March 2000

THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA Math Spans All Dimensions

April 2000 is Math Awareness Month

Interactive version of the complete poster is available at: http://mam2000.mathforum.com/ FOCUS March 2000

FOCUS is published by the Mathematical Association of America in January. February. March. April. May/June. August/September. FOCUS October. November. and December. a Editor: Fernando Gouvea. Colby College; March 2000 [email protected] Managing Editor: Carol Baxter. MAA Volume 20. Number 3 [email protected] Senior Writer: Harry Waldman. MAA In This Issue [email protected] Please address advertising inquiries to: 3 "Math Spans All Dimensions" During April Math Awareness Carol Baxter. MAA; [email protected] Month President: Thomas Banchoff. Brown University 3 Felix Browder Named Recipient of National Medal of Science First Vice-President: Barbara Osofsky. By Don Albers Second Vice-President: Frank Morgan. Secretary: Martha Siegel. Treasurer: Gerald 4 Updating the NCTM Standards J. Porter By Kenneth A. Ross Executive Director: Tina Straley 5 A Different Pencil Associate Executive Director and Direc• Moving Our Focus from Teachers to Students tor of Publications and Electronic Services: Donald J. Albers By Ed Dubinsky FOCUS Editorial Board: Gerald 6 Mathematics Across the Curriculum at Dartmouth Alexanderson; Donna Beers; J. Kevin By Dorothy I. Wallace Colligan; Ed Dubinsky; Bill Hawkins; Dan Kalman; Maeve McCarthy; Peter Renz; Annie 7 ARUME is the First SIGMAA Selden; Jon Scott; Ravi Vakil. Letters to the editor should be addressed to 8 Read This! Fernando Gouvea. Colby College. Dept. of Mathematics. Waterville. ME 04901. 8 Raoul Bott and Jean-Pierre Serre Share the Wolf Prize Subscription and membership questions 10 Call For Papers should be directed to the MAA Customer Thirteenth Annual MAA Undergraduate Student Paper Sessions Service Center. 800-331-1622; e-mail: [email protected]; (301) 617-7800 (outside 11 The Anneli Lax New Mathematical Library U.S. and Canada); fax: (301) 206-9789. By Don Albers Copyright © 2000 by the Mathematical Association of America (Incorporated). 12 Short Takes Educational institutions may reproduce articles for their own use. but not for sale. 13 Secretary Riley Responds to Open Letter provided that the following citation is used: "Reprinted with permission of FOCUS. the 14 Employment Opportunities newsletter of the Mathematical Association of America (Incorporated)." About the Cover: This first ever four-color cover of FOCUS depicts a portion of the Periodicals postage paid at Washington. DC paper version of the poster for Math Awareness Month. April 2000. To see the "real" and additional mailing offices. Postmaster: interactive electronic version of the poster, go to http://mam2000.mathforum.com. Send address changes to the MAA. P.O. Box The concept and the design of the poster are due to Tom Banchoff of Brown Univer• 90973. Washington. DC 20090-0973. sity and Davide Cervone of Union College. copyright Thomas Banchoff Productions. ISSN: 0731-2040; Printed in the United States Inc. of America. FOCUS Deadlines May/June Aug/Sept October Editorial Copy March 22 July 14 Display Ads April 4 July 28 August 21 Employment Ads March 30 July 21 August 10 2 March 2000 FOCUS "Math Spans AU Dimensions" During April Math Awareness Month

"Math Spans All Dimensions" is the the MAA has that charge. Based on their whose work connects in some way to the theme for Math Awareness Month 2000, experience with the experimental MAA theme of dimensionality. The people who sponsored by the Joint Policy Board for electronic journal Communications in have agreed to participate go way beyond Mathematics, comprised of representa• Visual Mathematics, MAA president Tom the expected mathematicians and physi• tives of the MAA, the AMS, and SIAM. Banchoff and his collaborator Davide cists to include an author of children's As in recent years, mathematics depart• Cervone of Union College have raised the books (Madeleine L'Engle, author of A ments nationwide are being encouraged concept of a poster to a new level. Wrinkle in Time), a choreographer (Julie to organize a wide range of activities to Strandberg of Brown University), and This year's Math Awareness Month focus attention on mathematics during the even a cartoon character (Geri, one of the poster exists in two forms. The first is a month of April. JPBM has been promot• characters created by Pixar Animation, paper poster which will be distributed to ing mathematics in this way since 1991, who appears in Toy Story If). As one mathematics and mathematical sciences when the first Math Awareness Week had might expect, Edwin A. Abbott, author departments in colleges and universities. "Mathematics: It's Fundamental" as its of Flatland, gets a prominent place also. The second (for some, this is the real theme and highlighted applications in poster) is an electronic poster that can Clicking on the images on the poster industry, technology, and science. Last be accessed on the web at http:// takes one to pages giving more informa• year, the week was expanded to a month, www.mam2000.mathforum.com. tion on the person pictured and on the and a web site at the Math Forum (http:// mathematics involved, so that the poster www.mathforum.com/mam/past.html) The central image of the poster starts as itself becomes a useful beginning point provided support for and reports on the a string of zero-dimensional points, then for Math Awareness Month activities. many activities organized to bring a becomes a I-dimensional curve, then greater awareness of the importance of expands to a two-dimensional strip, Production and distribution for the Math mathematics to teachers and students at which then expands to a 3-dimensional Awareness Month 2000 poster has re• all levels and to the general public. cornucopia. Extensions beyond the third ceived support from Wolfram Research, dimension are accessible only by com• Inc .• Each year one of the organizations in the puter. Around the poster are clickable JPBM takes the responsibility for the windows, each "inhabited" by a person design of the MAM poster, and this year

Felix Browder Named Recipient of National Medal of Science By Don Albers

Felix Browder, who is a University Pro• to the U.S. when he was five years old. fessor at Rutgers University, has been He says that he was a bookish child and named a recipient of a 1999 National liked all subjects. He attributes his inter• Medal of Science. He was cited for pio• est in mathematics to reading E.T. Bell's neering work in nonlinear functional Men ofMathematics when he was in sev• analysis, opening up new avenues in non• enth grade. He describes that book as a linear problems, and for being a leader "marvelous piece of historical fiction." in the scientific community to broaden Browder earned his doctorate at the age the range of interactions among disci• of 20 from Princeton in 1948. Before plines. joining Rutgers University, he spent Browder, 72, is one of three brothers, all twenty-three years at The University of of whom are mathematicians. His Chicago, including a twelve-year stint as younger brothers, Andrew (Andy) and chair of the department. William (Bill), have spent most of their In 1999 he became President of the careers at Brown University and American Mathematical Society.• Princeton University, respectively. Both Bill and Felix have served as presidents Don Albers is the Associate Executive of the American Mathematical Society. Director and Director of Publications Felix Browder Browder was born in Moscow and came and Electronic Services for the MAA. 3 FOCUS March 2000 The Curriculum Revisited: Updating the NCTM Standards A Proposal By Kenneth A. Ross

By Sol Garfunkel The National Council of Teachers of Responses received from the ARGs in Mathematics (NCTM) published the Cur• 1997-98 were weighed by the writers as In a 1989 study and follow-up analysis riculum and Evaluation Standards for they produced Principles and Standards ofCBMS reports, the late Gail Young and School Mathematics in 1989, with fol• for School Mathematics: Discussion I noted that the number of students tak• low-up documents on standards on teach• Draft, released in October 1998, at which ing mathematics courses above the level ing (1991) and assessment (1995). After time the ARGs were asked to review the of calculus in departments of mathemati• gathering reactions from members and draft. According to the NCTM, the cal sciences had been steadily declining. others, the Council made a decision early ARG's reviews were central to the set of We also demonstrated that a great deal in 1996 to proceed with updating the reactions NCTM solicited and received of mathematics instruction at this level Standards and targeted the year 2000 for from a wide range of audiences. The feed• is taking place in departments other than release of the next document. back was synthesized into a set of key mathematics. I am sure that there are issues used both to guide the writers as many reasons for this trend, over several In shaping the updated document, NCTM they revised the document and as the fo• of which we have no control. However, sought the views of many different cus of a review sponsored by the National there is one area in which we have al• groups, especially the mathematical sci• Research Council. The full set of com• most complete control, namely the en• ences community. One of the first out• ments was also available to the writers try-level undergraduate curriculum. reach actions of NCTM was to request electronically to allow easy access to the that the presidents of the Conference The central importance of mathematics feedback on particular topics or sections. Board of the Mathematical Sciences ap• in our increasingly complex and techno• point or designate a committee to serve The final Principles and Standards for logical world is undeniable, and the pos• as an Association Review Group (ARG) School Mathematics document will be sibilities for new applications almost end• to provide input to the process. The MAA presented at the NCTM Annual Meeting less. We miss an extraordinary opportu• was one of the 12 professional mathemat• in Chicago on April 12,2000. According nity when we fail to convey this excite• ics organizations which formed an ARG to NCTM, this document has truly been ment to our students. If we were to ask and gave input throughout the process of a team effort, drawing on the wisdom of students at the end of their first year of updating. The MAA's ARG is the the many people who contributed their collegiate mathematics what mathemat• President's Task Force on the NCTM input along the way. The MAA task force ics is and how is it used, we know what Standards; it has fourteen members and represented a broad cross-section of in• we would hear. We would find out how is chaired by Kenneth A. Ross. formed views within the mathematics much calculus (reformed or unreformed) community. Some members were highly they retained. We know the breadth and Input from the ARGs began before the critical of the 1989 Standards, some were richness of our subject; how then do we first word was written. As you can imag• very supportive of the 1989 Standards, expect students starting their studies to ine, there were often diverse and even and several were in between. Neverthe• gain these insights and hopefully con• opposing positions. Consider, for ex• less, this group worked harmoniously tinue on in mathematics? ample, the following question from the and, in general, was able to provide con• second of four rounds of questions sub• I argue that we need to adopt the model sensus recommendations to the NCTM. mitted by NCTM: "How should the Stan• used by the other sciences, namely an The time and effort of the members of dards address mathematical proof? introductory course that focuses on de• our task force was invaluable. The reports Why?" The range of responses from vari• veloping basic principles and concepts of the MAA task force can be found on ous ARGs included: while introducing students to a broad MAA Online at http://www.maa.orglpast! range of subject matter. The intent is • Some traditional proof-axiom should maa_nctm.html. For more information on clear. For those students who stop taking be replaced with more applied math• the release of Principles & Standards and mathematics after one year, they will ematics. on how to obtain a copy (which will be have a stronger sense of what mathemat• free to current members of NCTM), go • Rigorous and structured proof need be ics is about. For those who go on, they to http://www.nctm.orglstandards2000/. will have an appreciation for the differ• experienced by only a small percent• age of high school students. ent branches of mathematics as well as Kenneth A Ross is Professor of Math• their contemporary applications. In this • The word "proof' should be used con• ematics at the University of Oregon and way, in our first course, we can be states• sistently beginning grade 8. They need a past president of the MAA. He is chair men for our subject, showing its breadth, to see the need for airtight arguments. of the MAA Coordinating Council on its modernity and its power.• Meetings, ofthe Carus Monographs Edi• Our task force's response to the second torial Board, and of the President's Task round of questions is discussed in an ar• Sol Garfunkel is the Executive Director Force on the NCTM Standards. of COMA?, the Consortium for Math• ticle in the American Mathematical ematics and its Applications. Monthly (March 1998, volume 105, pages 252-255). 4 March 2000 FOCUS

A Different Pencil thinking from the teacher to the student. An excellent and highly readable article Moving Our Focus from Teachers to Students by Donald L. Finkel and G. Stephen Monk ("Teachers and Learning Groups: By Ed Dubinsky Dissolution of the Atlas Complex," in C. Over the last decade, mathematicians sions about what to do in the classroom. Bouton and R.Y. Garth (Eds.), Learning have begun to pay more and more atten• in Groups, pp. 83-97, reprinted in MAA In the paragraph in question, there are 7 tion to how they teach and how their stu• Notes 44) makes a strong case for such a sentences. The word I (i.e., Franzova) dents do (or do not) come to understand transformation and gives some first sug• appears 6 times as the subject of a sen• mathematical concepts, develop the abil• gestions on how to carry it out. tence or phrase. We are told that the ity to make calculations, and become teacher becomes excited, can show, can Another way of increasing the attention good problem solvers. MAA's Project work out, can stimulate, and can solve. we pay to what is going on with our stu• NExT provides a forum for young math• All we read about the students as active dents has to do with a development in ematicians to ask questions and share participants is that they "like the idea of our profession over the past decade that ideas about teaching and learning. seeing the final answer and comparing it is parallel to the development of our in• MAA's Project CLUME runs workshops to the one in the back of their textbook," terest in pedagogy. I am referring to the and minicourses and produces written which is hardly a notion newly brought rapid growth of the field of Research in material all designed to help faculty use out by technology. The remaining three Undergraduate Mathematics Education cooperative learning as a pedagogical paragraphs do not tell us any more about (RUME). New groups more or less con• strategy. Activities devoted to mathemat• what the author's students are doing or nected with the MAA such as the new ics education are now a major part of the feeling, or, what is most important of all, special interest group of the MAA annual winter mathematics meetings and learning. (SIGMAA) called the Association for the summer Mathfest. Finally, our pro• Research in Undergraduate Mathematics fessional publications are devoting in• As a proponent of and participant in edu• Education (ARUME), and a Research in creasing space to articles about teaching cation reform in general and the use of Undergraduate Mathematics Education and learning. technology in general, I cannot reiterate Community (RUMEC) have come into often enough what I first said many years With all of this progress, I think we are being; there is a joint AMSIMAA Com• ago: in the mathematics classroom, in the ready to take a further step forward and mittee concerned with RUME and which last analysis, what the teacher says or begin to sharpen our critiques of teach• publishes an occasional volume of re• does is of little or no importance; what ing methodologies so as to move from search papers; reports of research are an really matters is what goes on with the anecdotal analysis to a more solid foun• integral part of the programs of the an• students. ("A Learning Theory Approach dation. We should also try to refocus our nual mathematics meetings; and MAA to Calculus," in (Z. Karian, ed.) Symbolic attention from what we as teachers do to publications are beginning to include re• Computation in Undergraduate Math• outcomes in terms of student learning. search reports as well as summaries of ematics Education, MAA Notes, 24, pp. published research. The article, "What is so good about them 48-55, \992.) anyway ... " by Nora Franzova, in the A So I think that although there is much Education reform and the use oftechnol• Different Pencil department of the Janu• work to be done and a lot of progress yet ogy are highly controversial and there is ary 2000 issue of FOCUS, is a good ex• to come, we can be optimistic about the major opposition. Those of us who are ample that illustrates both our progress future of undergraduate mathematics edu• convinced of the value of these innova• in becoming more aware of teaching is• cation. By heightening our awareness of tions will not succeed in bringing our sues, and some of the steps we still need pedagogical issues and incorporating the colleagues along by pointing out how to take. results of research in our thinking about wonderful we think the new methodolo• what might be going on in the minds of We can be very grateful to Franzova for gies are. We simply must start biting the our students, we can vastly improve the the first six paragraphs of this article. bullet and ask the hard questions about quality of our teaching. The beneficia• There, she points out that her objections what effects these pedagogical ap• ries of this will be our students, who will to using technology in her classes were proaches have on students' understand• come to understand more mathematics at largely based on the unjustified assump• ing of mathematical concepts and their higher levels of profundity, and society tion that what worked for her, a future applications, on students' ability to per• as a whole, which will benefit from a mathematician, was also the right thing form mathematical calculations, on their stronger mathematical research commu• for her students, who will largely go in attitudes towards mathematics and on the nity and a more mathematically literate different directions. But then, in the main role in which mathematics plays in our general population .• paragraph describing the effects of her students' future professional and personal current use of CAS (computer algebra lives. Ed Dubinsky is Professor of Mathemat• systems), she demonstrates how difficult ics at Georgia State University. He was One way of doing this is for college math• it is to get away from this largely teacher• Second Vice-President of the MAAfrom ematics faculty in general to refocus our centered point of view in making deci- January 1998 to January 2000. 5 FOCUS March 2000 Mathematics Across the Curriculum at Dartmouth While the cries for increased numeracy of the undergraduate population have fed By Dorothy I. Wallace the development of mandatory general over me until I explained myself thor• At the front of the room the art professor education courses in "quantitative lit• oughly. Why do you accept this from a is demonstrating techniques of block eracy" throughout the country, Dart• scientist?" Discussion breaks out about printing to a dozen students. On the board mouth has taken a different and more dif• the information we take at face value, the is a diagram of a graph of subgroups ficult road, with the creation of a broad authority of the "expert" and the role of drawn by the students, indicating which swath of courses designed to attract rather critical thinking as it pertains to science of the seventeen wallpaper groups are than conscript students into mathematics. and mathematics. contained in each other. The students are This alternate path stems from a lengthy getting ready for their fourth assignment: "Pattern, Applications of Calculus in discussion of the goals of a liberal arts printing a series of three block prints, Medicine and Biology," "Integrated education. One of the best descriptions each of which displays a symmetry group Mathematics and Physical Science," and of these goals is due to Gerald Holton, containing that of the previous one. The "A Matter of Time" are just a few of the historian of science, who twenty-five finished prints will take hours of work, years ago made his case in an essay on require mathematical precision, and the teaching of physics: dazzle the eye. "Here I must explain in more detail just A room of thirty premedical students why I believe it to be wrong to force a watches as the professor connects some non science student to take, as is often flexible plastic tubes to an apparatus. done to "fulfill a science requirement," This class has been developing a model simply the regular introductory specialty for changes in blood pressure due to con• course given by a science department. I stricting arteries. In addition to actual start from a general belief that the total medical data, they are using this appara• orienting process of a young student in tus to test their model. Later, students Dorothy Wallace pictured with Heidi Wi/• college, it seems to me, has at least five will say this class "opened their eyes" to Iiams, class of 2003. goals. the fact that math is "more than just tak• 26 courses developed or enhanced at "If he or she is to emerge as an educated ing a derivative" and has many applica• Dartmouth College as part of the Math• and sane person from our educational tions in real life. ematics Across the Curriculum project institutions, the student should be well Forty first year students are gathered in funded by the National Science Founda• on the road to recognizing which are his groups of three or four to work out a prob• tion in 1995. In addition to courses, this own talents, whatever they may be; sec• lem in vector calculus as both their math project sponsored the development of ond, he should know enough about his professor and their physics professor look many materials, including an interdisci• physical home, this universe, not to feel on. They know that the physics they plinary text in math and physics, parts of either overwhelmed by it or a total learned yesterday ought to inform the a text on the math and biology of Lake stranger in it; third, he should know how problem they are working on right now, Victoria, (intended to address the diver• to be in fruitful relationship with his fel• and that the math they are studying to• sity of students taking math), several new low men; fourth he should know what the day is likely to be used in tomorrow's modules in statistics and data analysis, past means and what the probable future physics class. They help each other mas• and a collection of course readers in may be; and fifth, he should know the ter the material they know they will need. mathematics and humanities. All of these difference between, and the relative func• More of these students will be inclined materials make interdisciplinary teaching tions of, his mind and his souL" ("Phys• to major in engineering by the end of of math more accessible to a national ics and Culture, Criteria for Curriculum their two quarters of intensive interdisci• audience. Design", Thematic Origins (~f Scientific plinary study than when the class began, Thought, Harvard University Press, By 1998, the MATC project had benefited making the course a recruiting force for 1973). over 2,000 students at Dartmouth, di• engineering. rectly involved 178 faculty at Dartmouth Holton's vision of what an interdiscipli• A mathematics professor is explaining the and collaborating institutions, created 78 nary physics course could be offers a basis of relativity theory to a lecture hall modules, books and videos, and spon• model which Dartmouth independently of a hundred and sixty liberal arts stu• sored or cosponsored five workshops pursued with respect to mathematics. The dents, who sit quietly taking notes. The serving faculty in mathematics, literature, process of delineating their goals and silence is broken by the professor of com• history, philosophy, art, art history, biol• designing their courses created consen• parative literature, who demands to know ogy, geology, and engineering. Other in• sus and camaraderie among faculty. The why the students do not question the in• stitutions interested in such interdiscipli• courses themselves fostered a new atti• formation they are receiving. "Do you nary activities might find the course syl• tude toward mathematics among the stu• believe him? This would never stand in labi and materials at (http:// dents taking them. Clearly a large vari• one of my classes! If I said something www.dartmouth.edu/-matcl) a useful fea• ety of courses would have different kinds incomprehensible, students would be all ture. of impact on students, some resulting in 6 March 2000 FOCUS measurable differences in mastery of the mathematics, some improving retention The National Commission on Mathematics & Science Teaching in science majors, some affecting the at• for the 21st Century Wants Input titudes of the students toward mathemat• ics. Independent evaluators studied the The National Commission on Mathemat• that an adequate supply of highly skilled impact of the Dartmouth courses on stu• ics and Science Teaching for the 21 st individuals enter and remain in the math dents through subject tests, surveys and Century, chaired by former Senator and and science teaching profession. The interviews with individual students. astronaut John Glenn, wants your input! recommendations will also help make Three results stand out across all the cur• certain that throughout the span of a The Glenn Commission has created an riculum interventions as potential guide• teacher's career, he or she has the oppor• interactive discussion forum site to gather posts to future development in any math• tunity to learn, generate, accumulate, and ideas on ways to ensure high quality ematics curriculum: share knowledge about math and science teaching in mathematics and science at content and teaching methods. Commis• Students' interest in mathematics is more all grades nationwide. Visitors to the site sion members include business and edu• important than their perceived math abil• have the opportunity to watch presenta• cation leaders; public officials at the Fed• ity in determining whether they study tions from Commission meetings and eral, national, state, and local levels; and more mathematics. Many students who offer comments about what they've heard teachers of mathematics and science. view themselves as able mathematicians (or not heard) and what other visitors had forego college mathematics because they to say. You can find the discussion forum and see no career utility or intellectual reward. background information on the Glenn The Commission is preparing a report for Commission at http://www.ed.gov/ Real-life applications make mathematics Secretary of Education Richard W. Riley americacounts/glenn. The Commission more approachable and more interesting. in the fall of 2000 that will include a small invites you to return regularly to this site Whether students' interests are pre-med, number of recommendations and corre• as new material is posted for comment. pre-engineering or pre-history, connect• sponding action strategies to help ensure ing mathematics to their existing inter• ests transforms math from a "cut and dried" requirement to a relevant tool for advancing their learning. Expanding the range of mathematics top• ARUME is the First SIGMAA ics accessible to average college students As reported recently in FOCUS, the Mathematical Knowledge." It illustrated increases their interest in mathematics. MAA has approved the creation of spe• an interesting parallel between mathema• To most entering college students, cal• cial interest groups (known as ticians discussing a problem on a listserv culus is upper level math. As a result, SIGMAAs) within the Association. The and coming to resolve different assump• many who do not need calculus in their first such group to be established and tions about it and Deborah Ball's third careers tum away from college math al• approved is ARUME, the Association for grade class trying to decide whether zero together. Students were excited by Research in Undergraduate Mathematics was an even number and having to deal courses that offered non-calculus topics Education. with two different views (or working (combinatorics, number theory, group definitions) of "even." theory, probability, etc.), revealing unsus• At the January Joint Mathematics Meet• pected new worlds of mathematics to dis• ings, a SIGMAA Reception was held, and ARUME will sponsor the Fifth Annual cover and enjoy. ARUME was welcomed as the first Conference on Research in Mathematics SIGMAA by MAA president Tom Education, to be held in Chicago on Sep• For many students, these courses have Banchoff. The ARUME Coordinator for tember 21-24, 2000. Visit the conference been a source of great insight into the 2000 is Annie Selden, who can be reached web page at http://galois.oxy.edu/mickey/ doing of science and math. As one of the by email at [email protected]. Queries rume2000.html for more information on future engineers in the Integrated Math• about membership should go to ARUME the conference. ematics and Physical Science sequence Secretary/Treasurer David Meel at Information on SIGMAAs in general, put it: "Math and science are scary and [email protected]. messy and wonderful and exciting. It's including the procedures for establishing no longer about right and wrong answers; Prior to its business meeting, ARUME a SIGMAA and a model charter, is avail• there are so many more things to think sponsored a talk by Hyman Bass and able on MAA Online at http:// about. IMPS math and science isn't Deborah Ball entitled "Making Believe: www.maa.org/features/SIGMAAs/ cameo, homogenized topics; it's the real The Collective Construction of Public sigmaa.html. • thing at times-headaches and all." •

Dorothy I. Wallace is Professor ofMath• ematics at Dartmouth College and the Principal Investigator for the Mathemat• ics Across the Curriculum program. 7 FOCUS March 2000 Raoul Bott and Jean-Pierre Serre Share the Wolf Prize Read This! The Wolf Foundation has announced that pology, alge• Recently Reviewed on MAA Online Raoul Bott of Harvard University and braic geom• Jean-Pierre Serre of the Co\1ege de etry, algebra The MAA Online book review column France wi\1 share the $100,000 Wolf Prize and number is still going strong. The latest reviews in Mathematics for 2000. The prize will theory, and for are featured at the main Read This! page be awarded next May in Jerusalem. his inspira• at http://www.maa.org/reviews/ tionallectures Raoul Bott reviews.html. and writing." was recog• Serre holds Recently reviewed books include: nized for his degrees from "deep dis• j, Euclid: the Creation of Mathematics, by the Ecole coverIes In lean-Pierre Serre Benno Artmann Normale topology Superieure and the Sorbonne. His work Geometry Civilized: History, Culture, and differ• runs through a wide range of subjects, and Technique, by 1. L. Heilbron ential ge• including algebraic topology, algebraic ometry and geometry, group theory, and number Surfing Through Hyperspace, by Clifford their appli• theory. He is known as an inspired and A. Pickover cations to inspiring lecturer, and his books are leg• Lie groups, The Shaping ofDeduction in Greek Math• endary for their clarity and precision. by Reviel Netz differential ematics, Raoul Bott Through lectures, courses, and books, he operators, has left a significant mark on the math• Mathematical Expeditions, by Reinhard and mathematical physics." Bott holds an ematics of the second half of the twenti- Laubenbacher and David Pengelley Engineering degree from McGill Univer• eth century. sity in Canada and a Ph.D. in Science The Nothing That Is, by Robert Kaplan from the Carnegie Institute of Technol• The list of recent Wolf Prize Laureates The Teaching Gap, James W. Stigler and ogy in Pittsburgh. He has been a mem• in Mathematics includes Robert James Hiebert ber of the Harvard Mathematics depart• Langlands, Andrew Wiles, Yakov G. ment since 1959. His more recent work Sinai, Elias M. Stein, Joseph B. Keller, Assessment Practices in Undergraduate has centered in the connections between and Laszlo Lovasz. For more on the Wolf Mathematics, ed. by Bonnie Gold, Sandra differential geometry and theoretical Foundation and the Wolf Prize, visit the Keith, and William Marion physics which have emerged in recent Foundation web site at http:// Starting Our Careers, ed. by Curtis D. decades, especially in string theory. www.aquanet.co.il/wolf/. • Bennett and Annalisa Crannell Jean-Pierre Serre was recognized for his Photograph of Raoul Batt courtesy of Jane Cinderella: the Interactive Geometry "many fundamental contributions to to- Reed/Harvard University. Software, by Jtirgen Richter Gebert and Ulrich H. Kortenkamp Short Course on Error-Correcting Codes at the The Magical Maze, by Ian Stewart Los Angeles Mathfest Math Trek: Adventures in the MathZone, Vera Pless of the University of Illinois at coding procedures. A very useful theo• by Ivars Peterson and Nancy Henderson Chicago and William C. Huffman of rem on weight distributions will be given. Statistics and Society, ed. by Daniel Loyola University of Chicago will offer Promising classes of codes, such as cy• Dorling and Stephen Simpson a short course on Error-Correcting Codes clic codes and self-dual codes, wi\1 be at the Los Angeles Mathfest, to be held explored, as wi\1 famous codes from these Imaginary Numbers, ed. by William on August 3 to 5, 2000. A description of classes such as the Golay codes. Well• Frucht the course is given below. Check the next known algebraic structures give practi• Proof, Logic, and Conjecture: the issue of FOCUS for the full Mathfest pro• cal information needed to use these Mathematician s Toolbox, by Robert S. gram and information on how to sign up. codes. Very good codes often "hold" very Wolf good combinatorial designs. Relations Error-Correcting Codes with combinatorial designs can be used RealAnalysis: A HistoricalApproach, by Vera Pless and William C. HutTman to decode the code. Error-correcting Saul Stahl. The practical origins of coding are in the codes provide the high fidelity in com• reliable transmission of digitally encoded pact disc recordings. They are also the information. This is the motivation for the means whereby information can be trans• study of error-correcting codes. Linear mitted from outer space to earth. A panel codes will be defined and many examples wi\1 examine some of these achievements given detailing various encoding and de- and possible difficulties .• 8 The Random Walks of George Polya Gerald L. Alexanderson

George P6lya enjoyed the esteem of the mathematical community not only for his deep and Influential contributions in a variety of mathematical fields. but also for his groundbreaking work in the teaching of mathematics. His standing in the latter area could rest solely on his having written one of the most widely read books in mathematics. the still-popular How to Solve It. In addition to his championing problem-solving. he contributed to mathematics important results in complex and real analysis. inequalltites. mathematical physics. comblnatorics. probability theory. number theory. and geometry. He coined the phrases "random walk" and "central limit theorem" and gave to mathematics the P61ya Enumeration Theorem. along with many other ideas used widely today. The present work describes how such versatlllty came about and. along the way. tells some enlightening stories about mathematics and mathematicians.

Paperbound Edition: Cascbound Edition: Catalog Code: RWP Catalog Code: WAY .. 32oPp .• Paperbound. 2000 320pp .• Casebound. 2000 ISBN 0-88385-528-3 ISBN 0-88385-531-3 . List Prloe: $29.95 Member Price: $23.95 List PrIce: $41.95 Membei' Price: $32.95···

Tbe .Math· Chat Book Frank Morgan this book shows that mathematics can be fun for everyone. It grew out of Frank Morgan's live. call-in Math Chat TV show and biweekly Math Chat column in The Christian Science Monitor. The questions. comments. and even the answers come largely from the callers and readers themselves. This book makes no attempt to fit any mold. Although written by a research mathematician. It goes where the callers and readers take It. over a wide range of topics and levels. Almost anyone paging through it will find something of Interest. Why does the new year start earlier In Europe? Why is the Fourth of July on a different day of the week each year? How can you be elected President with lust 22% of the vote? Can a computer have free will? Didn't some kid find a mistake on the SATs? Do airplanes get lighter as passengers eat lunch?

Catalog Code: MCH 124pp .• Paperbound. 2000 ISBN 0-88385-530-5 List Price: $19.95 Member Price: $16.00

The Beginnings and Evolution of Algebra Isabella Bashmakova and Galina Smirnova

There is hardly a branch of mathematics whose evolution has undergone as many surprising metamorphoses as has algebra. and these metamorphoses are described by the authors with vividness and clarity. The special merit . of the book Is that it corrects the widespread view that up to the 1830s the mainspring of the development of algebra was the investigation and solution of determinate algebraic equations. and especially their solution by radicals. The authors show that this viewpoint is one-sided and gives a distorted view of of its evolution. Specifically. they show that the role of indeterminate equations in the evolution of algebra was no less important than that of determinate equations.

Catalog Code: 001-23 196 PP .. Paperbound. 2000 ISBN- 0-88385-329-9 ... List Price: $24.95 Member Price: $19.95 FOCUS March 2000 Undergraduate Poster Session a Success

A record 65 posters were presented on tion for about 2 hours. Each poster was The success of the session was beyond Friday January 21 at the Undergraduate evaluated by three judges and each judge everybody's expectations. The organizer, Student Poster Session sponsored by the was given no more than six posters. To Mario Martelli, received numerous favor• MAA CUPM Subcommittee on Under• achieve a more reliable ranking posters able comments on the professionalism, graduate Research in conjunction with were assigned so that the same three enthusiasm, and knowledge of the pre• the Joint Mathematics Meetings in Wash• judges would not evaluate two or more senters. Many judges told Mario that they ington, DC. One hundred and sixteen stu• different posters. Fifteen $100 prizes, did not expect to find the posters' con• dents were there to present their posters, offered by the MAA, the American Math• tent so interesting and challenging. "Stu• whose content and quality demonstrated ematical Society, the Council on Under• dents, judges and visitors had a great that undergraduate research is flourish• graduate Research, and by an anonymous time," said Mario. "The students present• ing. MAA supporter, were awarded to the best ing were such a bunch of marvelous kids posters. The full list of winners is given that we can safely say the future of math• The evaluation of the posters was handled below. ematics is in great hands!" • by 35 judges who worked with dedica-

Best Undergraduate Research Posters at the January 2000 Call For Papers Joint Mathematics Meetings Thirteenth Annual MAA Undergraduate Student Spanning Tree Edge Densities, Michael The traveling salesman and a tale offour Paper Sessions Ferrara (Stevens Institute of Technology ) cities, Melissa Desjarlais (Alma College) Tranversality (sufficient) conditions for The Trials and Triangulations of a Zero• Student papers have been a traditional bifurcation: a geometric viewpoint, Gary Divisor Graph, Andrea Frazier (Illinois part of the program for the MAA sum• Mikaelian and Susanne Sindi (California College) mer meeting, and this year is no excep• State University Fullerton) tion. The Thirteenth MAA Undergradu• Reve's puzzle, Danielle Arett (Augsburg ate Student Paper Sessions will take On the analytic geometry of the travel• College) place at the MAA Mathfest 2000 in Los ing salesman problem, Kathleen Bellino Bi-symmetric invariants, Emily Puente, Angeles, CA, August 3 to 5, 2000. and Rekha Narashiman (James Madison Monica Castro-Simmons, and Thomas University; Arizona State University) Partial support for travel by students pre• Jose Castillo (Wellesley College; Univer• senting papers will be available on a lim• Triangle Iterations and Algebraic Num• sity of Puerto Rico-Humacao; Harvard ited basis. Complete details on submis• bers, Matthew Lepinski, Alexander Diesl, University) sion procedures and applications for Tegan Cheslack-Postava, and Adam On the Sato-Tate conjecture for genus two travel support will be published in the Schyler (Rose-Hulman Institute of Tech• Nikolai Roussanov and Carleton April issue of FOCUS. This information nology; Williams College; Williams Col• curves, Bosley (Harvard University) will also be available on the MAA home lege; Williams College) page at http://www.maa.org/students/ Graphs with (Edge) Disjoint Links in Dynamics of a ball bouncing on nonlin• students_i ndex. html. Every Spatial Embedding, Katherine ear curves, Daniel Mathews, Gary Students are advised to begin making Mikaelian and Suzanne Sindi (California Sharrow, Jennifer Hespen, Trent Lalonde, and Nathan Thomas (University of Ken• plans now regarding participation. The State University Fullerton) tucky, Lexington; SUNY Postdam; deadline for student paper submissions Number Theoretic Balls in Boxes, Clarkson University; Clarkson Univer• is Friday, June 30, 2000. Jayadev Athreya and Lukasz M. sity) Please direct all inquiries to Dr. Charles Fidkowski (Iowa State University; Diminnie via email at Harvard University) Modeling Pollution Dispersion in Large Complex Spaces, Jeffrey Housman [email protected] or by Probabilit}· of False Prostate Cancer (Sonoma State University) phone at (915) 942-2317 ext 238 .• Diagnosis Using a Logistic Function The Growth of Generalized Diagonals in Given Age and fit PSA Ratio, Aldo Crossa, Brisa N. Sanchez, Johnny a Polygonal Billiard, Noah Salvaterra and Brian Wickman (Pennsylvania State Guzman, and Andie Hodge (Wittenberg University) • University; University of Texas, EI Paso; California State University, Long Beach; University of the Virgin Islands) 10 March 2000 FOCUS The Anneli Lax New Mathematical Library

By Don Albers ing or anything like that, so I ended up doing everything [editing, copy editing, layout, cover design] ! The layout was fun; it was like playing with paper dolls." Acquisition of good material is vital to the success of any publishing program, and Anneli had something of a Midas touch when it came to attracting mathematics manuscripts. The first of her acquisitions, Numbers: Rational and Irra• tional by Ivan Niven, was published in 1961 and is in its fourteenth printing. Her second, What is Calculus About by W. W. Sawyer, also published in 1961, is in its eighteenth printing. Her list of authors was remarkably strong• Beckenbach, Bellman, Chinn, Coxeter, Davis, Greitzer, Klamkin, Niven, Ore, P6lya, Sawyer, Steenrod, and Yaglom to name a few. When asked about her editorial accomplishments, she mod• estly responded: "I think it had to do with my being very slow when I read. I don't instantly get the gist of it. I have to understand every dam little step, which slows me down terribly and which is one of the reasons that I never learned For thirty-eight years, until her death in 1999, Professor Anneli very much, but it is good for checking errors and making Lax served as Editor of the New Mathematical Library (NML), sure everything is okay." one of the comer stones of the MAA's publications program. In During her thirty-eight years as Editor of the NML, she 1958, Edward G. Begle, head ofthe School Mathematics Study brought thirty-nine volumes to publications-a truly remark• Group, (SMSG), appointed a special panel of twelve people to able achievement! It is easily argued that the NML is produce a series of short expository books for high school stu• Anneli's series, and it serves as an enduring monument to dents on various topics not usually covered in the high school her contributions to quality mathematics exposition. In rec• curriculum. Richard Courant, Lax's dissertation advisor, be• ognition of her great work on the NML, in October of 1999 came aware of her editorial skills while she was working on the New Mathematical Library was renamed the Anneli Lax her doctorate at New York University. She claimed that Cou• New Mathematical Library. • rant hired her for editorial tasks because "I seemed more liter• ate than most people. In the fifties, according to Lax, publish• Don Albers is the Associate Executive Director and Direc• ers didn't have people who could do mathematical copy edit- tor of Publications and Electronic Services for the MM.

NUMBERS: WHAT IS FIRST CONCEPTS r"\ RATIONAL CALCULUS OF TOPOLOGY '.~I OVER AND AND IRRATIONAL HH (,EDlllfHIY OF MAPPINGS OF ABOUT? 'it (,,",tNTS tURVES CIRCLES AND OISIo(S OVER AGAIN IVAN NIVEN w. w. SAWYER W.G.CHINN AND N.E.STEENROD

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Some of the volumes in The Anneli Lax New Mathematical Library from her first to her last.

11 FOCUS March 2000 Short Takes International Conference on Technology 221 North Grand Blvd., St. Louis, MO in Education 63103 [Email: [email protected]; Phone: Seventh Annual Hudson River Under• 314-977-2436J. graduate Mathematics Conference An International Conference on Technol• ogy in Mathematics Education will be CUPM Curriculum Initiative Gets The seventh annual Hudson River Un• held on July 5-7, 2000, at the Lebanese• National Attention dergraduate Mathematics Conference American University in Beirut, Lebanon. As FOCUS readers know, the MAA's will be held on April 8, 2000, at Vassar The conference organizers hope that it Committee on the Undergraduate Math• College in Poughkeepsie, NY. The con• will provide an opportunity for educators ematics Program (CUPM) is undertaking ference includes presentations on math• to share thoughts and experiences, and an ambitious plan to study the mathemat• ematics by both faculty and students. also that it will allow extensive contact ics curriculum and come up with recom• Conference sessions are designed so that between educators from the developed mendations for what and how we should some presentations are accessible to un• nations and those from developing coun• teach our students. CUPM has been col• dergraduates in their first years of study, tries, particularly the Middle East. Invited lecting ideas and opinions from a wide and others are accessible to third or fourth speakers include Deborah Hughes Hallett range of professors, in and out of math• year undergraduate mathematics majors. from the USA, Celia Hoyles from the ematics, and their efforts have been high• Additionally, Peter Hilton will give a pre• UK, Bernard Winkelmann from Ger• lighted in an article in the Chronicle of sentation on some generalizations of the many, and Peter Jones from Australia. Higher Education (January 7,2000, page Chinese Remainder Theorem. Visit the conference web site at http:// www.lau.edu.lb/news-events/conferences/ A 14). Describing the curriculum review You can find out more about HRUMC as "what will likely be the greatest change by visiting the conference web site at ictme/main-index.html for more informa• tion. in mathematics since calculus reform in http://www.skidmore.edu/academics/mcs/ the early I 990s," the Chronicle includes hrumc.htm. New Officers of the Association quotes from Tom Berger, chair of CUPM, and cites the United States Military Acad• Michigan Section Chooses Top Ten The year 2000 brings several changes in emy at West Point as one of the leaders the leadership of the MAA. Marcia Sward The Michigan Section of the MAA re• in this area. The article notes that the cently polled its members to determine stepped down as Executive Director, the two MAA vice-presidents (Anita Solow mathematical community is still far from the top ten mathematical achievements consensus on the curriculum, and CUPM of the twentieth century. About thirty dif• and Ed Dubinsky) concluded their terms, and Gerald Alexanderson left the Execu• is working on giving everyone a chance ferent events, ranging from "Lebesgue's to share ideas and comments (for ex• Dissertation" to "Development of Linear tive Committee after having been a mem• ber (in various capacities) for 17 years. ample, see Sol Garfunkel's article in this Programming", were nominated, and bal• issue). Send your comments on the math• lots were distributed asking members to Tina Straley became Executive Director at the beginning of the year. Barbara L. ematics curriculum to CUPM by email rank their top five choices. Here are the at [email protected]. Michigan Top Ten: Osofsky, First Vice-President, Frank Morgan, Second Vice-President, and Ann Bylaws Change I. The Development of the Digital Com- E. Watkins, President-Elect, took office puter at the end of the Joint Meetings and will With only one dissenting vote, the by• 2. GOdel's Incompleteness Proof now be members of the Executive laws change announced in the Decem• 3. Einstein's Relativity Theory Commitee. ber issue of FOCUS and on MAA Online 4. Proof of Fermat's Last Theorem was approved at the Business Meeting of (Wiles) Who's NExT? the Association held at the January Joint 5. Hilbert's Talk at the 1900 Congress Project NExT, which stands for New Meetings. As a result, the MAA no longer 6. Classification of Finite Simple Groups Experiences in Teaching, is one of the has a Finance Committee. Functions for• 7. Development of Linear Programming most successful programs of the MAA. merly performed by the Finance Com• (Dantzig) It is a great way for new members of the mittee will now be the responsability of 8. Mathematization of Quantum Mechan• mathematics profession to explore new the Executive Committee. For the details, ics (Von Neumann) ideas in teaching, develop connections check the changes at http://www.maa.org/ 9. The Development of Fractal Geometry with other mathematics professors, learn aboutmaa/bylaws99.html. (Mandelbrot) more about the mathematical community, Teacher Shortages Cause Concern 10. Applications of Mathematics to and generally acquire valuable tools for Cryptology. their professional life. Applications for Extensive media reports and op-ed pieces have highlighted the current acute short• The results of the Michigan Section's Top this year are due on April 14. More in• age of mathematics and science teachers Ten vote can also be found online, at formation and application materials are at the high school level. Responses have http://www.cst.cmich.edu/units/mth/ttm2k1 available at the Project NExT web site at ranged from emergency measures, such topten.htm. Perhaps other MAA sections http://archives.math.utk.edu/projnextl, or as the granting of extra work visas to al• will want to produce their own lists! contact T. Christine Stevens, Dept. of Mathematics and Mathematical Com• low foreign teachers to come to the puter Science, Saint Louis University, United States, to plans for systemic 12 March 2000 FOCUS change. These range from attempts to a Certificate of Appreciation for her great nology in the classroom. Intel will spend simplify the certification process to pro• contributions to the MAA. In response, $100 million and Microsoft will donate posals that would offer special rewards she thanked the Association and said that 400,000 copies of its Encarta 2000 ency• to young people going into the teaching she had been "blessed with good work to clopedia and Office 2000 Professional profession. Despite the shortage and the do and good people with whom to do it." software for what is believed to be the occasional bidding wars it has engen• largest private effort to spur the use of Later that day, the Marcia Sward Lobby dered, teacher salaries still lag behind technology in education. at the MAA building was dedicated. those of people with comparable train• Among the renovations for the Sward In the U.S., an estimated 100,000 teach• ing in other professions, which may ac• Lobby was the installation of a tiling de• ers will be encouraged to participate in count for part of the problem. signed by Marjorie Rice and Doris the program. "Master teachers" will be Schattschneider (check MAA Online for chosen for training in each school dis• Marcia Sward is more information about the tiling). A ban• trict. These teachers will then train their Executive Director Emerita quet in Sward's honor was the closing colleagues. Each master trainer will re• At the Joint Mathematics Meetings in event of the Joint Mathematics Meetings. ceive a laptop computer when they sign Washington, DC, the MAA Board of up for the 10 four-hour training sessions. Governors named Marcia Sward "Execu• Intel and Microsoft To Launch Major Intel's announcement can be found on the tive Director Emerita." As the Executive Training Program For Teachers web at http://www.intel.com/pressroom/ Director of the MAA from 1989 to 1999, Two giants of American technology, Intel archive/releases/ed012000.htm .• Sward has played a fundamental role in and Microsoft, are funding a three-year the life of the Association for many years. "Teach to the Future" program to train At the Business Meeting, Sward received 400,000 teachers to use educational tech-

EMPWYMENf ()ppoRl1JNITIFS Secretary Riley Responds to Open Letter CALIFORNIA Early in January, Secretary of Education riously because the panel required pro• Richard Riley responded to the open let• grams to demonstrate measurable im• SAN DIEGO MESA COLLEGE Assistant Professor, Mathematics ter from several mathematicians object• provement in students' learning. "Un• The San Diego Community College District is ing to the findings of the Expert Panel doubtedly," he went on to say, "there are currently accepting applicationsfor an Assistant that chose "exemplary" and "promising" other materials that can or will demon• Professor, Mathematics position for a full-time school mathematics programs. Riley ex• strate achievement gains in both basic assignment beginning Fall, 2000. The Assistant pressed appreciation for the interest the skills and problem solving. If you or oth• Professor, Mathematics will be expected to teach signers of the letter showed in mathemat• ers cosigning the letter have such mate• programming in a higher level language and ics education, and argued that it was im• rials or programs, we welcome their sub• courses ranging from pre-algebra through lin• portant to find areas where all of the par• mission in the next round." The panel will ear algebra and differential equations. Also, the ticipants in the debate were in agreement. review science programs this year, then applicant must possess the ability to integrate For example, he said, all agree that "the review mathematics programs again in the computer and other technology as teaching very best mathematics programs must in• 2001. and learning aids. Successful candidates must possess a Master's degree in Mathematics or clude mastery of basic skills and the use Finally, Riley addressed the issue of the Applied Mathematics; OR, a Bachelor's degree of those skills in solving complex prob• lack of representation of research math• in Mathematics or Applied Mathematics AND a lems." Another area of agreement, he ar• ematicians on the panel, conceding that Master's Degree in Statistics, Physics, or Math• gued, is that children must learn both the "additional representation of research ematics Education. Salary range for this tenure• "traditional basics" and "the basics of a track position is $3,428-$5,149 per month and mathematicians knowledgeable about K- new information age", which include includes an excellent benefits package. To ob• 12 mathematics education would "communicating mathematical ideas, ap• tain the required District application, please con• strengthen panel deliberations." plying mathematics in real-world set• tact the San Diego Community College District, tings, and problem solving." The full text of Secretary Riley's letter Employment Office, 3375 Camino del Rio can be seen at the Department of Educa• South, Room 330, San Diego, CA 92108, (619) Riley then discussed the panel's findings 584-6579,1-800-648-4023 (if outside Califor• tion web site, at http://www.ed.gov/News/ more specifically, acknowledging that nia). Internet Website: http:// Letters/000106.html. • this is an area of disagreement, but argu• www.sdccd.cc.ca.us/jobs. Filing Deadline• ing that the findings should be taken se- April 13, 2000. AAlEOE.

Employment contiuned on page 14. 13 FOCUS March 2000 mendation on teaching and research sent to the University, Box 7388, Winston-Salem, NC INDIANA Hiring Committee. Evaluation of applications 27109. DEPAUW UNIVERSITY will begin on or after December 6. As an EEO/ The Department of Mathematics at DePauw AA employer, Williams especially welcomes OHIO University invites applications for a two-year applications from women and minority candi• OBERLIN COLLEGE term appointment starting in the fall of 2000. dates. Oberlin College has a full-time, continuing po• Duties include teaching three undergraduate sition beginning with the academic year 2000- courses (twelve contact hours per week) each 2001. Responsibilities include teaching under• semester and winter term. Ph.D. preferred, WILLIAMS COLLEGE graduate courses in mathematics (5/year), super• master's required. DePauw is a private liberal Department of Mathematics vising honors students, and sustained scholarly arts college with 2200 students located forty-five Williamstown, Massachusetts 01267 production. A Ph.D. degree (in hand or expected miles west of Indianapolis. Tentative full-time visiting position in mathemat• ics for the 2000-2001 year, probably at the rank by August 31,2000) is required. Preference will Applicants should send vita, statement of pro• of assistant professor; in exceptional cases, how• be given to candidates who are interested in and fessional goals and teaching philosophy, and ever, more advanced appointments may be con• experienced with applied mathematics (all spe• three letters of recommendation to Underwood sidered. Excellence in teaching and research, cialties considered except statistics and opera• Dudley, Mathematics Department, DePauw and Ph.D. required. tions research). Candidates must demonstrate po• University, Greencastle, IN 46135. E-mail: tential excellence in teaching. Send a letter of [email protected]; phone: 765-658-4488; Please have a vita and three letters of recom• application, curriculum vitae, academic tran• fax: 765-658-4732. Review of applications will mendation on teaching and research sent to Visi• scripts (graduate and undergraduate, unofficial begin March 15 and continue until the position tor Hiring Committee. Evaluation of applications transcript are acceptable initially), and 3 letters is filled. More information about DePauw can will begin on or after January 15 and continue of reference to Michael Henle, Department of be found at its website, www.depauw.edu. until the position is filled. As an EEO/AA em• Mathematics, Oberlin College, Oberlin OH DePauw University is an equal opportunity. af• ployer, Williams especially welcomes applica• 44074 by February 15, 2000. Oberlin College firmative action employer. Women and minor• tions from women and minority candidates. admitted women since its founding in 1833 and ity candidates are encouraged to apply. has historically been a leader in the education of NORTH CAROLINA African-Americans. AA/EOE. KANSAS METHODIST COLLEGE PENNSYLVANIA TABOR COLLEGE Mathematics Instructor CEDAR CREST COLLEGE Mathematical Sciences Department Methodist College, an Equal-Opportunity em• Faculty Position in Mathematics Hillsboro, KS 67063-1799 ployer, welcomes applications for a full-time po• Applications are invited for a tenure-track posi• Tenure-track faculty position in computer sci• sition in Mathematics, starting in August 2000 tion at the Assistant Professor rank commenc• ence/mathematics starting fall 2000; prefer Ph.D. at the beginning of the 2000-0 I academic year. ing no later than August I, 2000. Cedar Crest is in computer science with a strong background A Masters Degree in Mathematics is required a small, liberal arts college for women located in mathematics but will consider Ph.D. in math• and a Ph.D. in Mathematics is preferred. Teach• on a beautiful park-like campus in Allentown, ematics with a strong background in computer ing responsibilities include introductory math• Pennsylvania, a medium-sized city within two science. Successful candidate must be commit• ematics courses with possibility of upper divi• hours of New York City and Philadelphia. The ted to excellence; will teach (and develop) math• sion course in area of specialization. Methodist college offers B.S. and B.A. degrees in math• ematics and computer science courses, direct un• College, in harmony with its tradition, takes se• ematics and Pennsylvania teaching certification dergraduate research, sustain professional riously the ethical and moral development of stu• in secondary mathematics. This faculty mem• growth, and support the mission and goals of a dents. Members of populations traditionally ber will teach mathematics courses for majors, Christian liberal arts college. Further informa• underrepresented in higher education are encour• but will also be expected to teach a broad range tion: www.tabor.edu, or Professor Frank aged to apply. Send a letter of application in• of service courses in mathematics for science, Brenneman at [email protected] or cluding a statement of professional goals and humanities and arts students, with a teaching load 316.947.3121. Tabor is an AAIEOE and wel• teaching philosophy, full resume, three letters of 12 credit hours per semester. Minimum quali• comes applications from women and minority of reference, and graduate transcripts to : Dr. fications: Ph.D. in mathematics or applied math• candidates. All applications: Dr. Lon Fendall, Shivappa Palled, Head, Department of Math• ematics, promise of excellence in teaching at the Dean of the Faculty. ematics and Computer Science, Methodist Col• lege, 5400 Ramsey Street, Fayetteville, NC undergraduate level, a desire to mentor math• 28311-1420, (910) 630-713317125. Deadline for ematics and mathematics education students, and MASSACHUSETTS submissions is March 13, 2000. a commitment to continued research. The suc• cessful candidate must be able to demonstrate WILLIAMS COLLEGE not only mathematical expertise but also an abil• Department of Mathematics WAKE FOREST UNIVERSITY ity to communicate mathematics clearly and ef• Williamstown, Massachusetts 01267 Applications are invited for two positions in fectively to undergraduate students. Applicants Anticipated tenure-track position in mathemat• mathematics at the Visiting Assistant Professor should send a letter of intent, a curriculum vita ics, pending administrative approval, beginning level beginning August 2000. A Ph.D. in math• and three letters of reference to Marie E. Wilde, fall 2000, probably at the rank of assistant pro• ematics or equivalent is required. The sole duty Mathematics Search Committee, Cedar Crest fessor. In exceptional cases, however, more ad• is to teach three sections of mathematics each College, 100 College Drive, Allentown, PA vanced appointments may be considered. Excel• semester during the nine month academic year. 18104. Questions should be directed to mewilde lence in teaching and research and a Ph.D. are Send letter of application and curriculum vitae @cedarcrest.edu. Applications should be re• required. to Richard Carmichael, Department of Math• ceived by April 1,2000 to receive full consider• Please have a vita and three letters of recom- ematics and Computer Science, Wake Forest ation. 14 March 2000 FOCUS LA SALLE UNIVERSITY Philadelphia, Pennsylvania " .. L "('~ Department of Mathematics ~ .,. and Computer Science Tenure-track Mathematics Positions MAA Partnerships:: g La Salle University invites applications for a Interdisciplinary Workshops ~O(jNO"1.\O+• tenure-track Mathematics position effective Fall. 2000. La Salle is a Roman Catholic institution for Faculty of higher Education in the tradition of the De La Salle Christian Brothers. The university strives to offer. through effective teaching. quality edu• cation founded on the idea that intellectual and Teams of faculty build cross-disciplinary partnerships and spiritual development go hand in hand mutually work together on interdisciplinary materials complementing and fulfilling one another. Can• developed by NSF Mathematical Sciences and their didates should hold the Ph.D. in Mathematics Applications throughout the Curriculum projects, or Applied Mathematics. The duties of the posi• adapting these and developing their own materials. tions are those typically associated with a fac• ulty position including teaching twelve hours Room and board provided for all participants. each semester. undergraduate advising. and com• Limited travel funds available. mittee assignments. Please submit a curriculum vita and three letters Engineering and Mathematics of recommendation (with at least one address• Rensselaer Polytechnic Institute, Troy, NY June 5-10, 2000 ing the applicant's teaching experience) to Linda J. Elliott. Chair. Department of Mathematics and Life Sciences and Mathematics Computer Science. La Salle University. 1900 West Olney Avenue. Box 258. Philadelphia. PA Carroll College, Helena, Montana July 17-22, 2000 19141-1199 ([email protected]). Review of applications will begin immediately and con• For information and applications: tinue until the positions are filled. http://www.maa.org/pfdev/pfdev_calendar.html#PARTNERSHIPS Or contact: Maureen Callanan: mcallana@ maa.org La Salle University is an Equal Opportunity. Affirmative Action employer. 202-387-5200 FAX 202-265-2384

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Allegheny Mountain April 7-8. 2000 Metro New York May 7, 2000 Bronx Pacific-Northwest June 15-17,2000, South Campus, Community College of Community College, NY University of British Columbia, Vancouver, Allegheny College, Pittsburgh, PA BC, Canada Michigan May 5-6, 2000 Central Michigan Eastern PA & Delaware April 8, 2000 University, Mt. Pleasant, MI Rocky Mountain April 7-8, 2000 Colorado Messiah College, Grantham, PA State University, Ft. Collins, CO Missouri April 14-15, 2000 Central Florida March 3-4, 2000 University of Missouri State University, Warrensburg, Seaway April 14-15,2000 SUNY Oswego, South Florida, Tampa, FL MO Oswego, NY

Illinois March 30-April 1,2000 North Nebraska-Southeast South Dakota April Southeastern March 10-11, 2000 UNC• Central College, Naperville, IL 28-29, 2000 Nebraska Wesleyan, Lincoln, Charlotte, Charlotte, NC NE Indiana Spring 2000 Earlham College, Southern California March 4, 2000 Richmond, IN New Jersey April 8, 2000 Georgian Court University of California, Los Angeles College, Lakewood, NJ Intennountain March 24-25, 2000 Southwestern April 7-8, 2000 Arizona Southern Utah University, Cedar City, UT North Central March 3 I-April I, 2000 State University, Tempe, AZ Iowa April 14-15, 2000 Simpson College, Duluth Convention Center, Duluth, MN Texas April 6-8, 2000 University of Texas Indianola, IA Northeastern June 16-17, 2000 St. Paul's at Austin, Austin, TX Kansas March 3 I-April I, 2000 Baker School, Concord, NH Wisconsin April 14-15, 2000 University of University, Baldwin City, KS Ohio April 7-8, 2000 Marshall University, Wisconsin-Superior, Superior, WI Kentucky March 31 - April I, 2000 Eastern Huntington, WV Kentucky University, Richmond, KY Oklahoma-Arkansas March 3 I-April I, MD-DC-VA April 28-29, 2000 Bowie State 2000 Arkansas Tech University, University, Bowie, MD Russellville, AR 15 From the MAA. •• CALL 1-800-331-1622 , Archimedes What Did He Do Besides Cry Eureka? Sherman Stein Series: Classroom Resource Materials Using only high school-level mathematics, Stein presents an accessible account of Archimedes' accomplishments. He discusses the life of Archimedes, the discovery of Archimedes' manuscript in 1906, and Archimedes' methods for figuring out the law of the lever, center of gravity, the parabola, floating bodies, the spiral, the sphere, and pi. Helpful information is appended, including a discussion of Archimedes' system of notation. -Booknews

his book has only one purpose: To make the with the few tools at his disposal is astonishing. He Tdiscoveries of Archimedes easily accessible to a was like a one-person Institute of Advanced Study, wide audience, from anyone with a background in making fundamental discoveries in the fields of high school algebra to a busy practicing geometry, mechanics and hydrostatics. mathematician. The exposition is leisurely and supported by some Many people have heard of two things about 120 illustrations. Any reader who is aware that the Catalog Code: ARClYDOO Archimedes; He was the greatest mathematician of graph of y = x' is a parabola can follow all the 168 pp., Paperbound, 1999 antiquity and he ran naked from his bath crying: reasoning. Although the book uses only high school ISBN 0-88385-718-9 "Eureka, eureka." Few of us, layperson or mathematics, professional mathematicians will find List: $24.95 mathematician are familiar with the accomplishments much here of interest as well. MAA Member: 519.95 on which his reputation rests. This book answers the Contents: Introduction • The Life of Archimedes • questions by describing in detail his astonishing The Lever· The Center of Gravity • Big Literary accomplishments: how he developed the theory of Find in Constantinople. The Mechanical Method; the lever and the center of gravity; how he used the Two Sums • The Parabola; Floating Bodies. The center of gravity to study whether a floating object Spiral· The Ball. Archimedes Traps it would tip over; how he summed a geometric series • Appendices: Affine Mappings • The Floating and the squares; and how he found the volume and Paraboloid • Notation; References. surface area of a sphere. His ability to do so much

Inverse Problems Activities for Undergraduates Charles W Groetsch Series: Classroom Resource Materials Usually in mathematics you have an equation and you want to find a solution. Here you were given a solution and you had to find the equation. I liked that. -Julia Robinson

nverse Problems are hard to define, yet nearly all Scripts in MATLAB keyed to Computations in the Imathematicians recognize an inverse problem modules are provided in an appendix (the M-files when they see one. As children we learn about the may be downloaded from author's Webpage). Each direct problem of multiplication; given two module opens with advice on the course level of Catalog Code: IPR/YDOO numbers we find their product. The corresponding the module, mathematical and scientific 310 pp., Paperbound, 1999 inverse problem is to find a pair of factors of a prerequisites, and the type of technology ISBN 0-88385-716-2 given number. appropriate for the module. List: $26.00 This book introduces mathematics instructors to MAA Member: 520.50 inverse problems and provides them with resources that are useful for teaching the lessons of inverse problems to students in the first two The Mathematical Association of America Periodicals Postage paid at undergraduate years. The problems are 1529 Eighteenth St., NW Washington. DC and introduced by an historical essay that Washington, DC 20036 additional mailing offIces provides, without any formal mathematics, a scientific and cultural context for the mathematical lessons that follow. The next four chapters deal with inverse problems in Precalculus, Calculus, Differential Equations and Linear Algebra. Each chapter contains six modules on specific inverse problems in the subject matter of the chapter. The modules consist of brief introductions for the teacher, an Activities section for the student, and a concluding section of notes and suggestions for further reading.