THE NEWSLETTER OF THE MA THEMA TICAL ASSOCIATION OF AMERICA Mathematicians Honored by National Academy Volume 15, Number 2 Three mathematicians are among the sixteen through funds provided by individuals selected by the National Academy IBM Corporation. of Sciences (NAS) to receive awards honor• The NAS Award for Scien• ing their outstanding contributions to science. tific Reviewing is given in In this Issue The awards will be presented on April 24th at a different field each year. a ceremony in Washington, DC, during the The field for the 1995 4 John Nash and academy's 132nd annual meeting. the Nobel Prize award is mathematics. The NAS Award in Applied Mathematics and Robion C. Kirby, a profes• Numerical Analysis goes to Julian D. Cole, sor in the Department of 5 The Craft of the Margaret Darrin Professor of Applied Mathematics at the U ni ver• Teaching Mathematics in the Department of Mathe mati• sity of California at Berke• cal Sciences at Rensselaer Polytechnic Insti• ley (Berkeley, California), tute (Troy, New York) and Joseph B. Keller, 9 Personal will receive the award for the Lewis M. Terman Professor of Mathemat• the list of problems in low Opinion ics and Mechanical Engineering in the De• dimensional topology that partment of Mathematics at Stanford he both created and main• Joseph B. Keller 12 A Building for University (Stanford, California). Dr. Cole has tained. Generations have Mathematicians made fundamental contributions to applied been greatly influenced by mathematics and numerical analysis, charac• Kirby's list. The award of terized by deep physical and mathematical $5000 was established by 13 New P61ya insights. Dr. Keller is known for his seminal Annual Reviews, Inc. and Lecturer contributions to applied mathematics, in par• the Institute for Scientific ticular his geometrical theory of diffraction Information in honor of J. 14 Workshops and his work on water-wave propagation. The Murray Luck. award is set at $10,000 and was established Robion C. Kirby 19 MathFest 1995 Albert W. Tucker, 1905-1995 38 Employment Former MAA president and chair of the teacher, but his love of mathematics led him to Princeton Mathematics Department Albert delay his teaching career in order to earn a Opportunities William Tucker died on January 25, 1995 of master's degree at Toronto and then a Ph.D. at complications of congestive heart failure. A Princeton. He arrived at Princeton in 1929 and pillar of the MAA for many years, he left be• remained there the rest of his life (except for hind a mathematical career of education, re• sabbatical and fellowship leaves). His research search, and service with few equals. in topology led to appointment and promotion at Princeton, culminating in the Albert B. Dod Albert William ('AI') Tucker was born in Professorship of Mathematics in 1954. He was Ontario, Canada in 1905. His father was a chair of the Princeton Mathematics Department mathematics teacher and later became a Pres• from 1954 to 1964. byterian minister. Al Tucker's life reflected his father's in its love of mathematics, high In 1948 George Dantzig, the father of linear moral standards, and concern for others. While programming, visited Princeton to try to inter• Tucker excelled in school, his only chance to est John von Neumann in studying the math• go to a university rested in winning one oftwo ematical foundations of linear programming. The Mathematical province-wide scholarships to the University Von Neumann was uninterested, but Tucker, who Association of America of Toronto. When he failed to eam one during happened to give Dantzig a ride to the train sta• 1529 Eighteenth Street. NW his senior year, he was forced to repeat the tion on his way home, found the topic intriguing Washington. DC 20036 year to try again-this time successfully. He and expressed interest in studying it. Thus be• planned to become a school mathematics See Tucker on page 3 FOCUS April 1995 Editorial FOCUS This is the story of one young person at one four-year college. It has a happy ending. But FOCUS is published by The Mathematical if the story is at all indicative of what happens elsewhere, then it carries a worrying Association of America, 1529 Eighteenth message. Street Northwest, Washington, DC 20036- Last December, Melissa, as I will call her, completed her first semester of college 1385, six times a year: February, April, June, mathematics. She was one of a small number of students in the class who scored an A. August, October, and December. Her instructor remarked that not only was she one of the brightest students in the class, Editor and Chair of the MAA Newsletter she was also one of the most active in terms of class participation. Nothing remarkable Editorial Committee: Keith J. Devlin, so far. We might not get as many A-students as we would like, but there are plenty of them Saint Mary's College of California about. Associate Editor: Donald J. Albers, MAA Melissa was a little unusual in that she was only 15 when the course began, having Associate Executive Director and Director enrolled for two college courses while still ajunior at the local high school. But again, of Publications and Programs nothing remarkable. There are plenty of examples of such early developers. Managing Editor: Harry Waldman, MAA What might surprise you is to learn that Melissa's grade in high school math the previous Production Specialist: Amy Stephenson• year had been C and that the high school had refused to let her take any further math Fabbri, MAA courses unless she repeated the entire course and scored a B or better. Proofreader: Meredith Zimmerman, You might also raise an eyebrow to hear that the director of Special Education Programs MAA for the district had recently advised Melissa that she should leave school early, forget her desire to study science, and seek a career as an air hostess. (I should perhaps explain the Copy Editor: Nancy Wilson, Saint Mary's involvement of the Special Education unit. Melissa has a number of diagnosed learning College of California disabilities that qualify her for a modified education program as a 'Section 504' student. Letters to the editor should be addressed to: The disabilities manifest themselves largely in her writing, and the recommended modi• Keith Devlin, Saint Mary's College of fications consist solely of being allowed extra time to take exams and complete assign• California, P.O. Box 3517, Moraga, CA ments.) 94575; e-mail: [email protected] "Perhaps Melissa's mathematical talent had been so hidden that the high school math• The FOCUS subscription price to individual ematics teachers and the Special Ed director had failed to see it," you might hazard. members of the Association is $6.00, Maybe, but you should know that, as a 504 student, Melissa had undergone an intensive included in the annual dues. (Annual dues program of testing by an educational psychologist, who had classified Melissa as in the for regular members, exclusive of annual 95 percentile in most intellectual categories and the 99 percentile in some of them. On subscription prices for MAA journals, are top of that, Melissa's father is a professional mathematician, and had spent a consider• $68.00. Student and unemployed members receive a 66 percent discount; emeritus able time trying to explain to the school math teacher that his daughter's relatively minor members recei ve a 50 percent discount; new educational disabilities obscured a remarkable mathematical ability. At the start of the members receive a 40 percent discount for year he had predicted to the teacher that Melissa would score a C on the course if little the first two membership years.) or no allowance were made for her learning disability (she did score a C) and would perform extremely well if given adequate time (she scored a 97%, the highest mark in Copyright © 1995 by The Mathematical the class, when allowed extra time in an end-of-semester examination). Association of America (Incorporated). Educational institutions may reproduce So what on earth went wrong? How could a high school mathematics teacher get it so articles for their own use, but not for sale, wrong? How could a trained director of Special Education Programs get it so wrong? I provided that the following citation is used: should point out that the school system in question is generally regarded as one of the "Reprinted with permission of FOCUS, the best public school systems in the nation, with all the numerical indicators putting it in newsletter ofThe Mathematical Association the top 95 percentile. of America (Incorporated)." Before I suggest an answer to the above questions, I should come clean and admit that Second-class postage paid at Washington, the "Melissa" of this story really is called Melissa, and she is my daughter. This is how DC and additional mailing offices. I come to know so much about this case. Postmaster: Send address changes to the Membership and Subscriptions De• Having talked at some length with the math teacher involved, I think that a large part of partment, The Mathematical Association of the problem is that she and I had entirely different conceptions of what mathematics is. America, 1529 Eighteenth Street Northwest, Though the teacher espoused all the fashionable rhetoric about mathematics being cre• Washington, DC 20036-1385. ative and the importance of focusing mathematics education on open-ended discovery, ISSN: 0731-2040 she did not seem to believe it. For this teacher, when the chalk hit the board, mathematics Printed in the United States of America. was about the mastery of dull, mindless, algorithmic procedures. To her, Melissa's 'how' Printed on recycled paper. and 'why' questions---questions that were to impress her college instructor a few months later-indicated a lack of basic understanding that simply obstructed progress in the mechanics. For this teacher, success was measured not in striving for genuine under• standing but in learning how to solve the problems in the book. If this is a one off story, then the worst that has happened is that one young child had an unfortunate experience and I have wasted good editorial space. Melissa has left school See Editorial on page 3 2 April 1995 FOCUS

Tucker from page 1 ulty from small levels, including chair of the influential gan Tucker's second mathematical career, colleges. He spent College Board Commission on School in mathematical programming and game half of the 1956- Mathematics. He was an advisor to Alfred theory, a career that produced the famous 57 academic year P. Sloan on the establishment of the Sloan complementary slackness conditions of on the train as the Fellowship program. He was the found• linear programming, the Kuhn-Tucker MAA National r~.. ing editor of the Princeton Mathematics theorem, and more. In the next dozen years, Lecturer, giving Notes series and the Annals ofMathemat• he helped train most of the initial leaders over one hundred ics Studies series. His many honors in• in this field, people such as Kuhn, Gale, talks and visiting cluded a 1961 honorary degree from Wolfe, Shapley, Goldman, Luce, Balinski, over sixty colleges across the country. Dartmouth and the 1980 von Neumann Edmonds, and Lucas. Eight of the gradu• (This was a record number of visits in Prize ofthe operations research societies. ate students and post-docs supported on the national lecturer program; when John his mathematical programming research Kemeny, the succeeding MAANational His dedication to teaching and to his stu• project went on to become members of the Lecturer, tried to match Tucker's num• dents is what friends will remember most. National Academy of Sciences in applied ber, he collapsed in mid-year with a se• When he was a graduate student teaching mathematics, economics, and computer rious bout of pneumonia.) calculus, he believed that the professor science. They included Ralph Gomory, overseeing the course, who taught a sec• His instructional style was characterized former IBM vice president for research tion of honors students, was pacing the by great attention to communicating con• and current head of the Sloan Foundation, course too fast for other students. Tucker's cepts precisely and concisely. A classic and Marvin Minsky, director of the MIT repeated protests led to dismissal proceed• example of this style is the now famous Artificial Intelligence Lab. Another, John ings from Princeton, but he put his respon• Prisoner's Dilemma which he developed Nash, was awarded the 1994 Nobel Me• sibility to his students above everything in 1950 for a lecture to a group of psy• morial Prize in economics for results in else (a sympathetic dean rescued him). In chology faculty interested in uses of mod• his 1950 thesis under Tucker. 1945 at age 40 he stopped submitting his em mathematics with psychology. research papers to journals in order to gi ve Tucker befriended and served as a mentor Al Tucker was one of the first recipients younger colleagues a better chance to get to hundreds of talented mathematical of the MAA's Distinguished Service published (he used conference proceed• minds at Princeton and elsewhere at vari• Award, in 1968, for contributions that ings and Annals Studies volumes instead). ous stages in their careers. For example, included serving as MAA president, In the 1950s and 1960s while he was de• von Neumann disapproved of Nash 's new AAAS vice-president, and the initial partment chair, he maintained a full two• approach to game theory but Tucker, mathematical consultant to the course-a-semester teaching load and was unfazed by von Neumann's opinion, en• President's Council of Scientific Advi• the coordinator for the freshman calculus couraged Nash to strike out on his own. sors. He held numerous leadership posi• course in fall or spring. He explained: "As During this period, Tucker also taught a tions in mathematics education efforts at chair of the department, I felt it was my score of continuing education summer the doctoral, undergraduate, and school duty to lead the freshman calculus course courses to high school teachers and to fac- because it was the most important activity Editorial from page 2 year, with student after student, at school of the department." and is now established in college with a after school, in state after state, but with• He is survived by his second wife Mary, 4.0 GPA. Her love of mathematics and out the happy ending. For that would rep• three children, and six grandchildren. The science has been rekindled and she talks resent a huge and tragic loss of intellectual children continue his tradition of profes• of majoring in mathematics. Her intense talent that we can ill afford to squander. sional service: sons Alan and Tom are past feeling of being let down by a school sys• And if that is indeed what is happening, MAA first vice-presidents and currently then it seems that we, the professional tem that seemed to care more for its nu• serve as chairs of the MAA Education mathematicians of the country, are the ones merical ratings than the education of the Council and CUPM, respectively, while who have to act. We have to find a way to individual students has not transferred to daughter Barbara is special assistant to the ensure that future generations of math• a general dislike of learning. As I said at president of Brown University responsible the start, Melissa's story has a happy end• ematics teachers really understand math• for the $500 million Annenberg Program ing. ematics, that they acquire not just the rhetoric of good math teaching but the for Schools. But what if this is not a one off story? substance, and that they are able to recog• What if there are hundreds and thousands The friends of A. W. Tucker have nize genuine mathematical talent when it of Melissas spread across the nation? established a fund to name is placed in their care. Judy Roitman has Melissas whose parents are not mathema• a room in the MAA Washington something to say on this important issue ticians able to spot their children's abili• in this month's Personal Opinion section oMce after him. ties. Melissas whose parents are not in a on page 9. position of being able to persuade a local Contributions can be sent to the college to ignore the school record and -Keith Devlin MAA BuDding Fund, Tucker enroll them in appropriate courses. The above opinions are those of the Room, MAA, 1529 18th St. NW, What worries me is the thought of FOCUS editor; and do not necessarily rep• Washington, DC 20036. Melissa's story being repeated year after resent the official view of the MAA. 3 FOCUS April 1995

John Nash and the Nobel Prize Thus, the improvement vector v is pro• portional to the strategy vector s. Now David Gale Suppose in a given n-tuple some player is (key observation) there must be at least getting a payoff ofp by playing the mixed The December issue of FOCUS had as one pure strategy, say, the kth, such that 1tk strategy s. We will say that her ith pure lead article an excellent and informative is positive while k is not improving, for if strategy is improving ifby switching from exposition by editor Keith Devlin of the all such pure strategies gave a payoff higher s to strategy i she would get a payoff Pj accomplishments of John Nash leading to than p then so would s. It follows that the which exceeds p (again assuming the other his being awarded the Nobel Prize in eco• proportionality constant 2.jVj in (*) is zero, players do not change their strategies). An nomics. I would like to point out, how• so all improvements are zero and s is an equilibrium point is then an n-tuple in ever, that it contains one, well actually two, equilibrium point. which no player has any improving pure inaccuracies. First, a minor historical strategy. Define the improvement Vj from This clean and economical proof was typi• point. I was not, as the article stated, a switching to strategy i by cal of Nash the mathematician but it was, fellow graduate student of Nash's but was of course, not the reason he was awarded a Fine Instructor, having gotten my de• v. = { Pj - P if i is improving the Nobel Prize. Nor was it the fact that he gree the year before. The reason I got into I 0 otherwise. defined the concept of eqUilibrium point; the act was that John's official adviser, Al Theimprovementk-vector, v=(v .. ··, vk)is this rather natural notion had already been Tucker, was away on sabbatical that year l the vector whose ith coordinate is v .. defined quite explicitly back in the 19th and I was acting as a sort of go between. I century. Nash's achievement was to show The Nash mapping is now N( cr) + cr', where On a more substantive mathematical mat• that, in what was then and probably still is for each s in cr, ter, in talking about Nash's proof of the the most important case, equilibrium equilibrium point theorem, the article N(s) = s' = (s + v)/(i + 2.jVj ). points actually existed. Since Nash's dis• states that, "Both the Proceedings an• covery there have been at least dozens and (The denominator in this formula is nec• nouncement and the Annals version use more likely hundreds of research papers essary in order to make s' a probability the more general Kakutani's Fixed Point on the subject of non-cooperative games vector.) By the Brouwer Theorem this Theorem (1946) in place of Brouwer. "This and in almost all of them the primary ob• (clearly continuous) mapping has a fixed is not correct. The quickie proof in the jective is to find and characterize the prop• n-tuple. If cr is an eqUilibrium point, then NAS Proceedings did use the Kakutani erties of the Nash equilibria. It might be by definition all the v's are zero so cr is a Theorem, but in the Annals version Nash's said that Nash's result gave birth to an fixed point. The problem is to show that, lovely proof, which also takes barely a entire theory, and this is a thing that doesn't conversely, every fixed point is an equi• paragraph, uses only the Brouwer Theo• happen very often. librium point, so suppose cr is a fixed point, rem. I realize that FOCUS does not nor• and hence each mixed strategy satisfies mally publish proofs, but in view of its David Gale is a professor ofmathematics historical importance perhaps an excep• (*) s = (s + v)/(i + 2.jv) at the University of California at Berke• ley. tion could be made in this case, so here is for each of the players. Nash's charming argument, slightly ex• panded for expository purposes. New Undergraduate Research Prize Funded Recalling Devlin's exposition, we are The new prize for undergraduate students ... stands to recognize and encourage the dealing with a game in which each of n in mathematics (FOCUS, December excellent mathematical research that un• players has a finite set of pure strategies. 1994, p. 4) has recently been funded by a dergraduates are already doing. Under• A mixed strategy s is simply a probability gift from Mrs. Brennie Morgan of Allen• graduates are working on problems of distribution on (or convex combinations town, Pennsylvania. The gift will endow current research interest, proving theo• of) these pure strategies: s = (pI .. ··' Pk)' a $1 ()()() prize to be awarded annually for rems, writing up results for publication, where Pj is the probability with which the outstanding research in mathematics by and giving talks on their work. They are ith pure strategy is played. For any n-tuple an undergraduate student or group of stu• making significant contributions to math• of pure strategies s = (Sl .. ··' s.) there is a dents from any college or university in ematics." (real number)payojfPj to each of the play• the U.S. or its possessions, Canada, or To apply, undergraduates submit one or ers and this payoff extends in the obvious Mexico. more published or unpublished papers that way to n-tuples of mixed strategies. Such The prize, to be known as the Frank and represent their work. Professors can also an n-tuple is an equilibrium point if no Brennie Morgan Prize for Outstanding nominate students. To be eligible for the player can increase his payoff by switch• Research in Mathematics by an Under• first award, students must have been un• ing to a new strategy, assuming the other graduate Student, will be awarded jointly dergraduates in December 1994 and must players do not switch theirs. by the AMS, MAA, and SIAM. submit their papers no later than June 30, Nash proves that every game has an equi• Frank Morgan, a professor of mathemat• 1995. Details on the application proce• librium point by defining a mapping from ics at Williams College, whose mother, dure will be announced on the WorldWide the set of n-tuples of mixed strategies to Brennie Morgan, endowed the prize, said Web SIAM Undergraduate Home Page itself as follows: this about the new award: "The new prize in the future (http://spicerack.unh.edu/ -siamug). 4 April 1995 FOCUS The Craft of Teaching David S. Moore Remarks on receiving the MAA's 1994 denied, in practice if not in words, by the statistics course Awardfor Distinguished College or Uni• faculty culture of research universities. for liberal arts versity Teaching of Mathematics, San That culture is now under intense pres• majors, in Francisco, California, January 1995. sure, and will surely change. Requiring which I dispar• that teachers reach at least the journey• aged anecdotal In thinking about what I might offer on man level in the craft of teaching is a evidence. I'm this occasion, I reread the remarks of my change that is already in progress. going to disparage anecdotal evidence illustrious predecessors Alan Tucker and about teaching. Remember the J. J. Price. I can hardly surpass Alan Here's a less controversial deduction from statistician's motto: "In God we trust; all Tucker's account of "The Joy of Teach• the fact that teaching is a craft: good teach• others bring data." Our individual experi• ing,"13 enriched by his father's experiences ing is based on the teacher's learning. We ence, both as students and later as teach• as well as his own. My colleague J. J. Price teach in large measure because we love ers, is atypical. As students, we were the also mentions his father, and I can hardly learning. survivors, the fittest by some quite eso• surpass his enthusiasm and his mix of good "Learning" naturally means first of all teric standards of fitness. As teachers, we advice and instructive anecdotes. 12 learning our subject. Statistics, which is tend to rely on "what works for me." What So, at the risk of dishonoring my father• my subject, is connected with a large body we think works for us may in fact be rela• yes, he too was a teacher, and so was my of nonacademic professional practice. The tively ineffective. There is an abundance mother-I will offer remarks on a differ• continuing revolution in computing has of evidence from the study of innovations ent theme. The theme is announced by my transformed the practice of statistics in the in all fields that loosely designed uncon• title. I also note that I found nothing to generation since I left graduate school. A trolled studies give innovations a much disagree with in Alan's and J. J.'s com• bit more slowly, our standards of what higher rate of success than more careful ments on teaching. Nothing tunes the neu• constitutes interesting research have also studies, especially controlled randomized rons like a little disagreement, so I'm going changed. More slowly yet, the content of experiments. A rule of thumb for assess• to say some things you may disagree with. introductory instruction has changed. It is ing innovations in education is that all In fact, since there is no time for nuance, fair to say that statistics as a field has drawn innovations succeed in the hands of the I'll be deliberately provocative and say a bit away from mathematics back toward innovator, and that none succeed in other some things that you will disagree with. its roots in scientific inference and analy• hands. That rule is fortunately not quite sis of data. The content of up-to-date in• true, but it is true enough to be disconcert• Teaching As A Craft struction, even for beginners, looks quite ing. different now than it did a generation ago. Some teachers may have charisma. Not I. Learning About Teaching My image of a sound teacher is that of a The reports of the ASA-MAA joint focus group on statistics reflect these shifts in skilled craftworker, a master machinist, I am convinced that we mathematical sci• the field. If you teach statistics-particu• say, who knows exactly what she must do, entists have much to learn from the psy• larly if you are a mathematician rather than brings the tools she needs, does the work chologists and education researchers who a statistician-their reports are a good with straightforward competence, and can provide data rather than anecdote. So place to continue learning the subject. I My takes pleasure in ajob well done. She does radical a conviction must start with a con• her work right every day, and every day's own views on the content of basic statis• version experience. Here it is. 9 10 work fits the larger plan of her project. tics instruction appear in Moore 1992. • Near the beginning of my career, I was The craftworker's skill is quite separate I have considerable empathy for mathema• walking to a meeting with a senior educa• from her enthusiasm on that particular day, ticians who find themselves teaching sta• tional psychologist. Out of politeness, I which, as C. S. Lewis said in another con• tistics, because I too was trained as a asked what he was doing. He had graduate text, depends more on the state of our di• mathematician. Jack Kiefer, the great students sitting in the back of college class• gestion than on any more cosmic influence. mathematical statistician who was my Ph.D. advisor, sent me out into the world rooms with stopwatches. I felt that glow A craft is a collection of learned skills with these words, "There's lots of statis• of superiority that comes from knowing accompanied by experienced judgment. tics any sociologist knows that you don't that I, unlike my colleague, did real re• The great advantage of thinking of teach• know." I have tried to learn. search. What had they found? "Wait thirty ing as a craft is the recognition that any• seconds," he said. "Very few teachers wait But learning our subject can be assumed. one can learn it. Competent teaching long enough when they ask a question of I want to talk primarily about requires no special gift, no actor's person• learning to the class. Wait thirty seconds." I tried it. Gerald Alexanderson's letter ask• ality, no divine spark. And if anyone can teach. Thirty seconds of silence seems intermi• ing me to make this presentation said that learn to be a competent teacher, then all nable; then the students began to respond "anecdotal accounts of novel approaches who are employed to teach have the obli• to the question. The psychologist was right. are especially encouraged." I read his let• gation to learn. That seems a mild and ter just after teaching the first class of a obvious deduction. It has, however, been See Craft of Teaching on page 6 5 FOCUS April 1995

Craft of Teaching from page 5 "Of course." What Should We Be Learning That put an end to my mathematician's "Evaluating value added after ten years Now? contempt for people who sit in the back of isn't feasible. So we can't evaluate teach• classrooms with stopwatches. ing." Learning continues through a teacher's life. For example, when I was embarking Shortly thereafter, during one of the re• "Wonderful! I knew that all along." curring debates about student evaluation on a large video project, I consulted a of teaching, I read several surveys on the I suggest that this is simply an attempt to colleague in Purdue's Department of Com• subject by educational psychologists. avoid being held accountable for our work. munications (a discipline even more What do students respond to when they Learning is the student's responsibility. declasse than educational psychology). He evaluate our teaching? Here, based on lots Our job is to provide a framework for learn• pointed me to literature on the cognitive of data,8 are the big three in order: ing. One reason why evaluating learning effects of video. I learned some interest• is a poor way to evaluate teaching is that ing and helpful principles-see Moore. 11 I. Instructional skill (talk to the class rather students compensate. Ifthe teacher is poor, At the present, teachers who keep learn• than to the board, give clear explanations, they spend more time with the text, or even ing about teaching ought to be thinking foster student participation, give relevant meet to learn from each other. This last about applications, etc.) strategy is so effective that a really bad • Active learning (alternatives to lectures) 2. Respect and rapport (especially not teacher might in principle actually improve demeaning students) learning. In practice, the students drop the • Technology, especially multimedia course, but imagining what might happen • Total Quality Management. 3. Organization (clear structure, commu• in principle allows us to say that a bad nicate expectations, efficient use of class teacher may be better than a good teacher, All of these phrases trigger emotional re• time). a statement that catches the Alice-In-Won• action in many faculty. All are surrounded Our students, with midwifery by educa• derland quality of much faculty talk about by hype, but all have genuine promise tional psychologists, offer us this three• teaching. The craftmanship of a teacher, under the hype. We ought to study before point outline of the craft of teaching. on the other hand, can be evaluated. Data we react. show that students do evaluate it, that they Active learning is the Big Idea of the cur• Enthusiasm is no substitute for craftsman• do so consistently, and that student evalu• ship. As an undergraduate at Princeton, I rent wave of reform in the teaching of the ations correlate well with peer evaluations. mathematical sciences. Both proponents once had a teacher, a justly reknowned (They do not, by the way, correlate well mathematician, whose enthusiasm for and opponents have been shouting a bit. with self evaluations.) Teachers interested The difference between the camps is that mathematics was unsurpassed. As a diffi• in data rather than anecdote might look at cult proof of a subtle result moved towards the proponents point to a body of system• the references given in chapter 48 of atic study that we ought not to simply ig• its climax, he became more animated. His Davis.2 voice rose, he wrote faster, the chalk dust nore. See, for the case of statistics, the 4 flew. When the board was full, and we I learned from education researchers what surveys by Garfield and Ahlgren and J students were writing desperately, hoping makes up the craft of teaching. Many ex• Garfield. Krantz, on the other hand, pre• to record this wisdom for later digestion, perienced teachers have of course learned fers anecdote to data: If he swept a diagonal swath across the board on their own. you read Steven Krantz's Lectures have been used to good effectfor with the eraser and wrote the triumphal recent AMS book How to Teach Math• more than 3000 years .... Turn on your tele• conclusion along the swath. ematics/ you will find similar emphases. vision and watch a self-help promoter; or The points Krantz makes most often seem a television evangelist, or a get-rich-quick Notice also that these aspects of the craft to be "Prepare!" and "Respect your stu• of teaching can be evaluated easily. Shall real estate huckster. These people are not dents!" Preparation is the key to points 1 using overhead projectors, or computer we rehearse the usual faculty conversa• and 3 in my outline and respect is exactly tion on evaluation of teaching? simulations, or Mathematica. In their own point 2. Because I will criticize Krantz a way, they are lecturing, and very effec• bit, let me first note that he gets the biggest "Of course we want to evaluate learning, tively. (p. 13) not teaching in itself." points right. As Krantz remarks, the ca• sual talk of teachers often reveals a quite This is not a nuanced discussion of the "Of course." different attitude. How often do you hear advantages and disadvantages of lectur• "And of course we want to evaluate the it suggested that this elementary and trivial ing. His attitude toward technology is simi• value added, not just what the students mathematics can be taught without care• larly simplistic: ful preparation? How often do you hear know, because otherwise we favor teach• We do not want to teach our students to laments about the sorry state of the stu• ers of well-prepared students." push buttons. We want them to think dents? You are listening to slovenly work• "Of course." analytically ... . Being able to push some ers who take no pride in their work, indeed, buttons and render a beautiful picture or who appear to think their work beneath "And of course we want to evaluate what transparency of a graph in '.l(J is not the students retain after ten years, not at the them. same as understanding the information end of the semester." contained in the graph. (p. 50)

6 April 1995 FOCUS

Of course we "do not want to teach our like to be treated as valued customers. The be managed. Have we any notion how ir• students to push buttons." We nonetheless faculty rose howling from their seats. "Stu• rational and self-centered this faculty cul• don't give them tables of the trigonomet• dents aren't our customers. TQM is an ture seems to anyone not carefully ric functions. We ought to ask, as Krantz industrial model that doesn't apply to us." socialized into it? never does, what aspects of student work There followed half an hour of denuncia• The point is not that someone other than can be fruitfully automated. We ought to tion almost completely uninformed by professors should manage our teaching. It ask, as multimedia progress encourages understanding of how TQM works in in• is rather that we have a collective respon• us to do, what aspects of the teacher's work dustry or of how its principles have been sibility to plan and organize instruction. can be fruitfully automated. We ought also modified for use in higher education. As industry (there he goes again) has to ask, as some multimedia enthusiasts do Those interested in learning before de• learned, team efforts beat individual ac• not, what roles are better reserved for nouncing might read the papers by Hogg tivity in both efficiency and quality. From human instructors. And we ought to seek and Hogg5 and Wild. 14 this broader perspective, thinking about answers from data and systematic study The point of even mentioning TQM is to TQM returns us to our starting point, the rather than from anecdote. remind ourselves that teaching is a system outline of the craft of teaching as evalu• I hope my message is clear: we can learn that we should manage. Some system prob• ated by students. You don't like the word from those whose professional subject is lems are obvious: "manage?" Talk about "prepare" and "or• the study of teaching and learning. Not of ganize" instead. You don't like thinking • Of what use are the brilliant innovations course without critical thinking of our own. of students as (in part) customers? Think you made this semester if they are not Yes, the current wave of reform does un• about "respect and rapport" instead. We institutionalized, and so vanish as soon dervalue lectures. Yes, technology is of• can change the words, but we can no longer as you leave the course? ten oversold. Nonetheless, we ought not avoid the substance of the discussion. to confuse our personal experience as • Should not students who sign up for the teachers and our professional expertise as same course actually experience the same Two Conclusions mathematical scientists with professional course in all sections every semester, My first conclusion is harsh (but true): To expertise in the field of teaching and learn• unless change is planned? improve teaching in more than local and ing. We can learn from those who do seri• Overlooking for the moment the fact that temporary ways, our culture has to change. ous work in other fields. If we are serious almost all faculty respond "No" to the about teaching, we will try to learn from • Accept that good teaching is a craft. In• second question, we see that we face man• them. Contempt for other tribes is as en• sist that all who want to practice this craft agement issues. Denunciation of TQM demic in academia as it is in human his• study it and demonstrate at least basic isn't specific: it is triggered by any men• tory. It is also narrow-minded and smug. competence. Admit that students can tion ofthe word "management." Manage• evaluate competence and have a right to TQM and All That: Managing ment of instruction opposes the attitude do so. that Krantz puts so concisely: Instruction • Accept that instruction is a shared re• The truth is that, as a college teacher; you Recently another interloper has joined sponsibility that needs collective man• are an autocrat and a monarch and can do educational research in the contempt of agement. pretty much as you please. But there is no those faculty who know about it: Total need to flaunt this before your students. • Adjust incentives: why learn a craft that Quality Management, or TQM. Your ad• (p.3) isn't rewarded? (We have now heard this ministrators almost certainly know about so often that I allow it to pass without it, as TQM is making a strong movement This is touchy, isn't it? Many of us define comment.) into the nonacademic parts of colleges and academic freedom as the right to be "an universities. Your local statisticians may autocrat and a monarch." I have encoun• My second conclusion is more positive. also know about it. For example, I spent a tered an enthusiastic young mathemati• Almost all teachers teach because they love week at Motorola two years ago learning cian who was certain that the right way to learning. With only a little redirection, our how TQM is practiced by an organization introduce the derivative to freshmen was love oflearning can be applied to improve that does it very well. via semigroups of operators. I have a col• our teaching. When the poet A. E. league who, believing against all evidence Housman was named Professor of Latin Not long ago our dean was musing about that most people learn best when presented in University College, London, in 1892, TQM at a meeting of the School of Sci• with the general case first, introduces in• his introductory lecture concerned the ence faculty council. He was pleased and tegrals and expected values as linear goals of liberal learning. Housman con• impressed by the effects of a TQM pro• functionals on quite general function siders the usual justifications, and dis• gram in the nonacademic areas at Purdue. spaces-to sophomore business students. misses them. The purpose ofliberal study, How nice it is, he said, and how remark• Both approaches are mathematically im• he says, is to awaken the joy of learning: able a change from past experience, to be peccable. Both are pedagogically disas• treated as a valued customer. The as• The pleasure of learning and knowing, trous. Can these instructors do this? Of though not the keenest, is yet the least sembled faculty nodded: how nice that course. They are professors. They are "au• those bureaucrats treat us well. Perhaps, perishable ofpleasures; the least subject tocrats and monarchs." They can do as they the dean went on, our students would also please. It is unthinkable that they should See Craft of Teaching on page 8 7 FOCUS April 1995

Craft of Teaching from page 7 4Garfield, J. and Ahlgren, A. "Difficulties ematical Association of America, 1992; to external things, and the play ofchance, in Learning Basic Concepts in Probability D. C. Hoaglin and D. S. Moore (eds). and the wear of time. And as a prudent and Statistics: Implications for Research." man puts money by to serve as a provision Journal for Research in Mathematics IOMoore, D. S. "Teaching Statistics As a for the material wants of his old age, so Education 19: 44-63. Respectable Subject." Statistics for The too he needs to lay up against the end of Twenty-First Century in MAA Notes 26. his days provision for the intellect.6 5Hogg, R. and Hogg, M. "Continuous Washington, DC: Mathematical Associa• Quality Improvement in Higher Educa• tion of America, 1992; F. Gordon and S. We teachers strive to incite our students to tion." International Statistical Review 63: Gordon (eds). lay up some provision for their intellect. 35-48. Our own catholicity of interests and obvi• IIMoore,D. S. "The Place of Video inNew 6Housman, A. E. "Introductory Lecture." ous pleasure in learning and knowing are Styles of Teaching and Learning Statis• our best allies in doing so. A. E. Housman: Selected Prose. Cam• tics." The American Statistician 47: 172- bridge, England: Cambridge University 176. References Press, 196 I; John Carter (ed). ICobb, G. "Teaching Statistics." Heeding 12Price, J. J. "Open Secrets." FOCUS 14 7Krantz, S. G. How to Teach Mathemat• the Callfor Change: Suggestionsfor Cur• (August 1994): 6-7. ics: A Personal Perspective. Providence, ricular Action in MAA Notes 22. Wash• RI: American Mathematical Society, 1993. I3Tucker, A. "Reflections on the Joy of ington, DC: Mathematical Association of Teaching." FOCUS 14 (June 1994): I & America, 1992; L. A. Steen (ed). 8Kulik, J. A. and McKeachie, W. J. "The 8. Evaluation of Teachers in Higher Educa• 2Davis, B. G. Tools for Teaching. San tion." Review of Research in Education. 14Wild, C. "Continuous Improvement of Francisco: Jossey-Bass Publishers, 1993. Itasca, IL: Peacock, 1975; F. N. Kerlin• Teaching: A Case Study in a Large Statis• 3Garfield, J. "How Students Learn Statis• ger (ed). tics Course." International Statistical tics." International Statistical Review 63: Review 63: 49-68. 9Moore, D. S. "What is Statistics." Per• 25-34. spectives on Contemporary Statistics in David S. Moore is a professor ofstatistics MAA Notes 2 I. Washington, DC: Math- at Purdue University.

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8 April 1995 FOCUS PERSONAL OPINION What Will Be the Effect of a Standards-based Education on College Students? Judy Roitman This was the title of a panel that I spoke on and the brightest will be lost, and no one When I read the at the symposium Math Reform Goes To will graduate from high school knowing Standards it is College, sponsored by the Mathematical significant mathematics. clear to me that Sciences Education Board, at the National Many opponents of the Standards add that "applications" includes applications to Academy of Sciences last year. None of in fact this has already happened. other areas of mathematics, and I have the panelists had an answer, of course, heard this view defended quite eloquently since no answer exists right now. But the I agree that basic skills, appreciation for by K-12 teachers. But when other people question raised a lot of issues, and it is algorithm, sense ofthe subject's direction, read the Standards it is clear to them that, those issues that I would like to address appreciation of formal systems and ab• as an award-winning high school teacher here. straction, and mathematical content are once told me, "Meaningful mathematics missing in many of my uni versity students, is something that a child can apply in his Just what are the Standards? and have been for a long time. I don't think or her daily life." What do we mean by we can blame the Standards for this. They applications, and how large a part should The National Council ofTeachers of Math• simply haven't been around long enough. they play in the curriculum? ematics' Curriculum and Evaluation Stan• While back in 1989 there were some cur• dards, published in 1989, took some time riculum projects compatible with the Stan• The Standards coincides with and to be noticed by mathematicians not di• dards already in existence, they had been strengthens another movement in educa• rectly involved in K-12 education, and around for only a couple of years. No child tion, the concern with equity. It's becom• probably still is not familiar to most of us. currently past 9th grade has had the possi• ing indefensible to teach a course called The Curriculum and Evaluation Standards bility of what is known as a Standards• Business Math in high school which is just was followed by the Professional Stan• based education, and very few children in arithmetic. But when you decide that no dards and about a dozen short volumes in 9th grade or earlier have spent the bulk of child of remotely normal intelligence is to an addenda series. Soon to appear are the their mathematical education in what are be thrown on the mathematical junk heap, Assessment Standards and a Framework known as Standards-based classrooms. you have to ask how to teach all children, for Constructing a Vision ofAlgebra. The Just because the NCTM formally adopted and what to teach, and this turns out to Standards, as these have collectively been them doesn't mean the average school lead to some very hard questions. What called, is exerting a profound influence on district or classroom teacher has changed worked for those of us reading this is K-12 education in the United States. As very much of what she or he does. No, the known not to work for the majority of those of us not involved directly in K-12 students in my freshman classes (some of children-that's why we literally have have become aware of the we Standards, whom are seniors who have taken fresh• thousands of students in my university have tended to divide into two camps: those man math courses many times in order to taking essentially high school mathemat• who defend the Standards and those who graduate) are products of the old system. ics (half of them in a course misnamed attack it. College Algebra) before they can take a The fact that people of good will and intel• university math course required for gradu• I defend the Standards. Here is my ver• ligence can disagree so vehemently about ation. We are not unusual in this. How are sion of what they say: The mathematics the Standards tells us that they are, in fact, we going to teach algebra and geometry that children learn in school will be mean• quite ambiguous. In some sense what you successfully and, these days, probability ingful. It will make sense, it will be cre• read into them is what you get, and just and statistics and a little finite combinato• ative, it will not be severed from other because someone says that what they do is rics, to all children, starting in kindergar• human activities, technology will be used Standards-based doesn't mean it is. I be• ten and going through high school? And appropriately, and there will be real math• lieve the Standards provides an opportu• what is the algebra and geometry and prob• ematical content. nity for real mathematics to be done in the ability and statistics and a little finite com• Here are the accusations against the Stan• classroom. Others believe the Standards binatorics that we believe all children dards: None of the above will happen. will drive real mathematics out of the class• should learn? That we believe all future Basic skills will be lost, appreciation for room. That is the overriding issue in the college students should learn? That we algorithm will be lost, in K-12 the sense debate over the Standards. believe all future engineers and scientists of the subject's direction will be lost, ap• and mathematicians and economists and preciation of formal systems will be lost, What are the controversial etc.-the heavy users of mathematics• appreciation of abstraction will be lost, issues raised by the Standards? should learn? These are hard questions. I mathematical content will be lost, the best and many others think that the best an- The Standards emphasizes applications. 9 FOCUS April 1995 swer is to strengthen the curriculum in lished a mathematics paper, have a Ph.D. be talked at or even down to; mathemati• interesting directions. But others disagree in mathematics, or teach upper division cians are considered unspeakably elitist, (read on for process vs. content). mathematics courses. While every mem• arrogant, and naive by non-mathemati• ber of the NCTM (the vast majority of cians; and folks from education depart• The Standards calls for the development whom are K-12 teachers) was given a ments are considered dull, obfuscating of mathematical reasoning. But this means chance to respond to drafts, classroom drones by mathematicians and irrelevant very different things to different people. realities made it hard to involve K-12 by K-12 teachers. Needless to say, this is Some very thoughtful high school teach• teachers on the Standards committees as not helpful. There are smart people every• ers are throwing out theorem proving in well. The Standards-writing committees where, and these smart people need to work geometry classes-the Standards doesn't were predominantly Ph.D.s in education across disciplinary turf and prejudicial tell them to do so, but they feel they have who do not teach K-12 classes. I'm not lines. permission if they see fit. On the other sure what effect this had on the actual hand, all teachers who use the Standards, I started off saying that I defend the Stan• documents, but it certainly has had its from kindergarten on, demand that chil• dards. This doesn't mean that I agree with political consequences, both in mathemat• dren defend arguments and explain their everything that supposedly supports the ics departments, and to some extent also reasons. What should mathematical rea• Standards-I couldn't, because there are in K-12 classrooms. soning mean at which level of mathemat• too many contradictory claims--or that I ics? When should formal proofs be The questions the Standards raise are consider them etched in stone for all time. introduced, and how? important ones. Whether or not the math• Yes, I believe that there are some trends ematics community has been involved in which could be dangerous in mathematics Less emphasis on algorithms the past, we need to be involved in the education-there are always dangerous The Standards calls for less emphasis on future. Each community with a major in• trends in education, although one person's standard algorithms. This doesn't neces• terest in mathematics education-the K- danger is another person's opportunity. I sarily mean no emphasis, although some 12 community, the mathematics educators, absolutely believe that mathematicians people have interpreted it that way, includ• the mathematicians-has its own perspec• need to be listened to in K-12 education, ing mathematicians. (The issue isn't algo• tive, and all of these perspectives are and that our role is considerably more than rithm vs. no algorithm, but standard needed if things are going to improve the simply nodding our heads in agreement algorithm vs. a child's discovered algo• way they should. with whatever other people have cooked up. But if we want to be listened to, we rithm.) How much emphasis on standard What should we do next? algorithms is appropriate? have to listen. We have to admit that, Now we come to the punch line, which is whether or not we agree with their conclu• There is the issue of process vs. content. I that nobody' s got everything right. We will sions, some folks who are not mathemati• see the Standards as allowing thinking, if not improve mathematics education by cians know some things we can learn from. you will, into the mathematical curricu• impugning each other's professional in• lum-that's what seems to be meant by And we have to watch ourrhetoric, or we'll tegrity, by sneering at each other's profes• process-hence allowing for more inter• continue to ensure that the mathematics sions, by assuming that we're right and esting content. A mathematics supervisor community has no voice in what is going everyone else is wrong. Yet that's exactly I know believes approvingly that process on in K-12 education. what's been happening: K-12 teachers are is so much more important than content as denigrated by college folks as people to Judith Roitman is a professorofmathemat• to make content almost not matter-the ics at the University of Kansas. purpose ofthe mathematics curriculum for her is to teach kids how to think. How much time do we devote to exploring the process of doing mathematics, and how Volunteers Wanted does this effect the content we teach? This The Association is always looking for ways to involve more members in its activities. is not an easy question. If you would like to participate more by joining an MAA committee please write me There is something else about the Stan• or contact me bye-mail requesting a form to volunteer for committee work. Let me dards which isn't always publicly talked know which committees you might be interested in joining and your experience in the about, but which probably leads to a lot of relevant area. Naturally, we cannot promise to get you onto the committee of your the resentment among mathematicians, choice. Many committees do not have openings every year. There are also some and that is that very few mathematicians committees for which there are more volunteers than we can appoint. But the Commit• were involved in their creation. People tee on Committees will do what it can. Please let me hear from you. don't talk about it because when you do you get very angry responses of, "Oh yeah, G. L. Alexanderson, MAA Secretary just how do you define 'mathematician,' Department of Mathematics you elitist mathematician you." But it's a Santa Clara University fact that very few of the people involved Santa Clara. CA 95053 in writing any of the Standards have pub- e-mail: [email protected]

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~ 1995 Wolfram Research,Inc MalhemaflCalsa Jeglstered trademafk 01 WOlfram Research,lnc MarhematlCa IS not assocaated WIth MathemallCa PolICy Resean:h. 1nc or MathTech,1nt All other product names mentioned are trademarb of their IJ1)(\l.alrs FOCUS April 1995 A Building for Mathematicians

If you were asked to design a brand new buildingforyourcampus in which to teach and do mathematics. what would it look like and what would you put in it? Geraldine Wojno Kiefer. a marketing con• sultant for the architectural firm of van Kent State's new mathematics building with Entrance lobby shows colorfully clad geo• its geometric outlines and sine curve roof metric forms and Fibonacci sequence floor Dijk. Pace. Westlake & Partners. in Cleve• pattern. land. Ohio. describes the process and the outcome for one campus that did just that. When Kent State's Department of Math• ematics and Computer Sciences found themselves in need of a new building a few years ago, they decided they wanted more than the simple four walls and a roof: what was required, they felt, was a build• ing that captured the spirit of the disci• plines that would be in the new building. The mathematics library with its sine curve A close view of the library ceiling and clere• Rapid growth and differentiation within ceiling. story windows. the department, among other factors, had number of private colleges and secondary At the initiation of the project, the archi• led to the university's decision to house it schools in northeastern Ohio. tect made two lengthy visits of existing in its own facility. Originally located on departmental facilities, discussing, then The process of realizing the new building two floors of an older building, with refining relevant issues, problems, and began with a detailed program worked out courses taught campus-wide, by the late potential solutions. In addition, the project by the department, led by Richard K. 1980s Mathematical Sciences was feel• team visited other facilities on campus Brown, director of operations at ICM (In• ing a double strain: overcrowding and which met the department's criteria, for stitute for Computational Mathematics, a dispersion. Faculty offices were too few example, an auditorium for industrial en• department program which supports re• in number for needed privacy, the math• gineering. During the initial, schematic search in mathematics and computer sci• ematics library was too small, and there design process, a number of schemes were ence), and Olaf P. Stackelberg, chair of was little space for interaction. Although essayed in a hands-on review process. A the Department of Mathematics and Com• highly focused in program and curricu• consensus was reached very quickly and puter Science. Not only did this program lum, the department lacked a physical what the building would become emerged. outline needed facilities and space require• focus. The expansion of the campus had During the next design stage, three-dimen• ments, prioritizing three key areas (a math• resulted in the construction of three adja• sional physical models called "layer cakes" ematics library, colloquium room, and cent science buildings to the east of a new were prepared, showing floor-to-floor re• lounge), it also diagrammed, in "bubble" student union and library complex. lationships and major volumes. These were fashion, key departmental and interdepart• also made explicit in isometric and per• There was an obvious location for the new mental relationships. For example, the spective color drawings generated through building-opposite the Biology and colloquium room was given a centralized the architect's CAD system. Again the Chemistry buildings and facing Summit place, easily accessible from faculty and colloquium room provides an apt example: Street, the main east-west artery. The graduate student offices, and adjacent to parabolic and asymmetrical, thus complex oblong site suited the building perfectly, seminar rooms, classrooms, and computer in plan, this space was represented in sev• and rotating the main classroom/office labs. Although the planning and design eral drawings and from various positions building back from the adjoining computer process would result in alterations to this to show that its shape would provide op• labs provided space for a welcoming out• initial diagram, particularly since the func• timum visibility for audiences as well as door court. tions were rearranged over three floors, for resident and visiting lecturers. The architectural firm chosen to carry out key relationships remained intact. Further stages of design development re• the design, van Dijk, Pace, Westlake & This and other "simple" resolutions, not sulted in the preparation of detailed plans, Partners, was a known presence on cam• the least of which was the timely and on• elevations, and a model, which were made pus, having designed the Biology Build• budget completion of the building, re• available to facuIty and graduate students ing in 1968. Other academic credits flected a highly successful collaborative for review and comment. The final design included facilities for the University of process in which the architect and depart• emerged from a complex approval pro- Akron, Cleveland State University, and a mental representatives functioned as a team. 12 April 1995 FOCUS

ations. cess involving numerous representatives Flexibility and functionality are apparent Letter to the Editor of the state and the university, as well as throughout the building, including its com• Dear Keith, the departmental-architectural project petently integrated computer network .. The team. The department was so fully behind network, controlled through a centralized Having just read for the second time your the design that when state officials twice computer facility on the first floor, inter• editorial in the December 1994 FOCUS, I challenged the library-the building's connects every office, classroom, semi• can only second your comments. Our stu• flagship space-Brown and Stackelberg nar, and presentation room. The dents have been taught to take and pass convinced them that it was not only nec• department is also electronically linked to tests. They have come to desire algorithms essary, but to be retained exactly as de• the campus-wide computer network, to the for passing exams, and have little patience, signed. Ohio Academic Research Network if any, for understanding. They can not be legitimately blamed, for we have made The department wanted a facility that was (OARNET), and the worldwide Internet. them what they are, even if it is painfully not only functional, but distinctive. The The construction budget did not permit annoying. When I teach freshman calcu• architect responded with shapes, volumes, utilization of state-of-the-art fiber optics lus, I spend an enormous amount of time materials, and detailing that symbolize technology, but the design team was able directly and indirectly ironing out the mathematics. "One look at the building to integrate that capability into the design wrinkles put in their minds by some poorly makes it clear that it has to be a math de• by wiring the building for future fiber prepared high school teacher. partment," Stackelberg said. connections. As part of a very successful college team The roof is expressed as a sine wave which Ifone word were to be selected to describe to help the teaching of mathematics in high is repeated in the interior linear metal ceil• Kent State's new Mathematical Sciences schools, I have great sympathy for the usual ing. An undulating, sloping roof plane, the facility, it would be "interactive." The American high school teacher. I have an• ceiling drops down from the clerestory product of an intensive, continual dialogue ecdotes sufficient to fill a barge, painful, which gives even, north lighting. Natural between faculty, graduate students, and exciting, and heartbreaking in the extreme. lighting is controlled to protect the architects, the facility fosters interaction. departmenfs volumes. Up and down fluo• Every effort was made to maintain the Roger Pinkham rescent lighting, perpendicular to the intimacy and camaraderie that character• Stevens Institute o/Technology stacks, is also controlled to reduce glare ized the department in its original loca• and eliminate shadows. The colloquium, tion. computer lab wing, ground floor classroom Perhaps the finest accolade, recently given wing, and stair and elevator tower are in• by a student, was comparison of the build• terrelated mathematical forms, expressing ing to a temple, a place with abiding spirit. the "building blocks" of the program. The A spirited expression for the 90s, it prom• manipulation of economical materials• ises to energize its functions and the uni• metal, brick, and Dryvit on the exterior, versity well into the millennium. and paint and vinyl wall covering in the interior-is innovative and striking. Underwood Dudley New P61ya Lecturer A variety of sophisticated, elegant, yet preeminently functional cues mark Kent Professor Underwood Dudley of DePauw University in State's Mathematical Sciences Building Indiana has been chosen by the Board of Governors to be as an architectural and mathematical suc• the MAA's fifth George P6lya Lecturer. Previous P6lya cess, including ample, well lit hallways Lecturers have been John Ewing, Patricia K. Rogers, Carl with "break-out" spaces for discussion and Pomerance, and Robert Osserman. vistas to the surrounding campus; ample offices, each with a blackboard, flexible Professor Dudley received his bachelor's and master's de• storage area, and its own window; a modu• grees from the Carnegie Institute of Technology and his lated primary color scheme with each pri• Ph.D. from the University of Michigan, Ann Arbor, where mary keyed to a single floor; a thoughtfully he wrote his dissertation in number theory under the super• designed faculty lounge whose progres• vision of William LeVeque. After two years at Ohio State sively expanding volume culminates in a University he moved to DePauw where he has taught since 1967 and where he was spacious, dramatic view to the country• department chair from 1990 to 1993. He is the author or editor of several popular books: side; and a commodious student lounge Elementary Number Theory, A Budget ofTrisections, Mathematical Cranks, and Read• easily accessed from both entrances. Even ings for Calculus. He holds the record for length of service as an associate editor of the classrooms, the bare bones, cannot be Mathematics Maga<:ine-eightMn years and still counting. He has also served as as• dismissed as standard. Radiant ceiling sociate editor of the American Mathematical Monthly (1992- ), as editor of the Pi Mu heating provides unobstructed floor space Epsilon Journal (1993- ), and as editor of the New Mathematical Library series of the for a variety of seating and discussion situ- MAA (1994- ). From 1979 to 1980 he was president of the MAA's Indiana Section. His Erdos number is 1.

13 FOCUS April 1995 ATLAST 1995 Linear Algebra Workshops Mathematics Labs ATLAST is an NSF project to augment the teaching of linear algebra through the use of for DERIVE software tools. Two faculty workshops on the use of software in teaching linear algebra will be offered this summer. Participants will learn about existing commercial linear June 5-9, 1995 algebra software packages and will be trained in the use of the MATIAB software package. Attendees will learn how to incorporate computer exercises and laboratories The MD-DC-VA Section will sponsor into undergraduate linear algebra courses effectively. this five-day workshop at Frostburg State University on the western shore of Mary• Participants will work with exercises from the forthcoming ATLAST book and will be land. This is the twenty-first year that the expected to design additional computing exercises at a level suitable for assigning to an section has sponsored a workshop. undergraduate linear algebra class. These exercises will be class tested during the school year following the workshop and then submitted to the project director for inclusion in Dr. Marvin Brubaker (Messiah College) the ATLAST database. Some of these exercises will either be included in later editions and Dr. Carl Leinbach (Gettysburg Col• of the ATLAST book or made available to the general public through the Mathematics lege) will be the presenters. They have been Archives at the University of Tennessee, Knoxville. very active in presenting regional and na• tional workshops on the applications of The project was conceived by the Education Committee of the International Linear DERIVE to mathematics. This popular, Algebra Society (ILAS). Steven J. Leon of the ILAS Education Committee serves as the inexpensive, and easily-learned computer ATLAST project director and the assistant director is Richard Faulkenberry. Both are in algebra package will be used to amplify the Mathematics Department of the University of Massachusetts at Dartmouth. The and extend learning experiences in calcu• ATLAST project is funded by a National Science Foundation faculty enhancement lus, linear algebra, and differential equa• grant. tions. The cost for the workshop, including This is the fourth year of ATLAST workshops. Past workshops have been a rousing fees, room (double occupancy), and board success. We are confident that the 1995 workshops will be even better. is $260. 1995 ATLAST Workshops and Presenters Further information is available from Jack Biggs, Dept. of Math, Frostburg State Uni• June 21-24 July 19-22 versity, Frostburg, MD 21532; (301) 689- Seattle University, Washington College of William & Mary, Virginia 4181; or Ben Fusaro, Dept. of Math Dr. Jane Day, San Jose State University Dr. David Hill, Temple University Sciences, Salisbury State University, Salisbury, MD 2180 I; (410) 543-6470. All teachers of undergraduate linear algebra courses at colleges or universities in the U.S. are invited to apply. The deadline for applications is March 20, 1995. Late appli• cations will be accepted on a space available basis. Each workshop is limited to thirty Functioning in the participants. The ATLAST Project provides room and board for all participants ac• cepted. A screening committee will review applications and notify applicants early in Real World April. For further information and application forms, contact Steven Leon, ATLAST Project Director, Department of Mathematics, University of Massachusetts at Dartmouth, The Math ModelinglPreCalculus Dartmouth, MA 02747; (508) 999-8320; fax: (508) 999-8901; e-mail:atlast@umassd. Reform Project edu. An NSF-Supported Faculty Workshop Long Island, NY, June 9-10, 1995 Calculus in a Real and Complex World See an alternative to standard Precalcu• July 17-21, 1995, University of Massachusetts at Amherst lus or Algebraffrig courses in the spirit of the Calculus reform movement. The Due to the large number of applicants and the great success oflast year's workshop, this emphasis is on applications of mathemat• NSF-funded workshop will be offered again this summer. ics' focusing on families of functions, All expenses for tuition, room, board, and study materials will be provided for high fitting functions to data, difference equa• school, college, and university calculus instructors. There will be hands-on experience tions, modeling periodic phenomena, with Mathematica computer software and TI -82 calculator-based laboratory and graph• probability simulations, and applications ing calculator; small and large group discussion on pedagogy, assessment, and content; of matrix algebra. The course can serve an overview of calculus reform efforts nationally; and experience developing course either as a one- or two-semester prepara• materials. tion for calculus or as a capstone math• ematics experience. The presenters include Frank Wattenberg, who developed and wrote the textbook and !Mathematica-based lab manual for Calculus in a Real and Complex World and taught For further information, contact Sheldon it for six years, and Mary Ann Connors, who has taught the course for two years. Gordon, Suffolk Community College; (516) 451-4270; e-mail: sgordon@ Information and applications are available from Mary Ann Connors, Department of ccmail.sunysb.edu. Mathematics and Statistics, Lederle Graduate Research Tower, University of Massa• chusetts, Amherst MA 01003; (413) 545-0907; e-mail: mconnors@math. umass.edu.

14 April 1995 FOCUS Calculus Reform Workshop Program Ten years ago at the Anaheim Joint Math• In addition, participants will be asked to that often accompany curriculum reform ematics Meetings, the AMS-MAA panel consider their own situations and formu• (e.g., the need for new resources, skepti• discussion on "Calculus Instruction, Cru• late plans of action for their home institu• cism of client disciplines, colleague resis• cial But Ailing" launched a movement to tions. tance). reform the way calculus is taught in this Workshop instructors will be drawn from For general information, contact Don country. Numerous reformed programs the ranks of those who have led the reform Small, Department of Math Sciences, have been developed, several with seed movement. They will share their experi• USMA, West Point NY 10996;(914)938- money from the NSF, in which content ences as curriculum reformers and, in 2227; fax: (914) 938-2409; e-mail: has been streamlined, applications have particular, how they overcame obstacles [email protected]. been stressed, technology has been ex• ploited, and pedagogy has been changed. Small group projects, writing assignments, 1995 NSF Calculus Reform Workshops multiple representation of functions, and Call or write the local contact for specific information. a renewed emphasis on learning how to learn mathematics are characteristic of May 28-June 2 Calculus June 18-23 St. Olaf Project reformed programs. Reform: Activities and Projects Instructors: Arnie Ostebee and Paul Zorn The NSF has recently renewed funding Instructors: Don Small (U.S. Military (St. Olaf College) for a program of calculus reform work• Academy) and Willie Taylor (Texas Local Contact: Clayton Dodge shops directed by Don Small (U.S. Mili• Southern University) Dept. of Math tary Academy). The purpose of these Local Contact: Della Bell University of Maine workshops is to disseminate the fruits of Dept. of Math Orono, ME 04469-5752 the reformed programs on a national level Texas Southern University (207) 581-3908 wherever calculus is taught-high Houston, TX 77004 schools, community colleges, four-year (713) 527-7002 June 18-23 Harvard colleges, and universities. There will be Consortium Project sixteen one-week workshops offered, June 5-10 Integrated/Core Instructors: Wade Ellis, Jr. and Ed Lodi eight each in the summers of 1995 and (West Valley Community College) 1996, at sites nationwide. Each workshop Approach to Calculus Local Contact: Denny Burzynski will have twenty-four participants chosen Instructors: Chris Arney and Don Small Dept. of Math not only because they teach calculus, but (U.S. Military Academy) West Valley Community College because they exercise leadership in the Local Contact: Marie Vanisko Saratoga, CA 95070-5697 high schools, community and four-year Dept. of Math (408) 374-0741 colleges, and universities in their areas. Carroll College All expenses except travel will be paid by Helena, MT 59625 June 18-23 Calculus Resources the NSF grant. (406) 447-4451 Instructors: Wayne Roberts (Macalester These five important threads will be wo• College) and Marcella Beacham (Daly ven through each workshop. June 11-16 Calculus in Context College) I. History and present state of the Calcu• Instructors: Harriet Pollatsek and Don Local Contact: James Wilson lus Reform Movement O'Shea (Mount Holyoke College) Dept. of Math Local Contact: David Ford Daly College 2. Participant involvement as a student Dept. of Math 6741 S. Indiana Ave under the pedagogy being promoted by Emory University Chicago, IL 60637 the Calculus Reform Movement Atlanta, GA 30322-2390 (312) 838-7632 3. In-depth experience in the reform pro• (404) 727-7962 gram associated with the workshop July 9-14 An Active instructors and a general overview of June 18-23 Project Calc Approach with Projects other major reform programs Instructors: David Smith and Lang Moore (Duke University) Instructors: Steve Hilbert and Diane 4. Experience in the use of technology for Local Contact: Joel Cohen Schwartz (Ithaca College) teaching mathematics Dept. of Math Local Contact: Chris Christensen 5. Participant input ("My Favorite Prob• University of Denver Dept. of Math lem," development of a curriculum Denver, CO 80208-0001 Northern Kentucky University topic, etc.) (303) 871-3292 Highland Heights, KY 41076 (606) 572-6672

15 FOCUS April 1995 Program in Mathematics for Young Scientists (PROMYS) Boston University, July 2-August 12, 1995 PROMYS offers a lively mathematical solving group which meets with a profes• obtained from PROMYS, Department of environment in which ambitious high sional mathematician three times per week. Mathematics, Boston University, III school students explore the creative world Special lectures by outside speakers offer Cummington Street, Boston, MA 02215; of mathematics. Through their intensive a broad view of mathematics and its role (617) 353-2563. Applications will be ac• efforts to solve a large assortment of un• in the sciences. cepted until June I, 1995. usually challenging problems in number PROMYS is a residential program de• theory, the participants practice the art of 1995 Summer Graphing signed for sixty high school students en• mathematical discovery-numerical ex• tering grades 10 through 12. Admission Calculator Short Course ploration, formulation and critique of con• decisions will be based on the following jectures, and techniques of proof and criteria: applicants' solutions to a set of for College Faculty generalization. More experienced partici• challenging problems included with the pants may also study abstract algebra, com• application packet; teacher recommenda• Organized by Frank Demana and binatorics, and the Riemann zeta function. tions; high school transcripts; and student Problem sets are accompanied by daily Bert Waits, Ohio State University essays explaining their interest in the pro• lectures gi ven by research mathematicians gram. The estimated cost to participants is Twenty-seven one-week short courses with extensive experience in Professor $1300 for room and board. Books may are scheduled for the summer of 1995 Arnold Ross's long-standing summer cost an additional $100. Financial aid is for college faculty at sites around the Mathematics Program at Ohio State Uni• United States. There is a $150 registra• versity. In addition, a highly competent available. PROMYS is dedicated to the principle that no student will be unable to tion fee. To obtain more information, staff of eighteen college-aged counselors attend because of financial need. write Bert Waits and Frank Demana, lives in the dormitories and is always avail• Short Course Program, Department of able to discuss mathematics with students. PROMYS is directed by Professor Glenn Mathematics, The Ohio State Univer• Each participant belongs to a problem Stevens. Application materials can be sity, 231 West 18thAve., Columbus, OH 43210. Eleventh Annual Allegheny Mountain 1995 American Section Summer Short Course Regions Math The course will be held June 26--30 and will be given by Fernando Gouvea of Colby College. The five-day workshop examines the background work necessary to under• League Competition stand the basic mathematics behind the current work in the proof of Fermat's Last Theorem. The American Regions Math League an• nounces its 1995 competition, June 2-3, Topics include: at Pennsylvania State University and the University of Iowa. If teams are inter• • Modular fonns, the easy part (definition, Heeke operators, eigenfonns, L• ested, ARML is ready to open a third site functions) at the University of Nevada at Las Ve• gas. • Elliptic curves, the easy part (definition, minimal Weierstrass fonn, invariants, group structure, reduction mod p. L-functions) TheARMLcompetition is the largest on• site event ofits kind in the country, draw• • Elliptic Curves. the fancy part (torsion points, Galois representations) ing fifteen-member teams of high school • Modular fonns, the fancy part (functional equation for the L-function. the students from every region. Teams are Heeke algebra, Galois representations, the Taniyama conjecture) organized on a local basis. For infonna• tion on organizing an ARML team or • Ribet and Wiles: the Frey curve and its Galois representation, defonnation joining an existing team, contact Mark theory and Wiles' theorem. Saul, 711 AmsterdamAvenue, New York, NY 10025; (212) 666-5188; e-mail: The course will be held at Allegheny College. Course registration is $120 and room and 73047,[email protected] or Bar• board is $140, for a total of $260. bara Rocrow, Bronx High School of Sci• For further information and an application, contact George Bradley, Department of ence, 75 West 205 St., Bronx, NY 10468. Mathematics and Computer Science, Duquesne University, Pittsburgh, PA 15282; (412) 396-5115; e-mail: [email protected].

16 April 1995 FOCUS MAA to Dedicate Headquarters Room to Benjamin Banneker On May 19, 1995 the MAA will dedicate In 1791, he made the astronomical obser• Residing on a farm his a room in honor of Benjamin Banneker in vations to determine the survey lines for entire life, people the refurbished Dolciani Mathematical the District of Columbia. It has been said would travel to visit Center in Washington, DC. that he was the first African American him throughout his federal employee. That same year, he com• Banneker was a self-taught mathemati• later years. He sup• pleted calculations of the motions of the cian, astronomer, and free man of color, posedly kept a log of sun, moon, planets, and tides for the first who was born in 1731 in Baltimore County, the ones who he felt of his seven almanacs, which appeared in Maryland, near what is now Ellicott City. were most important. 1792. He had only a few years of schooling, Bannekerdied peace• during which arithmetic was the only Banneker wrote to Secretary of State Tho• fully on an October Sunday in 1806, fol• mathematics he was taught. The one-room mas Jefferson in August 1791, attacking lowing a walk. He was 74 years old. schoolhouse he attended was open only notions of Black inferiority and including Many of the scientific instruments and during winter months, and when Banneker his almanac in manuscript form. Jefferson books Banneker used were returned to his was old enough to farm full-time with his forwarded the almanac to the Academy of friend George Ellicott, but only two of his father, he could no longer attend class. Sciences in Paris with a letter citing it as personal items survived him: his Bible and Later in his life he studied more advanced evidence ofthe equal talents of Blacks and a featherbed. All other possessions, includ• topics, including trigonometry and loga• describing its author as "a very respect• ing manuscript copies of his almanacs as rithms. At age 57, he used borrowed in• able mathematician" who had been em• well as his famed clock, were destroyed in struments and texts to teach himself ployed in the survey of the District. his house, which caught fire while he was astronomy. Jefferson also referred to the very elegant being buried. solutions of geometrical problems by His first scientific achievement was the Banneker. Both Banneker's letter and completion of a wooden clock which he Although numerous rooms in the Dolciani Jefferson's reply were published in the hand carved and assembled after having Center have been named to commemo• almanac of 1793 to strengthen the anti• seen only two timepieces, a pocket watch rate mathematicians, until now none have slavery movement. and a sundial. People came from miles been for a prominent minority mathema• tician. This recognition for Benjamin around to see it and hear it strike the hour. He was known to be extremely well read, Banneker will make the mathematics com• Completed in 1753, the wooden clock a lover of nature, devout, and talented in munity and society at large more aware of operated with precision until his death over music and rhyme (he would sometimes his contributions and those of other mi• fifty years later. pose mathematical problems in rhyme). nority mathematicians. Planned Giving Program off to a Good Start MAA Mastercard Many MAA members have enthusiastically table remainder trust. Gerald Porter, MAA responded to former President Don Treasurer, told the Board how easy it was The MAA has signed an agreement with Kreider's request of last November to in• to donate the proceeds of a life insurance MBNA to create an MAA MasterCard clude the MAAin their estate planning. This policy and announced that he was mak• that will be offered to all MAA members request was accompanied by a copy of the ing the MAA the beneficiary of a life in• with no annual fee. The MAA will re• new MAA newsletter LEGACY, devoted to surance policy. Linda Hill, the Chair of ceive a royalty for each new account that ideas and practical advice about estate plan• the MAA Committee on Sections and remains open 90 days and a percentage ning. It was sent to all members aged 50 or member of the Executive Committee, also of all charges made on the MAA cards. older. announced a gift of life insurance, as did The agreement was approved by the Marcia P. Sward, MAA Executive Direc• Since the MAA has a small endowment for Board of Governors at its meeting on tor. an organization of its size, the Board of August 14, 1994 as a service to members Governors approved a planned giving cam• Ifyou would like acopy of LEGACY, How and as a way of raising funds to support paign to ensure the Association's future to Make a Will that Works, and Better Es• the MAA. You should have received a fiscal strength and its capacity to respond tate Planning, or a personal financial af• flyer in the mail describing the card. You positively to the needs of its members and fairs record that will help you organize all are, of course, under no obligation to the mathematical community in general. your major financial records into one accept it. As part of the marketing agree• As a result of the new program, several document, contact Maureen Callanan at ment, MBNA will call selected individu• Board members announced planned gifts the MAA bye-mail at [email protected] als as a follow up to the mailing. We to the MAA, totalling about $278,000. or by phone at 1-800-331-1622. If you apologize for any inconvenience this may President Kenneth Ross disclosed a major would like to discuss the planned giving cause. charitable gift from his parents, Edward and program in more detail, please call Marcia Edith Ross Brinn, in the form of a chari- P. Sward at the same number. 17 FOCUS April 1995

81. He was an MAA member for 48 years. R. Kent Nagle, professor, University of In Memoriam South Florida, died in October 1994, at 47. Robert Goldrick, software specialist, He was an MAA member for 14 years. BertilAnderson, retired, Plandome, NY, died Grumman Aerospace, died at 39. He was an Peter O'Halloran, associate professor, Uni• on September 22, 1994 at 90. He was an MAA member for 9 years. versity of Canberra, Australia died on Octo• MAA member for 24 years. Dennis Grantham, associate professor, East ber 25, 1994 at 63. He was an MAA member FrankAyres, retired, Dickinson College, died Texas State University, died on January 24, for 16 years. He also was the founder of the on August 6, 1994 at 93. He was an MAA 1995 at 55. He was an MAA member for 28 Australian Mathematics Competitions and member for 73 years. years. the Australian Mathematical Olympiad Stewart Baker, retired mathematician, Na• Frank S. Hawthorne, retired, New York State Committee, and past president of the tional Security Agency, died on January 16, Education Department, died on February II, Canberra Mathematical Association. 1994. He was an MAA member for 62 years. 1995 at 80. He was an MAA member for 52 John Oxley, retired, New York, NY, died on years. Gerald Becker, professor emeritus, San Di• September 22, 1994 at 67. He was an MAA ego State University, died on July 3, 1994 at Clarence Heinke, professor emeritus, Capi• member for 44 years. 70. He was an MAA member for 36 years. tal University, died on July 8, 1994 at 81. He Hasell Palmer, retired, North Augusta, SC, was an MAA member for 48 years. Raymond Frank Bell, professor emeritus, died on June 2, 1994. He was an MAA mem• West Virginia Institute of Technology, died Adrien Hess, retired, Montana State Uni• ber for 46 years. on October 25, 1994 at 83. He was an MAA versity, died on May 23, 1994 at 86. She was Joseph Pekarsky, retired, New Jersey Insti• member for 61 years. an MAA member for 38 years. tute of Technology, has died at 77. He was Mabel Nowlan Bomhoff, retired, St. Peters• Aughtum Howard, retired, Eastern Kentucky an MAA member for 19 years. burg, FL, has died at 98. She was an MAA University, died on October 14, 1994 at 87. O. Peterson, retired department chair, Em• member for 61 years. She was an MAA member for 50 years. poria State University, died in November J. Maxey Brooke, retired, Dallas, TX, died Jerry W. Jones, department chair, Aiken 1994 at 92. He was an MAA member for 71 on April 13, 1993. He was an MAA member Technical College, has died at 49. He was an years. for 31 years. MAA member for 24 years. Ted Raburn, vice-president, Internet Systems Paul Clifford, retired professor, Montclair Andrew Kirby, retired, Fordham University, Corporation, has died at 48. He was an MAA State College, has died. He was an MAA has died. He was an MAA member for 48 member for 7 years. member for 46 years. years. Joseph Rich, retired physicist, G.E. Corpo• Ronald Deford, professor emeritus, U ni ver• Anita Levine, professor emeritus, Cupertino, ration, Research and Development Center, sity of Texas at Austin, died at 92. He was an CA, has died at 83. She was an MAA mem• died in March 1994 at 77. He was an MAA MAA member for one year. ber for 49 years. member for 34 years. James Desmond, associate professor, John Lewis, retired, Teaneck, NJ, died on Leon Robbins, Wayne, PA, died on Decem• Pensacola Junior College, died on August August 13, 1994 at 84. He was an MAA ber 19, 1993. He was an MAA member for 17, 1993, at 58. He was an MAA member member for 55 years. 39 years. for 28 years. Mrs. R. McLean, retired, Loyola University, E. Roessler, professor emeritus, University Elden Egbers, retired, Olympia, WA, died died on November 6, 1994 at 72. She was an of California, Davis, has died. He was an on March 20, 1994 at 72. He was an MAA MAA member for 42 years. MAA member for 55 years. member for 34 years. Lyle Mehlenbacher, professor emeritus, Bertram Ross, professor emeritus, Univer• Richard Eiseman, consultant, Rand Corpo• University of Detriot, has died at 84. He was sity of New Haven, died in October J 993 at ration has died. He was an MAA member an MAA member for 57 years. 76. He was an MAA member for 33 years. for 29 years. William Meyer, retired professor, Univer• Rafael Sanchez-Diaz, professor emeritus, Nathan Fine, retired, Pennsylvania State sity of Chicago, died on November 17, 1993 New Mexico Institute of Mining and Tech• University, died on November 18, 1994 at at 78. He was an MAA member for 51 years. nology, died on January I, 1993 at 91. He was an MAA member for 42 years. 78. He was an MAA member for 52 years. Clark C. Miller, president, Clark C. Miller Joseph Fontana, associate professor, Uni• Corporation died on July 28, 1994 at 51. He Leslie Whitford, retired, Dayton, OH, has versity of Alabama, died on July 3, 1994, at was an MAA member for 13 years. died. She was an MAA member for 35 years. 62. He was an MAA member for 5 years. William Miner, retired, Raleigh, NC, died Annie John Williams, Durham High School, Leonard Fuller, retired professor, Kansas on December23, 1993 at 77. He was anMAA Durham, NC, died on November 19, 1994 State University, has died. He was an MAA member for 30 years. at 81. She was an MAA memberfor45 years. member for 47 years. Bill C. Moore, retired, Texas A&M, died on William Wooten, Lake San Marcos, CA, has Aaron Galuter, Chelsea Publishing, New October 3, 1993, at 86. He was an MAA died. He was an MAA member for 36 years. York, NY died at 77. He was an MAA mem• member for 60 years. Royal Zeigler, retired, Radium Springs, NM, ber for 32 years. William Munro, retired professor, Univer• died on September 10, 1994 at 74. He was an Basil Gillman, professor emeritus, Drake sity of Minnesota, died on January 20, 1993 MAA member for 47 years. University, died on November 22, 1994 at at 77. He was an MAA member for 53 years. 18 April 1995 FOCUS MathFest, Burlington, Vermont 1:15 p.m.-2:35 p.m. MAA PANEL DIS• August 5-9, 1995 CUSSION NCTM: A vision of algebra. I: 15 p.m.-3: 15 p.m. MAA MINICOURSE #1: PART A Interdisciplinary lively ap• Sweet New England plications. What do you get when you combine Doris 1:15p.m.-3:15p.m.MAAMINICOURSE Schattschneider, Andrew Granville, a teddy bear factory, a #4: PART A An activity-based approach cider mill, a museum, and a cruise on Lake Champlain? to teaching introductory statistics. 2:00 p.m.-3:30 p.m. AMS COMMITTEE If you are a mathematician or a family member of a mathematician, the answer is a good ON SCIENCE POLICY PANEL DIS• time. Burlington, Vermont is the place. August 5-9 is the time. And the MAA-AMS CUSSION MathFest is the occasion. 2:45 p.m.-5:oo p.m. MAA STUDENT PA• Competing with the gorgeous scenery and the friendly welcome of summertime New PER SESSIONS England, the MAA and AMS have planned a varied array of sessions for those who 2:45 p.m.-5:00 p.m. PME CONTRIB• decide to combine business with pleasure and make the trip to Burlington. UTED PAPER SESSIONS Schattschneider's MAA Earle Raymond Hedrick Lectures will cover the topics of tiling, 3:00 p.m.-4:30 p.m. AWM PANEL DIS• symmetry and order, and aperiodicity and quasicrystals, and Granville will give an CUSSION AMS-MAA invited address titled It's as easy as ABC. These are just two of the many 2:50 p.m.-4:10 p.m. MAA PANEL DIS• mathematical highlights on the packed three-day program of events. CUSSION The SSIs and systematic re• Non-mathematical attractions include a dinner and cruise on Lake Champlain, a visit to form in mathematics. the Shelburne Museum, a trip in the Green Mountains, a visit to Cold Hollow Cider Mill, 3:15p.m.-5:15p.m.MAAMINICOURSE and a tour of the Vermont Teddy Bear Factory. #3: PART A Calculus: An active ap• Who could bear to miss this event? proach with projects. 3: 15 p.m.-5: 15 p.m. MAAMINICOURSE #5: PART A The use of software in an introductory linear algebra course. 4:00 p.m.-6:00 p.m. MAA SECTION SATURDAY, AUGUST 5 Lecture I Thefascination oftiling. Doris OFFICERS MEETING J. Schattschneider 4:30 p.m.-5:00 p.m. AWM MEMBER• 9:00 a.m.-5:oo p.m. MAA BOARD OF 10:40 a.m.-12: 10 p.m. AMS PROGRESS GOVERNORS SHIP MEETING IN MATHEMATICS LECTURE Fully MAA CONTRIBUTED PAPER SES• Noon-4:00 p.m. MATHFEST REGIS• nonlinear elliptic second order equa• SIONS TRATION tions: Recent development. Nicolai V. 1:00 p.m.-5:oo p.m. OPTIONAL TOUR Krylov 4: 10 p.m.-6:oo p.m. Achieving K-12 and Higher Education Collaboration in Sys• OF SHELBURNE MUSEUM 12:25 p.m.-12:55 p.m. AMS BUSINESS temic Reform Programs, I. 1:00 p.m.-6:00 p.m. AMS COUNCIL MEETING 4: 10 p.m.-6:oo p.m. Interactive Mathemat• MEETING 1:00 p.m.-2:30 p.m. PME COUNCIL ics Video Games, I. 6:30 p.m.-1O:oo p.m. OPENING BAN• MEETING 4: 10 p.m.-6:oo p.m. Popularizing Math• QUET AND RECEPTION 1:15 p.m.-2:05 p.m. MAA-MU ALPHA ematics, I. SUNDAY, AUGUST 6 THETA INVITED ADDRESS A math• ematical kaleidoscope for motivation 4:25 p.m.-5:45 p.m. MAA PANEL DIS• 8:00 a.m.-4:oo p.m. MATHFEST REG• and understanding. Jeanne F. Nelson CUSSION Reform ofthe preparation of mathematics teachers. ISTRATION MAA CONTRIBUTED PAPER SES• 8:30a.m.-9:20a.m.AMS-MAAINVITED SIONS 4:25 p.m.-5:45 p.m. MAA PANEL DIS• CUSSION Using real data in an intro• ADDRESS It S as easy as ABC. Andrew I: 15 p.m.-4:05 p.m. Implications of the ductory statistics course. J. Granville NCTM Standards for College Level 9:00 a.m.-5:oo p.m. MAA COMMITTEE Teaching, I 5:15 p.m.-6:15 p.m. MAA-PME STU• DENT RECEPTION ON STUDENT CHAPTERS HOSPI• 1:15 p.m.-4:05 p.m. Symbolic Computa• TALITY CENTER tion in the Undergraduate Mathematics 6:30 p.m.-9:30 p.m. OPTIONAL DIN• 9:00 a.m.-5:oo p.m. BOOK SALES AND Classroom, I NER AND CRUISE ON LAKE CHAMPLAIN EXHIBITS 1:15 p.m.-4:05 p.m. Innovative Teaching 9:35 a.m.-IO:25 a.m. MAA EARLE in First-Year College Mathematics 9:30 p.m.-ll:oo p.m. AWM OPEN RE• RAYMOND HEDRICK LECTURES: Courses, I CEPTION 19 FOCUS April 1995

MONDAY, AUGUST 7 2:45 p.m.-4: 15 p.m. AMS COMMITTEE Robert D. MacPherson ON EDUCATION PANEL DISCUS• 12:25 p.m.-12:55 p.m. MAA BUSINESS 7:00 a.m.-8:30 a.m. BREAKFAST FOR SION MEETING MAA STUDENT CHAPTER FAC• 4:oop.m.-6:oo p.m. MAA MINICOURSE ULTY ADVISORS, SECTION COOR• 1:40 p.m.-2:30 p.m. MAA STUDENT #2: PART A Instructional aspects of DINATORS, AND PME ADVISORS LECTURE Cauchy, Dirichlet, and the mathematics on the Internet. birth ofreal analysis. David M. Bressoud 8:00 a.m.-4:oo p.m. MATHFEST REG• MAA CONTRIBUTED PAPER SES• ISTRATION MAA CONTRIBUTED PAPER SES• SIONS SIONS 8:30 a.m.-9:20 a.m. AMS-MAA INVIT• 4:05 p.m.-6:00 p.m. Implications of the ED ADDRESS Strings, beams, mem• 1:40 p.m.-3:35 p.m. Innovative Teaching NCTM Standards for College Level branes, and plates: Finding properties in First- Year College Mathematics Teaching, II. ofvibrating systems from nodes or nodal Courses, II. lines Joyce R. McLaughlin 4:05 p.m.-6:oo p.m. Symbolic Computa• 1:40 p.m.-4:45 p.m. Popularizing Math• tion in the Undergraduate Mathematics 9:00 a.m.-5:oo p.m. MAA COMMITTEE ematics, II. Classroom, II. ON STUDENT CHAPTERS HOSPI• 1:40 p.m.-3:40 p.m. MAA WORKSHOP TALITY CENTER 4:15 p.m.-5:40 p.m. MAA SPECIAL ON SCHOOL REFORM PRESENTATION Does the culture in 9:00 a.m.-5:00 p.m. BOOK SALES AND 1:45 p.m.-3:45 p.m. MAA MINICOURSE mathematics really need changing? EXHIBITS #1: PART B Interdisciplinary lively ap• 4:30 p.m.-6:oo p.m. MAA PANEL DIS• 9:35 a.m.-lO:25 a.m. MAA EARLE plications. CUSSION Using EPIC in calculus and RAYMOND HEDRICK LECTURES: pre-calculus classes. 1:45 p.m.-3:45 p.m. MAA MINICOURSE Lecture I Symmetry and order. Doris J. #2: PART B Instructional aspects of Schattschneider 4:30 p.m.-6:00 p.m. MAA PANEL DIS• mathematics on the Internet. CUSSION Assessment in the age of the 1:00 p.m.-I :50 p.m. NAM DAVID graphing calculator. 1:45 p.m.-3:45 p.m. MAA MINICOURSE BLACKWELL INVITED ADDRESS #3: PART B Calculus: An active ap• Speaker and title to be announced. 6:45 p.m.-8: 15 p.m. PME BANQUET proach with projects. I :oop.m.-3:oop.m. MAA MINICOURSE 8:30 p.m.-9:30 p.m. PME J. SUTHER• 2:45 p.m.-4:45 p.m. MAA STUDENT #4: PART B An activity-based approach LAND FRAME LECTURE Tilings as WORKSHOP ON THE INTERNET diffraction gratings. Marjorie Senechal to teaching introductory statistics. 3: 15 p.m.-4:40 p.m. MAA SPECIAL I :00 p.m.-3:00p.m. MAAMINICOURSE 8:30 p.m.-I 0:00 p.m. COMMITTEE ON PRESENTATION A reform college al• #5: PART B The use of software in an THE PARTICIPATION OF WOMEN gebra curriculum integrating technol• introductory linear algebra course. SPECIAL PRESENTATION Are we ogy. there yet? The Off-Off-Broadway ver• MAA CONTRIBUTED PAPER SES• sion. 4:00 p.m.-5:30 p.m. MAA PANEL DIS• SIONS CUSSION NCTM's core curriculum: 1:00 p.m.-3:35 p.m. Achieving K-12 and TUESDAY, AUGUST 8 Making mathematics count for every• one-The big ideas. Higher Education Collaboration in Sys• 8:00 a.m.-Noon MATHFEST REGIS• temic Reform Programs, II. TRATION 5:45 p.m.-9:00 p.m. MAA RECEPTION AND BANQUET FOR 25-YEAR I :oop.m.-3:55 p.m. Interactive Mathemat• 8:30 a.m.-9:20 a.m. AMS-MAA INVIT• MEMBERS ics Video Games, II. ED ADDRESS Title to be announced. 1:00 p.m.-5:00 p.m. MAA STUDENT Brian C. White WEDNESDAY, AUGUST 9 PAPER SESSIONS 9:00 a.m.-5:oo p.m. MAA COMMITTEE 9:15 a.m.-3:30 p.m. OPTIONAL TOUR 1:00 p.m.-5:00 p.m. PME CONTRIB• ON STUDENT CHAPTERS HOSPI• LAKE CHAMPLAIN SCENIC FERRY / UTED PAPER SESSIONS TALITY CENTER AUSABLE CHASM 1:00 p.m.-2:25 p.m. MAA PANEL DIS• 9:00 a.m.-5:00 p.m. OPTIONAL TOUR CUSSION An interdisciplinary view of STOWE/GREEN MOUNTAINS/ changes in undergraduate SMET edu• COLD HOLLOW CIDER MILL cation. 9:00 a.m.-5:oo p.m. BOOK SALES AND 1:00 p.m.-2:50 p.m. MAA WORKSHOP EXHIBITS ON SCHOOL REFORM 9:35 a.m.-10:25 a.m. MAA EARLE 1:00 p.m.-5:oo p.m. OPTIONAL TOUR RAYMOND HEDRICK LECTURES: OF VERMONT TEDDY BEAR FAC• Lecture III Aperiodicity and TORY/SHELBURNE FARMS quasicrystals. Doris J. Schattschneider 2:35 p.m.-4:oo p.m. SUMMA SPECIAL 10:40 a.m.-12: 10 p.m. AMS PROGRESS PRESENTATION Intervention projects IN MATHEMATICS LECTURE for minority precollege students. Compactifications of spaces of lattices.

20 April 1995 FOCUS

for motivation and understanding, (MAA• Diane D. Schwartz, Stanley E. Seltzer, Burlington, Vermont Mu Alpha Theta Lecture); Sunday, 1:15 and Eric E. Robinson, Ithaca College. Part p.m. A: Sunday, 3:30 p.m.-5:30 p.m.; Part B: University of Vermont Tuesday, 1:45 p.m.-3:45 p.m. Enrollment August 6-8, 1995 MAA Minicourses limit: 40; registration fee: $45. This Minicourse # 1: Interdisciplinary lively minicourse will address issues relating to Burlington MathFest including the 97th applications, organized by Frank R. the use of group projects and in-class ac• Summer Meeting of the AMS, 73rd Sum• Giordano and David C. Arney, United tivities in calculus, including an overview, mer Meeting of the Mathematical Asso• States Military Academy. Part A: Sunday, examples of projects and activities, and ciation of America (MAA), and summer 1:15p.m.-3: 15 p.m.; PartB: Tuesday, 1:45 the impact on the curriculum. The orga• meetings of the Association for Women in p.m.-3:45 p.m. Enrollment limit: 40; reg• nizers, who have been teaching calculus Mathematics (AWM) and Pi Mu Epsilon istration fee: $45. Interdisciplinary appli• using group projects since spring 1989, (PME). cations can be used to weld mathematics have found that open-ended projects chal• lenge students to develop problem-solv• The Joint Meetings Committee which with the concepts of other disciplines to ing skills beyond looking for a similar bears the financial responsibility for these provide student growth in modeling and problem solved in the text or class notes. meetings has made decisions to reduce problem solving. This minicourse will They use in-class activities to help the stu• costs by eliminating some traditional ser• discuss projects that can be used in a wide dents to become active learners and to vices at MathFests and making substitu• range of mathematics courses, with the develop the skills to successfully complete tions for some others. We hope that applications related to subjects in chemis• the projects. participants will support these changes as try, biology, physics, engineering, eco• a way to make the MathFest financially nomics, technology, and social sciences. Minicourse # 4: An activity-based ap• viable. Associate secretary: Robert J. Projects are designed to take four to six proach to teaching introductory statistics, Daverman. hours of student effort and can be done in organized by Richard L. ScheatTer, Uni• groups or individually, and some require versity of Florida, and Ann E. Watkins, A special MAA task force on the school• a computer or calculator. Participants will California State University, Northridge. college interface, chaired by R. D. Ander• work with materials prepared for students Part A: Sunday, 1: 15 p.m.-3: 15 p.m.; Part son, is organizing several panel and instructors in printed, video, and multi• B: Monday, 1:00 p.m.-3:00 p.m. Enroll• discussions, workshops, and a session of media formats. ment limit: 40; registration fee: $45. This contributed papers dealing especially with minicourse is for teachers of introductory the NSF's initiatives on systemic reform Minicourse # 2: Instructional aspects of statistics who want to change their course and with several NCTM reports. mathematics on the Internet, organized by Brian E. Smith, Dawson College from a traditionallecture-and-listen model AMS-MAA Invited Addresses (Montreal), and Sandra Villas, DonaAna to activity-based lessons. Participants will Andrew J. Granville, University of Geor• Community College. PartA: Monday, 4:00 be engaged in a series of field-tested, gia, It sas easy as ABC, Sunday, 8:30 a.m. p.m.-6:00p.m.; PartB:Tuesday, 1:45 p.m.- hands-on activities that illustrate many of 3:45 p.m. Enrollment limit: 40; registra• the key concepts taught in an introductory Joyce R. McLaughlin, Rensselaer Poly• tion fee: $65. The orientation of this statistics course. They will play the role of technic Institute, Strings, beams, mem• minicourse is on locating mathematics students, actually working through a se• branes, and plates: Finding properties of resources on the Internet and using them lection of activities. Experienced instruc• vibrating systems from nodes or nodal in the mathematics classroom or labora• tors will explain how they have made use lines, Monday, 8:30 a.m. tory. One part of the course will focus on of the activities in various settings. Each Brian C. White, Stanford University, Title identifying different types of mathemati• participant will be supplied with copies of to be announced, Tuesday, 8:30 a.m. cal resources and the Internet search tools the student pages and the instructor notes, which are required to locate them. We will which include suggestions for assessment describe how to find FTPsites for archived for the activities. This Activities-Based 73rd Summer files, using ARCHIE servers; Gopher serv• Statistics (ABS) project is funded by the Meeting of the MAA ers' and the VERONICA searches that find NSF. them will also be discussed. The second Minicourse # 5: The use ofsoftware in an part of the course will deal with applica• MAA Invited Addresses introductory linear algebra course, orga• tions of the Internet in the teaching of nized by Homer F. Bechtell, University Doris J. Schattschneider, Moravian Col• undergraduate mathematics, and specific of New Hampshire. Part A: Sunday, 3:30 lege; Lecture I: The fascination of tiling; examples will be presented. The course p.m.-5:30p.m.;PartB:Monday,I:00p.m.- Lecture II: Symmetry and order; and Lec• will involve a combination of demonstra• 3:00 p.m. Enrollment limit: 80; registra• ture III: Aperiodicity and quasicrystals tions and hands-on experience; handouts tion fee: $45. The focus of this minicourse (Earle Raymond Hedrick Lectures); Sun• will be provided. is on developing goals and strategies for day, Monday, and Tuesday, 9:35 a.m. Minicourse # 3: Calculus: An active ap• the successful implementation of com• Jeanne F. Nelson, Kamehameha Schools proach with projects, organized by puter-aided instruction into an undergradu• (Honolulu), A mathematical kaleidoscope Stephen R. Hilbert, John C. Maceli, ate introductory linear algebra course.

21 FOCUS April 1995

Emphasis is on introducing software in - Symbolic computation in the unde rg radu• ment of Mathematics and Computer Sci• order to increase mathematical maturity ate mathematics classroom, Sunday and ence, Western Carolina University, and the depth of understanding for the Monday afternoons. Organized by Ronald Cullowhee, NC 28723-9049; phone: 704- concepts without compromising the theo• I. Sklar *, Department of Computer Sci• 227 -7245; FAX: 704-227-7240; and retical development. Problem sets will be ence, St. John's University, St. Vincent's Ralph DeVane, Western Carolina Univer• distributed and the construction of prob• College, Grand Central & Utopia Park• sity. We live in the "video age", so why not lem sets will receive special attention. ways, Jamaica, NY 11439; phone: 718- make it work for us within our mathemat• Familiarity with software for linear alge• 990-6161 (X7212); FAX: 718-990-1882; ics classes? Make a math lesson out of bra is a prerequisite. During the course, e-mail: [email protected]; some video game. Utilize some "math participants will not have access to com• and Richard C.O'Lander, St. John's Uni• game" software. Write your own math puter software, but will develop outlines versity. The creative use of computer al• game software (computer or calculator). for problem sets based on their experience gebra systems is resulting in a revolution This is only one aspect of using technol• with linear algebra software. in the way we teach mathematics. These ogy, but if you have done any of the above, systems have been effectively used in share your experience with others. Please MAA Minicourses are open only to per• teaching calculus, linear algebra, differ• include a clear statement of your equip• sons who register for the MathFest and ential equations, combinatorics, probabil• ment needs. pay the regular registration fee. Interested ity, and statistics. This session invites participants should complete the MAA - Popularizing mathematics, Sunday and papers on experiences with the use of a Minicourse Advance Registration Form Tuesday afternoons. Organized by Eric symbolic computation system in teaching at the back of this issue and send it directly R. Muller*, Department of Mathematics, mathematics. Subject areas not mentioned to the MAA office so as to arrive by June Brock University, St. Catharines, Ontario, above are especially welcome. 30, 1995; the MathFest Advance Regis• L2S 3AI Canada; phone: 905-688-5550 tration/Housing Form must be sent to -Innovative teaching infirst-yearcollege (X3297); FAX: 905-682-9020; e-mail: AMS. After the deadline, potential par• mathematics courses, Sunday and Tues• [email protected]; and Ber• ticipants should call the MAA headquar• day afternoons. Organized by Aaron I. nard R. Hodgson, Universite Laval. Pa• ters at 800-331-1622 to check on Stucker*, Department of Mathematics pers on successful activities to popularize availability. The MAA reserves the right and Statistics, Washburn University, To• mathematics are solicited. Of special in• to cancel any Minicourse which is peka, KS 66621; phone: 913-231-1010 terest are activities aimed at popularizing undersubscribed. Should this occur, those (XI491); e-mail: [email protected]; mathematics both outside the classroom, registered in advance will be notified and and Howard L. Penn, U.S. Naval Acad• among families, seniors, policy makers, will receive a full refund. emy. This session will present talks de• etc., and in the university classroom for scribing innovative techniques in the students enrolled in mathematics "service" MAA Contributed teaching of mathematics courses typically courses, including prospective elementary Paper Sessions taught in the first year of college. Innova• school teachers. Submissions should in• -Implications ofthe NCTM standards for tive techniques include (but are not lim• clude some documentation of the activi• college level teaching, Sunday and Mon• ited to) the use of technology, writing ties, some information on who developed day afternoons. Organized by Darien projects, and cooperative learning. and ran them, the segment of the popula• tion to whom they were aimed, how often Lauten*, Department of Mathematics, - Achieving K-12 and higher education the programs have run, and some indica• University of New Hampshire, Durham, collaboration in systemic reform pro• tion of their degree of success. NH 03824-3591; phone: 603-868-7133; grams, Sunday and Monday afternoons. FAX: 603-862-4096; e-mail: dlauten@ Organized by Richard D. Anderson*, Submission procedures for MAA con• christa.unh.edu. New secondary math• Louisiana Systemic Initiative Program, tributed papers: Sessions generally must ematics curriculum projects funded by the 1885 Wooddale Boulevard, II th floor, limit presentations to ten minutes, but se• National Science Foundation engage stu• Baton Rouge, LA 70806; phone: 504-922- lected participants may extend their con• dents in learning situations aligned with 0690; FAX: 504-922-0688. With much tributions up to 20 minutes. Individuals the NCTM Curriculum and Evaluation national emphasis on systemic reform of should forward the following directly to Standards for School Mathematics. Char• mathematics education at both the K-12 the organizer (indicated above with an *): acteristics of these projects include and higher education levels, this session the name(s) and address(es) of the changes in mathematics content, use of targets examples of effective collabora• author(s) and a one-page summary of the technology, new pedagogical approaches, tive efforts involving personnel and/or paper. The summary should enable the mathematics in context, inclusion of all institutions at the two levels. The collabo• organizer(s) to evaluate the appropriate• students, and emphasis on student under• ration, formal or informal, can be in either ness of your paper for the selected ses• standing of mathematics. As a result of or both directions. Hopefully, the examples sion. Consequently, you should include as these projects, students will arrive at will point the way for others to get in• much detailed information as possible postsecondary institutions with new ex• volved. within the one-page limitation. Your sum• pectations and experiences. This session mary must reach the designated orga• - Interactive mathematics video games, will address project approaches, teacher nizer by Monday, April 24, 1995. The Sunday and Monday afternoons. Orga• development issues, evaluation, and stu• organizer will acknowledge receipt of all dent learning. nized by Richard L. Stephens*, Depart-

22 April 1995 FOCUS paper summaries. If the organizer accepts An Interdisciplinary View of Changes Using EPIC in Calculus and Pre-calcu• your paper, you will receive a standard• in Undergraduate SMET Education: lus Classes: Monday, 4:30 p.m. to 6:00 ized abstract form and further instructions. Monday, 1:00 p.m. to 2:25 p.m, organized p.m., organized by James Burgmeier and by Susan L. Forman, Mathematical Sci• Larry L. Kost, University of Vermont. Other MAA Sessions ences Education Board (MSEB). In April Panelists will discuss the pedagogical as• NCTM: A Vision of Algebra: Sunday, the NRC and the NSF cosponsored a two• pects of using EPIC (Exploration Pro• I: 15 p.m. to 2:35 p.m., organized by Gail day convocation, From Analysis to Ac• grams In Calculus), a computer package Burrill, University of Wisconsin, Madi• tion: Undergraduate Education in Science, designed to assist students and teachers son, and president-elect of the National Mathematics, Engineering, and Technol• with the concepts and problems of calcu• Council for Teachers of Mathematics ogy (SMET). Workshops addressed issues lus. It is menu-driven, supports textbook• (NCTM) . This is a discussion of the many concerning the changing climate of un• style function input, and does both issues inherent in a reconceptualization of dergraduate SMET education for students, numerical and symbolic calculations. algebra at the school level. It is clear that faculty development and preparation, and Assessment in the Age of the Graphing changes in algebra for life in the 21 st cen• institutions. The panel will present a sum• Calculator: Monday, 4:30 p.m. to 6:00 tury must be carefully coordinated and mary of the issues and recommendations p.m., moderated by Mary M. Lindquist, jointly addressed at the K-12 and higher that emerged from the workshops. Panel Columbus College. Panelists will address education levels. The graphing calculator members include Hyman Bass, Columbia assessment issues in the interface of grades is beginning to have a profound effect on University and chair of MSEB, and Jay 9-12 and 13-14 mathematics. In some lo• what aspects of algebra students must Labov, Colby College and staff director of cales high school mathematics is adapting know, understand, and be able to do; at the the NRC Committee on Undergraduate more quickly to the existence of the graph• college level, the emerging school changes Science Education. are forcing college placement officers and ing calculator than is college-level math• mathematics faculty to rethink placement Workshops on School Reform: Monday, ematics. Thus, important issues of policy and course content, respectively. 1:00 p.m. to 2:50 p.m., and Tuesday, 1:40 placement, of assessment, and of course p.m. to 3:40 p.m., organized by Richard content are emerging. Both the ACT and The SSIs and Systemic Reform in Math• D. Anderson, Louisiana Systemic Initia• the SAT are being invited to send repre• ematics: Sunday, 2:50 p.m. to 4: 10 p.m., tive Program. The intent is to provide sentatives to participate in the panel dis• moderated by Stephanie Williamson, opportunities for broader dissemination cussion. Louisiana Systemic Initiatives Program. and dialogue within the higher education Are We There Yet? The Off-Off-Broad• Four of the ten original SSIs (Connecti• community about school mathematics way Version: Monday from 8:30 p.m. to cut, Louisiana, Montana, and Nebraska) curriculum projects and reform issues at 10:00 p.m. The Committee on Participa• have had mathematicians in key leader• the K-4, 5-8, and 9-12 levels. The projects tion of Women (Carole B. Lacampagne, ship roles. These SSIs will report on their involve substantial rethinking of what and chair) is presenting a dramatized program experiences in effecting standards-based how mathematics should be learned and on evolving gender issues in the mathemat• mathematics reform in their states, both at understood. the K -12 and higher education levels. ics community. This is a preview of a pre• SUMMA Special Presentation on Inter• sentation at the winter meetings in Reform of the Preparation of Math• vention Projects for Minority Precollege Orlando. Emphasis is placed on incidents ematics Teachers: Sunday, 4:25 p.m. to Students: Monday, 2:35 p.m. to4:oop.m., where faculty have learned how to encour• 5:45 p.m., moderated by Genevieve M. organized by WilliamA. Hawkins, MAA, age young women or resolve difficulties Knight, Coppin State College. A panel of director of SUMMA (Strengthening with colleagues. Discussions will be used representatives of the initial three NSF Underrepresented Minority Mathematics to revise the script for the presentation in Collaboratives of Excellence in Teacher Achievement). Orlando. Additional contributions are de• Preparation (Louisiana, Maryland, and sired. Please be assured that the identity of The Urban Systemic Initiative Pro• Montana) will give reports on their roles all contributors will be treated with the gram-Getting Mathematicians In• in the reform of teacher preparation in utmost confidentiality. Brief descriptions volved: Monday, 3:00 p.m. to 4:20 p.m., mathematics. All have been active in re• of incidents thought suitable for dramati• moderated by Madeleine Long, National form initiatives and have much to share zation may be sent to the scriptwriter, Science Foundation. This panel will dis• with others concerned with this issue. David E. Boliver, Department of Math• cuss issues surrounding the Urban Sys• ematics & Statistics, University of Cen• Using Real Data in an Introductory Sta• temic Initiatives recently funded by the tral Oklahoma, 100 North University tistics Course: Sunday, 4:25 p.m. to 5:45 NSF. There are opportunities for univer• Drive, Edmond, OK 73034-5209; e-mail: p.m., moderated by Robert W. Hayden, sity-level mathematicians and school per• [email protected]. Plymouth State College, forthe jointAMS• sonnel to help design and implement MAA-ASA Statistics Committee. Panel• effective professional development pro• A Reform College Algebra Curriculum ists include Richard J. Cleary, St. Michael's grams, as well as teacher preparation pro• Integrating Technology: Tuesday, 3: 15 College, Richard L. Scheaffer, University grams affecting inner-city systems. The p.m. to 4:40 p.m. Ongard Sirisaeng• of Florida, and J. Laurie Snell, Dartmouth need for collaborative efforts leading to a taksin, Linda Becerra, and William College. change of culture is evident. Waller, University of Houston-Down• town, will present this session to intro-

23 FOCUS April 1995 duce a reform college algebra curriculum Breakfast for MAA Student Chapter ture, David R. Dorman, Middlebury Col• that integrates technology as a fundamen• Faculty Advisors, Section Coordinators, lege, and David S. Dummit and Jonathan tal medium. The major emphasis is on and PME Advisors: Monday morning. W. Sands, University of Vermont; Sun• conceptual understanding based on real• Contact Apama W. Higgins, University of day, Monday, and Tuesday afternoons. world applications rather than rote drill Dayton, chair of the MAA Committee on Potential theory, Kohur N. Gowri and artificial examples. The materials are Student Chapters (higgins@udavxb. Sankaran, McGill University; Monday in the form of a series of laboratory mod• oca.udayton.edu). and Tuesday afternoons. ules. Each module consists of closed labo• ratory worksheets, open laboratory Other MAA Activities Ramsey theory, Bruce M. Landman, Uni• assignments, postlaboratory quizzes, and Board of Governors: Saturday, August versity of North Carolina, Greensboro; expository materials. The modules create 5,9:00 a.m. to 5:00 p.m. Open to all MAA Sunday, Monday, and Tuesday afternoons. a collaborati ve environment that moti vates members. Soap bubble geometry, Frank Morgan, students to explore and experiment with Section Officers: Sunday, 4:00 p.m. to Williams College; Sunday, Monday, and mathematical concepts. Mathematica 6:00p.m. Tuesday afternoons. high-level functions have been developed as a tool to nurture this learning environ• Business Meeting: Tuesday, 12:25 p.m. There also will be sessions of ten-minute ment for students with very little knowl• Open to all MAA members. contributed papers. See the January issue edge of computers. MAA Banquet for 25-year Members: for details on how to submit abstracts for all AMS sessions. Note that the deadlines NCTM's Core Curriculum: Making Tuesday, 6:30 p.m. to 9:00 p.m. Featured listed above for receipt of abstracts are Mathematics Count for Everyone-the speaker is Colin C.Adams, Williams Col• firm and late papers cannot be accommo• Big Ideas: Tuesday, 4:00p.m. t05:30p.m., lege, Mel Slugbate's bus tours of the uni• dated. moderated by James R. C. Leitzel, Uni• verse and beyond. See the Social Events versity of Nebraska, Lincoln. This panel section for ticket details. Other AMS Sessions will discuss various initiatives designed AMS Invited Addresses Committee on Science Policy Panel Dis• to change the nature of9-12 mathematics, cussion: Sunday, 2:00 p.m. to 3:30 p.m. in particular programs that concentrate on John H. Ewing, Indiana University at "Mathematics for All" at that level. The Bloomington, A century ago; a century Committee on Education Panel Discus• implications for changes in introductory from now (History of Mathematics Lec• sion: Monday, 2:45 p.m. to 4: 15 p.m. ture), Monday, 10:40 a.m. courses at the college level are important Other AMS Activities at both the developmental and Nicolai Krylov, University of Minnesota, Council Meeting: Saturday, August 5, nondevelopmental levels. Minneapolis, Fully nonlinear elliptic sec• 1:00 p.m. to 6:00 p.m. MAA Student Activities ond order equations: Recent development (Progress in Mathematics Lecture), Sun• Business Meeting: Sunday, 12:25 p.m. David M. Bressoud, Macalester College, day, 10:40 a.m. Cauchy, Dirichlet, and the birth of real Activities of analysis, Tuesday, I :40 p.m. (Student Robert D. MacPherson, Institutefor Ad• Other Organizations Lecturer). vanced Study, Compactijications ofspaces of lattices (Progress in Mathematics Lec• Association for Women in Mathemat• Student Workshop on the Internet: ture), Tuesday, 10:40 a.m. ics (AWM) Tuesday, 2:45 p.m. t04:45 p.m., organized Panel Discussion: Sunday, 3:00 p.m. to by Dennis DeThrck, University of Penn• AMS Special Sessions 4:30p.m. sylvania. All students planning to attend Topological graph theory, Dan Archdea• Membership Meeting: Sunday, 4:30 p.m. should check the appropriate box on the con, University of Vermont; Sunday, to 5:00 p.m. Advance RegistrationIHousing Form. Monday, and Tuesday afternoons. Open Reception: Sunday, 9:30 p.m. to Student Paper Sessions: Sunday and Algorithms for graphs and matroids, 11:00 p.m. Monday afternoons. Interested students Olivia M. Carducci and Gary P. Gor• are invited to send papers to Ronald F. don, Lafayette College; Sunday and Mon• National Association of Mathemati• Bames, Department of Mathematics, U ni• day afternoons. cians (NAM) versity of Houston-Downtown, One Main Monday, I :00 p.m. (David Blackwell Lec• St., Houston, TX 77002-1094 Classical harmonic analysis, Roger Lee ture). ([email protected]) by June 26. Cooke and Mike Wilson, University of Vermont; Sunday, Monday, and Tuesday Pi Mu Epsilon (PME) MAA-PME Student Reception: Sunday, afternoons. 5:15 p.m. to 6:15 p.m. A detailed program ofPME activities will Analysis on Lie groups and homogeneous be available at the Registration Desk. MAA Committee on Student Chapters spaces, HongmingDing, Saint Louis Uni• Marjorie Senechal, Smith College, Hospitality Center: Open Sunday, Mon• versity; Sunday and Monday afternoons. day, and Tuesday, 9:00 a.m. to 5:00 p.m. Tilings as diffraction gratings, Monday, Number theory related to Stark's Conjec- 8:30 p.m. (1. Sutherland Frame Lecture).

24 April 1995 FOCUS

Sessions for Contributed Papers: Sun• prizes. For AMS, recipients of three Leroy MAA 25-Year Member Banquet: The day and Monday afternoons. P. Steele Prizes: one for writing a truly MAA is planning its eighteenth annual fundamental paper, one for a work or se• banquet on Tuesday for those individuals Council Meeting: Sunday, 1:00 p.m. to quence of works that has been shown to be who have been members of the Associa• 2:30p.m. of lasting value, and one for an outstand• tion for twenty-five years or more. After a Reception: Sunday, 4:45 p.m., cospon• ing career, will be announced. AWM will reception beginning at 5:45 p.m., dinner sored by PME and MAA. award the Alice T. Schafer Prize. For will be served at 6:30 p.m. The entree is MAA, the recipients of the Merten M. chicken tarragon. Tickets are $25. Banquet: See the Social Events section. Hasse Prize, and various awards for out• Tours standing journal articles, namely, the Carl Other Events of Interest Because of its many attractions and mar• B. Allendoerfer, Lester R. Ford, and Book Sales and Exhibits velous climate, Vermont is a premier va• George P6lyaAwards, will be announced. Open Sunday, Monday, and Tuesday, 9:00 cation destination. The following tours are Diners will have the opportunity to meet a.m. to 5:00 p.m. Books published by the recommended as typical of the area in the with the recipients on Saturday, August 5, AMS and MAA will be sold at discounted summer and are available exclusively to at 7:30 p.m. The banquet will be preceded prices somewhat below the cost for the mathematicians and their families. Tick• by a cash bar reception at 6:30 p.m. The same books purchased by mail. These dis• ets should be purchased through advance entree is roast prime rib of beef au jus. counts will be available only to registered registration, as seats are limited and Tickets are $25 per person, including gra• participants wearing the official meetings many tours may sell out early. Please tuity and taxes. badge. VISA and MasterCard will be ac• indicate preference for tour( s) on the Tour cepted for book sale purchases at the meet• Because this event occurs the evening form, include applicable payments, and ings. Other commercial publishers may before the first day of the meetings and send the form directly to Accent TraveV be represented at the meeting. seating is very limited, very few, if any, CTN by July 5. NOTE: Should these tours tickets will be available for purchase on not meet a minimum of 30, they will be Information Booths: All meeting partici• site, so be sure to purchase your ticket when canceled and full refunds issued. All tours pants are invited to visit theAMS and MAA you register in advance. will take place as scheduled, rain or shine, membership information booths during the and no refunds will be made because of meetings. A representative will be avail• Dinner and Cruise: Travelers! Wayfar• weather. No food is included in the price able at each booth to answer questions ers! Refined Persons! (Professional Gam• of the ticket listed below unless specified. about membership, publication, and other blers unwanted!): Join your colleagues on Pick up and drop otT will be at the Liv• programs. Complimentary coffee will be Sunday evening for a three-hour cruise inglLearning Center. available at the AMS booth. These booths aboard the Spirit of Ethan Allen on beau• will be open the same days and hours as tiful Lake Champlain and reminisce about Shelburne Museum: This tour takes us the book sales. the days when steamboats churned these to one of the great treasure houses of waters to bring entertainment and com• American arts, architecture, and artifacts. Social Events merce to Burlington. A delicious buffet The museum offers 37 period homes and It is strongly recommended that tickets for including chicken cordon bleu with su• historic structures on 45 acres near Lake events be purchased through advance reg• preme sauce, baked scrod with lemon herb Champlain and houses a collection of over istration, since only a very limited num• crumbs, carved roast beef, and several 200,000 pieces of Americana. The Mu• ber of tickets will be available for sale vegetable side dishes (plus strawberry seum Visitor's Center houses orientation on-site. Ifyou must cancel your attendance shortcake for dessert!) will be served on exhibits; the Round Barn features audio• at a ticketed event, you are eligible for a board. Also, for your cruising and dining visual presentations on the museum's his• 50% refund provided you return tickets to pleasure, entertainment will be provided tory and reconstruction of the bam. the Mathematics Meetings Service Bureau by The Al Alessi Trio. Buses depart for the Complimentary jitney service takes you (MMSB) by July 31. After that date no dock from the Living and Learning Cen• around the grounds. 1:00 p.m.-5:00 p.m., refunds can be made. Special meals are ter promptly at 5:30 p.m. Tickets are $32 Saturday, August 5, $28/adult, $23/child. available upon request at all banquets, per person, $26 for children 6-11 (no including vegetarian, but this must be in• Vermont Teddy Bear Factory/ charge for children 5 and under eating from dicated on the Advance Registration and Shelburne Farms: This tour begins with parent's plate). Return is at 9:00 p.m. to Housing (ARH) form. All prices include a stop at the Vermont Teddy Bear Com• the Living/Learning Center. tax and gratuity where applicable. mons. You will visit the factory to see how AWM Reception: All participants are in• these cuddly little friends are created. You N.B. Persons staying in university resi• vited for camaraderie and refreshments, may shop at the factory as well as among dence halls should be aware that room and Monday, 9:30 p.m. other factory outlet stores in the common. board is offered as a package only, and Then, we're off to Vermont's most well• meals cannot be purchased individually. PME Banquet: This popular annual event known agricultural landscape and former will take place on Monday, August 7, at Opening Banquet: The special feature of estate. See an award-winning audiovisual 6:45 p.m. Tickets are $10 for PME mem• this banquet held in the Ballroom of the presentation about the evolution of the bers and their families; $17 for nonmem• Burlington Sheraton Hotel will be the Farms from an agricultural estate to a bers. awarding of AMS, AWM, and MAA nonprofit conservation education organi- 25 FOCUS April 1995 zation. Enjoy the Farm Store, Walking well as their badges, programs, and ap• • Students: Those currently working to• Trail, Visitor Center, and the spectacular propriate tickets by mail two to three weeks ward a degree or diploma, regardless of views from Lone Tree Hill. 1:00 p.m.-5:oo before the meeting (unless the appropri• income. Students are asked to determine p.m., Monday, August 7, $24/person. ate box signaling the contrary was checked whether their status can be described as on the ARH form). graduate (working toward a degree be• Stowe Area: On our way into the Green yond the bachelor's), undergraduate Mountains, we will stop at the Cold Hol• Because of possible delays in delivery of (working toward a bachelor's degree), low Cider Mill to see how apple cider is the U.S. mail to Canada, it is strongly sug• or high school (working toward a high squeezed the old-fashioned way and gested that advance registrants from school diploma). sample the finished product. Then on to Canada choose to pick up their registra• the lovely village of Stowe and its many tion material at the meeting as opposed to • Unemployed: Any person currently un• unique gift and specialty shops. After lunch having it mailed. Please note that a $3 employed, actively seeking employment, at The Shed, we'll drive to the base ofMt. replacement fee will be charged for pro• and not a student. It is not intended to Mansfield. You don't have to wear hiking grams and badges that are mailed but are include any person who has voluntarily boots!-our climb to the top of Vermont's not brought by participants to Burlington. resigned or retired from his or her latest highest peak is by way of an eight-passen• position. Final Advance Registration: Those who ger enclosed gondola. After our descent register by the final deadline of July 14 • Emeritus: Persons who qualify for from the summit, we'll stop at famous Ben must pick up their badge and program at emeritus membership in either the Soci• & Jerry's Ice Cream Factory. Here we'll the MathFest. Unfortunately, it is not pos• ety or the Association. The emeritus sta• find out the story behind the successful sible to provide final advance registrants tus refers to any person who has been a makers ofthis delicious ice cream and get with housing or tickets to special events in member of the AMS or MAA for twenty a free sample in the bargain! 9:00 a.m.- advance. Please note that the July 14 years or more and who is retired on ac• 5:00p.m., Tuesday, August 8, $44/person, deadline is firm, and any forms received count of age or on account of long-term lunch included. after that date will be returned! disability from his or her latest position. Champlain Scenic Ferry/Ausable This rate is also extended to any CMS It is essential that the ARH form (found at Chasm: Carved by nature over millions member who has retired from his or her the back of this issue) be completed fully of years, Ausable Chasm is a geologic position. and clearly. Each person must complete a wonder. We will cross scenic Lake separate copy of the ARH form, but all • High school teacher: Any person whose Champlain on the pleasant LCT Ferry, and registrations from one family or group may primary employment is teaching in any then it's a short ride to the chasm. Once be covered by one payment. Please print high school or secondary school. there, you make your way down a walking or type the information requested, and be trail into the heart of this deep gorge which • Librarian: Any librarian who is not a sure to complete all sections. Absence of has been cut by the rushingAusable River. professional mathematician. information (missing credit card numbers, The adventurous may choose to take a boat incomplete addresses, etc.) will cause a • Third-world country participant: ride through the rapids (included); a shuttle delay in processing. Those participants from the third world takes you back to the gift shop and restau• where salary levels are radically rant. Casual clothing and sturdy footwear Registration Fees noncommensurate with those in the U.S. are strongly recommended. 9: 15 a.m. - 3: 30 by July 14 on site p.m., Wednesday, August 9, $56/person. • Temporarily employed: Any mathema• Member of AMS, tician currently employed but who will Canadian Mathematical Society, How to Register in Advance become unemployed by June 1, 1995, MAA, PME $125 163 The importance of advance registration and who is actively seeking employment cannot be overemphasized. Those who Emeritus Member of AMS or any mathematician in a postdoctoral register in advance pay fees considerably or MAA,Graduate Student, position. lower than those who register at the meet• Unemployed, High School ing. There are two separate advance reg• Teacher, Librarian, Third-World • Nonmembers who register at the non• istration deadlines, each with its own Country Participant $35 45 member fee will receive mailings con• taining special membership offers from advantages and benefits. Undergraduate Student 20 26 AMS andMAA. ORDINARY advance registration June Temporarily Employed 95 120 Registration fees only partially cover the 15 Nonmember 194 252 expenses of holding meetings. All math• FINAL advance registration July 14 High School Student 2 5 ematicians who wish to attend sessions Ordinary Advance Registration: Those One-day Member n/a 89 are expected to register and should be pre• who register by the ordinary deadline of One-day Nonmember n/a 139 pared to show their badge, if so requested. Badges are required to obtain discounts at June 15 may make housing reservations at MAA Minicourses by June 30 special rates offered only through the theAMS andMAABook Sales. Ifadvance Minicourses #1,3,4,5 $45 MMSB. They will receive formal ac• registrants arrive too late in the day to pick knowledgments prior to the meetings as Minicourse #2 65 up their badges, the acknowledgment of

26 April 1995 FOCUS registration received from the MMSB acts one color monitor. Such requests should be an opportunity for the posting of both as proof of registration. be addressed to the MAA Associate Sec• applicant resume forms and announce• retary (Donovan Van Osdol, Department ments of open positions in a designated Advance registration forms accompanied of Mathematics, University ofNew Hamp• area on the meetings bulletin board. No by insufficient payment will be returned, shire, Durham, NH 03824-3591; provisions will be made for holding inter• therefore delaying the processing of any [email protected]). These requests views; while interviews are encouraged, housing request, or a $5 charge will be should be received by June 1. arrangements will be the responsibility of assessed if an invoice must be prepared to each employer and applicant. Messages collect the delinquent amount. Overpay• All other speakers requiring additional may be left on the meetings message board. ments ofless than $2 will not be refunded. equipment should contact the logistics Participants interested in securing a room coordinator for the meetings at the AMS There is no extra charge for members of for a short, informal interview should office in Providence at 401-455-4l39, or the families of registered participants, check with the logistics coordinator at the electronic mail to [email protected] by except that all professional mathemati• Registration Desk for availability. June 1. Requests for equipment made at cians who wish to attend sessions must the meeting most likely will not be satis• Information Distribution: A table is set register independently. fied because of budgetary restrictions. up in the exhibits area for dissemination Participants should check with their tax of information of possible interest to par• Camping and RV Facilities: There are preparers for applicable deductions for ticipants but not promoting a product or several campgrounds, most with RV fa• education expenses as they pertain to this program for sale. Those who wish to dis• cilities, in the general area. Interested par• meeting. play information promoting a product or ticipants should contact the MMSB at program for sale may do so in the book If you wish to be included in a list of in• [email protected] sale area at the Joint Books, Journals, and dividuals sorted by mathematical inter• a list. Promotional Materials display for a fee of est, please provide the one Mathematical Car Rental: Budget Rent A Car has been $35 per item. Reviews classification number of your ma• designated as the official car rental com• jor area of interest on the ARH form. (A Those who would like to display material pany for the Burlington MathFest. To re• list of these numbers appears on the back separate from the Joint Books table must serve a car at special rates, call oftheAMS and MAAabstract forms.) The reimburse the meeting for room rental and 800-772-3773 and request group ID# master copy of this list will be posted on any extra furnishings requested (tables, VNR2MATHF. These rates are applicable the meetings bulletin board near the reg• chairs, easels, etc.). This latter display is one week prior to and one week after the istration area. also subject to space availability. MathFest and include unlimited mileage. Electronic Advance Registration: This Availability of these rates is limited. Valid The administration of these tables is in the service is available for advance registra• driver's license and credit card are re• hands of the exhibits coordinator under tion, and housing arrangements if desired, quired. Minimum age for drivers is 25. guidance from the Joint Meetings Com• by requesting the forms via e-mail from Taxes, optional coverages, fuel, drop mittee. To request a contract or more in• [email protected], or by telnetting to charges, additional driver fees, and other formation, please contact Exhibits e-MATH, selecting [10] GOPHER from optional items are additional. Weekly rates Coordinator, MMSB, P.O. Box 6887, the main menu, then selecting [11] Meet• require a five day minimum. Providence, RI 02940; 401-455-4143; ings and Conferences and following the [email protected]. Car Class Daily VVeekly VVeekend instructions for the required forms. VISA (per day) Mail/Messages: All mail and telegrams or MasterCard is the ONLY method of should be addressed with participant's payment which will be accepted forelec• Economy $36 $189 $39 name, UVM Conference Office, Attn: tronic advance registration, and charges Compact 36 189 39 MathFest, 30 South Park Drive, to credit cards will be made in U.S. funds. Colchester, VT05446. Those received will Intermediate 41 199 44 Miscellaneous Information be posted on the message board near the Audio-Visual Equipment: Standard Full size 47 239 49 registration area. Mail not picked up will be forwarded after the meeting to the equipment in all session rooms is one Luxury 54 279 58 overhead projector and screen. (Invited 50- mailing address given on the participant's minute speakers are automatically pro• E-mail: Internet access via telnetortn3270 registration record. will be available at the Computer Lab, 113 vided with two overhead projectors.) Note: There will be no provision for leav• Waterman (basement level). Participants Blackboards are available only in rooms ing telephone messages at the MathFest are advised to check with technicians at where they currently exist and cannot Registration Desk; participants should their own college or university to identify be produced upon request. supply the telephone number of their ho• the numerical address of their machine, as tel or dormitory to persons interested in Speakers in MAA sessions requiring ad• well as its name, and bring this informa• contacting them. ditional equipment may make written re• tion with them, since not all locations can quests for one additional overhead be contacted by name alone. Parent-Child Lounge: Open Sunday projector/screen, 35mm carousel slide pro• through Tuesday, 9:00a.m. t05:00p.m. in jector, or VHS video cassette recorder with Employment Opportunities: There will 27 FOCUS April 1995 the LivinglLeaming Center, furnished with used to send meetings' staff (not officers Travel from the airport: A taxi from the casual furniture, a crib, a changing area, or other staff) to MathFests, thereby keep• Burlington Airport to the campus costs and VCR and monitor. Any child using ing the costs ofthe meeting (and registra• approximately $6-$8. this lounge must be accompanied by a tion fees) down. Automobile approaches to campus: parent (not simply an adult), who must be The following specially negotiated rates responsible for supervision of the child. Burlington is easily accessible via Exit are available only for the period August 3- This lounge will be unattended, and par• 14W off Interstate 89. Driving times are 10: 5% discount off first class and any ents assume all responsibility for their 5.5 hours from New York City, 3.5 hours published USAir promotional round-trip children. See the Tours section for other from Boston, and 1.5 hours from Montreal. fare, or 10% discount off unrestricted activities suitable for children. The Sheraton Hotel & Conference Center coach fares with seven-day advance res• is located at the exit going west. To reach Parking: Participants staying in hotels or ervations and ticketing required. These the Living/Leaming Center, continue west residence halls should refer to the housing discounts are valid providing all rules and in the right-hand lane, which takes you to page for parking instructions. There are restrictions are met and are applicable for Colchester Avenue; take an immediate left, limited public parking areas on campus; travel from the continental U.S., Bahamas, then position yourself in the right-hand MathFest participants may find the most Canada, and San Juan, P.R. Discounts are lane. Cross Williston Road to Spear Street. convenient to the meetings is the metered not combinable with other discounts or Follow the MathFest signs to the Living/ lot next to the AgriculturelEngineering promotions. Additional restrictions may Learning Center. Building. Cost is approximately $2.25/day apply on international travel. For reserva• with no in/out privileges. tions call (or have your travel agent call) Weather: Temperatures range from 65° 800-334-8644 between 8:00 a.m. and 9:00 to 85°, cooler at night. Humidity is typi• Registration Desk for the MathFest: p.m. Eastern DaylightTime. Refer to Gold cally not a problem. Billings Hall: noon to 4:00 p.m. on Satur• File Number 41380077. day, and 8:00 a.m. to 4:00 p.m. on Sunday and Mon• day, and 8:00 a.m. UNIVERSITY OF VERMONT CAMPUS to noon on Tues- day. Those who B did not want their 00Il VI.Hor'a Parking ~1~ , badges, programs, and tickets mailed w ~ PernlH Parking ~~?ro Route 89, should pick them II::: ===~======~~======~..JL_---(l--:::=~§EAST AVENUE ¥r.. o~::ra~~pote~, up here. Travel: USAir has been selected as the official air• line for the meet• ing for its generally conve• nient schedule to Burlington. Given the volatility in airfares because of "fare wars", we cannot guarantee that these are the o lowest fares. KEY However, we 1. Billings Student Center strongly urge par• 2. Ira Allen Chapel 3. University Campus Center at Billings ticipants to make 4. Waterman 5. Cook Physical Sciences use of this special 6. University Store deal if at all pos• R... rvolr 7. Balley/Howe Library 8. AgrlculturelEnglneerlng Building sible, since the 9. Llvlng/Leamlng Complex 10. ""arshiAustlnfTupper Halls AMS and MAA 11. Harrls-""lIIs Complex can earn compli• 12. Sheraton Burlington (Headquarters) mentary tickets on Sheraton Is 0.8 miles (l5-mlnute walk) from these carriers. ( ! To Downtown Billings Student Center. and Route 7 (1 Inch approximately equal to .10 mile) These tickets are

28 j } Personal Information CI) Name Membership ~ all that apply Mailing Address, ______AMS o CMS o Q) Telephone e-mail ______MAA o ...... Affiliation ______PME o InfOl'llllltlon (Please limit affiliation to 35 characters - one line only) AWM o Nametoappearonbadge ______GuestBadge ______

If you do not wish your program .nd lNIdge to be m.lleci to you on July 12, pl.ce • check In the box. 0 Registration Fees Total Payment IIIIthfest by July 14 .t meeting c.t.. orv Tot.1 o Member AMS, CMS, MAA, PME $125 $163 Registration Fee(s) o Nonmember $194 $252 o Graduate Student $35 $45 Event Tickets o Undergraduate $20 $26 Dorm Payment or Hotel Deposit o High School Student $2 $5 o Unemployed $35 $45 TOTAL Amount Due o Temporarily Employed $95 $120 $_-- o Third World Fee $35 $45 Make checks payable to the AMS. Canadian checks must be o Emeritus Member of AMS or MAA $35 $45 marked "U.S. Funds". You may charge this total to your VISA or o High School Teacher $35 $45 MasterCard. o librarian $35 $45 o One-day Member $89 Card Number: o One-day Nonmember $139 Card Type: _____ Expiration Date: _____ Signature: Event Tickets Name on Card: ______Event I Tlx PrIce Per Togi PI_.. complete this form .nd retum It to: Opening Banquet Mathematical Meetings Service Bureau (MMSB) Regular $25 P. O. Box 6887 Vegetarian $25 Providence, Rhode Island 02940 Dinner and Cruise U.S.A Adult $33 401-455-4143 or 1-800-321-4267 x 4143 Children 6-11 yrs $11 PME Banquet Members and Families $10 For OffIce U .. Only Nonmembers $17 MAA 25-year Banquet Codes: Regular $25 Options: Vegetarian $25 Hotel: TOTAL for Event Tickets $-- Dates: t. tour form In till. I ...... s.. ..".... Dorm: Room Type: Deadlines Hotel Deposit: ______Advance Registration/Residence Hall Reser. June 15, 1995 Dorm Payment: Hotel changes/cancellation thru MMSB July 5,1995 Final Advance Registration (no housing) July 14, 1995 TOTAL Am!. Paid: 90% Refund on Residence Hall Package July 25, 1995* Room/Board Paid: $ ______50% Refund on Events July 31, 1995* 50% Refund on Registration Cancellation August 4, 1995* Room/Board Due: $ ______Remarks: ·no refunds after this date General Information

Wh ....ppllc.ble, p ..... check off OM of the following o I will be making my own reservations. Name of hotel or motel: o I live in the area or will be staying privately with family or friends. o I plan to share a room with ______, who is making our reservations.

University Reservations

Full prepayment for room and board is required. Purchase of a Special Req.... t.: room and board package (breakfast and lunch) is required, and it is included in the rates listed below. All rates are per per- son. Mathfest participants may occupy the residence halls from Saturday, August 5 to Wednesday, August 9 only. Acknowledgment of your residence hall reservations will be sent to the address indicated on the reverse side of this appli- cation. Please mark applicable rates listed below and enter the totals where applicable. There is no children's rate, but sleep- ing bags are allowed.

De.crlptlon At II of Da,. Total PI.... -/ all that apply Single $36 x Male o Double $32 x Female o TOTAL $ ___ Smoker o Rates are per person. Nonsmoker o Dat•• nd Time of ArrIv.1: Dat•• nd Time of Departu.. : ______

N.me. of Other Occupant. Departu.. Dat. Child? (give age) ____ Child? (give age) ____

Child? (give age) ____

.....orlty of room. will ...... Igned In the Llvlng/L_mlng Complex; "'rsh/Au.tln/TUpper will ... used for ov.rflow. Hotel Reservations

PI_.. Indlc.t. type of room: Specl.1 Req.... t.: o Single $89 o Double $89 o Triple $89 o Quad $89 To IIIII.. nt ... room, please Include $89 by check or provide a credit card number. o Deposit enclosed o Hold with my credit card Card Number· ______Exp. Dat... e ___ Dat•• nd Time of Arrlv.l: f ~ :: Dat•• nd Time of Departu.. : ______N.me. of Other Occupant. Departu.. Dat. Child? (give age) ____

Child? (give age) ____ Child? (give age) ____

All hot.1 ....rvatlon .... for the ...... ton Burlington at 870 Williston Road, Burlington, ¥T. > "CI.,•. -.... ~et How to a room Hotel Housjug ~ General Information Participants are required to guarantee their reservations with either a first-night deposit by check or a major credit card. Changes and/or cancellations for the Sheraton will be accepted Participants are required to register for the Mathfest in order to obtain residence hall and hotel by the MMSBthrough July 5, 1995. The Sheraton Burlington will not take reservations accommodations through the Mathematics Meetings Service Bureau (MMSB). Reservations for directly before July 18, 1995. Reservations at the other hotels listed must be reserved the Sheraton Burlington and residence halls can be obtained through the MMSBonly. All reser• through the hotels directly prior to July 3, 1995. Mention of attending the Mathfest or MFC will vation requests must be received in writing by the MMSBprior to June IS, 1995. Be sure to insure the convention rates listed. The MMSBcannot guarantee the availability of the special complete the housing section of the Advance Registration/Housing (ARH) Form (located at the convention rates listed below after July 3 at those other hotels. Rates listed are subject to a end of this issue) to insure accurate housing arrangements. 7'J6 Vermont state tax. Nonsmoking rooms and rooms accessible to the physically challenged are available at all properties. Please call the MMSBfor further information, if necessary. University HousiO&

All rooms on campus are offered through a room/board package (breakfast and lunch) only; cost is Sheraton Burlington HoIidayInn included in the rates below. A very limited number of rooms (room only; no meals) will be available (Headquarters) for walk-ons. 1068 Williston Road Williston Road South Burlington, 05403 Residence Halls: llving/Leaming Complex (LILC) (used for majority of rooms) 870 vr Marsh/Austin/TUpper (MAn (used for overflow) Burlington, vr 05403 (800) 799-6363 (802) 865-6600 (802) 863-6363 Rates: Single: $36 0.8 miles from the University of Vermont 1.2 miles from the University of Vermont (per person) Double: $32 Note: There is no children rate. Sleeping bags are allowed. Single, double, triple, quad - $89 Single - $79, double (2 beds) - $79, Children under 18 yrs. free in room with double (king) - $89 Each hall has two lounges w/small kitchenette (refrigerator, stove, sink), no utensils included; parents $10 per additional person no smoking is allowed in public areas. Smoking is allowed only inside sleeping rooms. The Free parking Children under 18 yrs. free in room with residence halls are not air-conditioned. Free airport shuttle parents Lounge, two restaurants Free parking Residence Hall Rooms: in LILC - suites that contain two doubles, two singles, a common area, All rooms have two phones and data port Free airport shuttle two bathrooms. Fitness center, indoor pool Lounge, restaurant in MAT - typical dormitory style; bathrooms at end of halls. Windows which open Exercise room, indoor/outdoor pool Meals: There are no refunds for missed meals. A limited number of meals are available on a cash In-room coffee makers Windows which open basis ($6 breakfast, 58 lunch). Vegetarian meals are available; Kosher are not. Laundry facilities

Meal Cards: Meal cards will be included with your registration materials. If your registration materi• als are not mailed, they will be available at dormitory check-in. Lost meal cards are nonrefundable Howard Johnson Econolodge and cannot be replaced. Participants who lose their meal cards are encouraged to buy their remaining meals on a cash basiS. One Dorset Street 1076 Williston Road Dining Halls/Hours: Breakfast: The Weathervane, LILC; 7:00- 8:30 a.m South Burlington, vr 05403 South Burlington, vr 05403 Lunch: Cook Commons, behind Billings Student Center; 11:30 a.m.- 1:30 p.m. (802) 863-5541 (800) 55-ECONO; (802) 863-1125 1.2 miles from the University of Vermont 1.4 miles from the University of Vermont Check-in Desk: Located in the Fireplace Lounge in the LlLC or at Billings Student Center. Staggered check-in hours and exact location will be determined at a later date based on dates of major arrivals; Single/double - $65 Single - $59, double - $65 for arrivals off-hours, check instructions in front of LlLC for assistance: the maximum wait for $6 per additional person $5 per additional person response is 15 minutes. Children under 19 yrs. free in room with Children under 19 yrs. free in room with Received at Check-In: Key and instructions for keypad use (on the front door of aSSigned residence parents parents hall). Bed linen, three towels, one washcloth, soap, and a glass will be placed on the bed; towels and No elevators (2 stories) Free parking washcloth to be exchanged daily in a central location. Free parking Free airport shuttle Lounge, restaurant Free continental breakfast Parking: Temporary parking for dormitory check-in at Director's Circle in front of LlLe. Permits sold Refrigerators in some rooms Lounge, restaurant (lunch & dinner) @ S2.25/day or SI2.S0/week during major check-in periods at the Check-in Desk and at the Local Children's playground, recreation area Health spa, outdoor pool Information Desk in the registration area. Exercise room; indoor/outdoor pool 52-acre nature trail General: Gym passes sold during major check-in periods at the Check-in Desk and at the Local Windows which open Windows which open Information Desk for S6/week. A limited supply of fans are available for rental at a cost of 5S/day at Laundry facilities ~ dormitory check-in. o (":J ~ ~ ~ \I) Plea.e complete a .eparate form for each individual attending. Burlington Mathfest Personal Participant Information

Name Mailing Address ______

Fax ______Telephone • ....._ check .... Iaox for all tours JOU ..... to att.....

o Stowe Area Tour Tour registration forms o Shelburne Museum must be received by o VT Teddy Bear/Shelburne Farms .luIyS.1'" o Ausable Chasm

Fees for Tours h Tour Stowe Area Tour $44.00 per person CI) Shelburne Museum $28.00 per person $23.00 per child VT Teddy Bear/Shelburne Farms $24.00 per person ., ~ Ausable Chasm $56.00 per person

Name Mailing Address ______

Telephone Fax ______Authorization Signature ______. ______Terms

Cancellation ...... Ity For further information PrIor to .luly 18. 1.... refunds will be made subject to a $25.00 non-refundable penalty fee. on tours contact Aft., .luly 18. 1.... all payments are nonrefundable. Accent Travel/CTN:

R...... only till. fonn ...... ,...... to: Telephone Accent 'IftIveIJCTN 8ON784803 x3 R O. Box 753 Wllllaton, VT 0M8S Fax 8ON7M128

G:\GROUP\6277REG.DOC April 1995 FOCUS

Burlington Mathfest MAA Minicourses Advance Registration Form Burlington, Vermont, August 6-8, 1995

To register for MAA Name: Minicourse(s), please complete THIS FORM Mailing Address: ---- or a PHOTOCOPY OF THIS ------FORM and return with your payment to:

Minicourse Coordinator Telephone: ------Mathematical Association of America e-mail: 1529 Eighteenth Street, N.W. Washington, DC 20036 Telephone: 202·387·5200, Registration 800-331-1622 I would like to attend 0 1 Minicourse o 2 Minicourses After the deadline, potential Please enroll me in MAA Minicourse(s): # and # ______participants are encouraged In order of preference, my alternatives are: # ____ and # ______to call the MAA headquar• ters at 800-331-1622 to I plan on registering for the Burlington Mathfest ONLY in order to attend check on availability. The o MAA reserves the right to the MAA Minicourse(s). Should the course(s) of my choice be fully subscribed, a cancel any Minicourse which full refund of the Mathfest advance registration fee will be made. is undersubscribed. Should this occur, those registered in advance will be notified Payment and will receive a full refund. MAA Minicourses Make checks payable to MAA. Canadian checks must be marked "US Funds". are open only to persons You may also charge this total to your VISA or MasterCard. who register for the Mathfest and pay the regular registration fee. Check enclosed: $___ _ o MasterCard o VISA

Card number ______Exp. date _____ Each participant must fill out a separate Minicourse Signature on card ______Advance Registration Form. Enrollment is limited to two Minicourses. Deadlines

MAA Minicourse Advance Registration: June 30, 1995 Cancellation in order to receive a 50% refund: August 4, 1995 Minicourse Fee 1 Interdisciplinary Lively Applications 545 2. Instructional Aspects of Mathematics on the Internet 565 3. Calculus: An Active Approach with Projects 545 4. An Activity-Based Approach to Teaching Introductory Statistics 545 5. The Use of Software in an Introductory linear Algebra Course 545

33 FOCUS April 1995

Minicourse #1: Interdisciplinary Lively Applications, Frank Giordano and David Arney, United States Military Academy. Part A: Sunday, 1:45 PM-3:45 PM; Part B: Tuesday, 1:45 PM-3:45 PM. Enrollment limit: 40; registration fee: $45. Interdisciplinary applications can be used to weld mathematics with the concepts of other disci• plines to provide student growth in modeling and problem solving. We will discuss projects that can be used in a wide range of mathematics courses, with the applications related to subjects in chemistry, biology, physics, engineering, economics, technology, and social sciences. Projects are designed to take 4 to 6 hours of student effort and can be done in groups or individually, and some require a computer or calculator. Participants will work with materials prepared for students and instructors in printed, video, and multimedia formats.

Minicourse #2: Instructional Aspects of Mathematics on the Internet, Brian E. Smith, Dawson College (Montreal), and Sandra Villas, Dona Ana Community College. Part A: Monday, 4:00 PM- 6:00 PM; Part B: Tuesday, 1:45 PM-3:45 PM. Enrollment limit: 40; registration fee: $65. The orientation of this minicourse is on locating mathematics resources on the Internet and using them in the mathematics classroom or laboratory. One part of the course will focus on identifying dif• ferent types of mathematical resources and the Internet search tools which are required to locate them. We will describe how to find FTP sites for archived files, using ARCHIE servers; Gopher servers, and the VERONICA searches that find them, will also be discussed. The second part of the course will deal with applications of the Internet in the teaching of undergraduate mathematics, and specific examples will be presented. The course will involve a combination of demonstrations and hands-on experience; hand• outs will be provided.

Minicourse #3: Calculus: An Active Approach with Projects, Stephen R. Hilbert, John C. Maceli, Diane D. Schwartz, Stanley E. Seltzer, and Eric E. Robinson, Ithaca College. Part A: Sunday, 4:00 PM- 6:00 PM; Part B: Tuesday, 1:45 PM-3:45 PM. Enrollment limit: 40; registration fee: $45. This minicourse will address issues relating to the use of group projects and in-class activities in calculus, including an overview, examples of projects and activities, and the impact on the curriculum. The organizers, who have been teaching calculus using group projects since spring 1989, have found that open-ended projects challenge students to develop problem-solving skills beyond looking for a simi• lar problem solved in the text or class notes. They use in-class activities to help the students to become active learners and to develop the skills to successfully complete the projects.

Minicourse #4: An Activity-Based Approach to Teaching Introductory Statistics, Richard Scheaffer, University of Florida, and Ann Watkins, California State University, Northridge. Part A: Sunday, 1:45 PM-3:45 PM; Part B: Monday, 1:00 PM-3:00 PM. Enrollment limit: 40; registration fee: $45. This minicourse is for teachers of introductory statistics who want to change their course from a traditional lecture-and-listen model to activity-based lessons. Participants will be engaged in a series of field-tested, hands-on activities that illustrate many of the key concepts taught in an introductory statis• tics course. They will play the role of students, actually working through a selection of activities. Experienced instructors will explain how they have made use of the activities in various settings. Each participant will be supplied with copies of the student pages and the instructor notes, which include suggestions for assessment of the activities. The Activity-Based Statistics (ABS) project is funded by the NSF.

Minicourse #5: The Use of Software in an Introductory Linear Algebra Course, Homer Bechtell, University of New Hampshire. Part A: Sunday, 4:00 PM-6:00 PM; Part B: Monday, 1:00 PM-3:00 PM. Enrollment limit: 80; registration fee: $45. The focus of this minicourse is on developing goals and strategies for the successful implementa• tion of computer-aided instruction into an undergraduate introductory linear algebra course. Emphasis is on introducing software in order to increase mathematical maturity and the depth of understanding for the concepts without compromising the theoretical development. Problem sets will be distributed, and the construction of problem sets will receive special attention. Familiarity with software for linear algebra is a prerequisite. During the course, participants will not have access to computer software but will develop outlines for problem sets based on their experience with linear algebra software.

34 April 1995 FOCUS The Lighter Side of Exploring Mathematics Game Theory and Strategy Mathematics With Your Computer Philip D. Straffin, Jr. Proceedings of the Eugene Strens Arthur Engel This important addition to the New Math• Memorial Conference on Recre• ematical Library series pays careful atten• Today personal computer gives its owner ational Mathematics and its History s tion to applications of game theory in a tremendous power which can be used for wide variety of disciplines. The applica• Richard K. Guy and Robert f. experimental investigations and simula• tions are treated in considerable depth. The Woodrow, Editors tions of unprecedented scope, leading to book assumes only high school algebra, mini-research. This book is afirst step into In August of 1986 a special conference on yet gently builds to mathematical think• this exciting field. recreational mathematics was held at the ing of some sophistication. Game Theory University of Calgary to celebrate the This is a mathematics book, not a and Strategy might serve as an introduc• founding of the Strens Collection. Lead• programming book, although it explains tion to both axiomatic mathematical think• ing practitioners ofrecreational mathemat• Pascal to beginners. It is aimed at high ing and the fundamental process of ics from around the world gathered in school students and undergraduates with a mathematical modelling. It gives insight Calgary to share with each other the joy strong interest in mathematics, and into both the nature of pure mathematics, and spirit of play that is to be found in teachers looking for fresh ideas. It is full and the way in which mathematics can be recreational mathematics. Martin Gardner of diverse mathematical ideas requiring applied to real problems. says of recreational mathematics: "I don't little background. It includes a large Since its creation by John von Neumann know of any better way to hook the inter• number of challenging problems, many of and Oskar Morgenstern in 1944, game ests of students." which illustrate how numerical theory has contributed new insights to computation leads to conjectures which The papers in this volume represent a trea• business, politics, economics, social psy• can then be proved by mathematical sure trove of recreational mathematics by chology, philosophy, and evolutionary bi• reasoning. a star-studded cast: Leon Bankoff, Elwyn ology. In this book, the fundamental ideas Berlekamp, H.S.M. Coxeter, Ken Fal• You will find 65 interesting and substan• of game theory share the stage with appli• coner, Branko Griinbaum, Richard Guy, tial mathematical topics in this book, and cations of the theory. How might strategic Doris Schattschneider, David Singmaster, over 360 problems. Each topic is illustrated business decisions depend on information Athelstan Spilhaus, Stan Wagon, and with examples and corresponding pro• about a rival company, and how much many others. grams. The major goal of the book is to use would such information be worth? When You will not soon find another collection the computer to collect data and formulate is it advantageous to vote for a candidate of wonderful articles on recreational math• conjectures suggested by the data. It is as• who is not your favorite? What can we ematics by a more distinguished group of sumed that readers have a PC at their dis• learn about the problem of "free will" by authors. If you are interested in tessella• posal. imagining playing a game with an Om• tions, Escher, tiling, Rubik's cube, nipotent Being? Game theory gi ves insight 264 pp., Paperbound, 1993 pentominoes, games, puzzles, the arbelos, into all of these questions. ISBN 0-88385-636-0 Henry Dudeney, or change ringing, then List: $38.00 MAA Member: $26.50 200 pp., Paperbound, 1993 this book is a must for you. Catalog Number NML-35IFOC ISBN 0-88385-637-9 Ifyou believe that recreational mathemat• You need a Pascal compiler in order to use List: $27.50 MAA Member: $22.00 ics must be the mathematics that is fun, the 3.5" IBM-compatible disk packaged with Catalog Number: NML-36IFOC then look no further, for The Lighter Side this volume. of Mathematics is full of fun. 376 pp., Paperbound, 1994 ISBN 0-88385-516-X List: $38.50 MAA Member: $29.00 Catalog Code: LSMAIFOC

!Send this order fo;; to: The MAA, 1529 Eight~h Str~, NW, Washingt;: DC 20036,1-800-331-1622; FAX: (202) 265-2384------, II Name Membership Code ______: Address (Pkase copy the first six digits that appear on the t"" lim ofyuur mailing /abel) I I I City State Zip Code Quantity Catalog Number Price I IPayment 0 Check 0 VISA 0 MASTERCARD I

ICard Number I I . I ISignature Expiration Date I Foreign Orders Please add $3.00 per item ordered to cover postage and I Ihandling fees. The order will be sent via surface mail. !fyou want your order TOTAL ~nt by air, ~ ~ b~a.£EY .!!!.s~ r!!.u !.Fr~r~ ~oice for y~ ~e!:- ______:..J 35 FOCUS April 1995

THE BEST IN MATHEMATICAL Lion Hunting and Other Algebra and Tiling A Radical Approach to Mathematical Pursuits Sherman Stein and Sandor Szabo Real Analysis A Collection ofMathematics, Verse, Often questions about tiling space or a David Bressoud and Stories by Ralph P. Boas, Jr. polygon lead to other questions. For This book is an undergraduate introduc• Gerald L. Alexanderson instance, tiling by cubes raises questions tion to real analysis. Use this book as a and Dale H. Mugler, Editors about finite abelian groups. Tiling by tri• textbook for an innovative course, or as a As a young man at the Institute for Ad• pods or crosses raises questions about resource for a traditional course. If you vanced Study in Princeton, Ralph Philip cyclic groups. From tiling a polygon with are a student and have been through a tra• Boas, Jr., together with a group of other similar triangles, it is a short step to inves• ditional course, yet still do not understand mathematicians, published a light-hearted tigating automorphisms of real or com• what real analysis is about and why it was article on the "mathematics of lion hunt• plex fields. Tiling by triangles of equal created, read this book. ing" under a pseudonym (1938). This areas soon involves Sperner's lemma from sparked a sequence of articles on the topic, topology and valuations from algebra. This course of analysis is radical; it returns several of which are drawn together in this to the roots of the subject, but it is not a The first six chapters of Algebra and Til• book. history of analysis. It is rather an attempt ing form a self-contained treatment of to follow the injunction of Henri Poincare: Lion Hunting includes an assortment of these topics, beginning with Minkowski 's let history inform pedagogy. The author articles that show the many facets of this conjecture about lattice tiling of Euclid• wrote the book as a first encounter with remarkable mathematician, editor, writer, ean space by unit cubes, and concluding real analysis, laying out its context and and teacher. Along with a variety of his with Laczkowicz's recent work on tiling motivation in terms ofthe transition from lighter mathematical papers, the collec• by similar triangles. The concluding chap• power series to those that are less tion includes Boas' verse and short sto• terpresents a simplified version ofRedei's predictable, especially Fourier series. ries, many of which are appearing for the theorem on finite abelian groups: if such Bressoud marks some of the traps into first time. Anecdotes and recollections of a group is factored as a direct product of which even great mathematicians have his numerous experiences and of his work subsets, each containing the identity ele• fallen in exploring this area of and meetings with many distinguished ment, and each prime order, then at least mathematics. mathematicians and scientists of his day one of them is a subgroup. A remarkable are also included. geometric implication of this result is The book begins with Fourier's introduc• developed in Chapter 2. tion of trigonometric series and the prob• The mathematical articles in this collec• lems they created for the mathematicians tion cover a range of topics. They include Algebra and Tiling is accessible to un• of the early nineteenth century. Cauchy's articles on infinite series, the mean value dergraduate mathematics majors, as most attempts to establish a firm foundation for theorem, indeterminate forms, complex of the tools necessary to read the book are calculus follow, and the author considers variables, inverse functions, extremal found in standard upper division algebra his failures and his successes. The book problems for polynomials, and more. courses, but teachers, researchers and pro• culminates with Dirichlet's proof of the fessional mathematicians will find the Boas' wit and playful humor are reflected validity of the Fourier series expansion book equally appealing. Beginners will in the verses included in this collection. and explores some of the counterintuitive find the exercises and the material found The verses reflect the phases of his career results Riemann and Weierstrass were led in the appendices especially useful. The as author, editor, teacher, department chair, to as a result of Dirichlet's proof. "Problems" section will appeal to both and lover of literature. A section of the beginners and experts in the field. The To facilitate graphical and numerical in• book describes the feud that Boas suppos• book could serve as the basis of an under• vestigations, Mathematica commands and edly had with Bourbaki. Also included are graduate or graduate seminar, or a source programs are included in the exercises. many amusing anecdotes about famous of applications to enrich an algebra or However, you may use any mathematical mathematicians. geometry course. tool that has graphing capabilities, includ• We profit from Boas' labor, and treasure it ing the graphing calculator. 224 pp., Hardcover, 1994 as an inheritance. We should allow our• ISBN 0-88385-028-1 336 pp., Paperbound, 1994 selves in some measure to walk along his List: $34.00 MAA Member: $26.00 ISBN 0-88385-701-4 path. This collection will allow the reader Catalog Code: CAM-2s/FOC List: $29.00 MAA Member: $22.00 a glimpse of that path. Catalog Code: RAN/FOC 240 pp., Paperbound, 1994, ISBN 0-88385-323-X List: $35.00 MAA Member: $25.00 Catalog Code: DOL-Is/FOC 36 April 1995 FOCUS

EXPOSITION • • • JUST PUBLISHED! All the Math Linear Algebra Problem Assessing Calculus That's Fit to Print Book Reform Efforts Articles from the Manchester Paul Halmos A Report to the Community Guardian This is a book for mathematicians at all James R. C. Leitzel and Alan C. Keith Devlin levels. Paul Halmos tells us, "Even if I Tucker, Editors know some answers, I don't think I under• Assessing Calculus Reform EtTorts: A Between 1983 and 1989 Keith Devlin, re• stand a subject until I know the questions. Report to the Community provides a re• search mathematician, author, and educa• The questions in mathematics are called view of various aspects of the calculus tor, wrote a semi-monthly column on problems-and although I learned some reform movement. This study gives an mathematics and computing in the English linear algebra a long time ago, until now assessment of the current attitudes and in• national daily newspaper, The Manches• I have made no serious effort to examine volvement of mathematical sciences de• ter Guardian. This book is a compilation the problems that the solutions are based partments-their faculty and students-in of many of those articles. It is witty, enter• on. I wrote this book to organize those efforts to revise calculus instruction. taining, and easy to read. questions-problems-in my own mind." A key finding of the assessment study is The mathematical topics range from This book can be either the main course or that how calculus is taught has changed simple puzzles to deep results including the dessert for someone who needs linear more than what is taught. The changes in open problems such as Faltings Theorem algebra-and nowadays that means every instructional practice, more frequent use and the Riemann Conjecture. You will find user of mathematics. It can be used as the of technology, and increased focus on articles on prime numbers, how to work basis of either an official course or a pro• building students' conceptual understand• out claims for traveling expenses, calcu• gram of private study. ing are finding their way into both pre• lating pi, computer simulation, patterns calculus and post-calculus mathematics and palindromes, cryptology, and much If used as a course, the book can stand by courses. This has encouraged increased more. itself, or if so desired, it can be stirred in with a standard linear algebra course as interest in research about how undergradu• This book is meant for browsing by any• the seasoning that provides the interest, ate students learn mathematics. Many of one who regularly reads a serious news• the challenge, the moti vation that is needed the institutions that currently report using paper and has some interest in matters by experienced scholars as much as by reform materials in experimental sections scientific or mathematical. Keith Devlin beginning students. have plans to move their efforts to course• tells us "from the mail I received I know wide adoption in the near future. The fact that the readers of the column were a var• The best way to learn is to do, and the that in the past two years over 95% of in• ied bunch. They ranged from students at purpose of this book is to get the reader to stitutions using a reform text continue schools in their early teens (occasionally DO linear algebra. The approach is using a reform text the next year (for at even younger!), to retired people in their Socratic: first ask a question, then give a least some sections) indicates that calcu• nineties (often the ones who best succeed hint (if necessary), then, finally, for secu• lus reform is likely to be around for the in cracking the brain teasers I occasion• rity and completeness, provide the detailed foreseeable future. ally included in my articles); from prison answer. Data is provided on the number of institu• inmates to executives in the computer in• 340 pp., 1994, Paperbound tions at each of the levels of postsecondary dustry; from truckers to schoolteachers; ISBN 0-88385-322-1 education that are engaged in reform ef• both men and women." List: $35.00 MAA Member: $25.00 forts and also gives information on fac• It you think that nothing of interest has Catalog Code: DOL-16/FOC ulty and student involvement, and reviews happened in mathematics since the time of texts produced by some of the major of Pythagoras, this book will change your curriculum development projects. The ap• mind. Keith Devlin presents mathematics pendices to the report include brief de• as a living human enterprise, both a sci• scriptions of selected calculus reform texts ence and an art. Use order form and a complete listing of the NSF awards made during the seven years of the Calcu• 345 pp., Paperbound, 1994 on page 35, lus Initiative. ISBN 0-88385-515-1 List: $32.50 MAA Member: $25.00 100 pp., Paperbound 1994 Catalog Code: ATMAFOC or call ISBN 0-88385-093-1 List: $15.00 1-800-331-1622 Catalog Code: ACRE/FOC

37 FOCUS April 1995

Agder College Marshall University, a comprehensive higher E:\IPLO\,\IE~T OpPolnl \;ITIES Department of Mathematics education institution, is located in Huntington, West Virginia, just across the Ohio River from Rates for FOCUS EmploymentAdvertise• Agder College is one of the largest colleges in Ohio, and thirteen miles from the Kentucky bor• ments are $65.00 per column inch (one inch Norway. The professional activity is organized der. There are approximately 12,500 students and minimum), billed to the nearest 112 inch. in 8 departments. The college has nearly 600 employees and 6000 students. Agder College 600 faculty. The department has 17 regular fac• All advertisments are set with a one-line offers different courses at all levels including ulty members and about 15 part-time faculty and headline, centered, boldface, consisting of several main subjects. graduate assistants. The department offers the institution name, unless additional bachelor's and master's degrees in mathematics PROFESSORSHIP IN MATHEMATICS headline infonnation is provided. Ads will and service courses for many other degree pro• EDUCATION appear in the same language in which they grams. Applications are invited for a position as Profes• are submitted. Applicants should send a letter of application, a sor of Mathematics Education at Agder College FOCUS offers a 15% discount for the same current curriculum vita, and names, addresses, beginning either January I, 1996, or an agreed three and phone numbers of three professional refer• advertisement in or more consecu• upon later date. ti ve issues. All invoices include a tear sheet. ences. Nominations and applications should be Advertising Copy Deadlines: The first of A Ph.D. degree in mathematics or a Ph.D. degree sent to: in mathematics education together with a master's the month, two months prior to publica• Dr. Herbert Tesser degree in mathematics or equivalent is required. tion. FOCUS is published in February, Chair of Search Committee April, June, August, October, and Decem• Evidence of scholarly work in mathematics edu• cation is also required. Marshall University ber. Huntington, WV 25755-2580 Advertisers should contact: Amy Fabbri, The application must contain complete informa• tion about the applicant's education and FOCUS Advertising Coordinator, The Application review will begin March 27, 1995 professional activities, including a curriculum and continue until position is filled. Anticipated Mathematical Association of America, vitae and graduate transcripts. The above should starting date is Fall 1995. Women and minorities 1529 Eighteenth Street, NW, Washington, be submitted in 4 copies. Scientific works which are encouraged to apply. Marshall University is DC 20036-1385; (202) 387-5200; fax: the applicant wants considered (and a list of these ) an Equal Opportunity/Affirmative Action Em• (202) 265-2384; e-mail: [email protected] are to be sent in 3 copies. ployer. A letter of intent to apply will be accepted until Santa Clara University June I, 1995, and a complete application should The Ohio State University Applied Mathematics Department follow as soon after as possible. Scientific work Department of Statistics School of Engineering in progress may be submitted within 4 weeks of Visiting Professorship in Statistical Education this day. Santa Clara University The Ohio State University has been at the fore• Applications are invited for the position of assis• Send application to: Agder College, front of an innovative movement in statistical tant professor in the Applied Mathematics Personalseksjonen, Tordenskjolds gt 65, N-4604, education. Our focus has been on the effective Department. The position is tenure-track. The Kristiansand, Norway. use of technology in the classroom in conjunc• primary function of the department is to teach Further information can be obtained by contact• tion with the implementation of a "learn through service courses in mathematics on the under• ing Professor Asvald Lima, phone discovery" and "data analytic" philosophy. As graduate and graduate level for the School of +47.38.07.95.72 or e-mail: [email protected]. part of these efforts, the Department of Statistics Engineering. The department also awards the has available a Visiting Professorship in Statisti• Masters degree in the areas of numerical analy• Women are particularly encouraged to apply. cal Education or a Post-doctoral position in sis, engineering mathematics, and probability and AgderCollege is an Equal Opportunity Employer. Statistical Education beginning Fall 1995. The statistics as applied to the engineering fields. Professorship would be appropriate for a senior Teaching duties include undergraduate courses Marshall University person on sabbatical. The Post-doctoral position in numerical methods and differential equations. Chair, Department of Mathematics is intended for recent Ph.D. recipients with an The candidate will also be expected to teach Marshall University invites applications and interest in statistical education. The purpose of graduate courses in one or more of the following nominations for Chair of the Mathematics De• the position is to offer faculty interested in statis• areas: complex variables, numerical analysis, partment. Minimum qualifications include a tical education the opportunity to teach courses graph theory, optimization theory. Research ac• Ph.D. in mathematics, broad mathematical inter• that make extensive use of technology (state-of• tivity is required. ests, and a history of successful teaching and the-art Macintosh Labs, lecture halls with scholarly activities. Applicants should also pos• high-end video and computer projection equip• Deadline for applications is May I, 1995. Appli• ment, experiment with technology-based cations should be sent to Search Committee, sess effective communication and leadership skills, as well as experience in innovative pro• teaching, and pursue technology-based course Applied Mathematics, School of Engineering, development. The professorship could addition• Santa Clara University, Santa Clara, CA gram development. Demonstrated administrative ally involve further development of existing 95053. Do not send letters of recommendation abilities, success in obtaining external funds, and courses, development and implementation of until requested by committee. good interpersonal skills are highly desirable. creative used of technology, labs, and/or devel• The Chair will represent the department to the Santa Clara University is an equal opportunity/ opment and implementation of technology-based administration, provide leadership in both cur• affirmative action employer, and welcomes ap• course materials. Duties are negotiable, but will ricular and faculty development, and promote plications from women, persons of color, and include teaching one or two undergraduate mathematics to the Marshall University commu• members of other historically underrepresented courses per quarter. Courses include ourtechnol• nity. Experience in curricular activities across U.S. ethnic groups. ogy-based course intended for students in the Arts disciplines is preferred. and Humanities, our technology-based course for Qualifications should be sufficient for full pro• Social Science majors. our technology-based fessor with tenure. Salary will be commensurate course for science majors, and our sequences for with qualifications and experience. engineering majors. Candidates should have a

38 April 1995 FOCUS

serious interest in statistical education. Salary in the use of technology in mathematics instruc• negotiable. Applicants should send a CV, tran• tion, or research potential in discrete or Preparing for a script, and three letters of reference. computational mathematics. The department New Calculus The Ohio State University is an Equal Opportu• operates two microcomputer labs and is prepar• nity/Affirmative Action Employer. Qualified ing to open a PC classroom. We have an extensive Conf!Nence Proceedings women, minorities, Vietnam-era veterans, dis• developmental math program, and serve many abled veterans, and individuals with disabilities nontraditional and part-time evening students. Anita Solow, Editor are encouraged to apply. Applications requested West Virginia State College is a historically black Among the background papers pre• by May I, 1995 to college, which has evolved into a fully acces• sented at this 1993 conference are over• Professor William Notz sible, racially diverse, and multi-generational views of developmental projects in baccalaureate institution. Because of this tradi• Department of Statistics calculus reform, precalculus reform at tion, the College enrolls a wide range of students The Ohio State University and assists them in achieving their academic, the college level, and mathematics cur· 1958 Neil Avenue civic, and career potential through quality under• riculum reform at the high school level. Columbus, Ohio 43210·1247 graduate programs in a campus environment In addition, there are background pa• nationally recognized as a "Living Laboratory of pers on the current status and special SUNY College at Fredonia Human Relations." West Virginia State College problems and potential for curricular The Department of Mathematics and Computer (WVSC) is the largest institution of higher edu• reform in community colleges, and in Science invites applications for tenure-track po• cation in the Charleston metropolitan area serving colleges with large proportions of mi• sitions in mathematics. A doctorate in approximately 4,700 students. mathematics or mathematics education is re• nority students. The remaining two Applicants should send a letter of application quired. Candidates must have a commitment to background papers summarize the re• (including e-mail address and fax number, if excellence in teaching and to continued schol• sults of the MAA Survey of the current available), curriculum vitae, academic transcripts, arly activity along with an interest in curriculum and three letters of reference by April 15, 1995 state of calculus reform at the college development, especially the application of tech• (or until suitable candidates are chosen), to level and changes in the AP Calculus nology. Candidates who can document excellence Program. in teaching are likely to be ranked higher in our Barbara J. Oden, Ph.D. selection process. Review of applications will Vice President for Academic Affairs The core of the meeting program was a commence April 15, 1995 and will continue until West Virginia State College series of four concurrent workshops on the position is filled. Fredonia actively encour• P.O. Box 1000, Campus Box 192 Content, Teaching Strategies, Institu• ages applications from women and minority Institute, WV 25112·1000. tional Context, and Course Context. candidates and is an Affirmative ActionlEqual Opportunity Employer. Send a letter of applica• Reports from each workshop form the tion, a curriculum vita, and three letters of seCond part of the volume. In these re• reference to: ports, each workshop group examines Dr. Nancy Boynton, Chair the future ofthe reform movement from Mathematics Search Committee the perspective of their topic. Mathematics and Computer Science The contributed papers, the third part SUNY College at Fredonia of the volume, represent the best think• Fredonia, NY 14063·1198 ASSISTANT/ ing on calculus and precalculus reform [email protected] ASSOCIATE from those who are actively involved in the movement. Simon's Rock College PROFESSOR One-year, sabbatical replacement position in Science And The fourth part of the volume is a col• mathematics for 1995-96. Send letter of applica• Mathematics Education lection of brief descriptions of a num• tion, curriculum vita, and three letters of ber of developmental projects in the recommendation to Prof. Robert Snyder, Simon's Candidates should have an calculus and precalculus refoon move• Rock College of Bard, Gt. Barrington, MA 10230. extensive background in science ments. The listing of projects is a valu• and mathematics, proven ability able resource providing helpful West Virginia State College as an educator of teachers, and information about a diverse set of Faculty Positions (2) the skill needed to develop a projects. PreparIng for a New Calcu• Department of Mathematics dynamic new science and math• ematics education curriculum. lus should be read by every mathemat• The Department of Mathematics invites applica• Review of applications will begin tions for two tenure-track positions effective ics educator who teaches at the calculus immediately and continue until or precalculus level. August 1995. Primary responsibility to teach the positions are filled. approximately twelve credits of undergraduate Appointment begins September, 250 pp., Paperbound, 1994 mathematics, possibly including secondary math 1995. Send letter of application, ISBN 0-88385-092-3 methods or computer science courses, per semes• vita, and at least three letters of ter. Duties also include student advisement, recommendation to Jeffrey Kane, Lbt:$25.00 curriculum development, committee work, and Dean, School of Education, CtIIIIlog Cob: NTE-361FOC scholarly activity. Ph.D. in Mathematics or Math• Adelphi University, South ematics Education preferred for the second Avenue, Garden City, New York To order, position. Rank and salary negotiable. Preference 11530. Equal Opportunity / will be given to those applicants with experience Affirmative Action Employer. call 1-800-331-1622

39 Calendar National MAA Meetings Other Meetings August 6-8,1995 Seventieth Annual Joint October 1995, North Dakota State Uni• July 30-August 4, 1995 Ninth Summer Meeting, University of Ver• versity, Fargo, ND Iberamerican Conference on Mathemat• mont-Burlington, Burlington, VT NORTHEASTERN June 9-10, 1995, ics Education (IACME IX), Santiago, January 10-13, 1996 Seventy-ninth An• Bates College, Lewiston, ME Chile. Contact: Organizing Committee, nual Meeting, Orlando, FL. Board of November 17-18, 1995, Salem State Col• lAC ME IX, Casilla 33081, Correo 33, Governors Meeting January 9, 1996 lege, Salem, MA Santiago, Chile; fax: 56-02-6811739; e• mail: [email protected]. January 9-7, 1997 Eightieth Annual Spring 1996, Hampshire College, Meeting, San Diego, CA. Board of Amherst, MA August 9-18, 1995 Conference on Governors Meeting January 8, 1997 NORTHERN CALIFORNIA October Fermat's Last Theorem, Boston U ni ver• January 7-10,1998 Eighty-firstAnnual 21-22,1995, Cal Poly tech State Univer• sity. For more information, contact: Meeting, Baltimore, MD. Board of sity, San Luis Obispo, CA Fermat Conference, Department of Governors Meeting January 6, 1998 Mathematics, Boston University, Bos• (joint meeting wI S. California Section) ton, MA 02215; [email protected]. Sectional MAA Meetings OHIO April 21-22, 1995, Miami Univer• sity, Oxford, OH August 16-19, 1995 Fifth Conference of ALLEGHENY MOUNTAIN April the International Algebra Society, Geor• PACIFIC NORTHWEST June 15-17, 1996, Indiana Univ. of Pennsylvania, In• gia State University, Atlanta, GA. For diana, PA 1995, Whitman College, Walla Walla, WA more information, contact Frank Hall, IOWA April 21-22, 1995, University of ROCKY MOUNTAIN April 21-22, Dept. of Math & Computer Science, Northern Iowa, Cedar Falls, IA 1995, University of Southern Colorado, Georgia State University, Atlanta, GA Pueblo, CO KANSAS April 14-15,1995, Wichita State 30303; (404) 651-2253; e-mail: University, Wichita, KS April 1996, Mesa State College, Grand [email protected]; or Paul Van Dooren, Junction, CO Universite Catholique de Louvain, METRO. NEW YORK May 6, 1995, CESAME, Batiment Euler A.119, B- Hunter College-CUNY, New York, NY SEAWAY April 21-22, 1995, Hobart & William Smith Colleges, Geneva, NY 1348 Louvain-la-Neuve, Belgium; 32- MICHIGAN May 5-6,1995, Grand Val• 10-47-8040; e-mail: vdooren@anma. November 3-4, 1995, Skidmore College, ley State University, Allendale, MI ucl.ac.be. Saratoga Springs, NY MISSOURI April 1996, Southeast Mis• October 12-24, 1995 Seventeenth An• souri State Univ., Cape Girardeau, MO 1996, Elmira College, Elmira, NY nual Meeting of the North American SOUTHERN CALIFORNIA October Spring 1997 Missouri Western State Col• Chapter of the International Group for 21-22, 1995, Cal Poly tech State Univer• lege, St. Joseph, MO the Psychology of Mathematics Educa• sity, San Luis Obispo, CA Spring 1998 Southwest Missouri State tion (PME-NA XVII), Columbus, OH. University, Springfield, MO (joint meeting wI N. California Section) Deadline for Poster Session proposals is NEBRASKA-SOUTHEAST SOUTH TEXAS March 28-30, 1996, Texas Tech June 30,1995. For a copy of the Final DAKOTA April 28-29, 1995, Creighton University, Lubbock, TX Announcement, contact Doug Owens, University, Omaha, NE Spring 1997 Southwest Texas State Uni• 253 Arps Hall, The Ohio State Univer• sity, 1945 North High Street, Columbus, NEW JERSEY April 29, 1995, William versity, San Marcos, TX OH 43210-1172; (614) 292-8021; fax Paterson College, Wayne, NJ WISCONSIN April 12-13, 1996, Univer• (614) 292-7695; e-mail Owens.93@ sity of Wisconsin-Platteville NORTH CENTRAL April 21-22, 1995, osu.edu. Carleton College, Northfield, MN

FOCUS APRIL 1995 The Mathematical Association of America Second class postage paid at Washington, DC and 1529 Eighteenth Street, NW additional mailing offices Washington, DC 20036-1385