Memories of Arnold Ross

January 2003 FOCUS

1 FOCUS January 2003

FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, FOCUS August/September, October, November, and December. January 2003 Editor: Fernando Gouvêa, Colby College; [email protected] Volume 23, Number 1 Managing Editor: Carol Baxter, MAA 4Remembering Henry L. Alder (1922-2002) [email protected] By Gerald Alexanderson Senior Writer: Harry Waldman, MAA [email protected] 7Lowell W. Beineke Named Editor of The College Please address advertising inquiries to: Mathematics Journal Carol Baxter, MAA; [email protected] President: Ann E. Watkins, California State 8A Year in the Life of the MAA: The Statistics University, Northridge By Ann Watkins First Vice-President: Carl C. Cowen, Second Vice-President: Joseph A. Gallian, Secretary: 10 NSF’s Advanced Technological Education Program Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: John W. Kenelly By Victor Katz Executive Director: Tina H. Straley 12 NSF Beat: Opportunities at the National Science Foundation Associate Executive Director and Director of Publications and Electronic Services: By Sharon Cutler Ross Donald J. Albers FOCUS Editorial Board: Gerald 13 Report: 14th General Assembly of the International Alexanderson; Donna Beers; J. Kevin Mathematical Union Colligan; Ed Dubinsky; Bill Hawkins; Dan By Harry Waldman, based on a report by Donald G. Saari Kalman; Peter Renz; Annie Selden; Jon Scott; Ravi Vakil. 14 Short Takes Letters to the editor should be addressed to Fernando Gouvêa, Colby College, Dept. of Mathematics, Waterville, ME 04901, or by 15 Letters to the Editor email to [email protected]. Subscription and membership questions 17 Memories of Arnold Ross should be directed to the MAA Customer By Glenn Stevens Service Center, 800-331-1622; e-mail: [email protected]; (301) 617-7800 (outside 18 Being a Mathematics Educator in a Department of Mathematics U.S. and Canada); fax: (301) 206-9789. Eileen Fernandez Copyright © 2003 by the Mathematical Association of America (Incorporated). On the cover: Lake Fibonacci is a recently created reservoir at the Maryland Science and Educational institutions may reproduce articles for their own use, but not for sale, Technology Center, located in Bowie, MD. The lake's remarkable centerpiece is a mas- provided that the following citation is used: sive, yet elegant fountain that spurts water as high as 36 feet into the air. Created as a “Reprinted with permission of FOCUS, the mathematical sculpture by artist and mathematician Helaman Ferguson, the fountain is newsletter of the Mathematical Association made up of more than 45 tons of Texas granite, layered in alternating colors and rising to of America (Incorporated).” a height of 18 feet. It is supported by a concrete and steel platform atop pilings pounded 40 feet into the lake floor. For more on Lake Fibonnaci see Ivars Peterson's Oct. 21, 2002 Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: MathTrek column on MAA Online at http://www.maa.org/mathland/ Send address changes to FOCUS, mathtrek_10_21_02.html. Photograph courtesy of Helaman Ferguson. Mathematical Association of America, P.O. Box 90973, Washington, DC 20090-0973. FOCUS Deadlines ISSN: 0731-2040; Printed in the United States of America. May/June August/September October Editorial Copy March 15 July 8 Display Ads March 25 July 10 August 20 Employment Ads March 11 June 11 August 13

2 January 2003 FOCUS Arthur Benjamin and Jennifer Quinn Named New Editors of Math Horizons

Arthur Benjamin, of students. In 1993, she Harvey Mudd College, joined the faculty at and Jennifer Quinn, of Occidental College in Occidental College, Los Angeles where she have been selected as currently chairs the the new editors of Math mathematics de- Horizons, beginning partment. with the September 2003 issue. Their term Quinn has served as will last five years. Newsletter Editor for the Southern Cal- Professor Benjamin Jennifer Quinn Arthur Benjamin ifornia Section of the earned his B.S. in MAA, is an Associate Applied Mathematics Editor for Math- from Carnegie Mellon and his PhD in for Fibonacci numbers. In addition to ematics Magazine, and is completing her Math-ematical Sciences from Johns spending time with his wife and two sixth and final year on the board of the Hopkins. Since 1989, he has taught at daughers, he enjoys tournament Spectrum book series. In 2001, she was Harvey Mudd College, where he is backgammon, racing calculators, and honored to receive the Distinguished currently Chair and Professor of performing magic. Teaching Award for the Southern Mathematics. He has served as Editor of California section of the MAA. Her the Spectrum book series for MAA, and Jennifer Quinn truly feels as if she has research interests include combinatorial currently serves on the editorial boards led a charmed life. She had the privilege proof, graph theory, and combinatorial of Mathematics Magazine and the UMAP of earning a B.A. from Williams College, matrix theory. Other pursuits include Journal. In 2000, he received the MAA’s an M.S. from the University of Illinois, too much committee work, home Haimo Award for Distinguished College Chicago, and a Ph.D. from the University renovations, and raising a beautiful and University Teaching. His research of Wisconsin, Madison. She cannot millennium baby boy. interests include game theory and imagine a professional career that doesn’t combinatorics, with a special fondness include doing mathematics and teaching

CBMS Announces 2003 Regional Research Conferences

The Web of Modularity very year, the Conference Board of the University of Memphis E June 3–7 Mathematical Sciences (CBMS) and the http://troy.msci.memphis.edu/cbms University of Illinois at Urbana- National Science Foundation (NSF) Champaign sponsor Regional Research Conferences Free Boundary Problems in Partial Differ- in various areas of mathematics. The ential Equations and Applications http://www.math.uiuc.edu/cbms/ conferences are intended to stimulate in- May 18–22 Fully Nonlinear Equations in Geometry terest and activity in mathematical re- Wayne State University June 23–27 search. Each lasts five days. About 30 http://www.math.wayne.edu/~gzlu/cbms/ University of Notre Dame funded participants are invited to each cbms.html conference, ranging from established re- http://www.nd.edu/~cbms/ searchers to graduate students and other Stochastic Partial Differential Equations See newcomers to the field. Five conferences and their Applications http://www.cbmsweb.org/NSF/ for more information. will be offered this year: May 19–23 2003_conf.htm Illinois Institute of Technology CBMS is also calling for proposals for conferences for next year; see Expansion Methods in Combinatorics http://www.iit.edu/~duan/SPDE.html http:// May 13–17 www.cbmsweb.org/NSF/2004_call.htm.

3 FOCUS January 2003

Remembering Henry L. Alder (1922-2002)

By G. L. Alexanderson

If one were asked, “ Who would be best R. Ford Award for Expository Writing for described as representing the MAA?”, the his beautiful article, “Partition Identi- name that would leap to mind is, “Henry ties—from Euler to the Present,” that ap- Alder,.” From 1956, when he was elected peared in the American Mathematical Chair of the Northern California Section, Monthly in 1969. This work described a until his death, Henry was given one sig- broad range of ideas in partition theory, nificant responsibility after another in the and “Present” in the title included work Section and at the national level. He per- from some of his own research papers in formed these tasks splendidly, always con- the Bulletin of the American Mathemati- scientiously and carefully, with meticu- cal Society and the Pacific Journal of Math- lous attention to detail, and showing wis- ematics. Certain generalizations of the dom, diplomacy, and tact. He truly be- Rogers-Ramanujan identities involve lieved in the importance of the work of what are now called Alder polynomials. the Association. Through his many years When he published that paper in the of tireless service and his inviting others Monthly the editor, Harley Flanders, into the profession through his collegial- wrote that Henry has probably contrib- ity and mentoring, Henry Alder personi- uted more than anyone else to the present fied the spirit of the MAA. Sadly for the vitality of this Association.” The same MAA, his family, colleagues, and friends, could be said today. Henry died of cancer on November 6, 2002, at the age of 80, at his home in Henry L. Alder Henry Ludwig Alder was born in Davis, California. Duisburg, Germany on March 26, 1922, happened. He chaired the Committee on but with Swiss citizenship. He and his Between 1960 and 1975, he was the na- the Deborah and Franklin Tepper Haimo family moved to Zürich in 1933 where he tional Secretary of the MAA, and in rec- Awards for Distinguished College or Uni- finished school and started his college ognition of that outstanding service, he versity Teaching of Mathematics and is education at the Eidgenössische was designated Secretary Emeritus, the largely responsible for the successful Technische Hochschule. In 1941 he trans- only person in MAA history to be so hon- implementation of that important pro- ferred to the University of California, ored. A few years later he was elected na- gram, funded through an endowment Berkeley, where he received his B.A. in tional President for 1977-78. In 1960 he from another former MAA President mathematics and chemistry in 1942. He had been approached by Carl Deborah Tepper Haimo. He chaired the remained at Berkeley, with the exception Allendoerfer, then President of the MAA, first committee on the Sliffe Awards and of service in the U.S. Army Air Corps in about being nominated for Secretary. He was largely responsible for the formula- 1944-45, and wrote a dissertation under asked what the principal responsibilities tion of that program by which we reward the direction of the eminent number would be. Allendoerfer told him that it teachers of the most successful teams par- theorist, D.H. Lehmer, competinlg his was largely the care and feeding of Presi- ticipating in the American Mathematics Ph.D. in 1947. After one year as an in- dents. Henry took that admonition seri- Competitions. Other committees Henry structor at Berkeley, he moved to the ously, but at the same time he realized that chaired most effectively include the University of California, where he re- the Secretary has the potential for mov- Gung-Hu Committee (the group that mained until his retirement, except for a ing an organization along. The Secretary each year nominates the winner of the sabbatical in Zurich. At Davis he was a can hold the office for a significant pe- Distinguished Service Award), the Coun- renowned teacher, both in his own field riod of time and provides the institutional cil on Awards, and the Committee on the of number theory but also in statistics, memory of the organization. Presidents 25-Year Member Banquet. an area in which he and his colleague, come and go, but the Secretary often stays Edward B. Roessler, wrote a successful on. There is scarcely any aspect of MAA ac- textbook that ran through six editions. tivities that has not been touched by On his own campus he served as depart- Secretary and President were only the Henry’s sage counsel and good judge- ment chair, and chair of various commit- most visible offices that Henry Alder held ment. In 1980 he received the tees, including one on minority under- in the MAA. He served on innumerable Association’s most prestigious prize, the graduate research participation, another MAA committees over the years, and Award for Distinguished Service to Math- on culturally disadvantaged students. when he was chair of a committee, things ematics. Earlier he had received the Lester Statewide, he chaired the Board of Ad-

4 January 2003 FOCUS missions and Relations with Schools of self was an exceptionally able speaker, and the University of California system, according to reports from his students, When asked why the Northern Califor- among others. an inspiring teacher. A colleague of mine, nia Section of the MAA has been so suc- as an undergraduate at Davis, took four cessful, he immediately responded that Professor Alder served mathematics courses in number theory from Henry there are four reasons (as usual, the re- across a wide range, from school math- and says of his teaching, “Henry had the sponse was spontaneous, but still the ar- ematics through research. For the Pacific ability both to awe students and put them guments were numbered): (1) a strong Journal of Mathematics, he served on its at ease at the same time. His presence Secretary-Treasurer; (2) a good represen- Board of Governors from 1960 to 2002 would fill the room and his humor, his- tation of different kinds of schools—a and, from 1970 on he was Chair of its In- torical anecdotes and charming phrases rotating system for choosing meeting sites vestment Committee. His interest in kept all of us at the edge of our seats. He and officers, through research universi- school mathematics resulted in his ap- had an uncanny knack for teaching stu- ties, comprehensive state universities, lib- pointment to the California State Board dents how to write good proofs, both by eral arts colleges, two-year colleges, and of Education, the first mathematician and his beautiful examples as well as by his industry [a practice probably due to first UC faculty member to receive such clear hints that made proof-writing seem Henry’s influence]; (3) high quality an appointment. Another indication of speakers, chosen for their ability to reach the great range of his interests was his an audience; and (4) an executive board service as chair of the Council of Scien- where past officers stay on after their tific Society Presidents in 1980, and from terms of office and continue to contrib- 1956 to 1959 he was the first national ute, thus assuring continuity. He always president of Mu Alpha Theta, the national reminded his colleagues that at an MAA high school and junior college mathemat- meeting, a lecture should be given for the ics club. I could give more examples of benefit of the audience, not the benefit his many areas of service to mathematics of the speaker. Up to the last year or so, and to education; the list is long. Henry attended almost every Section Ex- ecutive Board meeting, and when the Those who knew Henry Alder well always Section’s annual meeting was held in marveled at how organized he was. With Davis last March, Henry was the person an incredible memory he could call up in charge of local arrangements. It was precedents and procedures like few oth- an enormously successful meeting, a ers. Subsequent MAA secretaries came to tribute to Henry’s planning and consci- rely on Henry for advice on the handling entious attention to detail. In 1998 the of bylaws changes, responding to legal Sectional Certificate of Meritorious Ser- questions on incorporation, and such. He vice was given to Henry at the Baltimore was a master of Robert’s Rules of Order. meetings. It was appropriate that he was If someone was planning to take a pro- recognized in this way for his contribu- posal to the MAA’s Board of Governors, tions to the Section, even well after he it was wise to be prepared for Henry’s had received the Award for Distinguished analysis. If he approved of the proposal Service at the national level. he would come up with a set of argu- Henry Alder served as president of the MAA ments (numbered of course) as to why from 1977-78. This photograph hangs in Henry was a person of absolute probity, he favored the proposal. On the other the stairwell of the MAA headquarters. It always fair to his colleagues and gener- hand, one had to be prepared for a com- is part of a gallery of portraits of MAA ous with his time. In all my years of work- parable list, seemingly thought out after presidents. ing with him on many committees and considerable study, of all the reasons this boards, I never heard him speak harshly same proposal was a bad idea. of a colleague. On a proposed course of easy. Henry inspired me to become a action he could be forceful in putting In the Northern California Section he was number theorist and I strive to live up to forth his arguments, but they were never responsible for procedural guidelines his example today.” In 1976 he won the ad hominem. He never spoke in a mean- enunciated early on but still used by the UC Davis Award for Distinguished Teach- spirited way. He was serious, always sin- officers today—for example, the “Alder ing. In 1999 he endowed a fund in the cerely promoting what he was convinced Rule”, now extended to our national UC Davis Mathematics Department that was good for the organization, but he was meetings, that says, “Don’t invite a will support a $2000 prize each year to not without humor. Ken Ross reports that speaker for a meeting program unless the mathematics graduate student when he was elected Secretary of the someone on the program committee has deemed to be the best teacher. Additional MAA in 1983, Henry was “the first per- heard the speaker and can vouch for the revenue from the fund will be used to son to congratulate [him]” and then went quality of his or her exposition.” He him- enhance undergraduate teaching. on to emphasize that “as Secretary, [Ken]

5 FOCUS January 2003 would have a great deal of power and honored teacher, and a man who has pointed out that Lenin was Secretary of made unparalleled contributions of time the Communist Party, never President.” and energy to the professional activities of mathematicians.” Henry’s manner of dealing with people set the tone for relations between MAA We can say the same today after more officers, board members, and Washing- than forty years. We shall miss him. ton office staff that, I think, still prevails— one of civility and of concern for the feel- Let me close on a very personal note. ings of one’s colleagues. He has left a last- Henry was responsible for my becoming ing mark on the quality of this great or- involved deeply in the activities of the ganization. When he received the Distin- MAA. I always thought of him as a men- guished Service Award in 1980, the cita- tor. When I became MAA Secretary and tion included the following: “He has had later President, when faced with a prob- tremendous and profound influence on lem I always thought, “What would all of mathematics, and more than any Henry do?” I felt I was attempting to carry other person, he has charted the course on, in some small way, the work that he of the Mathematical Association of had done so well. America for the past twenty years.” There are mathematicians who have added Henry Alder served as secretary to the MAA He is survived by his wife Benne, who is greatly to mathematics through their re- from 1960-1975. This photograph is dis- a professional actress; a son and daugh- search activities. Still others have contrib- played on the second floor of the MAA head- ter-in-law, Lawrence and Janice Alder; uted through their teaching. Finally, some quarters building, together with portraits of two granddaughters, Allison and mathematicians are willing and energetic other MAA secretaries and treasurers. Catherine; two brothers and other fam- workers on behalf of the professional or- ily members. ganizations. But there are few among us who fill all three of these roles. Thus it is Gerald L. Alexanderson has been both Sec- appropriate that we today honor Profes- retary and President of the MAA. sor Henry L. Alder, an able researcher, an

6 January 2003 FOCUS Lowell W. Beineke Named to Be Editor of the College Mathematics Journal

Lowell Beineke, Schrey Professor of Beineke says that if forced to give up one Throughout his career, Beineke has Mathematics at Indiana University- or the other, he’s not sure which it would participated in many MAA activities, Purdue University, Fort Wayne, Indiana, be, although the day-to-day teaching regularly attending national and section has been selected as the new editor of the would probably win out. His favorite meetings. He has served as both College Mathematics Journal, beginning President and Governor of the Indiana with the January 2004 issue. He will serve Section, and is currently the liaison for for five years. his department and Advisor to the IPFW Student Chapter (one of the Charter Beineke joined the MAA when he was Chapters). Among his honors, he is awarded a membership as a student at proud to have received both the Dis- Purdue in the early 60s. Following tinguished Teaching and Distinguished graduation, he attended the University Service Awards from the Indiana of Michigan, from which he received his Section. doctorate in 1965. He then joined the faculty of Purdue at the Fort Wayne He is pleased to have this opportunity campus (now IPFW), where he has spent to edit the College Mathematics Journal his entire professional career, moving and will try his best to maintain its through the ranks and being awarded the excellence as a vehicle for the Schrey Professorship in 1986. Five years dissemination of mathematics for of that have been spent in England, college educators. including one on a Fulbright Exchange at the (then) Polytechnic of North Lowell W. Beineke “I am excited,” he said, “by the challenge London and three sabbaticals at the of the position, but also recognize that Oxford University Mathematical if the MAA goals for the CMJ are to be Institute. Lowell W. Beineke met, it will require the assistance and cooperation of many, many others. So, Beineke’s research has been in graph along with the other editors, I ask you theory. His thesis was on the thickness to please submit not only appropriate of graphs and was written under the articles, but also ideas and suggestions for supervision of Frank Harary. He is articles and authors. With your author of just over a hundred papers in cooperation, the excellence of the MAA the field; some of his favorite areas are journals will continue without topological graph theory, connectivity, interruption.” tournaments, line graphs, and multi- dimensional trees. He and Robin Wilson In addition to his mathematical and of the Open University have written and university lives, Beineke’s interests edited five books on graph theory, the include gardening, reading, running, most recent being Graph Connections, cryptic crosswords, and travel. He and his a collection of chapters relating graph English wife Judith have two children: the theory to various other areas of older, Jennifer, is an Assistant Professor mathematics. He referees numerous of Mathematics at Western New England papers every year and serves on the College, while her younger brother, Editorial Board of the Journal of Graph Philip, is a graduate student in statistics Theory. at Stanford.

Although IPFW does not award doctorates, he has supervised four theses, three at Purdue West Lafayette and one courses to teach are graph theory (of at Western Michigan University. These course), geometry (including non- opportunities have provided one of the Euclidean), foundations of higher math, links between his teaching and research. math history, and calculus (definitely!). While complementing one another, the two activities also compete for time.

7 FOCUS January 2003 A Year in the Life of the MAA: The Statistics By Ann Watkins

A Year of Publications Number of members of largest SIGMAA (RUME): 1264

American Mathematical Monthy Number of new outside grants funded: 14 Total number of pages: 945 Total value of funded grants: $2,330,832 Number of manuscripts submitted: 719 Number published: 103 Number of professional development workshops: 8 Number of people who refereed manuscripts: ~ 300 Number attending: 224

Mathematics Magazine Number of U.S. citizens receiving Ph.D.s in mathematics: 532 Number of manuscripts submitted: 282 Number of new Project NExT Fellows: 71 Number published: 60 Number of Fellows so far: 626 Number of referee reports requested: 321 Percentage received: 88% A Year of Programs for Undergraduates

The College Mathematics Journal Number of junior and senior mathematics majors: 58,900 Number of CMJ authors: 77 Number of undergraduates who are MAA members: 1,199 Number of CMJ referees who, on being asked what was hap- Number of undergraduates who receive Math Horizons: 17,000 pening with the paper they had been sent ten weeks ago, replied Number taking the Putnam exam: 2,954 that they had not looked at it, were not planning on looking at Number of active Student Chapters: 173 it, and didn’t know that they needed to tell anyone about that: 1 Number of students attending MathFest: 193 Number of new books published by the MAA: 23 Number of papers they presented: 107 Number of those that are all-electronic: 1 Number of mathematicians attending MathFest: 908 Average number of MAA books sold per month on Number of papers they presented: 116 amazon.com: 385 A Year of the American Mathematics Competitions Average number of visits to MAA Online per day: 4,637 Average number of pages hit per visit: 12 Number of 8th grade and below students participating in the AMC 8: 169,654 Number of articles published last year in MAA journals by MAA Number of 12th grade and below students participating in the president: 1 AMC 12: 136,714 Number of expository writing awards received by MAA presi- Number of students participating in the USA Mathematical dent: 0 Olympiad: 325 Number who came to Cambridge to take the USAMO: 202 A Year of Membership Number of students participating in the Mathematical Olym- piad Summer Program: 178 Number of full-time and part-time two-year college, four-year college, and university mathematics professors: 48,015 Rank of the U.S in the International Mathematical Olympiad.: Total MAA membership: 32,558 3 out of 84 Number of gold medals presented at the IMO: 39 Number of individuals who contributed to the MAA: 1,391 Percentage won by U.S. team: 10% Average contribution: $123.89 A Year of Governance Number of MAA staff members: 35 Ratio of members to staff: ~q 930/1 Number of pages in nine issues of FOCUS: 280 Ratio for the AMS: ~ 180/1 Number of pages in agendas for two Board of Governor’s meet- Ratio for SIAM: ~ 148/1 ings: 241

Number of full-time graduate students in mathematics: 26,168 Number of members in largest MAA section Number of graduate students who are MAA members: 2,419 (Southeastern): 2065 Number of members in smallest MAA section A Year of Programs for Members (Intermountain): 164 Number of governors representing Southeastern Section: 1 Number of new SIGMAAs approved: 3 Number of governors representing Intermountain Section: 1

8 January 2003 FOCUS

Number of e-mails sent by the MAA president: 2817 A Year of Complaints to the MAA President

A Year of Section Meetings Complaints about the letter from the MAA president asking people to give money to the MAA in their will: 2 Number of section meetings: 38 Complaints about the letter asking people to give money be- Average attendance per meeting: 144 fore they die: 0 Average number of students per meeting: 41 Average number of two-year college faculty per meeting: 10 Number of e-mails complaining that the MAA president didn’t Largest attendance at a section meeting (Texas): 301 respond to a previous e-mail that requested no further com- Largest percentage of members attending a section meeting munications from the MAA: 1 (Mississippi-Louisiana): 51% Largest number of student papers at a section meeting Most common complaint (having to speak on the same pro- (Ohio): 38 gram as Pólya lecturer Ed Burger): 4 Number of times Pólya lecturer Ed Burger spoke at section meetings: 6 A Year of Thank-Yous Number of chicken dinners eaten by MAA president at section meetings: 7 I receive many letters and emails thanking me for the work that Number of blue-grass bands heard by MAA president at the MAA does. Often these come from high school students section meetings: 1 grateful for their experience with the American Mathematics Competitions or from retired members who enjoy their jour- A Year of National Meetings nals even more now that they actually have time to read them. I would like to add my thank-you to all of you for your dedica- Total attendance at winter meeting in San Diego: 4665 tion and hard work towards advancing the mathematical sci- Number who were students: 717 ences and for making the two years I’ve served as president pro- Number of panel discussions: 50 ductive ones for the MAA.

Total attendance at MathFest in Burlington: 1239 Number of minutes the MAA president enjoyed her job in the Number of states represented: 47 last year: 525,600. Number of foreign countries represented: 10 Percentage change in MathFest attendance in six years: +62% Ann Watkins’ term as MAA President ends after the January 2003 Percentage change in NASDAQ over same period: -22% Joint Mathematics Meetings.

Corrections

1) The article in our December issue on Manjul Bhargava’s ap- 4105264352⋅ ⋅⋅ + ⋅⋅⋅6432264325+ ⋅⋅⋅ + ⋅⋅⋅, pearing in the Popular Science list contained two unfortunate errors. First, Bhargava’s thesis was not about the “Fifteen Theo- respectively. rem.” Second, the article’s title suggests that the “Fifteen Theo- rem” was the major reason for Bhargava’s selection as one of 3) In the article on Heron’s formula in the November issue, the “Brilliant Ten.” That is, of course, incorrect: the selection the volume of the tetrahedron with base 1, 1, 1 and slant heights was based on all of Bhargava’s work so far. 2,22 , should be 5/12 not 56/ . (Corrected by the author and Peter Ross.) 2) In the article on Fibonacci’s Liber Abbaci in the November issue, a typesetting error introduced extra plus signs and el- We regret the errors. lipses into two of the formulas on page 7. They should read

517105⋅⋅⋅+ 5410⋅⋅ ⋅5+ 5435⋅⋅⋅+ 5432⋅⋅⋅ and

9 FOCUS January 2003 NSF’s Advanced Technological Education Program

By Victor J. Katz

Which NSF educational program is experiences. Furthermore, prospective The Community College of Philadelphia the main source of outside funding for teachers at Green River spend many (CCP), which has a strong program in projects developed by community col- hours on Saturdays and in the summer elementary mathematics, is using ATE leges, supports improved education for working with local 4th grade students in funds to develop a new degree option for the high-technology industries that are mathematics, thus gaining valuable expe- students planning to be secondary math- so crucial to our nation’s economy, and rience. One of the reasons that students ematics teachers. As part of this process, helps fund the creation of math curricula attend community college is location near CCP is expanding its articulation agree- for at least half of the nation’s prospec- the student’s home and the low cost. Since ments with many Philadelphia-area four- tive elementary school teachers? The an- these reasons often still apply after a stu- year colleges, so that students can swer is the Advanced Technological Edu- dent has completed two years, Green seamlessly transfer into a Baccalaureate cation Program (ATE). This program, River has arranged with Central Wash- program. Two basic courses being devel- established in 1992, has made grants that ington University for the latter to conduct oped for the program are Teaching with have had an enormous effect in increas- junior and senior level courses on its cam- Technology and Problem Solving in Math ing the technical competencies of thou- pus to make it as convenient as possible and Science. CCP graduates in this pro- sands of students in community colleges for students to complete their teaching gram will thus be expected to be experts all around the country. degrees. And since the students’ field ex- in the use of teaching technologies and periences are at nearby schools, the also have a large repertoire of problem The ninth annual National ATE Princi- project has found that once students have solving strategies. In order to recruit and pal Investigators Conference was held in completed their degrees, they tend to get retain students in the teaching program, Washington on October 24-26, 2002. jobs in the immediate area, helping these CCP is developing an innovative market- Entitled “Assessing the Impact,” the schools to get high quality teachers with ing strategy with the School District of conference’s goals were to demonstrate a strong mathematics and science back- Philadelphia in order to promote the pro- how these grants have succeeded in their ground. gram at college fairs. It also is creating mission over the years. Many of the cur- customized systems of advising and rent projects had booths in the exhibit Prince George’s Community College mentoring to help insure that students hall where they displayed some of their (PGCC), in Maryland, is leading a simi- complete the program. (Contact: Marcia work and had a chance to share their ideas lar effort to develop and implement sci- Epstein, [email protected]). with others. We will report here on some ence and mathematics courses for of the projects, and suggest that you con- preservice elementary teachers in Although the projects above have limited tact the Principal Investigators or check Maryland’s community colleges. In par- components dealing with the training of the web sites of the projects of most in- ticular, the college is working with community college faculty to prepare terest to find out how you can either join Maryland’s four-year colleges to insure prospective schoolteachers, two national with them or begin to replicate some of that students with the new Associate of organizations have ATE grants specifically their ideas. Alternatively, if some of the Arts degree in teaching will be able to designed for this purpose. The American ideas here spark some new ideas of your transfer easily to any of those colleges to Mathematical Association of Two-Year own, you should take the opportunity to complete their degree. The courses at Colleges (AMATYC) is conducting a submit proposals to the ATE program PGCC, like those at Green River, have a project entitled Teacher Preparation, yourselves. constructivist and inquiry-based flavor, Mathematics and Technology: A National based on materials developed through the Dialogue. One major component of this Project TEACH, centered at Green River Maryland Collaborative for Teacher project has been a series of regional con- Community College in Auburn, Wash- Preparation and consistent with NCTM ferences addressing the mathematics and ington (Their website address: http:// and NCATE Standards. The faculty at technological preparation of prospective www.projectteach.org; email address: PGCC is also working with local high K-8 teachers at two-year colleges as well [email protected]), is a collabo- schools to recruit students into the pro- as the broader issue of two-year college rative effort with Central Washington gram. Interestingly enough, given that the involvement in teacher preparation. University and six nearby school districts. need for math and science-trained teach- These conferences addressed current re- Not only has the project developed new ers is expected to be larger over the next search results in mathematics pedagogy, course materials for prospective K-8 decade than the capacity of Maryland’s held dialogues on the mathematics that teachers, materials which emphasize four-year colleges, plans are underway to prospective teachers should know, and problem solving and the use of technol- develop four-year teaching programs at discussed issues of course creation and ogy, but it is also working hard to recruit some of the community colleges them- articulation with four-year institutions. talented students into teaching and to selves. (Contact: Patricia Basili, But AMATYC also conducted two very provide practical and diverse early field [email protected]). successful workshops in the summer of

10 January 2003 FOCUS

2002 designed to help teachers at two- styles to meet the program’s goals. Thus ics courses for the various technical pro- year colleges work with prospective el- their teaching of technical mathematics grams cover the standard topics of tech- ementary and middle school teachers. is far different from what it used to be. nical mathematics over a two-year period, These workshops will be repeated at other They are working more closely with the the topics are all taught in relation to rel- locations in the summer of 2003. In ad- technology teachers, and teaching the evant problems. NJCATE is also working dition, with the experience gained in necessary mathematical skills when and with a local school system to help them these workshops, AMATYC will begin in as they are needed for solving important develop integrated technical high school March, 2003 to conduct Traveling Work- technology problems. With some flex- curriculum units based on their own shops in Teacher Preparation. Thus, you ible scheduling, so that more mathemat- model. can ask AMATYC to come to your cam- ics can be taught one week if needed and pus to help your faculty deal with issues less another week, the students are more Many other ATE projects are developing in preparing teachers. For more informa- engaged in the mathematics when it is new curricular materials to go along with tion, check the website http:// taught and are becoming more capable the project-centered approach to teach- amatyc.dtcc.edu. of using it at the appropriate time. The ing mathematics, whether in mathemat- teachers too are more enthusiastic. One ics courses themselves or in interdiscipli- Another national project is being con- told me that she had been virtually nary programs. For example, Capital ducted by Phi Theta Kappa, the honor burned out by teaching for several years Community College in Hartford, CT, in society for community colleges. The in a traditional style with indifferent re- cooperation with the Kennedy Space project, Preparing Tomorrow’s Science sults. Now, she is energized. Her students Center and AMATYC, produced two vol- and Math Teachers: The Community are succeeding at a much higher rate, and umes of Mathematical Explorations, all College Response, involves teams from she is very pleased with the outcomes. based on NASA space activities, to be used seven community colleges with exem- She has seen numerous students whose in various mathematics courses. For ex- plary teacher preparation programs initial reaction to mathematics was ample, the first Laboratory Technical Ac- mentoring colleagues at an additional “avoidance” being turned on by the sub- tivity in the first volume is entitled “Spare eighteen colleges. The mentoring teams, ject, and she has also seen students with Parts of the Space Shuttle.” There are consisting of a community college edu- low self-esteem have their horizons raised 250,000 parts on a shuttle, some of which cator and a four-year college faculty to the point that they are finding excel- are repairable and some of which are remember, are helping these eighteen col- lent technical jobs with their hard-won placed once they wear out. Decisions leges replicate or adapt the knowledge, skills. One of the goals of the program is must be made as to how many spares experience, and materials already devel- to spread the teaching philosophy should be on hand, either on the ground oped via site visits, conferences, and in- throughout the South Carolina commu- or on the shuttle, and when to order re- teractive technologies. They will soon be nity college system. So the lead math placements, especially of very expensive able to disseminate these activities na- teachers in the project are serving as men- parts, based on a probability of suffi- tionally. Interestingly, among the seven tors throughout the system, to improve ciency equation. The activity, designed to “exemplary” programs are the three com- technical education all over the state. be worked on by a team, requires algebra munity colleges whose projects are dis- They welcome inquiries from other states and precalculus skills, some of which will cussed above. (Contact: Diane Eisenberg, as well. (Contact: Lynn Mack, probably be developed as the activity is [email protected]). [email protected]). being used. Capital College is also pro- ducing a new series of books entitled Among the most enthusiastic ATE Another highly successful ATE Center is Mathematical Journeys, which consist of awardees is the group of faculty from the New Jersey Center for Advanced Tech- Laboratory Activities designed to be used South Carolina involved in the South nological Education, whose main office either in an interdisciplinary course or an Carolina ATE Center of Excellence, is at Middlesex County College, (http:// interdisciplinary club. For example, there mainly from Piedmont Technical College www.njcate.org). A key to their success is a lab entitled “I’ve Got Your Number,” and Florence-Darlington Technical Col- has been the partnerships they forged which explores several aspects of the cel- lege (http://scate.org). The goal of the cen- with corporations in New Jersey. These lular phone industry. The mathematics in ter has been to increase the quality, quan- partnerships allowed them to develop this laboratory includes geometry of tity, and diversity of South Carolina en- new programs that insured the employ- circles and polygons, graphing tech- gineering technology graduates, and it is ability of their graduates. Just as in South niques, introductory statistics, and piece- succeeding in its goals. The emphasis in Carolina, they used an integrated curricu- wise functions. Mathematical Journeys the new courses developed for the pro- lum model, in which the teaching of contains detailed instructions on how to gram is problem-solving, and the initial mathematics, among other subjects, was create a course out of the materials, with evaluation of the program shows that stu- project centered. In particular, they de- guides as the types of mathematical skills dents graduating in it are far more confi- veloped “just-in-time” methods of deliv- necessary for each unit and how those dent in their problem-solving skills than ery, so that students learned the math- should be introduced. There is even ma- students coming out of the regular pro- ematics necessary to solve important terial on marketing such an interdiscipli- gram. The mathematics teachers in this problems, many coming out of genuine program have had to adjust their own industry needs. Although the mathemat- continued on page 12

11 FOCUS January 2003

continued from page 11 where they interviewed and videotaped engineering and technology profession- technicians to determine and demon- als. The teachers participate in various nary course both to administrators, col- strate what mathematical skills were be- workshops and engage in project-based leagues, and students. (Web site: http:// ing used. Mathematical activities based learning activities. In addition, they work www.ccc.commnet.edu/MWP) on these visits were then developed. All with their own students during the school of these industry “snapshots,” including year on engineering challenges, where Other community colleges have also de- video clips, warm-up quizzes relevant to students working in teams with profes- veloped mathematics course materials the industry, and worksheets for further sors and engineers attempt to find inno- which meet their own needs, but which exploration are now available on a CD. vative solutions to real world problems.. will probably also meet the needs of oth- Wake will be hosting an AMATYC work- This project has been helping teachers ers. For example, Wake Technical Com- shop in summer, 2003 dealing with Work- learn better ways to integrate science and munity College created and tested class- place Research. technology into the classroom, and has room activities for integrating mathemat- directly helped numerous students ics and algebra-based physics (http:// Another project involving cooperation through such additional activities as a www.wake.tec.nc.us/math). In order to with industry is the Middle School Ad- middle school discovery camp and work- help students further in determining vanced Technology Education Project at study programs in local industries. (Con- what skills they will need in the work- Cleveland State University, Cuyahoga tact: Terri Byrnes,[email protected]) place, Wake also developed a project of Community College, and Lorain County Workplace Research. Community college Community College, all in Ohio. This For further information, go to the ATE and high school instructors visited indus- project pairs middle school mathemat- website: http://www.nst.gov/ATE. tries throughout central North Carolina, ics, science and technology teachers with

NSF Beat: Opportunities at the National Science Foundation

By Sharon Cutler Ross

Scientists, engineers, and educators who ences, Undergraduate Education (DUE), people; willingness to speak one’s mind. fill rotational assignments at the NSF are and Elementary, Secondary, and Informal The pace at the Foundation is much faster a key element in providing “the talent and Education (ESIS). But the lines between than at a university, a different bureau- resources that are critical to meeting the areas are frequently crossed and a rota- cratic style prevails, and thus there are NSF’s mission.” The Foundation con- tor can expect to wear many hats. “It’s additional qualities that are helpful in tracts with rotators principally through perhaps as close as you can come to a making for a good experience as a rota- two programs: Visiting Scientists, Engi- functioning interdisciplinary depart- tor—a flexible mindset, a willingness to neers, and Educators (VSEE) and the In- ment,” says Lee Zia, a Program Director deal with interruptions, the ability to tergovernmental Personnel Act (IPA). in DUE. Zia, who presently has a perma- work under tight time constraints, and Briefly, a VSEE rotator takes a non-paid nent position at the Foundation, has an ego that can relinquish ownership of leave of absence from his or her home served as a rotator. He cites the opportu- projects and writing. institution and receives a salary from NSF. nities to see the workings of the NSF from Appointments are for up to one year with the inside, to see the national picture in Washington, DC, obviously has much to the possibility of another year. Under the science and mathematics education, and offer as a place to live. As NSF staffers, IPA, a rotator is on loan from her or his to help shape projects as his reason for rotators have additional resources for home institution for up to two years as applying to be a rotator. Spud Bradley, professional development such as Con- intermittent, part-time, or full-time staff. ESIS Section Head for Instructional Ma- gressional hearings and workshops and Again, an extension is possible. Both pro- terials Development, gives similar reasons talks sponsored by the National Research grams have a mechanism, Independent for his work at the Foundation. “Seeing Council as well as those sponsored by the Research/Development, to arrange for things from a national perspective, work- Foundation itself. The collegial atmo- time during the work year at the home ing with national leaders, and helping to sphere at the Foundation often leads institution for continuing work with shape programs” are important factors people from their original interest in graduate students or other ongoing for Bradley. coming to the NSF into exploring and projects. working in other areas. A tour at the NSF Many of the same qualities that make for has the potential for career renewal or re- Mathematicians and mathematics educa- success in academia or industry are also direction as well as providing a venue for tors are most likely to serve in the Direc- useful in working at the NSF—good com- contributing to mathematics and science torate of Human Resources in areas such munication skills, especially writing; in- education in the nation. as the Mathematical and Physical Sci- terest in new things; ease in dealing with

12 January 2003 FOCUS Report: 14th General Assembly of the International Mathematical Union

By Harry Waldman, based on a report by Donald G. Saari

The 14th General Assembly of the In- the selection of slates of names for the tion proposed by the US NCM and international Mathematical Union (IMU) next Executive Committee. troduced by the US delegation. This reso- was held on August 17-18, 2002, in lution reflects a worry that travel and Shanghai, China. The American delega- Resolution. The General Assembly recom- other restrictions which have been im- tion consisted of Salah Baouendi (Dept. mends the guidelines for receiving Collo- posed, or suggested that they will be im- of Math, University of California at San quia support from the IMU be further de- posed, on the free flow of responsible sci- Diego), Jennifer Chayes (Microsoft veloped and made available on the IMU entists and mathematicians will have an Corp., Seattle), David Eisenbud (Direc- website. These scarce funds should go pri- adverse effect on mathematics both here tor, MSRI, University of California, Ber- marily to supporting mathematicians from in the US and abroad. As an illustration, keley), Yum-Tong Siu (Dept. of Math., developing countries and high quality in- this includes concern about a May, 2002, Harvard University), and Donald Saari, ternational conferences that take place in ad which was placed in an European (Chair, Dept. of Math, University of Cali- developing countries. newspaper urging a boycott, it includes fornia at Irvine). Much of the General As- concern about visa problems and other sembly business was carried out by four Background: The issue here was to make possible restrictions imposed on math- committees, and the US was represented more precise procedures for IMU spon- ematicians wishing to work with col- on each of them: Chayes served on the sored conferences. leagues in the US. Finance and Dues committee, Eisenbud on the nominating committee, Saari on Resolution. The General Assembly of the In addition, two relevant items of legis- the resolution committee, and Siu on the IMU endorses the “Best Practices” docu- lation passed involved a a 10% dues in- teller and credentials committee. ment of the Committee on Electronic In- crease and the selection of Spain for the formation and Communication, also en- site of the 2006 International Congress Several resolutions were passed. dorsed by the IMU Executive Committee of Mathematicians. at its April 13, 2002, meeting. In particu- Resolution. The General Assembly recom- lar the Assembly endorses the provisions Finally, new officers of the IMU were mends continuing the tradition of the 1994, designed to ensure access by mathemati- elected during the general assembly . 1998, 2002 ICMs by holding an Emmy cians of the developing world to current They are: Noether lecture at the next two ICMs (2006 mathematical literature: the posting of the and 2010) with the selection of the speak- articles on personal homepages and serv- President: John Ball (UK) ers to be made by an IMU appointed com- ers and the practice now beginning with Vice Presidents: Jean-Michel Bismut mittee. several publishers of making journal ar- (France) and ticles in electronic form freely accessible five Masaki Kashiwara (Japan) Background: This is the first of the three years after they have been published, or Secretary: Phillip Griffiths (USA) resolutions proposed by the US NCM and even sooner. introduced by the US delegation. For sev- The newly elected Executive Council con- eral meetings of the GA, the US delega- Background:This was the second resolu- sist of: Andrey Bolibruch (Russia), Mar- tion has consistently but unsuccessfully tion proposed by the US delegation. tin Grotschel (Germany), Zhi-Ming Ma proposed resolutions to ensure the selec- (China), Ragni Piene (Norway) (the first tion of more women and minorities as Resolution. Notwithstanding these times woman ever elected to the Executive major ICM speakers. of heightened tension and security con- Council), Madabusi Raghunathan (In- cerns, we urge a continuation of scientific dia). Resolution. The General Assembly of the exchange and publication. The IMU op- IMU expects the Executive Committee to poses efforts either by governments, orga- develop a proposed mechanism to involve nizations, or individuals to restrict contacts members from the National Committees and interactions in the world mathemati- for Mathematics, not on the Executive cal community. Specifically we oppose Committee, to assist in the selection of holding individual mathematicians liable slates. This Proposal should be put forth to for the actions of their governments. The the 2006 General Assembly. IMU endorses the principles expressed in the International Council for Science Background: It was felt during the meet- (ICSU) ARTICLE 5 of STATUTES. ing that people beyond those on the Ex- ecutive Committee should be involved in Background: This was the third resolu-

13 FOCUS January 2003 Short Takes

That’s Wrong! DIMACS Reconnect ’03 Conferences help faculty improve their teaching. It also suggests that “university leaders or gov- DIMACS, the Center for Discrete Math- erning boards should create endowments While we make every effort to get ematics and Theoretical Computer Sci- to recognize faculty members who, over things right, it’s inevitable that every once ence at Rutgers University, sponsors Re- time, have made significant contributions in a while FOCUS and MAA Online will connect Conferences every year. They are to teaching.” The full report is online at contain mistakes. When that happens, we intended to expose faculty to current re- http://www.nap.edu/catalog/10024.html. are always willing to run corrections (see search topics that are relevant to the class- page 9, for example), so please let us room, to create the opportunity to write Summer Mathematics Program for know when we’ve messed up. The quick- classroom materials based on such top- Women at Carleton est way is to email [email protected]. ics, and to “reconnect faculty to the math- Thanks! ematical sciences enterprise by exposing The Department of Mathematics at them to new research directions and Carleton College plans to offer again this New Officers for NCTM questions.” There will be three confer- year their month-long summer math- ences in 2003: “Some Current Problems ematics program for eighteen math- The National Council of Teachers of in Coding Theory” will be held at Salem ematically-talented first- and second-year Mathematics has announced the results State College, June 15 -21, 2003; “Central- undergraduate women. By introducing of the 2002 election. Cathy L. Seeley of ity in Graphs with Applications to the them to new and exciting areas of math- Cedar Park, TX will be President-elect for Theory of Location of Facilities” at the ematics that they would not see in a stan- 2003-2004, and will serve as NCTM Presi- Illinois Institute of Technology, July 16- dard undergraduate curriculum, and by dent in 2004-2006. New members of the 13, 2003; and “Internet Algorithms: Mod- honing their skills in writing and speak- NCTM Board of Directors were also eling the Web as a Graph, with Applica- ing mathematics, the program leaders en- elected: Cynthia Bryant of Salem, MO, M. tions to Information Gathering and deavor to encourage these women to pur- Kathleen Heid of State College, PA, Mari Search” at DIMACS/Rutgers University, sue advanced degrees in the mathemati- Muri of Cromwell, CT, and Anthony A. August 10-16, 2003. Funding for lodging cal sciences, and, more importantly, to Scott of Elmwood Park, IL. Their term and meals is available through a grant increase each woman’s confidence in her will start on April 2003 and they will serve from NSF. Visit http://dimacs.rutgers.edu own abilities and connect them all into a for three years. Kathy Heid, who is cur- or email [email protected] supportive network to carry them rently a member of the MAA Board of for more information. through their undergraduate and gradu- Governors, will move from one board to ate education. the other with hardly a break. Improving College and University Teaching At the heart of the program are two de- Fewer Math and Science Ph.D.s manding, intense courses under the su- A recent report from the National Re- pervision of female faculty who are ac- According to an article in the Chronicle search Council focuses on Evaluating and tive in research and renowned for their of Higher Education (Monday, November Improving Undergraduate Teaching in Sci- teaching. Besides the coursework, par- 11, 2002; online, for subscribers only, at ence, Technology, Engineering, and Math- ticipants take part in a variety of math- http://chronicle.com/daily/2002/11/ ematics. It argues that while the quality ematical events: panel discussions on 2002111101n.htm), the total number of of the research of scientists and math- graduate schools and careers, colloquia Ph.D’s awarded in the United States has ematicians is carefully evaluated, “the on a variety of topics, recreational prob- declined sharply over the last few years. evaluation of teaching in these fields has lem-solving, and visits from at least one In fact, the 2001 number is the same as been haphazard and less exacting.” In REU organizer and the organizer of the the 1993 number. The decrease is mostly addition “professors who excel in the Budapest Semester. The mathematical due to fewer Math, Science and Engineer- classroom are sometimes given little rec- part of the program is balanced with op- ing degrees (down 6.5% since 1998). ognition on their own campuses, let alone tional weekend events including canoe- Doctorates in other fields decreased by in the wider academic community.” Fi- ing, hiking, picnics, and tubing. only 0.9% during the same period.On the nally, “faculty members and administra- other hand, the Chronicle points out that tors often believe that it is nearly impos- Please refer students who you feel would the percentage of doctorates awarded to sible to objectively gauge the effectiveness benefit from this program to the web page women has increased. The survey was of teaching skills.” The NRC report argues at http://www.mathcs.carleton.edu/smp or produced by the University of Chicago’s that the tools for correctly evaluating have them contact Deanna Haunsperger National Opinion Research Center; check teaching effectiveness and the impact of at Dept. of Math/CS, Carleton College, out their website at http:// curricula do exist and should be used by Northfield, MN 55057 (e-mail: www.norc.uchicago.edu for more infor- colleges and universities. The report rec- [email protected]). The mation. ommends that colleges and universities application deadline is February 21, 2003.

14 January 2003 FOCUS

Letters to the Editor In Memoriam: René Thom, 1923–2002 Another Article on Heron’s Formula

I enjoyed reading Reuben Hersh’s “A Nifty Derivation of Heron’s René Thom, one of the most important mathematicians of Area Formula” in the November 2002 issue of FOCUS. Hersch’s the century and winner of the Fields Medal, died on October derivation, like other clever results in elementary mathematics, 25 in his home in Bures-sur-Yvette, France. He was 79 years is one which is often rediscovered. I last encountered it (essen- old. tially the same derivation, but with a different proof) in Roger C. Alperin’s “Heron’s Area Formula” in the March 1987 issue (v. Born in Montbéliard, Thom attended the École Normale 18, no. 2) of The College Mathematics Journal, pp. 137–8. Superieure between 1943 and 1946 and then quickly established himself as an important mathematician. His work on cobordism Roger B. Nelsen and characteristic classes led to his being awarded the Fields Lewis & Clark College Medal in 1958. In 1963 he was made a permanent professor at the Institut des Hautes Études Scientifiques (IHES) and re- Generalizing Heron’s Formula mained there until his retirement in 1988.

There actually is a nice “formula for the volume of a tetrahe- Thom made many contributions to mathematics, philosophy dron as a function of the lengths of the six edges,” but it’s just of mathematics, and mathematics education, but since the 1970s not symmetric in all six edges, only in each of two subsets of his name has been most closely attached to “Catastrophe three edges (which is consistent with the last paragraph in Theory”, an attempt to use the theory of singularities as a tool Hersh’s article). It’s given on p. 13 of Pólya’s Patterns of Plau- to understand discontinuous phenomena in the real world. sible Inference (Volume II of Mathematics and Plausible Reason- Thom argued for the wide applicability of this theory. Unfortu- ing, 1954). With edges a, b, and c meeting in the same vertex nately, the projected applications failed to arise or were not quite and edge e opposite to a, f opposite to b, and g opposite to c, the convincing. Nevertheless, catastrophe theory is considered a sig- formula is nificant precursor of the more recent work in “chaos theory.”

2222222222 Thom was a critic of what he felt was sometimes an excessive 144Vabcbcecaf=++ 4 − + − ()()fascination with proof. He argued that sometimes imprecise and 2 2 unrigorous work contained fundamental insights. On the other 222 2222 22 2 2 ()abg+ −− abce+ −− bca+ − f hand, he once asserted that “it is unethical for a mathematical ()()researcher to use a result the proof of which he does not ‘under- 2 stand’ (except for the specific case where he wants to disprove 22 2 2 −ca()+ b− g the result),” a very high standard indeed. Several important newspapers (including the New York Times, (In standard notation the formula doesn’t look as ugly as the the Washington Post, the Guardian, and Le Monde) published above, especially taking into account the partial symmetry.) On major obituaries of Thom, several of which can still be found p. 45 of Pólya’s Mathematical Discovery, Volume I, 1981, he gives online. A biography can be found at http://www-groups.dcs.st- two special cases of the formula (a trirectangular tetrahedron and.ac.uk/history/Mathematicians/Thom.html. and a tetrahedron with e = a, f = b, g = c) where the formula simplifies, and each he refers to as an “analogue to Heron’s theo- rem”. (Jerry Alexanderson suggested this last reference.)

Peter Ross Santa Clara University Have You Moved?

The MAA makes it easy to change your address. Please inform the MAA Service Center about your change of Letters commenting on material published in FOCUS (or re- address by using the electronic combined membership sponding to other letters) are always welcome. Send them by list at MAA Online (www.maa.org) or call (800) 331- email to [email protected] or by snail mail to Fernando 1622, fax (301) 206-9789, email: [email protected], Gouvêa, Department of Mathematics, Colby College, Waterville, or mail to the MAA, PO Box 90973, Washington, DC ME 04901. Letters will be edited for publication 20090.

15 FOCUS January 2003

2002 Clay Research Award Winners Announced

The Clay Mathematics Institute (CMI) ten years in the field of decision theory, ogy under William Thurston. After this, presented the 2002 Clay Research Awards complexity, and the relation between the his work evolved into the frontiers of at its Annual Meeting, held on October geometry of sets and their information problems in combinatorics and analysis. 30, 2002, at the American Academy of content. For some years he has been in- Schramm is an example of a person us- Arts & Sciences in Cambridge, Massachu- terested in finding a polynomial time al- ing training in one field to elucidate an- setts. The Awards, presented by CMI gorithm to test whether a given number other one. Currently, Schramm works as President Arthur Jaffe and Directors is prime. Although random algorithms a Senior Researcher in the extraordinary Landon Clay and Lavinia Clay, went to can solve this problem with high certainty mathematics group at Microsoft in Oded Schramm, for his work on the in polynomial time it remained a long- Redmond, Washington. Schramm’s Loewner equation, and to Manindra standing challenge to find a method that groundbreaking study of the stochastic Agrawal, for his work on primality test- works in every case. Agrawal solved this Loewner equation led to the solution of ing. Each winner was made a Clay Insti- problem in August 2002, working with many problems, by him, by his collabo- tute Prize Fellow, and received a bronze two undergraduate students: Neeraj rators, and by others. It led to major model of the CMI logo, which is an el- Kayal and Nitin Saxena. Their proof es- progress in probability theory, in the egant sculpture “Figureight Knot tablishes the correctness of a conjecture theory of percolation and of random Complement vii/ CMI” by sculptor made in 1999 by Agrawal and Somenath walks, as well as in related topics of con- Helaman Ferguson. Biswas. (See the November issue of FO- formal field theory. CUS for an expository account of the Agrawal, who was born in May 1966, has Agrawal-Kayal-Saxena result.) For more information on the Clay Re- since 2001 been a full professor at the search Award and the winners, visit their Indian Institute of Technology in Kanpur, Oded Schramm came to the United States site at http://www.claymath.org. India. He has been active over the past in 1987 as a graduate student in topol-

16 January 2003 FOCUS Memories of Arnold Ross doubt that Arnold’s influence has been profound. A steady stream of outstand- By Glenn Stevens ing scholars has flowed out of Arnold’s program since the very beginning. Many of these individuals now hold research rnold Ross entered my life in the form A positions at many of the nation’s most of a personal letter that came to my home prestigious institutions—not just in in the central valley of California in the mathematics, but also in a variety of fields winter of 1969, when I was just a sopho- ranging from astrophysics to economics. more in high school. The hand-typed letter, which was addressed personally to me, It is significant, I think, that Arnold made and signed personally by Professor Ross, his contribution to American mathemat- offered a warm invitation to join the com- ics not through his own research contri- munity of mathematicians by attending an butions, but through the development of eight week summer program at the Ohio high quality programs of mathematics State University in Columbus, Ohio. My education. Indeed, Arnold’s devotion to decision to accept that invitation proved mathematics education ran much deeper to be a defining moment in my life. It was than the creation of the Ross Program for not only the beginning of a life devoted which he is best known. Arnold repeat- to mathematics. It was also the begin- edly emphasized that the principles of his nings of a friendship with Arnold that program were relevant not just for the would continue until his recent death on Arnold Ross education of highly talented young September 25, 2002 at the age of 96. people. The basic principles that Arnold Another personal letter from Arnold ar- repeated so often and so consistently— Over almost five decades, countless young rived in January of the following year in- that knowledge comes of experience, that people with early promise for creative re- viting us back for more advanced inves- language is a basic tool of mathematics, search in mathematics and science re- tigations and asking us to “help” the new and that “the opposite of boredom is not ceived such invitations from Arnold to first-year students in the program. fun,” are applicable to a broad spectrum join his program. Those of us who ac- Arnold’s invitation was irresistible. He of students. His insistence on this point cepted were treated to an unforgettable had a remarkable way of making each of was just one of many ways that his deep experience of mathematical exploration. us feel special and he never failed to re- respect for the potential of learners at all The program was built around a delight- mind us of our responsibility to the rest levels manifested itself. Arnold himself ful collection of handwritten and mim- of the community. Altogether, I joined ran a very successful program in the 60’s eographed problem sets designed by Arnold’s program for a total of five sum- for minority students in Columbus, Ohio Arnold himself. Through our work on mers, three times as a student and twice that he provocatively named Horizons these problems we honed our powers of as a counselor. Many of my peers were Unlimited. Moreover, his work deeply in- independent exploration and learned the involved even longer. Together we inter- fluenced many others in mathematics art of skeptical conjecture, proof and dis- acted not just with Professor Ross, but education who have developed their own proof. Professor Ross’s famous exhorta- also with his colleagues, including such programs for young people from a wide tion “to think deeply of simple things” has memorable personalities as Kurt Mahler, range of backgrounds. been deeply etched in the psyches of all Hans Zassenhaus, and Ivo Thomas. The who passed through his program. We all OSU mathematics department, which Arnold Ross was a deeply compassionate benefited from his gentle reminders that Arnold chaired for many years, welcomed man whose energy and optimism seemed rich concrete experience precedes signifi- us warmly into graduate seminars offered inexhaustible. He ran his summer pro- cant discovery, that “language is our in the summertime. I am especially grate- gram every summer from 1957 through friend,” and that good abstraction ful for an invitation from Professor John 2000, when he finally retired from the amounts to condensation of diverse ex- Hsia to join his seminar on quadratic program at the age of 94. Until the very perience united by a few fundamental forms one summer. Through these inter- end of his life, Arnold bore a mischievous ideas. Arnold often said that “no one actions, the “children of the Ross Pro- gleam in the eye that reflected his untir- leaves the program unchanged.” Indeed, gram” came to see research mathematics ing efforts to enrich the talents of young at the end of the eight weeks we were as the work of a community of individu- people and to introduce them to the joys mentally exhausted and, as I can say from als and we came to see ourselves as mem- of a life of inquisitive exploration. personal experience, many of us swore bers of that community. never to return. However, once back in Glenn Stevens is Professor of Mathematics the traditional school environment, the It has been said that Arnold Ross influ- at Boston University and is the director of need for more intellectual challenge be- enced American mathematics of the 20th the PROMYS program ( came intense and we felt a yearning to go century more than any other single indi- http:// ), a program for high back. vidual. Such statements can be neither www.promys.org school students inspired by the Ross Pro- proved nor disproved, but there is no gram.

17 FOCUS January 2003 Being a Mathematics Educator in a Department of Mathematics By Eileen Fernandez

When I first accepted a position in strategy to generate papers on how to share ideas and ask for advice on matters Montclair State University’s Department enhance the teaching of certain calculus of teaching and research. of Mathematical Sciences, people asked, topics, how to tweak certain instructional “Why are you working in a“mathematics formats to improve problem solving in Go to conferences in both disciplines department when your degree is in geometry amongst prospective teachers, education?” My response then, which and how to address students’ mis- This is a tough one, mainly for financial remains true today, was simple: in order understandings of functions in pre- reasons. Balance is the key. I take into to be a mathematics educator, one must calculus. Remember to get your students’ account where the meetings are and to maintain a solid footing in the classroom written permission before you collect what extent what I have to offer matches and in one’s area of education research. data from them and be careful in writing the topics for paper session. Sharing I was all too familiar with the dangers of up results in which you are both rooms with friends will help you and losing this footing. One foot out of the researcher and teacher. your department pay for this effort. classroom generates research that fails to serve education’s stakeholders (among Work with mathematicians and educators Talk about your work them teachers, students, principals, administrators or parents). And a foot out I’ve had to work hard to achieve this, but Recently, I was talking to a statistician in of education research fails to spread ideas the payoff has been enormous. I have my department who described her initial about how to enhance the teaching and served on committees and done skepticism and wariness at qualitative learning of mathematics. professional conference work with research. (Most of my research in professors in our university’s education mathematics education is qualitative.) I have known since high school that I department. I have also collaborated on She told me that by hearing me (and wanted to be a mathematics educator research projects with mathematicians in others) talk about our work and its (although I didn’t know at the time that my department. As a result, I’ve met theoretical underpinnings, she has come such a profession existed). I tried to colleagues who are not only valuable to value the role that this methodology balance both disciplines through my resources, but also good friends. Of can play in generating research and education (a Masters in mathematics and course, you do not have to stay within enhancing statistical methods. I’ve also a Doctorate in mathematics education). your university. I am collaborating on a had colleagues tell me that they didn’t When I com-pleted my studies, I book for middle school teachers, and know (until they met me and saw my discovered that I qualified for positions have applied for a grant, with two work) what research in mathematics in both education and mathematics colleagues from my graduate school days education was like. They confessed to departments. It was not an easy choice: I (in education) and one new colleague (in conceptualizing math-ematics education wanted to teach mathematics but knew mathematics) who are from three as just mathematics teaching. They now that some mathematicians were different universities. realize it is a social science complete with prejudiced against mathematics a wide variety of theoretical frameworks educators. I worried about being able to Seek out the mathematics community’s and methodologies that can be used to do genuine research in mathematics outreach to education efforts generate new education theories or education and about how my research inform practice at a wide variety of levels. would be viewed and whether it would It is not unusual these days to see math- So talk about your work, not just in be valued. It has taken some work, but I ematics projects dedicated to improving departmental seminars, but also at lunch feel I’ve found a good place for myself. education. One of my more rewarding or in the departmental lounge. Since others are in my position, I wanted experiences was with the MAA’s Project to share some of the strategies I’ve had NExT. One of this project’s many There is no choice that works for that have helped me maintain the objectives is the initiation of young everyone. Some mathematics educators delicate footing required to be a faculty into mathematics academic life. will end up in departments of education. contented educator in a department of Not only did NExT provide me with These strategies have helped make the mathematics. forums for sharing work I had done in option of working in a mathematics the classroom, but it also exposed me to department work well for me. Use your classrooms as a forum for research numerous resources for enhancing my teaching, giving presentations, applying Eileen Fernandez is in her fourth year as With opportunities to teach either for grants, and maintaining balance an assistant professor of mathematics and mathematics or mathematics education between work and personal life. It is still mathematics education at Montclair State courses, mathematics educators have a reassuring to find fellow NexTers (and University in Upper Montclair, NJ. rich forum for doing research, complete their numerously colored dots) at with students and their genuine meetings of the MAA or AMS and to obstacles. I have successfully used this know that I can use the NExT listserv to

18 January 2003 FOCUS Read This!

By Fernando Q. Gouvéa By M. L. Frame and B. B. Mandelbrot. Mathematics Review by George Ashline. Awareness Week

The MAA Online book review column, Proofs Without Words II, 2003 Read This!, continues to actively review By Roger B. Nelsen. books that are of interest to a wide Review by Robert C. Stolz. The theme for this year’s mathematics audience of mathematicians. Between Awareness Week has just been an- the Briefly Noted section and the full- The Education of a Mathematician nounced. It will be Mathematics and Art. length reviews, we have covered more By Philip J. Davis. FOCUS will have more detailed informa- than 300 books, with many more to Review by P. N. Ruane. tion in a future issue; for now, visit http:/ come. All those reviews are still available /www.d.umn.edu/~jgallian/art.html for on MAA Online. Mathematical Olympiads: Problems and essays, links, references, possible speak- Solutions From Around the World, ers, and the MAM2003 poster. What have we reviewed recently? Here’s 1999-2000 a partial list: Edited by Titu Andreescu and Zuming Feng. Chance, Luck and Statistics Review by Mihaela Poplicher. By Horace C. Levinson. Review by Charles Ashbacher. How to Ace the Rest of Calculus By Colin Adams, Abigail Thompson, The Math Life and Joel Hass. A film by Wendy Conquest, Bob Drake, Review by Kevin Anderson. and Dan Rockmore. Review by Henry Cohn. All the Mathematics You Missed [But Need to Know for Graduate School], Fractals, Graphics, and By Thomas A. Garrity. Mathematics Education Review by Mariah E. Hamel.

19 FOCUS January 2003

EMPLOYMENT OPPORTUNITIES

CALIFORNIA faculty/open_faculty_positions.htm), FLORIDA curriculum vitae, transcripts, and minimum of three reference letters to CAL STATE POLYTECH. UNIV., Faculty Search Committee, Mathematics BROWARD COMMUNITY COLLEGE POMONA Department., CSPU Pomona, 3801 W. Broward Community College (BCC) is Department of Mathematics Temple Ave., Pomona, CA 91768-4007; a large, three-campus, three-center urban Four tenure-track positions [email protected]; 909-869- institution serving approximately 50,000 Mathematics Education (Two positions: 4008; Fax: 909-869-4904; http:// credit and non-credit students in Assistant Professor and Associate/ www.csupomona.edu/~math. AA/EEO. Southeast Florida. BCC is the principal Assistant Professor). Teach provider of undergraduate higher undergraduate courses in math education for the residents of Broward education, collaborate with others on GEORGIA County. Through a wide variety of campus involved in math education. degree and certificate programs and Opportunity to teach lower and upper continuing education courses, the college division math courses, provide in-service GEORGIA COLLEGE AND STATE attracts a great diversity of students. The programs for local schools, help to UNIVERSITY college is also a source of cultural develop master’s in mathteaching, advise Department Chair, Department of enrichment; a resource for community students seeking secondary teaching Mathematics and Computer Science development, business, and industry; credential. Minimum qualifications: Applications are invited for Department and an avenue for continued skill Doctorate in math education with Chair. Department of Mathematics and upgrading and enhancement and master’s degree in mathematics (or Computer Science. At least five years of retraining. equivalent) or Ph.D. in mathematics, teaching experience is required and A completed employment application, with strong background in math administrative experience is desirable. copies of graduate transcripts & letter education. ABD’s will be considered. Applicants must have a doctorate in of intent must be received by January Must know about trends in math mathematics, computer science or 31, 2003 to be considered for education, uses of technology in math related field. The department offers employment. education. Preference to those able to undergraduate degrees in mathematics supervise student teaching. Mathematics and computer science and minors in Mathematics Faculty, FOUR Positions (Two positions: Asst Prof) Teach mathematics, computer science, actuarial Available Master’s degree with 18 undergraduate, graduate, and service science and quantitative analysis and has graduate semester hours in Mathematics courses in math, participate in excellent teaching and laboratory required. Three positions at Central curriculum development, and advise facilities. There are twenty-one faculty Campus(#247): undergraduate and graduate students. positions in the department distributed Dedication and enthusiasm for teaching Preference to those with expertise in one as follows: five computer science, two a must. Applicant should be willing to or more of: algebra, control theory, mathematics education, thirteen teach the entire span of Math courses differential equations, estimation theory, matheamtics, and one chair. As the from Pre-Algebra to Calculus III. Ap- geometry, number theory, stochastic University System of Georgia’s plicant will contribute time and effort to differential equations, topology. designated public liberal arts university academic endeavors at the department, Minimum qualifications: Ph.D. in and a member of the Council of Public campus and college levels. Willing and Mathematics or Statistics. Completion Liberal Arts Colleges (COPLAC), able to incorporate technology in the of terminal degree by 9/03. All positions: GC&SU is committed to combining the classroom and must be open to new Expected to serve on department and educational experiences typical of teaching strategies to enhance student university committees, engage in esteemed private liberal arts colleges with success. scholarly activities. Required: Evidence the affordability of public higher of, or potential for, teaching excellence, education. GC&SU is an Equal One position at North Campus (#117): directing master’s theses, engaging in Opportunity/Affirmative Action Experience teaching both college scholarly activities, working with diverse Employer. Review of applications will preparatory and college level student body. Salary dependent on begin December 6, 2002 and continue Mathematics courses with an qualifications. Initial review of until the position is filled. For additional understanding of the needs and concerns applications 1/8/03. Review will continue information and the application of community college students. Must until position is filled or closed. Submit procedure, go to: http://www.gcsu.edu/ have experience using appropriate application form indicating position area facultyjobs. technology and must be willing to work (forms are available at http:// with varying instructional modalities. www.csupomona.edu/~academic/

20 January 2003 FOCUS

Upon selection, official transcripts will January in Baltimore. The University of be required. South Florida is an affirmative action, MICHIGAN Salary ranges (based on degree & years equal opportunity, equal access of experience) are: Master’s (18 grad employer. Applications from women and GRAND VALLEY STATE UNIVERSITY semester hrs in discipline), $31,963- minorities are encouraged. According to Grand Valley State University, in $41,552; Doctorate (24 grad semester hrs Florida law, applications and meetings Allendale, Michigan, is accepting in discipline), $37,716- $47,305. regarding them are open to the public. applications for the position of For disability accommodations, please Postdoctoral Teaching Fellow, with Applications available: http//: contact the department at (813) 974- employment to begin in August 2003. www.broward.edu/jobs/bccjobs.jsp or 2643 at least five days in advance. Candidates must have a doctorate in the 800-682-3646 or 954-201-7338. Submit Mathematical Sciences or Mathematics application packages to: Broward Education by August 2003 (completed Community College/ HR, 225 E. Las Olas MASSACHUSETTS not earlier than May 2000). Blvd., Ft. Lauderdale, FL 33301. BCC is committed to the principle of diversity. The fellowship is a two-year visiting We are interested in receiving ap- WILLIAMS COLLEGE position with a renewal option for a third plications from a broad spectrum of The Williams College Department of year. This position is designed to offer people including women, minorities, Mathematics and Statistics invites candidates the opportunity to develop veterans, & disabled individuals. applications for two positions in broad instructional and scholarly mathematics and one position in potential in a department committed to UNIVERSITY OF SOUTH FLORIDA statistics, beginning fall 2003, all at the excellence in the teaching and learning rank of assistant professor (in of undergraduate mathematics. Fellows The Department has two non-tenure- exceptional cases, more advanced will have the opportunity to teach earning, nine-month (teaching) undergraduate courses and work in close Instructorship positions available on our appointments may be considered). We are seeking highly qualified candidates mentoring relationships with main (Tampa) campus. These positions who have demonstrated excellence in department faculty. In addition to are annually renewable. Minimum structured mentoring centered on qualifications include Ph.D. (or teaching and research, and who will have a Ph.D. by the time of appointment. instruction, fellows will explore avenues equivalent) in Mathematics or a closely- for scholarship through interactions with related field earned by August 25, 2003, current faculty, and present a monthly and documented interest and ability in Williams College is a private, residential, highly selective liberal arts college with seminar in their area of professional undergraduate teaching. Applicants with expertise. three years of experience teaching an undergraduate enrollment of undergraduate students are preferred. approximately 2,000 students. The teaching load is two courses per 12-week For more information, including Further details of these positions include: semester and a winter term course every responsibilities of the position, and Equivalent of 12-hour teaching other January. In addition to excellence important details on how to apply, see load.Course-release time may be earned in teaching, an active and successful our position description at http:// for course supervision and/or course research program is expected. www.gvsu.edu/math/jobs.html. Review development. Instructors will be of completed applications will begin primarily teaching general-education To apply, please send a vita and have three February 17, 2003. mathematics courses to Freshmen and letters of recommendation on teaching Sophomores. and research sent to the Hiring NORTHERN MICHIGAN UNIVERSITY By February 15, 2003, send application Committee, Department of Mathematics The Department of Mathematics and materials (including AMS Cover Sheet and Statistics, Williams College, Computer Science invites applications and curriculum vitae) and have three Williamstown, MA 01267. Teaching and for two tenure-track positions in letters of reference, at least two of which research statements are also welcome. address teaching, sent to: Evaluations of applications will begin on mathematics at the rank of assistant or after November 25 and will continue professor beginning with the 2003-2004 Instructor Search Committee until the positions are filled. Williams academic year. Successful candidates Department of Mathematics College is dedicated to providing must have a Ph.D. in an area of the University of South Florida awelcoming intellectual environment for mathematical sciences by August, 2003. 4202 East Fowler Avenue, PHY114 all of its faculty, staff and students; as an For more information, visit our web site Tampa, FL 33620-5700 EEO/AA employer, Williams especially at http://math.nmu.edu/career/ encouragesapplications from women position.html. EEO/AA Inquiries about these positions may be and underrepresented minorities. For sent to [email protected]. moreinformation on the Department of Note: Members of the Search Committee Mathematics and Statistics, visit http:// will be attending the joint meetings in www.williams.edu/Mathematics.

21 FOCUS January 2003

in writing materials useful in the graduate colleges/schools. Its diverse MONTANA classroom and reconnecting them to the student population is comprised of 9,000 mathematical sciences enterprise by undergraduates and 5,000 graduate ROCKY MOUNTAIN COLLEGE exposing them to new research directions students. Located in New York City and The Department of Mathematics at and questions. The three programs: Westchester County, Pace draws its Rocky Mountain College invites “Some Current Problems in Coding strength from being a unified institution applications for a tenure-track position Theory” at Salem State College, June 15 that offers students a choice of several beginning fall, 2003. The successful 21, 2003; “Centrality in Graphs with campus locations, each with its own candidate will need a strong background Applications to the Theory of Location distinctive atmosphere. For more in analysis, and demonstrate obvious of Facilities” at Illinois Institute of information, visit our websites at: http:/ enthusiasm and talent for undergraduate Technology, July 16 13, 2003; “Internet /webpage.pace.edu/mathny/ and http:// teaching both at the introductory and Algorithms: Modeling the Web as a www.pace.edu/dyson/academics/ upper levels. Classes taught will include, Graph, with Applications to Information mathwest/ but are not limited to, differential Gathering and Search” at DIMACS / equations, vector analysis, advanced Rutgers University, August 10 16, 2003. Candidates for the position should calculus, complex variables and Applicants accepted to participate will submit a letter of application, a topology. The candidate will also be receive lodging and meals through NSF curriculum vitae, an AMS Standard expected to teach part of the traditional funding. For more information or an Cover Sheet, a teaching statement, four-semester calculus sequence. The application form, visit our web site at research statement, and three letters of successful candidate must be committed http://dimacs.rutgers.edu/reconnect/. recommendation sent separately to: Prof. to undergraduate teaching with a Or, contact the Reconnect Program G. Taiani, Chair, Search Committee, demonstrated ability to teach effectively Coordinator, at Dept. of Mathematics, Pace University, to students of varied interests and [email protected] or (732) 1 Pace Plaza, New York, NY 10038. backgrounds. A Ph.D. or ABD in 445-5928. Review of applicants began November mathematics is required, and the 30th and will continue until the position successful candidate will play a large role is filled. in shaping the future direction of the NEW YORK program. In their applications, Pace University is an Equal Employment applicants should address their interests and Affirmative Action Employer, M/F/ in teaching in an undergraduate, liberal- PACE UNIVERSITY H/V, committed to ensuring a diverse arts environment that emphasizes close Dyson College of Arts and Sciences learning and working environment. faculty-student interaction. Department of Mathematics Women and minorities are encouraged Applications will be screened beginning The Department of Mathematics, Dyson to apply. February 15, 2003. Send letter of College of Arts and Sciences, Pace application, statement of teaching University invites applications for a full- philosophy, curriculum vitae, and three time, tenure-track position at the NORTH CAROLINA letters of recommendation which address Assistant Professor level to begin the candidates interest in and September 2003. Applicants should have commitment to excellent teaching, to: GUILFORD COLLEGE a Doctorate degree in Mathematics, Bob Robertson, Director of Personnel, Position Description – Mathematics–– Applied Mathematics, or Rocky Mountain College, 1511 Poly For Fall, 2003 Statistics. All fields of research will be Drive, Billings, MT 59102. E-mail Guilford College, a private liberal arts considered. Responsibilities include inquiries to [email protected]. AA/EOE college affiliated with the Society of teaching undergraduate courses in Friends, invites applications for a tenure- mathematics, developing curriculum, track position in mathematics beginning NEW JERSEY maintaining an active research program in August of 2003. Completion or and sustaining scholarly activities. The imminent completion of a Ph.D. in successful candidate must have a strong RUTGERS UNIVERSITY mathematics is required. Interest in and commitment to undergraduate DIMACS Reconnect ’03 Conferences: ability to teach creatively in lower-level education, and present evidence of Current Research Relevant to the courses such as pre-calculus, elementary excellence in teaching and research. The Classroom statistics, mathematics for teachers, and position will be located at campuses in The Reconnect ’03 Conferences mathematics for the liberal arts through both New York City and Westchester sponsored by DIMACS (the Center for upper-level courses for mathematics County, a northern suburb. Discrete Mathematics and Theoretical majors is required. The Mathematics Computer Science) are geared towards Department teaches courses that service Founded in 1906, Pace University is a exposing faculty teaching under- science, business, education, and private comprehensive university that graduates to current research topics computer studies students among others, offers more than 300 majors and 3,000 relevant to the classroom, involving them and all candidates must be committed to courses within six undergraduate and

22 January 2003 FOCUS working effectively with the broad range certification programs; and developing Requirements include Ph.D. in of student interests and abilities this collaborative partnerships with mathematics by appointment date, encompasses. Preference will be given to educational and/or commercial entities. ability to teach a wide range of candidates with interests in computer An earned doctorate in mathematics introductory and advanced studies, interdisciplinary teaching, and education is required; a master’s degree undergraduate courses, and a directing independent studies of various in mathematics, teaching experience at commitment to establish a research sorts (including undergraduate the elementary or secondary level, and program for undergraduate students. research). Responsibilities include experience with university programs that Submit letter of application, cv, teaching a minimum of 12 credit hours provide collaborative college credit at the statement of teaching philosophy, and per semester, continuing scholarly high school level is preferred. Teaching five references (names, addresses activity (broadly interpreted), advising assignments may involve travel to including email, telephone) to: Dean students, college committee service, and regional sites and/or distance learning John T. Sieben - College of Natural teaching as needed in the evening formats. See our website Science and Mathematics, Texas continuing education program. at’www.cup.edu/employment for Lutheran University, 1000 W. Court St., application information. Cal U is AA/ Seguin, TX 78155; fax (830) 372-6095, A complete application includes a letter EEO. phone (830) 372-6007, e-mail of interest, a personal statement on [email protected]. Review of applications teaching, a vita, graduate transcripts, and will begin January 15, 2003 and continue three letters of recommendation (at least TENNESSEE until the position is filled. Texas two of which explicitly support teaching Lutheran University is an equal excellence or its potential). All materials opportunity employer and encourages should be sent to Search Committee, TENNESSEE TECHNOLOGICAL women and minorities to apply. Web Department of Mathematics, Guilford UNIVERSITY page: www.tlu.edu. College, 5800 W. Friendly Ave., Department of Mathematics Greensboro, NC 27410. Application One tenure-track instructor position materials should arrive by February 21, starting 8/03. 2003 for first consideration. Advertising Information for Minimum master’s in mathematics Display & Classified Ads Guilford College seeks applications from required. College mathematics teaching people representative of diversity based experience preferred. Evidence of Mechanical Specifications on age, race, gender, sexual orientation, excellent teaching required. Trim Size: 8 1/2 " wide x 10 3/8 " high disabilities, ethnicity, religion, national Screen: 150-line halftone origin, career and life experiences, socio- Duties: Teaching lower division courses, Full page bleed 8 3/4" x 11 1/4", (10% economic background, geographic roots, advising, outreach, scholarly activity extra charge) as well as members of the Society of and/or service. Color: FOCUS standard second color Friends. EOE/AA available (15% extra charge). Initial screening January 22, 2003, open Column width: 2 5/16", 4 13/16", 7 3/8" until filled. Printing: Offset, saddle-stitched

PENNSYLVANIA For complete job description and How to send your Materials: application procedure, see Electronic files: Laser output should ac- www.math.tntech.edu or contact company your electronic files. PC and CALIFORNIA UNIVERSITY OF MAC based files must be sent as Post- PENNSYLVANIA Brian O’Connor script files (please subset and embed all Mathematics Education: Department of Search Committee Chairperson fonts). PDF files are also acceptable. Mathematics and Computer Science. Box 5054 TTU Duties will include teaching introductory Cookeville, TN 38505 Camera-ready art: Should be prepared and upper level undergraduate and according to the mechanical specifica- graduate courses in mathematics and an AA/EEO tions shown on this page. applications-based elementary education Classified Rates (includes a a free list- mathematics sequence (MAT 120/130); ing in MAA Online to appear the same seeking external funding to support TEXAS month as the print ad): $2.25 per word. research interests, facility upgrades, and/ or outreach programs; serving as a Contact the MAA Advertising liaison with the College of Education to TEXAS LUTHERAN UNIVERSITY Department toll free at 1-866-821- ensure course compatibility of content Department of Mathematics invites 1221, fax: (703) 528-0019 Classified and teaching methodology with applications for a tenure-track assistant and MAA Online ads may be sent via elementary and secondary education professorship beginning August 2003. email to [email protected].