prof. Jacqueline Brannon Giles was the program director and Professors Wade Ellis, Queen Hamilton, and William Hawkins were workshop presenters. HCC Central College’s Academic Dean, Dr. Cheryl Peters served as an administrative consultant to assure that the interface between the workshop activities and the HCC system was smooth. The workshop was funded by the National Science Foundation and adminis- tered by the Mathematical Association of America.

25 FOCUS August/September 2003

H.S.M. Coxeter (1907-2003)

Harold Scott McDonald Coxeter, noted ematical papers on many different sub- C. Escher’s geometer and author of many books, jects. work. Coxeter passed away on March 31 at the age of was a Fellow 96. Known as Donald to family and But while Coxeter’s research was impor- of the Royal friends, Coxeter was educated at the Uni- tant and creative, his talents as an exposi- Society of Ca- versity of Cambridge and came to the tor may have been even greater. His ex- nada (1947), University of Toronto in 1936. There, he pository books are classics to which Fellow of the was active as both teacher and researcher those who love the subject find them- Royal Society, until his death. selves returning over and over. Two of London those books were published by the MAA: (1950), and Coxeter made important contributions Non-Euclidean Geometry and Geometry Companion H.S.M. Coxeter to geometry and related areas, focusing Revisited (the latter co-authored with S. of the Order especially on group theory and discrete L. Greitzer). His most famous book is of Canada groups, graph theory, projective geom- probably Introduction to Geometry, writ- (1997). He also received several honor- etry, the theory of polytopes, and non- ten in 1969 and still in print from Wiley. ary degrees. Euclidean geometries. As happens to many creative and influential mathema- In addition to mathematics, Coxeter Coxeter is survived by his daughter Su- ticians, Coxeter’s name has been attached cherished music and the arts, and was san Thomas and his son Edgar. He will to several mathematical objects, includ- particularly interested in connections be missed by all of the mathematics com- ing Coxeter groups and the Coxeter between mathematics and the arts. He munity. graph. He wrote more than 200 math- was intimately involved in studying M.

In Memoriam Barbara Beechler died on March 18, 2003. She was an active member of the Association and served as a governor of the Southern California section. She was an MAA member for 53 years.

James Crawford died on May 8. He had been an MAA member for 42 years and was honored with an MAA teaching award by the EPADEL Section in 1998.

Robert James, co-author of one of the first dictionaries of mathematics, first published in 1942. He was an MAA member for 51 years.

Geraldine D. Smith, editor and author of many mathematics textbooks, was 100 years old when she died in June. She was an MAA member for 49 years.

FOCUS will print short death notices of MAA members. Please send names, dates, and one or two biographical sentences to the editor at [email protected].

26 August/September 2003 FOCUS Letter to the Editor

I am writing to comment on the article, the K-12 community see NCLB not as a embraces the suspicions, the concerns “The Four As: Accountability, Accredi- legitimate effort to improve the quality cannot be dismissed out of hand. Mo- tation, Assessment, and Articulation” by of education but rather as part of a sys- tives aside, it is important to think care- Peter Ewell and Lynn Arthur Steen, which tematic effort to undermine support for fully about consequences. This was just appeared in the May/June, 2003, issue of public education in this country. underscored by recent news reports that FOCUS. states such as Texas are now scrambling It is tempting to dismiss this concern as to weaken their standards in order to In evaluating the issues raised in this ar- paranoia. To be sure, people in public cope with the provisions of NCLB. ticle it is of fundamental importance for education are prone to be suspicious of your readers to be aware of some con- an administration whose secretary of From this perspective, the remark that troversial aspects of the “No Child Left education has publicly declared that he “[m]any feel that higher education’s turn Behind” legislation (NCLB) that were considers parochial schools superior to is next” is rather ominous. The math- not fully explicated by your writers. I public schools. ematics community needs to pay close became aware of these aspects only attention. through my work as a member of a local Nevertheless, the educators raise some board of education, and I suspect that telling points. For example, results (the Daniel Frohardt relatively few of your readers are famil- proportion and number of ‘failing’ Wayne State University iar with them. schools and districts, based ultimately on the raw scores of individual students on The authors reply: Earlier this month I attended a meeting various exams) are to be reported uni- organized by a senior member of con- formly nationwide, even though the level This remark was intended to be ominous. gress that was attended by several dozen of rigor on the actual exams varies widely Professor Frohardt’s concerns are well local school officials and a handful of from one state to the next. Another ex- founded, as is his urging that the math- state legislators as well as some high- ample is the shortage of new funding for ematics community become better ac- ranking state education officials. The dis- this major initiative that will require sig- quainted with the implications of NCLB. cussion made it clear that many within nificant resources. Whether or not one

27 FOCUS August/September 2003

What’s the Best Textbook?—Elementary both approaches. A “closed” book can Number Theory give students a satisfying feeling of hav- ing mastered something, for example. But By Fernando Q. Gouvêa I have always preferred an “open” style advanced course with a computational that constantly hints at deeper questions. The “best textbook” is, of course, not a emphasis could be based on A Course in In number theory, this is particularly cru- well-defined concept. The phrase imme- Computational Number Theory, by David cial in the treatment of quadratic reci- diately brings questions to mind: Best for Bressoud and Stan Wagon (Key College procity, perhaps the biggest theorem in what purpose? Who is the professor? Publishing, 2000), also reviewed in MAA the elementary course. The quadratic Who are the students? Online (http://www.maa.org/reviews/ reciprocity theorem can be presented in bresswagon.html). such a way that the student gets no hint At Colby, the introductory number of why it is important (the most com- theory course is offered in alternate years In the end, though, I prefer a more tra- monly used proof is not helpful). I want and attracts a wide range of students. ditional teaching style, and I don’t really the author to work at opening up hori- Because it has few pre-requisites, pro- want to make my course too dependent zons, and particularly so when it comes spective mathematics majors can take it on the computer. Many of the students to the really deep results. in order to find out what this math thing who take the course would be happy to is all about. The class usually includes use a program like Mathematica, but In the end, my choice is A Friendly Intro- several such students, plus mathematics many others have little experience with duction to Number Theory, by Joseph H. majors and a few computer science ma- computers and would prefer not to have Silverman, a book that works hard to be jors. Some students are very experienced to deal with such a large and complicated approachable. Its one fault is the fact that at reading and writing proofs, others are computer program. I do encourage them it doesn’t include a proof of quadratic very much beginners at this game. to use computational aids (at least a cal- reciprocity. But I can supply that. culator, but preferably something that Silverman does a great job of exactly My goals for the course reflect this var- can do infinite-precision integer arith- those things I care about: his book is ied audience. I want to give students a metic, such as a TI-89 or the GP-PARI pro- readable; it makes students aware of the taste of the fascination of the subject, to gram). I try to leave enough room for role of both experimentation and proof; have them realize how easy it is to spot personal choice and variation. it includes many pointers to deeper ques- number-theoretical patterns and how tions and even to open questions. Even difficult it is to predict whether the pat- Two other important factors need to be the jokes are the sort that I would make! terns, once found, will be easy or hard to considered. The first is whether one is prove. I emphasize numerical experi- going to expect students to read their No matter how much I may like a book, mentation, but I also emphasize the im- textbook. I usually want them to do that, the real test happens with real students portance of finding proofs. and I hope they will get something out in a real classroom. My impression is that of their reading. That puts severe con- Silverman’s book does what I want it to What kind of textbook is helpful for such straints on the choice of textbook. A few do. Students can read the book and use a course? There are actually many of my personal favorites, such as H. it as a complement to what happens in choices. One could choose a text that is Davenport’s The Higher Arithmetic and class. (I tell students early on that it is not useful as a reference, a place for students Daniel E. Flath’s Introduction to Number my plan to transcribe the textbook on the to look for formal proofs of statements Theory, turn out not to work very well blackboard!) I don’t come anywhere near handled informally in class. I have made with students. Davenport, for example, to covering all the material in the book, this choice in courses for more advanced is a penetrating and readable book, but but that is to be expected. students, but for this course I feel such a he rarely delimits his proofs and theo- book would be too hard to handle. Most rems in a formal way. For students who The reader might object that I cannot of my students don’t have enough expe- are just starting out, this makes the book possibly have looked at all the number rience of the typical terseness of formal very difficult to read and understand: it theory textbooks on offer. The reader mathematics books. is already hard enough for them to un- would be right. Life is too short. It’s derstand proofs; asking them to figure perfectly possible that I’ve completely A second possibility would be to choose out where the proof starts and ends with- missed some wonderful book. Perhaps a textbook that emphasizes the compu- out clear textual markers is asking too one of my readers will let me know about tational side of the course, using the com- much. it. puter either to create an interactive class- room or as a source for interesting prob- The second crucial factor is whether the What’s the Best Textbook is the overall lems. For an interactive and exploratory book is “open” or “closed.” What I mean title for a series of articles discussing text- course, I would probably choose Discov- is this: Does the book hint at the glories books for mathematics courses. If you’d like ering Number Theory, by Jeff Holt and and mysteries of number theory, or does to contribute an article (even one contest- John Jones (Freeman, 2001), which was it simply try to do a good job of present- ing the conclusions of this article), please reviewed in MAA Online (see http:// ing the subject without pointing to fur- contact the editor at [email protected]. www.maa.org/reviews/dnt.html). A more ther questions? I can see arguments for 28 August/September 2003 FOCUS

EMPLOYMENT OPPORTUNITIES Advertising Information for 2003 Grant Funding Display & Classified Ads Available NEW YORK Mechanical Specifications The Calculus Consortium for Higher Trim Size: 8 1/2 " wide x 10 3/8 " high CORNELL UNIVERSITY Education (CCHE) is a small non-profit Screen: 150-line halftone The Cornell University Department of public charity which is the outgrowth of Full page bleed 8 3/4" x 11 1/4", (10% ex- an NSF funded project in innovative Mathematics invites applications for our tra charge) Teaching Program Visiting Faculty coursework in undergraduate education Color: FOCUS standard second color Positions beginning August 16, 2004. (the Calculus Consortium based at available (15% extra charge). Harvard.) The mission of CCHE is to Two or more half-time visiting positions Column width: 2 5/16", 4 13/16", 7 3/8" (any rank) for mathematics professors on improve the teaching of mathematics in Printing: Offset, saddle-stitched sabbatical/other leaves from colleges, secondary schools, two-year colleges, four-year colleges, and universities. It universities, and engineering schools. How to send your Materials: Candidates with substantial experience supports workshops, meetings, confer- Electronic files: Laser output should ac- teaching undergraduate mathematics, ences or research projects in innovative company your electronic files. PC and coursework. With that goal in mind grant and with teaching and research interests MAC based files must be sent as Post- compatible with current faculty, are requests are hereby being solicited in script files (please subset and embed all those four areas. Grants are usually for 1 sought. Successful candidates are fonts). PDF files are also acceptable. expected to pursue a program of study year and for less than $25,000. Proposals and/or research at Cornell. For should be less than five pages in length Camera-ready art: Should be prepared information about these positions and and be accompanied by a budget using according to the mechanical specifica- NSF Form 1030. They should be sent to application instructions, see: http:// tions shown on this page. www.math.cornell.edu/Positions/ CCHE, P.O. Box 22333, Carmel, CA Classified Rates (includes a a free listing facpositions.html Deadline December 1, 93922 or Email: [email protected], Fax: in MAA Online to appear the same (831) 624-7571 by November 15th for 2003.Cornell University is an Affirmative month as the print ad): $2.25 per word. Action/Equal Opportunity Employer. consideration by the Board of Directors in early January. Requests for an earlier Contact the MAA Advertising Depart- review date will be considered on an in- ment toll free at 1-866-821-1221, fax: dividual basis. If there are any questions, (703) 528-0019 Classified and MAA please contact Thomas Tucker, Math- Online ads may be sent via email to ematics Department, Colgate University, [email protected]. Hamilton, NY 13346, Email (preferred): [email protected].

New MAA Section Governors for 2003 Kansas Elizabeth G. Yanik, Emporia State University Missouri Leon M. Hall, University of Missouri-Rolla New Jersey Reginald Luke, Middlesex County College Northeastern Laura L. Kelleher, Massachusetts Maritime Academy Ohio Thomas A. Hern, Bowling Green State University Pacific Robert A. Beezer, University of Puget Sound Northwest Southeastern Benjamin G. Klein, Davidson College Southwestern William D. Stone, New Mexico Institute of Mining and Technology Seaway Luise-Charlotte Kappe, SUNY Binghamton

29 FOCUS August/September 2003 MAA Section Meeting Schedule Fall 2003 and Spring 2004

ALLEGHENY MOUNTAIN MICHIGAN OKLAHOMA-ARKANSAS

March 26-27, 2004-West Virginia May 7-8, 2004-Oakland University, March 26-27, 2004-University of Central Wesleyan College, Buckhannon, WV Rochester, MI Arkansas, Conway, AR

FLORIDA MISSOURI PACIFIC NORTHWEST

February 20-21, 2004-University of April 2-3, 2004-Southeast Missouri State June 24-27, 2004-University of Alaska, Central Florida, Orlando, FL University, Cape Girardeau, MO Anchorage, AK

ILLINOIS NEBRASKA-SOUTHEAST SOUTH ROCKY MOUNTAIN DAKOTA April 1-3, 2004-Roosevelt University, April 16-17, 2004-Colorado College, Schaumburg, IL April 2-3, 2004-University of Nebraska Colorado Springs, CO at Kearney, Kearney, NE INDIANA SOUTHEASTERN NEW JERSEY October 18, 2003-Goshen College, March 26-27, 2004-Austin Peay State Goshen, IN November 8, 2003-Raritan Valley University, Clarksville, TN Community College, North Branch, NJ April 2-3, 2004-Indiana State University, SOUTHERN CALIFORNIA Ter re Haute, IN NORTH CENTRAL October 4, 2003-Cal Poly, Pomona, CA IOWA October 24-25, 2003-University of Sioux Falls , Sioux Falls, SD SOUTHWESTERN April 16-17, 2004-Central College, Pella, IA April 23-24, 2004-Winona State April 2-3, 2004-Northern Arizona University, Winona, MN University, Flagstaff, AZ KENTUCKY NORTHEASTERN SEAWAY April 2-3, 2004-Murray State University, Murray, KY November 21-22, 2003-Wellesley November 7-8, 2003-Rochester Institute College, Wellesley, MA of Technology, Rochester, NY LOUISIANA-MISSISSIPPI June 3-4, 2004-Roger Williams April 23-24, 2004-SUNY College at March 4-6, 2004-Southeastern Louisiana University, Bristol, RI Cortland, Cortland, NY State University, Hammond, LA NORTHERN CALIFORNIA, NEVADA, TEXAS MD-DC-VA HAWAII April 1-3, 2004-Texas A&M University, November 7-8, 2003-Johns Hopkins February 28, 2004-California State Corpus Christi, TX University, Baltimore, MD Hayward, Hayward, CA Spring 2004-Salisbury State University, WISCONSIN Salisbury, MD OHIO September 26-28, 2003 (Meeting for METRO. NEW YORK October 17-18, 2003- Ohio Northern Project NExT Wisconsin) Bundy Hall University, Ada, OH Conference Center, Menomonie, WI May 2, 2004-Nassau Community College (SUNY), Garden City, NY March 26-27, 2004-University of April 16-17, 2004-University of Cincinnati, Cincinatti, OH Wisconsin-Platteville, Platteville, WI

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