\ olume IJ. :"umller 6 The Ne\\ stetter of the :\Iathematical Association of America Den'mller )9l)J An Aperiodic Convex Space-filler is Discovered Earlier this year, Princeton mathematician Conway's discovery was announced at the John Horton Conway discovered a convex Regional Geometry Institute held this past polyhedron that will fill space, but only summer at Smith College. There, the par• aperiodically. The space-filler is a biprism, ticipants(over 100,includingundergraduate that is, two slant triangular prisms fused REU participants, graduate students, high together (its faces are four congruent tri• school teachers, and research mathemati• angles and four congruentparallelograms). ~ cians) assembled cardboard models of the Several years ago, Peter Schmitt, at the ~ biprism and stacked them to witness the University of Vienna, described a non-con- § aperiodic space-filling. One participant, vex aperiodic space-filler, and Conway's ~ Ludwig Danzer, of the University of biprism fills space in a similar manner. First, ~ Dortmund, noted that Conway's tiling was ~ copies of the tile fill a layer (and in this single g not face-to-face, and quickly devised an layer, the tiling is periodic), and layers are ~ "improved" version. The parallelogram stacked to fill space. However, adjacentlay- E: faces ofDanzer's biprismare inscribedwith ers must be rotated with respect to each An example ofConway s tiling built at the Regional congruent triangles (which are considered other by a fixed irrational angle, thereby Geometry Institute at Smith College as faces) and when his polyhedronis stacked ensuring that the tiling is aperiodic. in the same manner as Conway's, the tiling is aperiodic and also face-to-face. Inside the New Employment Register s. Brent Morris point two members each to the JCEO. AMS few of their requested candidates. staff see to the day-to-day functions of the The JCEO recognized that the ER's effec• The Mathematical Sciences Employment ER, whose mission is to serve as an honest tiveness waseroding, andthatemployers had Register (ER) underwent a major change at and fair broker in the mathematical job begun to drift slowly away. Since the ER the 1993 San Antonio meeting: it has a new market, bringing together interested appli• treated applicant and employer requests algorithmfor scheduling interviewsbetween cants and employers. employers and applicants. The two-day ER, equally, a larger supply ofapplicants meant held annually at the joint meetings, usually Prior to the 1993 San Antonio meeting, the fewer scheduled interviews initiated by em• comes in the middle of a new Ph.D. ER utilized rather aged "black box" soft• ployers. Applications inundated math mathematician'sjob search, sometime after ware to generate the interview schedules. departments, especially larger ones, whose the fall's first optimistic mailing of applica• Data was fed into a black box, an algorithm members found little marginal value in sit• tions, but before the spring's cold panic. In ran, and schedules were spit out. tingthrough 48 fifteen-minute interviews in San Antonio while 200-plus applications recent years, the ER has offered only slight This old scheduling algorithm was awaited them at home. comfort to applicants, even as it has changed procrustean in its treatment ofrequests: all dramatically to serve the community better. were equally likely----employers and appli• After a careful review, the JCEO decided to A more thorough understanding of the new cants, one-way and mutual. refocusitsefforts. The purpose of the ER no ER willnotnecessarily help anapplicant find longer would be merely scheduling inter• As long as the numbers of employers and a job, but it may reduce some frustration views, but would be scheduling interviews applicants were approximately equal, the during the process. most likely to lead to a campus interview or ER's system worked well. Because of the further actions toward employment for an The ER is the responsibility of the Joint tightening job market, however, the para• applicant. The newpolicy statement reads: Committee on Employment Opportunity digm had recently changed, and employers .(JCEO). The MAA, AMS, and SIAM ap- had been expressing concern over seeing too PleaseseeEmployment Registeronpage4 FOCUS December 1993 FSCUS Table ofContents FOCUS is published by The Mathematical Association of America, 1529 Eighteenth Features Street Northwest, Washington, DC 20036• 1385, six times a year: February,April, June, August, October, and December. Meetings Deadlines 4 Editor: Keith J. Devlin, Saint Mary's College ofCalifornia Associate Editor: DonaldJ.Albers,MAA AssociateExecutiveDirector, and Director Secretary's Report and Proposed Bylaws Revisions ..5 ofPublications and Programs

Chair ofthe MAA Newsletter Editorial Committee: JosephA. Gallian, University ofMinnesota at Duluth Minority Students and Mathematical Careers 6 ManagingEditor: Harry Waldman, MAA

Production Specialist: Amy E. Stephenson, MAA Intervention Grants Information 7 Letters to the editorshould be addressed to: Keith Devlin, Saint Mary's College of California, P.O. Box 3517, Moraga, CA A Retrospective of John Dieudonne 8 94575.E-mail: devlin@ stmarys-ca.edu The FOCUS subscription price to individual members of the Association is $6.00, included in the annual dues. (Annual dues The New Job Diary, Part 2 18 for regular members, exclusive of annual subscription prices for MAA journals, are $68.00. Studentand unemployed members receive a 66 percent discount; emeritus 1994 Summer Institutes 21 members receive a50percentdiscount;new members receive a 40 percent discount for the first two membership years.) Copyright © 1993 by The Mathematical Mathematics at the AAAS Winter Meeting 24 Association of America (Incorporated). Educational institutions may reproduce articles for their own use, but not for sale, provided that the following citation is used: "Reprinted with permission of FOCUS, Departments the Newsletter of The Mathematical Association of America (Incorporated), 1993." Networks in FOCUS 15 Second-class postage paid at Washington, DC and additional mailing offices. Postmaster: Send address changes to the Membership and Subscriptions Depart• Editorial 12 ment, The Mathematical Association of America, 1529 Eighteenth Street Northwest, Washington, DC 20036-1385. PersonalOpinion 13 ISSN: 0731-2040 Printed in the United States of America. Printed on recycled paper EmploymentOpportunities 25 December 1993 FOCUS Cincinnati Meetings Update The annual jointmeetingsofthe American is "Are women getting all the jobs?" thoughts about this crucial area ofschool mathematics. MathematicalSociety and theMAAwill be David A. Smith, Duke University, will be held in CincinnatiduringJanuary 12-15, a participant in the Wednesday morning Corrections 1994.The programannouncementappeared panel discussion on "Revising the AP in the OctoberissueofFOCUS and also in The paneldiscussion, LifeAfterRetirement, calculus syllabus." the Octoberissue ofthe AMS Notices. organized by Andrew Sterrett, Denison The Mathematical Sciences Education University and the MAA, will be held on Additions Boardis sponsoringa "FocusGroupon the Thursday,5:45p.M. to6:45p.M. DraftNCTMAssessment Standards,"sched• The MAA Teaching Awards Presentations The Two-Year College Reception will be uled from 5: 15p.M. to 6:30p.M.on Friday. on Friday will be followed by a recital at heldat5:45p.M. to7:00p.M.onThursday. The AssessmentStandards will helpdeter• 8:45p.M. honoringMAASectionalandNa• mine how schools measure what students tional Teaching Awardees; Jane Price, John A. Dossey will not be able to partici• are learningin mathematics. The purposeof violin, and Ruth Price, piano, will be per• pate in the Assessing Calculus Reform the meeting, organizedby Susan Forman, is forming Sonata in D minor by Brahms. Efforts panel scheduled for Saturday, to gathercomments and advice about the I:OOp.M. to 2:00p.M. The Associationfor Womenin Mathemat• Standards from members oftheAMS and ics will present its Louise Hay Award for MAA, which will then be sent on to the lead• Contributions to Mathematics Education ershipofNCTM. Copies ofthe Standards during the Joint Prize Session on Thurs• document (or a summary thereof) will be day afternoon rather than at the AWM available at the registration area. Please at• business meeting. The title ofthe AWM tend all or part ofthe sessionand shareyour panel discussion on Wednesday afternoon

Summer Joint Meetings Vancouver, Canada

The CarlB. Allendoerfer Award, for authors Members ofthree North American math• ofMarkov Chains, CMJ 23 (1992), 373• of expository articles published in ematicalsocieties convergedon the campus Math• 385, and to DanaN. Mackenzie, ofKenyon ematics Magazine, went to Xun-Cheng of the University ofBritish Columbia, in College, for his paper Triquetras and Huang, ofthe New Jersey InstituteofTech• Vancouver,Canada, in August, as theMAA, Porisms, CMJ 23 (1992),118-131. theAmerican Mathematical Society, and the nology, for his article From Intermediate CanadianMathematical Society held their ValueTheorems to Chaos, which appeared The Merten M. Hasse Prize is designed to first everthree-wayjointsummermeeting. inMM 65 (1992), 91-103. encourageyoungermathematicians to take up the challengeofexpository writing, and Sir Michael Atiyah was this year's Earle The LesterR.Ford Awards, given to authors is awarded by the Association every two ofexpositorypapers publishedin the Raymond HedrickLecturer. Sir Michael, Ameri• years for an expository paperpublishedby who isMasterofTrinityCollegeCambridge canMathematicalMonthly, wentto Donald the Association where at least one of the E. Knuth, ProfessorEmeritus at Stanford and Directorofthe Isaac Newton Institute authors is youngerthan forty years ofage. It for Mathematical Sciences in Cambridge, University, for his paperTwoNotes onNo• was given to JonathanM. Borwein, PeterB. chose as the theme for his three lectures: tation, whichappearedin AMM99 (1992), Borwein,andDavidH.Bailey,for their paper Recent Developments in Geometry and 403-422,and to CarstenThomassenofthe Ramanujan, modular equations, and ap• Physics.Acapacity audiencelistened to Sir Technical University ofDenmark, for his proximations to pi, or how to compute one Michaelconcentrateon historical matters in article TheJordan-Schonflies Theorem and billion digits ofpi, AMM 96 (1989), 201• his first lecture, turning to three dimensional the Classification of Surfaces, AMM 99 219.The two Borweinbrothers are at Simon (1992), 116-130. space in the second, and four dimensions in Fraser University, Bailey is at the NASA the third. The George P61yaAwards, for authors of Ames ResearchCenter. The Hedrick Lectures, established by the expository papers publishedin the College Three ofthe Association'sSectionAwardees MAA in 1952, are named after Earle went to Lester Mathematics Journal, H. for DistinguishedTeaching, honoredat the Lange and James W. Miller, respectively RaymondHedrick, the first Presidentofthe January meeting in SanAntonio, gave dis• Association, who died in 1943. ProfessorEmeritus at San Jose State Uni• plays ofthe classroomskills thathadled to versity and a Ph.D. student at Southern Alsoofparticularnote to MAAmembers, their awards. They were V.FrederickRickey MethodistUniversityin Dallas, Texas, for among the many and varied events at the (Bowling Green State University), Doris their paperA Random LadderGame: Per• meeting, was the awarding ofa numberof Schattschneider(MoravianCollege), and mutations, Eigenvalues, and Convergence Associationprizes. PhilipD. Straffin, Jr. (Beloit College). FOCUS December 1993 Meetings Deadlines Kenneth A. Ross MAAAssociate Secretary posals to me by June 15 so thatI can start also Thesecommitteeshaveconsidered"late" Thesedays our Joint Annual Meetings in making the schedule and have an idea of proposals, and probably will in the future, Januaryand our Joint MathFests in August howtheprogramwillevolve.These remarks but they preferto avoid this because then the have rich programs. The planning and applytotheprogramelementsthataresolely decisionsare made by the committeechairs scheduling is quite complicated. Many my responsibility: panel discussions, spe• ratherthan the full committees. program elements come from various cial presentations, workshops, readings, MAA committees;a few are suggested by TheCommitteeon Minicourses(Joan Weiss, plays, recitals, etc. Similarly, the absolute interested individuals. Several people have chair) does its planninga yearin advance, deadline forarranging allprogram elements asked me what the deadlines are. Here are and so proposals are due thirteenmonths for August meetings is February1, and I the general restrictions; minicourses and prior to the meeting. The extra month is encourage everyone to submit their pro• sessionsofcontributedpapersarediscussed needed so that the proposals can be circu• posals to me prior to or at the January in the next paragraph. In orderto keep our lated to the committee and studied prior to meetings. membershipfully informed, it is essential the actual committee meeting at which they that all programelementsfor the January Minicourses and sessions ofcontributed are discussed. The Committeeon Sessions meetings be set and announced in the Oc• papers are monitored by committees to ofContributed Papers (Elizabeth J. Teles, tober issues of FOCUS and the AMS whichproposalshavetobesubmitted.There chair) also does itsplanning wellin advance. NOTICES. Therefore, the absolute dead• are advantages to having these important Proposals are due atorpriorto theAMS• line for arranging all program elements for program elements carefully monitored, but MAA Joint meeting held twelve months January meetings is Augustl. However, I a disadvantage is that it takes committees prior to the meeting to which the pro• encourageeveryone to submittheirpro- longerthan individuals to processpropos- posal refers.

Employment Registerfrom page 1 1. Mutual requests views to other applicants. To counterbal• ance employers' requests, applicants' The Employment Register should sched• 2. Employerrequests high priority requests are most likely to ule interviews with the highest a priori 3.Applicant"highpriority" requests be scheduled. Average applicants may probability ofproducing ajob, and this is not get as many interviews, but the inter• most likely to occur when the employer 4. Applicantnormal requests views should be their top choices. has requested the interview. The Employ• After eachinterview isscheduled,applicants ment Register best serves applicants by Despite extensive testing ofthe new algo• are reordered so those with the fewest inter• attracting as many employers as possible, rithm, the atmosphere was tense on the first views are given priority for the next round. and this is most likely to occur when night the software went to work. When a employer requests are given priority. The algorithm contained a few potential program is run only once a year, there is a traps, however. During past ERs there had scant margin oferror. The old, discredited To implement this policy, a new schedul• always been a small numberof "hot"appli• algorithm was on line as an emergency ing algorithm was needed. The JCEO cants (those particularly well-qualifiedand backup, on the assumption: better poor contracted with R. Jarvis, D. Shier, and requested by dozens of schools). For the schedules than none. M. Myers of Clemson University for the mostpart, the new algorithm allowed mar• software; appropriate software was not But there was no need to worry. The soft• ket forces to determine scheduling and did availablecommercially or from any other ware performedflawlessly, and the results not try to createan artificial equality ofap• professional society. exceededourhighestexpectations. The 1993 plicants. Since the order of scheduling ER scheduledas many interviews as it had The Clemson-produced software was de• interviews strongly favored employers, this in previous years, but the quality (as mea• livered on schedule; it is robust, flexible, meant employers would get most oftheir sured by the desirability ofthe interview) and can handle all situations the JCEO pres• requests, some applicants would have many increased. ently foresees facing the ER. interviews,andanumberofapplicantswould have only two or three. There were 491 applicants and 68 employ• In essence, here is how the Jarvis-Shier• ers (representing 92 positions) at the 1993 Myers algorithm schedules interviews Was this the fairest way to run the ER? ER. Here are some figures showing the during forty periods overtwo days: Aftera greatdeal ofdebate, the JCEO de• performance of the Jarvis-Shier-Myers • Employers requestup totwentyinterviews. cided this was indeed the best way to run the schedulingalgorithm: ER. Ifthe ER ignored marketforces, then •Applicants request up totwenty interviews, • 100% of mutual requests were satisfied. the market would ignore the ER. The ER marking four as "highpriority." serves noone well by scheduling interviews • 100%of employerrequests were satisfied. • Interviews are scheduled in the following of low interest to employers; employers order: become frustrated and can deny inter- Please seeEmploymentRegisteronpage 14 December 1993 FOCUS Secretary's Report and Noticeof Proposed Bylaws Revisions

G. L.Alexanderson, Secretary

At the Vancouver meetings in August the meet before the business meeting and that Similarly, the first sentence of Article VI, BoardofGovernors,inadditiontocovering cannot have the newly appointed members Paragraph5, which now reads theusualagenda,heardreportsonelectronic attendasofficialmembersofthecommittee "A groupof notless thantwenty-five mem• services and discussed at some length ways and those committees that meet after the bers ofan existing Section may petition the in which the Association can enhance the business meeting andhence have thenewly Boardto partition the area and the Section flowofinformationthroughimprovedelec• appointed members officially on the com• into two or more Sections." tronic services for the membership. This mittee but not the retiring members of the discussion will guide the newly appointed committee. This awkwardproblem has, in would be changed to Committee on Electronic Services in for• fact, been avoided by having committee "A group oftwenty-fivemembers of an ex• mulating recommendations for action. chairs invite both retiring members and isting Section may petition the Board to newly appointed members to attend such KennethRoss,AssociateSecretary,reported partitionthe areaandthe Sectionintotwo or meetings.This has sometimes led toconfu• to the Business Meeting in the absence of more Sections." sion,however,in theMeetings Department the Secretary. One of the items reported on in Providence. The current practice also And similarly, the first sentence of Article was the successofthecurrent Coordinating means that the Association has two presi• VI, Paragraph 6, which now reads Councilstructureinfacilitatingtheappoint• dents at every other January meeting, one mentofMAACommittees. Representation "A group of notless thantwenty-five mem• beforethebusinessmeetingandanotherone on committees is broader now than it has bers residing oremployed in thatpart of the after.The BoardofGovernorsrecommends been in the past, due in part to a wider range area of an existing Section which they de• thattheword"business" bedeletedfromthe of recommendations for committee mem• sire to become part of another existing frrstsentenceofArticleIV, Paragraph l(d), bership. The Committeeon Committees is Section may petition the Board to redefine and the word "conclusion" be substituted stillsolicitingnamesofMAAmemberswho the geographic boundaries of the Sections for "adjournment" sothat the sentence cur• would like to serve the Association in this affected." rently reading way.Those interested should write me or would be changed to contact me bye-mail (galexanderso@ ''The beginningandendofthetermofevery "A group oftwenty-five members residing scuacc.scu.edu). officerand member ofthe Board (except as or employed in that part of the area of an provided inSection (b) ofthis Article) shall At the Business Meeting the membership existing Section which they desire to be• occurattheadjournmentofthe annualbusi• approved a bylaws change shortening the come part of another existing Section may ness meeting." time between the mailing of ballots and the petitiontheBoardtoredefinethegeographic closeoftheelectionforPresident-Elect,First would in the future read boundaries of the Sections affected." Vice-President,andSecondVice-President. "The beginningandendofthetermofevery (3) New Business at a Business Meeting (SeeFOCUS,ApriI1993,page3.) officerand member of the Board (except as There is concern that the currentArticleof In Vancouver the Boardof Governors ap• provided inSection (b)ofthisArticle) shall the Bylaws on business meetings ofthe As• proved another series of bylaws revisions occur at the conclusion of the annual meet• sociation (Article V) couldpermit binding proposedby the ad hoc Committee on By• ing." actionon items brought to thefloor without laws and recommended by the Executive (2) Changes in Wording The Board of priornotice,providingaquorumoffifty (50) andFinanceCommittees.Thefollowingare Governorsrecommendsthefollowing. They members were present. the proposedchanges, and this constitutes are stylistic changes only. Hereisthecurrent articlecoveringbusiness formal notice to the membership that these meetings of theAssociation: changes will be proposed at the Business In ArticleV,Paragraph 4, theparagraph that Meeting inCincinnati on January 13,1994. now reads "ArticleV.Business Meetings of the Asso• ciation (1) Tenns of Office The current Bylaws "At allbusinessmeetingsoftheAssociation specify that terms of officers, some Board aquorum shall consist of not less than fifty 1.A business meeting of the Association members, and most committee members (50) members and nobusiness may be val• shallbeheldannually,atsuchtimeandplace begin and end at the adjournment of the idly transacted at ameeting at which fewer as the Board may direct. Other business annual(January)businessmeeting.Thiswas than aquorum are present." meetings of the Association may be called appropriate when the business meeting of would be changed to from time to time by the Board or by the President of the Association to be held at theAssociation tookplace on thelastdayof "At allbusinessmeetingsoftheAssociation the annual meetings, but with the recent aquorumshallconsistoffifty(50)members such time and place as may appear from the formatfor thejoint meetings, thisprovision andnobusinessmaybevalidlytransactedat call. leads tothecuriousproblemof havingcom• ameeting at whichfewer than aquorum are mittees that meet at the annual meeting fall present." technically into two categories: those that Please see Bylaws on page 6 FOCUS December 1993

Another very effective aspect of the con• Minority Students in Southeast Get ference was the interaction of undergraduates with mathematics Boost Toward Mathematics Careers graduate students. Minority graduate students from the University of Mary• Sylvia T. Bozeman land, the University of Massachu• setts-Amherst, Wesleyan University, Given the excitement and enthusiasm of incommunications), FredaPorta-Locklear Georgia Institute of Technology, Clark the students, it could have been a festival (Numerical analysis with partial differen• Atlanta University, and Clemson Univer• of any kind. Fifty students from twenty tial equations), and Wanda Patterson sity presented part one of the panel colleges and universities located in nine (Geometry in Banach spaces). Another discussion, Straight Talk About Graduate states gathered at Spelman College in highly informative and motivational School. For the remainder of the confer• Atlanta, GA to hear mathematicians dis• speaker was Johnny Houston (Minorities ence, graduate students could be seen cuss their research and to explore the in the mathematical sciences). Students during breaks with small groups of in• possibilityofbecoming mathematical sci• were also able to attend a lecture given by tense listeners close by. Students even entists. Over a three day period during ProfessorAderemi Kuku, Presidentof the requested an additional lunch time ses• March 1993 the second MATHFest for African Mathematical Union, whose visit sion with the graduate students to undergraduate mathematics majors was to Atlanta was jointly hosted by the insti• continue discussions on issues raisedear• held to encourage minority students to tutions of the Atlanta University Center. lier. Students and non-students praised entergraduate school and pursue careers In addition to the content ofthe presenta• the informality and friendly atmosphere in the mathematical sciences. tions, students were equally impressed by which enhancedinteractions between stu• the lineup ofmathematicians with whom The lineup of dynamic speakers who gen• dents, presenters, faculty and graduate they could identify as role models. One erated unquestionable excitement about students, and promoted networking commented that the "speakers were very mathematical research included several which could continue after the confer• passionate about their subjects" while oth• rather recent recipients of doctoral de• ence. ers felt that the main strength of the grees in the mathematical sciences: Iris conference was the diversity of the speak• To give balance to the conference, stu- Mack (Financial engineeringto aerospace ers, both in their backgrounds and their engineering), Danielle Carr (Mathemati• presentations. Please see Careers on page 21 cal biology), Nathaniel Dean (Graph theory

Bylaws from page 5 (4) Rules of OrderBylaws should include awkward situation is created. An able and a reference to the rules by which the meet• conscientious incumbent may feel uncom• 2. Notice of any business meeting of the ingsoftheorganization are tobe conducted. fortable having to compete in a contested Association shall be given by the Secretary Ours do not.The Board of Governors there• election. And, on the other hand, it may to each memberofthe Association at least fore proposes the addition ofa new Article be difficult for the Executive Committee thirty (30) days priortothe date set for each X that would read as follows: to find someone who is willing to run meeting. against a current member of the Finance "ArticleX. Parliamentary Authority Committee where people will likely as• 3.AnymemberoftheAssociationmaywaive The rules containedin thecurrent edition of sume that the incumbent will be notice with the same effectas if due notice Robert'sRulesofOrderNewlyRevisedshall re-elected. The BoardofGovernors there• had been given. govern the Association in all cases to which fore recommends that Article IV, 4.At all business meetings of the Associa• they areapplicable and inwhich they are not Paragraph 1(g), be changed. The second tion a quorum shall consistofnot less than inconsistentwith these bylaws and any spe• sentence which currently reads cial rules of order the Association may fifty (50) members and no business may be "At least two nominations shallbe made for adopt." validlytransactedatameetingatwhichfewer each office to be filled in the case of Gover• than a quorum are present." The current Article X would thenbe renum• nors (except Sectional Governors) and To this article the BoardofGovernors rec• bered Article XI. members of the FinanceCommittee." ommends adding the following Section 5: (5) Changes in Election of Members of would be changed to "5. An item can be formally acted upon at a the Finance Committee The current By• "At least two nominations shall be made for business meeting of the Association only if: laws specify that when there is an opening each office to be filled in the case of the (1) it has been proposed by the Board of for one ofthe two elected membersofthe Governors(exceptSectionalGovernors)and Governors, (2) it has been submitted to the FinanceCommittee,theExecutiveCommit• members of the Finance Committee, except Secretary thirty (30) days in advance of the tee will send the names of two nominees to in the case in which the ExecutiveCommit• meeting, or (3) it receives unanimous con• theBoard. This works wellwhen theincum• tee wishes to nominate for re-election a sent at the business meeting for bent isnot running forre-election, but when current memberof the Finance Committee. consideration for approval by acclama• the Executive Committee nominates an in• In this case only one nomination by the tion." cumbent and one other person, an Executive Committeeis required." ~------December 1993 FOCUS of institutionalization through local or SUMMA Grants for Intervention state funding (perhaps after start-up federal funding from a variety of pro• Projects Available grams)? • Support: Can you demonstrate an abil• The MAA plans to award small grants To provide maximum flexibility, ity to mobilize internal and community for development of mathematics-based unexpended funds may be carried for• resources to sustain an intervention intervention projects in spring 1994. ward. An institution is expected to supply project? SUMMA is soliciting college and univer• matching funds or in-kind support as an •Adaptation: How might a successful ex• sity mathematicians and their department indication of commitment to the develop• isting project be adapted to your local and institution to submit planning pro• ment of the project. While the MAA will conditions, or what is the need for inno• posals for the advance work necessary to fund the planning activities, it willnotfund vation? host mathematics-based intervention the project itself. These grants will not projects for middle and high school stu• support any indirectinstitutional costs. • Timeline: When will you carry out the dents, targeting underrepresented planning activities? minority students. Projects may replicate Who May Apply Submission of Proposals an already successful project, adapt com• • Minority institutions; or ponents of other projects, or be entirely Proposals should be submitted as soon as innovative. Planned activities should in• • colleges and universities which have stu• possible, but no later than February 1, clude those characteristics in successful dent bodies with a high percentage of 1994. All proposers will be notified by projects such as LessonsforHBCUsfrom underrepresented minorities (at least February 15, 1994. Mathematicians re• Precollege Mathematics and Science Pro• 20%) and a successful track record in ceiving grants are expected to attend a grams. These lessons are summarized at developing minority students' interests workshop at MAA Headquarters Febru• the end of this announcement. The goal of in mathematics and science; or ary 25-27, 1994. The MAA intends to the planning should be a formal proposal • colleges and universities in which the award ten to twelve grants. The SUMMA for a project to be submitted to public or institution or department has demon• staffis available to discuss your potential private agencies for funding. strated that the faculty have the proposal at any time. willingness and capacity to replicate or For further information, contact: Objectives adapt successful projects. Dr. William Hawkins, Director of the Specific objectives of the SUMMA small Evaluation of Proposals SUMMA Program grants program are to: Proposals will be evaluated by members Mathematical Association of America • Encourage mathematicians to develop of the MAA Committee on Minority Par• 1529 Eighteenth Street NW projects to increase minority participa• ticipation in Mathematics, the Director Washington, DC 20036 tion in mathematics; of SUMMA, and the Executive Director (202) 387-5200 • Provide funds for directors' visitations of the MAA. FAX: (202) 265-2384 to established projects; e-mail: [email protected] The single-spaced, three-page-maximum • Enable the director to work with the proposed plan should include: Characteristics of Effective host institution to recruit faculty and further develop the foundation for the • Concept: What ideas and philosophy do Projects you have for a project? project through other methods; What has been learned? Despite the dif• • Carry out a feasibility study; • Rationale: Why will your institutions be ferences among current highly successful a welcoming host for the project? • Provide the director the opportunity to intervention projects, there are some participate in a proposal writing work• • Objectives: What are the objectives of characteristics which all effective projects shop; your planning project? targeting minority students seem to have • Secure technical assistance in proposal • Activities: What tasks do you plan to in common. These have been identified in writing and fundraising; undertake to design your project? several reports and are synthesizedin this listofCharacteristics ofEffective Precollege • Personnel: What are the name, position • Make it possible for the project director Intervention Projects. to contact private foundations, public and qualifications of the proposed agencies, and industry for additional project director? Who else will be in• • Projectgoals are clearly articulated and support. volved in the planning? How? measurable; • Evaluation: How will youjudge the suc• • Strong academic component; focus on Nature of the Grant cess of this planning? enrichment, not remediation; Grants are a maximum of $5000 and will • Budget: How will your planning funds • Hands-on learning opportunities and be awarded to the project director's in• be spent, (personnel, travel, materials, use of computers; stitution. Grants must be spent within the telephone, workshop attendance, release • Highly competent teachers who believe year. Project directors have obligations time, etc.)? that students can learn the material; in accepting the grants. They must design • Commitment: What is the host • Heavy emphasis on every-day appli• a project and submit versions of a pro• institution's potential for long-term cations ofmathematics and on careers posalbeginning inMay 1994,untilfunded, commitment? with the assistance of the SUMMA staff. • Future funding: What is the likelihood Please see Small Grants on page 8 FOCUS December 1993 Mathematician, Musician, and Cook A Personal Retrospective of Jean Dieudonne, 1906-1992, by Chantal Shafroth

Aspacious apartmentoverlookingtheEiffel teachers at Ecole Normale were eminent Tower, a brightstudy containinga full wall mathematicians such as Picard, Cartan, bookcasedecorated with antique boiseries Lebesgue, Montel, Denjoy, and Julia; and and facing a large desk, a music room in• his fellow students becamehis colleagues, cluding a grand piano and a hi-fi collaborators, and friends for life. After system-suchistheenvironment whereJean studying at Princeton, Berlin, and Zurich, Dieudonnespent the last 12years ofhis life. Dieudonnecompletedhisdoctoral disserta• Thecalendarupon the desk shows the last tion in 1931 on the theory of analytic day he sat here, a week before he died on functions ofa complex variable, underthe November 29, 1992 at the age of 86. The direction ofPaul Montel. Greekdictionary reveals his last endeavor: In his words, "the two most importantevents learning Greek in orderto read Euclidand ofhis life" occurred in the fall of 1934. He Aristotle in theiroriginal texts. met his future wife Odette, who, for almost Jean Dieudonne was born in Lille, France, 60 years, gave him the love and supporthe on July 1,1906. His father was a self-made needed. When Jean would be lost in the making new lists according to some new man who, in spite ofa modest beginning, clouds, thinking about aproof, Odette would classification, so it was not surprising that becameCEO ofa large textilecompany.He choose the suit and tie he neededto attend a he participated with enthusiasmin the writ• was very demanding ofhimselfand others, meeting.When frustrated, Jean wouldhave ingofthe treatise. In 1940,Dieudonne began had a keen sense ofduty, and spent his lei• one ofhis legendary tantrums, and Odette writing a bulletin called La Tribu, which sure time studyingon his own. He showed would show patience and understanding. provided internalcommunicationamong the his son what "effort and willpowercan ac• And whenhe wanted to entertain, she was dispersed group, and he became a "key always a very gracious hostess. complish.") player."3 He wrote several chapters himself, Jean Dieudonne's passion for mathematics The otherimportanteventofthat year was and, according to Henri Cartan, "noarticle began when he encountered Algebra at the the birth of the Bourbakigroup. Dieudonne waspublished withoutJean Dieudonne read• age offourteen. This led him to enterI'Ecole was mditrede conference at the University ing it and including his final touch."] Normale Superieure de Paris in 1924. His ofRennes. His friends from EcoleNormale Furthermore, he often made up all of the had similarpositions in otherFrenchpro• exercises.Adrien Douady, anothermember Small Grants from page 7 vincial universities.Most commutedtoParis ofthe team, said that "fifty percent ofthe in the field; twice a month to attend a seminaire de energyofBourbaki came from [Dieudonne] alone." I Dieudonne felt that his participa• • Teaching strategies that take into ac• Mathematiques, led by Gaston Julia. The count the needs, socioeconomic JuliaSeminardiffered from otherexisting tioninthegroup broadened hismathematical backgrounds, and cognitive develop• seminars: each year it concentrated on a knowledge considerably, forcing him to ment of adolescents; special topic, such as group theory or Hil• tackle new material, extending his research • Multi-year involvement with students; bertspaces, and speakers were required to to topology and algebra, and exposing him to the original ideas ofhis teammates. The • Strong directors and a committed and choose the simplest approach in theirpre• stable staff; sentations. This forced them to synthesize Bourbakigroup still exists. It has published about50 volumes and, like the Academyof • Involvement ofappropriate staff mem• existinginformation, creating a great impe• Science, renews itselfby choosing its own bers; tus in theirresearch. Agroupcomposedof Cartan, Chevalley, Delsarte, Dieudonne, members. • Stable, long-termfunding base with mul• tiple funding sources; Dubreuil, Leray, Mandelbrot, de Possel, and In 1937, Dieudonne left the University of Weil beganmeeting before the seminarat • Recruitment ofparticipants from a rel• Rennes tojoinhis friend Jean Delsarteatthe Capoulade, acafe in the Latin Quarter. Their evant target population in a defined University ofNancy where heremained until area; goal was towrite a treatise on analysis which 1952. He was not really interestedin peda• wouldchange the teaching ofmathematics • Involvement with universities, colleges, gogy and often admittedthathe becamea at the university level and also be useful to industries, schools, community-based professornot because he was interested in organizations; researchers,physicists,and technicians.2The teaching, but as a way of continuing his first volume ofElements de Mathematique • Parental and community support; mathematical research; however, "thisdid was published in 1939 under the name • Development of a peer support system; not stop him from giving fascinating classes Nicolas Bourbaki. Dieudonne was always and seminars, incredibly clear, which com• • Evaluation, long-term follow-up, care• attractedby the art ofcompilation; dictio• municated his passion.'?' ful data collection; naries and encyclopedias were his favorite • Networking through a consortium. readings. From a young age, he enjoyed Dieudonne spentseven years in the United December 1993 FOCUS attention. His third passion, gourmetcooking, was a In Algebra, he worked on delight for all his friends. Wherever noncommutative rings, intro• Dieudonne lived, he would invite three or duced the socle of a ring, four couples to his home and prepare for generalizedWedderburn'stheo• thema Frenchmeal similarto thatofa fine rem, and developedGalois theory restaurant. For the occasion, he would usu• for simple and semi-simplerings. ally chase Odettefrom the kitchen. Once, he His work on Lie groups and Lie gavea selectgroupa lessonon puffpastry. hyperalgebrasover afieldofchar• Laterin life, his granddaughterbecamehis acteristic p > 0 led him to "his cookingpartner. Odette recalls how he often most influential discovery, the enjoyedstoppingin somegite de France on introductionofformal groups.?" his way to or from Nice; in a gorgeous site with scrumptiousfood he could forget about In Topology, Dieudonne made the university'sproblems. valuablecontributions. He made "Enormousenergy and an incrediblepower States, from 1952 to 1959, the first at the acritical study ofcertain topologi- University ofMichigan and six at North• cal spaces, gave a new proof of the ofworkcoupledwith a sharp sense oforga• westernUniversity.Alex Rosenberg,one of Hahn-BanachTheorem,introducedthe idea nization, such was the secret of his his colleaguesat Northwestern,remembers ofcontinuous partitionofunity, andextended achievements. He would get up at five 0'clock, spend an hour gardening, then write "how much interesthe tookin the day-to• the ideaofparacompactspaces. Theseno• day affairs ofthe department, working at tions proved to be very important in his five pages ofBourbaki before starting his day as dean at Nice."?Afew years ago, building itupand takingan active interestin functional analysis and differential geom• the graduate students." Butthese weredif• etry. In collaboration withL. Schwartz, he after his retirement, when he was crisscross• ing the globe givinglectures, he stoppedat ficult years: his son and daughter were publishedin 1949 an importantpaperon the growingup and, for them, a Frencheduca• duality between vector spaces, La dualite my house for acoupleofdays. Without any tion was imperative. As a result, the family dans les espaces (F) et (LF). appearance ofweariness from his travel, he arose the next day at the crack of dawn, was oftenseparated. With muchmodesty, he was able to put his grabbed Mathematics Today,Twelve Infor• devotion to work in the service ofothers. In 1959, Dieudonne returned to Paris to mal Essays' from the bookshelf, and by "Forten years, he was literallyAlexandre becomeProfessorat the Institutdes Hautes breakfasttime was ready to discuss Roger Grothendieck'sscribe, writing and proving Etudes Scientifiques. In 1964, he was elected Penrose's essay The Geometry ofthe Uni• theorems, underthe direction ofthis bril• President de la Societe Mathematique de verse,convincing me thatteaching Euclidean liantmathematician, whomhe thoughthad France. A year later, he became the first Geometry was useless. Dean ofthe ScienceFaculty at the Univer• something interesting to say."' The result sity of Nice. He had no desire to get involved was the publication of Elements de He was always learning something new to in administration, butfelt it was his duty to Geometric Algebrique, which has revolu• stay abreastofrecentdevelopments. He did accept the position. Opposedto the student tionized the field. not acceptmediocrity, but showedconsid• eration and love for those he cared for. unrestof 1968, he remainedat the helm dur• On January24, 1968,hewaselectedamem• Frankness and honesty were two otherim• ing difficult times and "successfully ber ofthe prestigiousAcademicdesSciences, portanttraits ofhis character, which proved managed the University of Nice Science and on November29, 1969, he receivedhis to be key factors when he became dean of Faculty as an enlighteneddespot." I academiciansword. From 1931 until his retirement from the Jean Dieudonne was a fasci• UniversityofNice in 1969, Dieudonne was natingperson, "a giant inevery very prolific. His activeparticipationin the sense of the word."! He had Bourbakigroup (until 1970) was onlypart threepassions: mathematics, of his work. He was an extremely broad music, and gourmetcooking. mathematician with an "encyclopedic An accomplished pianist, he knowledge." I The "exceptionallyrich work ofJ. Dieudonne'"consists ofsome 130 pa• often found time in his full pers in a variety of fields: Analysis, schedulefor an hour ofpiano. Topological Vector Spaces, Algebra, and He loved classical chamber Algebraic Geometry. music, relaxedby listening to it, and when he lived in InAnalysis, which washisfirstresearchfield, Evanston, was adevotee of the he used ingenious techniques to study the Fine Arts Quartet. He was also zeros ofhoiomorphic functions ofvarious very knowledgeablein music; classes, and he was the first to use p-adic in Nice he gave a lecture on From left to right: Roger Godment, Jean Dieudonne, Andre analysis, which has since received much Gabriel Faure. Weil, Saunders Mac Lane, and J. Piere Sere, in 1954. FOCUS December 1993 the faculty. He had firm convictions and wouldnot acceptany compromise. Recognition and Rewards in His retirementfrom the University ofNice in 1969 did not turn him into an idle man. Mathematics Departments Muchto the contrary, free from administra• TheCommitteeon Professional Recogni• nificantly largerthan the proportion offac• tive duties, he was able to devote himself tion and Rewards, a committee ofthe Joint ulty who thinkso. And the overwhelming entirely to mathematics. He completedEl• Policy Board for Mathematics, has been majority ofthose responding say that re• ements d'Analyse (nine volumes)," a working for abouta yearand a halfand ex• search isnow and should continue tobe"very monumental work, then wrote ten other pects to putout its report in early 1994. At important" in decisions about salary in• works, some aimed atstudents, such as Cours issue is the question ofwhat contributions creases and aboutpromotion and tenure. de Geometric Algebrique, others aimed at are recognized and rewarded in mathemat• The committee also found that, in depart• mathematicians, and others justfor "readers ics departments. interested in Science" such as Pourl 'honneur ments where the major emphasis has deI'esprithumain."In this remarkablebook, How does your own institution value teach• traditionally been on research, teaching has translated into English as TheMusic ofRea• ing, curriculum development, mentoring, become more important; while in depart• son, and into Italian as L'Arte de Numeri, public awareness ofmathematics, exposi• ments where the major emphasis has Dieudonnewantedhisreaders tounderstand tory writing, and serviceto the community? traditionally been on teaching, research has becomemoreimportant. the artofmathematics by understanding what TheCommittee made site visits to twenty• mathematicians do, the problems they are three academic mathematics departments, Among the questions the Committee will trying to solve, and the tools they are invent• ranging from Ph.D.-granting departments explore in its report are the degree to which ing to solve them. to departments in two-yearcolleges. They faculty are dissatisfied with the currentre• The last years of his life were devoted to also conducted a survey ofover600 math• wards system and what aspects of it they history ofmathematics. Underhis direction, ematicsdepartmentchairs and nearly 2000 would like to see changed. Otherissues also and with the collaborationoften othermath• faculty members. The Committeegathered beingexaminedare how well departments ematicians, Hermann published Abrege further information by way of panel discus• communicateintemally and with theirdeans, d'HistoiredesMathematiques, 1700-1900,11 sions and presentations at national and provosts, and presidents. In addition to pre• whichhas alreadybeentranslated into sev• sectional meetings ofthe AMS, the MAA, sentation and interpretation ofthe survey erallanguages, includingJapanese. In 1981, and SIAM. and site visit findings, the report will make Jean DieudonnepublishedHistoryofFunc• One interesting finding from the survey was recommendations to departments and to the tional Analysis, and in 1989, History of that the perceptions of departmentchairs and community for ways to improve the rewards system. Algebraic and Differential Topology, 12 faculty often differ considerably. For ex• which, according to his biographer, Pierre ample, at all kinds of institutions, the The above was abridged from an article Dugac, is "a masterpiece that will outlast proportion of chairs who think teaching written by Allyn Jackson, published in the everythingelsehe has done." ability is importanttosalary increases is sig- November issue ofthe AMS Notices. References 8Mathematics Today, Twelve Informal Es• 'Jean-Paul Dufour, La Mort du says,ed. L. Steen(Springer-Verlag, 1978). Mathematicien Jean Dieudonne, Le Monde, 2 December1992. "Iean Dieudonne, Elements d'Analyse (Gauthiers-Villars, 1982). (An English 2LilianeBeaulieu, "A ParisianCafe and Ten translation ofthe eighthvolume, Treatise Proto-BourbakiMeetings (1934-35)," The onAnalysis, vol. VIll, was publishedJune Mathematicallntelligencer, Vol. 15, No. 1993by Academic Press.) 1. !OJean Dieudonne, Pour l'Honneur de 3Liliane Beaulieu, from a personalletter. l'EspritHumain (Hachette, 1987). 4L. Schwartz, quote from La Mort du "Jean Dieudonne, P. Dugac, etal.,Abrege Mathematicien Jean Dieudonne. d' Histoire des Mathematiques, 1700-1900 (Schwartz was Dieudonne's student be• (Herman, 1986). fore becoming his colleague at the University ofNancy.) 12Jean Dieudonne, A History ofAlgebraic and Differential Geometry, 1900-1960 5M.Braconnier,AllocutionitI' occasionde (Birkhaiiser, 1989). la remise it Jean Dieudonne de son epee d'academicien, 29 November 1969. Chantal Shafroth is an Assistant Professor ofMathematics at North Carolina Central 6Alex Rosenberg, from a personal letter. FOCUS isprintedon Recycled University. 7M. Douady, quote from La Mort du andRecyclable paperwith soy Mathematicien Jean Dieudonne. based inks. Please recycle. December 1993 FOCUS MAA Custom-Designed Tests A New Service for MAA Placement Test Program Subscribers Design your own placement test with the help of our new custom-designed test service. This service uses a computer-based test generating system to produce similar versions of multiple-choice mathematics tests.

The features of this service are: • Test items produced for the various versions of a tests are ofcomparable difficulty to the catalog items you select, and yield tests with comparable means. • The items on these tests have function driven stems and distractors. • The tests are ofcamera-ready quality. • The system is flexible and allows a user to create a test or to select additional versions of one of the twelve tests currently available.

For further information contact: Placement Test Coordinator Mathematical Association ofAmerica 1529 Eighteenth St., NW Washington, DC 20036

Geometer's Sketchpad Two Regional Minicourses

December 3-4, 1993 at Seattle Central Community College December 11, 1993 at Towson State University

During the month ofDecember the MAA Minicourse Committee, with the support oflBM and the Interactive Mathematics Text Project, will sponsor two courses on the innovative new software, the Geometer's Sketchpad.

The Seattle Central Community College course will be presented byJim King of the University ofWashington. In addition to the presentation on Geometer's Sketchpad, there will be a briefpresentation on MathKit byJim Swift ofBumby South 2000 Secondary School in Vancouver, British Columbia.

Doris Schattschneider of Moravian College will present the course at Towson State University. This one day course will be held in the IMTP Lab in the Cook Library.

To register or for additional information please contact:

Lisa Johnson Mathematical Association ofAmerica 1529 Eighteenth St., NW Washington, DC 20036 1-800-331-1622 e-mail: [email protected] FOCUS December 1993

rarymathematicians, he,andthey, buildupon the work of those that have gone before. In how many otherareas ofhuman activity Editorial can you find such a dramatic instance of a struggle toward a common goal that unites people across time and across continents? In what other subject can a question raised The proofofFermat'sLast Theoremby An• sentence"Foreveryintegern greaterthan over 350 years ago be as fresh and crisp and drew Wiles last summercertainly got a fair 2, the equation meaningful today as it was when the ink on amountofmediaattention. And, on the ba• x"+yn=zn Fermat's page was still wet? In what other sis of"anypublicity is goodpublicity", that walk oflifecan one be so sure of the absolute is all to the good ofmathematics. has no whole number solutions." (The truth of a particular statement as happens case n = 3 has been known for hundreds The second oftwo articles by GinaKolatain with a mathematical proof? of years, of course.) the New YorkTimes, an in-depth focus that An event of unusual, and perhaps unique, appearedon June 29, was a particularly well• And yet, even Kolata missedwhatis surely human cultural significance takes places, written piece that managed to capture the most newsworthy aspect ofthe proof, and what do we read in our newspapers? something ofthe essence ofthe true nature namely, the culturalsignificanceofWiles ' Misstatements of the problem, incorrect il• ofmathematical researchand life within the achievement. Forgetthe technicaldetails of lustrations of the result, silly asides about mathematical community.Whenit comes the proof(a taskthat for all but a handful of balancing checkbooks, and a plethora of to covering mathematical issues, Kolata mathematicians is decidedly easy, since the idiotic remarks as to how "useless" the re• towers way above any of her colleagues technical details ofWiles' argumentwill de• sult is in the "real world", as if the yardstick writing for othernewspapers, to say nothing feat mostofus). Considerinsteadwhat has of human culture is its utility. oftelevision folk, most ofwhom seem un• been achievedon a human cultural level. able to distinguish mathematics from In grand and regrettable unison, the press Back in the middle of the 17th Century, a elementary arithmetic. missed a great "human interest" story con• French mathematician scribbles a problem cerning our culture and instead treated the The average newspaperwriterclearly has in the margin of a textbook. Over the years, culmination of over three centuries' work trouble understandingbasic English, as wit• a great many mathematicians work on this leading to the proofofFermat's Last Theo• nessed by the writer who stated that problem. These mathematicianslive allover rem as little more than the solution to a mathematicians had always suspected, but the globe, they speak different languages, particularlyhard homeworkproblem. Sad. priorto Wiles had not known for sure, that and in many cases they never meet one an• Very sad. the equation other. Over time, the many contributions made by these mathematicians eventually -Keith Devlin .x3+y3=Z3 lead to a solution-and make no mistake has no whole number solutions,thereby com• about it, Wiles' proofnot only rests upon the The above are the opinions ofthe FOCUS pletely misunderstanding the English work of a significant number of contempo- editor;anddo notnecessarily represent the official view ofthe MAA. letter to the Editor

DearEditor, Chantal Shafroth quoted mighthavebeen At the university, students may have to write from the science concentration exam, but examsor tumin homeworkassignments in Re: Articleby ProfessorShafroth(FOCUS, the general examhas the same format and orderto pass courses, but the majorexams June 93) may ask a similar question for a rational are oral: the Vordiplompruefung, after 2 Thearticle supportedmy own experience. function insteadofa trig function. years, and the Diplomhauptpruefung, at the (I was born in Germany and wentthrough end ofthe studies. Theseexams provide the Of the students who enroll in the first re• the German school system, got a Diplom in only grades, apart from the thesis, which quiredmathcoursefor elementary teachers Mathematics, and then came to the U.S., appearon a grade reportfor an employer. at Eastern Michigan University, a substan• and obtaineda Ph.D. from the Universityof The coursesoften don'tcarrygrades, or the tial portionplaces into a BeginningAlgebra lllinois atChicago. Since 1984,Ihave taught grades are only keptinternally.This shows courseorlower. atEastern Michigan University.) Ihave some a clearemphasison the final understanding remarks: 2.Theoral componentofthe examinations ofthe material. in Germany is worth remarking. The abitur 1.Itis importantto realize thatin the Ger• I enjoyreading FOCUS. exam has anoral part which might be waived. man school system EVERYBODY who (At least that' showitwas twenty years ago.) Regards, wants to attend a university has to pass the Much ofone's grade in each course at the abitur examination, including the mathemat• precollege level is based on in-class work, GiselaAhlbrandt ics portion. This is true in particularfor all class participation, and oral reports onhome• EasternMichigan University elementary teachers! The exam which workassignments. December 1993 FOCUS

does not reflect what takes place in the modemclassroom. Students gain access to information in a Personal Opinion mannerthatis neitherplannednorwholly expectedby instructors. Students havethe powerto performcomputationsofcomplex, real-worldproblems. In doing so, they are . Teaching, Learning, and Publishing in wontto "jumpover"theory, oftenintuiting it, sometimeschallengingit. Theycan con• the Age of the Inconceivable duct experiments, change variables, and explore mathematical ideas orreal-world Alexander Kugushev datawithease, in a highly visual, graphic, Whoin 1988couldhave conceivedoftoday,s tions and aspirations. Thenumberoffaculty and dynamic(as opposedtoverbal and static) world'spoliticalmap and psychologicalcli• and theirdiversityhaveequally increasedin environmentunableto be reflectedin a text• mate? In 1989-91, power relationships the interveningforty-some years. book of canned lectures. Students' around the globe changed with lightning transformationsarea wonder; they are em• Conditionsfor changeresultingfrom these speed, leavingus gasping. In large partthis powered, active, enthusiastic, no longer human and economic factors have been happenedbecausecomputersand computer• boredandpassive. awaitinga catalyst. In the mathematicalsci• driventelecommunicationsacceleratedthe ences' it came in theform ofthePC and, to The New Educational disseminationofinformation. a lesserextent, the graphingcalculator.The Publishing Thesesameforces affectall aspectsofmod• advent ofthese technologies has allowed, em life, highereducation included. In the and alsorequired, a series ofadaptations, For an educational publisher, what is the mathematical sciences,changein teaching perhapsthe mostimportantbeingthe alter• appropriateresponse to all this?Certainly and in learning is spurred by electronic ation ofthe relationshipbetweenthe teacher not businessas usual, meaning"Wepublish media, its operationalease, andincreasing and the learner,whichtraditionallyinvolved books."Theproperresponsemusttakeinto affordability.Whilenewdevelopments are an activeinstructoranda relativelypassive accountnew circumstancesand new oppor• taking place, it is notyetclearwhatwill be recipientofknowledge. tunities. Faculty need help in making the the ultimateconsequencesfor education. A transitionfrompastto future. Theyare con• Nowthe computerandthe graphingcalcu• safeguessis thatthe results will be striking, tinually busy, with ever-diminishing latorare beginningto enfranchise students thatthey will affectfaculty andeducational availabletime, and theirinstructionalfacili• to gainindependentinsights, reducingthe publishers,and that ultimatelythey may take ties are in transition, while the public role ofthe lecture and the lecturer. Some• forms as inconceivable today as ournew• educationsystemsofferonlylimitedfunds thing akin to a laboratorysubstitutesfor the worldpoliticalrelationships werein 1988. to supportthis transition. Thereis also un• classroom, and the instructor's function certainty about how and when the new becomesmorelike a coach,mentor,or con• Effect on Faculty environmentwill becomefully functional. sultant. And, at the sametime, there is pressureby Forcenturies, the lecturewasthe exclusive students to use computersfor instructionin way to transmitknowledgein mathematical Anothereffectofthesedevelopmentsis that arealworldcontext. fields. This was natural and effective be• the orderofinformationacquisitionchanges; it becomes less disciplined, more creative cause Undertheseconditions,publishers' conven• and productive. Thus, we beginto see anew tional offerings-a textbook plus a few • there wasno alternative; and unfamiliar learning culture emerge, afterthoughtancillaries puttogetherat the whose ultimateoutcome is notyetclear. It • the environmentwas intimate andselect; lastmoment-donot servecurrentneeds. challengesthe traditional mode,content, and Addressingthe faculty's changingcircum• • the informationprovidedsuitedthe needs sequenceofinstruction. Notall faculty will stances istheeducationalpublisher'sprimary ofthe times, reflecting a slowly-changing welcomethat. challengeat the turn ofthe 21stCentury, and accumulationofknowledgethatwouldsuf• should include a range ofoptions that are fice for a graduate for the rest of hislher Effect on Educational bothcustomer-orientedand reflectiveofthe professionallife. Publishers emergingeducationalenvironment. Overthe lastforty years, this patternbegan Forthe betterpartofthe pastfive centuries, Providing Educational Prod• to change, as cultural, economic, demo• educationalpublishersproducedtextbooks graphic, social, and technologicalconditions by "canning" professors' lectures. This ucts of the Future evolved. In 1950, there were two-million worked well because there was no better Publishers need to address the following relatively select, homogeneous higheredu• alternative, it replicated the classroom's menuofrequirements: cationstudentsin the UnitedStates. Today teachingllearningprocess, and the informa• thereare morethanfourteen million. They tion provided had lasting value. Now the CustomizationNew technologies in book are an enormouslydiverse lot---culturally, rules are changing for publishers as well. demographically, andin terms ofmotiva- Canninglectures will no longersufficeas it Pleasesee Teachingon page 14 FOCUS December 1993

them as demeaning theirteaching abilities. are plausible: Teaching from page 13 The realities ofintroducingnew ideas in the • Student input, and not solely that ofthe 1990s require an explicitand detailedstate• faculty, will increasinglyinfluence publish• production allow easy "custornization" of mentofan innovative author'sobjectives ers' offerings. publishers' offerings and respond to latent and the specific means to implementthem. demand among faculty. "Customization" This is especially true when part-time or •A sharp trend toward customization of may mean differentthings: abbreviation of adjunctfaculty are placed intounfamiliar educational products will develop. large textbooks, permutation of topic se• teachingcontexts. •Efforts to address individual learning styles quences, narrowing of focus, combining The Student's Role New learning devices will increase. different resources into an "integratedpack• will need to incorporate the student as an age", and other possibilities. Its aim is to • Students will exercise more freedom in active ratherthan passivelearner.The defi• meet the specific needs ofa specific instruc• shoppingforeducationalproducts pricedand nition-theorem-proof approach to tor, orcourse, or program. Current textbooks packaged to fit theirexpectations. mathematical instruction is becomingless are the oppositeof"customized", trying as pertinent. The new environmentis causing • Publishers will create tutoring devices, they do to reach as wide an audience as students to acquire knowledge differently, electronic and in print, to support the less possible. through insights stemmingfrom activities experiencedand the part-time instructor, the Software and the Laboratory Setting The connectedto real-world problems. Thus, the part-timestudent,andtheoff-campuslearner. new products will perforce combineprint new educational products must combine this •At the lowerdivisionlevel, publishers will and electronics, especially in cases where mode oflearningwith knowledge generated provide pre-packagedcourses rather than courses involve laboratory activities using by faculty in the classical mode. mere textbooks with ancillaries. computers or graphing calculators. New ways ofphysically integrating learning and TheNew Authorship •The cleftbetween teaching and research teachingdevices will be calledfor. The new The new educationalproducts will require a faculty will become more pronounced. "package"may be abox, the "textbook"one different approach to authorship. No longer •Agrowing partnership between educational ofseveral items within it. In fact, printmay will a single author, or even a team ofco• publishers and teachingfaculty may result. eventuallycometo support software. authors, be able to embraceall the activities The above observations reflectevents that The Instructor's Guide In presenting a new required. Publishers willneed toput together already occurepisodically throughout the teaching idea, a primaryobjectivefor pub• teams ofauthors to supportthe ideas ofthe educational system. They suggestthatthe lishers is to make it easy for the faculty to originating authorand translate them into time is now to begin making the transition to implement. So it is time for publishers to the ancillary elements ofthe package. the age oftheinconceivable, for faculty and cease being squeamish about theimportance The New Environment for educational publishers alike. ofthe"Instructor'sResource Manual". Such manuals are often presented with a semi• The effects ofall these changes are not com• AlexanderKugushev iseditorandpublisher apologetic disclaimer, lest faculty perceive pletely foreseeable; however, the following ofDuxbury Press in Belmont, California.

ofapplicants to interviewers was approxi• ticians find research positions or non-aca• Employment Registerfrom page 4 mately seven to one. demic positions. Ittends to attract smaller schools, certainly not large research univer• • 62% ofapplicant high priority requests • Employers who responded to the 1993 sities. Because of the preponderance of were satisfied. follow-up survey (78%) reported sending teaching schools using the ER, applicants out94 invitations to ER applicants for on• • 9% of applicant normal requests were should have a good command of spoken campus interviews. satisfied. English and strongclassroomexperience. • In San Antonio the average number of • Employers averaged39 interviews. The ER cannot guarantee an applicant an interviews for an applicant was between five interview with his or her top choice, nor can • Applicants averaged6 interviews. and six. it guarantee any interview at all. What it • 15 applicants had 3 or fewer interviews. • Mostjobslisted require a doctorate. does is provide a sophisticatedand invalu• able service to both applicants and • 26 applicants had 10 or more interviews. • Most jobs listed are for academic positions employers, endeavoring to help everyone at undergraduate institutions. To further increasesatisfaction with the ER, move toward the next stage of the hiring the JCEO is attempting to make partici• • Over halfofthe interviewingemployersin process. pants-especiallyapplicants-awareofits San Antonio indicated they were restricted realities. Thefollowing statements are in• by theirinstitutionor companytohiring only cluded in announcements for the 1994 ER U.S. citizens or permanentresidents. in Cincinnati: Severalinferencescan be drawn from these • At the 1993 ER in San Antonio, the ratio facts. The ERisnot likely to help mathema- December 1993 FOCUS

cally converted to an IP number by a name server behind the scenes. In some cases, however, you may want to refer to a station Networks in FOCUS directly by its IP number. The name of a station usually reveals something about its origin. For example, The Internet: Some Tools for Efficient Usage addresses ending in . edu refer to edu• cational institutions in the United States, Bert G. Wachsmuth . em to commercial institutions in the United States, . org to non-profit orga• It all started with a frustrated student upon method of communication between nizations, . de to German Internet who told me she had to write a term pa• parties), the Internet also has gateways to members, and so on. peraboutcomputercrimebut was unable networks andservicesthatarebasedon other to locate appropriate references in our protocols. (Krol: What is the Internet?• Selected Services library.Although I suspected the student Working Draft, FYI) did not use the library services to their The following are briefdescriptions ofim• fullest extent, I thought the perfect place The Internet, in effect, ties togethera large portant services. Some suggestions for their to locate such information would be the collection of computernetworks through a usage in mathematics can be found in Sec• computer itself. common standard calledTCP/IP(Trans• tion3, "CaseStudies." mission Control Protocol/Internet I have used the Internetroutinely for elec• Protocol). Users of any of the networks 2.1. BasicConnections: Telnet and tronic mail and occasionally to access a can utilize services provided by other Ftp computer atanother university,but Idid not networks through this standard. Cur• Telnetand Ftparetwo programs that allow fully know what the Internet was or how to rently, there are about 700,000 networks connection from one computerto another use itefficiently; however, I suspected that tied together to form the Internet, and through the Internet. Both programs are information on most any topic would be the number is growing rapidly. based on similarprotocol,butofferdifferent accessible through the Internet. Iembarked services. on a quest to search out methods for finding By using 'smart' software, the user is andretrievinginformationfrom theInternet. shieldedfrom mosttechnical details and can By using Telnet, you can logon to a com• After several weeks I was not only success• concentrate on the purpose inmind. Usually puteranywhere on the Internet and use that ful, but I was amazed by the wealth of a user need not be concerned with intricate computeras ifitwere sitting in front of you. information available, and the ease with details ofhow theInternet worksor isimple• The remote computerprocesses your com• which it could be retrieved. I was able to mented at a given site. mands. Only keystrokes and the terminal

Internetfrom page 15 sota. It was originally created as a fast, methodofproviding services over anetwork. simple, distributed, campus-wide informa• The end-user uses a client program to ac• articles tagged with one or more universally• tion search andretrieval system. Ease ofuse cess information by communicating with a recognized labels, called newsgroups (or and implementation has made Gopher in• server program. Typically the server and 'groups'for short)....Iftheabove definitionof creasinglypopularon the Internet. Since its client are running on different machinesand Usenetsounds vague, that'sbecause it is.It is original release, manyfolks on the Internet communicate over the network. You need aimostimpossibletogeneralizeoverall Usenet have contributed to its growth, submitting not have a serverofyour own to be able to sites in any non-trivial way. Usenet encom• patches, servers, clients, and linking their use the client. passesgovemmeniagencies,largeuniversities, local servers into the worldwide networkof The full-text database is a model designed high schools, businesses ofall sizes, home Gopher servers. Now there are even gate• explicitly to search documents on any word computersofalldescriptions, etc.(Kehoe: Zen ways to seamlessly access a variety of that appears in those documents. The old and the Art of the Internet: A Beginner's non-Gopher services such as FTp, Archie, approach was tohaveasetofkeywordswhich WAIS, USENETnews, whois servers, etc.... Guide to the Internet.) you couldsearch on, andthese words repre• This network ofGopher servers is at your senteda small subset ofall the words in the Usenet can be thoughtofas a collection of disposal from a Mac, PC, or workstation documents. (Torkington: WAIS Introduc• topics, called groups, ranging from the bi• connectedto the Internet. (from documen• tion) zarreto the scientific. In eachgroup, notes tation of TurboGopher) are placedby individuals,universities, com• WAfS (Wide-Area-Information-System) Gopher is an appropriate name. Univer• panies, or governmentalorganizations. You is similar to Gopher in that it shields the sities and companies worldwide decide canread these notes, downloadthem, and, user from the intricacies of the Internet. on information potentially valuable to if you like, reply. Somenotescontainques• You can view pictures, read documents, users. They place this information under tions, some, answers to previous notes, or obtain programs with a single key• the guidance of a computer program others, informationofgeneral interestto a stroke, without knowing where the called a Gopher server. Users access that group. Some may even contain complete document is located or whattype ofdocu• information via another computer pro• ment it is. However, rather than computerprogramsor pictures. Beforeread• gram called a Gopher client. Using a maneuvering through a hierarchical ing any ofthese notes, you have to decide Gopherclient, you encounter a hierarchi• menu, and only occasionally using key• whichtopics areofinteresttoyou and 'sub• cal list of topics, documents, pictures, word searches, WAIS is based on a search scribe' to them. Some groups have a programs, and otherinformation. Choose mechanism from the beginning. You en• moderatorwho decides whichnotes should from thatinformation whatyou wish. The ter the information you are looking for in be posted. beauty of the Gopher system is that it an English sentence, and WAIS does its shields users from most complexities of I subscribe to the groups sci .math(gen• utmost to locate information relating to the Internet. You can, for example, con• eral discussions about mathematical your sentence. You usually start with a nect to the University of Minnesota's questions for novices as well as mathema• broad topic and refine it as the search Gopherserver, read an on-line help docu• ticians), sci.math.research progresses. A nice feature of WAIS-based mentaboutGopher Services, then display (discussions aboutmathematical research), searches is that you neednotenteran exact a satellite picture oflast week's weather camp. binaries. ibm. pc (computer keyword. WAIS services usually give you overNorthAmerica. Next, read informa• an 'indexofmatching,' basedon how well programs for MS-DOS basedcomputers), tion aboutgrants offeredby the NSF, then the found document agrees with your and camp. binaries. mac (computer search the Library ofCongress for exact search specification (in WAfS's opinion). programs for the Macintosh). Now and references. Finally, search the Internetfor You then continue, searching only those againI read thesegroups' ongoingdiscus• any references to symbolicmath. You need hits with a high index of matching, or sions, andoccasionally I discovera useful not know where the information is actu• decide to follow a new tangent. computerprogram. ally located or what type of information 2.3. Finding Information by Key• is offered. The Gopher server-client 2.5. Talking Across the World: model will take care of everything. word: Gopher Internet Relay Chat 2.4. Finding More Information: Gopher n. 1. Any ofvarious short tailed, A world-wide 'party line' protocol that al• burrowing mammals of the family WAIS lows one to converse with others in realtime. Geomyidae, of North America. 2. (Amer. IRC is structured as a network ofservers, WAIS is a database system that exploits two each ofwhich accepts connectionsfrom cli• colloq.) Native or inhabitantofMinnesota: recently popularizedcomputersciencecon• ent programs, one per user. (LaQuey the Gopher State. 3. (Amer. colloq.) One cepts: the client-servermodel, andfull-text Parker: Internet Users' Glossary) who runs errands, does odd-jobs,jetchesor databases. It gives users theabilityto search delivers documentsforoffice staff. 4. (Com• existing databases ofarticles, books, refer• Internet Relay Chat (lRC) is another puter tech.) software following a simple ences, abstracts and specialist information server-clientmodel, developed in Finland protocol for burrowing through a TCPIIP (such as genome databases, usenet group in 1988. You connect to a server and are internet. ( ..) archives, Ftp-site listings, etc.), and for then able to 'talk' in real-time to others people with information topublish itat little connected. All discussions are dividedinto The Internet Gopher protocol and the first groups, called channels (private, public, expense and effort over the Internet. Gopher software was developed by the moderated, secret, or open). You mustjoin Gopher Team at the University ofMinne- Theclient-servermodelisa commonlyused a channel (and gain permission to speak, December 1993 FOCUS in some cases) before entering into a dis• erized catalog of their inventory available puter package SPSS in our introductory cussion. Another possibility is starting across the Internet. That means you can statistics classes to simulate a 'real-world' your own channel and waiting for others search different library catalogs (even data analysis process. It is difficult to to join. Members may be located on your from universities in different countries) obtain data sufficiently interesting and campus, in North America, or in any of directly from your computer. Some librar• complex to design challenging exercises more than twenty countries around the ies offer, in addition, special searches of for our students. Using Gopher and a few world. selected research journals. The AMS of• minutes of queries across the Internet, I Messages typed by a channel member are fers on-line searches of their publications. found the ICPSR data collection (Inter• displayed nearly immediately on every There are services, such as CARL, that university Consortium for Political and other channel member's screen, allow• allow you to search for an article contain• Social Research). It makes available data ing international 'party line' ing keywords, then have the article faxed from social studies surveys and can send conversations. Join the Chess group and to you (for extra, however). A few librar• you the appropriate information in elec• be challenged by someone in China, or ies accessible through Telnet are: tronic form. Just use Gopher and search for the keyword ICPSR. search out others for useful conversation. Dartmouth College (t e 1 net I am German, so I search out and speak 1ib . dartmauth. edu no user name As a survey of our students indicated, this my native language with people in Ger• needed) data has improved their interest in statis• many. tics. Some students have spent Library of Congress (telnet dra. cam considerable time playing with SPSS and no user name needed) 2.6. Miscellaneous the data, thereby improving their under• Briefly, here are some additional services New York Public Library (telnet standing of a statistical computerpackage the Internet has to offer. nyplgate. nypl. argusername: nypl) and the intricacies of a 'real-world' data analysis process. Talk University of Berlin (t e 1 net elib. zib-berlin. ed user name: Talk is one program which may not be 3.2. AMS Gopher Access elib) available for any platform. Talk-some• The AMS offers its own Gopher server, times called Phone-works like an The best method, however, for accessing available at e-math. ams. argoYouwill ordinary telephone, except speaking and a library is via Gopher. Most gopher sites have immediate access to lots of informa• listening is replaced by typing and read• offerasone oftheirchoices L ibrary ac• tion relating to mathematics. Search and ing. cess, and list many, many libraries order AMS publications, flip through the available for searching. For mathemat• Address the program by telling it with catalog of mathematically-oriented li• ics, the Gopher client of the AMS gives whom you would like to communicate• braries, become a book reviewer for the numerous mathematically-oriented li• next door or halfway around the world. AMS, receive the latest employment in• braries, and automatically connects you Should the recipient be at a booted ma• formation, and much more. chine that has the Talk standard as well. 3.3. Derive Manual for Calculus implemented, a message will appear on SCV Library the screen, informing him or her that There is another kind of service the WearecurrentlyintheprocessatSetonHall someone wishes to talk. Issuing his or her Internet offers that has not yet been dis• of restructuring our calculus sequence to own command for Talk, communication cussed: Listserv. Interested in regularly incorporate thecomputer programs Derive is established, and messages appear si• getting information about a particular and Maple.Weneededtodevelopsomeex• multaneously on each screen. topic? Youcan send e-mail requesting you ercises to make use of these symbolic Archie be included on an automatic mailing list. algebra packages, yet improve the stu• Whenever there is new material about This allows you to search all sites that dents' understanding of mathematical your topic, it is sent to your e-mail ad• have public domain programs or docu• theory and usage. With Gopher,WAfS, and dress. There are several documents ments available through the Internet for available on the Internet describing this Usenet, we were able to locate free infor• specific names (or substrings). You need kind of service in detail. mation on symbolic algebra packages, to know the exact name, or at least an from simple descriptions of the capabili• exact substring, of the name of the docu• For example, you could automatically re• ties of different programs to completely ment you are attempting to locate. ceive preprints of mathematical research worked-out computerexercises. Wehave papers and other material in Several modified some of this information and Finger Complex Variables about once a month. Obtaining information about another Many of the preprints can be sent in their incorporated it in our own "Lab Notes user of the Internet with an account on a entirety (usually in TeX format) if you for Calculus," thereby eliminating the Unix machine is the expertise of Finger. request it. Details of this service are cur• need to reinvent the wheel. You might locate a colleague's home rently being changed to allow Gopher In fact, we found that most information phone number, determine whether some• access. one has any unread mail waiting in their about symbolic algebra packages relates mailbox, or perhaps check how many 3. Case Studies to Maple and Mathematica, while there is users are currently working on a particu• a lack of material on Derive. We will lar network on the Internet. 3.1. ICPSR Data, SPSSAnalysis in shortly make available to the Internet our Statistics computer exercises using Derive, hope- Library Access Many libraries nowadays have a comput- At Seton Hall, we use the statistical com- Please see Internet on page 19 FOCUS December 1993

Another item that I have The New Job Diary beenpursuing lately is de• veloping a proposal to Edward Aboufadel establish a ComputerCo• Our intrepid diarist continues his account ordinatorin the department. ofhis first year as a university professor. I wrote something right This episode takes him from the beginning beforeThanksgi ving, and of December 1992 through to the end of have been chatting with January 1993. many of my colleagues aboutit since then. Theidea December9: Members ofthe DEC (De• has beenkickingaroundfor partmentEvaluationCommittee)observed a while, butno onehad ac- my classes twice last week. They came to tuallywrittenaproposalyet. Ed Aboufadel with his office mate Henry Gates. my eveningcourses,whichIrequested, since A few people asked me if! the studentsin there are livelierthan my af• wantedto be the ComputerCoordinator, and wardto dealing withthebureaucracy here. ternoon course. I thought I would be more I guess that I do, as long as I don't end up I gota senseofwhattroublelies aheadwhen nervous than I was as they sat and tooknotes steppingon anyone's feet. See, I'mstarting I suggestedthatwe purchasea newdeskfor ofmy work. Afterwards, the DECmembers to thinkaboutdepartmentpolitics, too. oneofourcomputers. Therewas a niceone said that they would talk about what they on sale at Caldor's this week. Apparently observedduringthe formal interviewin Feb• Justwaituntil the election for department thingsare not that simple. Howdid ourChair ruary.We endedup, though, discussing the chairnextspring! put it?: "ThePurchasing Departmentstill pros and cons ofusing a computerto help December19:Well, Finals Weekhas come thinks it's 1960." teachgraphingoftrigonometricfunctions. andgone. I have administered threeexami• At the departmentmeeting, we also hearda A few days later, one member ofthe DEC nations this week. Then came a marathon observed that Irarelyreferto my students by reporton spaceuse at Southern. Apparently grading session, andnowI havefigured out the averageoffice size nationwidefor a col• namein class. This is probablybecauseI'm my final grades. n~t very good with names. legefaculty memberis 100-125 squarefeet. In a way, the students hereare justlikeany• Ourofficesare 80 squarefeet. There was a Yesterday I turnedin my applicationforre• whereelse-theirtalents vary widely. In a reason for this-so that no one would be assignedtimefor research. Theapplication classof22,1gavethreeA+s andsix Fs, with foolish enoughto suggestputtingtwopro• was a bit difficult for two reasons. First, I the otherthirteen in between. And.justlike fessors in one office. was limitedto two pagesto describe whatI anywhereelse, Finals Week was fullofchaos. intendedto do, andsecond, Fall 1993 seems Ifyou notice, I mentionedmy officematea I lostcountofthe numberoftimessomeone few paragraphsback. a long timeaway. I talkedto the Deanabout knocked on my open door to ask, (I) "Are thesedifficulties. He was pleased with the you the mathdepartment?" and, (2) "Doyou So, looking ahead, I'm hoping to catch up two-page summarythat!wrote, particularly know where my math final is at?" on someresearch timeoverthis five-week with the reference to a New YorkTimesar• break that I have. I'm also heading to the ticle thatwas published lastApril and was We hada full- fledgeddepartmentmeeting JointMathematics Meetings in San Anto• related to my work. He also said that the twodays ago. The first hour we listenedto nio. (Oneofthe perksofthisjobis thatthere selectioncommitteeunderstood that it is not apoliceofficerat Southerntalkaboutsecu• are somefunds for travel.) I'm sure thatfor possible to describe exactly what you are rity and theft and what is being done on me it will be quitea contrastto last January's going to work on ten months from now. I campus. Therehasbeen a rash ofthefts on "party"in Baltimore, as I am nothuntingfor will know by February if I have been se• campus. Two weeks ago, my office mate ajobthis time. lected. came in one morning to discoverhis radio andtelephone stolen, butnothingelse, and January23, 1993: Aftertraveling all around Thenew issueofFOCUS arrived yesterday thankfully I was spared. Ithas madeall ofus thecountry, I am backin Connecticutwith withthe secondpart ofmy JobSearchDiary a bit paranoid, though. ourSpringSemesteronly two days away. inside. I havereceived positivecomments again from my colleagues here, although Also at the meeting, my proposal to estab• I spentthe firstfew weeksofmy Christmas oneperson wonderedif the following com• lish a Computer Coordinator (CC) was breakat my parents' housein FortWayne. I ment from the diary applied to Southern: approvedby the department, as was my of• quickly learnedthatPh.D. ornoPh.D., par• "Twoofmy interviewsleftme uninterested fer to becomethefirst Cc. Next stop is the ents still insistthatyou geta haircut. in working for those schools. I wishI could Dean. Older members ofthe department Last week I went to the Joint Meetings in just cross these schools offof my list, but commentedthat!was learningquickly,since San Antonio.Thesemeetings were reward• these are desperate times for new Ph.D.s, I said, "Sinceno one isjumpingat the chance ing to me for a numberofreasons. and I may not be able to be choosy." I ex• to becomeComputerCoordinator, I guess plainedto him that I didn'tinterview with I'll do it." One reason is that I was a minorcelebrity Southernin Baltimore. there. I was greetedby manypeoplethat had As CC, I'm looking forward to enlivening read the first twoparts ofmy "Job Search ourcomputerroom. I am not looking for- December 1993 FOCUS Diary" and were wondering whether ornot I also went to a numberof presentations in dental. In graduate school, the mantra is I ever got a job. A few people who were eitherMathematicsorinMathematicsEdu• "Research! Research! Research!" yet once involvedin thisyear's job hunt were glad to cation. I noticed that a number of the you areout, youseethatpeople moveahead discoverthattheywerenotalone.Onegentle• Mathematics talks were being given by bybecomingdepartmentchairs,experiment• man told me that his departmenthad been people my age, and it made me wonder if ing with graphing calculators, or, so far in receivinge-mailfromprospectiveapplicants theseweregraduatestudentspresentingtheir my case, writing for FOCUS. You like to asking for a detailed description of the re• theseswork.Later, I learned that inorder to feel that you are in control of your career in search interests of members of his give a presentation at the Joint Meetings, the same way you control your car while department, and he attributed this wave of you merely need to apply and be accepted. driving from New York to Chicago, but questions to my articles. In other words, you don' tneed to beinvited sometimes you areforced totakedetours or in order to give a talk. I did not know this. scenic routes and you never get to Chicago The article also earned me an invitation to at all. (Besides, Chicago isn't hiring.) be a guest at the meeting oftheJoint Com• Some other highlightsfor meinclude: Rob• mitteeonEmploymentOpportunities.I was ert Osserman's address on "The Shape of My scenic route has led me to Southern pleased tolearn that the people in chargeof the Universe," the controversial Jenny Connecticut State University, anditistime theEmployment Register are verycommit• Harrison outlining a way to integrate func• for me to get back to work. Coming up for ted to reforming the Register.Apparently tionsover fractal sets,andan analysis ofthe me: myAnnuaJ Evaluation; applying for a there were significantchanges made from best strategywhenspinningthe Showdown SummerResearchGrant; applyingtogivea last year. SinceIdidn' teven getan on-cam• Wheel on "The Price is Right" TV game talk at a conference; coordinating the de• pusinterviewlastyearbyusingtheRegister, show. partment computing resources; and, of any change is welcome. course, teaching four courses. Itseemstomethatinthisprofession, differ• Finally, the gentleman in charge ofMAA ent people find different ways to advance To be continued . .. Publications expressed an interest in my their careers, andoften these ways are acci- future work.

Internetfrom page 17 3.5. Usenet on Fermat's Last before the news finally made it into Theorem printed form. I found the news first on fully thereby saving time for other uni• Usenet, in the newsgroup sci . math, versities. When Prof. Wiles announced that he which I subscribe to and regularly read. proved the missing link for Fermat's Last It was not always, admittedly, the most 3.4. E-Mail Addresses: Netfind Theorem, the news spread through the serious information that I read, but many Internet within hours to many universi• Use the Internet to find e-mail addresses comments were absorbing. When Ifinally ties around the world. There was an through a service called Netfind, avail• had a chance to hear much more about outburst of questions and information able either through Telnet or by using the proof in person during a recent con• across the Internet. People were discuss• ference in Montreal, I probably knew a Gopher.Again, Gopheris the more conve• ing the implications of the proof long nient method. Please see Internet on page 20

To find an address via Telnet, first con• Service Address (selected) Chart A nect to aNetfindserver.They are available, for example, at: Usend usenet.coe.montana.edu news.yale.edu telnet bruno.cs.colorado.edu sol.ctr.columbia.edu username: netfind quip. eecs . umich. edu (Posting OK) telnet netfind.oc.com news. fu-berlin.de(Germany) username: netfind Gopher To use Gopher, connect to the Gopher gopher. tc . umn. edu (University of Minnesota-General) server at Minnesota (gopher.tc.umn.edu), e-math. ams . org (AMS Gopher-Math. Interest) then choose the following menu items: gopher.math. lsa . umich. edu (University of Michigan-Math.Interest) Phone Books; Internet-wide e• laurel. euromath.dk (Euromath Gopher in Denmark) mail address search; Gopher to begbick. law. cornell. edu (Cornell Law School-Experimental) Netfind Gateway; Search Netfind for E-mail addresses. WAIS usually provided with client program Remember to provide as much informa• IRe csd.bu.edu tion as possible concerning the person's ucsu.coloradb.edu address you wish to find. For example, irc.caltech.edu the keywords wachsmuth dartmouth sunsystem2.informatik.tu-muenchen.de(Germany) will find my e-mail address. FOCUS December 1993 lot more about this particular subject than systems administrator. you are interested in any of these programs, many of my colleagues, simply from turn• upload the package via Ftp (see example ing on my computer for a couple of IBM compatibles must have access to the Internet and musthave below).IfFtpaccessis toodifficult,feel free minutes every other day. Novell sLan Work• place installed. For details on Lan to write to me and I will send you the neces• 4. Technicalities Workplace, also refer to your local sys• sary programs for a nominal fee. tems administrator. All IBM software is You then need to get that file to your 4.1. Requirements for Your available for so-called packet-driven Macintosh computer and convert it prop• Machine TCP/IP access, but installation varies erly. Ask your systems administrator how according to network types. Youmay want to do that. All the software listed below can be used to experiment with the publicly accessible on a Macintosh or a PC. Installing soft• Ftp sites to find the necessary software Similar client programs are also available ware for Unix machines is more difficult yourself, or ask your local systems ad• for Unix-based computers; however, they and should be left to a local systems ad• ministrator. usually have to be compiled before they can ministrator; however, publicly accessible be used, and installationshouldbe leftto the Internet sites are given so that you can 4.2. Where to Get the Software local systems administrator. test the various services without going The software listed in chart B is free or re• There are specialized Telnetsites which al• through any installation process. quires a small fee after using the program low access to the services mentioned above Your Macintosh must have access to the for a period of time. I do not claim that the without requiring a client program (other Internet and must have MacTCPinstalled. software is the best available. It is simply than Telnet). ChartClistsa seriesofsites,the For details on MacTCP, referto your local easyto obtain,easy touse,andaffordable. If servicestheyoffer, and how to login. Other sitesmay offer similar services. Macintosh - MacTCP ffiM-Novell Chart B 4.3. Where to Find the Servers Telnet Ftp: ftp.ncsa.uiuc.edu built in If you installed the client software, you Dir: Telnet/mac/Telnet2. 5 will need the address of a server. It is usu• Nrume:Telnet2.5sit.hqx ally best to use a server that is located geographically close to you. Ask your lo• Ftp Ftp: dartmouth. edu built in cal systems administrator for more Dir: pub/mac information. To start, some selectedserv• Name: Fetch-2.1.sit.hqx ers are listed in chart A.

Usenet Ftp: sumex-aim. stanford. edu F~: ftp.utas.edu.au 4.4. How to learn About Dir: info-mac/comm Dir: pc/trumpet/lwp-version More Services Nrume:the-news-224.hqx Nrume:newslwp.zip Many other services are available through the Internet that have not been mentioned Gopher F~:sumex-aim.stanford.edu F~:boombox.micro.umn.edu here. The best way to find out about them Dir: info-mac/comm Dir: pub/ gopher/ incoming is by using the Internet itself. Use either Nrume: turbo-gopher-105.hqx Nrume:gopher.exe and gopher.doc Gopher or WAIS to locate documents de• scribing your interest.Chances are it's WAIS Ftp: think. com no working program found available somewhere on the Internet. You Dir: public/wais can also use eitheroftheseservices to find Name: wais-for-mac-l. l.sea.hqx client software for Archie, Finger, Talk, and other programs. IRe F~:sumex-aim.stanford.edu Ftp: ftp.utas.edu.au As an exercise, find out how to access these Dir: info-mac/comm Dir: pc/trumpet/lwp-version fun services: Name:ircle-135.hqx Name: irclwp.zip Weather Info: get an update about cur• To obtain the program TurboGopher for a Macintosh, you would do the following: rent weather forecasts - Find a machine that has Ftp installed (most Unix systems) and login Sports Info: find out how the Mets are -Type: ftp doing -Type: open sumex-aim.stanford.edu NASA Info: check the time-table for the latest space shuttle missions - Type: anonymous (when asked for a user name) - Type: -guest (when asked for a password) Supreme Court: obtain the exact word• ing of latest Supreme Court rulings - Type: cd info-mac/ comm (to change to the appropriate directory) White House: obtain copies of President - Type: dir turbo* (to see if the file is actually there, and check the version) Clinton's speeches and policy state• - Type: binary (to change to binary mode for uploading programs) ments. - Type: get turbo-gopher-105. hqx (to upload the file to your computer) Some documents that describe many December 1993 FOCUS more features of the Internet are: ChartC Service How to reach it Notes Hitchhiker's Guide to the Internet Usenet rn or nn (local Unix machine) Internet Gold - Finding the Nuggets Gopher telnet uxl.cso.uiuc.edu login as: gopher Internet Users' Glossary WAfS telnet sunsite.unc.edu login as: swais Introduction to Gopher Merit's Cruise of the Internet IRC telnet tiger.itc.univie.ac.at 6668 no login necessary WAIS Introduction Archie telnet archie.sura.net login as: qarchie What is the Internet - Working Draft, FYI. Zen and the Art of the Internet: A 1994 Residential Summer Institutes for Beginner's Guide to the Internet. Search for these documents using Gopher Mathematically Talented Undergraduates or WAIS with appropriate keywords. Careers from page 6 University of California at Berkeley, June l8-July 30 dents were not required to do all of the The sixth annual Summer Mathematics Institute (SMI) at UC Berkeley seeks appli• listening. Several students who had con• cants from African-American, Hispanic-American, and Native-American ducted research on their own campuses undergraduate men and women who are considering research careers in mathematics or during summer research programs and related fields. Approximately 30 students will receive room and board, a $2,000 came prepared and gave presentations stipend, and the cost oftransportation to and from Berkeley.The SMI is a cooperative on their work. Then it was time for the project of the mathematics departments at UC Berkeley and the University of Texas professionals, including seven faculty at Austin. Program organizers are Professor Uri Treisman (Texas) and Professor Leon members accompanying the students, to Henkin (UC Berkeley). listen along with peers to what the stu• dents had accomplished. In so doing, the Mills College, June l8-July 30 students inspired each other to reach for The fourth annual intensive mathematics program at Mills College is seeking applica• greater achievements. tions from undergraduate women of all ethnic groups who are considering research Rounding out the three days of activities careers in mathematics and related fields. Approximately 20 students will be admitted were otherpanels on graduate school and to the 1994 program; each will receive room and board, a $2,000 stipend, and a travel related issues with faculty participants allowence. The SMI is supported by grants from NSF, the NSA, and Grenetech, Inc. from Carnegie Mellon University, Program organizers are Lenore Blum (Mathematical Sciences Research Institute); Howard University, University of Mary• Steven Givant (Mills College); Leon Henkin (UC Berkeley); and Deborah Nolan (UC land, Hampton University, GeorgiaState Berkeley). University, and the University of Geor• Faculty members are asked to seek outcandidates for the programs and to encourage gia. This provided a unique opportunity them to apply. All applicants must have completed withdistinction at least one year of to obtain information on applying to, and college mathematics beyond freshman calculus by June 1994. In addition, applicants attending a graduate school as well as fi• to the Mills Program must have completed one course that involves extensive exposure nancing advanced study. to discovering and writing proofs. Also represented at the conference were the National Physical Science Consor• Institutedescription tium, which provides graduate support Participants explore in depth two areas of mathematics. Part of this exploration will to minority students, and the National take place in seminars consisting of approximately 12 students each and taught by Security Agency of the Department of active research mathematicians. Seminar students will be encouraged to tackle chal• Defense, which provided financial sup• lenging problems individually, in small groups, and in consultation with graduate port to make the conference possible. student mentors. In addition, there will be weekly colloquia designed to provide par• Conference coordinators, Teresa ticipants with a broad view of current work in mathematics. Lastly, students will Edwards, Nagambal Shah, and Sylvia participate in informal workshops that will (1) assist them in making informed deci• Bozeman of the Spelman College math• sions about graduate school, (2) give them current information about fellowships and ematics faculty, were quite pleased with financial aid opportunities to support their graduate studies, and (3) make them aware the results of the second MATHfest for of career opportunities for mathematicians. undergraduates. In a symbolic gesture of determination to institute an annual con• Theapplication deadlinefor both programs is February II, 1994. Furtherinformation ference of this type, the MATHfest Torch and application forms for the Institute at UC Berkeley can be obtained by calling Olga was passed from James Turner, origina• Alvarez at (512) 471-3285, by electronic mailing [email protected], or tor and director of the first MATHfest at by writing to the Office of Special Projects, College of Natural Sciences, University of Hampton University, toTeresaEdwards, Texas, W.e. Hogg Building #204, Austin, TX 78712. Further information and applica• current director, and on to Latricia tion forms for the SMI can be obtained by calling Kathy Guarnieri at (510) 430-2226 Edwards, a student at Southern Univer• or by writing to SummerMathematics Institute, clo Mills College, Oakland,CA 94613. sity, Baton Rouge, LA. FOCUS December 1993

NEW NEW NEW NEW NEW

The Search for E.T. Bell Memorabilia Mathematica Out of the Mouths also known as John Taine The Philomath's Quotation Book of Mathematicians Constance Reid Robert fdouard Moritz A Quotation Book for Philomaths RosemarySchmalz

No one today writes about mathematics and math• When Robert Edouard Moritz compiled his Published as a companion volume to Robert ematicians with more grace, knowledge, skill, and book of quotations, Memorabilia Edouard Moritz's Memorabilia Mathematica, clarity, and no one is going to produce a more Mathematica, which appeared in 1914, he Rosemary Schmalz's Out of the Mouths of delightful, informative, accurate account ofEric stated that his primary objective was to seek Mathematicians picks upwhere Moritz left off. Temple Bell and his work, and that ofhis alter-ego, out the exact statement of and exact refer• Her work will give you a sense ofthe "story" of the prolific pioneer ofsciencefiction, John Taine. ences for famous passages about mathemat• twentieth century mathematics. This is a fine book. -Martin Gardner ics. He searched the writing notonly ofmath• Outofthe Mouths ofMathematicians: A Quo• ematicians, but poets, philosophers, histori• tationBookforPhilomaths is a compilation of Eric Temple Bell (1883-1960) was a distin• ans, statesmen, and scientists as well. His 727 quotations from 292 contributors, almost guished mathematician and a best selling sources ranged from the works ofPlato to the all ofwhom are twentieth century mathemati• popularizer ofmathematics. His Men ofMath• writings of Hilbert and Whitehead. His sec• cians. The book also offers readers the ematics, still in print after almost sixty years, ond objective was to produce a volume that opportunityto broaden theirideasaboutwhat inspired scores of young readers to become would be a source of pleasure, encourage• mathematics is by offering many definitions of mathematicians. Underthe name'JohnTaine," ment, and inspiration to both mathemati• mathematics, making comparisons of math• he also publishedsciencefiction novels (among cians and non-mathematicians alike them The Time Stream, BeforetheDawn, and The ematics to computing and to the fine arts, and Crystal Horde) that served to broaden the sub• Themorethaneleven-hundredfullyannotated showing similarities between many aspects of ject matter ofthatgenre during its early years. selectionsin this book,gatheredfrom theworks mathematics and religion. The complete ref• ofthree hundred authors, covera vast range of erence for each quotation allows the reader to In The Searchfor E.T. Bell, Constance Reid has subjects pertaining to mathematics. Grouped continue exploration into a favorite area. A given us a compelling account of this compli• in twenty-one chapters, theydealwith suchtop• large topic index makes the book quite user• cated, difficult man who never divulged to icsasthedefinitionsandobjectsofmathematics; friendly. Someofthe subjectcategoriesinclude: anyone, not even to his wife and son, the story the teachingofmathematics; mathematicsas a The Development of Mathematics, Exhorta• of his early life and family background. Her language or as a fine art; the relationship of tions to Aspiring Mathematicians, Pure and book is thus more of a mystery than a tradi• mathematics to philosophy, to logic, or to sci• Applied Mathematics, About Mathematicians tionalbiography. Itbeginswith the discoveryof ence; the natureofmathematics, and thevalue (by name), Anecdotes and Miscellaneous Hu• an unexpectedinscriptionin anEnglish church• of mathematics. Other sections contain pas• mor, Particular Disciplines in Mathematics, yard and a series ofcryptic notations in a boy's sages referring to specific subjects in the field Moments ofMathematical Insight, Mathemat• schoolbook. Then comes an inadvertent rev• such as arithmetic, algebra, geometry, calcu• ics and the Arts,... and much more. elation, by Bell himself, in a respected lus, and modern mathematics. Of special This bookwill give pleasure to any philomath. mathematicaljournal...You will have to read interestis the extensive amountofmaterial on It can be used to facilitate a literature search or the book to learn the rest. greatmathematicianswhichprovidesirreplace• to give quickaccess to an appropriate quotefor ableglimpses into the livesand personalitiesof Includes a collection ofover 75 photographs. writers and speakers. mathematical giants. 384 pp., Hardbound, 1993 440 pp., Paperbound, 1993 304 pp., Paperbound, 1993 ISBN 0-88385-508-9 ISBN 0-88385-321-3 ISBN 0-88385-509·7 List: $35.00 MAAMember:$28.00 List: $24.00 MAAMember:$19.00 List: $29.00 MAA Member: $23.00 Catalog Number BEIX. Catalog Number: MEMO Catalog Number OMMA December 1993 FOCUS

NEW NEW NEW NEW NEW

KnotTheory Proofs WithoutWords Charles Livingston Exercises in Visual Thinking RogerB. Nelsen I learned moreabout knots after an hour with the bookthan I thought I could, Justwhat are "proofs withoutwords"? First ofall, most mathematicians andI am glad that it is hereon my desk so that I may spend more time with it would agree that they certainly are not "proofs" in the formal sense. and, I hope, learn more. -Paul Halmos Indeed, the question does not have a simple answer. Proofs without words are generally pictures or diagrams that help the readersee why a Knot Theory, a lively exposition of the mathematics of knotting, will particular mathematical statement may be true, and how one could appeal to a diverse audience from the undergraduate seeking experi• begin to go about proving it. While in some proofs without words an enceoutside the traditional rangeofstudies to mathematicianswanting equation or two may appear to help guide that process, the emphasis is a leisurely introduction to the subject. Graduate students beginning a clearly on providing visual clues to stimulate mathematical thought. program of advanced study will find a worthwhile overview, and the Proofs without words bear witness to the observation that often in the reader will need no training beyond linear algebra to understand the English language to seemeans to understand, as in "to see the point ofan mathematics presented. argument." The interplaybetween topology and algebra, known as algebraic topol• Proofswithoutwords have a long history. In this collection you willfind ogy, arises early in the book, when tools from linear algebra and from modemrenditionsofproofsfrotnancientChina,classicalGreece, twelfth• basic group theory are introduced to study the properties of knots, century India--even one based on a published proof by a former including the unknotting number, the braid index, and the bridge President of the United States! However, most ofthe proofs are more number. Livingston guides you through a general survey of the topic recent creations, and many are taken from the pages ofMAAjournals. showing how to use the techniques oflinear algebra to address some sophisticated problems, including one of mathematics' most beautiful The proofs in this collection are arranged by topic into six chapters: topics, symmetry. Thebookcloses with a discussionofhighdimensional Geometry and Algebra; Trigonometry, Calculus and Analytic Geom• knot theory and a presentation ofsome ofthe recent advances in the etry; Inequalities; Integer Sums; Sequences and Series; and Miscellaneous. Teacherswillfind thatmanyofthe proofs in this collec• subject-the Conway, Jonesand Kauffman polynomials. Asupplemen• tion are well suitedfor classroom discussion andfor helpingstudents to tary section presents the fundamental group, which is a centerpiece of think visually in mathematics. algebraic topology. An extensive collection ofexercises is included. The readers of this collection will find enjoyment in discovering or rediscoveringsomeelegantvisualdemonstrationsofcertain mathemati• 264 pp., Hardbound, 1993 cal ideasthatteacherswillwanttosharewith theirstudents. Readersmay ISBN 0-88385-027-3 even be encouraged to create new "proofs without words." List:$31.50 MAAMember:$25.00 160 pp., Paperbound, 1993, ISBN 0-88385-700-6 List:$27.50 MAAMember:$22.00 Catalog Number CAM-24 Catalog Number PWW

ORDER FORM Membership Code TheMAA 1529 Eighteenth Street, NW Washington, DC 20036 Name:..- _ 1-800-331-1622 Fax (202) 265-2384 Addressj, _

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Foreign Orders Please add $3.00 per item ordered to cover postage and handling fees. The order willbe sentvia surface mail. If you want your order sent by air, we will be happy to send you a proforma invoice for your order. FOCUS December 1993

ematical researchers can also effectively AMS Meeting in San Francisco to Offer reach a broad scientific audience. We in Section A of the AAAS know that Strong Mathematics Program the increasingrepresentation and partici• Warren Page pation of mathematicians at AAAS Annual Meetings are important means The 1994 Annual Meeting of the AAAS, The above symposia are only a few ofthe for deepening public awareness and ap• 150 or so AAAS program offerings in the February 18-23, in San Francisco, willfea• preciation of the manifold ways that physical sciences, life sciences, and the so• ture manyoutstandingexpository talks by mathematics contributes to science and prominentmathematicians. Theseinclude cial andbiological sciences that willbroaden society. I need and welcome your sugges• thefollowingsymposia (three-hoursessions) the perspectivesofstudents and profession• tions for symposia topics and individuals als alike. Indeed,AAAS Annual Meetings and invited talks sponsored by Section A who might be able to organize them. (Mathematics) ofthe AAAS: areshowcases of Americanscience, deserv• ing greater participation by mathematicians. I hope that you will have the opportunity to • Phase Transitions, organizedby Jennifer In presenting mathematics to the AAAS attend some ofthis year'sexciting symposia TourChayes(UCLA). Presenters will be: ProgramCommittee, I have found the com• in San Francisco. For details see the October Jennifer Tour Chayes, Christian H. mittee genuinely interested in more 8th issue ofScience. I invite you to attend Borgs (Free University ofBerlin); D.B. symposiaon mathematicaltopics ofcurrent our Section ACommittee Meeting, 12:00• Abraham (Oxford University); and interest. The Section ACommitteeis look• 2:00p.M., Sunday, February 20, Teakwood Steve Kivelson (UCLA). ing for organizers and speakers who can B Room at the San Francisco Hilton. The • Mathematics, Sculpture, andArchitecture, present substantialnew material in under• committeemeeting is open to all who wish organized by Nathaniel Friedman, standable ways. to stimulate interest and activities of the (SUNY-Albany). Presenters will be: mathematical sciences within the AAAS. The task is not easy, but outstanding success Harriet Brisson (Rhode Island College); Please send to me, and encourage yourcol• ofthe mathematics symposiaat last year's Stewart Dickson (Post Group Digital leagues to send me, symposiaproposals for AAAS Annual Meeting in Boston proved Center, Hollywood, CA); Nathaniel future AAAS meetings. thateffortand inspiration can accomplish Friedman, Charles Perry (Sculptor); and wonders. That meeting's mathematics Rhonda Roland Shearer (Sculptor). WarrenPage is Secretary ofSection A ofthe program showed that first-rate math- AAAS. • The Unreasonable Effectiveness ofNum• ber Theory, organized by Stefan Burr (CUNY), and Manfred R.Schroder(Uni• versity of'Gottingen). Presenters will be: MAA Statement of Ownership ~ Statement of Ownership, Manfred R. Schroder, Fan R.K. Chung ~ Management and ...; Cifculatlon (Bellcore), Stefan Burr; Jeffrey C. IRequited by 39 U.S.C. 36851 FOCUS

Lagarias (AT&T Bell Labs). J. F,.q""ne. 01 I..... Annual Subo<"oMn P"OO Six t1_1 per y...r in reb., April. June. Sept., OCt.. «ndDec. ~""""~""~;;;;;,,,,,,,,,,,,",~.,",.,","tl,,,""••"'~a'""'~"~=""'rd;Princeton University). The Hathe_ttcal A..odltlon of Aaer1ca, 1529 Eighteenth St., N.W., Wa'hington, DC 20036-1385

• Topical Theme lecture: Fermat's Last Keith J. Devlin, School of Selence, St. Kary'. College of C.tifomia, Moras., Col 94575 Theorem, by Karl Rubin (Ohio State Harry W.td_n, 1529 Eighteenth St., N.W., W••hington, DC 20036-1385 University). ,'S'§:~~:¥-Z;7:::7i"~'""=::::""=';' Other symposia that will be of interest to Th••"hom.""l ..""",,, of .."I" r" :,:::,::::::.:h ::Qj,~j~, mathematicians and mathematicseducators include: • Is Visualization REAllY Necessary for Science, organizedby Nahum Gershon,

(MITRE). P'''~12 .. P,.eocllng12M... lho -..."""i, ., h'OMOIIJ-,w.u""''''~'''_J _1n912Monfll. P_.MdN....."oFm.. ~o.'.

• The Third International Math and Science "',TotolNoo,COlI""'''''''''''''"''' 32,302 30,740 •. P..,IOnCl,oo,A_..... C~e...... '-S.... '...ougohdo_._e."...... _ ...... _ 0 0 Study, organized by Dorothy M. Guilford 2._S._...."... ,~-",...--~ - 26,483 24,008 ;;::;':"a.I'~:,='".leCICI'WI (NAS), and Daniel Horvitz (National In• c...... 26,483 24,008 O,F,.. O""''''''IOI'~.M... ,C .. ,..... 01heo_. stitute of Statistical Sciences). S-1oo,C""'lII"""'""V._01,,*F...C_ 3,279 4,787 E. TO'" 00",*" .... lS-ofC_OJ 29,762 28,750 c"" ... _o""...... • Face Recognition by Computers and "OU0<4 ..... loho... lod. __ .h .. P' ...... 2,540 1,990 2. A.,.'n".... _ ...._ 0 0

G, Tor"'"l$ooooofE:,FI"'l__"",,_p'''' __ '''~1 People, organized by James C. Bartlett 32,302 30,740 1~_Tl1Io~._.8' 0.._ " I c.rttty ttoIIt... aw.....,.. mecM by ~ ~e-::-.-... (University ofTexas) and BertS. Moore ~abo¥tt"'l:lNNCIMdcom" ..... (University of Texas). ... _ 3528. 1.-, 1991 @? December 1993 FOCUS

ommendation to: EMPLOYMENT ADVERTISEMENTS MATHEMATICS Applications are invited for a tenure-track Numerical Analysis c/o Ronald B. Kirk, Chair RatesforFOCUSEmploymentAdvertisements position in mathematics beginning August Department of Mathematics are $65.00per column inch. 1993. We seek a PhD mathematician who is committed to excellent teaching of under• Southern Illinois University at Carbondale FOCUS offers a 15% discount for the same graduates, will maintain active scholarship and Carbondale, Illinois 62901 advertisementin threeor moreconsecutiveis• is willing to contribute to divisional and univer• The closing date for applications is December sues. (The MAA will invoiceadvertisersafter sity activities. The area of expertise is open, 10, 1993 or until the position is filled. SIUC IS the first occurrence specified in insertion or• but the ability to teach in an area of modern AN EQUALOPPORTUNITY/ACTIONAFFIR• ders.All invoicesinclude a tear sheet.) applied mathematics is desirable. MATIVE EMPLOYER. Women and minorities AdvertisingCopy Deadlines:The first of the Send letterof interest, curriculum vitae, gradu• are particularly encouraged to apply. month, two months prior to publication. ate transcripts and three letters of support to: FOCUS is publishedin February,April,June, Dr. Addison Frey Topology Position September.October.and December. Division of Mathematics After these deadlines,we advise potentialad• and Computer Science Department of Mathematics vertiserstotelephoneMAAheadquartersabout Alfred University Southern Illinois University at advertisingspace availability in these issues. 26 N. Main Street Carbondale Advertisers shouldcontact: Alfred, NY 14802 Carbondale, Illinois 62901 (E-mail: [email protected]) Amy Stephenson, FOCUS Advertising Manager Applications are invited from qualified candi• The Mathematical Association of America We particularly encourage women and minor• dates for a tenure-track position beginning 1529 Eighteenth Street, NW ity applicants. Alfred University is an Equal August 16, 1994. The rank will be at the assis• Washington, DC 20036-1385 Opportunity Employer. tant or associate professor level depending C~(2) 387-5200, fax: (202) 265-2384 on qualifications of the candidate. A PhD in e-mail: focusrsrnaa.org Review of applications will begin January 25, mathematics with specialization in topology 1994andwill continue until the position isfilled. - preferablyalgebraictopology- is required. Volunteer Tutoring Program at Candidates must have demonstrated excel• lence in research or potential for such, and Montgomery College - Rockville Wake Forest University must be qualified to teach graduate level Volunteer mathematicians are urgently Department of Mathematics and courses in algebraic topology. Evidence of needed to tutor one or more hours per week. Computer Science teaching effectiveness is required (foreign applicants must provide evidence of ability to Depending upon the number of tutors avail• Applications are invited for a position as In• teach in English effectively). Send letter of able, tutoring will be offered one-on-one or in structor or Visiting Assistant Professor in application, resume, and three letters of rec• small groups. Mathematics. The term is one year, renew• able for up to three years. Rank is dependent ommendation to: Please call Helen McCarron, Coordinator, upon qualifications, and a Master's degree or Volunteer Tutoring Program, (301) 530-0490 Topology Position PhD degree in Mathematics or Statistics is or GeorgeJefferson, StudentActivities Office, c/o Ronald B. Kirk, Chair required, Dutiesconsist only ofteaching three Montgomery College, (301) 279-5092 Department of Mathematics courses per semester. A strong interest and Southern Illinois University at Carbondale preparation for teaching calculus and intro• Carbondale, Illinois 62901 Penn State Erie, Behrend College ductorystatistics is desirable.The department has 22 members, offers a BS and MA in math• The closing date for applications is December Mathematics Faculty Position: A tenure-track ematics, and a BS and MS in computer 10, 1993 or until the position is filled. SIUC IS position for fall 1994. Applicants must have science. Send a letter of applications and re• AN EQUALOPPORTUNITY/ACTIONAFFIR• strong commitment to undergraduate teach• sume to Richard D. Carmichael, Chairman, MATIVE EMPLOYER. Women and minorities ing including topology and algebra, with Department of Mathematics and Computer are particularly encouraged to apply. research interests in areas of applied math• Science, Wake Forest University, Box 7388, ematics, numerical analysis, probability, or Winston-Salem, NC 27109. AAJEO employer. partial differential equations to develop an Murray State University externally funded research program involVing Department of Mathematics & undergraduates. PhD required; postdoctoral Numerical Analysis Position and teaching experience a plus. Behrend is a Statistics 4-yearand graduatecollege offering the BS in Department of Mathematics Position: Search extended for Asst. Profes• mathematics within the Penn State system. Southern Illinois University at sor. Starting:August1,1994. Qualifications: Application deadlineisJanuary15, 1994. Send Carbondale Doctorate in mathematics or mathematics education with at least a master's degree in resume, transcripts, a brief description of re• Carbondale, Illinois 62901 search interests, and arrange thatthree letters mathematics; evidence of outstanding teach• Applications are invited from qualified candi• of reference be sent to Dr. Roger Knacke, ing, a successful record of scholarly activity or dates for a tenure-track position attheassistant Division of Science, DepartmentMATH-F,The the potential for continuing scholarly activity, professorlevel beginning onAugust 16, 1994. Pennsylvania State University at Erie, Erie, and a strong commitment to teacher educa• PhD in mathematics with specialization in PA 16563-0203 tion. Responsibilities: Maximumthreecourse numerical analysis required. Evidence of teaching load of a range of courses including An Affirmative Action/Equal Opportunity Em• teaching effectiveness is required (foreign content/methods courses for prospective K• ployer applicants must provide evidence of ability to 12 teachers, continuing research/scholarly teach in English effectively). Send letter of activities, and university/departmental service; Women and Minorities Encouraged to Apply application, resume, and three letters of rec- FOCUS December 1993 seek external funding, work in collaboration Marist College Carleton College with public schools to help implement the Mathematics Faculty - Tenure Track The Department of Mathematics and Com• Kentucky Education Reform Act. Application Fall1994 puter Science has one tenure-track and one Deadline: December 17, 1993. To Apply: two-year position to begin September, 1994. The Marist College Division of Computer Sci• Send a letterof application, vita, and copies of A PhD in math or applied math is required and ence and Mathematics invites applicationsfor graduate transcripts to Department of Math• evidence of teaching excellence is essential. one (1), possibly more depending on funding, ematics & Statistics, Murray State University, In addition to applicants with a pure math tenure track faculty positions in mathematics Murray, KY 42071. Murray State University is background, we are interested in candidates beginning Fall 1994. Responsibilities include an equal opportunity education and employ• with applied interdisciplinary training or mod• teaching 12 hours per semester at the under• ment opportunity, M/F/D, AA employer. eling experience in the biological or physical graduate level, continuing scholarly activity sciences. Review of applicants will begin Dec. and institutional participation. 1 and continue until positions are filled. United States Military Academy Minimum qualifications include a PhD in math• Carleton faculty teach 2 courses per term, 3 Department of Mathematical Sciences ematics or a closely related field, interest and terms per 9-month year. Preference will be USMA seeks mathematics faculty at the As• ability to teach all mathematics courses at the given to candidates able to teach 1 or 2 intro• sociate and Assistant Professor level. undergraduate level, and a commitment to ductory statistics courses per year. Carleton Applicants must be U.S. citizens, hold an research. The position is open to applicants is an Affirmative Action / Equal Opportunity earned PhD in mathematics, applied math• from all research areas. Employer; applications are specifically invited ematics, operations research, or statistics. from women and membersof minoritygroups. Marist College is a four year liberal arts insti• Responsibilities include teaching various core tution. The Division of Computer Science and Send letter of application, resume, graduate and electivecourses, coordinating curriculum Mathematics administers undergraduate transcripts, and three letters of recommenda• development, carrying out research, partici• majors in mathematics, computer mathemat• tion to David Appleyard, Chair, Department of pating in faculty committees, and providing ics, computer science, computer information mathematics and Computer Science, One educational leadership. Send curriculum vi• systems, and a graduate program in computer North College Street, Northfield, MN 55057• tae, letters of recommendation, academic science. The Division currently employs 24 4025. (email: [email protected]).At transcripts, and if claiming veteran's prefer• full-time faculty including 13 in mathematics. least one letter should specifically address ence, DD 214 to U.S. MilitaryAcademy, Civilian The College is equipped with state-of-the-art teaching. Personnel Office, Attn: Mrs. Vicki Nunnally, computer hardware and software. West Point, NY 10996-1995. The deadline for Carleton is a highly selective liberal arts col• applications if February 1, 1994. Review of resumeswill begin immediatelyand lege 35 miles south of Minneapolis/St. Paul. will continue until the position is filled. Please The department has 12 full-time members. A submita letter of application discussing teach• commitment to teaching in a liberal arts set• University of Alaska Southeast ing philosophyand research interests, resume ting is essential. Research is supported and Assistant Professor of Mathematics, tenure and three letters of recommendation to: Dr. encouraged. In the fall of '93, the department track position starting August 1994. PhD de• Onkar P.Sharma, Chair, Division of Computer moved into a new buildinq with excellentfacili• gree in mathematics required. Teaching Science and Mathematics, MPO Box 905, ties for learning and teaching. Computing experience at college level required. Must be Marist College, FOCUS, Poughkeepsie, NY resources available to the department include competent and willing to teach precollege 12601. four teaching laboratories equipped with Mac through upper division mathematics courses. Quadras, NeXts, 486 PC's, DEC microvax, Marist College is committed to the principle of Teach twelve hours per semester. Advise Raster tech 3/85 workstations, and access to diversity, and welcomes applications from undergraduate students. Perform appropriate a central VAX cluster. The department em• women and members of ethnic minorities. University and public service. This is a nine• ploys a full-time computer technician. month teaching track position. Research is Marist College is an Equal Opportunity/Affir• welcome but not required fortenure or promo• mative Action Employer. tion. Salary is competitive and commensurate Mathematics Department with qualificationsand experience. Applicants Tenure track position at Assistant Professor must submit completed application form, cur• Mathematics - Eastern Illinois University, rank beginning 8/22/94 to teach undergradu• riculum vitae, official transcripts, three letters Charleston, IL 61920. Beginning 8/22/94. ate/graduate mathematics education and of reference, and a one page statement of Subject to availability of funding. Two posi• mathematics, and supervise secondary Philosophy of Mathematics Education. Appli• tions. Department grants undergraduate schools student teachers. Teaching load: 12 cations must be received by January 17, 1994. degrees in Mathematics (pure, applied, and hours/sem. Salary range: $32,677to $45,786. Application forms may be obtained from: teacher certification options), Mathematics and Qualifications: doctorate (or near completion) Computer Science, and Masters degrees in in mathematics or mathematics education with University of Alaska Southeast Mathematics and Mathematics Education. a strong mathematics background, evidence Personnel Services Duties include teaching wide spectrum of of quality teaching, potential for scholarly 11120 Glacier Highway courses in support of these programs as well growth. Secondary school teaching experi• Juneau, AK 99801-8675 as service courses and general education ence preferred. Send letters of application, Telephone: (907) 465-6263 courses. Excellence in teaching expected. vita, transcripts (unofficial ok), three letters of The UniversityofAlaska is anAAlEOemployer Applications from all areas of pure and ap• reference to Dr. Robert Washburn, Chair, and educational institution. Women and mi• plied mathematics, statistics, and mathematics Search 93-269, Southern Connecticut State nority candidates are encouraged to apply. education welcome. PhD in appropriate disci• University, 501 Crescent St., New Haven, CT pline required. Applications due 1/15/94. Send 06515. Full consideration given to applica• application letter, transcript, three letters of tions received by 1/15/94. AAlEOE. recommendation to Ira Rosenboltz. Equal opportunity, equal access, affirmative action employer committed to achieving a diverse community. December 1993 FOCUS Western Washington University candidate will be responsible for teaching OH 44691. Review of applications will begin Mathematics Education undergraduate math and computer science on January 22, 1994 and continue until the courses and is expected to participate in un• position is filled. The College of Wooster is an A tenure-track position in the Department of dergraduate research by either collaborating equal opportunity, affirmative action employer. Mathematics beginning Fall 1994. Responsi• on currentfacultyprojects or starting their own bilities include teaching mathematics project. education courses and lower division courses Mathematical Olympiad Summer in mathematics, and developing inservice Applicants should submita resume,the names opportunities. Candidates should be excel• of at least three references and a statement Program of the Mathematical lent teachers, professionally active and regarding teaching and research interests to Association of America committed to the mathematics preparation Dr. Robert P. Marande, Chair, Mathematics/ Applications are being solicited for instructors (methods and content) of preservice and Physics Department, Philadelphia College of for the Mathematical Olympiad Summer Pro• inservice elementary teachers. Recent el• Pharmacyand Science,600 South43rdStreet, gram, conducted annually bythe Mathematical ementary teaching experience and an Philadelphia, PA 19104. Applications will be Association of America. This four-week sum• appropriate advanced degree preferred. Send accepted until the position is filled. mer program is held in alternate years at the a letter addressing qualifications and interest US Military Academy and at the US Naval The Philadelphia College of Pharmacy & Science is an in position, a vita, transcripts, and three letters Equal Opportunity/Affirmative Action employer with a Academy, where it will be in 1994.Twenty four of recommendation by January 15, 1994 to strong commitment to racial, cultural and ethnic diver• outstanding high school mathematics students Dr. T.J. Ypma, Department of Mathematics, sity, Nominationsof and applicationsof individuals from are chosen for the program on the basis of Western Washington University, Bellingham, a broad spectrum of backgrounds are encouraged. their performance ontheAmerican Mathemat• WA 98225-9063. AAlEOE ics Competitions and their potential as members of the US team to the International Spalding University Mathematical Olympiad (IMO). Six students University of Tennessee Department of Mathematics are selected forthe IMO team during the four• week session, and are given specialized at Chattanooga and Science coaching for their participation in the IMO. All Department Head The Department of Mathematics and Science participants receive in-depth enrichment in The University of Tennessee at Chattanooga of Spalding University invites applications for important mathematical topics to stimulate invites applications for the Head of the De• a tenure-track position asAssistant Professor their continuing interest in mathematics and partment of Mathematics. A PhD in a of Mathematics beginning August 1994. help prepare them for future study of math• Mathematical Science, at least five years of Teaching responsibilities will be general un• ematics. Instructors in the program provide college mathematics teaching experience,and dergraduate courses in mathematics, accelerated instruction in Geometry, Number qualifications commensurate with the rank of including introductory statistics. Qualifications Theory, Combinatorics, and Advanced Analy• Associate Professor or higher are required. to teach computercourses would be an asset. sis. Experience working with high-ability Applicants should provide evidence of lead• The successful applicant will demonstrate a students and familiarity with olympiad-type ership in curriculum development, teaching, dedication to teaching within the context of competitions is desired. Some instructors also public service and research/scholarly activi• the liberal arts. Normal load is 12 credit hours; serve as coaches for the IMO team, and ac• ties. Inthis primarily undergraduate institution, duties also include committee work and stu• company the team to the international the faculty is expected to exhibit excellence in dent advising. PhD required, full-time teaching competition, to be held in 1994 in Hong Kong. teaching while maintaining a strong commit• experience desirable; salary negotiable. Send Applicants should send a copy of their Cur• ment to research and public service. The letter of application, vita, three letters of refer• riculum Vitae and a statement of related mathematics departmenthas 23 faculty mem• ence, and a brief statement of educational experience to: Professor Walter Mientka ,Ex• bers including a ChairofExcellence inApplied philosophy to: Edwin C. Weber, Chair, De• ecutive Director, American Mathematics Mathematics. Located in a very scenic metro• partment of Mathematics and Science, Competitions, Department of Mathematics politan area of 400,000, UTC has a student Spalding University, 851 South Fourth Street, and Statistics, University of Nebraska, lin• enrollment of 8300. Send applications to Dr. Louisville, KY 40203. Screening of applicants coln, NE 68588-0658 Applications are due DeWayne S. Nymann; Chair of the Search will begin in February, 1994 and will continue January3, 1994. Itis expected that instructors Committee, Dept. of Mathematics, UTC, Chat• until position is filled. AAlEOE will be selected by February 15, 1994. The tanooga, TN 37403-2598. Screening of MAA is an equal opportunity/affirmative ac• applicant's credentials will begin on January tion employer. 3, 1994, and will continue until the position is The College of Wooster filled. Women and minorities are encouraged Wooster, Ohio to apply. UTC is an Equal Opportunity Em• Two positions are available beginningAugust, ployment/Affirmative Action/Title IX/Section DEPARTMENT OF MATHEMATICS 1994, one tenure track, both with three year 504/ADA Institution. AND ACTUARIAL SCIENCE initial appointments. One position will include math education courses. The College of Indiana University Northwest, Wooster, an independent liberal arts college Gary, Indiana Assistant Professor with a commitment to excellence in under• The Department of Mathematics and Actu• Mathematics/Physics Department graduate education, seeks persons to teach arial Science invites applications for both a The Mathematics/Physics Department of the introductory and advanced undergraduate tenure-track assistant professorship and lec• Philadelphia College of Pharmacy and Sci• courses in Mathematics and to direct student turer. ence is accepting applications for a research projects, Ph.D. in Mathematics is Assistantprofessor--A Ph.D. in mathemat• tenure-track faculty position at the assistant required. Experience in Computer Science is ics and a strong commitment to teaching professor level starting in the fall of 1994. desirable. Send vita, transcripts, and three undergraduates is expected. Applicants with Candidates should have a PhD in math or letters of reference to Charles R. Hampton, a knowledge of statistics, operations research applied math with a strong computer science Chairperson, Department of Mathematical or ability to teach acturial science courses will and statistics background. The successful Sciences, The College of Wooster, Wooster, FOCUS December 1993 be given preference. mathematicsor should expectto receive same ate school transcripts to: by June 1994. Applicants should be commit• Lecturer- A Masters in mathematics and a Lothar A. Dohse, Chair ted to teaching as a primary responsibility and strong commitment to teaching undergradu• Department of Mathematics to directing student research. The normal full ates is expected.Applicants showing progress University of North Carolina at Asheville time teaching load in 12 credit hours. The toward a Ph. D. will be given preference. Asheville, NC 28804-3299 university is located in a dynamic area within Send applications with vita, three letters of 60 miles of New York City, New Haven, and UNCA is an Equal Opportunity/Affirmative recommendation and transcripts to: Dr. A. Hartford. Many professional and cultural op• Action Employer; women and minorities are Mizrahi, Department of Mathematics and Ac• portunities exist. Screening will begin encouraged to apply. tuarial Science, Indiana University Northwest, immediatelyand continue until a suitable can• 3400 Broadway, Gary, Indiana 46408. Dead• didate is selected. Applications should be line for applications is March 1, 1994. Indiana received by 2/1/94 in order to be guaranteed SUNY Farmingdale University Northwest is an Affirmative Action, full consideration. Send a letterof application, Fall 1994 anticipated tenure track vacancies Equal Opportunity Employer. resume, and the names of three references at the assistant professor rank. Teaching re• to: Josef Friedman, Associate Chair, Depart• sponsibilities may include remedial through ment of Mathematics and Computer Science, all levels of undergraduate mathematics. SCHOOL OF MATHEMATICS, Western Connecticut State University, 181 Teaching emphasized with scholarship and UNIVERSITY OF MINNESOTA White St., Danbury, CT 0681 O. An Equal Op• service expected. Expertise in the use oftech• portunity/Affirmative Action Employer. TemporaryAssistantProfessor,Mathematicsand nologyin the teaching of mathematicsdesired. Mathematics Education, for recent Ph.D.s inter• Minimum qualifications, doctorate in math• ested in working in mathematics education in a ematics, statistics, oroperations research. The major mathematics department. Areas include Central College department is particularly interested in candi• graduate training, undergraduate curriculum re• Pella, Iowa dates with expertise in Applied Mathematics, form, programs for mathematically gifted Mathematics/ComputerScience: Tenure-track however, otherareas will be considered. Con• secondary school students, and networking. 9• position beginning September 1, 1994. PhD sideration will also be given to candidateswho monthappointment,non-tenuretrack,2-yearinitial in Mathematics required; ability to teach math• expect to complete all degree requirements period, renewable for up to 2 additional years. ematics education and/or computer science by August 15, 1994 (necessary for appoint• Work with the University'sTalentedYouth Math• courses desirable; demonstrated ability and ment). Letter of application and resume, ematics Program (UMTYMP), departmental commitment to provide high quality under• including the names and telephone numbers initiatives, and various networking grants. Pro• graduate teaching essential. Primary duties ofthree references must be received by Janu• jected academic year salary $31,0000000,OOO. include teaching, advising, and sharing in the ary 21, 1994. Address correspondence to: Dr. Summerappointmentsmaybeavailable.Respon• departmental duties. Support for the institu• Robert V. Mark, Dean, School of Arts and sibilities: Teaching in the UMTYMP calculus tional mission is expected. Central College is Sciences, State University of New York, Col• component. Work with the Director on K-12 and on the 3x3 modified quarter system; faculty lege of Technology, Farmingdale, NY 11735. undergraduatecurriculum development, innova• normally teach 7 courses/year with no more The College is an Equal Opportunity/Affirma• tive graduate programs and activities, and than 3 in a term. Central College is an inclu• tive Action Employer. systemic networking projects.Conduct research sive community welcoming students, faculty, with the Directorand staff leadingto publications. and staff from any cultural, ethnic, and reli• Qualifications: Ph.D. degree in mathematics by gious traditions. It is a private liberal arts Clemson University beginning of appointment. Teaching experience college, affiliated with the Reformed Church Department of at the undergraduate level required. Research in America, with study abroad programs in 8 Mathematical Sciences experience in educationally related programs, locations. Send resume, transcripts, and three Applications and nominations are invited for especially with undergraduate curriculum devel• letters of recommendation to: Dr.W.H. Bearce, the position of DepartmentHead available July opment or innovative educational programs for Dean of the College, Central College, Pella, 1, 1994. Qualifications include a PhD degree, talented secondary school students desirable. IA 50219. Review of applications will begin on teaching experience, proven research ability, Send curriculum vitae, 3 letters of recommenda• January20, 1994. Central College is an equal and leadership potential. Administrative ex• tion (inclUding at least one letteron teaching and opportunity/affirmative action employer. We perience is highly desirable. The department educationalexperiences),andstatementof inter• activelyseek and encourageapplicationsfrom integrated the areas of algebra/combinatorics, estandbackgroundtoDr.HarveyKeynes,School persons of color and female candidates. of Mathematics, University of Minnesota, 206 analysis, computational mathematics, opera• Church StreetSE, 127Vincent Hall,Minneapolis, tions research, and probability/statistics into MN 55455.THE UNIVERSITY OF MINNESOTA The University of North Carolina at balanced undergraduate and graduate pro• grams. With 54 faculty and 90 graduate IS AN EQUAL OPPORTUNITY EDUCATOR Asheville AND EMPLOYER. students, it is the largest unity within the Col• The Mathematics Department at UNCA has lege of Sciences. A candidate is sought who an entry level tenure track position open be• is committed to the mathematical sciences ginning August 1994. PhD is required. UNCA philosophy and who will provide strong lead• Western Connecticut State is a small public liberal arts college dedicated ership for future development. Initial screening University to undergraduate education. Typical teaching will begin February 1, 1994; applications will Applications are invited for a tenure track load is 3-4 courses per semester. In addition be accepted until the position is filled. Vitae Assistant Professor position in mathemat• scholarly work and university service are ex• (Withnames and telephone numbers of three ics for fall 1994. Preference will be given to pected. Application deadline is February 1, references) should be sent to : Professor applicants with a background in algebra and 1994. All interested candidates send a resume, Douglas R. Shier, File HS, Clemson Univer• in discrete mathematics and with a research a statement clarifying ones teaching philoso• sity, Box 341907, Clemson, SC 29634-1907. background similar to the interests of the de• phy, 3 letters of recommendation (at leastone Clemson University is an AA/EO Employer. partment. Applicants should have a PhD in should address teaching ability), and gradu- December 1993 FOCUS Mathematics/Physics Pomona College SEARCH EXTENDED Tenure Track Faculty Positions and Claremont, California University of St. Thomas Pomona College seeks applications for a ten• Dept. of Mathematics, St. Paul, MN Department Chair Assistant Professor of Physics. PhD in ure track position, at the assistant professor Assistant Professor of Mathematics level. The strongestcandidateswill have post• physics, experimental preferred. Teach 12• Applications are sought for a non-tenure track doctoral experience and be excited about 14semester hours inphysicsand mathematics position inmathematics. Applicants must have teaching our culturally and intellectually di• (introductory). Oversee physics laboratory completed a Ph.D. in an area of discrete math• verse student body, of which about a third of equipment and operation. Professor Tai• ematics, be recognized for quality the mathematics majors are women. They Hyung Kwon, Chair, Search Committee. undergraduate teaching, have a well-defined should also be committed to continuing a research agenda, and share a commitment to Assistant Professor of Mathematics. PhD strong research program. liberal arts education. Candidates should also in mathematics. Teach 12-14semester hours. Send application materials to: The Search consider their role in contributing to the mis• Professor Donald Alexander, Chair, Search Committee, Department of Mathematics, sion of the University. The University of St. Committee. Pomona College, Claremont, CA91711-6348. Thomas, located in the heart of the attractive Department Chair. PhD in mathematics or Twin Cities metropolitan area, has, for over a Include a curriculum vitae and 3 letters of rec• physics. Minimum of five years university ommendation (which include evaluations of century, provided a strong program of liberal teaching experience desired. Teach 8-10 se• teaching), graduate school transcripts, and a arts education in the Catholic tradition. The mester hours plus usualchair duties. Professor Department of Mathematics offers a compre• description, written for the non-specialist, of Anne Battle, Chair Search Committee. research accomplishments and plans. Let us hensive undergraduate program. Application know if you will be at the JanuaryAMS meet• materials, including a letter of interest, a CV, Salaries negotiable. Positions begin August ing. We especially encourage applicants from and three letters of recommendation (includ• 1994. Interested candidates send resume and traditionally under-represented groups. ing comments of the applicant's experience three letters of recommendation to appropri• Pomona College is an AAlEO employer. and promise inthe areas ofteaching and schol• ate search committee chair, Department of arship) must be received by January 1, 1994. Mathematics and Physics, University of Applications should be sent to Suzanne Montevallo, Montevallo, AL 35115. Review DARTMOUTH COLLEGE Lechtman, Department of Mathematics, Uni• of applications begins January 20, 1994. UM versity of St. Thomas. St. Paul, MN 55105. in an Affirmative-EqualOpportunityInstitution John Wesley Young Research The University of St. Thomas is an equal op• andqualifiedminoritycandidates are encour• Instructorship in Mathematics portunity/affirmativeactionemployer.Qualified ages to apply. Individuals with disabilities who The John Wesley Young Research Instructor• women and persons of color are particUlarly require a reasonable accommodation in or• ship is a two year post-doctoral appointment encouraged to apply. der to respond to this announcement and/or for promising new or recent PhD's whose re• participate in the application process are en• search interests overlap a department courages to contact the Office of Personnel member's. Current departmental interests Mathematics Chair Search Service at (205) 665-6055 for esslsterx». include areas in algebra, analysis, combina• torics,computer science, differentialgeometry, Rose-Hulman Institute of Technology is a logic and set theory, number theory, probabil• school of 1350 strong (mean SAT scores • Western Carolina University 680 math, 540 verbal) science, engineering, ity and topology. Teaching duties of four Department of Mathematics and Computer ten-week courses spread over two or three and mathematics students. Science: Tenure track position in Mathemat• quarters typically include at least one course The Department of Mathematics consists of ics Education beginning Fall 1994. PhD or in the instructor's speciality and include el• 17 faculty who take teaching seriously. Fac• equivalent in Math Education required. Qual• ementary, advanced and (at instructor's ulty are active in regional and national ity teaching in both mathematics and math option) graduate courses. Nine-month salary professional organizations and are leaders in education; continued scholarly activity and of $34,000 supplemented by summer (resi• curriculum efforts to use computers in instruc• service expected. Applicants should provide dent) research stipend of $7,556 (two-ninths). tion and to teach innovative curriculum a current vita, graduate transcripts, and three Send letter of application, resume, graduate combining science, engineering, and math• letters of reference to: Dr. Harold Williford, transcript, thesis abstract, description of other ematics. Chair, Search Committee, Department of research activities and interests if appropri• Mathematics and Computer Science, West• ate, and 3 or preferably 4 letters of We seek a Chair to begin in Fall 1994. ern Carolina University,Cullowhee, NC28723. recommendation (at least one should discuss Send request for more information, inquiries, WCU is an EO/AA Institution. Closing date is teaching) to PhyllisA. Bellmore, Mathematics February 1, 1994. and Computer Science, 6188 Bradley Hall, and applicationsto: Chair Search Committee, Hanover, NH 03755-3551. Applications re• Department of Mathematics, Rose-Hulman Institute ofTechnology,TerreHaute,lN 47803, ceived by Jan. 15 receive first consideration; Mathematics applications will be accepted until position is USA. E-mail: [email protected]. Assistant Professor, tenure-track position. filled. Dartmouth College is committed to affir• Phone (812) 877-8391. Teach wide range of undergraduate math• mative action and strongly encourages A complete application includes avita, a state• ematics courses in a multi-purpose college applications from minorities and women. ment of mathematical, pedagogical, and environment. Preference for candidates with administrative philosophy, and three letters of high school teaching or computer science recommendation. Evaluation of applications experience. Begins Fall 1994. Women and begins December 15, 1993. minorities encouraged to apply. Send appli• cation, including vita, statement of career objectives, and three letters of recommenda• tion to: Chairperson, Mathematics Search Committee, School of Arts and Sciences, FOCUS December 1993 Eastern Oregon State College, 1410 "L" Av• Department of Mathematics enue, La Grande, OR 97850-2899. Closes College of Natural Sciences and February 1, 1994, or until filled. Inquiries: Williams College Robert Brandon, Telephone (503) 962-3631; Mathematics Department of Mathematics E-mail [email protected]. AAlEOE Indiana University of Pennsylvania Williamstown, Massachusetts 01267 Indiana University of Pennsylvania invites applications for a tenure-track position in el• Anticipated visiting position for the 1994-95 University of Evansville ementary and/or secondary mathematics year, probably at the rank of assistant profes• Department of Mathematics education to begin in the Fall of 1994. The sor; in exceptional cases, however, more appointment is anticipated at the Assistant advanced appointments may be considered. Applications are invited for a tenure-track Professor level. Associate Professor is pos• Excellence in teaching and research and doc• position as assistant professor of mathemat• sible in the case of exceptional qualifications. torate are expected. Please have a vita and ics beginning August, 1994. PhD in The department recognizes a greater need in two letters of recommendation on teaching mathematics and a strong commitment to elementary mathematicseducation, although and research sent to Visitor Hiring Commit• teaching required. Background or interest in those with a secondary mathematics educa• tee. Evaluation of applications will begin teaching in at least one of the following areas tion background are encouraged to apply. November 15, and continue until the position preferred: actuarial mathematics, mathemat• is filled. As an EEO/AA employer, Williams ics for elementary teachers, mathematics Responsibilities: especially welcomes applications from women modeling. Responsibilities include teaching and minority candidates. 9-12 hours per semester in a wide range of 1.Teach undergraduate and graduate courses undergraduate mathematics courses, continu• in elementary and/orsecondary mathematics education and advise students. The normal ing scholarly activities, and Universityservice. University of Wisconsin-Platteville Send application letter, resume, transcripts, course load is 12 semester credit hours. Du• and 3 letters of reference to: ties include teaching courses in mathematics Department of Mathematics content and mathematics pedagogy, and su• At least two tenure-track positions as assis• Dr. J. Robert Knott, Chairman pervising field experiences. tant professor in mathematics avaiiableAugust Mathematics Department 21,1994. Qualifications: PhD in mathematics University of Evansville 2. Continue scholarly growth. or statistics required, primary responsibility is Evansville, Indiana, 47722 3. Participate in university, college, and de• broad undergraduate teaching in mathemat• ics or statistics; evidence of excellent The University of Evansville is an Equal Op• partment committees. undergraduate teaching experience; excellent portunity/Affirmative Action Employer. Required Qualifications: communication skills, capable of maintaining 1. PhD / EdD by September 1994 in an area a continuing program of scholarly activity; and indicate eligibility for continuing employment Xavier University related to mathematics education with gradu• ate course work in mathematics education. inthe United States. Salary: $31,000-$34,500 Cincinnati OH 45207 depending upon qualifications and experience. Applications are invited for an assistant/asso• 2. Evidence of effective teaching experiences The Department of Mathematics has 21 fac• ciate professor tenure track position in in mathematics at the elementary and/or sec• ulty.The university enrolls approximately 5000 Computer Science starting fall 1994. Teach• ondary level. students with programs in engineering, liberal ing/research experience preferred. Applicants arts, business, education, industry, and agri• 3. Evidence of successful research or research should have PhD in Computer Science, how• culture. UW-Platteville is an affirmative action, promise in mathematics education. ever, those having a doctorate in a related equal opportunity employer. Women and mi• field with appropriate computer experience are 4.Academic preparation and evidence of ability norities especially are encouraged to apply. also encouraged to apply. The position re• to teach mathematics content courses for el• The names of all finalists and of nominees quires strong commitment to teaching at the ementary and/or secondary education majors. and applicants who have not requested in undergraduate level, to scholarly research, writing that their identity not be revealed will and to service consistent with the mission of Preferred Qualifications: be released upon request. To be considered: Jesuit higher education. Research interests 1. Experienee with in-service presentations Send letter of application (including eligibility must be in mainstream Computer Science. and/or curriculum consultation. for employment), vita, transcript(s), and three Applications will be accepted until February 1, letters of recommendation to Dr.Alan Richert, 1994. Send a letter of application, resume, 2. Active participation in recognized profes• Chairperson, Department of Mathematics, copy of graduate transcripts, and three letters sional organizations. UW-Platteville, Platteville, WI 53818. Dead• of recommendation to: Janice B.Walker,Chair, Send letter of application, resume, under• line: January 21, 1994. Department of Mathematics and Computer graduate and graduate transcripts, and three Science. Xavier University is an EO/AA Em• current letters of reference to: Dr. Jacqueline ployer. Women and minorities are especially Gorman, Chair of Search Committee, Math• Ohio University encouraged to apply. ematics Department, Indiana University of Robert l. Morton Mathematics Pennsylvania, Indiana, PA 15705. (412) 357• Education Professorship 2608, Bitnet: JGORMAN@IUP. Dr. Robert L. Morton was perhaps the most IUP is an affirmative action/equal opportunity prolific author to ever have taught at Ohio employer. University. During his 42 years on the faculty, he wrote 9 books and co-authored junior high and elementary school mathematics text• books, which in different editions represented 180 books. Dr. Morton wrote 160 articles and 80 book reviews/monographs/miscellaneous pieces in addition to his two co-authored December 1993 FOCUS mathematicstextbook series by Silver Burdett Bowdoin College Roanoke College Co., Making Sure ofArithmetic and Modem Brunswick, Maine 04011 Department of Mathematics, Mathematics Through Discovery, which ex• Mathematics Department: Tenure track As• Computer Science, and Physics ceeded 50 million copies. He established the sistant Professorship in applied mathematics Robert L. Morton Mathematics Education Pro• Salem, Virginia 24153 starting fall, 1994. Initial appointmentforthree fessorship as "encouragement to others for Applications are invited for an entry level ten• years with renewal possible. Possibility of similar fulfillment of purpose." ure track position ofAssistant Professor in the second, non-tenure-trackposition - field open. department beginning August 1994. Ph D. in The Morton chair is funded by an endowment PhD required and strong research record or Mathematics required. Salary commensurate and affords a unique opportunity to negotiate potential expected. Normal teaching load is with qualifications and experience. Excellent specific responsibilities at an institution with two courses per semester. Candidates with teaching emphasized, active scholarship en• accredited baccalaureate, masters, and doc• record of effective undergraduate teaching couraged. Commitment to liberal learning toral programs in mathematics education. preferred. Review of candidates begins 1 expected. Roanoke College is a private lib• Activities may include research, publlshlnq, January, but applications will be considered eral arts college affiliated with the Lutheran directing graduate studies, teaching, academic until position is filled. Send resume and 3 let• church and is located inthe Roanoke Valley of advising, collaborating with the mathematics ters of recommendation to James E. Ward, Virginia. department, investigating unique technologi• Chair, Department of Mathematics, Bowdoin cal applications for mathematics, forming College, Brunswick, ME 04011. Include e-mail A completed application consists of a VITAE, partnerships with public schools, initiating address. Bowdoin College is committed to graduate and undergraduate transcripts, and special projects, and/or developing a math• equal opportunity through affirmative action. 3 letters of reference (at least one about teach• ematics, science, and technology research Women and members of minority groups are ing). Applications should be sent to Dr. W. D. and professional development center. encourages to apply and invited to identify Ergle, Chair, at the address above. Applica• themselves as such. tions completed by January 31, 1994 will The Morton Chair Professor will be expected receive first consideration. Roanoke College to define clear goals each year and negotiate encourages applications from qualified women responsibilities with the Dean of the College and minority candidates. An affirmative ac• of Education. The chair is a tenure track posi• tion, equal opportunity employer. tion for a prominent mathematics educator with a record of teaching excellence as well as experience in elementary and/or secondary school teaching. Rank and salary will be com• mensurate with the candidate's qualification. Essays in Humanistic Mathematics The screening process will begin January 3, 1994 and will continue untilthe position isfilled. Alvin White, Editor Please send letter of application and creden• tials to: A dazzling array ofessayists reveals humanistic mathematics in this volume, and in so doing goes beyond the facts, formulas, and algorithms that most students associate with mathematics to a The Morton Chair Search Committee presentationofmathematicsasan intellectualdiscipline witha humanperspective anda significant Dean's Office history.Humanisticmathematicschallengesdogmaticteachingstylesthatexpectstudentsto parrot 133 McCracken Hall the lecturer. Itdemands creativityfrom both the teacher and student. Ohio University Athens. Ohio 45701 Teaching mathematics humanistically seeks to place the student more centrally in the posi• tionofinquirerthanisgenerallythecase, while at thesame timeacknowledgingtheemotional Ohio University is an Affirmative Action/EEO climate ofthe activity oflearning mathematics. This type ofteaching encourages students Employer. Women and minorities are encour• to learn from each other and to better understand mathematics as socially constructed ages to apply. All inquiries applications, and knowledge, rather than as an arbitrary discipline. nominations will be treated confidentially. Teaching humanistic mathematics brings thefocus less upon the nature ofthe teaching and learning environment and more upon the need to reconstruct the curriculum and the discipline of mathematics itself. This reconstruction relates mathematical discoveries to personal courage, discovery to verification, mathematics to science, truth to utility, and Jacksonville University is soliciting appli• mathematics to the culture in which it is embedded. cations for two tenure-track Assistant Professor positions in mathematics. All fields Thehumanistic mathematicsmovement, whichbeganas the personalvision ofa few,has now of specialty are welcome, but preference for become a major part of mathematical culture. What was viewed with skepticism is now one position will be given to a Ph.D. in statis• accepted and expected. Humanistic mathematics is not a new discovery. It is a' recent tics. Applicants with experience or interest in rediscovery of ideas that go back to Plato. It has provided a vocabulary for previously computer-assisted instruction are particularly unarticulated concepts and approaches. desired. Responsibilities include teaching 12 The essaysin this volume illustrate and help to define humanistic mathematics. The variety hours per semester, continued scholarly ac• and scope indicate the richness and fruitfulness of the concept. Although each essay is tivity (broadly defined), and department! independent, a sense ofunityemerges. Aglimpse at the table ofcontentswillgive you an idea university service. Applications will be ac• ofthe excitement and range ofthe ideas presented. cepted until December 15, 1993. Send vita, cover letter addressing qualifications, and 212 pp., Paperbound, 1993, ISBN 0-88385-089-3 three letters of reference to Dr. Charles Lindsey, Chair, Department of Mathematics, List:$24. 00 Jacksonville University,Jacksonville, FL32211 Catalog Number NTE-32 See orderform on page 23. Calendar

NORTH CENTRAL April 22-23, 1994, Winona State Univer• National MAA Meetings sity, Winona, MN January 12-15, 1994 Seventy-seventh Annual Meeting, Cincin• NORTHEASTERN June 3-4, 1994, Salve Regina University, nati (Board of Governors, January II, 1994) Newport,RI August 15-17, 1994 Sixty-ninth Annual Joint Summer Meeting, NORTHERNCALIFORNIA February 12, 1994, San Jose City Minneapolis College January4-7,1995 Seventy-eightAnnual Meeting, San Francisco OHIO April 8-9, 1994, Miami University, Oxford, OH (Board of Governors, January 3, 1995) OKLAHOMA-ARKANSAS March 25-26,1994, Harding Uni• versity,Searcy,AR Sectional MAA Meetings PACIFIC NORTHWEST June 16-18,1994, University of Or• egon, Eugene ALLEGHENYMOUNTAINApril 8-9, 1994,West VirginiaUni• versity,Morgantown ROCKYMOUNTAIN April 15-16, 1994, South Dakota School of Mines & Tech., Rapid City, SD EASTERNPA& DELAWARE Nov. 13, 1993,CedarCrestCol• lege, Allentown SEAWAYApril 22-23, 1994, SUNY at Albany FLORIDA Feb 25-26, 1994, Daytona Beach Comm College, SOUTHEASTERN April 8-9, 1994, Carson Newman College, Daytona Beach Jefferson City, TN ILLINOIS ApriI22-23, 1994, Parkland College, Champaign SOUTHWESTERNApril 8-9, 1994,Glendale CommunityCol• lege, Glendale, AZ INDIANA March 19, 1994, DePauw University, Greencastle SOUTHERN CALIFORNIA March 5, 1994, Loyola INTERMOUNTAIN ApriI8-9, 1994, Westminster College, Salt Marymount University, Los Angeles Lake City TEXAS April 7-9, 1994, Texas A&M, College Station, TX IOWA April 15-16, 1994, Grinnell College, Grinnell WISCONSIN April 22-23, 1994, University ofWisconsin-Eau KANSAS March 11-12, 1994,Universityof Kansas,Lawrence, KS Claire, Eau Claire, WI KENTUCKY April 8-9, 1994, Morehead State University, Morehead LOUISIANA-MISSISSIPPI March 4-5, 1994,NichollsStateUni• Other Meetings versity,Thibodaux, LA April 13-16, 1994 Seventy-second Annual National Council of METROPOLITAN NEW YORK May 1, 1994, Merchant Ma• TeachersofMathematicsMeeting,Indianapolis.Formoreinfor• rine Academy, Kings Point mation, contact: NCTM, 1906 Association Drive, Reston, VA 22091-1593. MICHIGAN April 29-30, 1994, Alma College, Alma, MI January 2S-29, 1994 The Mathematics Deaprtment of Mont• MISSOURIApril 1994, Missouri Southern State College, Joplin, gomery County Community College and Texas Instruments MO are co-sponsoring a faculty development institute on using NEBRASKAApril 22-23, 1994, Nebraska Wesleyan University, the graphing calculator. For more information, contact Dr. Lincoln Roseanne Hoffman, Mathematics Department Montgom• ery County Community College, (215) 641-6405

FOCDS DECEMBER 1993 The Mathematical Association of America Second class postage paid at Washington, DC and 1529Eighteenth Street, NW additional mailing offices Washington, DC 20036-1385