FOCUS May/June 2000
FOCUS is published by the Mathematical Association of America in January, February, FOCUS March, April, MaylJune, August/September, October, November, and December. May/June 2000 Editor: Fernando Gouvea, Colby College; [email protected] Volume 20, Number 5 Managing Editor: Carol Baxter, MAA [email protected] Inside Senior Writer: Harry Waldman, MAA [email protected] 4 General Double Bubble Conjecture in R3 Solved By Joel Hass Please address advertising inquiries to: Carol Baxter, MAA; [email protected] 6 MAA Professional Development Workshops Summer 2000 President: Thomas F. Banchoff, Brown University 7 Have You Met Everybody ... ? First Vice-President: Barbara L. Osofsky, Second Vice-President: Frank Morgan, By Nora Franzova Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: 8 Finding Your Second (and Third ... ) Job Gerald J. Porter By sarah-marie belcastro and Michael Prophet Executive Director: Tina H. Straley Associate Executive Director and Director 9 bmovative Programs Address Professional Development of Teaching of Publications and Electronic Services: Assistants & Adjuncts Donald J. Albers By Teri ]. Murphy et al. FOCUS Editorial Board: Gerald Alexanderson; Donna Beers; J. Kevin 11 Short Takes Colligan; Ed Dubinsky; Bill Hawkins; Dan Kalman; Maeve McCarthy; Peter Renz; Annie Selden; Jon Scott; Ravi Vakil. 12 Standards Based Education By Robby Robson and M. Paul Latiolais Letters to the editor should be addressed to Fernando Gouvea, Colby College, Dept. of Mathematics, Waterville, ME 0490 I. 14 MAA and Tensor Foundation Announce New Awards Subscription and membership questions By Florence Fasanelli should be directed to the MAA Customer Service Center, 800-331-1622; e-mail: 16 Preliminary Announcement for Contributed Papers for [email protected]; (301) 617-7800 (outside New Orleans U.S. and Canada); fax: (301) 206-9789. Copyright © 2000 by the Mathematical 20 1999 Contributors to MAA Funds and Programs Association of America (Incorporated). Educational institutions may reproduce articles for their own use, but not for sale, 23 Employment Opportunities provided that the following citation is used: "Reprinted with permission of FOCUS, the newsletter of the Mathematical Association of America (Incorporated)." On the cover: A standard double bubble. Created by John Sullivan, University of Periodicals postage paid at Washington, DC Illinois at Urbana. and additional mailing offices. Postmaster: Send address changes to FOCUS, Mathematical Association of America, P.O. Box 90973, Washington, DC 20090-0973. FOCUS Deadlines ISSN: 0731-2040; Printed in the United States Aug/Sept October November of America. Editorial Copy July 14 September 15 Display Ads July 28 August 21 October 6 Employment Ads July 21 August 10 September 22
2 May/June 2000 FOCUS Georgia Benkart Named 2000-01 P61ya Lecturer MAA Earmarks Funds
The MAA's On a rotating basis, the MAA sections can for Student Activities Board of invite any of the current P6lya lecturers By Tina H. Straley Go v ern 0 r s to speak at a regional meeting. The award has selected includes a stipend and covers the travel The MAA is earmarking all revenues G e 0 r g i a expenses involved in attending the sec- generated by the MAA Visa Card to sup• Benkart, of tion meetings. The scheduling of specific port student activities at the Section level. the Univer- lectures is done by the Committee on Sec- Since 1989, the Exxon Education Foun• sity of Wis- tions, which is chaired by David Stone. dation has awarded the MAA annual consin, grants to support a variety of student ac• Madison, as Past P6lya lecturers were John Ewing, tivities. These activities, which have in• the newest Patricia Rogers, Carl Pomerance, Robert cluded the MAA Student Lecture, Student Georgia Benkart, new George P6lya Osserman, Underwood Dudley, Laszlo Workshops, and special paper and poster George P6lya Lecturer. Lecturer. She Babai, and Ronald Graham. Currently, sessions at national meetings, have in• will serve for two lecturers, Colin Adams (1998-99, creased student participation in MAA the academic years 2000-01 and 2001-02. 1999-00) and Joseph Gallian (1999-00, meetings and in mathematics in general. 2000-01), are visiting the Sections .• Unfortunately, the newly formed Exxon/ Mobil Corporation has informed us that Thomas Rishel Named Associate Executive they are no longer able to support stu• dent activities, so MAA has been actively Director for Programs and Services pursuing an alternative source of fund• ing. Thomas graduate Teaching and as Senior Lecturer Rishel, from in the department of mathematics. The MAA's activities and programs for Cornell students are an important part of the University, Rishel's service to the MAA includes Association's service to the mathemati• will become chairing its Task Force on Graduate Stu• cal community. Our programs foster the the MAA's dents and as a member of the MAA Task development of tomorrow's mathemati• Associate Force on Institutional Membership as cal pioneers and leaders. In order to con• Executive well as a member of the AMS-MAA Joint tinue to be able to fund these programs, Director for Committee on Employment Opportuni• the MAA has earmarked all revenue gen• Member ties. He is also the chair of the Selection erated by the MAA credit card (backed Services Committee of the MAA Professors for by MBNA Bank) for use in student ac• Thomas Rishel, new Asso• and Pro• the Future Program and is active in the tivities. I hope that you continue to sup• ciate Executive Director for grams in Seaway Section. port MAA's student activities by using MAA Member Services July 2000. your MAA credit card, or obtaining one and Programs. Rishel is the author of The Academic Job if you don't already have one. For infor• Rishel holds Search, published by the AMS; A Hand• mation on the MAA credit card call 1- a doctorate from the University of Pitts• book for Mathematics Teaching Assistants: 800-847-7378. Promo code: E4CB .• burgh and has published papers about Preliminary Edition, an MAA publica• c-spaces and Morita's M spaces. He has tion; and Writing in the Teaching and Tina H. Straley is the Executive Director spent the last twenty years at Cornell Learning of Mathematics, an MAA pub• of the Mathematical Association of University as the Director of Under- lication in the MAA Notes Series .• America. Proposed Fiscal 2001 Budget Calls for $2.8 Billion Increase in Science R&D President Clinton's budget for Fiscal proposal, with a requested increase in its Have You Moved? Year 2001, which he submitted to Con• budget of $675 million, or 17.3 percent. gress in early February, includes a $2.8 Mathematical programs at the Depart• The MAA makes it easy to change your billion increase for scientific research and ment of Energy (DOE) would also receive address. Please inform the MAA Service development across all federal agencies significant increases, while the request for Center about your change of address and disciplines. the Department of Defense's basic re• by using the electronic combined mem• search accounts would fare less well. The bership list at MAA Online (http:// New funding is directed at the core pro• President's request will be evaluated by www.maa.org) or call (800) 331-1622, grams of mathematical research at the Congress over the next few months. See fax (301) 206-9789, email National Science Foundation (NSF) and http://www.maa.org/features/ [email protected], or mail to MAA, other government agencies. The NSF budgetOO.html for an analysis of the pro• P.O. Box 90973, Washington, DC 20090. would benefit under the current budget posed budget. • FOCUS May/June 2000 General Double Bubble Conjecture in R3 Solved By Joel Hass components are enclosed the shape as• Each surface in this bubble has constant sumed is known as a "standard double mean curvature, or constant average In March 2000, the proof of the general bubble." This is made of pieces of three bending. This corresponds to a constant double bubble conjecture in R' was an• round spheres, meeting along a common pressure difference between the two re• nounced by four mathematicians: circle at an angle of 120· as in Figure 1. gions the surface separates. Constant Michael Hutchings of Stanford Univer• The double bubble conjecture asserts that mean curvature surfaces are very special, sity, Frank Morgan of Williams College, this shape is the most efficient one pos• but far too general to classify. In a com• and Manuel Ritore and Antonio Ros of sible in enclosing two given volumes. plicated soap froth, each piece of surface the University of Granada. Their proof More precisely, if VI and V2 are two has constant mean curvature, and can be completes a long history of work on the specified volumes, the conjecture is that far more complicated than just a piece of problem. the surface enclosing these volumes and a sphere. Fortunately, the surfaces used having smallest possible area is a standard in constructing an optimal two region Since early farmers started to fence off double bubble. The special case where bubble are very special. White, Foisy and fields and beer drinkers started to design VI =V 2 was established earlier [HHSJ. Hutchings applied symmetry arguments clay tankards, people have pondered how Hutchings, Morgan, Ritore and Ros have to show that the optimal double bubble to enclose as much as possible within a now established the double bubble con• is a surface of revolution-it is symmet• container. The Greeks dubbed these jecture for all volumes. ric under rotation around an axis. The "isoperimetric" (same perimeter) prob• possible configurations now become trac• lems. Zenodorus made the first known Here is a sketch of the proof. The first is• table, and Hutchings established that attempt to show that the circle is the sues that occur are existence and regu• there was a rather limited number of pos• shortest curve in the plane enclosing a larity. How do we know that any solution sible shapes for the cross-sections, some given area, some unknown time between that is a reasonable type of surface exists? of which are shown in Figure 2. Some of \ ( ) / } /
Figure 1: A standard double bubble Figure 2: Some possible cross sections of optimal bubbles:
the days of Archimedes (250 BCE) and It's possible to pose similar problems with the possible three-dimensional bubbles Pappus (350 CE). However, it was only no solution. Even if a solution exists, is are shown in Figures 3 and 4. The bubble in the nineteenth century that Weierstrass the optimal surface differentiable? The in Figure 3 is a torus bubble-one of its developed the analysis needed to provide existence and regularity results are due to two regions is topologically a solid torus, a complete proof. The optimality of the Fred Almgren and Jean Taylor see [ATJ. like the inside of a tire tube. The bubble round sphere in three-dimensional space Their work shows that there is an opti• in Figure 4 has three components, two of is an even harder problem. In 1882 mal bubble-like surface enclosing a given which are solid tori. It appears at first that Schwarz obtained the first proof. pair of volumes. This surface consists of this latter bubble encloses more than two smooth pieces having constant mean cur• volumes. However it needs to be shown Experiments with blowing soap bubbles vature, meeting along common curves at in the proof that the enclosed volumes give rise not only to spheres, but also to 120·, just like a soap film. (The same re• are connected, and that an optimal more complicated conglomerations of sult holds for optimal shapes enclosing bubble cannot contain a region divided bubbles. These can be foams with com• more than two volumes.) So what is this into two non-connected pieces. The con• plicated geometries, but when only two surface? nectedness of each region is still un-
4 May/June 2000 FOCUS known for bubbles with more than two bubble solution to R4. components, even in the plane. The proof of the double bubble conjec• An analysis due to Hutchings had shown ture joins recent breakthroughs such as that each region was connected when the [Weaire-Phelan] on the Kelvin Conjec• volumes were equal. This led to a solu• ture for partitioning R3, [Hales 1] on the tion of the equal volume case in [HS] by Kepler conjecture regarding the best a computational approach. The space of sphere packings, and [Hales2] on the all possible optimal surfaces, each of optimality of the hexagonal packing of which is a torus bubble, was described R2 . As a result, the study of optimal shapes precisely. Bya comparison to the standard has taken us to the point where the tech• double bubble, all the possible competi• niques have real connections in physical tors were ruled out. Looking at unequal and biological applications. The coinci• volumes, Hutchings, Morgan, Ritore and dence of the mathematical solutions and Ros extended Hutchings's arguments to Figure 3: A two-component torus bubble nature's shapes show us that we are study• show that the larger volume is always con• ing the right mathematical theories and nected and an instability argument to dard double bubble shows that it is un• equations. This has begun to be seen in show that the smaller volume has at most stable. exciting new studies of foams, crystal two components. The resulting possibili• growth, and other complex structures. ties were more general than for equal vol• It is worth noting that a comparison of umes, but still tractable. the general solution with the proof in the References: case of equal volumes indicates that a For each resulting possibility for an opti• good mathematical idea is still worth a [ABFHZ] M. Alfaro, J. Brock, J. Foisy, N. mal bubble configuration, Hutchings, year of computer time. Hodges and J. Zimba, The standard Morgan, Ritore and Ros construct a de• double soap bubble in R2 uniquely mini• formation which preserves the volume We should remark on some related re• mizes perimeter, Pac.J. Math. 159 (1993), enclosed in each region, but decreases the sults. A group of undergraduates work• 47-59. total surface area. In other words, they ing with Morgan in the Williams College establish that the non-standard configu• [AT] EJ. Almgren and J. Taylor, The ge• rations are unstable; they aren't even op• ometry of soap films and soap bubbles, timal among nearby shapes. For soap Sci. Amer. 235 (1976),82-93. bubble fans this has the disappointing consequence that we cannot expect to [HHS] J. Hass, M. Hutchings and R. create one of the non-standard shapes Schlafly, The Double Bubble Conjecture, with cleverly blown soap bubbles. Electronic Research Announcements, Amer. Math. Soc. 1 (1995),98-102. The tricky part of the proof is construct• ing the deformations. One way to deform [Halesl] Hales, T. C. ,Sphere packings. I, a bubble is to rotate the entire thing, an Discrete Comput. Geom. 17 (1997), no. 1, operation that doesn't change its area or 1-51. volume. What Hutchings, Morgan, Ritore and Ros do is to rotate only portions of [Hales2] Hales, T. C. , The Honeycomb the bubble, pieces carefully chosen to Conjecture, E-print math.MG/9906042 blend smoothly into the rest of the bubble. A nice analogy is given by a great [Weaire-Phelan] Weaire, D., Phelan, R., circle on the 2-sphere, like the equator, A counter-example to Kelvin's conjecture which is an example of an unstable geo• on minimal surfaces, Philos. Mag. Lett. 69 desic. Rotating a great circle gives another Figure 4: A three-component torus (1994),no.2, 107-110 .• great circle. But the rotation vector field, bubble the derivative of this rotation, has zeros Joel Hass teaches at UC Davis. He is one of at two points. If we just rotate a half of SMALL REU program had proved the the authors of the recently published book the great circle lying between these two general double bubble conjecture in the How to Ace Calculus, the Streetwise zeros, we still get a curve of the same plane in 1993 [ABFHZ]. In a remarkable Guide (see the review on MAA Online). length but create corners where we rotate. achievement in the summer of 1999, un• These can be smoothed off to shorten the dergraduates Ben Reichardt of Stanford, Figures 1, 2, and 4 provided by John curve. A length preserving deformation Yuan Lai of MIT, and Cory Heilmann and Sullivan, University of Illinois at Urbana. supported on a subset of a geodesic im• Anita Spielman of Williams College, plies it is unstable. Similarly a deforma• working together in that summer's Will• Figure 3: provided by Joel Hass of UC tion constructed on part of a non-stan- iams REU, extended the general double Davis and Jim Hoffman of MSRI. 5 FOCUS May/June 2000 MAA Professional Development Workshops Summer 2000
Viewpoints: Mathematics and Art The short course, presented by Professor address: http://www.math.unh.edu/ Robert Devaney, will focus on methods -blacklnewton/pre-regi stration. htm I. EPADEL Summer Workshop-June 4-9, by which ideas from dynamical systems 2000; Franklin & Marshall College, theory may be included in various parts Proofs and Conjectures: The Story of Lancaster, PA Registration Fee: $325 (in• of the undergraduate curriculum. These the Alternating Sign Matrix Conjecture cludes room and board) topics provide an ideal opportunity to Viewpoints is an intensive five-day work• give students (particularly lower division Ohio Section Short Course-June 28-30: shop featuring classroom-tested activities students) a glimpse of modern ideas in Cedarville College, Cedarville, OH and field trips which explore the connec• mathematics in a setting that is germane Discrete mathematics is now a regular tions between mathematics and art. Ac• to the course at hand. Please contact: part of the undergraduate mathematics tivities and materials from Viewpoints Annette Cooper at 970.247.7232, curriculum at most colleges. Too often, can be used collectively to form a full-se• [email protected]. the adjective "discrete" also applies to the mester course in Mathematics and Art individual topics which seem to bear little (such as the ones taught by the facilita• Teaching Statistics: Data, Concepts, Activities relationship to each other. They lack a tors), or as separate, independent mod• sense of historical development. The sto• ules to enhance and enliven courses rang• Allegheny Mountain Section Short ries and connections are missing. This ing from elementary algebra and geom• Course-June 19-23,2000: Allegheny Col• short course, presented by Professor etry to linear algebra, abstract algebra, lege, Meadville, PA David Bressoud of Macalester College, and real analysis (as also done by the fa• This short course, presented by Profes• provides a chance to share some favorite cilitators). Contact: Annalisa Crannell, sor Allan Rossman, aims to help instruc• stories. They interweave in often surpris• [email protected]. Web address: tors teach introductory statistics in ac• ing ways and each lead, in some fashion, http://www.iandm.edu/Departments/Math• cordance with the recommendations of to the story of the alternating sign ma• ematics/m_irantzlviewpoints/Deiault.html. a joint ASA/MAA committee: emphasiz• trix conjecture. There will also be a lot of ing statistical thinking with more data hands-on work, with opportunities to Partnerships: Engineering and concepts, less theory and fewer reci• explore the algorithms and patterns that and Mathematics pes. Participants will engage in hands-on arise. Registration Fee: $100. Please con• investigations of statistical concepts and tact: James Sellers at 937.766.7695, June 5-10: Rensselaer Polytechnic Insti• methods that can be adopted for imme• [email protected]. Web Address: tute, Troy, NY. Application Deadline: May diate use with students. Many of these http://www.cedarvi lie .edu/dept/sm/j as/ 1,2000 activities will make use of Minitab statis• maashortlshcou rse. htm. Participants will study materials devel• tical software. These activities include oped by NSF Mathematical Sciences and such topics as data collection, exploratory Partnerships: Life Sciences their Applications Across the Curriculum data analysis, randomness, and statistical and Mathematics program, and work in interdisciplinary inference. Sessions will also be devoted teams to adapt and develop materials for to discussing resources for teaching sta• July 17-22: Carroll College, Helena, MT use at their home institution. Topics come tistics and to issues of assessing students' Application Deadline: May I, 2000 from all levels of the undergraduate cur• learning of statistics. Registration Fee: Participants will study materials devel• riculum in mathematics and engineering $170; Room and Board: $140 Contact: oped by NSF Mathematical Sciences and using storyboarding and technological Steve Bowser, 814.332.5348, their Applications Across the Curriculum delivery. Applications for the workshop [email protected]. Web address: program, and work in interdisciplinary are accepted from teams of two to four, http://webpub.alleg.edu/employee/s/ teams to adapt and develop materials for which must include one mathematics and sbowser/sscOOAdv. htm. use at their home institution. Topics come one engineering faculty. This is a work• from all levels of the undergraduate cur• shop of the MAA Partnerships Project in In Search of Newton riculum in mathematics and population interdisciplinary mathematics and is growth, the environment, human physi• sponsored by a grant from the National Northeastern Section Short Course-June ology, animal population, and more. Ap• Science Foundation. Please contact: 25-30, 2000: University of New Hamp• plications for the workshop are accepted Maureen Callanan, (FAX) 202.483.5450, shire, Durham, NH from teams of two to four, which must [email protected] Web address: http:// www.maa.orglpfdev/engpartnership.html. include one mathematics and one life sci• This short course will focus on the com• ences faculty. This is a workshop of the bined calculus and physics curriculum at Teaching Dynamical Systems MAA Partnerships Project in interdisci• University of New Hampshire. Partici• Across the Curriculum plinary mathematics and is sponsored by pants will study updates and changes to a grant from the National Science both the calculus and physics curriculum, Rocky Mountain Section Short Course• Foundation. Please contact: Maureen and will examine class materials and the June 5-9, 2000: Fort Lewis College, Callanan, by (FAX) 202.483.5450, or studio format of instruction. Contact: [email protected]. Web address: http:// Durango,CO Kelly Black, [email protected] Web www.maa.orglpfdevengpartnership.html. 6 May/June 2000 FOCUS
Have You Met Everybody.•. ? Of course publishers also approached this and less bylaws, but I guess my timing was By Nora Franzova issue and I was able to pick up some "new wrong. age," reform/internet textbooks that have The undergraduate students' research some parts of the book available only over CCT hat place is a maze. It is so hard to poster session was very impressive and the internet. And let's not forget the TI find your way around:' commented my even more impressive was how many of corner, and their new TI -Interactive pro• friend when I told her that I was going to us walked over to the Omni (it was very gram, which I was hoping to see. It was the Marriott off of Connecticut Avenue cold outside) to see the session. The stu• not available at noon on Wednesday, but for the Joint Mathematics Meeting. "She dents were absolutely wonderful, excited later everything was working well and the was right:' I kept thinking as I stood in about their work, and I was glad to "TI green shirts" were busy as always. the middle of a huge lobby trying to fig• breathe in some of their enthusiasm. (Un• Wednesday was the first day for those in• ure out a bijective map between the room fortunately the room was so small that terested in downloading the Beta version assignments and the names appearing on very soon only the enthusiasm was left to of TI -Interactive and start testing it. the signs. breathe.) There were MAA books, Math Horizons My goal at this year's meeting was to On Saturday at 8 am I was ready to listen t-shirts and many other booths worth vis• gather all available information that to "Philosophies in Mathematics Educa• iting and mentioning, but hunger kicked would somehow help me in developing tion." The session covered calculator use, in, so I ventured out. We all know that an online math course for our college. I computer use, and their role in enforc• , the worst thing about conferences is that successfully made it to the Delaware Suite ing understanding instead of symbol one has to eat in a hotel. This one was a bright and early Wednesday morning to pushing. And there I found the answer great exception. Walking a hundred yards listen to "Innovative Uses of the World to all my problems. I found someone who to Connecticut Avenue in Washington Wide Web in Teaching Mathematics." would not mind doing my work for me DC means walking a hundred yards to the Unfortunately, the computers did not for free-http://www.math.temple.edu/ cuisine of the world. On one side of the find their way so successfully and ended -cow. Want to make students do their street are places with Thai and Indian up in the Maryland Suite, so the first homework, but don't want to grade it? Try food, and on the other bagel shops, couple of talks had to be a little less com• COW (Calculus on the Web). I assume Baskin Robbins, and McDonalds. One puter based and more jovial. Hardship by now everyone has contacted Dan Reich of the tired cashiers at McDonalds asked brings people together, and by lOam, at Temple University and he (and his col• me on Saturday, "When is this conference everybody in the room was in good spir• leagues) will soon reconsider their offer ending?" right after yelling into the crowd its and full of enthusiasm for each was of software and server for free, but I sure that there would be a lO-minute wait for holding a huge list of useful web links and hope to still get in. Since then I have Big Macs. No one listened to him. There some JavaScript tricks. Once the comput• played with COW. I still need to com• were curvatures to be discussed, job in• ers were finally working, the group had pare it to similar systems available, but at terviews to be analyzed, and web ad• a live interactive lecture on graphing de• this point it has met and exceeded my dresses to be exchanged. rivatives from the University of Keele in expectations (including the name). Great Britain, proving that the whole Since one always gets great pleasure from Very soon I realized that even though it world can be one classroom. a good lecture I tried to visit at least some is possible to walk in and out of different invited talks. "I am a MAA speaker, so I At noon the Exhibits and Book Sales sessions, the experience is best experi• will be friendly" announced Ronald Gra• opened and the real mingling started. For enced when I sit through an entire ses• ham in his opening speech for his invited starters, I picked up a new brain at the sion. Then I become part of a group that talk on "Combinatorics at the Cross• Thinkwell booth. It was blue in color and has a goal, an interest, whether it is con• roads," to the laughter of a crowded ball• mostly usable as a stress ball. Then, I trol theory, quantum computation or the room on Wednesday afternoon. And he made some soapy bubbles at Zometool, need of College Algebra reform (I defi• was. Soon afterwards I had to leave to while looking for the shortest paths. nitely believe there is a need for that.) teach my first class of the spring semes• However my primary interest was to in• ter. But I returned to see more math and There were so many interesting sessions vestigate the possible and impossible more friends, to make dates for lunch and talks and I could not attend all of ways of typing and posting math prob• meetings that I did not keep, to attend them. One about which I heard really nice lems, quizzes and discussions on the web. coffee meetings that lasted more than an things was the Teaching Awards Recipi• I found answers to my questions at the hour, to talk to graduates from my grad ents Presentation. I also did not make it booths of Math Type and Math (Internet school, and to talk to people I talk to only to any of the MAA Minicourses, which I Math Consortium). Both have taken up once a year, at this conference. really regret. But next year it will be all the endeavor of enabling our students to this good math stuff plus it will be in New type some math formulas without hav• Friday evening I visited the Isolated Orleans. Crawfish and beignets, here we ing to learn intricate cryptography. Math Teachers of Statistics annual meeting, come! • representatives were very persuasive, and where they discussed becoming a are even willing to come to a school and SIGMAA (Special Interest Group under Nora Franzova teaches at Harford Com• customize to one's needs. MAA). I was hoping for a little more stats munity College in Maryland.
7 FOCUS May/June 2000
the readers, to let us know what you think Finding Your Second (and Third ... ) Job about the following questions. We will amalgamate the responses in a follow-up By sarah-marie belcastro and Michael Prophet article in the Concerns ofYoung Mathema• ticians newsletter.
At the January 2000 Joint Meetings in sider those things that make you tense • How many teaching letters should Washington, DC the Young Mathemati• when you get up in the morning. you get? cians Network and Project NExT spon• sored a Panel Discussion entitled "Find• The best time to apply is 3 or 4 years out • Where can you get teaching letters if not ing Your Second Job." With the appar• of the doctorate; in general it's more dif• from your current department? ently improved job market, the topic of ficult for those with tenure to find jobs finding a second (or more • How many research let• generally a next) job seems to ters should you get? be on many peoples' minds, il• lustrated, for example, by the • Is it important to get a turnout at the Panel Discus• research letter from your sion of about 60 people. graduate advisor?
The panel discussion was or• • Who do you ask for re• ganized by Phil Gustafson search letters? (Mesa State University), mod• erated by Michael Prophet • How much credit do (University of Northern Iowa) people in the jobs get to• and included a panel of 4 ten• ward tenure? ure-track/tenured people: Ed• ward Aboufadel (Grand Valley • How does one point State University), Dan Schaal out, in the application (South Dakota State Univer• packet, the improve• sity), Michele Intermont The panelists at the discussion on "Finding Your Second Job" at the ments one has made (Kalamazoo College), and Washington, DC Joint Mathematics Meetings, January 2000 over time? (How do you Anita Solow (Randolph-Ma• express why are you com• con Woman's College). (mostly due to financial considerations patible with institution X now, whereas of the hiring department). you were not before?) The format was simple: the moderator posed various questions to the panel and Be highly selective; customize your appli• • What are some complaints that people discussion ensued. The audience was en• cation, particularly the cover letter. tend to have about their jobs, which can couraged to offer answers, as well as re• be resolved by changing jobs? sponses to panel answers. The default Mention your reasons for leaving your situation was supposed to be that of an current job in your application, but • What are some complaints that people applicant currently holding a tenure• phrase them positively. have in common about their various jobs, track job. We summarize below the main which usually cannot be resolved by points that were raised-a more detailed Be more concrete the second time around changing jobs? (and much longer) summary appears in in your teaching statement. Improve your the February 2000 Concerns of Young teaching. • How much personal/family information Mathematicians newsletter, available at should be included in the application http://www.math.uni/-prophetlpanel. Get a letter of recommendation from packet, and why? • someone (perhaps the chair, if appropri• A tenure track position gives you the time ate) in your current department. Please send responses to: and ability to create your own future op• [email protected] or portunities. Keep your vita updated, be• Consider letting an administrator know [email protected]. cause your situation may change and you that you're on the market in time to get may want or need to change jobs. your courses covered. If you like your sarah-marie belcastro and Michael current job, request a leave of absence Prophet teach at the University of North• A good reason to be on the market is a when you obtain a new job. ern Iowa and served this year on a hiring mismatch between your concerns and committee together. While Mike attempts those of your current institution. Con- Here are some more issues we would like to excel at competitive trivia, sarah-marie to see addressed. Therefore, we invite you, prefers to study feminist philosophy ofscience.
8 May/June 2000 FOCUS Innovative Programs Address Professional Development of Teaching Assistants & Adjuncts By Teri J. Murphy, William Branson, Sol Friedberg, Luise-Charlotte Kappe, James Madden, David Manderscheid, Lisa Mantini, Elena Marchisotto, Paul McCreary, Andrew Nestler, Jodie Novak, Sue Plisch, Natasha Speer, Julia Wilson, and Lee Zia
At the Joint Meetings in DC, the AMS- tage in this role. All of the speakers un- Need for Dissemination MAA Committee on Teaching Assistants derscored the need for departmental sup- and Part-Time Instructors organized the port (not just money) in providing op- The talks drew as many as 40 audience Special Session, "Innovative Develop- portunities for TAs, adjuncts, and perma- members. Some of these listeners at• ment Programs for Teaching Assistants nent faculty to discuss issues related to tended all 12 talks. Some of these listen- and Part-Time Instructors" (organizer, teaching. ers came from institutions that are exam• Teri J. Murphy). The Committee sought ining or re-examining the roles of expe• to gather and disseminate information Preparation vs. On-going Development rienced instructors, permanent faculty, about sample programs that support TAs and the administration in the prepara• and adjuncts in their efforts to be effec• The Special Session sought to showcase tion, development, and mentoring ofTAs tive instructors. The twelve 25-minute innovative programs that address the and adjuncts. Several people (speakers talks described a variety of models. Al• needs ofTAs and adjuncts in the current and audience-members alike) suggested though most of the programs were de• complex teaching environment. Tradi• that the mathematics community provide signed to meet the needs of a particular tional models of instructional training a forum for discussing issues and experi• institution, or team of institutions, some include orientation sessions before classes ences related to the preparation and de• themes nevertheless arose from the ses- start, and regular meetings of instructors velopment of these teachers of college sion. for a particular course. As with the infor• mathematics. mal conversations mentioned above, in Need, Momentum, and Support many cases, such efforts have been useful In the current environment of rapidly ris• but still leave a need for additional activi• ing costs for higher education and ever• The need for comprehensive develop• ties. One alternate model presented by increasing competition for the best stu• ment programs for TAs and adjuncts has several speakers builds on a philosophy dents, colleges and universities have be• reached a critical level. Some campuses of ongoing development. These programs come more conscious of students' needs maintain the tradition of handing new in• hold classes or seminars (some required, and more concerned about the quality of structors the textbook and a syllabus, with some voluntary, some counting for teaching. Mathematics departments are no additional preparation or develop• credit), in which participants (varying being told by their administrations, if ment opportunities. The result is a set of combinations of TAs, adjuncts, and per• they didn't already know it, that TAs need fledgling instructors who do the best they manent faculty) explore issues related to more preparation than being handed a can in isolation. For instructors who must teaching. Activities can include readings, textbook and a syllabus. Yet external pres• adjust to a new language and culture the discussions, analysis of case studies, ob• sures are not the sole motivation for the task is even more daunting. Many insti• servations and videotaping, consultations attention to the preparation and ongo• tutions have recognized this need. The with experienced instructors, assign• ing development of TAs. If we look programs described during the session ments to experiment, role-playing, mod• deeper, we find that, in fact, TAs are happy were examples of efforts to increase and eling activities and further reflection. In to develop. In many cases, they look for• improve development opportunities. addition to building skills, such activities ward to a career that includes teaching as Some of the programs described were center on helping instructors to reflect on a primary responsibility and they want initiated by TAs, some by faculty, some their own beliefs (which affect their be• to explore this part of their career while by teams of institutions. Several gradu• haviors) about teaching, learning, the they are graduate students. ate teaching assistants spoke about their needs and strengths of students, and the enthusiasm for teaching and their moti• nature of mathematics. Some programs While most of the talks described pro• vation for their own efforts to improve have the long-term goal of preparing par• grams for TAs, few speakers discussed development opportunities at their insti• ticipants for careers that include teach• programs that include or target adjunct tutions. They pointed out that many TAs ing. Such programs are particularly well• instructors. The Committee believes that engage in spontaneous, informal conver• placed for improving the quality of un• some of the themes discussed above are sations with other TAs as an outlet (of• dergraduate mathematics education relevant to adjuncts as well (e.g., the need ten, the sole outlet) for their interest in (short- and long-term) because the fac• for support and opportunities for col• teaching. They also pointed out that such ulty of the future (2- and 4-year colleges, laboration and development) and that informal interactions are useful but in• as well as research universities) are largely there are other issues yet to surface. Thus, adequate for addressing TAs' needs as drawn from the current pool of graduate the Committee would like to hear from current and future teachers. In addition, students. The speakers also believed that more programs that include or target they suggested that experienced TAs professional development programs can adjuncts. If you have information about themselves can play an impo~tant role in be used as tools to recruit students and such programs, please contact Murphy the design and implementation of devel• that graduate students who participate in ([email protected]) or Suzanne opment activities, and that their peer re• development programs have an advan• Lenhart ([email protected]) .• lationship to new TAs can be an advan- tage on the job market. 9 FOCUS May/June 2000
Call for Nominations: $4 million Gift to Trinity Col• Letter to the Editor Frank and Brennie Morgan Prize for lege Establishes Three H.L. Outstanding Research in Mathemat· Dorwatt Professorships About the "Math Wars" ics by an Undergraduate Student
T he Morgan Prize Committee is seek• T he Department of Mathematics at Concerning the "math wars", I'd like to ing nominations for the 2000 award. The Trinity College in Hartford, CT received enter the fray. Frank and Brennie Morgan Prize for a gift of $4 million from an anonymous Outstanding Research in Mathematics by alumnus, who was a mathematics major I used to think that we mathematicians an Undergraduate Student is awarded at Trinity and who had no previous his• and mathematics educators were, by and jointly by the AMS, MAA, and SIAM. The tory of giving to the College. The gift es• large, examples of intelligent life. I guess prize, which was endowed by Mrs. Frank tablishes the Robert C. Stewart Faculty I was wrong. Lately a lot of us have been Morgan of Allentown, PA, seeks to rec• Development Fund to endow three post• thumping our chests: "Me Tarzan! Me ognize and encourage outstanding math• doctoral teaching positions and to en• Smart! Me Know! Those other guys stu• ematical research by undergraduate stu• hance research opportunities for mem• pid!" dents. bers of the Department. The Fund is named after a long-time former member Let's see: I know some stuff you don't Nominations and research papers may be of the Department at Trinity whom the know and you know some stuff I don't submitted by a student or by a nomina• donor regarded as crucial in his develop• know. Of course the stuff I know is im• tor on behalf of a student. The recipient's ment. portant and the stuff you know is worth• research need not be confined to a single less. paper and need not be published, but When the program endowed by the Fund must have been completed as an under• becomes fully operational, Trinity will set Perhaps all this bravado is understand• graduate. The recipient must have been up three H. L. Dorwart Visiting Assistant able given that we are half-blinded by a enrolled as an undergraduate student in Professorships, to be filled on a staggered world undergoing incredibly rapid a US, Canadian, or Mexican college or three-year basis by new or recent doctor• change and so the future is a blur. university in December, 1999. ates. (Dorwart, a mathematician who died in 1998 at the age of96, was Stewart's Thus, if some of us can find temporary All submissions must include at least one mentor.) The areas of specialization of the comfort by planting our feet firmly in air letter of support from a person familiar visitors will be chosen to match the areas and speaking with great certainty, the rest with the student's research. See http:// of interest of members of the Depart• of us will understand, shrug our shoul• www.maa.orglawards/morgan_nom.html ment. ders, and look away. for more detail. The first position, for 2000-01, will be in Andrea Rothbart Nominations and submissions should be functional analysis, and it is anticipated Webster University sent to the Morgan Prize Committee, c/o that the next two hires will be in graph St. Louis, MO Robert Daverman, American Mathemati• theory and special functions. Aside from cal Society, University of Tennessee, De• highly competitive salaries, the visitors partment of Mathematics, 312C Ayres will also have adjusted teaching loads, as Hall, Knoxville, TN 37996-1330, by June will the members of the Department 30, 2000. Questions should be addressed whose areas they match. Department to Robby Robson, 2000 Morgan Prize members will also have increased sabbati• committee chair, [email protected]. cal opportunities. • Check out the Columns on MAA Online
MathTrek, MathMuse Devlin's Angle Math Chat Cut the Knot!
Ivars Peterson Keith Devlin Frank Morgan Alex Bogomolny Check them out at http://www.maa.orginews/columns.html 10 May/June 2000 FOCUS
Short Takes
Summer Short Course in Durango search work done by undergraduates, es• (sponsored by pecially the work coming from the vari• ~ Wolfram Re• Fort Lewis College will host an MAA ous undergraduate research projects. The search, Inc.) Short Course entitled "Teaching Dynami• journal's web· page at http:// ~.~ were awarded cal Systems Across the Curriculum" on www.morehead-st.edu/colleges/science/ second place June 5th-9th, 2000. The instructor for the math/mejam/ explains that the journal . ~....• n~ among 17 en• course will be Robert L. Devaney from "accepts papers which are outside the , trants from -III.,.,. Boston University. The author of several realm of the typical undergraduate cur• nine coun• ",,4 , textbooks in dynamical systems theory, riculum and which emphasize the appli• tries. The Devaney has also written Chaos, Fractals, cations of mathematics while maintain• Macalester and Dynamics: Computer Experiments in ing significant mathematical interest. Pa• entry was an Modern Mathematics and A Tool Kit of pers may be historical, expository, or Enneper surface sculp• Enneper sur• Dynamics Activities. completely original in nature but must ture face, a beauti• adhere to strict academic standards and ful minimal This course will focus on methods by must emphasize some aspect of the ap• surface with tremendous symmetry and which ideas from dynamical systems plications of mathematics." The editors esthetic appeal. Stan Wagon, one of the theory may be included in various parts encourage faculty supervising under• team members, said that the Enneper sur• of the undergraduate curriculum. These graduate projects to consider working face sculpture "has tremendous over• topics provide an ideal opportunity to with students to produce an article and hangs, which make working it in snow give students (particularly lower division then to submit it to the journal. Every• quite dramatic. Fortunately the weather students) a glimpse of modern ideas in one hopes this will encourage more un• turned cold on the last days."Visit the site mathematics in a setting that is germane dergraduates to do research and perhaps at http://www. math. maca I ester.ed u/ to the course at hand. to go on to graduate school. snow2000 to see the Macalester sculpture along with much more information NCTM Tries to Set the Record Straight about the competition. For more details Copernicus Missing and better photos of the sculpture, see the reaction to the recent intense debate April issue of Math Horizons. copy of Copernicus' De In A on school mathematics, the National revolutionibus orbium coelestium ("On the Council of Teachers of Mathematics revolution of the heavenly spheres") was Publishers Offer Prize for Proof of (NCTM) has released three one-page reported stolen from the St. Petersburg Goldbach's Conjecture documents aimed at "setting the record Science Academy this February. straight." The first document summarizes Copernicus' book is only one of 23 other NCTM's basic position on mathematics Bloomsbury Publishing (USA) and rare books from the 16th and 17th cen• teaching: "school mathematics must meet Faber and Faber (UK) have announced turies that seem to have been stolen from the needs of a much greater proportion that they are offering a one million dol• the Science Academy library. During the of students than in the past; technology, lar prize to any person who can prove last two years, two other copies of when used appropriately, can enhance Goldbach's Conjecture within the next Copernicus' famous book have been sto• learning; and the most important skill two years. The prize is being offered to len from libraries in Poland and in the that business and industry demand is an help promote the book Uncle Petros and Ukraine. Interpol is investigating, and li• ability to solve problems." The second Goldbach's Conjecture, by Apostolos braries worldwide have been warned to document discusses the NCTM Standards Doxiadis (see the review by Keith Devlin be on the lookout for the books. Keith and their impact on mathematics teach• on MAA Online's Read This! section, Devlin discussed the theft and the signifi• ing in the US and in Canada. The third which can be found on the web at http:// cance of Copernicus' book in the March presents NCTM's argument for why www.maa.orgireviews/reviews.html).To edition of Devlin's Angle, his regular col• school mathematics should change rather be eligible for the prize, the proof must umn for MAA Online. See http:// than stick to more traditional approaches. be submitted to a journal indexed by www.maa.orglnews/columns.htmlto ac• The three documents are available at the Mathematical Reviews by March 15,2002, cess the columns by Devlin and others NCTM web site at http://www.nctm.orgl must be published by that journal by that appear on MAA Online. about/commonsense.html. March 15,2004, and must be judged to be correct by a six-member judging panel New Undergraduate e-journal Macalester Team Sculpts Snow whose members will be mathematicians chosen by the publisher. See Faber's web new electronic journal called The site at http://www.faber.co.ukl (click on A the Elite Breckenridge International Morehead Electronic Journal of Applica• At "Book News") for more information on Snow Sculpture Championships, the tions in Mathematics was recently created. the prize .• Macalester College/Minnesota team Its purpose is to provide an outlet for re-
11 FOCUS May/June 2000
Standards-Based Education
By Robby Robson and M. Paul Latiolais
What does an undergraduate degree in A frequent first reaction to those arguing tial equations and computer modeling mathematics mean? Does its holder have for learning outcomes and standards is techniques to solve problems from other a well-defined set of abilities, knowledge, that we already have them. After all, each disciplines means more, and such state• and skills? Why is it of value? Exactly what of us has a list of topics, educational ob• ments backed by publicly available per• does it mean to have completed a linear jectives, and grading criteria for the formance standards mean the most. algebra or calculus course? Professional• classes we teach. The standards-based ism makes answering these types of ques• approach, however, demands that objec• Distributed Learning tions a responsibility; accountability and tives and assessment methods be publicly competition in higher education makes stated, explicitly linked, and agreed upon Finally, the Internet and enormous answering them a necessity. by a larger community. As mathemati• growth in adult learning are rapidly cians we may think of this as the injec• changing the educational economy. Stu• Standards-based education offers an ap• tion of rigor into the educational process. dents at traditional campuses can take proach to answering these questions in a on-line classes offered by established col• way that can inform and guide curricu• The Case for Standards-Based Education leges other than their own. "Virtual" in• lum and instruction. At its core is the es• stitutions add more choices and adult tablishment of explicit performance stan• The first case for standards and outcomes learners in the work force have other op• dards and learning outcomes that can be is that they promise to improve the qual• tions through corporate training centers. meaningfully assessed, universally under• ity and relevance of education. Good Degree requirements phrased in terms of stood, independently verified, and easily standards set clear expectations for stu• locally understood conventions and col• compared. Among its consequences is a dents and assessable learning outcomes lections of courses without explicitly de• system in which progress can be mea• help them measure and adjust their own fined learning outcomes will not work in sured by demonstrated proficiency rather progress. Instructors can better determine this global economy. Standards become than by courses passed, credits earned, or the effect of their teaching and colleagues necessary to define and maintain the comparison with peers. Our intention can gain confidence that students will quality and integrity of the degrees our here is to explain standards-based edu• have met the necessary prerequisites institutions offer and to allow compari• cation in broad terms and to state a case when they enter a class. Standards lend sons of competing programs. for taking it seriously. structure and guidance to curricular de• sign, and their public nature helps us talk Closing Thoughts What Are Standards? about our good work with administra• tors and with colleagues other disciplines. Ultimately, we may have to define stan• The standards of "standards-based edu• But even if we are skeptical about their dards for entire degree programs, which cation" specify knowledge and skills that utility, there is reason to take standards involves identifying and agreeing upon students must demonstrate in order to seriously: We may not have a choice. the skills, knowledge, and abilities desired progress or be awarded a certification of every successful major. This is not easy, such as credit or a degree. They also de• New Directions in Education and neither is formulating a clear picture scribe the performance corresponding to of how the desired outcomes can be dem• various levels of proficiency. When ap• Most states are implementing standards• onstrated and assessed. Addressing a plied to entire curricula, standards often based secondary education systems. Dis• single course is far simpler and often re• address general processes ("applies math• ciplines that use mathematics are going quires the work of no more than one or ematical techniques to solve problems down the same road at the collegiate level. two faculty members, but the process is from physics and engineering"), whereas For example, the Accreditation Board for both revealing and gratifying. We recom• standards for individual classes are more Engineering and Technology now re• mend that it be tried. likely to include specific sets of skills and quires all engineering programs to be knowledge ("can express vectors in a outcomes-based. Our students and our Web References on Standards-Based given basis" or "demonstrates an under• colleagues are coming to expect educa• Education standing of the fundamental theorem of tion to be defined and measured in terms Calculus"). The complete specification of of outcomes and standards, and we would Our article "Standards-based Education a standard includes sets of criteria for do well to try to meet these expectations. and its Implications for Mathematics Fac• demonstrating proficiency ("can accu• ulty" on MAA Online (http:// rately sketch the proof and use the fun• There are also pressures from outside of www.maa.orglfeatures/robson.html) pre• damental theorem to differentiate inte• academia. A list of courses does not mean sents more thoughts about the possible grals") and examples of sufficient, defi• much to a prospective employer. A state• shape, form and consequences of stan• cient, and exemplary performance. ment that a student can apply differen- dards-based education in mathematics
12 May/June 2000 FOCUS departments and also includes further online references. A comprehensive list• Meetings of the Association ing of resources of outcomes assessment, relevant to higher education, can be Spring Section Meetings National Meetings found at the North Carolina State Uni• versity site http://www2.acs.ncsu.edu/ Metro New York Mathfest UPNsurvey/resource.htm. A reference for May7,2ooo August 3-5, 2000 the implications of K-12 reform for Bronx Community College, NY Los Angeles, CA higher education in Science is the AAAS Project 2061 Higher Education blueprint Michigan Joint Mathematics Meetings ( http://www. p roj ect2 061 .0 rg/too I 51 May 5-6, 2000 January 10-13,2001 bluepoIiHigherEd/text.html). In Engineer• Central Michigan University New Orleans, LA ing, the Accreditation Board for Engi• Mt. Pleasant, MI neering and Technology criteria docu• Mathfest ment ( http://www.abet.orgleaC/2000.htm ) Northeastern August 2-4, 2001 includes both the new outcomes-based June 16-17,2000 Madison, WI and the conventional criteria used to ac• St. Paul's School credit engineering programs. A good Concord,NH Joint Mathematics Meetings source for K-12 standards-based reform January 6-9, 2002 the Mid-continent Research for Educa• Pacific-Northwest San Diego, CA tion and Learning site "Standards at June 15-17,2000 McREL" (http://www.mcrel.org/stan• University of British Columbia dards) .• Vancouver, BC, Canada
Robby Robson teaches at Oregon State University. M. Paul Latiolais teaches at Portland State University
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filII 1""t:rWII 1\ "dmllllif/'n'd hi S,'"lmn ({ Smtih, " ,\lanh (to: ,\I, /",/",,/11 ("01llf'I/1I1 SOll/" !,/II//\ 111"1 /lot hi' 11III/llIhl" III /Ill Italn '!"' ,'0111/"','/','//1/1" f"·,,I,flt (If,' 1I/ll4rtlllt t' {'/1I11 1\ wlt/,'nl nl1,'/I hi X,'\I }/'r~ 1.1/" ///I/lrlll/,',' ("0111('11/1\. 51 .\1".11\01/ :\n'1IIII'. .\','\1 }/J/--( .\T /(NJIIJ /I". 11I"/IIh," (/11/1/11111,' 1111.1 dllohill/l 1111 01/"'1"11/,', /I,,,, 11/111"111, "I'{"//\ 13 FOCUS May/June MAA and Tensor Foundation Announce New Awards By Florence Fasanelli Hundreds of women strument, researching and girls have taken ad• career options, and at• vantage of special pro• tending monthly meet• grams designed to en• ings. They also solve courage college, univer• posted mathematics sity, and high school problems, solved a real• participants to study life application pro• mathematics. Since vided by their mentors, September 1995, many and prepare portfolios such projects have been of their work on the established throughout program. the country with funds from the Tensor Foun• In 1999, a project was dation. This charitable funded to bring to• foundation, working gether hundreds of through the MAA, has printed studies, book recently awarded grants reviews, courses, work• for twelve projects shop curricula, and ar• (seven new and five re• .. ticles for publication in newals). SMASHing ~hrough barriers at Emporia ~tate Uni~ersity: 9t~ grade girls par- a volume of resources ticipating in SMASH (Summer MathematIcs and SCIence Holzday), JUlie 14-17, for those who are try- 1999. ing to make a difference Over the past five years, in the culture and help women succeed. the projects have varied greatly, both in An entirely different group of partici- terms of the participants they are target- pants were selected from non-traditional ing and in their means of carrying out students at Mercy College in a program On the campus of Manhattan College in the goals of the program. For example, renewed in 1996. Twelve women were Riverdale, NY, middle-school children an upper level mathematics course was paired with mentors from business and attend the Jonas Bronck Academy, a pub• developed in 1995 at Arizona State Uni- industry in internships of one to two lic magnet school established by the versity by Professor Helene Barcelo. This weeks at local organizations. Student re- Board of Education two years ago. With course focuses on the work and life of fe- sponsibilities included attending internet funding from the MAA/Tensor Founda• male mathematicians. Selected original training sessions, completing a career in- tion, beginning in 1999 for two years, fe- works of six women male college mathemat• mathematicians were ics majors initiated a studied together with MAAI TENSOR FOUNDATION mathematics club for their biographies and Grantees 2000-2001 middle-school girls. The the mathematical en• MathZone meets for two Niiket Acar Amy Miko, Peter Skoner vironment in which hours weekly at the The Penn State University Saint Francis College they worked: Florence Academy. The math• Nightingale and her ematics majors are re• Paul Chacon, James Derr, Bonnie L. Oppenheimer pioneering work in sponsible for the cur• Hortensia Soto-Johnson Mississippi University for Women riculum of the club, but statIstIcs; Sophie University of Southern Colorado Germain and her con• they receive strong con• Karen Schotter tributions to number tinuous support from Corine Fitzpatrick, Kathryn Weld Stevens Institute of Technology the faculty, including a theory; Sofia Kov• Manhattan College alevskaya and her series of five workshops Mazen Shahin work in analysis; Grace which introduce them to Angela C. Hare College Misericordia new curricular material, Chisolm Young and Messiah College her contributions to including game theory, Ann E. Trahanovsky-Orletsky topology; Emmy knot theory, and model• Joyce Hilliard-Clark Morris College ing. This program will Noether and her work North Carolina State University in algebra, and Julia expand in the academic Lynda Wiest Robinson and her years 2000-2001 to two Ann Kajander University of Nevada, Reno more schools in District work in logic. Lakehead University, Canada 10, a district where 80% 14 May/June 2000 FOCUS of the students are eligible for free lunch. At the heart of this program is the op• portunity for college students who are excited about mathematics to work with middle school girls. Another program being renewed for a second year of funding takes place each Attend The summer at the University of Southern Colorado. Twenty-four local high school Largest Annual students who have completed high school algebra are given an introduction to prob• Summer Meeting ability and statistics, Euclidean and non• Euclidean geometry, and a sense of col• lege life in this weeklong residential pro• of Mathematicia gram. Various problem-solving sites on the Internet are utilized each day, and in the evenings professional women speak about the mathematics they use in the workplace. The participants keep in touch with one another bye-mail after the camp is over. Building a community among young women who like mathematics is vital for them to persist in the field. The Lore-El Center for Women in Engi• neering and Science at Stevens Institute of Technology will establish an electronic mentoring program to encourage high school students to take a full and ad• vanced mathematics and science curricu• lum in high school. Twenty undergradu• ate members of the Society of Women Engineers will be trained both at the be• ginning and throughout the project in how to engage in effective e-mail mentoring. At a seminar where female instructors will teach dynamic laborato• ries, the mentors will each be assigned two men tees chosen by their high school teachers. At the end of the project an elec• tronic newsletter will be sent to partici• pants to keep them informed of special programs, scholarship opportunities and relevant career information. This pro• gram should help students connect their mathematics and science coursework to college majors and real life applications. Information about applying for a Tensor grant can be found on MAA Online at http://www.maa.org/projects/ maaprograms.html#tensor. The next tar• get date for proposals will be February 1, The Mathematical Association of America 2001. For further information contact Dr. 1529 Eighteenth Street. NW Washington, DC 20036 Florence Fasanelli, MAA/Tensor Founda• it tion Program Director, at MAA head• quarters.• 15 FOCUS May/June 2000 MAA Contributed Papers at the New Orleans Meetings Preliminary Announcement rejected, with a short message on what exploring these topics in undergraduate T he MAA is planning a wide range of information is missing or inappropriate. mathematics. Contributed Paper Sessions for the Joint All questions concerning the submission Wednesday and Thursday mornings Mathematics Meetings to be held in New of abstracts should be addressed to: Denny Gulick (*) Orleans in January 2001. The organizers [email protected]. Mathematics Department listed below solicit contributed papers University of Maryland Here are the codes you will need: MEET- pertinent to their sessions. Sessions gen• College Park, MD 20742-4015 1NG NUMBER: 962 erally limit presentations to ten minutes, phone: (301) 405-5157 but selected participants may extend their The EVENT CODE is the seven charac• fax: (301) 314-0827 contributions up to twenty minutes. Each ters appearing before the title of the e-mail: [email protected] session room contains an overhead pro• sessions shown below, e.g., MAA CP Al Jon Scott, Montgomery College jector and screen; black boards will not The SUBJECT CODE is the last two-char• be available. Persons needing additional acter letter/number combination from MAA CP Cl Innovative Uses of the World equipment should contact, as soon as the event code list, i.e., AI, B1. Wide Web in Teaching Mathematics possible, but prior to September 15,2000: the session organizer whose name is in• MAA CP Al Great Theorems of Mathematics This contributed paper session will focus dicated with an asterisk (*). Please note on creative uses of the World Wide Web that the submission procedure has This session focuses on expository talks in mathematics instruction. Proposals are changed and the dates scheduled for these on important theorems of mathematics. solicited on original uses of Web re• sessions remain tentative. The talks should address as much history sources in the classroom. We are looking Submission Procedures for MAA and applications as time will permit, but for presentations involving the use of real Contributed Papers should make some effort to show the au• data sets, instructional materials, interac• dience the spirit of the proof (or proofs) tive simulations, videoconferencing, or Submit your abstract directly to the AMS. of the result. The idea is to present to a other topics of interest for educators who Concurrently, send a one-page summary general audience theorems that "everyone are currently using, or planning to use, of your paper directly to the organizer. has heard of" but for which the proof is the Web in their classes. The summary need not duplicate the in• not generally well-known. The idea for Wednesday and Thursday afternoons formation in the abstract. In order to en• this session comes from conversations Marcelle Bessman (*) able the organizer{s) to evaluate the ap• overheard in department coffee rooms Department of Mathematics propriateness of your paper, include as where mathematicians from different Jacksonville University much detailed information as possible fields discuss the most significant results Jacksonville, FL 32224 within the one-page limitation. Your ab• in their own area. phone: (904) 744-3950 x7304 stract and summary must reach the AMS Wednesday and Thursday mornings e-mail: [email protected] and the organizer by Friday, September Cheryl Olsen (*) Brian Smith, McGill University 15,2000. Department of Mathematics The AMS will publish abstracts for the & Computer Science MAA CP D1 Re-Defining What a Mod• talks in the MAA sessions. Abstracts must Shippensburg University ern "College Algebra" Experience Means be submitted on the appropriate AMS Shippensburg, PA 17257 form. Electronic submission is available phone: (717) 477-1360 The term "College Algebra" encompasses via the Internet or email. No knowledge fax: (717) 477-4009 a wide variety of offerings ranging from of LaTeX is necessary, however, LaTeX email: [email protected] elementary algebra up through college and AMS LaTeX can be accommodated. Doug Ensley, Shippensburg University algebra and trigonometry courses and These are the only typesetting systems even precalculus courses. What is com• that can be used if mathematics is in• MAA CP B 1 Chaotic Dynamics and mon is an image of the students who take cluded. To see descriptions and to view Fractal Geometry such courses-those who lack some or all the electronic templates available, visit the of the traditional algebraic skills needed abstracts submission page on the Internet Ideas from Chaotic Dynamics and Fractal for calculus. Today, there are many pres• at http://www.ams.org/abstracts/ Geometry relate to most areas of the un• sures to re-define all of these traditional instructions.html, or send e-mail to: abs• dergraduate mathematics curriculum. courses which have prompted a major [email protected], typing HELP as the sub• This session invites papers which inves• MAA curriculum initiative to re-define ject line. tigate the impact of these two fields on what a "college algebra" experience Completed e-mail templates must be sent undergraduate mathematics. The papers, should be. This session seeks contributed to [email protected] with SUB• which should have an expository flavor, papers that will: (I) Present new visions MISSION as the subject line. Abstracts might include new developments in ei• for any of the courses that fall under the submitted electronically are quickly either ther chaos or fractals, interesting or novel "college algebra" rubric. (2) Describe in• acknowledged, with a unique abstract applications, undergraduate research ex• dividual experiences implementing such number assigned to the presentation, or periences, or innovative approaches for courses. This includes new content, new 16 May/June 2000 FOCUS pedagogical features (collaborative learn• warranted. Faculty who teach statistics• courses in a way that enhances math• ing, student projects, communication of in introductory courses, in sections of ematical understanding ideas, etc), assessment and evaluation, courses that satisfy general education re• • presentations of exemplary courses student reactions to the courses, and so quirements or prepare prospective el• or course modules. forth. (3) Discuss and/or demonstrate the ementary teachers, or in cooperation with Submissions are encouraged from teach• use of technology in such courses. (4) faculty from other disciplines-are in• ers in engineering, the physical and so• Discuss what is known about enrollment vited to contribute papers relative to data cial sciences, and management and pub• trends relating to these courses. (5) De• collection, use of technology and other lic policy, showing examples of how scribe the connections between college innovative, active learning experiences mathematics is used in their courses. Sub• algebra courses and courses in other dis• that they include in their statistics in• missions are also encouraged from math• ciplines. The session is being co-spon• struction. ematicians who have successfully incor• sored by the Committee on the Under• Friday and Saturday mornings porated such material into their courses. graduate Program in Mathematics Mary M. Sullivan (*) Friday and Saturday mornings (CUPM), the Committee on Calculus Rhode Island College William McCallum (*) Reform and the First Two Years 600 Mt. Pleasant Avenue Department of Mathematics (CRAFTY), the Committee on Two Year Providence, RI 02908 University of Arizona Colleges (CTYC), the Committee on phone: (401) 456-9851 Tucson,AZ 85721 Quantitative Literacy (CQL), and the fax: (401) 456-8379 Phone (520) 621-6886 CUPM Subcommittee on Service e-mail: [email protected] fax: (520) 621-8322 Courses. Carolyn Cuff, Westminster College e-mail: [email protected] Wednesday and Thursday mornings Mary T. Parker, Austin Community College Deborah Hughes Hallett, University of Sheldon P. Gordon (*) Arizona, Yajung Yang, SUNY, Farmingdale Department of Mathematics MAA CP FI Courses and Programs that Il• SUNY at Farmingdale lustrate Recommendations of the Math• MAA CP HI Serving the Needs of Devel• Farmingdale, NY 11735 ematical Education of Teachers Document opmental Students: Who Are They, Where phone: (516) 451-4270 Do They Come From, Where Do They Go? e-mail: [email protected] This session will focus on mathematics Florence S. Gordon, New York Institute courses and programs for future teach• Until we understand the needS of our de• of Technology, Arlene H. Kleinstein, ers that illustrate the recommendations velopmental students, how can we decide SUNY at Farmingdale, Mary Robinson, of the Mathematical Education of Teach• what kinds of courses they need? These University of New Mexico, Valencia Cam• ers (MET) Document (available at needs vary from one school to another. pus, Linda Boyd, Georgia Perimeter Col• www.maa.orglcbms/). Proposals should Contributions are invited from programs lege, Barbara Jur, Macomb Community describe clearly the intended audience of which have investigated the incoming College the course, its mathematical content, and background of their students, students' instructional strategies. future plans, where the students actually MAA CP El Innovative Practices in Wednesday and Thursday mornings end up, and how this knowledge has led Statistics Education Judith Covington (*) to program changes. Summaries of re• LSU -Shreveport search in these areas helpful to faculty Statistics instruction that reflects current Department of Mathematics teaching in these programs is also wel• thinking includes data analysis and de• One University Place come. sign of data production as well as prob• Shreveport, LA 71115 Wednesday and Thursday afternoons ability and inference as major content phon~(318)797-5354 Su Doree (*) areas. Students often have opportunities fax: (318) 795-4221 Augsburg College to produce real data and deal with the is• e-mail: [email protected] Campus Box # 61 sues that arise in dealing with real data. 2211 Riverside Avenue With use of technology, students are able MAA CP G 1 Integrating Mathematics Minneapolis, MN 55454 to analyze data more extensively and they and Other Disciplines phon~ (612) 330-1059 come to realize that statistical practice fax: (612) 330-1649, requires an iterative process of question, The session will present: e-mail: [email protected] data, and analysis. Their conceptual un• • discussions of the content of current Bonnie Gold, Monmouth University derstanding of statistics is quite different mathematics courses in the first two from understanding gained from analy• years in the light of the way other MAA CP 11 The Undergraduate sis of contrived, "clean" data that appears disciplines use mathematics and the Seminar in Mathematics in many texts. Students who have had expectations they have of our stu• active experiences with data collection dents This 10 minute contributed paper session and analysis using technology are better • discussions of how applications of will focus on the role and content of the able to interpret computer output of sta• mathematics in other disciplines can mathematics seminar in an undergradu• tistical information produced by others be incorporated into mathematics ate program for majors. Presenters should and consider whether conclusions are 17 FOCUS May/June 2000 address issues pertaining to: general concept presentations, but would are useful in helping students to apply the • appropriate topics and focus for such emphasize specific examples, activities, course material and to make connections seminars and resources for use in particular between mathematics and the real world. courses. We hope that the participants This session invites presentations about • seminar objectives and how they are will leave with great ideas about how to favorite instructional demos and course achieved and measured incorporate a CAS activity into one of projects appropriate for any level in the • requirements from student participants their courses. undergraduate mathematics curriculum • equitable student participation Friday morning designed to engage students and enable • developing and measuring student Kent M. Neuerburg (*) them to gain insight into mathematics. presentation skills Department of Mathematics Presenters who discuss demos are encour• Southeastern Louisiana University aged to present the demonstration, if time • the role of the faculty leader(s) Hammond, LA 70402 and equipment allow, and to discuss how • relationship and interplay with other phone: 504-549-2204 to use it in a classroom setting. Present• mathematics courses fax: 504-549-2099 ers who discuss projects are encouraged • appropriate place within the under• e-mail: [email protected] to discuss the specifics of how the project graduate curriculum Andrew Lang, Oral Roberts University was conducted and how it was evaluated. • prerequisites and credits for enrollment Proposals should describe how the demo/ MAA CP Kl Implementation of National project fits into the course, the use of • equitable grading Projects on Local Campuses technology or technology requirements, We seek submissions that will share in• if any, and the effect of the demo/project sights and experiences (both good and The role of mathematics educator has on student attitudes toward mathematics. bad) of faculty members who have led or changed immensely over the last decade. Friday morning are planning such seminars. Faculty are now expected to make proper David R. Hill (*) Wednesday afternoon use of technology, emphasize mathemati• Mathematics Department Barry J. Arnow (*) cal modeling, and develop interdiscipli• Temple University Department of Mathematics nary applications and/or courses. These Philadelphia, PA 19122 Kean University of New Jersey expectations have spawned a variety of phone: (215) 204-1654 Union, NJ 07083 successful national projects. The purpose fax: (215) 204-6433 tel: (908) 527 -2494 of this session is to enhance awareness of e-mail: [email protected] fax: (908) 527-3168 the different national projects, and to Sarah Mabrouk, Boston University e-mail: [email protected] encourage implementation at the local Lila F. Roberts, Georgia Southern University George Avirappattu, Kean University of level. Papers are solicited regarding local New Jersey adaptation and adoption of successful MAA CP M 1 Putting the "Service" Back national projects aimed at enhancing the into Service Courses MAA CP JI Computer Algebra Systems undergraduate mathematics curriculum. in Upper-Division Mathematics Courses Submission of proposals via e-mail is pre• Traditionally service course content in the ferred by the organizers. mathematical sciences has been driven by The use of Computer Algebra Systems Saturday morning the needs of client disciplines, needs (CAS) in the undergraduate curriculum Stuart Boersma (*) which are often conflicting. If we were to has become widespread over the past few Division of Mathematics consider "service" from the standpoint of years. However, most of the applications Alfred University students, what mathematical and quan• have been in the lower division courses; Alfred NY 14802 titative skills and principles will serve stu• in particular, these systems are seeing ex• phone: (607) 871-2258 dents regardless of major. For this session, tensive use in Calculus I, II, and III. This fax: (607) 871-2339 we invite descriptions of innovative session will provide the opportunity for e-mail: [email protected] courses that serve students in a broad participants to see applications of CAS in Constant J. Goutziers, SUNY Oneonta sense by teaching them mathematical or higher level courses. Such courses may quantitative skills they can apply to their include Ordinary and Partial Differential MAA CP Ll Classroom Demonstrations future studies and work. Papers should Equations, Numerical Analysis, Modern and Course Projects that Make a Difference give specific details about goals, course Algebra, Real and Complex Analysis, etc. development, implementation, and as• The list of courses that can utilize a CAS The use of course projects and classroom sessment. to aid learning is endless and we hope that demonstrations enables the instructor to Saturday morning the session will reflect this. We hope to show students that mathematics is mean• Thomas L. Moore (*) see applications in a variety of systems• ingful and applicable in a variety of real• Department of Mathematics standard packages like Mathematica, life situations. Demos, important tools for and Computer Science Maple, MathCAD, and MatLab; as well instruction in any class format, enable the Grinnell College as more specialized packages like GAP, instructor to engage the student on a level Grinnell, Iowa 50112 PARI, etc. The session would entertain beyond that created by lectures. Projects phone: (515) 269-4206 18 May/June 2000 FOCUS fax: (515) 269-4984 the role of proof in grades K-12. It is also Mathematics Department e-mail: [email protected] our plan to develop a network on issues Seattle University Ahmed Zayed, University of Central Florida in proof pedagogy. Papers should be sub• Seattle, WA 98122 mitted electronically to any of the three phone: (206) 296-5931 MAA CP NI College Mathematics in Depth organizers. fax: (206) 296-2179 with Dynamic Mathematics Software Wednesday afternoon e-mail: [email protected] Connie Campbell (*) Elizabeth Yanik, Emporia State University This session will seek contributors to Department of Mathematics present creative uses of software for ge• and Computer Studies MAA CP SI ARUME Session ometry, algebra, statistics, and other Millsaps College mathematical domains in support of Jackson, MS 39210 The Association for Research on Under• both exploration and reasoning across a phone: (601) 974-1371 graduate Mathematics (ARUME) aims to broad range of classical collegiate math• e-mail: [email protected] foster a professional atmosphere for qual• ematics. By inviting contributors and se• Draga Vidakovic, Georgia State College ity research in the teaching and learning lecting among contributions, we will give G. Joseph Wimbish, Huntingdon College of undergraduate mathematics contrib• special priority to presentations that take uted paper sessions for mathematics edu• the step *beyond* using the computer as MAA CP QI Mathematics in the Age of Euler cators and professional mathematicians a tool for motivation, experiment, or data interested in research on undergraduate collection purposes, and put the focus on Leonhard Euler (1707-1783) ranks mathematics education. Research papers using these tools for the development of among the greatest of mathematicians. that address issues concerning the teach• important content and sophisticated Building upon the achievements of the ing and learning of undergraduate math• mathematical reasoning. As examples, previous century-most notably differ• ematics are invited. Theoretical and em• we've seen presentations of explorations ential and integral calculus-Euler and pirical investigations using qualitative and extensions of vector fields, visualized his contemporaries advanced the fron• and quantitative methodologies are ap• with dynamic geometry software, linking tiers of mathematics and influenced all propriate. These should be set within es• symbolic and visual representations in that followed. This session invites exposi• tablished theoretical frameworks and ways that help students reason about dif• tory contributions on the work of Euler should further existing work. Reports on ferential equations. In another domain, and of other eighteenth century math• completed studies are especially welcome. exceptional statistical software now exists ematicians. Contributors might want to Julie M. Clark (*) that moves beyond the processing of the examine a theorem or two from Euler's Department of Mathematics data and helps students understand the nearly inexhaustible collected papers or & Computer Science nature and subtleties of the mathematics describe more generally his explorations Emory & Henry College behind statistical analysis. in a particular mathematical subfield. Of Emory, VA 24327 Saturday morning interest are reports of classroom experi• phone: (540) 944-6191 E. Paul Goldenberg (*) ences that have engaged the student with fax: (540) 944-4592 Education Development Center Euler's ideas. e-mail: [email protected] 55 Chapel Street Thursday afternoon Newton, MA 02158-1060 V. Frederick Rickey (*) MAA CP Tl General Contributed phone: (617)618-2513 Department of Mathematical Sciences Paper Session e-mail: [email protected]. United States Military Academy Jean-Marie Laborde, Laboratoire Leibnitz West Point, NY 10996-1786 This session is designed for papers that Grenoble, France, Barbara Pence, San Jose phone: (914) 938-4010 do not fit into one of the other sessions. State University fax: (914) 938-2409 Papers may be presented on any math• e-mail: [email protected] ematics related topic. Papers that fit into MAA CP PI Topics in Teaching, Learning, William Dunham, Muhlenberg College one of the other sessions should be sent and Exploring Proof to that organizer, not to this session. Pa• MAA CP RI Outreach Programs for pers should not be sent to more than one For most "proof" is the heart and soul of Women and Girls organizer. E-mail submissions are pre• mathematical activity. This session is de• ferred. voted to papers on proof in the classroom. The papers will describe programs cur• Howard L. Penn (*) We particularly invite papers on the fol• rently being offered to encourage women Mathematics Department lowing topics but will consider others: and girls to study mathematics. A wide 572 Holloway Rd. learning theory based expository or re• variety of projects will be described and United States Naval Academy search based essays, experiences derived the presenters will discuss what they have Annapolis, MD 21402-5002 from "transition" or "bridge" courses, the learned from implementing their pro• tel: (410) 293-6768 use of cooperative learning, and the ef• grams. fax: (410) 293-4883 fects of technology. In view of the N CTM Friday morning e-mail: [email protected] Standards 2000, we invite discussion of Kathleen Sullivan (*) 19 FOCUS May/June 2000 Jerry M. Hawn 1999 CONTRIBUTORS TO MAA FUNDS AND PROGRAMS Leon A. Henkin Fritz Herzog Gerald A. Heuer Each year, hundreds of members give Marvin Schaefer Arthur F. Miller James L. Higgins donations in support of the Greater MAA Doris J. Schattschneider Chester W. Mills Sandra N. Hilt Lynn A. Steen John A. Mitchem Fund as well as other MAA funds and Yukio Hirashita Maria W. Steinberg Morris Newman J.M.Holme programs benefiting the mathematical Robert Steinberg Lowell J. Paige Karl R. Huber community. Listed below are donors who Beresford N. Parlett D. Richard litis Benefactors John W. Petro contributed to one or more of these funds Lloyd K. Jackson (Donors contributing $500+) G. Baley Price Guy J. Johnson or programs during 1999.'" Memorial, Robert J. Reynolds William B. Johnson honorary, and Marcia P. Sward Fund do• Alfred Aeppli Pete E. Riley Louis Joseph Edward D. Baker Hans Samelson Tim Kanold nations are listed separately. Barbara J. Beechler John A. Schumaker Wilfred Kaplan William G. Chinn Dana S. Scott John B. Kelly The Marcia P. Sward Fund was initiated Robert L. Druet John K. Seymour Eleanor L. Kendrick Roy Dubisch Anita E. Solow Kathryn F. Kuiken by MAA Presidents during 1999, the fi• William L. Duren Olaf P. Stackelberg David E. Kullman nal year of Dr. Sward's distinguished ten• Richard L. Gantos James G. Timourian Kenneth Kunen year term as MAA Executive Director, for Marjorie Maher Karen K. Uhlenbeck Jean-Marie Labrie Eugene A. Margerum Marcellus E. Waddill Elliott Landowne the purpose of dedicating the MAA head• Constance Reid Buck Ware Patricia R. Lane quarters lobby in her honor. The Sward V. Frederick Rickey Frank W. Warner Anneli Lax Robert A. Rosenbaum Elizabeth B. Weinstock Fund was opened to other friends and Katherine P. Layton Kenneth A. Ross Alex Weintraub Don R. Lichtenberg colleagues of Dr. Sward in the fall of 1999, Norman E. Sexauer Susan S. Wildstrom Rudolf B. Lim and drew substantial support from many Martha J. Siegel Paul M. Zorn Hung-Wei Lin Andrew Sterrett, Jr. people wishing to pay tribute to her out• Robin H. Lock David R. Stone Sponsors Clifford A. Long standing contributions to the MAA. All Tina H. Straley (Donors contributing $100+ ) Norman W. Lord contributions to the Marcia P. Sward Marcia P. Sward Warren S. Loud Ann E. Watkins Joe F. Allison Fund are now used to benefit the MAA David C. Lukens John E. Wetzel Richard Anders Thomas A. Mackey Building Fund. Alfred B. Willcox Shiro Ando Joseph S. Mamelak Winifred A. Asprey Wanda L. Mammel Grand Patrons Joseph A. Ball 'Due to space limitations, only donors contribut• Andrew J. Matchett (Donors contributing $350+ ) Donald Batman Stephen B. Maurer ing $25 and above are listed in the 1999 MAA Do• Lynne A. Baur Robert E. Megginson nors list. However, all memorial, honorary, and Ronald M. Davis Phillip R. Bender David M. Merriell Sward Fund donors are listed. Gregory M. Dotseth Manuel P. Berriozabal William J. Mitchell Underwood Dudley Peter B. Bjorklund Frank Morgan Deborah Tepper Haimo T. Hoy Booker Timothy Murdock 1999 MAA DONORS Shirley A. Hill Bart Braden Alan G. Murray Mary M. Neff Ezra A. Brown Eugene D. Nichols Grand Benefactors Arnold M. Ostebee Robert L. Bryant Robert A. Northcutt (Donors contributing $1,000+ ) Peter H. Sellers Milo F. Bryn Victor T. Norton, J r. Allyn J. Washington Robert Bumcrot Rodney G. Olinger Henry L. Alder John H. Butchart Hironori Onishi Gerald L. Alexanderson Patrons Thomas R. Butts Philip Oppenheimer Richard D. Anderson (Donors contributing $200+) Mike Canjar Robert Osserman Tom M. Apostol Stephen R. Cavior Thane E. Plambeck Thomas F. Banchoff Howard E. Bell Phillip J. Chase Alan G. Poorman Raymond A. Barnett Stewart E. Boden Pak S. Chee Marjorie E. Poorman Lida K. Barrett Karl E. Byleen Michael P. Cohen Wilbur L. Pritchard Herbert M. Baruch, Jr. Susan L. Callahan Samuel G. Councilman George D. Pryjma Alice C. Beckenbach Nathaniel Chafee Jan W. Dash Maxwell O. Reade Mary L. Boas Jean Bee Chan Joseph K. Davidson Robert R. Reitano Malcolm K. Brachman Edmund A. C. Crouch Guy M. De Primo Joseph M. Rosenblatt Amy Cohen Keith J. Devlin Robert L. Devaney Shepley L. Ross lean E. De Valpine William E. Dorion Anthony B. Di Luna Zalman Rubinstein Barbara T. Faires Wade Ellis, Jr. Charles R. Diminnie Fred L. Rufus J. Douglas Faires Ruth A. Fish Clifford J. Earle David Sachs Andrew M. Gleason Ronald A. Gove David M. Einstein leffrev R. Sachs Ronald L. Graham J. H. Graham Sylvan H. Eisman David H. Sanders Bill Hassinger, Jr. Mark D. Hamlen Susanna S. Epp Kenneth V. Saunders Anna S. Henriques Betty F. Hinman Susan L. Forman David I. Schneider Richard A. Hord Cdr. Joseph A. Hughes, USN Joseph M. Gani Joel E. Schneider John W. Kenellv James F. Hurley Peter Garrity Alejandro R. Senpelli Donald L. Kreider Victor J. Katz Frederick S. Gass Jon W. Sentt Harry Lucas Daniel Kennedy Murray Gcchtman Marshall P. Scott Carolyn R. Mahoney Barry F. Kramer Maurice E. Giirnore Richard 1. Shaker Marie T. McKellor Robert N. Leggett Samuel Goldberg h'y O. Shen Betty Niven Anne M. Leggett Samuel W. Hahn Robert B. Silverstone Everett Pitcher William J. Lewis M. E. Hamstrom Louis Solomon John W. Poduska, Sr. William D. Maness William J. Hardell Carlos G. Spaht Henry O. Pollak Thomas J. Marlowe Joe T. Harris, J r. Ivar Stakgold Gerald J. Porter Celestino G. Mendez Adam O. Hausknecht T. Christine Stevens 20 May/June 2000 FOCUS John R. Stock Susan L. Friedman John W. Rebman Gerald E. Bergum D. Derk Swain Mary E. Froustet Irving S. Reed T. E. Berry Brad Tashenberg Jiro Fukuta Irma M. Reiner Nelson Bishop George B. Thomas, Jr. Joseph A. Gallian Philip Rice Richard M. Bittman John A. Thorpe James D. Gates Craig W. Roberts William E. Boyce Peter Ungar Elaine F. Genkins Jean-Louis Roque Thelma E. Bradford Paul J. Villemure Richard A. Gibbs Mrs. Donald Rose Deborah L. Brannen William M. Wagner Gordon R. Glabe Donald c:. Rose Erin Bredensteiner Joe F. Wampler Colin M. Glanville N. J. Rose Gary L. Britton Evelyn K. Wantland Robert A. Glover George M. Rosenstein Kenneth A. Brons James E. Ward Richard P. Goblirsch Donald K. Ryan Regina C. Brunner Barry H. Westgate Dewey M. Griffith VII Donald E. Sarason Mark J. Bruso Alvin M. White Linda J. Hagelgans John L. Scharf Damon D. Bryant, Jr. Stephen J. Willson John D. Hancock Charles M. Schneeberger Donald l.. Burkholder Izaak Wirszup John L. Hank Alan H. Schoenfeld Ralph S. Butcher Carol S. Wood William A. Hawkins, Jr. Blanche B. Schultz Ronald J. Chase Nicholas W. Yang Kathleen Hawryluk Henry A. See bald Jun S. Choa Charles 1'. Zahn Thomas Hazard Melvin A. Shader Leroy M. Christophe, Jr. William P. Ziemer James B. Herreshoff Chantal M. Shafroth Jane E. Clifford Gloria C. Hewitt Jack V. Shaw Philip Cobb Contributors V. Dwight House Frank C. Sherburne John C. Cock (Donors contributing $50+) James E. Householder Bonnie Sherwood Carolyn Connell Shirley M. Huffman David L. Skoug John W. Connelly Edward F. Aboufadel M. Gweneth Humphreys Muriel Skoug Kenneth L. Cooke J.M.Adams Harold V. Huneke David A. Smith Nicholas Copoulos Joe Albree James E. Huneycutt Linda R. Sons John J. Costello Edward Z. Andalafte Carol Hutchins Charles S. Stuckey Jere L. Courtney H. R. Andrews Scott B. Huxel Dorothy I. Sweitzer Steve Davis David F. Appleyard Franklin 1'. Iha Arthur D. Talkington Peter G. De Buda Etienne Archinard Eugene Isaacson Steve Taniguchi Michael D. Delahunty Lynn M. Aring Lynn H. Iwamoto Robert E. Tax Edward C. Deland Judith Z. Aronow G. Philip Johnson Laurence R. Taylor Daniele Donini Jean-Christophe Aubert Dan Kalman David C. Terr Joseph L. Doob Joseph Auslander Andrea Kennener John F. Thorne III Thomas L. Drucker Catherine C. Aust Thomas C. Kipps James C. Thorpe William H. Durfee Sheldon AxIer Benjamin G. Klein Roseanna F. Torretto Lincoln K. Durst Fredrick W. Barber James F. Koehler Elias Toubassi Earl F. Ecklund, Jr. Theodore J. Barth Elaine H. Koppelman Thomas W. Tucker Edwin G. Eigel Martin R. Bates Ralph M. Krause Visutdhi Upatisringa Julie A. England Frank S. Beckman Helen F. Kriegsman Mary A. Wallace Elaine C. Ensign William H. Beckmann Jen Lam John 1'. Ward Wilhelm S. Ericksen John A. Beekman George E. Lang Michael C. Ward Artishia A. Ervin Arthur 1'. Benjamin D. E. Lavender James D. Watson Pamela A. Ferguson Gary D. Berg Walter R. Lawson John V. Wehausen Edgardo Luis Fernandez Martin Billik Bernhard P. Leeb Cecilia Welna David L. Finn Steven E. Blasberg Bernard W. Levinger Kenneth J. Whitcomh William 1'. Fishback Kbenesh Blayneh Miriam B. Lindstrom James C. White Charles R. Fleenor Alexander Bogomolny Sally I. Lipsey D. Ransom Whitney Janet E. Ford Delmar L. Boyer Maurice Lipton John F. Wilkinson Theresa A. Francis Sylvia T. Bozeman John M. Long Robert S. Williams Lawrence E. Freeman Nancy J. Bray Nicholas J. Lord N. Convers Wyeth Steven A. Gabriel Thomas A. Breiter Robert B. Lumbert Michael Yanowitch 1'. K. Gardenier Austin R. Brown Ransom V. Lynch Wei-Jing Zhu Ann C. Garstang Marjorie V. Butcher J. J. Malone Marilyn J. Zweng Shirley Gearheart Raymond J. Cannon, Jr. Heinrich Mantel Michael D. Gilbert John E. Chavez Arthur P. Mattuck Sustainers Germana L Glier Theodore S. Chihara Robert G. Maule (Donors contributing $25+) Merrill B. Goldberg Daniell. A. Cohen Raymond A. Mayer, Jr. Basil Gordon Richard M. Cohn Thomas l.. McCoy Lateef A. Adelani Douglas C. Hartman J. Kevin Colligan Kim A. McKee Hanm K. Adongo Francis M. Henderson Thomas A. Cootz Robert J. Meier Howard B. Anderson Robert Hill Clyde I.. Corcoran Robert 1'. Mertz Florence R. Anderson Richard Hoffer Louis J. Cote D. D. Miller Karen S. Archambault Gerolf F. Hotlehner Carl C. Cowen Peter E. Moore Florence H. Ashby Herbert H. Holman Ann M. Curran l.. T. Maston Walter n. Augenstein John E. Homer Betsy Darken Herbert Nadler Bernice l.. Auslander Patricia M. Hughes M. Hilary Davies (Wick) Janis M. Oldham Roger A. Avelsgaard Astrit Ibroci G. Diantonio Anne F. O'Neill James H. Bagley Nancy J. Ingram Anne M. Donovan Calvin I. Owens Julio E. Barety Lynne K. Ipina Bernard A. Edison Glenn K. Painter Kim A. Barrett Rita Jeltsch-Fricker George W. Ellis Diethard Pallaschke James W. Beach David L. Johnson John E. Ewing Rachel H. Pearlman Michael Beals Gerald W. Johnson Michael B. Fein Lorenzo Peccati Helen P. Beard Harvey D. Johnson Manuel Feliciano Sharon E. Persinger William A. Beck Luella H. Johnson John C. Fenley George Piranian Imogene C. Beckemeyer Robert c:. Johnson Newman H. Fisher John 1'. Poole Jerry P. !lecker Agnes M. Kalemaris Stephanie A. Fitchett Ivan Pucclj Philip M. Beckman Diana Kalish John A. Fridy Michael F. Quinn Rohert J. !lecher Patricia A. Kan Thomas G. Railey John Bender Rosella Kanarik 21 FOCUS May/June 2000 Janis Karklins Joseph A. Schanberger Phillip J. Chase in memory of Ivan Niven Paul A. Kaschube Irene V. Schensted in memory of Robert P. Dilworth Dana S. Scott Herbert E. Kasube Ernest C. Schlesinger Amy Cohen in memory of Anneli Lax Vernon M. Kays John Schue in memory of Leon W. Cohen Martha J. Siegel Stanley Kelly-Bootie Laurence B. Schweitzer and James R. C. Leitzel in memory of Ivan Niven Patricia C. Kenschaft Guy B. Shaw Betsy Darken Katye O. Sowell Stan P. Kerr Ching-Kuang Shene in memory of James R. C. Leitzel in memory of Jesse C. Sowell David B. Kirk Jerry R. Shipman Pamela A. Ferguson David R. Stone Joseph E. Kist Louise A. Simon in memory of James R. C. Leitzel in memory of James R. C. Leitzel Richard F. Klier Robert C. Simonsen Susan L. Forman Dorothy l. Sweitzer Peter P. Klopfenstein Jennifer A. Slivoski in memory of James R. C. Leitzel in memory of my parents, who helped me learn, Ronald J. Knill John R. Smart Joseph M. Gani as I've tried to help my children Robert J. Kolesar Wilbur L. Smith in memory of Ruth Stephens Gani Elias Toubassi Gary R. Krumpholz Brian E. Smith Ronald L. Graham in memory of James R. C. Leitzel Gen Kubota Rubin Smulin in memory of Paul Erdos Peter Ungar Nancy L. Laing Katye O. Sowell John D. Hancock in memory of Anneli Lax Gerald M. Leibowitz W. Dean Spencer in memory of George Polya Marcellus E. Waddill Frances B. Lichtman Stephen E. Spielberg Shirley A. Hill in memory of John Neff Joseph c. Logue Adelaide C. Sprague in memory of John Neff Sigrid E. Wagner Charles J. Lombardo Roger A. Stafford Shirley A. Hill in memory of James R. C. Leitzel Milan Lukic Alfred T. Steele in memory of Gail Young Elizabeth B. Weinstock Wilhelmus A. Luxemburg Blair Sterba-Boatwright Carol Hutchins in memory of Max Schiffer Thomas K. Maddox Ronald J. Stern in memory of Max Zorn Kenneth J. Whitcomb John C. Mairhuber Rudolph M. Sternheimer Guy J. Johnson in memory of M. Leslie Madison Charles E. Mannix, Jr. Wilhelm F. Stoll in memory of Jean Steward Johnson Roger L. Mansfield R. E. Street William B. Johnson 1999 MAA DONORS Walter Markowitch, Jr. Bernardo Suarez in memory oflames R. C. Leitzel HONORARY GIFTS Peter P. Szabaga Tim Kanold Dorothy N. Matsui Winifred A. Asprey Peter C. Tan in memoryofW. E. Yunker Gus Mavrigian in honor of Vassar College Derek J. Thomsett John Kenelly Farley J. Mawyer Pak S. Chee Wilson Ruiz Torres in memory of Charmaine Voss Kenelly Richard F. McDermot in honor of Prof. Walter Rudin Charles R. Traina Peter P. Klopfenstein Jan L. McGarry Rose Cordero Agnes Tuska in memory of Dr. Ralph W. Klopfenstein Fred McKee in honor of Oswald and Beverly Cordero Jaroslav Tuzar Elliott Landowne Donald E. Mclaughlin Thomas L. Drucker Kirk C. Valanis in memory of Dunham Jackson James W. Mentele in honor of Prof. Jack Stodghill George A. Van Buskirk D. E. Lavender Edward P. Merkes Stephanie Eichenbrenner W. Van Der Meiden in memory of John Neff Richard A. Moore in honor of Jennifer Kazmarek Andrew H. Van Tuyl William J. Lewis Joan S. Morrison Mike and Kathleen Hawryluk Richard J. Vance in memory of James R. C. Leitzel Burt J. Morse in honor of Peter Francis Stebe Wolmer V. Vasconcelos Don and Betty Lichtenberg Thomas L. Morton Robert Hill Carlo M. Vecchi in memory of James R. C. Leitzel Sebastiano Mosca in honor of Thomas M. Boger Ronald G. Mosier Sigrid E. Wagner Robin H. Lock and Patti Frazer Lock Astrit Ibroci Marc Wallace in memory of James R. C. Leitzel Edgar H. Neal in honor of Prof. Kathryn Kuikeu Edward O. Nelson Azelle B. Waltcher Warren S. Loud Elaine H. Koppelman Charles W. Neville Kevin M. Ward in memory of Raymond W. Brink in honor of the birthday of Ivan Niven Nancy J. Warden Harry Lucas Dr. Martha Siegel Teruo Nushiro Bette L. Warren in memory of Gail Young Joan S. Morrison Francis G. O'Brien John C. Weaver David C. Lukens in honor of Martha J. Siegel John D. Oosterhout J. Ernest Wilkins, Jr. in memory of Stillman Drake John W. Poduska, Sr. Barbara L. Osofsky Henry G. Williams, Jr. Carolyn R. Mahoney in honor of Norbert Wiener Albert D. Otto Patricia S. Willis in memory of Wade Ellis, Sr. Gerald J. Porter Harold Oxsen Jerry D. Woods Mrs. Wanda L. Mammel in honor of the birthday of Neil A. Pateman Bernard J. Yozwiak in memory of Dr. Ruth Wycliff Stores Dr. Martha Siegel Stephen A. Pennell Joseph F. Zelle Betty Niven Zalman Rubinstein Allen Perkins Joseph L. Zemmer in memory of Ivan Niven in honor ofYanir Rubinstein Victor Pesta Lawrence J. Zimmerman Albert D. Otto Doris J. Schattschneider Charles G. Pickens Ben F. Zirkle in memory of James R. C. Leitzel in honor of Dr. Marcia Sward Dirk A. Plummer David E. Zitarelli Sharon E. Persinger Carlos G. Spaht John A. Poluikis, CSB in memory of James R. C. Leitzel in honor of Prof. Hubert Butts Mary Jo A. Prusko 1999 MAA DONORS Gerald J. Porter George Quillan MEMORIAL GIFTS in memory of Ivan Niven Richard Quint Robert W. Rector 1999 MARCIA P. SWARD Corrado D. Quintiliani Judith Z. Aronow in memory of Ivan Niven FUND DONORS Russell L. Ralph in memory of Abraham Haskell Taub Lynn A. Reed Henry L. Alder R.A. Rankin Alice C. Beckenbach in memory oflames R. C. Leitzel Gerald L. Alexanderson Lynn A. Reed in memory of Edwin Ford Beckenbach Constance Reid Richard D. Anderson Richard S. Rem pel Jerry P. Becker in memory of Anneli Lax Winifred A. Asprey Joaquin G. Rey in memory of E.G. Begle Irma M. Reiner Thomas F. Banchoff Norman J. Richert Phillip R. Bender in memory of Irving Reiner Mary Mclean Bancroft Charles E. Rickart in memory of Rev. Lester J. Heider, S.J. Charles E. Rickart Lida K. Barrett Charles D. Robinson Delmar L. Boyer in memory of Paul Erdos Howard E. Bell Mario G. Rodriguez in memory of Frederick Bodo Strauss V. Frederick Rickey Arthur T. Benjamin Paul C. Rogers Sylvia T. Bozeman in memory of James R. C. Leitzel Manuel P. Berriozabal Daniel Rosen in memory of James R. C. Leitzel Mrs. Donald Rose Gary L. Britton Jeanette A. Rubner John H. Butchart in memory of Dr. Donald Clayton Rose Helen Christensen David Ryeburn in memory of Harry Levy Joe and Gay Rosenblatt J. Kevin Colligan Anthony Sacremento Susan L. Callahan in memory of James R. C. Leitzel Carl C. Cowen in memory of James R. C. Leitzel Doris J. Schattschneider 22 May/June 2000 FOCUS Charles R. Diminnie volving undergraduates in research or profes• Wittig, Chair, Search Committee, Department John Ewing sional activities. The appointment to the en• of Mathematics and Statistics, Box 2220, Ruth A. Fish Susan Forman dowed Chair will provide a competitive sal• SDSU, Brookings, SD 57007-1297. Phone: Nancy J. Hagelgans ary at the rank of associate or full professor 605-688-6196. AAlEEO/ADA. William A. Hawkins, Jr. and budgetary support for program develop• Shirley Ann Hill ment and research activities. Applications Shirley Huffman WEST VIRGINIA D. Richard litis must include a letter of interest that briefly John Kenelly outlines a plan for the development of a pro• WEST VIRGINIA STATE COLLEGE Susan Kjellqvist gram that will involve undergraduates in re• Mathematics Faculty Position Genevieve M. Knight search or professional activities, a curriculum Julie Kraman West Virginia State College, a historically Donald L. Kreider vita, and the names of three references. Refer• David E. Kullman ences may be contacted during the initial Black, undergraduate Land-Grant institution Katherine P. Layton screening of applications; finalists for the po• which now serves a racially diverse, multigen• Stephen B. Maurer erational student body of nearly 5,000 seeks John A. Mitchem sition will be asked to provide three letters of to fill a tenure-track position in mathematics Timothy Murdock reference. Robert Allan Northcutt The position will remain open until filled. beginning August 15,2000. Primary respon• Abraham and Barbara Osofsky sibility is to teach approximately twelve cred• John W. Poduska, Sr. The appointment could begin as early as the its of undergraduate mathematics or com• Eileen L. Poiani Fall of 2000. Henry O. Pollak puter science course per semester. Duties also Gerald J. Porter include student advisement, curriculum de• G. Baley Price Loyola Marymount University is a compre• velopment, committee work and scholarly Richard Rempel hensive Catholic university whose focus is ex• Ken Ross activity. The missions of the college and the Joel E. Schneider cellence in undergraduate education. The department require that the search focus on Jon W.Scott Mathematics Department, housed within the candidates who demonstrate excellence in Frank C. Sherburne University's College of Science and Engineer• Martha J. Siegel teaching. Ph.D. in Mathematics or Computer Anita Solow ing, is a community of fifteen full time fac• Science preferred. Rank and salary negotiable. Linda Sons ulty members and 30-40 mathematics majors Preference will be given to those applicants Lynn Steen who work in an atmosphere of mutual respect with experience in the use of technology or Andrew Sterrett, Jr. and collegiality. Additional information about David R. Stone research potential. Thomas W. Tucker the LMU Mathematics Department and this William M. Wagner position can be found on the web at http:// The Department of Mathematics offers a BS Ann & William Watkins cse.eng.lmu.edu/-math_web/ Charles T. Zahn in classical mathematics and applied math• Paul Zorn Imumath.html. ematics and service courses to non -majors. We have an extensive developmental math pro• Please send applications and inquiries to: gram, and serve many nontraditional and EMPLOYMENT OPPORTUNITIES part-time students with both day and evening Dr. Gerald Jakubowski courses. The department operates two micro• Dean, College of Science CALIFORNIA computer labs and a PC classroom. Consis• and Engineering tent with the history and mission of the col• LOYOLA MARYMOUNT Loyola Marymount University lege, the West Virginia State College faculty UNIVERSITY 7900 Loyola Boulevard has formally stated its support for a college• Clarence J. Wallen, S.J. Los Angeles, CA 90045-8135 wide commitment to recruit and retain fac• Endowed Chair in Mathematics [email protected] ulty who are members of minority groups, es• 310-338-2834 pecially those who are African American. The Mathematics Department of Loyola Marymount University invites applications SOUTH DAKOTA Send cover letter (including email address and for the Clarence J. Wallen, S.J. Endowed Chair fax number if available), resume, statement in Mathematics. The individual holding the SOUTH DAKOTA STATE UNIVERSITY of teaching philosophy, a copy of graduate and Chair shall teach two classes per semester, Department of Mathematics and Statistics undergraduate transcripts and three letters of carry out his/her own research agenda, de• recommendation to Dr. Barbara J. Oden, velop programs that involve the undergradu• Assistant Professor position starting in mid Ph.D., Vice President for Academic Affairs, ate mathematics majors in research or pro• August 2000. Doctorate in statistics required West Virginia State College, Campus Box 192, fessional activities, and engage in departmen• by September 1,2000. Skills in teaching, re• Institute, WV 25112-1000. Additional infor• tal and University service. Individuals work• search, communication and interpersonal re• mation about the college is available at http:/ ing in any mathematical area, including math• lations required. Teach 12 hours per semes• /vww. wsc.edu/. screening of applications will ematics education (especially K-12 teacher ter, engage in service and scholarly activities. begin on April 14 and will continue until the preparation), are invited to apply. Closing date: June30, 2000; or, until filled. position is filled. Use of AMS Application Send letter of application, curriculum vita, Cover Sheet is appreciated. The appropriate candidate will have an estab• copies of transcripts of graduate work, and lished scholarly and academic record and arrange to have three letters of professional AN EQUAL OPPORTUNITY / AFFIRMA• should be able to demonstrate success at in- recommendation sent to: Dr. Timothy A. TIVE ACTION EMPLOYER 23 THE ART OF TEACHING Is THE ART OF DISCOVERY. -MARK VAN DOREN Success in the classroom should not be left to chance. Improve your students' understanding with educational tools that encourage exploration and discovery The TI-83 Plus. with powerful statistics features and Flash technology. frees students from mechanical computation and allows more focus on ideas and concepts. Flash lets you download new calculator software to your existing calculators. like you add software to a computer. Software applications from TI and other developers add new capabilities that introduce and reinforce key curriculum concepts. As a leader In educational technology, we design products that let you and your students explore, discover. and do more. Learn more about our products and support programs by visiting www.ti.com/calc I.MATHEMATIC~ TI. T,tle 5pon,0, ~TEXAS 8S :!2 www ti com/calc/tmo2001 ~ :» ~ = INSTRUMENTS "'I'~I hflllU IIMM_.t. ,H' , -800-TI-CARES ti-cares@lti com www.ti.com/calc The Mathematical Association of America Periodicals Postage paid at 1529 Eighteenth St., NW Washington, DC and Washington, DC 20036 additional mailing offices 40-:'