FOCUS February 2003

FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, FOCUS August/September, October, November, and December. February 2003 Editor: Fernando Gouvêa, Colby College; [email protected] Volume 23, Number 2 Managing Editor: Carol Baxter, MAA [email protected] Senior Writer: Harry Waldman, MAA Inside [email protected] Please address advertising inquiries to: Carol Baxter, MAA; [email protected] 3Major Donation Announced for New MAA Conference Center President: Ronald L. Graham By G. L. Alexanderson First Vice-President: Carl C. Cowen, Second Vice-President: Joseph A. Gallian, Secretary: 6So You Think You Want to be in Pictures… Martha J. Siegel, Associate Secretary: James By Dan Rockmore J. Tattersall, Treasurer: John W. Kenelly Executive Director: Tina H. Straley 8 The Kentucky Section Goes High-Tech: The tale of an e-newsletter Associate Executive Director and Director By Alex McAllister of Publications and Electronic Services: Donald J. Albers 10 Biology and Mathematics FOCUS Editorial Board: Gerald By Victor Katz Alexanderson; Donna Beers; J. Kevin Colligan; Ed Dubinsky; Bill Hawkins; Dan Kalman; Peter Renz; Annie Selden; Jon Scott; 14 Statistical Based Evidence that Web-Based Homework Helps Ravi Vakil. By L. Hirsch and C. Weibel Letters to the editor should be addressed to Fernando Gouvêa, Colby College, Dept. of 15 Short Takes Mathematics, Waterville, ME 04901, or by email to [email protected]. 16 Contributed Paper Sessions for MathFest 2003 Subscription and membership questions should be directed to the MAA Customer Service Center, 800-331-1622; e-mail: 20 MAA Awards Announced at Baltimore Joint Meetings [email protected]; (301) 617-7800 (outside U.S. and Canada); fax: (301) 206-9789. 21 Announcing MAA’s PMET Program Copyright © 2003 by the Mathematical Association of America (Incorporated). 22 Employment Opportunities Educational institutions may reproduce articles for their own use, but not for sale, provided that the following citation is used: 23 MAA Section Meeting Schedule 2003 “Reprinted with permission of FOCUS, the newsletter of the Mathematical Association of America (Incorporated).” Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: On the cover: Virginia and Paul Halmos, Los Gatos, California, 2002. Send address changes to FOCUS, Photograph courtesy of Leonard Klosinski. Mathematical Association of America, P.O. Box 90973, Washington, DC 20090-0973. ISSN: 0731-2040; Printed in the United States FOCUS Deadlines of America. August/September October November Editorial Copy July 8 September 16 Display Ads July 10 August 20 September 24 Employment Ads June 11 August 13 September 10

2 February 2003 FOCUS Major Donation Announced for New MAA Conference Center

By G. L. Alexanderson

The MAA recently received a write. But Paul Halmos has gift of $3 million from Paul and repeatedly written memo- Virginia Halmos to establish a rable and elegant expository Mathematical Sciences Confer- papers, with a style that is ence Center in Washington, DC. easily recognizable as his The Association plans to restore own. In the same work, page to its former charm the exterior 403, he wrote “I was, in I of its historic carriage house, one think decreasing order of of the three buildings in the MAA quality, a writer, an editor, a complex in the Dupont Circle teacher, and a research district, and to renovate com- mathematician.” pletely the interior to accommo- date conferences of up to 60 He has left his mark on writ- people, with ample additional ten mathematics in two space for mathematicians to meet “I am proud to be a teacher—Teaching is an ephemeral sub- commonly observed ways: in smaller groups or to work in- ject. It is like playing the violin. The piece is over, and it’s gone. he introduced “iff” as an ab- dividually. Up to now math- breviation for “if and only if” The student is taught, and the teaching is gone.” ematical meetings at the MAA and denoted the end of a are confined to two small confer- choose to enhance even further the abil- proof with what is some- ence rooms in the Vaughn Building or, if times known as a tombstone and now ity of the MAA to carry on this tradition too large, they are held in facilities in of producing fine exposition by creating often called a “halmos.” Washington hotels. Virginia Halmos, an alumna of Vassar The gift will fund the renovation and College, pursued graduate work in phi- construction of the space, along with fur- losophy at Brown. She and Paul married nishing and equipping the interior to in 1945 and since then she has been a provide a completely modern meeting supporter and partner to Paul through- facility. Beyond capital expenditures, the out his wide-ranging career. Larry gift will provide funds that will support Wallen, a longtime friend and mathema- the programs in the Center, which the tician at the University of Hawaii, in his donors envision as an ongoing series of contribution to the volume Paul Halmos: mathematically intensive workshops, Celebrating 50 Years of Mathematics symposia and seminars. Programs will (Springer, 1991), wrote of her: “Late that reflect the range of ideas and topics for summer [1955] I met Virginia (Ginger) which the MAA has been long known Halmos, a striking woman I recall think- through its many fine publications as ing. Any picture of Paul that omits Gin- well as programs at sectional and na- ger is grossly incomplete. In the first tional meetings. place, she’s crucial to keeping the entropy of the Halmos household improbably Paul Halmos has a long association with small and in keeping Paul and the cats One student’s remarked of Halmos’ lec- the MAA and a lifetime commitment to hale and hearty. This, of course, doesn’t tures: “…He often asked us to be mathematical exposition. He was editor define Ginger. She’s a woman of remark- ‘mindreaders,’ and tell us what he was of the American Mathematical Monthly able intelligence with a fine wit that not thinking.” from 1982 to 1986, and in 2000 he was everybody is privy to. She’s the ecologi- awarded the MAA’s Gung-Hu Award for this meeting facility. In his cal Halmos who fishes floundering liz- Distinguished Service to Mathematics. ards from the pool and worries about “Automathography,” I Want To Be a The Association was founded in 1915 to Mathematician (Springer, 1985), page wetlands.” As interested as she is in be- provide a home for the Monthly and, 390, Halmos explained the difference ing a good citizen of her community with through its many other publications, her volunteer work, in quietly support- between a survey [of research results] starting with the Carus Monographs in and an expository paper—something for ing animal welfare programs, and in fol- 1925, it has been an active proponent of the reader who is not an expert but is lowing her strong interest in literature good mathematical exposition ever since. (even in Latin), she has nevertheless lived curious about the subject, pointing out It is not surprising then that Professor that the latter kind of paper is hard to most of her life around mathematicians Halmos and his wife, Virginia, should and has an extensive knowledge of math-

3 FOCUS February 2003 ematical culture. With happy memories briefly to Illinois. Since then he has of visits to Oberwolfach, Ginger has held faculty positions at the following been an enthusiastic force behind the universities: Illinois, Syracuse, Chi- establishment of the MAA Conference cago, Michigan (Ann Arbor), Hawaii, Center since conversations on possibili- California (Santa Barbara), Indiana, ties began. Paul Halmos’ own fond remi- and Santa Clara, where he became pro- niscences of Oberwolfach appear in his’ fessor emeritus in 1995. He and his “Automathography,” pp. 384-87. wife now live in Los Gatos, California.

Professor Wallen mentioned cats. To Along the way Professor Halmos has know Paul and Ginger Halmos well one held visiting appointments at Harvard, has to know that they are both avid ani- Tulane, Montevideo, Miami (Florida), mal lovers. They have in recent years had California (Berkeley), Washington (Se- cats but they love dogs equally well. Don attle), Edinburgh, Chiao Tung (Tai- Albers, in one of his interviews with wan), and Western Australia, as well as Paul, noted that during the interview several visits to the IAS. He has writ- Paul had, sitting on his lap, Pizzicato (a ten over 100 research papers and many suitable name for a cat owned by some- reviews in his principal research fields one interested in words and music). of operator theory, algebraic logic, and When asked whether anything about ergodic theory, with additional work cats especially appealed to him, Paul re- in topological groups, probability, sta- plied: “Do animals have souls? People tistics, and Boolean algebras. Two vol- debate the subject, and I stand firmly on umes of his work appear as Selecta, the affirmative. But what is it that ap- Paul Halmos with Pizzicato. published by Springer-Verlag. peals? Well, they look nice, they’re in- the process of discovery. Of all the things teresting, they’re loving, they’re lovable, Honors have included a Guggenheim I saw in Dr. Halmos’ class I never saw and somehow one is in touch with an- Fellowship, membership in the Royal someone yawn and look at the clock.” other soul. They enlarge one’s life a little Society of Edinburgh and the Hungar- Another wrote: “That quarter the only bit.” ian Academy of Sciences, and honorary class I looked forward to was Paul doctorates from St. Andrews, DePauw, Halmos’. Our classroom discussions For his expository writing Paul Halmos Waterloo, and Kalamazoo. were always animated, interesting, and has received from the MAA the even sometimes humorous… He often Chauvenet Prize (1948), two Lester R. Widely known as an editor, in addition asked us to be ‘mindreaders,’ and tell him Ford Awards (1971, 1972), and the to his years of editing the Monthly, Paul what he was thinking. If we didn’t know George Pólya Award (1983), and, from Halmos has held similar positions with the answer to a question that he expected the American Mathematical Society, the Mathematical Reviews, the Proceedings of we should have known, he would swing Leroy P. Steele Prize for Mathematical the American Mathematical Society, the his arm in a motion that we came to un- Exposition (1983). Journal für die Reine und Angewandte derstand as our decapitation. Some of the Mathematik (Crelle’s Journal), Math- funnier moments in class came when we Highly respected as a teacher, and an ad- ematical Spectrum, the Indiana Journal realized that we could sometimes avoid vocate for a modified Moore method, he of Mathematics, as well as the Ergebniße this motion by giving a silly answer, caus- won both the sectional award and the der Mathematik, the Undergraduate Texts ing Dr. Halmos to laugh.” One former MAA’s national Deborah and Franklin series, the Graduate Texts series and the student wrote him to tell him how much Tepper Haimo Award for Distinguished Problem Books series for Springer-Verlag. he had enjoyed his classes, and closed College or University Teaching of Math- with “you are an inspiration and you ematics in 1993 and 1994, respectively. More than one generation of mathema- should demand that Santa Clara Univer- In support of these teaching awards, one ticians has benefited from his famous sity throw parades in your honor every former student wrote, “He stresses above and groundbreaking text, Finite-Dimen- month or so!” all the need for clear oral and written sional Vector Spaces (1942, 1958, 1974). communication of ideas as a prerequi- Others are devoted to his Measure Theory Paul Halmos received his B.S., M.S., and site to good mathematics. Several times, (1950, 1974), Naive Set Theory (1960, Ph.D. at the University of Illinois, writ- [as I was] struggling over an explanation, 1974), and the Hilbert Space Problem ing his dissertation under the direction he would cut me off and demand that I Book (1967, 1974, 1982). Four of his six- of J. L. Doob. After a period at the Insti- say exactly what I meant… [He asks] teen books are currently available from tute for Advanced Study (IAS), questions to draw out the answers. This the MAA: I Want To Be a Mathematician/ Princeton, where he was assistant to John technique thoroughly involves students An Automathography (1985, 1988), Prob- von Neumann (1940-42), he returned in class, giving them a personal stake in lems for Mathematicians Young and Old

4 February 2003 FOCUS

(1991), the Linear Algebra Problem Book doesn’t follow that communicating what Walter Savage Landor. That led to a ques- (1995), and Logic as Algebra (with Steven I know is always easy; it can be devilishly tion of a proper translation of the Latin Givant) (1998). Another popular book hard. To explain something you must inscription on Hadrian’s tomb. And so it of his is I Have a Photographic Memory goes. How many people today can rattle (1987). He has also written on how to off the nine ranks of angels in medieval write mathematics and how to give a angelology? We have all heard about mathematical talk in “How to write seraphim, cherubim, archangels, and mathematics,” L’Enseignement angels, but how many of us can come Mathématique 16 (1970), 123-52; “How up with the rest of them, the thrones, to talk mathematics,” Notices Amer. dominions, virtues, powers, and prin- Math. Soc. 21 (1974), 155-58; and “What cipalities? Virginia Halmos can and to publish,” Amer. Math. Monthly 82 does, in order of rank. (1975), 14-47, in addition to parts of his “Automathography.” Paul and Virginia Halmos have devoted their lives to the exposition and under- Paul Halmos has always made a case for standing of difficult ideas. Paul’s many the equal importance of proof and con- publications will live on for years to ceptual understanding in mathematics, come. Now this remarkable couple are so he emphasizes ideas in addition to making it possible for the MAA to con- proofs. This he shares with other great tinue in the dissemination of math- teachers. His concern for expository ematical ideas beyond the existing jour- writing was summed up nicely in his re- nals, books, regional and national meet- sponse to receiving the Steele Prize: ings, minicourses, and special sessions, “Not long ago I ran across a reference to Virginia Halmos at Brown circa 1947. with an ongoing series of programs at a publication titled A method of taking the MAA Conference Center in Wash- votes on more than two issues. Do you ington. Use of the facility will not be know, or could you guess, who the au- know not only what to put in, but also limited to the MAA. Other mathemati- thor is? What about an article titled On what to leave out; you must know when cal organizations will be invited to hold automorphisms of compact groups? Who to tell the whole truth and when to get programs at the Center. Two such orga- wrote that one? The answer to the first the right idea across by telling a little nizations have offices in the MAA question is C. L. Dodgson, better known white fib. The difficulty in exposition is buildings—the American Mathematical as Lewis Carroll, and the answer to the not the style, the choice of words—it is Society Washington Office and the head- second question is Paul Halmos. the structure, the organization. The quarters of the Conference Board of the words are important, yes, but the ar- Mathematical Sciences. The MAA is set- “Lewis Carroll and I have in common rangement of the material, the indication ting up an Advisory Board to advise the that we both called ourselves mathema- of the connections of its parts with each officers and MAA Board of Governors on ticians, that we both strove to do re- other and with other parts of mathemat- programs for the new facilities. The search, and that we both took very seri- ics, the proper emphasis that shows Board welcomes suggestions from MAA ously our attempts to enlarge the known what’s easy and what deserves to be members for activities to be held at the body of mathematical truths. To earn his treated with caution—these things are new Center. This is a great opportunity living Lewis Carroll was a teacher, and, much more important.” for the MAA to expand significantly the just for fun, because he loved to tell sto- programs it offers to members and the ries, he wrote Alice’s Adventures in Won- When I was thinking about how to write larger community it serves. derland. To earn my living, I’ve been a this announcement for FOCUS, I asked teacher for almost fifty years, and, just Virginia Halmos how she would like to for fun, because I love to organize and be described. She told me she is a “house- clarify, I wrote Finite-Dimensional Vec- wife.” While it is true that she has made tor Spaces. And what’s the outcome? I her career inside the home, she has dis- Gerald Alexanderson is Michael and Eliza- doubt if as many as a dozen readers of tinguished herself by reading widely and beth Valeriote Professor of Mathematics at these words have ever looked at either A participating in many community activi- Santa Clara University. method of taking votes… or On ties. She is truly a partner of Paul’s in her automorphisms… but Lewis Carroll is appreciation of the written word. I never immortal for the Alice stories, and I got fail to be amazed at the range of things the Steele Prize for exposition…” she knows about and her erudition. Our most recent e-mail exchange on literary “I enjoy studying, learning, coming to matters (the week before I started writ- understand, and then explaining, but it ing this) concerned a piece of verse by

5 FOCUS February 2003 So You Think You Want to be in Pictures… By Dan Rockmore

It all started with the movie so scary. Two years later, the re- “Good Will Hunting”: In his sult is”“The Math Life”, a docu- breakout role, Matt Damon plays mentary film on the people, a wrong-side-of-the-tracks kid, problems, and process of math- Will Hunting. While working as ematical research. It’s now avail- a janitor at MIT, he happens able for distribution through upon a mathematics problem Films in the Humanities and Sci- left on a blackboard. Unbe- ences, and will soon be appear- knownst to Will this is an incred- ing on a public television station ibly difficult problem, but in a near you. flash of insight (in spite of seem- ingly having no background in The making of “The Math Life” mathematics) he solves the prob- was one of the most interesting lem. He is thus propelled into and enjoyable projects I’ve ever what is portrayed as the high- undertaken. We crafted a list of powered and cutthroat world of Wendy Conquest interviews Michael Freedman for The questions and began interview- academic mathematics, and Math Life. ing a spectrum of mathemati- slowly comes to grips with the cians (hmm, maybe that’s the new opportunities afforded by the rev- what it means to “do” mathematics. In collective noun…). We asked people how elation of his genius. His best buddy (Ben short, I wanted to show that mathemat- they came to mathematics, what their Affleck) spurs him on, and of course ics is more than just numbers and math- earliest mathematical memories are, there is also a beautiful right-side-of-the- ematicians are more than just the ex- what sorts of mathematics they work on, tracks Harvard girlfriend (Minnie treme personalities that periodically what it is like to work on mathematics, Driver) to help him along, as well as a make it to the big, or little, screen. how is mathematics like art, and even kindly (albeit damaged) therapist (Robin asking what they find beautiful about Williams) who learns a thing or two It took a few years of knocking on doors mathematics. For many, this last ques- about life from helping Will work at various agencies and foundations, but tion proved to be the most difficult to through his anger management prob- eventually I found a sponsor at the Na- answer. lems. After several interviews a narrative Friends kept asking me what I line began to emerge. We decided thought of this “math movie.” I felt that what we wanted to tell were the same as many people did; I liked stories of the possible lives of a it. It is a good Hollywood love mathematician, from tentative story—but definitely not a movie childhood beginnings to working about math! But most people did see researcher, and to show that this is it this way: genius mathematicians, a road which is often anything but often arrogant and surely born to the straight and narrow. There are na- subject, puzzling over arcane dia- ive, wonder-inspired beginnings, grams on blackboards, and if not, as well as frustration-laden false sent to crack codes for some name- starts. Stanford’s Persi Diaconis less government agency. Yup, this is tells of being led to mathematics what, to many, it means to be a math- from mysteries of magic and card ematician. Jennifer Chayes of Microsoft Research being inter- shuffling. Princeton’s Ingrid viewed for The Math Life. Daubecheis remembers discover- Certainly, there are mathematicians ing the wonder of π after measur- that fit this bill, but there are others too tional Science Foundation: Joe Jenkins, ing the diameters and circumferences of —many others. I began to think about a Program Officer in the Analysis Pro- all the platters in the house. Dartmouth’s making a film that showed what research gram, thought that it sounded like a good Dorothy Wallace, (recipient of the 2000 mathematics was, in all of its diversity, idea. So, backed by a budget on the scale New Hampshire Professor of the Year both in terms of the people who do it, of “The Blair Witch Project”, filmmakers award), recalls that as a schoolchild, her and the intellects that are attracted to it. Wendy Conquest and Bob Drake and I lack of facility with fractions led some I also wanted to give some insight into set out to show that mathematics is not teachers to label her as slow. The road to

6 February 2003 FOCUS a career in math can be, and often is, a nical one. References to the visual arts are by Jean Taylor. Like many a mathemati- meandering one. Along the way we dis- scattered throughout “The Math Life.” cian, Taylor found her way to mathemat- cuss some of the things that attract ics after sampling the sciences. In her case people to mathematics. Off this narrative skeleton we hang some she was a graduate student in chemistry of the fruits of mathematical labor: before being bitten by the math bug. As Wallace’s story shows, mathematics is primes and the Riemann Hypothesis, While musing on what drew her away done by all kinds of people with all sorts geometry and topology in the guise of from chemistry she noted that in math- of different skills and apti- ematics you experi- tudes—not just the quiet kid ence a daily imme- in the back who got all the diacy with the subject multiplication problems that is often lost in the right. Those with a talent for lab sciences. She re- picturing things find their called one particular way to subjects like geometry lab experience in and topology. A love of num- which in order to bers leads others to become study collagen she number theorists. A fascina- had to spend count- tion with randomness is the less hours going first step on a road to prob- through shipments of ability and statistics. A desire frozen rat tails and to understand the workings stripping the collagen of the world can be the hook off the tails for later to becoming an applied processing. “Pretty far mathematician. from grand ideas” she says, “but in math- Indeed, Wallace’s story is but ematics… you don’t one of several cautionary The five regular polyhedra make an appearance in The Math Life. have this distance be- tales for educators embed- tween what you’re do- ded in’“The Math Life.” ing and what the big Cornell’s Steven Strogatz recalls almost, shape and symmetry, the paradoxes of idea is. It may be the details that you’re “being derailed,” by a classroom experi- probability, and of course a brief look at working on, but they’re still mathemat- ence. Microsoft’s Michael Freedman some math in the real world, in this case ics… It’s not frozen rat tails.” I couldn’t (winner of the Fields Medal) reminds us a brief interlude on synchronization of have said it any better myself! that an aptitude for mathematics is re- large systems, illuminated by the com- flected less in, “getting A’s on all the tests,” monality in flashing fireflies, cricket cho- Dan Rockmore is Professor of Mathemat- than in having a “quirky” mind, able to ruses, beating hearts, and clapping audi- ics and Computer Science at Dartmouth produce a different reason to explain why ences. Each of these examples is illus- College, Hanover, New Hampshire, where something is true. Many of the math- trated with computer graphics anima- he is also Vice-Chair of Mathematics. His ematicians we interviewed told horror tions. research interests focus on the mathemat- stories of being browbeaten for not get- ics of signal and image processing. ting the right answer in the “right” way. “The Math Life” is but fifty-two minutes long, and in that short space of time we Dan Rockmore can be contacted at These are beginnings that as often as not hope we have shown the general public [email protected] or by visit- almost led to ends. In essence it is the that the inside of the head of a mathema- ing his webpage at http:// same process writ large, that many (if not tician is not such a scary place —a good www.cs.dartmouth.edu/~rockmore. A re- all) of us relive during the long slow pro- sense of humor is just as important as view of The Math Life can be found on cess which is mathematical research. As the ability to focus the intellect. Math- MAA Online at http://www.maa.org/re- Arlie Petters says, this process is, in its ematicians are more than just the car- views/mathlife.html. own way, “a human experience”, one toon mix of genius and arrogance that which, as Peter Sarnak says, is probably we usually see on the big screen. We also not for the person who “needs a daily think we have given the public a sense of high.” More often than not you are what mathematics is. Those fifty-two “stuck,” hoping, living for that brief and minutes were distilled from almost thirty hard-earned moment of triumph when hours of interviews, and I came to see you “get it,” only to quickly return to be- the truth in the adage that “ninety-nine ing stuck once again. It is, for many of percent of what you shoot is left on the us, as much an artistic process as a tech- editing room floor.” Among these was one of my favorite little stories, one told

7 FOCUS February 2003 The Kentucky Section Goes High-Tech: The tale of an e-newsletter By Alex McAllister

At our 2000 Annual Meeting, I was sibilities. And so, at least for now, the to the local URL, http://web.centre.edu/ elected the Newsletter Editor for the Ken- KYMAA newsletter editor is also the ~mat/kymaa, where the web pages are tucky Section of the MAA (KYMAA). At KYMAA webmaster. stored at Centre College. Hopefully, this the same time, the section also voted to “permanent” URL and consistent use of eliminate the traditional paper newslet- Of course, serving as a webmaster re- relative URLs within the KYMAA web ter in favor of an electronic newsletter. quires some level of technical skills and pages will support the needed element Talk about a fundamental change in job resources beyond word processing. Sev- of portability. descriptions! eral years ago, I took an html course and developed sufficient skills with web edi- During the summer of 2000, I spent We now have a couple years of e-news- tors to start creating course web pages. some time reworking the website; keep- letters under our belt. Bill Fenton, our In addition, earlier in 2000, I revamped ing what was strong from the existing site Chair-Elect, has suggested that and mixing in some new ele- other sections might be interested ments. I also began the process of in learning of our experiences creating the email distribution list before the spring business meet- of KYMAA members that is used ings. So, here’s a bit of our story. to notify members when newslet- ters are posted. The national For several years before this vote, MAA office had a list that I could KYMAA had a voluntary elec- start from. In the end, I wound tronic newsletter program. The up visiting all of the math depart- vice-chair had established a basic ment websites in our section to website for our section and the gather email addresses. While newsletter editor had been sub- doing this, I realized that our e- mitting web-versions, produced newsletter could also provide an with Microsoft Word, of the news- important opportunity to “freely letters. Unfortunately, participa- spread the good news” of tion was rather minimal and this KYMAA activities to the math- particular blending of paper and ematicians at the universities, col- electronic media was somewhat leges, and community colleges in awkward. The vote in Y2K con- Screen Capture from a recent KYMAA online newsletter. our section. And so, our e-news- tinued the web-based version of letter not only facilitates commu- our newsletter, only e-participa- nication among KYMAA mem- tion became mandatory! my math department’s website and so I bers, but has also become an outreach to had some ideas for retooling the KYMAA nonmembers of the MAA who will hope- At our website, http://www.maa.org/ web site. I would recommend Web Style fully develop an interest in our section’s kentucky/, both members and non-mem- Guide: Basic Design Principles for Creat- activities. In fact, we have noticed a bers can readily access the newsletter as ing Websites, by Patrick Lynch and Sarah greater number and diversity in partici- well as other information about our sec- Horton (ISBN: 0300076744) to anyone pants’ home institutions at our last two tion and about mathematics in general. creating and maintaining websites. annual meetings. Furthermore, the newsletters are, in some sense, “permanently” available through As for technical resources, my home in- After gathering articles from officers and electronic archiving. Ultimately, our de- stitution is currently serving as the re- campus liaisons, I created the e-newslet- liberations of “to e or not to e?” have re- pository for the KYMAA website. When ter webpage and set up a link on the sec- sulted in re-focusing our website as the my tenure as newsletter editor is over, I tion website. After all this prep work, the primary media for communicating with expect the files for the website will be first KYMAA e-newsletter was produced each other and the wider world. transferred to the institution of the next and distributed in September 2000. editor. Interestingly enough, I learned Members of the section were notified After the annual meeting, I talked with that the MAA has reserved a URL for both by email and by physical postcard; the previous webmaster and newsletter each section. Shortly after our annual as mentioned above, some nonmembers editor and we recognized that this tran- meeting, I contacted the national office of the MAA were included in our email sition would be most easily accomplished and the MAA reset our reserved URL, distribution list. by a blending of their respective respon- http://www.maa.org/kentucky/, to “point”

8 February 2003 FOCUS

This process appears to be successful and tion has realized other benefits, includ- Reflecting back on the last two years of we continue to follow this approach in ing significant financial savings, from this e-newsletters, I must say that I have en- developing and distributing our e-news- conversion to an e-newsletter. Our an- joyed developing KYMAA’s website and letter three times per year. We recognized nual newsletter costs dropped from ap- e-newsletter and acknowledge that many that some members might not have ready proximately $1000 a couple years ago to members of our section have provided access to email or the web; therefore, I approximately $200 each of the last two important suggestions and support for also send a paper copy of the newsletter years. For the environmentally conscious, this venture. Both the section member- to the few members who have requested we have also significantly reduced the ship and the newsletter editor appear to traditional mailings. amount of paper and other physical re- be pleased with this approach (I’m even sources used in creating the newsletter. running for a second term as newsletter At the beginning of this process, I won- editor this spring!). I’ve noticed that a dered if breaking the established para- Of course, there’s still some grunt work. number of other sections have also digm of a paper newsletter would be suc- Each summer, the overall website needs started using an e-newsletter. I hope our cessful. However, the Spring 2000 vote in to be evaluated and updated and the story may be of some assistance for oth- support of an e-newsletter was a strong email distribution list needs to be up- ers considering and implementing this expression of active members seeking dated. In fact, maintaining the email dis- communication option. and embracing a change. Follow-up sur- tribution list has really been the most veys of KYMAA members indicate an difficult aspect of this new system. Many Alex McAllister ([email protected]) is overwhelmingly positive response to of our campus liaisons have played a key Assistant Professor of Mathematics at Cen- continuing the e-newsletter. role in this process, but there’s still a bit tre College and Newsletter Editor for the of web-surfing required each summer. Kentucky Section of the MAA. In addition to the added convenience and efficiency of e-communication, the sec-

The Mathematical Association of America is seeking a Director of Information Services

The director is responsible for •Developing and managing staff of three, including an IT manager, management of technological department budget IT assistant, and a webmaster. information services of the Association. The director must have The director will assist MAA The MAA currently has 8 servers the technical expertise to foresee, departments, committees, officers, and running on either Windows 2000 or suggest, and implement appropriate other MAA constituencies in NT. We host our own website using IIS. technology that can be used to help implementing various. This person The Association’s database runs on achieve MAA goals. Technical duties should be able to foresee and suggest Oracle. include: ways that technology could be used to achieve Association goals. The purpose Candidates for this position should •Researching, suggesting and of the Information Services have administrative experience and at implementing new technology as Department is to respond to the needs least five years of experience in the needed to further MAA operations of MAA Officers, volunteers, and staff, information services area, including and mission in an efficient and cost especially as they relate to enhancing extensive experience with all facets of – effective manner the value of membership. The director network management, security, and will respond to the needs and questions online services. Candidate should have •Overseeing, supporting and of several constituencies (Executive broad general knowledge of current maintaining internal systems Director, other directors, governing technologies. Association experience including hardware and software bodies of the Association) relating to a plus. the web site, web services, TIMSS •Managing the technical side of IT/ database and other information Web projects services projects including online Applicants should send letter, resumes, ordering, publishing, and discussion and salary requirements to Julie •Overseeing maintenance and lists. The director reports to the Kraman ([email protected]). improvement of TIMSS Executive Director and supervises a Association Management software

9 FOCUS February 2003 Biology and Mathematics

By Victor J. Katz

“The next big thing in mathematics? tant. These include the logistic model, differential equations, since one needs to Biology.” So wrote John Ewing, executive given by the differential equation consider the lead level in the blood, the director of the AMS in the September 20, soft tissue, and the bones. Since these 2002 issue of the Chronicle of Higher Edu- 1 dy y systems have constant coefficients, they = r1 –, cation. In fact, Mathematics Awareness   are generally solved by matrix methods. Month in April of 2002 was devoted to y dt K Systems of equations are also used to fol- Mathematics and the Genome. The which models the situation where there low the dispersion of drugs throughout MAM web site at http:// is a maximum environmental carrying the body. www.mathforum.org/mam/02/ contains capacity, as well as the more complicated much information about the mathemat- model given by the equation In molecular genetics the central process ics used in the genome project and in is the passing on of information from biology generally. The mathematics in- DNA to RNA; the RNA information is 1 dy  yy  volved is relatively sophisticated, and = r ––,11 then converted into information en- some of it is entirely new. y dt  θ  K  abling the cell to make enzymes, which in turn catalyze a specific set of chemical It is becoming increasingly clear that bi- which models the situation where a reactions that determine the biological ology will be providing significant chal- population tends to extinction if its size nature of the cell. To study these reac- lenges for the mathematical community is too low. The first equation, of course, tions requires the construction and so- over the next few decades. Not only must has a closed form solution, while the sec- lution of differential equations express- new mathematics be developed to enable ond, in general, does not. Nevertheless, ing the rates at which various reactants biologists to continue to make rapid with appropriate technology, the second are combining and producing new prod- progress, but also mathematicians must equation can be solved graphically and ucts. Some of the typical equations have be prepared to educate a new generation its salient characteristics analyzed.(See closed form solutions, generally involv- of biological and biomedical researchers the illustration on page 11.) Analogously, ing exponential functions, while others in our colleges and universities. the Lotka-Volterra system of equations do not. In any case, it is important for modeling the populations of predator the prospective biologist to understand The mathematics necessary for biology and prey, which again do not in general the modeling process, that is, how these today is not the mathematics that was have a closed form solution, can also be equations are formed and what their so- typically required of biology majors in analyzed graphically for various values lutions mean, both mathematically and the past: a year of calculus and perhaps a of the parameters. biologically. This process can be aided, semester of descriptive statistics. These of course, by appropriate software. Fre- courses are only a bare minimum today. Another useful biological population quently, however, one needs to study Although biology as currently practiced model is one that looks at the age distri- carefully the dependence of the solutions needs the basic concepts of calculus, it bution of a population. Given that the on the various parameters involved and requires far more sophisticated tools as number of individuals P(n, t) at a given this in turn requires a firm understand- well. We illustrate this with problems age n at time t is a major factor in deter- ing of the nature of differential equa- taken from biological and biomedical mining P(n+k, t+k), it turns out that suc- tions. research. cessful analysis of the population in- volves the use of certain matrices express- But differential equations are not suffi- It has long been evident that biologists ing this fact. The population density over cient mathematics for the study of DNA. need familiarity with differential equa- time then involves finding powers of this It turns out that an understanding of the tions and linear algebra. For example, in matrix, a process made simpler by look- enzymes that perform the reactions nec- population biology, we want to study the ing at eigenvalues. So biology students essary for the winding, unwinding, re- growth of one or several animal popula- who want to make a mark in this field combination, and transposition of DNA tions. The simple exponential model, of need to understand the basic concepts of requires an understanding of the topol- course, only works for a limited time, linear algebra. ogy of knots. After all, DNA is in the form when there are unlimited resources for of a double helix. The knowledge of what the population. Once resources become Both differential equations and linear kinds of twisting and untwisting is pos- limited, other models prove more impor- algebra are used in many other areas of sible as the DNA performs its tasks in the biology. A study of the activity of lead in life cycle of the cell often comes from re- the body requires looking at a system of cent work in knot theory. To infer the

10 February 2003 FOCUS process used by an enzyme, one needs to Clearly, a deep knowledge of graph systemic view of an organism much more understand when a strand of DNA must theory is required as well as a knowledge amenable to study. be broken and when it can just be un- of the construction of algorithms en- twisted. abling computers to perform the opti- One of the new technologies to which mization in a reasonable time. Not only bioinformatics is applied is that of In addition to the ideas of linear algebra, is this phylogenetic reconstruction used microarrays. A microarray is a chip con- differential equations, and topology, it is in determining ancestry among species, taining a huge amount of data in an or- becoming increasingly clear that a pro- but it also applies to the recent work in derly arrangement. Each unit of data is a spective biologist must understand data reconstructing human evolution by piece of DNA, with a physical size of analysis. With many experiments pro- looking at the mitochondrial genome. about 200 microns. The microarray then ducing millions of data points, it is nec- Since human mitchondria are inherited provides a medium for matching DNA essary to use computers for data mining, only from the mother, researchers were samples based on rules involving the that is, the automated search for patterns. able to determine the existence of our pairings of the bases making up the For example, there is an enormous common ancestor (called Eve) in Africa DNA. For example, the DNA “signature” amount of data about the diagnosis and about 200,000 years ago. This study has of a tumor consists of some 15,000 num- treatment of cancer patients. In a given also enabled biologists to begin to map bers. Mathematically, one can think of situation, we have symptoms, test results, the migration of human groups through- this signature as a point in a 15,000-di- the physical parameters of the individual, out history. mensional space. The idea is then to com- and the outcome of one or more medi- pare tumors by seeing if they are “close” cal interventions. Ideally, one then uses The problems discussed in the last two to one another in this space. Algorithms data mining to determine patterns, in- paragraphs require the use of comput- are necessary to achieve this determina- cluding, for example, a decision tree. ers. Before the advent of high-speed com- tion of whether the different tumors are Such a tree enables physicians to improve puting, biology research tended to be re- “clustered.” The hope is that “close” tu- their choices of treatment for current ductionist in nature. That is, one tried mors respond similarly to treatment, so patients. How does a machine make to decompose a biological system into as the use of microarrays will help sense of enormous amounts of data? The small subsystems as possible, and then oncologists make correct diagnoses and machine must be “taught,” so algorithms study each independently. After all, it is choose the best available treatment. must be developed for machine learning. easier to form and test hypotheses on Eventually, once the appropriate algo- This is a very active area of study in com- “small” systems. But with the use of com- rithms are developed, your doctor will puter science. puters, it is much easier to attempt dis- have your personal DNA sequence on the covery-based rather than hypothesis- computer and will use microarrays to Trees are important in another active driven research. That is, by applying diagnose your disease and figure out the area of biology, phylogenetics, the deter- computers to the data of the human ge- treatment to which you will respond. mination of how an organism has devel- nome project, for example, it is much oped from its evolutionary ancestors. easier to discover patterns and see the A final example of the use of mathemat- The goal here is to develop what is called importance of interdependencies, links, ics in biology involves fractals. Some of a phylogenetic tree, the leaves of which and communications among various the most visually striking examples of represent extant species. Each internal subsystems. The new subject of fractal forms are found in physiology. node of the tree represents a postulated bioinformatics, the application of com- The respiratory, circulatory, and nervous speciation event in which a species di- puter science to biology, which grew up systems are remarkable instances of vides into two populations that follow with the genome project, has made the fractals, branches subdividing and sub- separate evolutionary paths and become dividing and subdividing again. Al- distinct species. These trees are today constructed by computer programs based on the comparison of related DNA sequences or protein sequences in the different species. Ideally, similar species should be close together in the tree. The construction of such a tree is then an optimization problem. That is, one needs to assign numerical values (“lengths”) to each edge of the tree, where these values represent an evolutionary distance be- tween adjacent species. One then wants to minimize the sum of the lengths of all the edges.

11 FOCUS February 2003 though we do not know why these sys- dents and the need for flexibility in the ture of a system, interactions among com- tems develop this way, careful analysis curriculum of life science disciplines. ponents, data and measurement, visual- reveals fractal scaling. Among the hy- Agreement was reached that the core ization, and algorithms. Every student potheses are that the fractal structure should include the basic notions of cal- should acquire the ability to analyze issues makes the lungs more fault-tolerant dur- culus, probability, approximation, logic in these contexts in some depth, using ana- ing growth and enables the circulatory and mathematical thinking, and deduc- lytical methods (e.g., pencil and paper) system to achieve a homogeneous oxy- tive reasoning, as well as some work with and appropriate computational tools. An gen supply throughout the body. It is also statistics and computers. Such a course appropriate course of study would include known that healthy heartbeats are cha- should put special emphasis on the use aspects of probability, statistics, discrete otic rather than regular. If one plots heart of models, both as a way of organizing models, linear algebra, calculus and dif- rates over several time scales, one again information about and providing intu- ferential equations, modeling and pro- sees the fractal patterns of self-similar ition into systems that are too complex gramming. scaling. to understand otherwise. But any study of modeling should also discuss the limi- Many universities have attempted to de- Since there is so much advanced math- tations of the subject. The computer velop yearlong courses meeting at least a ematics that may be required in biologi- should be used wherever relevant as a substantial portion of these require- cal or biomedical ments, and textbooks research, the ques- have also appeared. tion becomes how One of the earliest mathematics de- such courses was at partments should the University of Ten- react. There seem to nessee, Knoxville. be two distinct as- The first semester of pects of the prob- the course deals with lem. First, we statistics, probability, should come to exponentials and some agreement on logarithms, matrix the minimum algebra, and se- mathematical re- quences and differ- quirements for a bi- ence equations. The ology major, par- second semester con- ticularly for stu- tinues the material dents who intend to on difference equa- go into research. tions, provides a sur- Second, we need to vey of differential figure out how to and integral calculus, teach future biolo- including the trigo- gists the advanced nometric functions, mathematics described above, without way of solving problems and analyzing and concludes with some work on dif- requiring them to be mathematics ma- models. ferential equations. And as recom- jors themselves. mended, the course always deals with the Interestingly, the Committee on Under- idea of modeling biological phenomena. The first problem appears well on its way graduate Biology Education to Prepare Students are expected to generate hy- to a solution. The MAA Committee on Research Scientists for the 21st Century, potheses and then attempt to verify them the Undergraduate Program’s Subcom- organized by the National Research using the mathematical tools being de- mittee for Curriculum Reform Across the Council, issued a report entitled veloped. First Two Years (CRAFTY) held one of BIO2010: Transforming Undergraduate its Curriculum Foundations Conferences Education for Future Research Biologists Solving the second problem is more dif- on the Mathematical Curriculum for (see http://www.nap.edu/books/ ficult, since so many different math- Health and Life Sciences Students in May, 0309085357.html) that suggested that a ematical ideas are now or may in the fu- 2000 and shortly thereafter issued a re- more demanding core of mathematics ture be necessary for prospective biologi- port (see the November 2002 issue of should be added to the undergraduate cal researchers. One university that has FOCUS or visit http://www.maa.org/fea- biology curriculum: attacked this problem is the University tures/currfound.html and the links found of Pennsylvania. on that page). It is essential that biology undergraduates become quantitatively literate, studying Starting in 1994, Penn designed a Ph.D. Two issues are addressed in that report, the mathematical concepts of change, program in computational biology and a core curriculum for all life sciences stu- modeling, equilibria and stability, struc- bioinformatics. The program was open

12 February 2003 FOCUS to students with a solid education in organizing a special invited conference disseminated, our membership must molecular, cellular, organismal, and evo- entitled Meeting the Challenges in Emerg- take the lead in implementing the rec- lutionary biology as well as a strong ing Areas Across the Life, Mathematical, ommendations on their own campuses. foundation in mathematics, statistics, and Computer Sciences. This conference, Just as it was impossible in the past for chemistry, and computer science. How- funded by the National Science Founda- mathematics departments to ignore the ever, Penn soon found that relatively few tion, will be held February 27– March 1, needs of engineering students, it will be of their prospective students, most of 2003 in Bethesda, Maryland. It will bring impossible in the future to ignore the whom had a B.S. in biology, appeared to together approximately seventy-five par- needs of biology students. And although have a rigorous enough mathematical ticipants from the life sciences, math- we cannot predict exactly what their background for the program. Thus, Penn ematics, statistics, and computer science, needs will be a decade or two from now, decided to put together undergraduate as well as representatives from disciplin- we can predict with confidence that bi- concentrations in computational biol- ary societies such as the American Sta- ology and medicine will need more and ogy. Such programs now exist within the tistical Association and the Association more mathematics to continue the re- biology department, the computer sci- for Computing Machinery and the fed- search aimed at fully understanding the ence department, and the mathematics eral agencies. The participants will be processes of life. department. In addition, Penn put to- divided into seven working groups, each gether a three-semester Master of Bio- of which will discuss curriculum, faculty Victor Katz is Professor of Mathematics at technology program with a track in development, and teaching and student the University of the District of Columbia. bioinformatics and computational biol- learning in a specific area of biological He is the author of an introductory text- ogy specifically designed for the needs of mathematics. The working groups are on book and many other books and papers on the biotech industry. bioinformatics, structural biology, com- the history of mathematics. He is currently putational cell biology, developmental visiting mathematician at the MAA. The Biological Mathematics concentra- biology, physiology, biocomplexity, and tion in the mathematics department in- phylogenetics. cludes year-long courses in advanced cal- culus and abstract algebra (including lin- Meeting the Challenges will have four ple- Have a RUMBUS! ear algebra), as well as courses in com- nary addresses, by Michael Summers Courtesy of the putational methods and statistics, among (University of Maryland, Baltimore others. It also requires a substantial num- County and Howard Hughes Medical Boston University ber of biology and chemistry courses. Institute), James Cassatt (National Insti- Student Chapter of The Computational and Mathematical tute of General Medical Sciences in the the MAA Biology concentrations in the biology National Institutes of Health), Judith department include some of those same Ramaley (National Science Foundation), courses as electives, but of course require and Lou Gross (Institute for Environ- Boston University will have its first more biology courses. Those programs mental Modeling, University of Tennes- RUMBUS on Saturday, March 22, also require a graduate-level course in see, Knoxville). The plenary speakers will 2003. A RUMBUS sounds, of course, computational biology as well as an in- help the participants confront their ma- like the name of a beautiful geometric terdisciplinary research project. jor mission, to think through the issues figure, but it is actually the Research of how best to educate future biology and by Undergraduates in Mathematics Interestingly, the upper-level mathemat- biomedical researchers and then to pro- Boston University Symposium, which ics courses required in all of these pro- duce a comprehensive report which will will feature Student Talks, a PosterFest, grams are the same courses taken by be widely disseminated to the nation’s Panel Discussions and a KeyNote mathematics majors in general, so it is stakeholders. Among the expected out- Speaker of world repute. This year’s up to the instructors (and the students) comes of the conference will be compre- speaker is Professor Frank Morgan of to connect these courses to biology prob- hensive listings of student resources, in- Williams College (settler of the lems. Other universities may decide to cluding recruitment and mentoring pro- Double-Bubble Conjecture, and many have special sections of upper-level grams, faculty retraining possibilities, things besides). courses specifically designed for biolo- and curriculum resources. Suggestions gists. will also be made on overcoming admin- The Symposium is meant for istrative hurdles to the necessary inter- undergraduates of the greater Boston Most colleges and universities will not be disciplinary cooperation. (The confer- Area and New England to come able to match the resources of the Uni- ence website can be found at http:// together for a day of activities, versity of Pennsylvania, but mathemat- pub.nigms.nih.gov/challenges.) information on the profession, and ics departments nevertheless need to pay relentless math fun. The symposium attention to the needs of prospective bio- The MAA has already been heavily in- web page at http://math.bu.edu/people/ logical researchers. To help in this regard, volved in this process of thinking about RUMBUS03 includes a program, the MAA, the American Association for education in mathematical biology. But instructions for participation and the Advancement of Science, and the once the results of this conference are local information. American Society for Microbiology are 13 FOCUS February 2003

Statistical Evidence that Web-Based Homework Helps By L. Hirsch and C. Weibel

Since 1996, dozens of mathematics de- population of students who did not at- who attempted most problems. This was partments have introduced an internet- tempt many web assignments. This sub- also true after adjusting for the effect of based homework system into their cal- population diluted the gains in final prior knowledge, measured either by our culus curricula. One popular choice is exam performance attributable to placement test or by their Math SAT (also WeBWorK, which was developed with WeBWorK, as the analysis detailed below a significant predictor). NSF support at the University of Roch- shows. ester. At Rutgers University, we were able Surprisingly, the data suggests a qua- to examine the effect of WeBWorK on In fact, we found that the effectiveness dratic relationship between the percent- student performance on the common fi- of WeBWorK depended dramatically age of WeBWorK problems attempted nal exam in our general calculus and the final exam score, with class. (This course excludes en- the best-fitting curve being gineering, physics, chemistry and concave up. In other words, mathematics majors.) Because students who do less than 50% WeBWorK was implemented in of the WeBWorK get less “mar- only two-thirds of all sections, we ginal” benefit on the final (i.e., could treat the course as a con- less improvement from doing trolled experiment, using the one more problem) than stu- non-WeBWorK sections as the dents who do over 80% of the control group. (We later verified WeBWorK. that there were no significant section effects.) A second sub-population con- sisted of upper-class students The study used data from the Fall who were taking calculus for 2001 semester of the general cal- the first time. Unlike the first- culus class at Rutgers. Out of over year students who placed right 1300 students in the class, we had into calculus, these students complete data (SAT scores, place- typically took precalculus first. ment scores as well as final ex- In WeBWorK sections, most of ams, etc.) for 1175 students. Of these students attempted be- these, 368 were in the control tween 40% and 80% of the as- group and 807 students in the signed WeBWorK problems. study group. Both groups sub- Sample WeBWorK problem. The score is 50% because one Here there was a three letter- mitted written homework as- answer is wrong. grade difference (from F to B) signments, but in the study between those who did most group about 11 written problems per upon how many of the problems were of the assigned WeBWorK problems and week were replaced by WeBWorK prob- attempted. The correlation between at- those who did only a few. lems. The WeBWorK questions were tempts and percentage of problems similar for each student, but were indi- solved was a remarkable .944, suggesting Upper-class students who were repeat- vidualized by varying the numerical pa- that once students began a problem they ing Calculus did not seem to derive any rameters from student to student. persisted until they had solved it. An benefit from attempting WeBWorK analysis of variance showed that only 9% problems. We are still in the process of Overall, the students in the web-based of the variability in WeBWorK scores studying this group in an effort to un- sections showed a small but statistically could be attributed to prior skill level, derstand the reason for the absence of significant improvement (of 4%) on the even among entering students, so the any correlation between the amount of final exam. This improvement was also number of problems attempted may be WeBWorK activity and final exam scores present after adjusting for placement an indicator of effort rather than ability. in this group. scores, which are a measure of prior skill level. As reported by us in the January Among first-year students in WeBWorK Lew Hirsch and Chuck Weibel teach at 2001 issue of the FOCUS, placement sections, most of whom attempted ev- Rutgers University. scores are the most significant predictor ery problem, there was a two-letter grade of success. The small difference between difference on the final (from D to B) be- group means is not surprising, because tween students who did not attempt the WeBWorK group contained a sub- many WeBWorK problems and those

14 February 2003 FOCUS

Short Takes ewstory.cfm?slug=14train.h22 for more time employment with significant teach- information. ing responsibilities at the college/univer- By Fernando Q. Gouvêa sity level are invited to apply to become Project NexT Fellows. The application Tenth Annual Hudson River GAO Calls for Monitoring of Teacher- deadline is April 11, 2003. For more in- Undergraduate Mathematics Education Projects formation, see the Project NExT Website, Conference http://archives.math.utk.edu/projnext/. In 1998, Congress created a program that HRUMC X, the tenth annual Hudson offered grants intended to improve the Project NExT receives major funding River Undergraduate Mathematics Con- quality of teaching in American schools. from The ExxonMobil Foundation, with ference will be held at Union College, The Department of Education set up the additional funding from The Dolciani- Schenectady, NY on April 12, 2003. The Teacher Quality Enhancement Grant Halloran Foundation, The American conference, which is funded by the An- Office to administer the program. On Mathematical Society, The Educational drew W. Mellon Foundation with addi- December 11, 2002, the General Advancement Foundation, The tional support from Union College, in- Accounting Office released a report that American Statistical Association, The cludes presentations on mathematics by concludes that the Department of Association of Mathematics Teacher both faculty and students, and both are Education is not adequately overseeing Educators, and the Greater MAA Fund. encouraged to participate. Conference the use of these funds. In particular, the sessions are designed so that some pre- GAO argues that DoE needs to set up “an Mathematics Project Wins Siemens- sentations are accessible to undergradu- effective system for communicating with Westinghouse Competition ates in their first years of study, and oth- grantees.” The report also argues that the ers are accessible to third- or fourth-year terms associated with the accountability Early in December, the Siemens undergraduate mathematics majors. provisions in the grants are so vague that Foundation announced the national This year’s conference will focus on in- it is impossible to determine success, and winners of the Siemens Westinghouse terdisciplinary talks, though talks in any therefore recommends that DoE provide Competition in Mathematics, Science, mathematical area are welcome. You can clearer definitions and more precise and Technology. High school students find out more about HRUMC by visit- measures of success or failure. See http:// from across the nation submitted reports ing the conference web site at http:// www.gao.gov/cgi-bin/getrpt?GAO-03-6 on their research to the Siemens www.skidmore.edu/academics/mcs/ for the full report. Westinghouse judges, then selected hrumc.htm. Those wishing to make a pre- students made oral presentations on sentation at the conference should sub- New Faculty: Consider Project NExT their work. At the end of the process, the mit an abstract via the web site by Feb- top prize in the individual category went ruary 27th, 2003. Project NExT (New Experiences in to Steven J. Byrnes, a senior at Roxbury Teaching) is an MAA professional Latin School in West Roxbury, MA, for a development program for new and mathematics project entitled “Poset- Demands for Teacher Quality Spur recent Ph.D.s in the mathematical Game Periodicity”, in which he proved a New Initiatives sciences (including pure and applied significant new theorem on poset games. mathematics, statistics, operations The award includes a $100,000 According to an article in Education Week research, and mathematics education). It scholarship that Byrnes plans to use to (December 4, 2002), the new federal rules addresses all aspects of an academic study mathematics at Harvard. See http:/ requiring under-qualified teachers to career: improving the teaching and /www.siemens-foundation.org for more upgrade their credentials by 2006 is learning of mathematics, engaging in information. spurring new initiatives outside of the research and scholarship, and more traditional teacher education participating in professional activities. It Sources programs. Since traditional schools don’t also provides the participants with a have an easy way to offer specific network of peers and mentors as they HRUMC: press release, Janine Wittwer, programs to school districts, various for- assume these responsibilities. William Zwicker. New teacher ed profit institutions, colleges that already initiatives: Education Week, December 4, have in-service teacher-training Each year, about sixty faculty members 2002. GAO report: Chronicle of Higher programs, and textbook publishers are from colleges and universities through- Education Daily News, December 13, rushing to provide solutions. School out the country are selected to partici- 2002, highlights section of GAO report, districts have welcomed such pate in a workshop preceding the MAA Project NExT: Joe Gallian. Siemens- partnerships because they need to get summer meeting, activities during the Westinghouse competition: AMS, Siemens into compliance quickly, but some summer MAA meetings and the Joint Foundation. educators worry that the programs do Mathematics Meetings in January, and an not offer the same level of preparation electronic discussion network. Faculty as traditional teacher preparation for whom the 2003-2004 academic year courses. See http://www.edweek.org/ew/ will be the first or second year of full-

15 FOCUS February 2003 Call for Papers Contributed Paper Sessions at MathFest 2003

The Mathematical Association of Contributed Paper Sessions Annapolis, MD 21402-5002 America will hold its annual MathFest, Phone: (410) 293-6768 Thursday, July 31 through Saturday, Au- Fax: (410) 293-4883 gust 2, 2003 in Boulder, Colorado. The MAA CPS A1 The Art/Science of Email: [email protected] complete meetings program will appear Using Mathematics in Applications in the April 2003 issue of FOCUS. Thursday and Friday afternoons MAA CP C1 Creative Use Of Technol- This announcement is designed to alert Mathematics is a valuable tool in a di- ogy in Teaching Mathematics participants about the contributed pa- verse array of disciplines. Many appli- Thursday and Friday afternoons per sessions and their deadlines. Please cation problems appeal to the systematic note that the days scheduled for these reduction, logic, and structure that This session will focus on innovative uses sessions remain tentative. mathematical techniques can offer. On of technology to support and enhance the other hand, using mathematics may the learning of mathematics in all col- The organizers listed below, indicated also produce a beautiful insight into an lege courses. In particular, we are inter- with an (*), solicit contributed papers application problem. This session seeks ested in the use of technology to support pertinent to their sessions. Sessions gen- to find application problems that illus- conceptual understanding and apprecia- erally limit presentations to ten or fif- trate the beauty and the power of math- tion of the application of mathematical teen minutes. Each session room con- ematics. Preference will be given to pre- principles to solving real world problems. tains an overhead projector and screen. sentations that easily lend themselves to This session is sponsored by the MAA Persons needing additional equipment be used as classroom modules in an un- Committee on Computers in Mathemat- should contact the organizer of their ses- dergraduate mathematics class. ics Education (CCIME). sion as soon as possible, but prior to Tuesday, June 5, 2003. Kyle L. Riley(*) Mary L. Platt(*) Department of Mathematics Mathematics Department Submission Procedures for and Computer Science Salem State College Contributed Paper Proposals South Dakota School of Mines 352 Lafayette Street and Technology Salem, MA 01970 Send the name(s) and address(es) of the 501 East Saint Joseph Street Phone: (978) 542-6928 author(s), and a one-page summary of Rapid City, SD 57701-3995 Fax: (978) 542-7175 your paper directly to the organizer Phone: (605) 394-2471 Email: [email protected] indicated with an (*). In order to enable Fax: (605) 394-6078 the organizer(s) to evaluate the Email: [email protected] Marcelle Bessman appropriateness of your paper, include Jacksonville University as much detailed information as possible within the one-page limitation. MAA CP B1 Innovations in the Teaching of Calculus MAA CP D1 Getting Students to Proposals should not be sent to more Thursday and Friday afternoons Explore Concepts Through Writing than one organizer. If your paper cannot in Mathematics be accommodated in the session it was The last several years have seen many Thursday afternoon submitted, it will be automatically presentations at various meetings on in- considered for the general contributed novative methods to teach calculus. This This session invites papers about assign- paper session. E-mail submissions are session is seeking talks about truly new ments and projects that require students preferred. The e-mail address is: ideas on how to teach all three semesters to write about mathematical concepts, to [email protected]. of calculus. These approaches can in- express concepts in their own words, to clude but are not limited to the use of interpret symbolic mathematics in their Your summary must reach the designated the computer or World Wide Web, stu- own words, and to write about math- organizer by Tuesday, May 6, 2003. Early dent projects, student group work and ematics, in general. These assignments submissions are encouraged. The innovative presentations of applications. can include conceptual papers such as organizer will acknowledge receipt of all having the students explain a concept in summaries. If your paper is accepted, the Howard Penn(*) their own words as an answer to a ques- organizer will provide you with an e-mail Mathematics Department tion, in the form of a letter to a friend, a template and directions on how to U.S. Naval Academy poem, or even a short story. Project re- submit an abstract for your presentation. 502 Holloway Road ports that require students to explain

16 February 2003 FOCUS fully all concepts used to someone who can be written in any language, however tion (or quantitative literacy) courses; (4) knows little or nothing about the math- they must be clean and WELL docu- placement/developmental programs; (5) ematics used in solving the project prob- mented. Any source code used to create mathematics for and in mathematics- lem, assignments that require students to the paper must also be submitted for intensive majors; and (6) innovations express theorems in plain English so that verification. Papers where existing pro- (e.g. reform courses). Programs of assess- one of their friends could understand, or grams such as Mathematica® were used ment in these six focus areas are espe- even simple assignments that require stu- will also be considered. cially invited, but programs of assess- dents to explain the meaning and the use ment in other curricular blocks may be of the variables and notations that they Charles Ashbacher(*) contributed. Contributions should use. Charles Ashbacher Technologies present a clear description of the assess- Box 294 ment design and results of a currently Each presenter is encouraged to discuss Hiawatha, IA 52233 active and continuing assessment pro- how the use of the assignment/project Phone (319) 378-4646 gram. The following outline is suggested: helped students to improve their under- Fax: (928) 438-7929 Background and goals: What did we standing of course concepts and how the E-mail: [email protected] hope to accomplish? Description: What use of writing in the course helped stu- did we do? dents to understand and to learn math- ematics. Of particular interest is the ef- MAA CP F1 E-Learning of • Developing the assessment program fect of such projects/assignments Mathematics Courses • Details of the assessment program throughout the semester on the students’ Thursday afternoon understanding of course concepts and • Revisions based on initial experience notations, the ability of students to com- This session invites papers that describe (if applicable) municate mathematics using words and e-learning mathematics courses. Papers symbols, and the attitude of students to- that deal with methods of design, imple- • Insights: What did we learn? ward mathematics. mentation, delivery assessment and • Findings and success factors maintenance of complete e-learning en- Sarah L. Mabrouk(*) vironments, as well as experiences imple- • Use of the findings Mathematics Department menting such courses are welcomed. • Next steps and recommendations Framingham State College 100 State Street, PO Box 9101 Elias Deeba(*) SAUM is gathering case studies of assess- Framingham, MA 01701-9101 Dept. of Computer & Math Sciences ment programs for consideration for Phone: (508)626-4785 University of Houston-Downtown publishing on the website below or in a Fax: (508)626-4003 One Main Street, Suite S-705 volume similar to MAA Notes #49, As- Email: [email protected] Houston Texas 77002 sessment Practices in Undergraduate Phone: (713) 221-8550 Mathematics. Presenters of papers con- Fax: (713) 221-8086 tributed to this session will be invited to MAA CP E1 Advances in Recreational Email: [email protected] submit a case study for consideration for Mathematics publication. More details can be found Thursday afternoon Ananda Gunawerdena at http://www.maa.org/SAUM/index.html. Carnegie-Mellon University There have been many recent advances Bill Marion(*) in recreational mathematics, some of Department of Mathematics which have involved the use of comput- MAA CP G1 Assessment of Student and Computer Science ers. This session is designed to give you Learning in Undergraduate Valparaiso University an opportunity to explain your recent Mathematics Valparaiso, IN 46383 work in the field. While the organizer Friday afternoon Phone: (219) 464-5422 encourages submissions that involve Fax: (219) 464-5065 computers, that is not essential for con- Papers are invited that describe an E-mail: [email protected] sideration. For the purposes of this ses- institution’s program of assessment of sion, the definition of recreational math- student learning in a curricular block of William Haver ematics will be a broad one. The primary undergraduate mathematics courses. Virginia Commonwealth University guideline used to determine suitability of The session is sponsored by the NSF-sup- subject will be the understandability of ported MAA Project “Supporting Assess- Bernard Madison the mathematics. For example, if the ment in Undergraduate Mathematics” University of Arkansas mathematics in the paper is commonly (SAUM). The curricular blocks that have found in graduate programs, then it been identified as focus areas by SAUM would generally be considered unaccept- are (1) mathematics major; (2) math- able. Supplemental computer programs ematics for teachers; (3) general educa-

17 FOCUS February 2003

MAA CP H1 The Special Interest of computer use for teacher certification Kira Hamman Group of the MAA on Research in and mathematics courses are a natural Hood College Undergraduate Mathematics Educa- place for much of this learning. However, tion (Research-to-Practice) to many of us it is not obvious what kinds Friday afternoon of topics and problems, let alone software MAA CP J1 Innovative Approaches in and even hardware, lend themselves to Quantitative Literacy The SIGMAA on RUME invites contri- the teacher education setting. Saturday afternoon butions that address research issues con- cerning the teaching and learning of un- This session invites papers that incorpo- Discussions about quantitative or math- dergraduate mathematics. This session rate technology in the design and imple- ematical literacy have become more will be devoted to expositions of research mentation of innovative courses for pre- and more common over the past few results and uses of research (RUME) in service or in-service teachers at any of the years. This session will allow faculty who teaching. Priority will be given to pro- pre K-12 levels. Presentations should have developed successful approaches to posals that include summaries of re- describe math education courses that share their work with others. Submis- search results together with implications have been totally re-designed or that in- sions should include a description of the for the classroom, or specific examples fuse technology into a traditional cur- course contents, the methods used, and describing how research results have in- riculum. Experiences might include: use the audience to whom the material is di- formed instruction in actual college of laptops; online or interactive TV rected. Indication should also be given classrooms. Proposals must clearly de- courses; web-based research, com- as to why the approach has worked. Pre- scribe the research and the classroom munication or lessons; discovery learn- sentations involving interdisciplinary aspects of the presentation, as well as the ing or investigations in a computer lab and team-taught approaches are encour- relationship between them. using popular computer algebra systems; aged, as are those for non-traditional evidence of how these courses impact students or those with weak mathemati- Anne Brown(*) either the teachers’ or their students’ cal backgrounds. Department of Mathematical Sciences learning of mathematical concepts. Indiana University South Bend Richard J. Maher(*) South Bend, Indiana 46615 Also of interest is discussion of materi- Mathematics and Statistics Phone: (574) 237-4427 als for MAT programs which attract tech- Loyola University Chicago Fax: (574) 237-6589 nologically-sophisticated teachers with 6525 N. Sheridan Road Email: [email protected] great variation in mathematical skills. Chicago, Illinois 60626 Papers that deal with assessment of such Phone: (773) 508-3565 Marilyn Carlson programs or implications for accredita- Fax: (773) 508-2123 Arizona State University tion or standards at the state or national Email: [email protected] level are also welcomed. It is our hope Jim Cottrill that the session will provide a forum for Illinois State University those who have had success in this area MAA CP K1 General Contributed to educate and inspire those of us who Paper Session are casting about for ideas. Thursday, Friday, and Saturday after- MAA CP I1 Technology Innovations noons in Mathematics Education for Carol Vobach(*) Elementary and Secondary Teachers University of Houston Downtown This session is designed for papers that Friday and Saturday afternoons 1 North Main Street do not fit into one of the other sessions. Houston, Texas 77002 Papers may be presented on any math- Recently, there has been a great deal of Phone: (713) 221-8968 ematically related topic. Papers that fit interest in designing mathematics Fax: (713) 221-8086 into one of the other sessions should be courses and programs for pre-service Email: [email protected] sent to that organizer, not to this session. teachers, for professional development of in-service teachers and for Master of Arts Ron Barnes Frank Ford(*) in Teaching (MAT) programs which University of Houston Downtown Department of Mathematics emphasize pedagogy but have a math- Providence College ematics component. The CBMS docu- Elias Deeba Providence, RI 02918 ment “The Mathematical Education of University of Houston Downtown Tel:(401) 865-2635 Teachers” and the NCTM standards call Fax: (401 865-1438 for the integration of technology in the John Hamman Email: [email protected] teaching of mathematics. Many states Anne Arundel Community College now require facility with various aspects

18 February 2003 FOCUS

Call for Student Papers

Students who wish to present a paper Dr. Thomas Kelley ([email protected]) at cation forms for PME student speakers at MathFest 2003 in Boulder, Colorado Henry Ford Community College (313) can be found on the PME web site must be nominated by a faculty advi- 845-6492. www.pme-math.org or can be obtained sor familiar with the work to be pre- from PME Secretary-Treasurer, Dr. Leo sented. To propose a paper for presen- Students who make presentations at the Schneider ([email protected]). Students who tation, the student must complete a MathFest, and who are also members of make presentations at the Annual Meet- form and obtain the signature of a fac- MAA Student Chapters, are eligible for ing of PME are eligible for partial travel ulty sponsor. partial travel reimbursement. The dead- reimbursement. The deadline for receipt line for receipt of applications is June of abstracts is June 27, 2003. Nomination forms for the MAA Stu- 27, 2003. dent Paper Sessions are located on MAA Online at www.maa.org under PME student speakers must be nomi- STUDENTS, or can be obtained from nated by their chapter advisors. Appli-

Free Copies of MAA Notes Volume on Calculus MAA American Reform Available Mathematics Competitions Program Seeks In the mid-1980s, the mathematics impact from 1988 to 1998, written by Su- MOSP-IMO Leader community initiated a movement to san Ganter (Clemson University) and change the standard undergraduate published by MAA in 2001. This publi- course in calculus. This change focused cation discusses the results from a study The MAA seeks a mathematician to on the need for raising students’ concep- conducted as a part of a larger effort by be Academic Director of the Math- tual understanding, while implementing NSF to evaluate the impact of reform in ematical Olympiad Summer Program new methods to reduce tedious calcula- SMET education at the undergraduate June 10 - July 7, 2003 in Lincoln, NE tions. Efforts were encouraged through level. and Leader of the US delegation to the funding initiatives by the National Sci- International Mathematical Olympiad ence Foundation (NSF) and others. The The report includes information from in Tokyo, Japan July 7-19, 2003. Must movement helped to develop a vision for more than 300 studies and writings be excellent mathematical problem calculus that is challenging and stimu- about calculus reform during this ten- solver, have excellent teaching skills and lating, with the primary goal being to year period. Information for the report be able to work with exceptionally tal- improve the quality of calculus courses was collected to investigate what was ented high schools students, and be able and the level of learning by students in learned about the effect of calculus re- to represent the USA and the MAA. these courses at all types of institutions. form on (1) student achievement and Please send letter of application and However, there are a limited number of attitudes, (2) faculty and the mathemat- resume by March 1, 2003, to Professor studies that document the impact of such ics community, and (3) the general edu- Steve Dunbar, MAA American Math- efforts in calculus. cational environment. ematics Competitions, 1740 Vine Street, Lincoln, NE. Please send your Funding from NSF is supporting the dis- Check with your mathematics depart- inquiries about the position to Pro- tribution to every college mathematics ment chair to see your institution’s free fessor Dunbar at 1-402-472-6206 or department of Changing Calculus: A re- copy. Questions may be directed to the [email protected]. port on evaluation efforts and national author at [email protected].

19 FOCUS February 2003 MAA Awards Announced at the Baltimore Joint Meetings

By Fernando Q. Gouvêa

As happens every year, the winners of Alvin R. Tinsley which asserts that the natural cannon- several important MAA awards were an- Missouri Section ball arrangement gives the maximum nounced at the Joint Mathematics Meet- density packing of the Euclidean 3-di- ings in Baltimore. A list with citations Lester H. Lange mensional space with congruent solid and responses can be found on MAA Northern California Section balls. The second is the Honeycomb Online at http://www.maa.org/news/ Conjecture, which says that any partition awards_jan03.html. Luise-Charlotte Kappe of the plane into regions of equal area Seaway Section has perimeter at least that of the regular Gung Hu Award for Distinguished Ser- hexagonal honeycomb tiling. Hales re- vice to Mathematics Fredric Tufte cently proved both conjectures, and the Wisconsin Section article gives both the history of the prob- The Yueh-Gin Gung and Dr. Charles Y. lems and an expository account of their Hu Award for Distinguished Service to Full citations and responses are available solution. Hales’ article is available online Mathematics is the most prestigious online. at http://www.ams.org/notices/200004/ award made by the Association. This fea-hales.pdf. year’s award went to Clarence F. Haimo Awards Stephens, who until his retirement in Morgan Prize 1987 was Chairman of the Department As announced in our November issue, of Mathematics at the State University of the Deborah and Franklin Tepper Haimo The Frank and Brennie Morgan Prize for New York at Potsdam. Stephens had a Awards for Distinguished College or Uni- Outstanding Research in Mathematics by major role in achieving the “Potsdam versity Teaching of Mathematics went to: an Undergraduate Student recognizes and Miracle.” His approach to the under- encourages outstanding mathematical graduate mathematics major at SUNY Judith Victor Grabiner research by undergraduate students. This Potsdam in the 1980s led to a new model Pitzer College year’s prize went to Joshua Greene for for creating a welcoming atmosphere for his work in combinatorics. His paper “A undergraduate mathematics majors at Ranjan Roy new short proof of Kneser’s conjecture” many other institutions. This achieve- Beloit College is to appear in the”American Mathemati- ment was the main reason for Stephens’ cal Monthly. It is related to the work in award, though of course he had already Paul Zeitz his undergraduate senior thesis “Kneser’s had a long and distinguished career in University of San Francisco conjecture and its generalizations”. A mathematics education before coming to description of Greene’s work and his re- SUNY Potsdam. A profile of Stephens All three winners gave talks at the Balti- sponse to the award can be found online. will appear in the March issue of the more meeting. For more information, see American Mathematical Monthly. the November issue of FOCUS or go to Further coverage of the Joint Mathemat- http://www.maa.org/news/ ics Meetings will appear in the March is- Certificates of Meritorious Service haimo_award_winners.html. sue of FOCUS.

The MAA presents Certificates of Meri- Chauvenet Prize torious Service to members who have Mathematics served the association in notable ways, The Chauvenet Prize is given for an out- both at the national and at the section standing expository article on a math- Awareness Week 2003 level. At each January meeting, about six ematical topic by a member of the Asso- such certificates are awarded. This year’s ciation. The prize is named for William certificates went to: Chauvenet, a professor of mathematics The theme for this year’s mathemat- at the United States Naval Academy. This ics Awareness Week has just been an- Larry J. Morley, year’s Chauvenet Prize went to Thomas nounced. It will be Mathematics and Illinois Section (ISMMA) C. Hales for his article “Cannonballs and Art. FOCUS will have more detailed in- Honeycombs,” which appeared in No- formation in a future issue; for now, Karin Chess tices of AMS, April 2000, vol. 47, no. 4, visit http://www.d.umn.edu/~jgallian/ Kentucky Section 440-449. art.html for essays, links, references, possible speakers, and the MAM2003 Hales’ article is about two famous prob- poster. lems. The first is the Kepler Conjecture,

20 February 2003 FOCUS ANNOUNCING MAA’S PMET PROGRAM

Preparing Mathematicians to Educate Teachers

A growing set of national reports calls for better preparation of the nation’s mathematics teachers by mathematics faculty. To help meet this need, the MAA has proposed a multifaceted program, Preparing Mathematicians to Educate Teachers (PMET).

The PMET program will have three major components:

(1) Faculty Training: summer workshops of varying durations and mini-courses at professional meetings; (2) Information and Resources: articles in professional journals, panels at meetings, multi-media websites and hard-copy material dissemination to support faculty instruction for teachers; (3) Mini-grants and Regional Networks: to nurture and support grassroots innovation in teacher education on individual campuses. PMET efforts will be focused particularly in California, New York, North Carolina, Nebraska, and Ohio.

An extensive article on the PMET program and how MAA members can participate will appear in the March issue of FOCUS.

PMET WORKSHOPS SUMMER 2003

For faculty preparing elementary teachers:

June 15-21, 2003, Arcata, CA, organized by Patrick Callahan

August 3-15, 2003, Boone, NC, organized by David Royster and Holly Hirst

June 1-7, 2003, Lincoln, NE, organized by Jim Lewis and Ruth Heaton.

For faculty preparing secondary teachers:

June 8-20, 2003, Potsdam, NY, organized by Ed Dubinsky (with second session to be held in Summer, 2004)

Check MAA Online for full information, including workshop descriptions, and applications: www.maa.org/pmet.

The PMET workshops for 2003 are contingent upon expected notice of awards from NSF/DUE and Texas Instruments.

21 FOCUS February 2003

EMPLOYMENT OPPORTUNITIES

MASSACHUSETTS ics. Requirements include a Ph.D. in mathematics, evidence of outstanding WILLIAMS COLLEGE teaching and a commitment to scholar- The Williams College Department of ship in mathematics. Send resume, tran- Mathematics and Statistics invites appli- scripts and three letters of recommenda- cations for two positions in mathemat- tion to: Lita Porter, Secretary, Depart- ics and one position in statistics, begin- ment of Mathematics and Computer In- ning fall 2003, all at the rank of assistant formation Sciences, Marymount College, professor (in exceptional cases, more Tarrytown, New York, 10591 advanced appointments may be consid- ered). We are seeking highly qualified PENNSYLVANIA candidates who have demonstrated ex- MOSE Math Ad cellence in teaching and research, and University of Pittsburgh at Bradford PDF who will have a Ph.D. by the time of ap- Mathematics: Tenure-track Assistant Rules do not print. pointment. Professor position to begin September 2003. Ph.D. or Ed.D. in math earned or Williams College is a private, residential, near completion. A strong commitment highly selective liberal arts college with to undergraduate education on a small an undergraduate enrollment of ap- rural campus and potential for scholarly proximately 2,000 students. The teach- work are essential. Applicants with math ing load is two courses per 12-week se- education background or a willingness mester and a winter term course every to develop this expertise will be given other January. In addition to excellence favorable consideration. Teaching assign- in teaching, an active and successful re- ments will include algebra, pre-calculus, search program is expected. and fundamentals of mathematics. Send letter, vita, official transcripts, and 3 let- To apply, please send a vita and have three ters of reference to: Dr. Yong-Zhuo Chen, letters of recommendation on teaching Math Search Committee, University of and research sent to the Hiring Commit- Pittsburgh at Bradford, 300 Campus tee, Department of Mathematics and Sta- Drive, Bradford, PA 16701-2898. The se- tistics, Williams College, Williamstown, lection process will begin March 10, MA 01267. Teaching and research state- 2003, and continue until the position is ments are also welcome. Evaluations of filled. Women and minorities are encour- applications will begin on or after No- aged to apply. Visit our website at vember 25 and will continue until the www.upb.pitt.edu. AA/EOE positions are filled. Williams College is dedicated to providing awelcoming in- tellectual environment for all of its fac- ulty, staff and students; as an EEO/AA Advertising Information for Display & Classified Ads employer, Williams especially encouragesapplications from women Mechanical Specifications and underrepresented minorities. For Trim Size: 8 1/2 " wide x 10 3/8 " high fonts). PDF files are also acceptable. moreinformation on the Department of Screen: 150-line halftone Full page bleed Mathematics and Statistics, visit http:// 8 3/4" x 11 1/4", (10% extra charge) Camera-ready art: Should be prepared www.williams.edu/Mathematics. Color: FOCUS standard second color according to the mechanical specifica- available (15% extra charge). Column tions shown on this page. NEW YORK width: 2 5/16", 4 13/16", 7 3/8" Classified Rates (includes a a free list- Printing: Offset, saddle-stitched ing in MAA Online to appear the same Marymount College of Fordham month as the print ad): $2.25 per word. University How to send your Materials: Marymount College of Fordham Univer- Electronic files: Laser output should ac- Contact the MAA Advertising Depart- sity anticipates an opening for a two-year company your electronic files. PC and ment toll free at 1-866-821-1221, fax: visiting Assistant Professor of Mathemat- MAC based files must be sent as Post- (703) 528-0019. Ads may be sent via ics position beginning fall 2003. Duties script files (please subset and embed all email to [email protected]. will include teaching a variety of elemen- tary and advanced courses in mathemat- 22 February 2003 FOCUS MAA Section Meeting Schedule 2003

ALLEGHENY MOUNTAIN METRO. NEW YORK OKLAHOMA-ARKANSAS

April 4-5, 2003-Penn State University May 3, 2003-La Guardia Community March 28-29, 2003-The University of DuBois, PA College (CUNY) Tulsa, Tulsa, OK

EASTERN PA & DELAWARE MICHIGAN PACIFIC NORTHWEST

April 12, 2003-Wilkes University May 2-3, 2003-Saginaw Valley State June 20-21, 2003-Whitman College Wilkes-Barre, PA University, University Center, MI ROCKY MOUNTAIN FLORIDA MISSOURI April 2003-United States Air Force February 21-22, 2003-Jacksonville April 4-5, 2003-Washington University Academy, Colorado Springs, CO University, Jacksonville, Florida St. Louis, MO SOUTHEASTERN ILLINOIS NEBRASKA-SOUTHEAST SOUTH DAKOTA March 21-22, 2003-Joint Meeting with March 28-29, 2003-Illinois College Atlantic Section of SIAM, Clemson, SC Jacksonville, IL March, 2003-University of South Dakota at Vermillion, Vermillion, SD SOUTHERN CALIFORNIA INDIANA NEW JERSEY March 8, 2003-Harvey Mudd College March 28-29, 2003-Butler University Claremont, CA Indianapolis, IN April 5, 2003-Kean University, Union, NJ SOUTHWESTERN INTERMOUNTAIN November 8, 2003-Raritan Valley Community College, North Branch, NJ April 5-6, 2003-New Mexico Institute of March 19-20, 2003, Weber State Mining and Technology, Socorro, NM University, Ogden, UT NORTH CENTRAL SEAWAY IOWA April 25-26, 2003- Malcalester College St. Paul, MN April 4-5, 2003 Alfred University April 4-5, 2003-University of Alfred, NY. Northern Iowa, Cedar Falls, IA Fall 2003-University of Sioux Falls Sioux Falls, SD November 7-8, 2003-Rochester Institute KANSAS of Technology, Rochester, NY April 4-5, 2003-Hays, KS NORTHEASTERN TEXAS KENTUCKY June 13-14, 2003-Massachusetts College of the Liberal Arts, North Adams, MA April 3-5, 2003-Sam Houston State April 4-5, 2003-Bellarmine University University, Huntsville, TX Louisville, KY NORTHERN CALIFORNIA, NEVADA, HAWAII WISCONSIN LOUISIANA-MISSISSIPPI February 22, 2003-College of Marin April 25-26, 2003-University of February 21-22, 2003-Mississippi Kentfield Campus, Kentfield, CA Wisconsin-Marathon County College, Clinton, MS Wausau, WI OHIO MD-DC-VA September 26-28, 2003 (Meeting for April 4-5, 2003-Ohio State University Project NExT Wisconsin) Bundy Hall April 11-12, 2003-Norfolk State Columbus, OH Conference Center, Menomonie, WI University, Norfolk, VA October 17-18, 2003- Ohio Northern University, Ada, OH

23