FOCUS NOVEMBER 2000

FOCUS is published by the Mathematical Association of America in January, February, ~ FOCUS March, April, May/June, August/September, October, November, and December. Editor: Fernando Gouvea, Colby College; November 2000 [email protected] Volume 20, Number 8 Managing Editor: Carol Baxter, MAA [email protected] Inside Senior Writer: Harry Waldman, MAA [email protected] 4 Fermat's Last Theorem: The Musical Please address advertising inquiries to: Carol Baxter, MAA; [email protected] 5 The Icosahedron Society President: Thomas F. Banchoff, Brown University 6 The Curriculum Foundations Project First Vice-President: Barbara L. Osofsky, Second Vice-President: Frank Morgan, By William Barker Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: 8 Going Beyond the Big Theorem of Gollnitz: A Breakthrough in Gerald J. Porter the Theory of Partitions and q-Series Executive Director: Tina H. Straley By Krishnaswami Alladi Associate Executive Director and Director of Publications and Electronic Services: 10 The Academic Job Search: An Applicant's Perspective Donald J. Albers By Darren A. Narayan FOCUS Editorial Board: Gerald Alexanderson; Donna Beers; J. Kevin Colligan; Ed Dubinsky; Bill Hawkins; Dan 11 Student Paper Sessions at Mathfest Kalman; Maeve McCarthy; Peter Renz; Annie Selden; Jon Scott; Ravi Vakil. 12 Letters to the Editor Letters to the editor should be addressed to Fernando Gouvea, Colby College, Dept. of 13 Mathfest 2000 Mathematics, Waterville, ME 04901. By Tom Banchoff Subscription and membership questions should be directed to the MAA Customer 14 ICME-9 in Japan: An Overview Service Center, 800-331-1622; e-mail: By Annie Selden [email protected]; (301) 617-7800 (outside U.S. and Canada); fax: (301) 206-9789. 17 MAA Announces Mathematical Sciences Digital Library Copyright © 2000 by the Mathematical Association of America (Incorporated). Educational institutions may reproduce 18 Knots in Science: MAA Short Course at the New Orleans Joint articles for their own use, but not for sale, Mathematics Meetings provided that the following citation is used: "Reprinted with permission of FOCUS, the newsletter of the Mathematical Association 19 Statistics Education Now Has a SIGMAA of America (Incorporated)." By Mary Sullivan and Dex Whittinghill Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: On the cover: the hand-cut lead crystal icosahedron that was presented to each member Send address changes to FOCUS, of the Icosahedron Society. Cover photo by Bob Sullivan. Mathematical Association of America, P.O. Box 90973, Washington, DC 20090-0973. ISSN: 0731-2040; Printed in the United States FOCUS Deadlines of America. January February March Editorial Copy November 15 December 15 January 19 Display Ads December 4 January 4 February 4 Employment Ads November 17 December 19 January 26

2 NOVEMBER 2000 FOCUS

Three Mathematicians Win National Teaching Awards for 2000

Edward Burger, Leonard F. Klosinski, interest of diverse audiences, the presi• the Director of the Northern California and Evelyn Silvia will be awarded the dent of Williams College has dubbed Ed Mathematics Project whose mission is to Deborah and Franklin Tepper Haimo Burger the "ambassador of mathematics." improve the quality of mathematics Awards for Distinguished College or Uni• teaching in the schools through profes• versity Teaching of Mathematics at the Leonard Klosinski sional development programs. She also Joint Prize Session and Reception to be of Santa Clara has played a major role in her department held on Thursday January 11, 2001, dur• University is per• helping graduate students and new fac• ing the Joint Mathematics Meetings in haps best known ulty with their teaching. She is a role New Orleans. Each of the winners will for his work on the model for high school teachers, for those speak at a special session to be held on William Lowell aspiring to be teachers, and for graduate Friday January 12,2001 from 3:30 to 5:00, Putnam Math• students. giving everyone at the Joint Meetings a ematical Competi• chance to get to know the winners and tion. For the last 25 At the University of California-Davis Pro• their teaching styles. years he has served Leonard Klosinski fessor Silvia has taught a wide variety of first as Associate subjects successfully. The extra materials Edward Burger of Director and then as Director of the that she provides to assist the students Williams College is Putnam Competition. Under his leader• are notable. Besides self help handouts passionate about ship the number of contestants has re• and packets of supplementary notes, she teaching. He in• mained constant or increased slightly has also written a series of popular com• spires his students despite the declining number of math• panion notes for courses where students with his enthusi• ematics majors nationally. In recent years, find the textbook difficult. They are called asm for mathemat• more contestants than ever have been rec• "Working Excursions;' and cover abstract ics and with his ognized for outstanding achievement on algebra, advanced calculus, and complex ability to make it the Putnam. His dedication and organi• variables. fun and interesting. zational skills have ensured that the con• Edward Burger As one of his col- test runs smoothly each year. Professor Silvia has served as a mentor in leagues puts it, an NSF-sponsored program "Minority Burger "enthralls, entices, goads, cajoles, In addition to being a leader on compe• Undergraduate Research Participation in fans sparks of curiosity, and converts titions, Professor Klosinski is a popular the Physical and Mathematical Sciences." math phobes into math fans by the hun• teacher, known for giving challenging Finally, in addition to her teaching and dreds." Burger's energy and dedication are courses to students who recognize their outreach activities, she continues to be a apparent to everyone. He often drops by value. In front of a class he is "lively, out• well-respected researcher in functions of in the evenings on groups of students going, theatrical, and seemingly sponta• one complex variable. • working on his assignments to see what neous." He has a loyal following of stu• they have done and to offer suggestions. dents who credit to him much of their development as professionals in com• Special Session at the Joint Burger is also noted for innovative puter science, mathematics, and various Mathematics Meetings courses. At Williams, he has offered an branches of science and engineering. in New Orleans innovative seminar on algebraic number theory, and he has also developed a suc• Evelyn Silvia is ac• Friday January 12,2001 cessful course, The Spirit ofMath, for stu• tive in teaching at from 3:30 to 5:00 dents who usually avoid mathematics. all levels, from grade school to Creating a Meaningful Piece of Burger is also a lively speaker who has graduate school. the Human Mosaic given numerous talks on a wide variety She has taught sev• Edward B. Burger of subjects outside Williams College. eral courses (in• These include conference addresses, talks, cluding supple• Teaching Through Problems and the lectures at other institutions, and appear• mental mathemat- Putnam Competition ances on radio and television. His talks Evelyn Silvia ics for deaf chil- Leonard F. Klosinski are successful because of his ability to dren, fifth grade engage and entertain his listeners while special math, pre-algebra 1, and geom• Reflections on Teaching and Learning still dealing seriously with the mathemat• etry) in the public schools, without com• Evelyn Silvia ics. Because of his ability to capture the pensation. From 1994 to 1999 she was

3 FOCUS NOVEMBER 2000 Teacher Preparation: the Discussion Continues

How to improve the quality of Ameri• sponsibility for educating teachers be nally, the report emphasizes the need for can mathematics and science teaching broadened beyond schools of education cooperation between schools and the continues to be an issue of national con• to include academics, school districts, and higher education community in order to cern. In September, the National Research society as a whole. achieve the goal of delivering the best Council issued a report called Educating mathematics and science teaching in our Teachers of Science, Mathematics, and The National Academy of Sciences estab• schools. Technology: New Practices for the New lished a Committee on Science and Math• Millennium. ematics Teacher Preparation in 1998 to As FOCUS went to press, a second report make recommendations about teacher on the subject was expected for early Oc• The report, which can be obtained from preparation based on the available re• tober, this time from the National Com• the National Academy Press at http:// search data. The report is the result of two mission on Mathematics and Science www.nap.edu, emphasizes that teacher years of work by the committee. In addi• Teaching for the 21st Century, usually education is a better category than teacher tion to its focus on professional develop• referred to as the "Glenn Commission" preparation, since the education of teach• ment of teachers, it notes that for teach• because it is chaired by former senator ers must in fact continue throughout ing to improve it is essential that teach• John Glenn. Preliminary reports in the their professional life. "Teacher education ers be accorded the same level of respect September 1 issue of Science indicated should ... be a seamless continuum that as other professionals. It describes the that there would be large areas of agree• begins well before prospective teachers education of teachers as a "top national ment between the two reports. The Glenn enter college and that supports them priority;' and calls for changes in the re• Commission report should be available throughout their professional careers." wards, incentives, and expectations for on the web at http://www.ed.gov/ Therefore, the report asks that the re- teachers that will reflect this priority. Fi- americacounts/glenn/toc.html. •

Fermat's Last Theorem: The Musical

Mathematics will show up on stage majors at Yale. Joshua Rosenblum once again in November, this in a mu• says he briefly considered a math• sical called Fermat's Last Tango, which ematics minor, but in the end didn't will premiere Off Broadway at the York get much beyond calculus, though Theater Company in New York City. he continues to nurture a recre• The musical, written by the husband• ational interest in mathematics. Both and-wife team of Joanne Sydney became fascinated by the story of the Lessner and Joshua Rosenblum, is in• proof of Fermat's Last Theorem, and spired by the story of Andrew Wiles' decided to write a musical on the proof of Fermat's Last Theorem, as subject. The show contains little made public by the PBS film "The mathematics, but what it does in• Proof" and the book Fermat's Enigma, clude it tries to get right. The authors by Simon Singh. Standing, left to right: are Chris Thompson (Profes• have also included some references sor Keane), Joshua Rosenblum (music and lyrics), and they hope will resonate with math• The musical tells the story of Profes• Jonathan Rabb (Fermat). In front, Joanne Sydney ematicians. For example, one of the sor Daniel Keane, who comes up with Lessner (book and lyrics). obstacles Fermat puts before Profes- a proof that Fermat couldn't possibly sor Keane in his game show is the understand, finds a flaw in the proof, and called "Prove My Theorem!" in which fact that mathematics is a "young man's then fixes the flaw under the watchful eye Professor Keane finds himself a contes• game." of Fermat and other dead mathemati• tant. The other great mathematicians end cians (who now all reside in the up getting tired of Fermat's antics, and Performances of Fermat's Last Tango will "AfterMath," of course). Fermat, decide to help the professor fix his proof. begin on November 21 and run through Pythagoras, Euclid, Newton, and Gauss The music combines operetta, blues, pop, December 31, Tuesday through Saturday. all feature in the show. The tone is light• and, of course, tango. The performance The York Theatre Company is located at hearted and whimsical. is almost completely sung through, with the Theatre at St. Peter's, Citicorp Cen• very little spoken dialogue. ter, 619 Lexington Avenue (at 54th Street), Towards the end of the story Fermat is New York, NY 10022. Fortickets,calI212- shown running a nightmarish game show Both of the play's authors were music 239-6200 .•

4 NOVEMBER 2000 FOCUS The Icosahedron Society

T he icosahedron was chosen as the logo of the MAA at the time of its founding in 1915. The newly formed Icosahedron Society recognizes those individuals who have been the Association's most gener• ous contributors.

The choice of the symbol of the Associa• tion for the name of this very special group of people signifies their very great importance to the MAA. Their generos• ity and dedication to the Association make it possible for the MAA to better serve our members and fulfill our mis• sion "to advance the mathematical sci• ences, especially at the collegiate level;' for many years to come.

The Hannah Carter Japanese Garden of the University of California at Los Ange• Pictured above are the first four charter members of the Icosahedron Society, along with les was the setting for the induction of Don Albers, MAA Associate Executive Director, Ken and Ruth Ross, Tom Banchoff, MAA the first charter members of the Icosahe• President, and Tina Straley, MAA Executive Director. Standing from left to right: Ed• dron Society. The event took place this ward Brinn and Edith Ross Brinn, Henry Alder, Deborah Tepper Haimo, Mary Alice and past summer during MAA's Mathfest, Marvin Shaefer, Don Albers, Ruth and Ken Ross, Tom Banchoff and Tina Straley. held on the campus of UCLA.

President Tom Banchoff unveiled the Enhance the interests, talents, and Lisa Kolbe, newly appointed Develop• magnificent hand-cut lead crystal icosa• achievements of all individuals in the ment Specialist, can be reached at MAA hedron presented to each member of the mathematical sciences, especially of Headquarters for information on the Society as a gift of gratitude and appre• members of underrepresented groups. Icosahedron Society and other develop• ciation. A picture of this beautiful sculp• ment efforts. Call 202-387-5200 or email ture graces the front cover of this issue. Influence institutional and public policy [email protected]. • through effective advocacy for the impor• The reception at the Japanese Garden was tance, uses, and needs of the mathemati• followed by the President's Dinner for the cal sciences. charter members of the Icosahedron So• ciety. The charter members are listed in The icosahedron is not a space filling Charter Members of the the display box on this page. solid. In one sense it stands alone and in Icosahedron Society another it requires others to complete the The icosahedron, one of the five Platonic whole picture. Henry L. Alder solids, represents water according to of Davis, California Plato. Water is the sustenance of life. Each of our Icosahedron Society mem• Thus, the icosahedron is a fitting symbol bers stands alone in extraordinary sup• Edith Ross Brinn for our sustaining members, whose con• port of the MAA through contributions and Edward Brinn tributions will ensure a long life for our of their time, dedication through their of Salt Lake City, Utah Association and the fulfilling of our goals deeds, and contributions to support the to: work of the Association. These shining Deborah Tepper Haimo stars add luster to the whole organization, of La Jolla, California Stimulate effective teaching, learning, and of which they are a part. assessment in the mathematical sciences. Mary Alice On behalf of the President, the Executive and Marvin Schaefer Foster scholarship, professional develop• Officers, and all members of the Associa• of Woodbine, Maryland. ment, and a spirit of association among tion, we thank these individuals for all of mathematical scientists. their support of the MAA.

5 FOCUS NOVEMBER 2000 The Curriculum Foundations Project

By William Barker

T he stereotype of the mathematics what students in that area need to learn reports to stimulate interdepartmental community as aloof-perhaps even a tad in their first two years of college math• discussions of their curriculum. Pro mot - condescending-towards other disci• ematics. ing and supporting informed discussions plines and their mathematical needs is with the partner disciplines may ulti• not uncommon among our science and The workshops are not intended to be mately be considered the most important social science colleagues. Fortunately a dialogues between mathematics and the outcome of the Curriculum Foundations major MAA effort that is underway chal• partner disciplines. Instead, each work• Project. lenges this stereotype: a series of disci• shop is a dialogue between representa• plinary workshops known as the Curricu• tives of the discipline under consider• The workshops have generated much lum Foundations Project. ation, with mathematicians present good will between mathematics and the merely to listen to the discussions and to partner disciplines. In particular, our col• The CF Project is part of a major MAA provide information on current curricu• leagues from the other disciplines have review of the undergraduate programs in lum trends in mathematics. For this rea• been extremely grateful-and perhaps a mathematics. The MAA's Committee on son, the majority of the twenty to thirty little surprised! -to be invited by math• the Undergraduate Program in Math• individuals invited to participate in each ematicians to state their views about ematics (CUPM) is currently studying the workshop are from the partner disci• mathematics education and to realize that undergraduate curriculum, taking into plines. their opinions are taken seriously. account the views of a broad segment of the mathematics community and its part• The major product of a CF workshop is Another pleasant surprise concerns the ner disciplines. The goal is a document a ten-page report summarizing the rec• funding of the CF Project. Although the that will assist mathematics departments ommendations and conclusions of the NSF supplied at least partial support for as they plan their programs through the workshop. It is written by the represen• several of the workshops, the vast major• first decade of the 21st century. Past tatives of the partner discipline, directed ity of the events have been funded entirely CUPM recommendations have strongly towards the mathematics community, by the local hosting institutions. Since influenced undergraduate mathematics and addresses a series of questions for• travel and lodging expenses are covered instruction. Future recommendations mulated by CRAFTY. Uniformity of style for all workshop participants, the host should have similar influence. is achieved across the reports by using institutions have contributed serious essentially the same set of questions for money to the project. We are sincerely Given the impact of mathematics instruc• each workshop. Having a common list of grateful for their generosity. tion-especially instruction during the questions also aids in comparing the re• first two years-on the sciences and ports of different workshops. As reported in the January, 2000 issue of quantitative social sciences, there is a need FOCUS, the first two workshops were for significant input from these partner The documents so produced will be held last Fall at Bowdoin College (Phys• disciplines. Hence the CUPM Subcom• widely circulated within the specific dis• ics and Computer Science) and at West mittee on Calculus Reform And the First ciplines as well as the mathematics com• Point (interdisciplinary instruction re• Two Years (CRAFTY) is gathering the munity in order to solicit a broad range lated to Physics and Engineering). The necessary information through a series of of comments. After such circulation, the workshops received some attention from eleven disciplinary workshops. reports will be published and used in the the national media, mostly notably in an formulation of the ultimate CUPM cur• article by Mark Clayton of the Christian These workshops, listed in the accompa• riculum recommendations. The reports Science Monitor, This article is still avail• nying display box, comprise the heart of will also be the focus of a Curriculum able on the Monitor's web page at http:// the Curriculum Foundations Project. Foundations Workshop to be held dur• csmonitor.com/durable/1999/11/091 They contribute to the foundational ma• ing 2001 at the U.S. Military Academy at fp13s1-csm.shtml. Two other workshops terials from which recommendations for West Point. have been held since then, with several the first two years of college mathemat• still to come (see the box on the next ics will be constructed. In addition to their role in the CUPM page). The project will conclude with an review, the reports can serve as valuable event at the Mathematical Sciences Re• Each workshop is focused on a particu• resources for initiating discussions be• search Institute in Berkeley, CA. This fi• lar partner discipline such as physics or tween mathematics departments and nal workshop will focus on the prepara• computer science, or on a group of re• their partner disciplines. Working from tion of mathematics majors. lated disciplines such as the health-related electronic versions of the reports cur• life sciences. The goal of each workshop rently available, some mathematics de• The Joint Meetings of the MAA and AMS is to obtain a clear, concise statement of partments have already begun using the in New Orleans this January will feature

6 NOVEMBER 2000 FOCUS a number of events centered on the Cur• CRAFTY ICUPM Curriculum Foundations Workshops riculum Foundations Project. In addition Contact:William Barker, [email protected] to presentations and panel discussions by participants in the workshops, a series of Completed: Statistics small focus groups will be organized by Physics and Computer Science Grinnell College the CUPM to discuss the CF workshop Oct. 12-15, '00 reports. Bowdoin College, Maine Oct. 28-31 '99 Thomas Moore [email protected] Each focus group, comprised of individu• William Barker, [email protected] Business, Finance and Economics als invited in advance, will discuss and Interdisciplinary (Math, Physics, analyze the implications of a single CF Engineering) University of Arizona Oct. 28-29, '00 report. Each report will be considered by West Point at least one focus group, and the insights Nov. 4-7, '99 Deborah Hughes Hallett [email protected] generated by these discussions will be fur• Don Small, [email protected] ther input for the CUPM curriculum re• WilliamMcCallum view. Engineering [email protected] Clemson University Mathematics Education If you are interested in participating in a May 4-7, '00 Susan Ganter, [email protected] Michigan State University focus group, please contact Bill Haver Nov. 1-3, '00 (Virginia Commonwealth University) by Health-related Life Sciences Sharon Senk email at [email protected] and in• Virginia Commonwealth University [email protected] dicate the reports in which you are inter• May 18-20, '00 ested. William Haver, [email protected] Biology and Chemistry Macalester College Further reports on the workshops and Upcoming: Nov. 2-5, '00 David Bressoud their results will appear in future issues Technical Mathematics (at two sites): [email protected] of FOCUS. Electronic copies of all the Los Angeles Pierce College, California reports so far are available at http:// Oct. 5-8, '00 Mathematics Preparation for the Major academic.bowdoin.edu/math/faculty/ Bruce Yoshiwara MSRI barker/dissemination/. • [email protected] Feb 9-11, '01 William McCallum William Barker is the chair of CRAFTY, J. Sargeant Reynolds [email protected] the CUPM Subcommittee on Calculus Re• Community College, Virginia form and the First Two Years. He can be Oct. 12-15, '00 contacted at Department ofMathematics, Susan Wood, [email protected] Bowdoin College, 8600 College Station, Mary Ann Hovis, [email protected] Brunswick, ME 04011. MAA Section Meetings November 2000 to March 2001

EASTERN PA & DELAWARE loUISIANA-MISSISSIPPI OKLAHOMA-ARKANSAS November 4, 2000-Penn State Abington, March 23-24, 200 I-University of Mississippi, March 30-31, 200l-Oklahoma Christian Abington, PA Oxford,MS University, Oklahoma City, OK

FWRlDA MD-Dc-VA SEAWAY March 2-3, 2001-Florida Gulf Coast University, November 17-18, 2000-American University, November 3-4, 2000 -SUNY at Fredonia, Fort Myers, FL Washington, DC Fredonia, NY

ILLINOIS NORTHEASTERN SOUTHEASTERN March 23-24, 200 I-University of Illinois at November 17-18, 2000-Providence College, RI March 30-31, 200 I-Huntingdon College, Urbana- Champaign, Urbana, IL Montgomery, AL NORTHERN CALIFORNIA INDIANA March 3, 200 I-Santa Clara University, Santa SOUTHERN CALIFORNIA March 23-24, 200 I-University of Indianapolis, Clara,CA March 2001-UC Irvine, Irvine, CA Indianapolis, IN TEXAS OHIO KANSAS March 29-31, 200 I-University of Houston• March 23-24, 200 I-Bowling Green State Clear Lake, Houston, TX March 30-31, 200 I-Emporia State University, University, Bowling Green, OH Emporia,KA For the complete calendar of section meetings visit: http://www.maa.org/sections/schedule.html.

7 FOCUS NOVEMBER 2000 Going Beyond the Big Theorem of G6l1nitz: A Breakthrough in the Theory of Partitions and q-Series By Krishnaswami Alladi study partitions whose parts have gaps at least 3, but then he realized that a certain additional condition was necessary in T he theory of partitions and q-series is an exciting area of order to connect these with partitions whose parts satisfy con• research that interacts with many fields within and outside of gruence conditions. Here is what he ended up proving in 1926: mathematics. A central portion of the theory involves results Theorem S: Let Sen) denote the number of partitions of n into such as the Rogers-Ramanujan identities, which imply inter• distinct parts == 1 or 2 (mod 3) . Let T(n) denote the number of esting theorems about partition functions. The deep theorem partitions of n into parts whose difference is ~ 3 with strict in• of Gollnitz is a famous example of such a partition theorem. In equality when a part is a multiple of 3. Then Sen) = T(n). March 2000, Alexander Berkovich, George Andrews, and I made a breakthrough by obtaining an identity that extends Gollnitz's In general, when the gaps increase, additional conditions are theorem, solving a problem that had been open since 1971. The required to connect such partitions with those satisfying con• consequences of this discovery are likely to be many. In this ar• gruence conditions. One of the deepest examples of such a par• ticle I shall outline certain major ideas in the theory of parti• tition theorem is the Gollnitz Theorem, proved in 1967: tions to explain the Gollnitz theorem and describe how the ex• Theorem G: Let C( n) denote the number of partitions of n into tension was formulated and proved. The theory of partitions was founded by Euler, who noticed distinct parts congruent to == 2.40r5{mod6). Let D(n) denote that generating functions could be used to prove elegant parti• the number of partitions of n in the form ml + m2 + ... + mv tion identities. By a partition of a positive integer n we mean a such that mv * 10r3, m; - m;+l ~ 6 with strict inequality if representation of n as a sum of positive integers (called parts), m;==O,1 or3(mod6). Then C(n) =D(n). two such representations being considered the same if they dif• fer only in the order of the parts. One of Euler's fundamental For example, the 7 partitions counted by C(22) are 22, 20+2, results is: 17+5, 16+4+2, 14+8, 11+5+4+2, and 10+8+4, and by D(22) Theorem E: The number ofpartitions ofan integer into odd parts are 22, 20+2,18+4,17+5,16+6,15+7, and 14+8. equals the number ofpartitions of that integer into distinct parts. On the congruential side, Schur's theorem deals with parti• tions into distinct parts in two residue classes (mod 3), while For example, there are six partitions of 8 into odd parts, Gollnitz's theorem deals with three residue classes (mod 6). Thus namely, 7+1, 5+3, 5+1+1+1, 3+3+1+1, 3+1+1+1+1+1, and Theorem G may be viewed as a result one level higher than 1+ 1+ ... + 1. There are also six partitions of 8 into distinct parts, TheoremS. namely, 8, 7+ 1,6+2,5+3,5+2+ 1, and 4+3+ l. My former teacher Basil Gordon drew my attention to the During the beginning of this century, the theory of parti• Gollnitz theorem. In 1989 Gordon and I had introduced a new tions underwent a glorious transformation under the magic technique, the method of weighted words, to obtain generaliza• touch of the Indian genius Srinivasa Ramanujan, who discov• tions of Schur's theorem. Our approach was to consider parti• ered a variety of startlingly beautiful results. One of the most tions into integers occurring in two primary colors A and Band beautiful is the following identity (also discovered independently to connect these with partitions into parts satisfying certain gap by L. J. Rogers): conditions and occurring in colors A, B, as well as in a second• (1) ary color AB formed out of it. We cast this in the form of an expansion for a double infinite product: ~ 1 (2) mI]o q5m+ q5m+4 )' (1 _ 1)( 1_ Ii (1 + Aqm )( 1+ Bqm ) In=l This is the first of the two Rogers-Ramanujan identities. In the entire theory of partitions and q-series, these two identities Schur's theorem follows from this, by replacing the colors A, are unmatched in simplicity of form, elegance, and depth. B, ABby residue classes 1,2 and 3 (mod 3), respectively. Schur's MacMahon and Schur showed that one can reinterpret (1) as a special gap condition for multiples of 3 gets interpreted as a partition theorem, as follows: condition attached to parts in the secondary color AB. Gordon and I then extended the method of weighted words to obtain a Theorem R: The number of partitions of an integer into parts generalization of the Gollnitz theorem. The idea is to use three differing by at least 2 equals the number ofpartitions of that inte• primary colors A, B, C and three secondary colors AB, AC, BC ger into parts which when divided by 5 leave remainder 1 or 4. formed out of them. The key identity is an expansion for the triple product Schur used the combinatorial interpretation to discover the "next level" partition theorem. First, he interpreted Euler's theo• rem as establishing the equality between partitions where the (3) Ii (1 + Aqm )( 1 + Bqm )( 1 + Cqln } gap between the parts is at least 1 (distinct parts) and partitions m=l whose parts are == ±1{mod 4). (that is, they are odd). Then he Gollnitz's theorem follows much as Schur's theorem followed reformulated (1) as Theorem R. Naturally, his next step was to from the previous identity. The colors A, B, and C correspond

8 NOVEMBER 2000 FOCUS to 2,4, and 5 (mod 6), respectively, and the secondary colors had proved earlier. To cast the new identity in the form of a AB, AC, and BC correspond to the pairwise sums, i.e., to 0, 1, Rogers-Ramanujan type partition theorem, we state a special and 3 (mod 6). Once again, our result also explained the strict case that comes out of it: inequality condition in Gollnitz's theorem as a condition at• Theorem Y2K: Let P( n) denote the number ofpartitions ofn into tached to parts in secondary color. Finally, setting C = 0 in (3), distinct parts congruent to 7, 11, 13, or 14 (mod 15). Let G(n) our result reduced to the identity for the double product (2). denote the number ofpartitions ofn into parts not congruent to 1, Thus this approach via partitions into colored integers allowed 2,4, or8 (mod 15) such that the difference between the non-mul• us to explain precisely in what sense the Gollnitz theorem was tiples of 15 is ~ 15 with strict inequality ifa part is not relatively an extension of Schur's theorem. Unfortunately, we did not have prime to 15, parts which are not relatively prime to 15 are> 15, a proof for this remarkable identity. the difference between the multiples of 15 is ~ 60 and the small• In November 1990, George Andrews arrived at the Univer• sity of Florida to give a lecture on the "Lost Notebook" of est multiple of 15 is ~ 30 + 30't if7 is a part, and ~ 45 + 30't if Ramanujan. The key identity caught his attention, and during not, where t is the number ofnon-multiples of 15 in the partition. his brief stay in Florida he thought of nothing else. Before he Then G(n)=P(n). left, he had produced a proof! But just as before, Berkovich and I did not have a proof of In 1971, George Andrews, who was the first to use comput• the four parameter identity. ers to search for partition identities, asked whether there exist As if history was repeating itself, George Andrews arrived in results beyond the Gollnitz theorem. In the language of parti• Florida in November 1999 for a conference, and we drew his tions into colored integers, the problem may be formulated as attention to the new identity. But this time, even Andrews was follows: is there a partition result that reduces to the Gollnitz theo• not able to prove it during his visit. This four parameter iden• rem in the same way that the Gollnitz theorem reduces to the Schur tity was much deeper and more intricate than anything he had theorem? Andrews, Gordon, and I have been thinking about this encountered. Over the next several months the three of us toiled for many years. In the spring of 1999, Alexander Berkovich ar• in reformulating the proof of the three parameter key identity rived at the University of Florida to conduct research with me. for Gollnitz's theorem in many ways hoping that one of these He had previously worked with the Heineman Prize winning proofs would "lift" to four dimensions. And indeed one such physicist Barry McCoy at Stony Brook and had discovered im• approach worked; the final details in the proof were completed portant new Rogers-Ramanujan type identities out of studies during March 2000, thereby solving the problem Andrews raised in Conformal Field Theory. I drew his attention to the Gollnitz nearly thirty years ago. theorem and the unsolved problem concerning results beyond This breakthrough opens up several exciting avenues of ex• it. In an amazingly short time, Berkovich mastered the tech• ploration. Using reformulations of the Gollnitz theorem, I had niques necessary to make significant contributions to this prob• obtained several important applications including new proofs lem. of Jacobi's triple product identity, a fundamental result in the Berkovich and I studied partitions into distinct parts in four theory of theta functions. Jacobi's identity has only one free pa• primary colors A, B, C, D. The difficulty was to connect these in rameter, whereas the expansion for the product in (3) has three a meaningful way with partitions into parts satisfying differ• free parameters, which is why it is so useful. The new identity ence conditions. It turned out that we had to consider all six has four free parameters, and so it definitely will have signifi• secondary colors AB, AC, AD, BC, BD, CD, and also the quater• cant consequences. nary color ABCD, but we had to discard all ternary colors ABC, Upon hearing the completion of the proof of the new four ABD, ACD, BCD. In October 1999, Berkovich and I discovered parameter identity, George Andrews sent the following con• an incredible four parameter identity (see box). The inclusion gratulatory note: "It has been a dream of mine since 1967 that I of the quaternary color meant that there were conditions that would someday see a generalization of the Gollnitz theorem. I cropped up in four dimensions that were invisible in three di• had rather lost hope after 30 years; so this is an especially deli• mensions, which was perhaps the reason this identity had re• cious moment." • mained undiscovered. When anyone of the parameters A, B, C, or D is set equal to 0, the four parameter identity reduced to the Krishnaswami Alladi is Professor of Mathematics at the Univer• key identity for Gollnitz's theorem that Andrews, Gordon and I sity of Florida.

Tt+Tab +···+Tcd -bc-bd-cd+4TQ_ 1 +3Q+2Qt I, AiBjCkDi I, q X{(l_qa)+qa+bc+bd+Q(l_qb)+qa+bc+bd+Q+b+cd} i.j.k.i constraints (q)a (q)b (q)c (q)i q )ab ... (q )cd( q)Q

= IT (l+Aqm)(l+Bqm)(l+Cqm)(l+Dqm), m=1 where the constraints are

i=a+ab+ac+ad+Q k=c+ac+bc+cd+ Q j = b + ab + bc + bd + Q l=d+ad+bd+cd+Q

9 FOCUS NOVEMBER 2000

The Academic ~ob Search in Mathematics An Applicant's Perspective

By Darren A. Narayan

I feel it appropriate to begin this article Questions on the Advertisement would like to go I did not hesitate to ap• with a "thank you" to all of the people ply and kept my fingers crossed. that fought to create jobs in the very tight A typical advertisement said to send a job market of the 1990's. Because of your cover letter, vita, transcripts, and arrange The Cover Letter efforts we were able to breathe a little for three letters of recommendation to be easier during our job searches. sent to the search committee. However I After asking many members of search ran into some ambiguities. committees, I concluded that the most Last year I was in the same boat with hun• important part of the application was dreds of other applicants, searching for Transcripts: The advertisement said to undoubtedly the cover letter. Many ap• an institution whose primary focus was send "transcripts". I was not sure exactly plicants sent out cover letters beginning on teaching, but which also valued schol• what kind of transcripts the school would with "Dear Search Committee, I am ap• arly research. Perhaps some of what I like. Did they want official or unofficial plying for a position in your College/Uni• learned can be helpful to this year's ap• transcripts? Are photocopies acceptable? versity" In most cases this letter is viewed plicants. Do they want my undergraduate tran• much differently from "Dear Professor scripts too? How about the summer Crawford, I am very interested in teach• The following article is meant to be a course I took at a completely different ing at Mount Allison University". source of information that I hope will school? I finally decided to send photo• reduce the stress level for some applicants. copies of transcripts from every school I I typically spent about 30-45 minutes Here is what I learned. It is impossible to attended and stated that official tran• combing through a department's web site give perfect advice, so I will just share scripts could be sent upon request. When looking to see if the school was a good some things that I wish I knew before I all was said and done I applied to about match for me. If it was, I wrote the cover started my search, including some advice 70 schools and none of them asked for letter emphasizing particularities that I from my Mom. Of course, this only cov• official transcripts. liked about the school. ers a few aspects of the process, so I en• courage you to talk with faculty members Preferred Research Area: Many adver• One thing that can turn search commit• and students and map out a winning tisements said that they are accepting ap• tees off is a poorly written cover letter. Be strategy. plications in all areas of mathematics sure to proofread it carefully. However if with preference given to applicants that you catch a typographical error after you The Game were in particular areas of mathematics. sent the letter out, don't stress about it. In some cases my area of research exper• Many search committees will be more Each institution is different and each tise was not among the preferred areas concerned with a good match than a search committee is different, but in the mentioned, so I was not sure if I should simple typographical error. However no end they are all looking for the same apply. I asked several faculty members, typos is the best situation, so time spent thing-a good match. They want some• and the consensus was that my chances proof reading is time well spent. one who will mesh well with their stu• would be slim. However they did men• dents, work well with the faculty, and be tion that there is always a chance that the The Joint Meetings of the AMS and a source of new ideas. advertisement was written by one faculty MAA in New Orleans member, or that the advertisement is Where can I find job postings? outdated and the needs of the depart• The first thing to say is that it is to your ment have recently changed. What I did advantage to go to the Joint Meetings! Probably the most useful site is the Em• was to ask the search committee chair, but They provide a chance to meet people, be ployment Information in the Mathemati• if it was a school I really liked I figured it interviewed, and to give a talk. cal Sciences (ElMS) at http:// could not hurt to apply. www.ams.org/eims on the AMS web site. Interviews: On your interviews one piece Other good places include MAA Online Deadlines: Many advertisements said of advice is to be energetic. In many cases at http://www.maa.org and the Chronicle something like "The review of applica• the department has just gotten a position of Higher Education Career Network Site tions will begin on December 10, but ap• approved and they are looking forward at http://jobs.chronicle.com/free/jobs/fac• plications will be reviewed until the po• to some "new blood" entering the depart• ulty/scitech/mathllinks. Advertisements sition is filled." I did everything to meet ment. They want someone who will be also appear in the AMS Notices and in the first mentioned deadline, but if a enthusiastic whether it is in teaching, re• FOCUS. deadline passed and I saw it was a place I search or service.

10 NOVEMBER 2000 FOCUS

I also found it useful to have a complete room. Lunch breaks at the last meeting Some final words list of questions. This is the time to ask were very short and the lines for restau• about the expectations for the position rants were very long. It was great to run If your job search is successful, congratu• such as teaching load, research expecta• to my hotel room and grab a quick lunch lations! However you might second-guess tions, availability of research grants, without missing a beat. yourself, because your job is most likely amount of committee work etc. In addi• not perfect. You might be searching for tion to these, I would ask about the The on-campus interview your dream school, with the perfect size department's future goals, and how the and a balance of teaching and research new faculty member might playa role. Most likely you will have a very busy that is perfect for you and also at a great schedule, including meetings with the location where you can live happily ever Give a talk Department Chair, other members of the after. Chances are this school does not department, and possibly the President, exist. However, you may succeed in find• I would greatly encourage you to give a Provost or Dean. You may be asked to give ing a match that, while not perfect, is talk at the New Orleans Meeting. Many a 45-minute colloquium talk or to teach "within epsilon". And who knows, over search committees will be interested in a class. time that epsilon might just go to zero. seeing an applicant's presentation style. It is a good idea to find out all informa• Darren A. Narayan recently completed a You can give a talk in an AMS special ses• tion regarding these talks. For example for job search and is an Assistant Professor of sion or an AMS contributed paper ses• the colloquium talk find out who the au• Mathematics at the Rochester Institute of sion. Although you are limited to one dience is. If you don't have a clear idea of Technology. He is also a fellow of Project AMS talk, you can give a second talk in what "junior mathematics majors" (say) NExT, a program of the Mathematical As• an MAA session and double your chances would know, find out! If you are asked to sociation ofAmerica supported in part by of being seen. teach a class, ask about the class, textbook the ExxonMobil Foundation. A longer ver• and assigning homework etc. sion of his article can be found on MAA My Mom's sixth sense: Bring a bottle of Online at http://www.maa.org/features/ water to the interviews because you will My Mom's sixth sense: Don't forget your narayan.htm!. be doing a lot of talking. I found it useful interview clothes. I left mine at home. No to keep snacks and beverages in my hotel comment!

Student Paper Sessions at Mathfest 2000

Student papers are an important Pseudoprimes, Carmichael and part of the MAA national meet• sigma-phi numbers ing. Student paper sessions were by Kevin Weis held at the Los Angeles Mathfest College of New Jersey on August 3 and 4 (For more about Mathfest, see the article by Who has my hat? MAA President Tom Banchoff on by Wendy Corp page 13.) Benedictine University Continuous motion ofa non-singu• There were 32 talks involving 35 lar matrix in Rn into the identity students from 26 colleges and uni• by Rebecca Torrey and versities and two high schools. Six Keith McCarron presentations were chosen as out• American University standing, and received awards of From left to right: Alison Leuthard, Meghan O'Brien, Irma $150 each. Mall Time M. E. T. Servatius, Charles Diminnie (Picture by Ron Irma M. E. T. Servatius Barnes, University of Houston-Downtown) The winners, who were an• Massachusetts Academy of Math• nounced at the Pi Mu Epsilon ematics and Science banquet on August 4, were: Random perfect matchings For more information on student paper Scaling multiwavelets to map integers to by Deborah Sinclair sessions, contact Charles Diminnie at integers University of Redlands [email protected] .• by Alison Leuthard and Meghan O'Brien University of St. Thomas

11 FOCUS NOVEMBER 2000 Letters to the Editor

On Post-Tenure Review

On the Post-Tenure Review opinions: for a tendentious (though logical) act of sessments."Would-be teachers are already both are right. The reviews are here to denial. It's the kind of thing that gives faced with having to deal with additional stay, and they're a lousy idea. Both articles mathematicians a bad name! education courses of questionable value, skirt one of the real issues-student constructing portfolios, mastering tech• evaluations. Students must respect their As part of the debate about when the new nology, meeting community service re• teachers, but they don't have to like them. Millennium begins, we might well ask quirements, facing diversity concerns, etc. True, happy students don't transfer or 2000 years since what? Professor Taisbak All this sounds good, but bright students drop out, but trying to keep TV-bred stu• shows us just how arbitrary was in mathematics, who have alternate ca• dents entertained is a perversion of edu• Dionysius's choice of the date for the Year reer opportunities, may see this as a de• cation. One of our Western system. Perhaps we terrent to becoming a teacher. Indeed, can agree that Jan 1, 2000, marked two teaching is already considered tough Victor Meyers thousand years since the year 1 BC, which enough, with five classes daily, discipline Retired MAA member is a date in fact a bit closer to Christ's birth problems, absenteeism, language barriers, than is the start of the year 1 AD! parental neglect, special needs accommo• Still the millennium dations, in-service development require• In any case, the real world solution to our ments, and peers that consider math un• AIthough I enjoyed most of the article, problem is coming soon. As of Jan 1, cool. "Dionysius, Zero and the Millennium," I 2001, the haggling can end and we'll all was put off by Christian Taisbak's insis• be in the 21st Century, free and clear. To get good mathematics students to con• tence that new Millennium and new cen• sider teaching, we should also be seeking tury will only begin on Jan 1, 2001. I Rudy Rucker higher teacher pay (the AFT reports that would not like to allow this popular ca• San Jose State University on average starting pay is $26,639 for nard to go once again unchallenged. teachers, $41,698 for math or statistics In a letter written in 1957, Dorothy L. Say• graduates), reduced workloads, realistic Even the most logical of us were a little ers said: "I can just remember the terrific expectations in today's world, and en• uneasy about the passage from 1999 to spate of argument and correspondence in hanced professional prestige for teaching 2000. Our particular calendar system is the papers ... when we moved into the 20th mathematics. We need to attract, and pro• of course arbitrary, but there's something century, some maintaining the 1900 was tect, our strongest students by ensuring uncanny about seeing so many nines be• the last year of the old century and others that school committees do not hire and come zeroes. It was natural to feel a bit that it was the first of the new. Every con• promote somebody's cousin of doubtful of Millennium Anxiety. ceivable authority was invoked, from Sa• competence. Otherwise, just adding more cred Common Sense to Astronomy and the requirements and "standards" will only Led by the media, the public responded Pope. I can't recollect who won, but I know serve to narrow the pool of good appli• to this unsettling event with two kinds of that, as the Song ofRoland says, 'Fierce was cants and increase the need for even more psychological defense mechanism. The the battle, and marvellous, and dread:" emergency hiring of less qualified candi• first defense mechanism was displace• (From The Letters of Dorothy Sayers, vol• dates. ment: our disturbingly irrational fears of ume 4, page 403). the Millennium were displaced to become Barry Schiller technological concerns about the Y2K More on teacher preparation Rhode Island College Bug. The second defense mechanism against Millennium Anxiety was denial: Articles in the August/September FO• See page 4 for more on the preparation of even though the year changes from 1999 CUS discussed proposed new standards teachers. to 2000, this supposedly is not a new Mil• and performance measures for prospec• lennium. tive teachers. But in mathematics, where teacher shortages are already developing, But to say that this means we are not yet another emphasis is also needed: to get in a new Millennium flies in the face of better math teaching, we need to attract ordinary linguistic usage. If something better math students to teaching in the Letters to the editor should be ad• happened in 1900, we say it happened in first place. dressed to: Fernando Gouvea, Colby the 20th Century. I'm writing the date College, Department of Mathematics, 2000 on my checks, and I should be al• At the same time that some politicians are Waterville, ME 044901; email: lowed to say I'm in the 21st Century. To bashing teachers, we are considering add• [email protected]. say otherwise is to sacrifice intelligibility ing even more "hoops" and "multiple as-

12 NOVEMBER 2000 FOCUS Mathfest 2000 By Tom Banchoff

W hat a good time we had at the tainly was an active issue at UCLA. from multivariable calculus combine to Mathfest at UCLA this August! Talk to analyze data and to predict the proper• anyone who participated and you will Ed Cat mull, the Chief Technical Officer ties of dense stars or black holes on the learn about the highlight that person ex• at PIXAR Animation Studios, had one of basis of the way light is deflected as it perienced. If you have never been to a the best-attended talks, on "The Math• passes them. Mathfest, it will make you want to come, ematics of Toy Story II". A member of and to join the growing number of MAA the MAA for many years, he spoke about As it happens, I had heard two earlier pre• members who plan to attend every year. early mathematics courses that influ• sentations by Professor Petters on the The last two summer meetings, in Provi• enced his later work in computer graph• same subject, and some of his work ap• dence and Los Angeles, set a standard for ics. He described his ongoing interest in pears on the Math Awareness Month the future, with well over 900 registrants visualization, in mathematics books as poster as well. I was very happy to learn at each one. We can all look forward to well as on the screen. about the latest developments in this im• another success in Madison, Wisconsin portant field, and those who heard about next August. The latter part of Catmull's presentation it for the first time appreciated their in• troduction to this particular application There were three plenary presentations of mathematics to physics. that made a great impression on me, partly at least because they treated topics The success of these and other main talks not included in traditional collegiate is a tribute to the committee that selects mathematics offerings. At the risk of not our speakers, together with cooperating reporting on the other plenary sessions organizations such as the National Asso• that I also enjoyed, I would like to reflect ciation of Mathematicians (NAM), spon• on what these three meant to me, and on sor of the talk by Arlie Petters. Together what they say about the MAA. Such an with all the staff at the MAA and the incomplete account can, I hope, still give meeting organizers from the AMS, they an impression of the wide range of ac• put together a program that truly gives tivities and interests of our Association, testimony to the vigor of mathematics at as exemplified at this Mathfest that so Arlie Petters of Duke University spoke on the collegiate level, and that is what the many of us enjoyed at UCLA. "Gravitational Lensing': Photo courtesy of MAA is all about. Thanks to all of them. Arlie Petters. Li Ping Ma was the first speaker, and from Just a final word about the UCLA meet• the beginning description of her early featured the award winning animated ing-many of us stayed on for some or days as a graduate student fresh from film "Geri's Game': together with outtakes all of the six-day conference on Math• China, she endeared herself to the recep• that revealed the geometric structure of ematical Challenges for the Twenty-First tive audience. She presented idea-provok• the many-faceted animations. Part of the Century, another successful meeting that ing illustrations and examples from her audience included secondary school stu• featured presentations about mathemati• Ph.D. thesis on the differences between dents with their teachers. Many of them cal research. This meeting, together with Chinese and American approaches to knew the speaker from what they had Mathfest 2000, provided a wonderful pre-service and inservice training for seen on the electronic poster for Math view of the panorama of mathematics, a teachers of mathematics in elementary Awareness Month April 2000. It was great truly remarkable summer experience. schools. to see them get the message that com• puter graphics, and computer animation We congratulate the AMS on organizing What factors in China help young teach• in particular, rely so heavily on math• this successful conference. Special thanks ers to become masters of their subjects, ematics. We have to keep that message up go to Ron Graham, who provided a tran• with profound understanding of funda• front. sition between the two meetings with his mental concepts, while the same trans• "Presidents' Lecture", co-sponsored by formation takes place less frequently in Mathematical physicist Arlie Petters gave Felix Browder, president of the AMS, and the US? The responsiveness of the audi• a great presentation on "Gravitational myself. For more on the Mathematical ence to this question was something that Lensing", illustrated with remarkable Challenges meeting, see page 16. impressed me. I'm not sure that even a photographs from deep space, together few years ago there would have been so with illustrations of the geometric theo• See you in Madison! • much interest at a national MAA meet• ries behind these visualizations of astro• ing in issues related to elementary edu• nomical phenomena. Singularities in the Tom Banchoff is President of the Math• cation and teacher training, but it cer- theory of optics, and critical point theory ematical Association ofAmerica.

13 FOCUS NOVEMBER 2000 ICME-9 in .Japan: An Overview

By Annie Selden

T he ninth International Congress on and research, practice, and theory of mative exchanges occur informally at the Mathematical Education (ICME) was mathematics education. Choices of topic receptions and happy hours or in the held from July 31 to August 6 in groups ranged widely, from the teaching halls. From a South African participant, Makuhari, Japan-a new conference city and learning of various subjects-alge• I learned about "sunshine teachers"-so thirty minutes east of Tokyo by train (but, bra, geometry, calculus, statistics-to dis• called because they spend their time out• due to the ubiquitous traffic, several tance learning, vocational mathematics, side enjoying the warm weather, rather hours away by car). This ICME, the first modelling, problem solving, proof, than remaining in the classroom with in Asia, was somewhat smaller than usual, constructivism, creativity, equity, math• their students. I was also told that many with just over 2000 participants. ematical competitions, entrance exami• university departments of education are nations, ethno-mathematics, and inter- closing, as South African students now Speakers were selected from a variety of prefer to prepare for more lucrative pro• countries. About half of the main lectur• fessions. From a Danish primary teacher, ers came from Europe and North I learned that pupils are taught by groups America, but there were speakers from of three or four teachers who remain with many other countries. The four plenary them for several years, providing great lectures and fifty regular lectures included stability while allowing the teachers to a wide range of topics, both theoretical specialize. It seems that the U.S. might and practical. From trends in mathemat• benefit from such a system because some ics education research to critical issues in primary teachers tend to avoid math• teaching symbolic expressions and the ematics. I also learned that a new Japa• role of politics in the development of nese curriculum to be instituted in 2002 mathematics in Africa, there was some• will emphasize values and have thirty thing for everyone. percent less mathematics.

Among the participants were mathema• The smorgasbord, something-for-every• ticians, mathematics education research• one, program ofICME left two first-time ers, K-12 teachers of mathematics, and a U.S. mathematicians inspired that "there variety of administrators, from school Hyman Bass, president of ICMI. are so many people around the world who principals to ministry of education staff. care about the quality and future of math• Some were interested in mathematics national comparisons such as TIMSS. In ematics education:' but they also longed education research results, whereas oth• addition, there were commercial and for more interaction with presenters. ers were more interested in collecting non-commercial exhibits, posters, short However, "all in all, we learned a great deal novel ideas for classroom use or in run• presentations, and reports from the vari• and had much of our recent reading in ning mathematical olympiads. They ous ICME Study Groups that meet an• mathematics education research rein• came from a wide variety of countries, nually. The sessions were spread between forced." Indeed, according to Mogens with Angola, Nepal, New Caledonia, Cay• the Convention Center in Makuhari and Niss, the mathematics education research man Islands, and Swaziland having one the nearby campus of Chiba Institute of component of ICME has become much participant each. The largest numbers Technology, with participants being effi• larger over the years. In the early years, came from Japan, with 942, and the U.S., ciently shuttled back-and-forth by bus. Congresses concentrated on good prac• with 222 participants. tice, as the research base had not yet been As with previous ICMEs, this interesting developed. In his plenary address review• The program also included thirteen but unrelenting succession of lectures, ing mathematics education research from working groups and twenty-three topic working groups, and topic study groups the 60's to the present day, Niss charac• study groups, with participants selecting was broken in mid-week for a day devoted terized this research as having reached the one of each. Choices included working to one's choice of Congress tours. These stage of young adulthood. groups for each level of mathematics edu• ranged from visits to local elementary, cation (from pre- and primary school to junior high, or high schools to more tour• ICME, which is held every four years, is two-year college, university, and adult isty trips to historic sites, downtown To• sponsored by the International Commis• education). kyo, Disneyland, or the elusive Mt. Fuji, sion on Mathematical Instruction hidden by clouds that lifted for just a few OCMI), whose president is Hyman Bass, Other groups devoted themselves to pre• moments. also President Elect of AMS. ICMI is a and inservice teacher education, lan• commission of the International Math• guage, assessment, technology, social and At international congresses such as this, ematical Union (IMU), whose congresses political dimensions, history and culture, some of the most interesting and infor-

14 NOVEMBER 2000 FOCUS are also qua• Short Takes gues that the greatest gains have come in drennial events Texas, Connecticut, Michigan, and North that alternate National Mathematics SAT Scores Carolina, "four states that have been lead• every two years Are Up ers in implementing standards and assess• with ICME. ments that reflect the vision of the NCTM standards." The advertisement concludes The Commis• he average score on the mathematics T by calling the other states to accept and sion also spon• portion of the SAT went up by three implement the standards "and develop sors studies points this year, to reach a 30-year high more rigorous math programs for their that usually re• of 514 out of a possible 800. Though students." The full text of the op-ed ad• sult in the pub• everybody's average went up, average vertisement is available on the web at lication of a scores for minority groups rose more study volume; http://www.exxon.mobil.com/opeds/ than the average scores for whites. Some index.html. such as The Annie Selden, with Mt. experts attribute the higher scores to an Role of the His- Fuji as a background. increase in mathematics requirements in Is I; (5) irrational? tory of Math- high schools and to ongoing efforts to ematics in the Teaching and Learning of reform the school mathematics curricu• Mathematics, just out from Kluwer. lum. Others seem to feel the change is We still don't know! Interest in the val• very small and does not represent a very ues of the zeta function at integer points The next study conference, on "The Fu• significant gain. The national average is goes back several hundred years. Euler ture of the Teaching and Learning of Al• now 13 points higher than it was in 1990. proved in the 18th century that 1;(2n) is gebra," will be held at the University of 2n a rational multiple of 1t , settling the Melbourne, December 10-14, 2001. Mathematical Art and Fun Web Site question for values at the even integers. About eighty participants will be invited Open for Business Values at the odd integers remain myste• to participate in this conference; for de• rio us. Apery proved in the 1970s that 1;(3) tails, see the website at http:// is irrational, but it's still not known www.edfac.unimelb.edu.au/DSME/icmi• Have you ever wanted to get yourself a whether it is transcendental. In a recent algebra/. For general information on set of Penrose tiles? You can find one at preprint, Tangy Rivoal has announced a ICMI, check out their website at http:// http://www.mathartfun.com. a new web proof that infinitely many of the values www.mathunion.org/ICMI/. site dedicated to products related to 1;(2n+ 1) are irrational. He shows this by tesselations, polyhedra, fractals, math• proving that the dimension over Q of the NCTM has posted reports from recipi• ematical art, and other neat stuff. The site, vector space spanned by {I, 1;(3), 1;(5), ... , ents of travel grants at http:// which combines some mathematical con• www.nctm.org/meetings/icmelicme-9/. tent with an online store, was created by 1;(2n+ I)} is greater than of equal to a con• These include photos of the opening cer• Dr. Robert Fathauer, a researcher at stant times log(n). This gives the first new emony and classroom visits, as well as NASA's Jet Propulsion Laboratory and information about the values of the zeta personal accounts of plenary and regular designer of tessellation puzzles. On a sub• function at odd integers since Apery's lectures, working group discussions, etc. page entitled "Why combine math and work. The preprint can be found at http://www.arxiv.org. Alex Bogomolny has also given personal art?" Dr. Fathauer argues that linking report on ICME-9 in his MAA Online mathematics and art "is good for your A Conference for Undergraduate columns (http://www. maa .org/news/ brain" and can help turn people on to Women columns.html). The next congress, ICME- mathematics, among other benefits. The 10, will be in Copenhagen, July 4-11, site also includes a small gallery of art 2004. As details become available, they which is inspired by mathematical ideas. T he Third Annual Nebraska Confer• will be posted at http://www.ICME-10.dk/ ence for Undergraduate Women in Math• start.htm. ExxonMobil supports NCTM Standards ematics will be held in Lincoln, NE Feb• ruary 2-4, 2001. This conference, which Written with help from Mark Davis, brings together talented undergraduate In an op-ed advertisement published in Shandy Hauk, and John Selden. • women mathematicians from around the the August 31 issue of the New York Times, country, will include undergraduate re• ExxonMobil made public its support for search talks, keynote addresses by math• Annie Selden is Professor of Mathematics the NCTM Standards for mathematics at Tennessee Technological University, Co• ematicians, and panel discussions. Some education. The "advertorial;' entitled "Go funding is available for participants. ordinator of the Association for Research figure, with rigor," says that the publica• in Undergraduate Mathematics Education Those interested in presenting a talk, or tion of the new Principles and Standards (a Special Interest Group of the MAA), just attending, please send email to for School Mathematics makes a good idea [email protected] or contact Ne• MAA Online Associate Editor for Teach• better, "because the standards have al• ing and Learning, and an Associate Editor braska Conference for Undergraduate ready demonstrated some gains." Quot• Women in Mathemtics, Department of of the College Mathematics Journal's Me• ing the results of the National Assessment dia Highlights. Mathematics and Statistics, University of of Educational Progress, ExxonMobil ar- Nebraska, Lincoln, NE 68588-0323.

15 FOCUS NOVEMBER 2000

AMS Meeting Explores Mathematical Challenges

One hundred years ago, in his famous Taubes as follows. "Taubes was a gradu• speech on mathematical problems, David ate student in physics at Harvard. He had Hilbert attempted to identify some math• the impression that everyone knew more ematical questions that were of central than he did at the time. He was feeling importance to mathematics at the turn depressed about how well he was doing of the century. This August, the Ameri• in some class where all the students acted can Mathematical Society brought to• like this was one of the easiest courses in gether some of the world's best mathema• Used with permission of the American the world. The professor, however, told ticians to attempt to "lift the veil behind Mathematical Society him that he got one of the highest marks which the future lies hidden" and chart a wide range of mathematical subjects, usu• in the class. He was quickly elated. But he course for mathematics in the 21st cen• ally at a very high level. soon thought of his classmates: You fak• tury. ers! You were all just faking the whole At the beginning of her talk, Karen time!" The meeting, entitled "Mathematical Uhlenbeck spoke about the paucity of Challenges of the 21 st Century:' was held women in university mathematics (and The overall impact of the conference will on August 7-12 at the University of Cali• about how they have been and are treated, probably take many years to be felt. Will fomia, immediately after the close of especially with regards to what is expected these talks set the agenda for the next cen• Mathfest 2000. A special lecture by of them). Only three of the invited speak• tury? Will listening to high -level talks on Ronald L. Graham on August 6 served as ers were women, and the percentage of other areas promote "cross-fertilization" a "bridge" between the two meetings. The women in attendance was low. A partici• of mathematical ideas? Whatever the case, following six days included a dense sched• pant in both conferences remarked that there is no question that "Mathematical ule of talks by some of the most creative at Mathfest, the previous week, there were Challenges for the 21 st Century" was one mathematicians of our time. many more women in attendance than of the most important meetings of the at the Mathematical Challenges meeting. last months of the twentieth century. Both the list of speakers and the audience One wonders what causes this difference included many famous mathematicians. in the demographics. For more information on the meeting, One participant estimated that during including a complete list of speakers and one of the plenary lectures "everyone in With so many high-powered speakers, it titles, visit http://www.ams.org/amsmtgs/ the Royce Hall auditorium was within 20 is inevitable that some participants felt a mathchalLhtmL See also the report on the feet of a Fields Medalist." From James G. little intimidated. Ed Dunne of the AMS meeting at http://www.ams.org/ Arthur on "The principle of functoriality" reports that Cliff Taubes attempted to re• amsmtgs/mathchaIUini.htmL. to Shing-Tung Yau on "Geometry and its lieve this feeling by telling about his days relation to physics", the talks covered a as a graduate student. He paraphrased

Michael Freedman of Alexander Beilinson of Maxim Kontsevich of Felix Browder, president of Microsoft Research the University of Chi• IHES talked about the AMS, had an important talked about "Quantum cago spoke "On the Geo• "Operads of Little Disks in role in putting together the Computation and metric Langlands Algebra and Topology." "Mathematical Challenges" Modular Functions." Conjecture."(Photo by (Photo by Allyn Jackson, meeting. (Photo by Allyn (Photo by Allyn Jackson, Allyn Jackson, AMS) AMS) Jackson, AMS) AMS)

16 NOVEMBER 2000 FOCUS Thoughts on Mathematical Challenges by Maeve McCarthy talks were far outside my field, but the speakers made a significant effort to give Hilbert gave his famous address to the ing that sense of unity that mathematics an overview of their specialty and to pose ICM on August 8, 1900. At their meeting sometimes lacks. If you came hoping to the problems of the future in terms that "Mathematical Challenges of the 21st hear or meet the leading specialist in your could be understood by the audience, re• Century': scheduled for the same week a area, you were probably out ofluck. I had gardless of specific background. It was century later, the AMS had a hard act to the impression that many of the younger nice to see that, in spite of the wide range follow. There were 32 invited addresses mathematicians in attendance were dis• of sub-disciplines in mathematics, it is from a wide variety of specialties over six appointed by this. The conference was a possible to communicate. days. As an applied mathematician, I was little intimidating at times - especially thrilled with the emphasis on partial dif• since most talks were not followed by There's no doubt that five hour-long talks ferential equations and various aspects of questions. Even when they were invited, each day was tiring. I have to confess that, computation. As a woman, I was disap• no one asked any. Any discussions had to having anticipated "conference burnout;' pointed that there were only three female happen during the breaks and at the re• I left on Thursday morning. Those who speakers and that the conference atten• ceptions. stayed for the duration must be ap• dance reflected the lack of gender balance plauded for their stamina.• in mathematics. The AMS provided us with an exhibition of what mathematics is today. I was Maeve McCarthy teaches at Murray State The lack of special sessions ensured that thrilled at several talks by the amount of University. She is a member of the Edito• no field was singled out, giving the meet- mathematics that I learned. Many of the rial Board of FOCUS and MAA Online.

MAA Announces the Mathematical Sciences Digital Library

When you start to design a new un• ond part will contain free online interac• by the library editors. Each unit will have dergraduate mathematics course, don't tive learning materials in mathematics a site for the reviews and substantive you wish there was a web site where you and its applications. The third part is a comments by users (including students) could go that would list all the relevant new MAA publication, The Journal of and authors, a file of users, and a link to published materials, both books and soft• Online Mathematics and Its Applications a moderated discussion group focused on ware, with reviews and user comments? (JOMA). these particular materials. Don't you wish there was a web site that provided a wide range of online learning The listing of all types of commercially JOMA will be the journal of the new li• materials in mathematics-materials of available learning materials in mathemat• brary. The standards for submission, re• high quality that had been reviewed and ics and its applications will be the first view, and editing of materials for JOMA selected by editors you trust? Don't you place faculty will look when designing a will be the same as for other publications wish there was an online journal that new or revised undergraduate course. of MAA. The journal will showcase ex• would feature the best online learning The site will provide publication infor• emplary materials and components, ex• materials in the mathematical sciences as mation, a short description of the prod• amine mathematics learning in an online well as interactive articles surveying avail• uct, a table of contents (where appropri• environment, discuss creation of peda• able online materials and others discuss• ate), and a link to the publisher's site for gogically sound online learning materi• ing how students learn online? Well the more information. Each title will have a als, and survey existing materials. The MAA has news for you! site for the reviews and substantive com• first issue of JOMA will appear in Janu• ments by users and authors, a file of us• ary of 2001. It will feature the results of The National Science Foundation has ers, and a link to a moderated discussion an earlier NSF grant to Math Forum to awarded the Mathematical Association of group. There will be links to relevant locate and publicize the best applets cre• America a two-year grant of almost materials in the library's collection of free, ated for online calculus materials. $900,000 to construct the Mathematical online materials. After the two-year life• Sciences Digital Library (MATHDL) as a time of the grant, publishers will be The principal investigator for the grant component of the emerging National Sci• charged a fee to have their materials listed. and first executive editor of the library is ence Digital Library. The MATHDL user These fees will provide a source of rev• Lang Moore of Duke University. Don software will be designed by Math Forum, enue to help support the whole library. Albers, Director of Publications for MAA, who will host the library's web pages. and Gene Klotz of Math Forum are co• MATHDL will consist of three related In contrast to the commercially available PIs. The first editor of JOMA is David web-based components. One part of the materials, the library's select collection of Smith of Duke University; the first asso• mathematical library will be an online online learning materials will be available ciate editor oOOMA for mathlets is Tom listing of all types of commercially avail• on the site. These materials will have been Roby of Hayward State University.• able learning materials in the mathemati• tested with students, submitted with peer cal sciences and their applications. A sec- review, and provided with another review

17 FOCUS NOVEMBER 2000 Knots In Science An MAA Short Course at the New Orleans .Joint Mathematics Meetings .January 8-9, 2001

The MAA will offer a Short Course on Knots in Physics assess the situation by presenting some Knots in Science at the Joint Mathemat• Louis H. Kauffman of the latest results in the field. ics Meetings in New Orleans this Janu• Department of Mathematics, Statistics ary. Organized by DeWitt Sumners of and Computer Science Physical Knots Florida State University, the course will University of Illinois at Chicago Jonathan Simon introduce the basic theory of knots and Department of Mathematics then present a number of fascinating sci• This talk will give a survey of relation• University of Iowa entific applications. ships between knot invariants (particu• larly the Jones polynomial and its rela• What happens to knot theory when the Knot theory had its beginnings in phys• tives) and methods and ideas from sta• knots, traditionally studied as purely one ics, in the work of Gauss, Kelvin and Tait. tistical and quantum physics. The talk will dimensional, completely flexible fila• It quickly became a very active area of begin with a recollection of easily under• ments, are given physical substance - in research in pure mathematics. Recently stood invariants such as the linking num• the form of thickness, rigidity, or some new scientific applications in biology, ber, coloring numbers for knots and links, kind of self-repulsion? Researchers have chemistry, fluid mechanics and physics fractions for rational tangles. Then poly• developed several measures of knot com• have been developed. Knots are I-dimen• nomial invariants of knots and links will plexity, modeled on these kinds of physi• sional strings that explore the entangle• be discussed and the bracket model of the cal "reality." We shall explore these ideas, ment complexity possible in 3-dimen• Jones polynomial will be constructed. see relations between different notions of sional space. Many physical objects are The bracket model provides a pivot point complexity, and compare the "ideal" con• string-like; macromolecules such as poly• for the discussion of more general invari• formations of knots that arise. We also ethylene and DNA exhibit knotting, and ants and the uses of statistical mechanics note that there are strong relations be• the DNA knots are diagnostic of cellular models and quantum field theory mod• tween these measures of complexity and metabolic function. Vortices that form in els in the topology. The talk will conclude behavior of actual knotted DNA mol• fluid motion can be long string-like ob• with a discussion of the role of knots in ecules. Audience members will receive a jects, and vortex entanglement has physi• theories of quantum gravity. genuine piece of rope and learn about cal ramifications. some easy-to-understand unsolved prob• Vortex and Magnetic Knots lems. The short course will consist of the fol• in Fluid Systems lowing lectures: Renzo L. Ricca Ideal Knots Department of Mathematics Andrzej Stasiak Introduction to Knots University College, London, England Laboratory of Ultrastructural Analysis Colin C. Adams University of Lausanne, Switzerland Department of Mathematics In this talk we discuss modern develop• Williams College ments in topological fluid mechanics and Ideal geometric representations of knots magneto hydrodynamics in the light of (ideal knots) are defined as minimal Throughout history, knots have played an recent work done on vortex and magnetic length trajectories of uniform diameter important role. They have appeared ev• knots. There has been tremendous tubes forming a knot of a given type. Ideal erywhere from art and literature to sea• progress and interaction of mathematics knots showed interesting relationships faring. In more recent times, they have and fluid dynamics and continuing re• and turned out to be good predictors of become an integral part of mathematics, finement of visualization techniques in certain average properties of randomly with applications from DNA to statisti• experiments and in direct numerical distorted knotted polymers. More re• cal mechanics. In this talk, we will dis• simulation of fluid flows. As a result, we cently we demonstrated that writhe of cuss their past history as well as their fu• can now develop, apply and test ideas and ideal knots seems to be quantized, ture, focusing in particular on the role tools borrowed from knot theory in or• whereby each crofosing of the torus type they play in mathematics. We will intro• der to study complex geometries and to• introduces a contribution to the writhe duce various concepts, including pologies of fluid systems. Issues of exist• of 1017 (or -1017), while each crossing of Reidemeister moves, crossing number ence and stability of knotted and linked the twist type introduces a writhe con• and unknotting number, which will be vortex filaments, energy aspects of mag• tribution of 417 (or -417). This observa• useful for the subsequent talks. All audi• netic braids and measures of structural tion allowed us to propose a new topo• ence members will have an opportunity complexity of vortex tangles are an ex• logical invariant that predicts the writhe to try their hand at making knots. ample of current research programs. We of ideal knots or the average writhe of

18 NOVEMBER 2000 FOCUS random knots of a given type just from (supercoiling) and topology (knotting ding is knotted. We shall discuss a proof minimal diagrams of the corresponding and linking) due to enzyme action, the that all except exponentially few such knot or link. enzyme binding and mechanism can of• embeddings are knotted in the limit when ten be characterized. This lecture will dis• the length of the simple closed curve goes Knots in DNA cuss topological models for DNA strand to infinity. One can also ask more deli• De Witt L. Sumners passage and exchange, and using the spec• cate questions such as which particular Department of Mathematics trum of DNA knots to infer bacterioph• knots are most likely and how badly knot• Florida State University age DNA packing in viral capsids. ted the embedding is likely to be. Some partial answers will be outlined, and some Cellular DNA is a long, thread-like mol• Knots in Polymers open questions will be discussed. ecule with remarkably complex topology. Stuart G. Whittington Enzymes that manipulate the geometry Department of Chemistry As always, there is a separate registration and topology of cellular DNA perform University of Toronto fee for this Short Course. Registration can many important cellular processes (in• be done using the form printed in the cluding segregation of daughter chromo• Polymer molecules in solution or in a October issue of FOCUS or on the web somes, gene regulation, DNA repair, and melt can be thought of as behaving like a at http://www.ams.org/amsmtgs/ generation of antibody diversity). Some piece of flexible string and, like a piece of 2025_intro.html. On-site registration fees enzymes pass DNA through itself via en• string, they can be self-entangled, or are $140 for MAA members, $190 for zyme-bridged transient breaks in the mutually entangled with other polymer nonmembers, and $60 for students, un• DNA; other enzymes break the DNA molecules. The situation can be modeled employed, or emeritus members. For apart and reconnect it to different ends. by randomly embedding a simple closed more information, contact De Witt In the topological approach to enzymol• curve in a three dimensional lattice such Sumners at [email protected] or by ogy, circular DNA is incubated with an as the simple cubic lattice. One can then mail: Department of Mathematics, enzyme, producing an enzyme signature ask whether the embedding is knotted Florida State University, Tallahassee, FL in the form of DNA knots and links. By and, if one repeats the procedure, what 32306-4510 .• observing the changes in DNA geometry the probability will be that the embed-

Statistics Education now has a SIGMAA

By Mary Sullivan and Dex Whittinghill

T he Mathematical Association of tion. Activities through which the A reception for SIGMAA members will America, in an effort to better serve its SIGMAA plans to interact with members be held in conjunction with the business members, has instituted a program of include sponsoring contributed paper meeting, which will be on Friday night Special Interest Groups, known as sessions at mathematics meetings, pub• from 6-8 pm. The officers for the calen• SIGMAAs. The latest SIGMAA to be cre• lishing a newsletter and Web page with dar year 2000 , listed below, hope to see ated is devoted to statistics education. It items of interest to instructors of statis• you there! will benefit the many MAA members who tics, and providing an email discussion teach statistics and who have a strong in• list to facilitate immediate interaction and SIGMAA on Statistics Education terest in improving statistics education. exchange of ideas. Other functions are Officers The new SIGMAA was chartered with the anticipated according to the interests of main goal of continuing the considerable members. Chair: Dex Whittinghill, Rowan activity in recent years of the Isolated University ([email protected]) Statisticians and Isolated Teachers of Sta• The MAA has made the process of join• Chair-Elect: Mary Sullivan, Rhode tistics groups. ing the SIGMAA on statistics education Island College ([email protected]) an easy one. MAA members will find a Past-Chair: Allan Rossman, Dickinson The primary purpose of the SIGMAA on check box on their dues renewal form and College ([email protected]) Statistics Education is to provide a forum interested persons simply indicate their Secretary: Ginger Holmes Rowell, through which MAA members who are willingness to be a member and include Middle Tennessee State University interested in statistics education can the $10 SIGMAA dues with their MAA ([email protected]) meet, interact, and exchange ideas; pro• renewal. The SIGMAA will meet formally Treasurer: K.L.D. Gunawardena, vide support for each other; and foster for the first time in January at the Joint University of Wisconsin-Oshkosh increased awareness of statistics educa- Mathematics Meetings in New Orleans. ([email protected]) •

19 FOCUS NOVEMBER 2000 Treasurer's Report -1999 Financial Year

Gerald J. Porter

I am pleased to report that the Operat• Year End Operating Fund Balance ing Fund had a surplus of $168,464 in (excluding extraordinary transfers) 1999. This surplus enabled us to return $400,000 • ______1_9_9_5-_1_9_9.:...9 ______---. $175,000 to the Investment Fund (that was withdrawn during 1995 and 1996) without adversely affecting our cash flow. $300,000 t------The Board of Governors had approved a balanced budget for 1999 that included a $200,000 t------$50,000 contingency fund. Significant differences from that budget were the fol• $100,000 t------:-::-:------lowing: $0 Income: book and journal income was under budget by $64,000; con- ($100,000) tributions were under budget by $148,000; interest income exceeded ($200,000) budget by $44,000 and indirect cost 1996 recovery by $10,000. ($300,000) L...-______---1

Expense: Salaries and Benefits were under budget by $152,000 because of staff vacancies; Marketing and Com• sion ofJSTOR subscriptions; but over• We discuss the operating budget, grant munications were under budget by all it also represents the recognition of activity, the headquarters building fund, $32,000 and depreciation was under the high quality of our journals. the American Mathematics Competitions budget by $54,000. and the investment fund individually be• • Meeting income increased signifi• low. Last but not least, I am glad to ac• In 2000 and beyond, the MAA will not cantly in large part because of the suc• knowledge the assistance of our Director have the staff vacancies that it had in cess of the Providence meeting. of Finance, Neil Beskin, in preparing this 1999. As a result, the MAA must work report. harder to increase income. • Upon the advice of our auditors we took a charge of $17,981 for slow sell• What happened in 1999 The chart on the right gives a quick over• ing books; in 1998 we wrote off view of the performance of the MAA Op• $27,609 of inventory. erating Fund (excluding extraordinary • Dues income increased by 3%. This was approximately the amount of the transfers from the Investment Fund) dur• • Funds spent on programs and ser• dues increase for 1999. This reverses a ing the last five years. The Operating Fund vices increased by $137,000. The ma• includes the journal and book programs, decrease in membership that had oc• jor factor ($94,000) was an increase in meetings, governance, and member ser• curred for the previous few years. meetings cost because of the success• vices. It does not include grant funded ful Providence meeting. We have also programs, the American Mathematics • Contributions (excluding the transferred $23,000 of project support $37,583 for the Building Fund) de• Competitions, or the operation of the to this category. creased by approximately $32,000. In MAA headquarters buildings. 1998 contributions had decreased by • The change in Administrative costs $40,000. This is a disturbing trend. The MAA Endowment Fund[ 1] in• is due to the inclusion of computer The MAA depends upon member creased in value by $117,709 before the support in 1999. In 1998 this was in• contributions. normal transfer of $45,330 to the Oper• cluded in the publications depart• ating Fund for programs and the extraor• ment. dinarytransfer of$175,000 to the Endow• • Journal income (other than dues) in• ment Fund discussed on page 13. At year creased by $85,000. In 1999 Journal in• • Part of the increase in journal costs end the value of the Endowment Fund come increased by $53,000. This is due and decrease in publication costs is a was $2,462,739. This includes both re• to a number of factors including reallocation of expenses from one cat• stricted and unrestricted funds. higher subscription charges and inclu- egory to the other.

20 , NOVEMBER 2000 FOCUS

Externally Funded Projects the end of 1998. During 1999, $45,330 B. Ford in memory ofWalter B. Ford. This was transferred from these funds to sup• trust had a value of $100,908 on Decem• During 1999 the MAA received external port prizes and other activities designated ber 31,1999. project support of $864,340. This was by the original donors to the MAA. An down from $1,007,533 received in 1998. additional $26,253 was transferred from The MAA is also the beneficiary of two Indirect cost recovery of administrative the Sliffe Trust. $2,704 was added to the Charitable Remainder Unitrusts. At the expenses was $111,933 down from endowment to the James Leitzel Fund. end of 1999 these were carried on our $128,756 in 1998. We expect that this will balance sheet at a value of $310,998 in increase in 2000 because of new grants. A extraordinary transfer of $175,000 conformance with IRS rules. from the General Fund to the Benefactor's American Mathematics Competitions Fund was recorded at the end of 1999. General Fund Balance This transfer was made to reverse previ- The MAA manages two high school and 0us extraordinary transfers that were re• The General Fund Balance is the cumu• a junior high school national mathemat• quired by the deficits of 1995 and 1996. lative sum of yearly balances in the Gen• ics competition. These activities are man• eral Fund. It is a measure of how the As• aged from our office in Lincoln, Ne• The MAA Endowment Funds are, ac• sociation has done over time. This bal• braska. Students who perform well on the cording to accounting standards, divided ance decreased last year by $6,536, which high school examination are invited to into Unrestricted, Temporarily Restricted was the surplus in the Operating Fund compete for participation on the U.S. and Permanently Restricted. The values for the year less the transfer of $175,000 Mathematical Olympiad team. This com• of these funds at the end of 1998 and 1999 to the Benefactors Fund. petition takes place through two addi• are listed in the box below. tional exams, the AIME and the USAMo. December 31,1998 December 31,1999 In 1999 the income from these examina• The last will and testament of Edith May tions totaled $987,444 while expenses Sliffe established a fund (The Sliffe Fund) were $932,443. to fund awards to selected teachers whose $224,187 $217,656 teams qualified in the American Math• Building Fund ematics Competitions. The MAA was se- lected as the Trustee of this fund. On General Fund Balance The Association owns two adjoining December 31,1999 the Sliffe Fund had a townhouses and a "carriage house" at value of $645,559. The MAA also is the 1527 and 1529 Eighteenth Street NW, trustee of a trust established by Clinton Washington, DC. The MAA Washington Endowment Fund office occupies 1529, most of the "carriage house;' and a small amount of 1527. The December 31,1998 December 31,1999 remainder of 1527 is rented to other Unrestricted Board designated $1,490,556 $1,851,620

Building Fund Income: $345,636 Temporarily restricted $431,594 $492,909 Permanently restricted $118,210 $118,210 Building Fund Expense: $341,629 $2,040,360 $2,462,739 mathematical organizations including Supporting Materials the AMS, and CBMS. In 1999 we "charged" ourselves $225,000 for the Supporting materials for this report are available on the World Wide Web. These space we occupied. That amount is in• include the following: cluded in Building Fund Income. 1. Building Fund Report, 1999: http://www.math.upenn.edu/-gjporter/maa/treasurer/ In 1999, depreciation on the building and 1999building.htm. renovations was $106,055. In 1999, the 2. American Mathematics Competitions-1999: http://www.math.upenn.edu/ Building Fund received contributions of -gjporter/maa/treasurer/1999amc.htm. $37,583, primarily for the Sward Lobby. 3. Income and Expense by Activity: http://www.math.upenn.edu/-gjporter/maa/trea• surer/1999income_ expense.htm. Endowment Fund 4. Grant Income and Expense: http://www.math.upenn.edu/-gjporter/maa/treasurer/ 1999grants.htm. The MAA Endowment Fund includes 5. Investment Fund Report: http://www.math.upenn.edu/-gjporter/maa/treasurer/ both restricted and unrestricted funds. At 1999investmentreport.htm. the end of 1999 the Endowment was val• 6. Balance Sheet: http://www.math.upenn.edu/-gjporter/maa/treasurer/ ued at $2,462,739 a 20% increase from 1999balance.htm.

21 FOCUS NOVEMBER 2000 Overview: The Operating Budget for 1999 Where the money came from Total income for 1999 was $4,814,602 up from $4,669,315 in 1998. This was derived as follows:

1998 1999

Dues $1,945,975 $2,008,578

Contributions $186,967 $154,956

Journals (other than from member subscriptions)[2] $836,332 $921,875

Publications other than journals $1,070,029 $1,025,461

Allocated Indirect Cost Recovery $87,705 $88,535 Transfer from Investments $62,842 $71,582

Indirect Costs on Grants $128,756 $111,933 Meetings/Minicourses/Shortcourses $231,086 $295,580

Building Management Fee $25,000 $25,000

Miscellaneous $94,623 $111,102

TOTAL $4,669,315 $4,814,602

Dues includes member dues, institutional dues, corporate dues, budget. This includes Olympiad activities and the American and a payment from the Life Membership Fund for life mem• Mathematics Competitions. bers. Investments are funds that are transferred from Investment Contributions include the Greater MAA Fund, the dues supple• Funds to support specified prizes and other activities as well as ment and other contributions to the Operating Fund but does special transfers. In 1999 there was a special transfer of$175,000 not include contributions to the endowment or to the Building from the General Fund to the Investment Fund to reverse ear• Fund. lier transfers. This transfer does not appear in the Operating Fund Budget presented here. Journals include non-member subscriptions, sales of back is• sues and royalties received. Indirect Costs on Grants is income on externally funded ac• tivities that support MAA administrative activities. Not all fund• Publications income includes sales ofMAA books and reports, ing agencies pay indirect costs. placement tests, and video tapes. Meetings and Courses are registration fees from minicourses, Allocated Indirect Cost Recovery is indirect costs recovered shortcourses, and the online courses; net income from the joint from MAA activities that are not included in the Operating meeting and all income from the summer Mathfest.

Where the money went Expenses[3] totaled $4,646,138 in 1999 compared to $4,294,860 in 1998.

1998 1999 Journals/Electronic Services $1,454,784 $1,810,724 Publications $845,042 $540,379 Inventory Allowance $27,609 $17,981 General Programs, Services and Projects $436,783 $574,066 Administration $850,212 $971,149 Governance $151,750 $175,140 Membership Processing $236,479 $275,707 Development $163,810 $157,710 Miscellaneous $128,391 $123,282 TOTAL $4,294,860 $4,646,138

22 NOVEMBER 2000 FOCUS

Journals/Electronic Services include the our participation in joint projects and ac• Membership Processing is the cost of cost of publishing and distributing the tivities such as JPBM. membership recruitment and fulfillment. Monthly, Mathematics Magazine, the eM], FOCUS, Math Horizons, and our Administration is the cost of operating Development includes the cost of the electronic newsletter, MAA Online. the Executive, Finance, Human Resources Development Department as well as costs and Computer Service Departments. related to the Greater MAA Fund. This is Publications is the cost of our book and These costs are not allocated to other ac• an investment in future gifts as well as video publication program. tivities. present contributions.

General Programs and Services includes Governance includes the costs related to Miscellaneous includes telephone, copy• the cost of awards, minicourses, MAA the Board of Governors, section officers, ing, postage and office supply expenses. portions of the joint meeting, the sum• executive and finance committees, and mer Mathfest, section support, SUMMA, the officers. student chapters, project support, and

[1] We use the name "Endowment Fund" to distinguish these assets from the MAA Investment Fund which consists of Endowment assets plus two trusts that the MAA administers.

[2] Journal income does not include the portion of member dues allocated for journal subscriptions. Those allocations are as follows: American Mathematical Monthly $406,445, Mathematics Magazine $188,853, College Mathematics Journal $180,737, and FOCUS $145,776.

[3] Expenses include direct expenses, allocated building expense, and allocated direct service expense for the publications, marketing, and member services departments. Costs attributable to Governance, the Executive and Finance Departments and the Development Department are not allocated. They appear as Administrative expenses.

EMPLOYMENT OPPORlUNmES

ARIZONA continue weekly until the positions are filled. AA/ tions will begin on December 1,2000. EOE. ARIZONA STATE UNIVERSITY Northern Arizona University has a Flagstaff cam• The Department of Mathematics at Arizona NORTHERN ARIZONA UNIVERSITY pus enrollment of approximately 15,000. The State University invites applications for a tenure• The Department of Mathematics and Statistics Department has 24 permanent faculty and of• track position at the Assistant Professor level, of Northern Arizona University invites applica• fers Bachelor's and Master's degrees with empha• beginning in the fall semester of 200 1. Applicants tions for the following positions: ses in mathematics, mathematics education and are required to have a Ph.D. in Mathematics, or statistics. a closely related field with a strong background (l) One tenure-track Assistant Professor in in Mathematics, and a demonstrated potential Analysis or a related area. Flagstaff is located at an elevation of 7,000 in the for excellence in mathematics education research (2) Two tenure-track Assistant Professors in cool pine forests of northern Arizona, near high and teaching at all levels. The successful candi• Mathematics Education, one in Flagstaff, one in mountains, several spectacular canyons, and date will be expected to conduct research and Phoenix. numerous other attractions. publish in the area of mathematics education, (3) One Lecturer, visiting for the 2001-2002 year provide quality teaching of undergraduate and but anticipated to become an annually renew• NAU IS AN EQUAL OPPORTUNITY/AFFIR• graduate courses in secondary and undergradu• able position. MATIVE ACTION INSTITUTION. MINORI• ate mathematics education and undergraduate TIES, PERSONS WITH DISABILITIES, VETER• courses in mathematics. Candidates should ex• Duties for the tenure-track positions include ANS, AND WOMEN ARE ENCOURAGED TO pect to participate fully in on-campus interdis• teaching undergraduate and graduate courses, APPLY. ciplinary mathematics education activities, and carrying on an active research program, and ser• appropriate professional service activities. vice. The visiting lecturer position is primarily a Department of Mathematics and Statistics, PO teaching and service position. Applicants should Box 5717, Northern Arizona University, Flagstaff, Applicants must send i) their resume, ii) an AMS have the experience and commitment needed to AZ 86011-5717. Cover Sheet, iii) a personal statement address• work with a diverse population. All four posi• ing their research agenda, iv) a statement of tions start in late August 2001. UNIVERSITY OF ARIZONA teaching philosophy, and v) arrange for at least The Mathematics Department at the University three letters of recommendation to be sent to: Please consult the web site http:// of Arizona may have tenure track positions in R.A. Renaut, Chair, Mathematics Education odin.math.nau.edu/ or write the appropriate various areas, including Mathematics Education, Search Committee, Department of Mathemat• screening committee chair at the address below subject to availability of funding, beginning fall ics, PO Box 871804, Arizona State University, for detailed qualifications, duties, and applica• 200l. Tempe, AZ 85287-1804. Review of the applica• tion requirements. The searches will remain open tions will begin on December 4, 2000, and will until further notice; however, review of applica- We encourage early application. Application re-

23 FOCUS NOVEMBER 2000 view begins November 1,2000, with applications All positions: Salary dependent on qualifications. and salary will be commensurate with experi• accepted until December 1,2000, or as long as Required: evidence of teaching excellence, abil• ence. The Department has a significant number positions remain unfilled. Send AMS Cover• ity to direct master's theses, potential for con• of faculty who are active in all aspects of teach• sheet, a letter of interest (specify position), cur• ducting scholarly activities. Completion of ter• ing and research in Mathematics Education (for riculum vitae with a list of publications, and a minal degree by Sept. '0 1. Review of applications the complete job description, please visit us at minimum of three (3) letters of recommenda• continues until position is filled or closed. Sub• our web sit at: http://math.fullerton.edu. Send tion (enclose or arrange to be sent), to: Person• mit application form (with name of position), all materials to: Chair, Search Committee in nel Committee, Department of Mathematics, curriculum vitae, transcripts, and min. of 3 ref• Mathematics Education, Department of Math• University of Arizona, P.O. Box 210089, Tucson, erence letters to Faculty Search Committee, Math ematics, California State University, Fullerton, Arizona 85721-0089. Dept., CSPU Pomona, 3801 W. Temple Ave, Fullerton, CA 92834. Applications will be re• Pomona, CA 91768-4007; 909-869-4008; Fax: viewed beginning November 15,2000. For full The AMS form can be downloaded from http:// 909-869-4904; e-mail: 1mborchert@ consideration complete applications must be www.ams.org/employment/coversheet• csupomona.edu. AA/EEO. See http:// received no later than January 5, 2001. Cal State info.html. www.csupomona.edu/-math. Fullerton is an AAlEO/Titie IX/ADA Employer.

The University of Arizona is an EEO/AA Em• CALIFORNIA POLYTECHNIC UNIVERSITY, CALIFORNIA STATE UNIVERSITY, ployer. MIWIDlY. SAN LUIS OBISPO FULLERTON Mathematics tenure-track position beginning The Department of Mathematics at California CALIFORNIA Fall 2001. Assistant professor appointment an• State University, Fullerton has two tenure-track ticipated. Salary commensurate with qualifica• openings at the assistant professor level begin• CAL STATE POLYTECH. UNIV., POMONA tions and experience. Excellence in teaching and ning fall 2001. For candidates with exceptional Department of Mathematics an active program in research/professional de• qualifications, appointment at the rank of asso• Four tenure-track positions velopment are expected. Doctorate in mathemat• ciate professor may be considered. Minimum Pure Math and Math Ed. (Asst Prof) Teach ma• ics or closely related field is required. Preferred qualifications are a Ph.D. in Mathematics or Ap• jor & service courses in secondary teaching/pure areas of interest are Applied Analysis (numeri• plied Mathematics awarded by August 20, 2001, option; advise students seeking secondary teach• cal and asymptotic analyses, differential equa• high potential in teaching and research, and ex• ing credential; interact with Center for Educa• tions, modeling), Combinatorics (algebraic and cellent communication skills. tion & Equity in Math, Sci. & Tech. (CEEMaST) probabilistic combinatorics, partitions, symmet• and College of Ed. (CElS). Min qual: Ph.D. in ric functions, symbolic computation), and To• The first position is in the fields of geometry or pure math with ability to teach geometry, num• pology (algebraic and differential topology, fixed differential geometry. An interest in the history ber theory or topology and strong background point and knot theories, low dimensional mani• of mathematics would be a plus. The second in math ed. or doctorate in math ed. with ability folds). Submit Cal Poly application form (request position is in applied mathematics in the fields to teach upper division pure math courses. Ini• via [email protected]), resume, brief statement of computational mathematics, differential tial review of applications 12115/00. of professional goals, three letters of reference equations (ordinary or partial), or dynamical (at least one addressing teaching experience), and systems. Math and Math Ed. (Asst Prof) Teach major & transcripts (unofficial okay initially) to: Depart• service courses in math, applied math, or stat as ment Chair, Mathematics Department, Cal Poly, Teaching duties include courses at the under• well as math ed courses; advise students pursu• San Luis Obispo, CA 93407. All materials must graduate and graduate levels. The successful can• ing a secondary teaching credential; interact with be received by the closing date: 12/1/00. Please didate is expected to be professionally active and CEEMaST and CEIS. Min qual: Ph.D. in math, indicate Recruitment Code: 13002 on all corre• to participate in departmental and university appl math, or stat and strong background in spondence. Cal Poly is strongly committed to affairs. Excellence in teaching and ongoing re• math ed. or doctorate in math ed. with ability to achieving excellence through cultural diversity. search activity are essential for promotion and teach upper division math, appl math, or stat The university actively encourages applications tenure. courses. Initial review of applications 1/19/01. and nominations of women, persons of color, applicants with disabilities, and members of Applicants should send a summary of their AppI.Math/Stat. (Asst/Assoc Prof) Teach major other under-represented groups. AAlEEO. teaching experience and current and future re• and service courses in appl math or stat, advise search plans, a current Curriculum Vita, at least graduate students. Preference will be given to CALIFORNIA STATE UNIVERSITY, three letters of reference addressing their back• applicants having multiple expertise in the fol• FULLERTON ground and potential in both teaching and re• lowing areas: differential equations, modeling Mathematics Education The Department of search, and transcripts of graduate work to: (deterministic and stochastic), random pro• Mathematics at California State University, Ful• Chair, Search Committee (specify Pure or Ap• cesses, estimation theory, numerical analysis, or lerton, has an opening for one tenure track po• plied), Department of Mathematics, California operations research. Min qual: Ph.D. in math or sition at the assistant or associate professor lev• State University, Fullerton, CA 92834-6850. For stat or related area. Initial review of applications els, beginning August 20, 2001. Responsibilities full consideration, they must be received by Janu• 2/2/01. include teaching courses in mathematics and ary 12, 2001. Further information regarding mathematics education; developing the teaching CSUF and the mathematics department can be Statistics (Asst/ Assoc Prof) Teach graduate stat skills of student teachers in mathematics; and found at http://www.fullerton.edu. Cal State courses, undergraduate and service courses in being active in research related to Mathematics Fullerton is an AA/EO/Title IX.! ADA Employer. stat or math; advise graduate students. Prefer• Education. Doctorate in an area directly related ence given to applicants with expertise in one or to Mathematics Education or Mathematics SAN JOSE STATE UNIVERSITY more of: statistical modeling, multivariate stat, awarded by the appointment date, and a Mas• Department of Mathematics biostat, design of experiment, estimation theory, ters Degree in Mathematics or a Bachelors De• and Computer Science statistical consulting. Min qual: Ph.D. in stat or gree in Mathematics with substantial graduate Two tenure track positions in mathematics. At math or related area. Initial review of applica• coursework in Mathematics is required. Rank least one will be in the area of statistics. Assis- tions 212/01.

24 NOVEMBER 2000 FOCUS tant professor rank is preferred, but appointment dates with an established research program, typi• and Computer Science to associate professor is possible in exceptional cally with some postdoctoral experience. For the CBX017 circumstances. To be considered for the position, analysis position, we are especially interested in Georgia College & State University candidates must have earned their Ph.D. in probability theory, Lie groups, or geometry with Milledgeville, GA 31061 mathematics by August 2001. Excellence in connections to dynamics; for the algebra posi• The cover letter should address career goals and teaching is of primary importance. Ideal candi• tion, we are especially interested in arithmetic views on teaching and scholarship in a liberal date will have an interest in establishing and pro• or algebraic geometry, number theory, algebraic arts university. [Final candidates for the position moting a pre-actuarial program. Candidates groups, commutative algebra, or algebraic com• will be required to submit official graduate and must be sensitive to the educational goals of a binatorics. Outstanding candidates in any area undergraduate transcripts.] Please indicate avail• multicultural population. Please send a cover of mathematics are encouraged to apply. ability for interviews at the January meeting of letter, vita, graduate transcript(s), and three let• AMS/MAA. ters of reference to Dr. Michael Burke, Chair, Teaching duties for each of the above positions Department of Mathematics and Computer Sci• are two courses per semester. For additional information on the department ence, San Jose State University, San Jose, CA and the position, please see the department's web 95192-0103. Cover letter should address your Wesleyan University is committed to increasing page at hup://www.gcsu.edu/acad_affairs/ approach to teaching and your willingness to live the diversity of its faculty and is an equal oppor• coICartsci/mathcomp_sci. in an area with a high cost of housing. Applica• tunity/affirmative action employer. tion deadline is March 1,2001. EOE/AAE. GC&SU is an Equal Opportunity/Affirmative Applications must be submitted by January 29, Action Employer. 2001. Applicants should arrange for at least four CONNECTICUT letters of recommendation, including one which SACRED HEART UNIVERSITY evaluates teaching, to be sent to the address be• INDIANA Mathematics low. WABASH COLLEGE Sacred Heart University, the third-largest Catho• Wabash College invites applications and nomi• lic University in New England is a dynamic, in• All correspondence and applications should be nations for the position of Chair of the Depart• dependent, coeducational, institution that is submitted to: ment of Mathematics and Computer Science. committed to excellence in academics and to the Preferred starting date ofJuly 2001. Wabash, a Catholic intellectual and liberal arts traditions. Mathematics Search Committee selective liberal arts College of 850 men, has been The main campus is in suburban Fairfield, one Department of Mathematics and nationally ranked for the percentage of its sci• hour north of NYC and three hours south of Computer Science ence graduates who go on to successful gradu• Boston. Wesleyan University ate work and is consistendy ranked by U.S. News Middletown, CT 06459 and World Reportas one of the best values among At this time we are anticipating two tenure-track liberal arts colleges. The College's endowment, Assistant Professor positions beginning in Au• E-mail enquiries may be directed to one of the largest nationally per student supports gust 2001. Ph.D. in Mathematics or Math Edu• [email protected]; please mention that competitive salaries, an engaging teaching and cation required. Specialization in Analysis and/ you are enquiring about the assistant professor• learning environment, a strong program of fac• or Statistics preferred. Commitment to teach• ships. ulty development, and a good educational value ing and the use of technology in the classroom for its students. Wabash is currendy in the pro• are essential. Expected to teach major and non• More information concerning the Department cess of building and renovating science and major mathematics courses. Candidates with of Mathematics and Computer Science and mathematics facilities. Our new Center for In• post-doctoral publications and grant writing about Wesleyan University can be found via quiry into the Liberal Arts will present Wabash preferred. Applications must include a complete http://www.math. wesleyan.edu/. faculty with the opportunity to have a major in• resume, transcripts, teaching philosophy, and fluence on the liberal arts nationally. With teach• three letters of recommendation. ing and administrative duties, the new chair will GEORGIA have the opportunity to continue the develop• Please direct applications to Rose Marie Kinik, GEORGIA COLLEGE & STATE UNIVERSITY ment of the 7-member department in a very sup• Chair, Mathematics Department, Sacred Heart The Department of Mathematics and Computer portive environment as the department prepares University, 5151 Park Avenue, Fairfield, CT Science invites applications for a tenure-track to move into the new facility. Applicants must 06432. EOE/ AA employer. Women and minori• position in mathematics at the assistant profes• have a Ph.D. in mathematics or computer sci• ties encouraged to apply. sor rank. A Ph.D. in mathematics or a closely ence, a commitment to undergraduate educa• related discipline is required, as well as a com• tion, demonstrated evidence of excellence in WESLEYAN UNIVERSITY mitment to teaching and scholarship at a public teaching, administrative and leadership skills, The Department of Mathematics and Computer liberal arts university. All specialties are welcome, and a record of scholarly activity, and should Science invites applications for the following with special consideration given to candidates enjoy the broad intellectual community offered positions in Mathematics to begin in the aca• who can help develop the department's actuarial by a quality liberal arts college. For additional demic year 2001-2002. Candidates for these po• science minor. Effective teaching, scholarship information please see our web page at http:// sitions must have a Ph.D. in Mathematics and and university/community service are require• www.wabash.edu/depart/math/. Applications, are expected to have strong records in both re• ments for promotion and tenure. Please send a including vita, statement of teaching philosophy, search and teaching. letter of application, CV, unofficial graduate description of scholarly interests, names, ad• transcripts, and three letters of recommendation dresses, and phone numbers of three references Assistant Professor of Mathematics: We seek to: who can address issues of teaching and admin• candidates for two tenure-track assistant profes• istration, should be sent to Robert 1. Foote, sorships, one in analysis and the other in alge• Search Chair Mathematics and Computer Science Chair bra. These positions are most suitable for candi- Department of Mathematics Search, Wabash College P.O. Box 352

25 FOCUS NOVEMBER 2000

Crawfordsville, IN 47933-0352. Applications will values of a diverse university community. Orleans, please indicate if you will be attending. be considered as they arrive, and will be accepted Review of applications will begin on December until the position is filled. Nominations and in• For additional information see http:// 15, 2000, and will continue until both positions quiries may be made by phone, mail, or e-mail faculty.ssu.edu/ -mathcosc/. are filled. to Robert 1. Foote, Mathematics and Computer Science Chair, 765-361-6429, Screening of applications will begin on Decem• Towson University, one of the eleven campuses [email protected] or to Mauri Ditzler, Dean ber 11, and will continue until the position is of the University System of Maryland, and the of the College, 765-361-6224, filled. Applicants should submit a cover letter second largest public institution in the State of [email protected]. Wabash College encour• including a statement of their teaching philoso• Maryland, is a comprehensive university offer• ages applications from women and minorities. phy, a resume, and three letters of recommen• ing Bachelor's and Master's degree programs. EOE. dation to: Towson University has an enrollment of approxi• mately 16,600 students and nearly 900 full-time Dr. Homer W. Austin equivalent faculty. The campus is situated on 328 KANSAS Search Committee Chair acres of beautifully landscaped and wooded BENEDICTINE COLLEGE Department of Mathematics and grounds just north of Baltimore and within 50 Computer Science: Full-time, tenure-track po• Computer Science miles of Washington, DC. sition beginning January or August 2001. Rank Salisbury State University and salary negotiable. Includes teaching intro• Salisbury, MD 21801 Towson University is an equal opportunity/af• ductory programming, upper-division CS, some firmative action employer and has a strong in• lower-division math. Requires an advanced de• Salisbury State University is an Affirmative Ac• stitutional commitment to diversity. Women, gree in CS or equivalent course work with an tion/Equal Opportunity Employer. minorities, persons with disabilities, and veter• advanced degree in math. Teaching experience ans are encouraged to apply. desired. Letter of application, vita, and three ref• TOWSON UNIVERSITY erences to Dr. Jo Ann Fellin, OSB, Chair, Depart• Applications are invited for two entry-level ten• ment of Mathematics & Computer Science, ure-track positions in mathematics, beginning MASSACHUSETTS Benedictine College, 1020 North 2nd Street, in Fall 2001. Applicants must have a Ph.D. in AMHERST COLLEGE Atchison, Kansas 66002. email: mathematics or statistics, and must provide evi• Applications are invited for a tenure-track posi• [email protected]. Applications accepted dence of excellent teaching and an active research tion in Mathematics at the Assistant Professor until position filled. EOE. www.benedictine.edu. program. Preference will be given to applicants level, beginning in August 2001. Amherst Col• in statistics, operations research, or optimization, lege is a private liberal arts college for men and but all specializations will be considered. Appli• women that emphasizes scholarship and excel• MARYLAND cants must have a commitment to teaching a lence in undergraduate teaching. The College has SALISBURY STATE UNIVERSITY variety of courses some of which require the use 1650 students and 165 faculty members. It is lo• MATHEMATICAL SCIENCES POSITION of technology or mathematics across the disci• cated in the valley of the Connecticut River in Applications are invited for one or more tenure• plines. The teaching assignment is nine contact Western Massachusetts. Our environment is en• track Assistant Professor positions, beginning 15 hours per semester. The salary is commensurate hanced by our proximity to the nearby Univer• August 2001. A Master's in mathematics and a with that for an entry-level position. sity of Massachusetts and Hampshire, Mount doctorate in mathematics or mathematics edu• Holyoke and Smith Colleges. cation are required. Candidates from all areas of The Mathematics Department mathematics are encouraged to apply, especially (www.towson.edu/mathl) offers Bachelor's pro• Departmental responsibilities include teaching those with backgrounds in geometry or teacher grams in pure mathematics, applied mathe• a wide range of undergraduate courses and su• preparation. Candidates must have a commit• matics, applied mathematics with computing, pervising undergraduate theses. Faculty are ex• ment to excellence in teaching, scholarly devel• actuarial science, and mathematics education pected to maintain vigorous research programs. opment, and service, and must communicate and Master's programs in applied and indus• Professors teach two courses each semester. effectively in spoken and written English. trial mathematics, and mathematics education. Applicants should hold a Ph.D. in mathematics. The department offers degrees in mathematics Applicants should submit a letter of application, The Department seeks candidates with broad and computer science, and numerous courses to the AMS cover sheet, a resume, a description of intellectual interests, a strong commitment to satisfy requirements for degrees in other areas. research, a statement of teaching experience and excellence in research and undergraduate teach• Successful candidates will demonstrate a com• philosophy, a copy of the graduate transcript and ing, and the ability to develop a research pro• mitment to undergraduate education and a will• have three letters of recommendation address• gram with opportunities for undergraduate par• ingness to teach a broad range of introductory ing both teaching and research sent to: ticipation. Candidates should submit a current mathematics courses as well as an ability to con• curriculum vita, a list of publications, graduate tribute to mid and upper-level offerings for ma• Professor Raouf Boules and undergraduate transcripts, a letter describ• jors. Chair, Mathematics Search Committee ing plans for teaching and research, and three Mathematics Department letters of recommendation. For full consider• Salisbury State University is committed to em• Towson University ation, applications should be completed by De• ployment equity and diversity in the workplace. 8000 York Road cember 1,2000. We especially welcome and encourage qualified Baltimore, MD 21252-0001. minority applicants, women and persons with Amherst College is an Equal Opportunity/Affir• disabilities to apply. Our employment goals are Applications or material sent bye-mail will not mative Action Employer, and encourages to create a workforce from a variety of back• be considered. Because we will have representa• women, minorities, and disabled persons to ap• grounds and experiences that will strengthen the tives at the AMS-MAA Joint Meetings in New ply.

26 NOVEMBER 2000 FOCUS

must provide a document of employment au• begin January 17,2001. Applications accepted Reply to: thorization for the U.S. Persons with disabilities until filled. Completed applications must in• Prof. David Cox, Chair have the right to request and receive reasonable clude resume,(MSU Standard Application Form, Search Committee accommodation. Women and minorities are graduate and undergraduate transcripts, and Department of Mathematics strongly encouraged to apply. three current letters of reference. Apply to Don and Computer Science Mattson, Chair, Mathematics Department, Amherst College See www.msu.edu and www.msu.edulunit/lbs. Moorhead State University, Moorhead, MN POBox5000 56563, (218) 236-2274; fax number: (218) 236- Amherst, MA 01002-5000 MINNESOTA 2168. e-mail queries to: [email protected]. MOORHEAD STATE UNIVERSITY E-mail: [email protected]. Mathematics Department Moorhead State University is an equal opportu• MICHIGAN Moorhead, MN 56563 nity/affirmative action employer and educator. MICHIGAN STATE UNIVERSITY Tenure-track position at rank of assistant pro• Women, minorities, and persons with disabili• Lyman Briggs School fessor to begin August, 2001. A Ph.D. or Ed.D. in ties are encouraged to apply. Assistant/Associate Professor of Mathematics mathematics education is strongly preferred. Michigan State University invites applications for Substantial progress toward a terminal degree is COLLEGE OF SAINT BENEDICT a tenure track, academic year, assistant/associ• required. Eligibility for licensure at some level SAINT JOHN'S UNIVERSITY ate professorship of mathematics position in the K-12 and good communication skills are re• Mathematics Department-Assistant Professor Lyman Briggs School, an undergraduate, residen• quired. Preference will be given to candidates The College of Saint Benedict/Saint John's Uni• tial, liberal arts science program within the Col• with evidence of successful teaching at the K-12 versity seeks candidates for a tenure track posi• lege of Natural Science. Candidates must have a and college level. Interest or experience in teach• tion in mathematics to begin Fall, 2001. The suc• Ph.D. in mathematics, mathematics education, ing a mathematics methods course and evidence cessful candidate must demonstrate a strong or statistics and a research record commensu• of ability to work effectively as a member of a commitment to undergraduate teaching in a lib• rate with an appointment at the assistant or as• teaching team are desired. Duties include teach• eral arts setting and should be prepared to teach sociate professor rank. Preference will be given ing mathematics education methods and con• a wide range of mathematics courses to majors, to applicants with at least five years experience tent courses and undergraduate mathematics minors, and general education students. A Ph.D. and who are particularly passionate about teach• courses. Other responsibilities include advising in the mathematical sciences is required. The ing mathematics to undergraduates. Duties in• students, developing in-service workshops, ser• department has thirteen full-time faculty mem• clude teaching two of the four Lyman Briggs vice to the university and maintaining an appro• bers, is supported by a separately staffed Math• mathematics courses offered each semester and priate level of professional activity. The teach• ematics Skills Center, and graduates approxi• supervising undergraduate teaching assistants. ing load is twelve hours per semester, which may mately 20 majors annually. include supervising student teachers. Screening This position offers exciting opportunities to of applications will begin January 17, 2001. Ap• Saint John's University, a liberal arts college for collaborate with faculty in the Department of plications accepted until filled. Completed ap• men, and the College of Saint Benedict, a liberal Mathematics, the Division of Science and Math• plications must include resume, MSU Standard arts college for women, are located four miles ematics Education, the College of Education, and Application Form, graduate and undergraduate apart in Central Minnesota just outside metro• the Drew Science Enrichment Program on ques• transcripts, and three current letters of reference. politan St. Cloud and 70 miles from Minneapo• tions about the teaching and learning of math• Apply to Don Mattson, Chair, Mathematics De• lis. Both are Catholic colleges in the Benedictine ematics at the undergraduate level. The Briggs partment, Moorhead State University, tradition. Students attend classes on both cam• School environment offers additional opportu• Moorhead, MN 56563, (218) 236-2274; fax num• puses, selecting courses from a common curricu• nities for integrating mathematics with the other ber: (218) 236-2168; e-mail: lum with identical degree requirements. Aca• science courses. [email protected]. Moorhead demic departments are joint and the academic State University is an equal opportunity/affirma• program is coordinated by the Provost for Aca• A complete application package consists of a tive action employer and educator. Women, mi• demic Affairs, with the assistance of the under• cover letter, curriculum vitae, a representative norities, and persons with disabilities are encour• graduate deans on each campus. This partner• scholarly paper, a personal teaching philosophy aged to apply. ship allows each college to offer to its students a statement, a list of undergraduate mathematics co-educational academic experience with ex• courses taught in the last five years, and the MOORHEAD STATE UNIVERSITY panded educational opportunities, while pre• names and addresses of three references, all sent Mathematics Department serving the single sex character and distinct heri• in a single mailing. The material should be sent Moorhead, MN 56563 tage of each institution. Additional information to the Mathematics Search Committee, Lyman Tenure-track position at rank of assistant pro• is posted on our website: http://www.csbsju.edu. Briggs School, Holmes Hall, Michigan State Uni• fessor to begin August, 2001. A Ph.D. in math• versity, East Lansing, 48825-1107. Complete ap• ematics or statistics is required. Preference will All applicants must submit a letter of applica• plications should be received by November 1, be given to candidates qualified to teach courses tion, statement of teaching philosophy, curricu• 2000; later submissions may be considered if in upper division undergraduate statistics, nu• lum vitae, copies of all transcripts, three recent suitable candidates have not yet been identified. merical analysis or mathematical modeling. Pref• letters of recommendation to: Questions should be directed to Ms. Kathie Ellis erence will also be given to candidates with suc• at the above address or (517) 353-6486 or cessful college teaching experience. Duties in• Saint John's University [email protected] clude teaching undergraduate mathematics Human Resources courses, advising students, service to the univer• Box 7188 Michigan State University is an Affirmative Ac• sity, and maintaining an appropriate level of pro• Collegeville, MN 56321-5000 tion/Equal Opportunity Institution. Applicants fessional activity. The teaching load is twelve *Or via email - [email protected] who are not U.S. citizens or permanent residents hours per semester. Screening of applications will

27 FOCUS NOVEMBER 2000

Applications received after December I, 2000 January 2, 2001. To enrich education through cannot be guaranteed consideration. Women diversity, TCNJ is an AA/EOE. http:// DOWLING COLLEGE and people of diverse racial, ethnic, and cultural www.tcnj.edu/-mathstat/. Department of Mathematics and backgrounds are encouraged to apply. The Col• Computer Science lege of Saint Benedict/Saint John's University are NEW YORK Dowling College invites applications for a ten• EEO/AA employers. ure-track position in Mathematics to begin in COLLEGE OF SAINT ROSE September 200 I. Applicants should have a Ph.D. NEBRASKA Tenure Track Faculty Positions or A.B.D. in Mathematics. The teaching load of CREIGHTON UNIVERSITY Computer Information Systems 12 credits per semester may be reduced through Creighton University invites applications for the The College of Saint Rose invites applications research released time. Salary and benefits are Clare Boothe Luce Professorship within the Col• for two tenure track faculty positions beginning very competitive and will be, with rank, com• lege of Arts and Sciences. The position is re• as early as the Spring, 200 I semester. Applicants mensurate with experience. The position is de• stricted by the Clare Boothe Luce bequest to the with a Ph.D. in Computer Information Systems, pendent upon funding. Henry Luce Foundation to women who are U.S. Computer Science or a closely related field will citizens. Creighton University is a Jesuit, Catho• be given preference but other applicants, espe• Dowling College is an Affirmative Action/Equal lic institution that encourages applications from cially those with an M.S. in CS or CIS, will also Opportunity Employer located on the south qualified individuals of all backgrounds who be considered. Faculty members are sought for shore of Long Island, fifty miles from Manhat• believe they can contribute to its distinctive edu• several introductory and intermediate under• tan. A detailed vita should be sent to: Math and cational traditions. The position is for a tenure• graduate courses and advanced graduate courses CSC Search, c/o Human Resources, Dowling track assistant professor in mathematics, statis• in areas such as computer literacy, programming, College, Idle Hour Blvd., Oakdale, NY 11769- tics or computer science. Candidates must have data structures, database management, computer 1999. www.dowling.edu. a Ph.D. prior to chair appointment and a research architecture, graphics, networking and software record commensurate with the expectations of engineering. Responsibilities at the college in• SUNY FARMINGDALE a chair position at this rank. Send letter of appli• clude teaching undergraduate and graduate Anticipated Vacancy for Tenure Track Position• cation, curriculum vitae, transcripts, statement courses; program development and promotion; Fall 2001. The Mathematics Department of of research program and goals, statement of student advisement; participation in college ac• SUNY Farmingdale announces anticipated va• teaching philosophy and three letters of recom• tivities; and active scholarship. cancy of tenure track position of Assistant Pro• mendation independent of the applicant to Luce fessor. Minimum qualifications-Ph.D. in Math• Search Committee Chair, Department of Math• Applicants must submit a current curriculum ematics, Applied Mathematics, Statistics or Op• ematics and Computer Science, Creighton Uni• vita, three letters of recommendation, and gradu• eration Research, at least two years of teaching versity, Omaha, NE 68178-2090. Review of com• ate transcripts. Applications should be addressed experience on the undergraduate level, strong pleted dossiers will begin December IS, 2000 and to Dr. Neal Mazur, Chair, Computer Informa• commitment to teaching of all levels of under• will continue until a suitable candidate is se• tion Systems Department, The College of Saint graduate mathematics. Experience in directing lected. Creighton University is an Affirmative Rose, 432 Western Avenue, Albany, NY 12203. Applied Mathematics student research projects Action/Equal Opportunity employer. Women Applications will be accepted until the positions is preferable. Salary depending on qualifications. and minority candidates are encouraged to ap• are filled. Dr. Mazur may be contacted at Application deadline: must be postmarked no ply. [email protected]. Additional informa• later than January 15,2001. Send resumes with tion about the campus can be found by visiting a brief statement of your teaching philosophy, NEW JERSEY www.strose.edu. The College of Saint Rose is an and the telephone numbers of three references Equal Opportunity, Affirmative Action Em• (no letters of references, please) to Dr. J. THE COLLEGE OF NEW JERSEY ployer. The College encourages applications from Neymotin, Chair of the Search Committee, De• DEPARTMENT OF MATHEMATICS AND women and members of minority communities. partment of Mathematics, SUNY-Farmingdale, STATISTICS: Applications are invited for a ten• NY 11735-102I.AA/EOE. ure track position in Mathematics Education CORNELL UNIVERSITY starting September 2001. The position requires Cornell University Math Department Visitor SUNY POTSDAM a Ph.D. or Ed.D in Mathematics, Statistics or Position Description: The following positions are Assistant Professor of Mathematics: The State of Mathematics Education, demonstrated record of for the Academic Year (August - May): 4 half time New York at SUNY Potsdam invites applications teaching effectiveness, and strong indications of visiting positions for math professors on sabbati• for one anticipated full time tenure track posi• research potential. Responsibilities include ca
/other leaves. Send two teaching references, tion effective September I, 200 I, at the rank of teaching up to 12 hrs./sem, which includes con• CV, proposal for research and/or study program, Assistant Professor. Responsibilities of the posi• tent and methods courses, supervision of stu• and how visit will benefit home institution to tion include teaching twelve hours per semester dent teachers, advising and committee service. Catherine Stevens, 320 Malott Hall, Cornell Uni• of undergraduate and/or first year graduate Preference for a candidate who can collaborate versity, Ithaca, NY 14853-4201. Candidates must courses. Required qualifications are Ph.D. in any with the Center for Inquiry and Design Based possess a Ph.D.; proven excellence in teaching area of mathematics with a strong interest in and Learning, which currently has state and federal and research. Deadline for Applications: Decem• preparation for teaching undergraduate major funding in excess of $3 million for Integrated ber 1,2000. For more info about the position or mathematics courses. Some preference will be Science, Mathematics and Technology Initiatives. institution/company: given to candidates in Algebra, but candidates Experience with in-service teachers preferred. from all areas are encouraged to apply. Applica• Send vita and three letters of recommendation, http://www.math.comell.edu/-math/Job_Opps/ tions, which must include letter of interest, a addressing teaching and research to: Search Faculty/positions.html. Cornell University is an statement ofthe applicant's philosophy ofteach• Committee, Department of Mathematics & Sta• Affirmative Action/ Equal Opportunity Em• ing, a resume, three letters of recommendation tistics, The College of New Jersey, PO Box 7718, ployer. describing teaching experience and abilities, and Ewing, NJ 08628-0718. Application deadline: a transcript (a copy is acceptable) should be sent to: Dr. Cheryl Chute Miller, Staffing Committee

28 NOVEMBER 2000 FOCUS

Chair, Department of Mathematics, SUNY proficiency) sent to: degree in pure or applied mathematics or statis• Potsdam, Potsdam, NY 13676 tics, demonstrated excellence in teaching, and ([email protected]). To ensure full consid• Search Committee evidence of outstanding research potential. eration, complete applications must be received Department of Mathematics Strong consideration will be given to candidates by January 15,2001. SUNY Potsdam is an equal University of Oklahoma whose research interests most closely comple• opportunity, affirmative action employer com• 601 Elm, PHSC 423 ment existing faculty and support a new profes• mitted to excellence through diversity. Norman, OK 73019-0315 sionally based Ph.D. program. Postdoctoral du• ties include teaching one course per term and being an active participant in the initiation of NORTH CAROLINA Phone: 405-325-6711 FAJ{:40S-32S-7484 the new Ph.D. program. MEREDITH COLLEGE e-mail: [email protected] Assistant Professor of Mathematics Further program information is available on the Applications are invited for one, possibly two, Screening of applications will begin on Decem• department's home page, www.mth.pdx.edu. full-time tenure-track position(s) to begin in ber 15, 2000 and will continue until the Qualified applicants are invited to submit an August 2001. Applicants must have a Ph.D. in position(s) is filled. application including (1) a letter of intent in• mathematics and demonstrated excellence in cluding AMS application cover page, (2) a cur• teaching. Experience with technology, innova• The University of Oklahoma is an Equal Oppor• riculum vitae, and (3) three letters of recommen• tive teaching techniques, and/or undergraduate tunity/ Affirmative Action Employer. Women and dation. research is highly desirable. Meredith College is minorities are Encouraged to Apply. OU has a a private comprehensive college of 2600 students policy of being responsive to the needs of dual• Send materials to: offering both liberal arts and professional pro• career couples. Search Committee grams. The College is located near the world• Department of Mathematical Sciences renowned research triangle area in Raleigh, OREGON Portland State University North Carolina. Applications will be reviewed P.O. Box 751 beginning December 15,2000 and continue un• PORTLAND STATE UNIVERSITY Portland, OR 97207-0751 til the position is filled. Send letter of applica• Department of Mathematical Sciences tion, resume, statements of teaching philosophy Mathematics Education Position Review of files will begin February 15, 2001 and and research goals, copies of transcripts, and Assistant or associate professor in mathematics continue until the position is filled. Portland three letters of support to: Dr. Virginia Knight, education, starting September 16,2001. Ph.D. State University is an Affirmative Action/Equal Head, Department of Mathematics and Com• in mathematics education with the equivalent Opportunity Institution. puter Science, Meredith College, 3800 of a masters degree in mathematics, demon• Hillsborough Street, Raleigh, NC 27607-5298. strated excellence in teaching, and evidence of TEXAS Meredith College seeks to increase diversity outstanding research potential. among its faculty and staff. Minority candidates SAM HOUSTON STATE UNIVERSITY are strongly encouraged to apply. Meredith Col• Teach mathematics and mathematics education Mathematics Position lege is an Equal Opportunity Employer. courses, advise students, and direct dissertations Specialty in Mathematics Education in a mathematics education programs includ• The Dept. of Mathematics, Computer Science, OKLAHOMA ing; middle school math graduate certificate; BS/ and Statistics seeks applicants in a tenure-track BA; MST/MAT; and Ph.D. in mathematics edu• position for a specialist in mathematics educa• THE UNIVERSITY OF OKLAHOMA cation. Develop a strong research program in tion. Rank and salary are negotiable. Applicants Applications are invited for one or more full• mathematics education that includes the pro• should have the equivalent of a masters' degree time, tenure-track position(s) in mathematics curement of external funding for research. in mathematics and hold a doctorate in math• beginning 16 August 2001. The position(s) is ematics education or mathematics with an em• initially budgeted at the assistant professor level, See also (http://www.mth.pdx.edu). Application phasis in mathematics education. Preference will but an appointment at the associate professor to include (1) a letter of intent, (2) a curriculum be given to persons having an interest in teach• level may be possible for an exceptional candi• vitae, and (3) three letters ofrecommendation. ing and developing curricula for prospective date with qualifications and experience appro• Send to: teachers. Experience in grant procurement, in• priate to that rank. Normal duties consist of service teacher education, use of technology in teaching two courses per semester, conducting Search Committee the classroom, research and publication are also research, and rendering service to the Depart• Department of Mathematical Sciences desirable qualities. Review of applications will ment' University, and profession at a level ap• Portland State University begin 1 November 2000 and continue until the propriate to the faculty member's experience. P.O. Box 751 position is filled. To apply submit a letter of ap• The position(s) requires an earned doctorate and Portland, OR 97207-0751 plication, full curriculum vitae, transcripts, and research interests that are compatible with those three letters of reference to: Mathematics Edu• of the existing faculty; preference will be given Deadline: December 31, 2000. Portland State cation Search Committee, Dept. of Mathemat• to applicants with potential or demonstrated University is an Affirmative Action/Equal Op• ics, Computer Science, and Statistics, Sam Hous• excellence in research and prior successful un• portunity Institution. ton State University, Huntsville, TX 77341-2206. dergraduate teaching experience. Salary and ben• efits are competitive. For full consideration, ap• PORTLAND STATE UNIVERSITY Sam Houston State University is an EEO/ AAP plicants should send a completed AMS cover Applications are solicited for a possible employer. For additional information on this and sheet, curriculum vitae, a description of current postdoctoral position (max 3 years) as an assis• other positions, access our web site at: and planned research, and have three letters of tant professor in mathematical sciences, start• www.shsu.edu/-hrdwww. recommendation (at least one of which must ing September 16,2001. Applicants must have address the applicant's teaching experience and (or complete by September, 2001) a doctoral

29 FOCUS NOVEMBER 2000

TEXAS CHRISTIAN UNIVERSITY Department of Mathematics Instructorship beginning August 2001. Ph.D. or master's degree in mathematics or statistics is required, as well as documented excellence in teaching. Instructors typically teach four classes per semester. Position is for one-year, but is re• newable indefinitely, provided that the instruc• tor continues to exhibit exceptional abilities in the classroom. A complete application consists of a vita, a statement on teaching experience and philosophy, undergraduate and graduate tran• scripts, and at least three letters of reference with emphasis on teaching.

Texas Christian University is a major teaching and research university of approximately 7,000 students; it is located in the Dallas-Fort Worth metroplex, a vibrant metropolitan area of 5 mil• lion people. TCU does not discriminate in ad• missions or hiring on the basis of religion. Send correspondence to: Search Committee, Depart• ment of Mathematics, TCU Box 298900, Texas Christian University, Fort Worth, TX 76129. Consideration of applications will begin Janu• ary 15,2001, and will continue until the posi• tion is filled. TCU is an Equal Opportunity/Af• firmative Action Employer.

VIRGINIA

EMORY & HENRY COLLEGE Emory & Henry College invites applications for a tenure-track position in mathematics at the undergraduate level, beginning in August, 2001. Doctorate in mathematics or mathematics edu• cation required. Eighteen or more graduate hours in computer science preferred. Possibility of joint Math/CS appointment. A strong com• mitment to undergraduate teaching is essential. Applicants should be able to teach a wide range of courses leading to a bachelor's degree in math• ematics. Emory & Henry College is a small lib• eral arts college in southwest Virginia, related to the United Methodist church, enrolling 1000 stu• dents. Closing date: December 15,2000. Apply with vita, graduate transcripts, three letters of reference and statement of teaching philosophy to Dr. Paul Blaney, Dean of Faculty, Emory & Henry College, Emory, VA 24327. AAlEOE.

Advertising Information The 2000 rates for FOCUS Employ• ment Advertisements are $99.00 per column inch (one inch minimum). Advertisers should contact: Carol Baxter, The Mathematical Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036; (202) 387-5200; fax (202) 265-2384; e-mail: [email protected].

30 a 'J'hc Mathclnatical Association of An~cl·ica

TeBching First A Guide for New Mathematicians Thomas W. Rishel

TlJal!hing Fir~t In this volume Thomas Rishel draws on his nearly forty years of teaching experience A GUIDE FOR NEW MATHEMATICIANS to address the "nuts and bolts" issues of teaching college mathematics. This book is written for the mathematics TA or young faculty member who may be wondering just where and how to start. Rishel opens the readers' eyes to pitfalls they may never have considered, and offers advice for balancing an obligation "to the student" with an obligation "to mathematics." Throughout, he provides answers to seemingly daunting questions shared by most new TAs, such as how to keep a classroom active and lively; how to prepare writing assignments, tests, and quizzes; how exactly to write a letter of recommendation; and how to pace, minute by minute, the "mathe• matical talks" one will be called upon to give.

This book is Rishel's answer to those who may suggest that good teaching is innate and cannot be taught. This he emphatically denies, and he insists that solid teaching starts with often overlooked "seeming trivialites" that one needs to master before exploring theories of learning. Along the way he also covers the general issues that teachers of all subjects eventually experience: fairness in grading, professionalism among students and colleagues, identifying and understanding student "types", technology in the classroom. All of the subjects in this book are considered within the context of Rishel's experience as a mathematics teacher. All are illustrated with anecdotes and suggestions specific to the teaching of mathematics.

Teaching First is a comprehensive guide for a mathematics TA, from the first semester preparations through the unforseen challenges of accepting a faculty position. Its aim is to prepare the new TA with clear suggestions for rapidly improving their teaching abilities.

Catalog Code: NTE-54/JR 155 pp., Paperbound, 2000, ISBN 088385-165-2 List: $19.00 MAA Member: $15.00

Name______Credit Card No. ______Address ______Signature ______,Exp. Date-'_ City______Qty Price $ Amount $______State Zip ______Shipping and Handling $______Phone Catalog Code: NTE-S4/JR Total $______

S/UppiDB and Handling: Postage and handling are charged as foDows: USA orders (shipped via UPS): S2.95 for the first book. and S 1.00 for each [JJ[]u@ITil@~ additional book. Caaadiaa orden: $4.50 for the first book and $1.50 for each additional book. Canadian orders will be shipped within 10 days of receipt of [?c'il~~ order via the futm available mull:. We do not ship via UPS into Canada unI_ the C\lIIOIMr opeciaIIy .equalS this service. Canadian customers who ~c'il~O~ requat UPS shipment will be billed an additional 7% of their total order. o.a-Orden: $3.50 per item ~ for boob sent surface mail Airmail IIftYice is available at a rate of Sl.OO per book. Fo. orden must be paid in US doIIan througb a US bank or !bro. a New York ~ CNdit card anIcn ..., .a:epted Iior aD CUItamen. AD orden muat be prepUd with the aapIiaa ofboab pardIued Iior naIc by boobtora mel wbaIaUen. W1:zen Topology Meets Chemistry Erica Flapan

The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, while learning the role these play in understanding molecular structures. Most of the results that are described in the text are motivated by questions asked by chemists or molecular biologists, though the results themselves often go beyond answering the original question asked. There is no specific mathematical or chemical prerequisite; all the relevant background is provided. The text is enhanced by nearly 200 illustrations and more than 100 exercises. Reading this fascinating book, undergraduate mathematics students can escape the world of pure abstract theory and enter that of real molecules, while chemists and biologists will find simple and clear but rigorous definitions of mathematical concepts they handle' intuitively in their work.

Catalog Code: TPC/JR Contents: Stereochemical Topology; Detecting Chirality; Mobius Ladders and Related Molecular Graphs; Different Types of Chirality and Achirality; Intrinsic Topological Properties of Graphs; Symmetries of 250 pp., Paperbound, 2000 Embedded Graphs; Topology of DNA. ISBn 0-521-66482-9 Ust:S2U5 mRR member: S24.95

Using History to Teach Mathematics Victor Katz, editor

This book is a collection of articles by international specialists in the history of mathematics and its use in teaching, based on presentations given at an international conference in 1996. Although the articles vary in technical or educational level and in the level of generality, they show how and why an understanding of the history of mathematics is necessary for informed teaching of various subjects in the mathematics curriculum, both at secondary and at university levels. Many of the articles can serve teachers directly as the basis of classroom lessons, while others will give teachers plenty to think about in designing courses or entire curricula. For example, there are articles dealing with the teaching of geometry and quadratic equations to high school students, of the notion of pi at various levels, and of linear algebra, combinatorics, and geometry to university students, as well as articles showing how to use historical problems in various courses and one dealing with mathematical anomalies and their classroom use. Although the primary aim of the book is the teaching of mathematics through its history, Catalog Code: nTf-51/JR some of the articles deal more directly with topics in the history of mathematics not usually found in 300 pp., Paperbound, 2000 textbooks. ISBn 088385-163-6 Ust: S32.95 The Mathematical Association of America Periodicals Postage paid at mRR member: S25.95 1529 Eighteenth St., NW Washington, DC and Washington, DC 20036 additional mailing offices

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