THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA Section Awards for Distinguished Teaching Volume 17, Number 4 Henry L. Alder It is a great pleasure to present the 1997 recipi• for nominating and selecting the award-win• ents of the Awards for Distinguished Teach• ning teachers. ing. The awards were conferred at the spring In this Issue The committee met on January 8 in San Diego. meetings of the sections. A representative from each section was invited 3 USAMO Winners The Committee on the Deborah and Franklin to this meeting to review in depth whether the Tepper Haimo Awards for Distinguished Col• distinguished teaching awards, after having 4 1997 Section lege or University Teaching of Mathematics been in effect for five years, are accomplishing recently nominated at most three of these dis• the purposes for which they were established. Teaching tinguished teachers for the national Deborah There was a consensus that they indeed have Awardees and Franklin Tepper HaimoAwards. The Board contributed to recognizing, rewarding, and of Governors acted on these nominations at its making wider use of the talents of outstanding 5 Participation of meeting on August 1, 1997 in Atlanta. college teachers of mathematics. There were several excellent suggestions intended to en• The committee has been greatly impressed with Women in the courage more people to submit nominations. the outstanding quality of this year's awardees MAA They will be communicated to all sections this and the wide variety of teaching strategies suc• fall. cessfully employed by these outstanding teach• 8 Fromthe ers. Such excellence has made ita great pleasure The national committee urges all members of Executive to read their files, but has also made the task of the Association to think of worthy candidates Director's Desk nominating the national recipients ofthe awards for these awards· and nominate them to the most difficult. appropriate section committee, including those residing in a section different from that of your 9 President's Report Those chosen for the national awards will make nominee. Even if your candidate should not be presentations on their successes as teachers at selected as a recipient ofthe award, remember the annual meeting in January 1998 in Balti• 11 New Members of that a nomination by itself is a distinct honor the Board of more. These sessions have become one of the and also that there is a simple procedure allow• highlights of the annual meeting. Because of ing a candidate to be nominated again if not Governors the favorable audience reaction, these presen• selected the first time. The larger the pool of tations are reprinted at least in summary form outstanding nominations, the easier it will be in FOCUS, and will appear on 21 Register early for MAA Online. to maintain the high standard for these awards the 1998 Joint The fact that twenty-five of the twenty-nine which have been so successfully established Mathematics sections selected awardees speaks well for the by the first six sets of awardees. Meetings support by the sections ofthe national effort to identify, reward, and honor the outstanding col• Henry Alder is a professor in the Department lege teachers of mathematics in the U.S. and of Mathematics at UC Davis and chair of the Canada. The national committee commends Committee on the Deborah and Franklin Tepper the sections' efforts in establishing procedures Haimo Awards for Distinguished College or University Teaching ofMathematics. His e-mail The Mathematical Association of America Postage paid at address is [email protected]. Washington, DC and 1529 Eighteenth Street, NW additional mailing offices Washington, DC 20036-1385 See page 4 for the awardees' photo spread FOCUS August 1997 FOCUS Editorial FOCUS is published by the Mathematical Association of America six times a year: February, April, June, August, October, Making the Invisible Visible and December. Mathematics is irrelevant to most people's invisible visible. This is a new slogan. Let Editor: Keith J. Devlin, Saint Mary's lives. That, at least, is what many people me give some examples of what I mean. College of California; devlin@stmarys• think, and what you occasionally read in ca.edu newspaper columns. When the popular Without mathematics, there is no way you Associate Editor: Donald J. Albers, MAA press clamors for better math skills among can understand what keeps a jumbo jet in Associate Executive Director and Director schoolchildren, what they mean is basic the air. As we all know, large metal objects of Publications and Electronic Services; numeracy, not mathematical thinking. don't stay above the ground without some• [email protected] thing to support them. But when you look It wasn't always so. Thirty years ago, ev• Editor-Elect: Harry Waldman, MAA; at ajet aircraft flying overhead, you can't eryone accepted that mathematics was [email protected] see anything holding it up. It takes math• terribly important-important for science, ematics to "see" what keeps an airplane Production Editor: Amy Fabbri, MAA; important for technology, important for aloft. In this case, what lets you "see" the [email protected] defense, important for the space race, and invisible is an equation discovered by the Copy Editor: Nancy Wilson, Saint Mary's important for economic growth. mathematician Daniel Bernoulli early in College of California; nwilson@stmarys• the eighteenth century. ca.edu Today's perception that mathematics is largely irrelevant comes at the worst pos• While I'm on the subject of flying, what is Advertising Coordinator: Joseph sible moment. As mathematicians, we Watson, MAA; [email protected] it that causes objects other than aircraft to know, even if most other people don't, that fall to the ground when we release them? Letters to the editor should be addressed to mathematics is more important in today's "Gravity," you answer. But that's just giv• Keith Devlin, Saint Mary's College of society than at any other time in history. ing it a name. It doesn't help us to under• California, P.O. Box 3517, Moraga, CA As members of the mathematics profes• 94575; [email protected]. stand it. It's still invisible. We might as sion, therefore, it is our responsibility• well call it magic. To understand it, you Subscription and membership questions and ours alone-to ensure that society have to "see" it. That's exactly what New• should be directed to the MAA Customer doesn't blow it. We must ensure that math• ton did with his equations of motion and Service Center, 1-800-331-1622; e-mail: ematics continues to receive support and mechanics in the seventeenth century. [email protected]; (301) 617-7800 (outside that enough people continue to pursue it. U.S. and Canada). Newton's mathematics enabled us to "see" A major part of the problem is that hardly the invisible forces that keep the earth The FOCUS subscription price to individual rotating around the sun and cause an apple members of the Association is $6.00, anyone knows what mathematics really included in the annual dues. (Annual dues is. If you pick someone at random on the to fall from the tree onto the ground. for regular members, exclusive of annual street and ask them to describe mathemat• Both Bernoulli's equation and Newton's subscription prices for MAA journals, are ics in a single sentence, the answer you equations use calculus. Calculus works by $68.00. Student and unemployed members are likely to get is something along the making visible the infinitesimally small. receive a 66 percent discount; emeritus lines, "Mathematics is using numbers." members receive a 50 percent discount; new That's another example of making the in• members receive a 40 percent discount for To counter this popular misconception, I visible visible. the first two membership years.) suggest we come up with and propagate U sing mathematics, we have already been Copyright © 1997 by the Mathematical one or two simple and easily remembered able to see into the distant past, making Association of America (Incorporated). slogans-sound bites if you like-that visible the otherwise invisible moments Educational institutions may reproduce capture in a single, easily remembered when the universe was first created in what articles for their own use, but not for sale, phrase, the very essence of mathematics. provided that the following citation is used: we call the Big Bang. "Reprinted with permission of FOCUS, the Here is one example: Mathematics is the Coming back to earth at the present time, newsletter of the Mathematical Association science ofpatterns. This slogan is not mine. how do you "see" what makes pictures of America (Incorporated)." I first saw it in print as the title of an article and sound of a football game miraculously Periodicals postage paid at Washington, DC in Science magazine, written by Lynn appear on a television screen on the other and additional mailing offices. Postmaster: Steen in the late 1980s, but Steen says it side of the country? One answer is that the Send address changes to the MAA, P.O. Box did not originate with him either. But pictures and sound are transmitted by ra• 90973, Washington, DC 20090-0973 whoever is the parent or creator of this dio waves-a special case of what we call ISSN: 0731-2040 particular slogan, I think it's a good one. electromagnetic radiation. But as with Printed in the United States of America. It captures both the nature and the scope gravity, that .... O· 1 :I fl.- - .. of mathematics. Here is another: Mathematics makes the ~!!i=~!!5!::!:r]e

2 August 1997 FOCUS mathematics. Maxwell's equations, dis• covered in the last century, make visible USAMO Winners, IMO Team Announced to us the otherwise invisible radio waves. Given to 182 students selected as a consequence Finally, using mathematics, we are able to of their performance on the 1997 American look into the future. For instance, prob• High School and American Invitational Math• ability theory and mathematical statistics ematics Examinations, the 1997 American let us predict the outcomes of elections, Mathematical Olympiad exam consisted of six often with remarkable accuracy, and we questions to be solved in six hours. The win• use mathematics to predict tomorrow's ners were: weather. Though in the case of looking Carl J. Bosley, Washburn Rural High School, into the future our view may be imperfect, Topeka, Kansas the use of mathematics nevertheless gi ves Li-chung Chen, Monta Vista High School, us a better view of the not-yet-happened Cupertino, California than we would otherwise have. To that John J. Clyde, New Plymouth High School, extent, it is another instance where math• New Plymouth, Idaho ematics makes the invisible visible. Nathan G. Curtis, Thomas Jefferson High I' II leave it as an exercise for the reader to School for Science & Technology (Alexan• provide more examples. That assignment dria), Reston, Virginia is optional. When it comes to spreading Kevin D. Lacker, Sycamore High School, Cin- these and other pro-mathematical slogans, cinnati, Ohio The 1997 USAMO Awardees on the Einstein Statue at the National Academy of Sciences. I don't think any of us has any option. We Davesh Maulik, Roslyn High School (Roslyn), Statue copyright 0 1978 Robert Berks need to do all we can to get the word out East Hills, New York and ensure the continued healthy survival Joshua P. Nichols-Barrer, Newton South High School (Newton Center), Newton, Mas- sachusetts of ou, ru.ciPlinf,Jjql Daniel A. Stronger, Stuyvesant High School (New York City), Little Neck, New York Top scorers Bosley, Chen, Clyde, Curtis, Nichols-Barrer (first place), and Stronger make up the U.S. International Mathematical Olympiad team. Bosley, Curtis, and Stronger competed in the 1996 IMO; Nichols-Barrerin 1995 and 1996. ThelMO took place July 24 and 25. The leader ofthe team was Titu Andreescu (Illinois Mathematics and Science The above editorial is abridgedfrom Keith Academy) and the deputy was Elgin Johnston (Iowa State University). Walter Mientka, Devlin s commencement address given at executive director of the American Mathematics Competitions, served as the official the University of California, Berkeley, on leader observer. Travel funds to the site of the IMO were provided by the Army Research May 23. The full text of the speech can be Office. Prior to the IMO, the USAMO winners at• found on MAA Online. tended the Mathematical Olympiad Summer Program (MOSP), June I8-July 16, sponsored by the Office The opinions expressed in the FOCUS edi• of Naval Research and the Matilda Wilson Founda• torial are those of the editor, and do not tion, with support from the University of Nebraska• necessarily represent the official views of Lincoln, the site of the program. theMAA.

Waits and Demana Win National Service Award In April, Professors Emeriti Bert K. Waits and Franklin Demana from The Ohio State University were presented the 1997 Glenn Gilbert National Leadership Award in Math• ematics Education by the National Council of Supervisors of Mathematics at their annual meeting in Minneapolis. The award recognizes the recipients' many years of in• service mathematics education work with teachers nationwide. Waits and Demana founded the internationally recognized T3 (Teachers Teaching with Ron Graham, AT&T. provided an enter• Technology) Program which began at Ohio State in 1986 as the C2PC (Computers and taining and educational lecture at the Calculators in PreCalculus) project. They were pioneers in developing pedagogical awards ceremony held in Washington methods using computer generated visualizations and incorporating the appropriate DC, June 16th. use of graphing calculators in the teaching and learning of mathematics. They are coauthors of two successful high school textbooks and many articles in professional journals.

3 FOCUS August 1997 1997 Section Awardees

Richard M. Dal'itt Eugene Wayne I.eI' H. ArmstrllllK Univer,ity of Louisville Pennsylvania State Uni\'ersity of ('emr.. 1 Kentucky Uni versity Florid .. Allegheny Mount,lin Flurida

Rhollda J. Hughe .~ I.owell Beilleke Bryn Mawr College Indiana nivcrsity Purdue EPADEL University Fort W.. ync Indiana

Rllger S. Pillkham Carlo .~ G. Spaht. /I Richard O. /Jill Stevens Institute of Louisi'lIl .. State Mi<:higan State University nivcrsity. Shreveport Techno logy Michigan Louisi ana- M is,issippi N~w Jl'r~cy

Troy 1_ J/icks Mona f'abricallt Universit y of Mis,ouri • Queensborough Rolla Community College Mis,ouri Metro New York

Steven R. DUllbar E. Richard U. Jan'inell I.ee May. Jr. University of Nebraska• Winona State University Sali shury State Universi ty Lincoln MD- DC- VA North Central Nebraska-SE South Dakota James J. Tattersall Jean Pedersen Providence Col!.:ge Santa Clara Uni versit y Nurtheastern Northern California

Brian D. Wick Douglas B. Aichele John S. Lancaster University of Alaska• Oklahoma State Marshall University Anchorage University Ohio Pacific Northwest Oklahoma-Arkansas

4 August 1997 FOCUS Participation of Women in the MAA - the Numbers

The Committee on Participation of Women in Mathematics has requested that the MAA collect data annually on the participation of women in mathematics and publish the data in FOCUS and MAA Online. This request was approved by the Board of Gover• Tlwmas Kelley nors at its August 1995 meeting in Burlington, Vermont. Metropolitan State College Michael E. GaKe of Denver University of Rochester Below is the information collected for the years 1995 and 1996. Rocky Mountain Seaway 1995 1996 1. Number/percent of female members of the MAA 8100 Womenl27% 7125 Womenl24%

~. Number/percent of female speakers at national meetings January 1995 January 1996 Lllkasz Prllski 161 Women/253 Men 215 Womenl41O Men University of San Diego Total: 414 Total: 625 Southern C;llifornia Female Speakers: 38.9% Female Speakers: 24.4% Alllle L /J/ldley August 1995 August 1996 Glendale CllnUl111nity 42 Women/67 Men 75 Womenl250 Men ColI~ge SOllthwc,tern Total: 109 Total: 325 Female Speakers: 38.5% Female Speakers: 23.1 % Annual Total Annual Total 203 Womenl320 Men 290 Womenl660 Men Total: 523 Total: 950 Female Speakers: 38.8% Female Speakers: 30.5%

Rho1lda L. Hatcher 3. Number/percent of female speakers at sectional meetings Texas Christian 1995 Spring 1996 niversity Texas Not available 270 Womenl571 Men Total: 841 Female Speakers: 32.1 % Fra1lci.

5 FOCUS August 1997 When Did Linear Algebra Enter the Curriculum? Carl C. Cowen

This article is abridgedfrom a lecture given on receiving the Deborah and Franklin Tepper Raimo Awardfor Distinguished College or University Teaching ofMathematics, San Diego, California, January 1997. Thefull text of the lecture can befound in MAA Online.

I taught linear algebra the first semester I Thus, in the past forty years or so, the lin• graduate student friend studying civil en• was in a college classroom and most se• ear algebra course has come into being as gineering and working on modeling vi• mesters since then. Today, it is a standard an abstract course for serious majors, has brations in buildings caused by part of any mathematics curriculum. But been revised into a first "intro to proof' earthquakes asked me how he could find it was not always so. In fact, linear alge• and "intro to abstract mathematics" course the eigenvalues of a 200X200 matrix that bra, as we know it today, has existed a for all math majors, and in many places were close to 12. (Unfortunately, at the comparatively short time. It first came to has now become a sophomore matrix-ori• time, I had no clue-the best advice I had be recognized as a subject in the 1930s. ented course for a wide variety of majors. to offer was to find all 200 and check which Particularly influential in this process were were closest to 12; I know better now!) In Why am I telling you this? I want you to the book of B. L. van der Waerden9 from the past two decades, the applications of realize that (regardless of the prevailing 1930 to 1931 and the book of Garrett linear algebra to real world problems have attitudes in your department) linear alge• Birkhoff and Saunders MacLane2 of 1941. mushroomed. The computer software bra has not "always" been done the way it Both were on "Modem Algebra," but in• Matlab provides a good example: it is is now, to suggest that we are in the middle cluded chapters on linear algebra. Histo• among the most popular in engineering of a "reform," and to use the history of the rian Jean-Luc Dorier5 regards Paul applications and at its core it treats every reform so far to point out where I think we Halmos' book6 Finite Dimensional Vector problem as a linear algebra problem. Sud• are and should be going. Spaces, first published in 1942, as the first denly students from all over the university book about linear algebra written for un• The first step is try to understand the de• are being advised to take a linear algebra dergraduates. velopments up to now. I believe that the course. The influx of these students with first courses grew out of the general axi• their different interests and, with the higher In 1936 and 1937 at Harvard, Birkhoff omatic approach to mathematics that was percentage of the population going on to taught an algebra course that included an common at that time. Historian Gregory college, the influx of students who are axiomatic treatment of vector spaces over MooreS regards the axiomatization of ab• mathematically not as well prepared have a field and linear transformations on finite stract vector spaces to have been com• forced many colleges and universities to dimensional vector spaces, and during pleted in the 1920s and many areas of change from courses dominated by proofs 1939-40 MacLane taught the same course mathematics had their foundations devel• of theorems about abstract vector spaces (see 8, page 295). I have looked at cata• oped in the first third of the century. I think to courses emphasizing matrix computa• logs from several colleges and universi• the success of the axiomatic method in tions and the theory to support them. ties to find out when their first this and related algebraic areas, as well as undergraduate courses in linear algebra Finally, why do we regularly teach linear the basic and important mathematical con• were taught. The separate linear algebra algebra? I believe that linear algebra de• tent, contributed to abstract algebra and course became a standard part of the col• serves a central place in the curriculum of linear algebra being given a prominent lege mathematics curriculum in the United math majors, and other students as well, place in the curriculum first for serious States in the 1950s and 60s and some col• because it is widely applicable, because it majors then for all math majors. leges and universities were still adding the is a subject where students can see, even course in the early 1970s. It appears that But the more recent phase of the reform without axiomatics, the development of a the linear algebra course I had in 1965 at has a different origin: I believe it is due to substantial mathematical theory, because Indiana University was one of the first the development and widespread use of it is a subject that provides the opportu• times it was offered there as a regular the computer in areas that apply mathemat• nity for students to see the role of that course although, at the time, I thought math ics. Surely engineers have known for more theory in doing computations and apply• majors had been taking it for decades. The than a century that many problems could ing mathematics, and because it provides catalogs make it clear that linear algebra be modeled as systems oflinear equations a vital arena where students can see the courses had been split away from the ab• or as eigenvalue problems. But what would interaction of mathematics and machine stract algebra courses that had developed be the point? Even in the 1950s, few engi• computation. I believe that the integration earlier. This was reflected in the very ab• neers could hope to solve a system of 100 of computation and theoretical mathemat• stract nature of the courses many of us equations in 100 unknowns; linear alge• ics is so natural in linear algebra that stu• took then: indeed, I could prove theorems bra was really irrelevant! By the 1970s dents (and faculty!) can use their on determinants of linear transformations engineers were beginning to use comput• experience with linear algebra as a start• on an abstract vector space but would have ers to solve practical problems using lin• ing point for seeking similar integration had difficulty in finding the determinant ear algebra. For example, in 1974, a in other mathematical areas. Linear alge- or inverse of a 4X4 matrix! 6 August 1997 FOCUS bra provides a course that is full of ideas, with material that is rewarding to learn Ten Mathematicians Elected to National and to teach, and is a subject where both student and teacher can be challenged to Academy of Sciences their best performance. Finally, I don't think students arriving as freshmen know The National Academy of Sciences has announced the election of sixty new members how to learn, certainly they don't know and fifteen foreign associates from eleven countries, in recognition of their distin• how to learn mathematics. Students need guished and continuing achievements in original research. to learn how to integrate a theoretical and Election to membership in the academy is considered one of the highest honors that can computational understanding of math• be accorded a U.S. scientist or engineer. The new elections bring the total number of ematics. Learning linear algebra can help current active members to 1773. them do that. Students who have learned how to learn linear algebra have learned The National Academy of Sciences is a private organization of scientists and engineers how to learn mathematics! dedicated to furthering science and its use for the general welfare. The academy was established in 1863 by a congressional act of incorporation, signed by Abraham Lin• References coln, that calls on the academy to act as an official adviser to the federal government, lAxler, S. "Down with Determinants!" upon request, in any matter of science or technology. American Mathematical Monthly vol. 102 The mathematicians elected are: (1995): 139-154. Michael Aizenman, Professor of Mathematics and Physics, Department of Physics, 2Birkhoff, G. and MacLane, S. 1941. A Princeton University, Princeton, NJ Survey ofModem Algebra. New York, NY: Charles H. Bennett, IBM Fellow, IBM TJ. Watson Research Center, Yorktown Heights, Macmillan. NY 3Carlson, D., Johnson, C. R., Lay, D. C., Jeff Cheeger, Professor of Mathematics, Courant Institute of Mathematical Sciences, and Porter,A D. "The Linear Algebra Cur• New York University, New York City, NY riculum Study Group Recommendations Joel E. Cohen, Professor of Populations, Rockefeller University, New York City, NY for the First Course in Linear Algebra." Carl De Boor, P.L. Chebyshev Professor of Mathematics and Computer Sciences, Center College Mathematics Journal vol. 24 for Mathematical Sciences, and Steenbock Professor of Mathematical Sciences, (1993): 41-46. University of Wisconsin, Madison, WI William Fulton, Professor of Mathematics, University of Chicago, Chicago, IL 4Carlson, D., Johnson, C. R., Lay, D. C., Edward Nelson, Professor of Mathematics, Department of Mathematics, Princeton Porter, A. D., Watkins, A, and Watkins, University, Princeton, NJ W., eds. 1997. Resources for Teaching Anthony J. Tyson, Distinguished Member of the Technical Staff, Lucent Technologies, Linear Algebra. Washington, DC: MAA Murray Hill, NJ 5Dorier, J. "A General Outline of the Gen• The newly elected foreign mathematicians are: esis of Vector Space Theory." Historia Mathematica vol. 22 (1995): 227-261. Grigory I. Barenblatt, Visiting Professor, Department of Mathematics, University of California, Berkeley, CA (Russia) 6Halmos, P.1942. Finite Dimensional Vec• Alain Connes, Professor, Institut des Hautes Etudes Scientifiques, and Professor, Col• tor Spaces. Princeton, NJ: Princeton Uni• lege de France, Paris, France versity Press. Foreign associates are non-voting members of the academy, with citizenship outside the 7Leon, S., Herman, E., and Faulkenberry, U.S. The election brings the total number of foreign associates to 309. R. 1996. ATIAST Computer Exercises for Linear Algebra. Upper Saddle River, NY: Prentice Hall. 25th Annual Mathematics and Statistics 8Moore, G. "The Axiomatization of Lin• ear Algebra: 1875-1940." Historia Conference Mathematica vol. 22 (1995): 262-303. Miami University, Oxford, OH 9van derWaerden,B.L.1930--31.Moderne Algebra, 2 vols. Berlin, Germany: Springer September 26-27, 1997 Verlag. The principal speakers will be Terry Herdman, Andrew Sterrett, and William Professor Cowen teaches at Purdue Uni• Pulleyblank. Abstracts for contributed papers should be sent to Prof. Charles Holmes, versity in West Lafayette, Indiana. His e• Dept. of Math & Statistics, Miami University, Oxford, OH 45056; (513) 529-5818; mail address is [email protected]. fax: (513) 529-1493; [email protected]. Conference programs with infor• mation concerning preregistration and housing are available. WWW: http:// miavx I.muohio.edu/-mstcwis/events.html

7 FOCUS August 1997 From the Executive Director's Desk Marcia Sward Which Way Did the Bicycle Go? and Other and its members. Through the Liaisons we by are providing mathematics departments It is extremely gratifying to watch the Intriguing Mathematical Mysteries, Joseph D.E. Konhauser, Dan Velleman, with a steady stream of information - MAA grow, with each passing year, in and Stan Wagon; an engaging collection current events, scholarly meetings, pro• influence and in its capacity to serve the of ingenious mathematical problems ... fessional development opportunities, pub• needs of our members and of our commu• solutions included! lications, activities for students, and other nity. There are so many things happening concerns of the profession. that I couldn't possibly write about them We established a partnership with Cam• all in this brief report. But to give you a bridge University Press (CUP) for distri• Professional Development sense of the energy and creativity that are bution of MAA books abroad. We are Almost everything we do at the MAA falls reshaping the MAA, here are a few high• delighted to see our books turning up in under the heading "professional develop• lights. bookstores all over the world! ment." We are proud to offer a number of Project NExT Math Horizons short courses, minicourses, and workshops around the country. A new activity is pro• Certainly Project NExT (New Experiences Math Horizons continues to grow as a fa• fessional development conducted over the in Teaching) ranks as one of the MAA's vorite of thousands of undergraduate stu• Web. This summer, our first Web courses most valuable programs. Under the in• dents and their teachers. During the past are being offered on an experimental ba• spired leadership of Chris Stevens and Jim year, Horizons featured profiles of math• sis. We expect to be launching many more Leitzel, NExT is providing professional ematicalluminaries William Perry (former such courses in the coming years. Let us development opportunities and a commu• secretary of defense), Ron Graham, Karen know what you would like to see on the nity of peers for eighty or so new Ph.D.s Uhlenbeck and Tom Banchoff. Warm Web. each year. The Exxon Education Founda• thanks to the many volunteers who con• tion, Project NExT's generous and proud tribute articles to the magazine, and to Fund Raising sponsor, recently extended funding for Editor Don Albers, for making Math Ho• We owe a large debt of gratitude to our another three years. rizons such an attractive and rich resource generous sponsors. Without them, many SUMMA for our students. of our excellent programs would not ex• ist. Sincere thanks go to the Alfred P. Sloan Strengthening Underrepresented Minor• Communications in Foundation, Bamberger Memorial Fund, ity Mathematics Achievement (SUMMA) Visual Mathematics Carnegie Corporation of New York, U.S. continues to reach out to underrepresented The newest entry in our family of math• Department of Education, Eskuche Foun• minority students and faculty in a variety ematics journals, Communications in Vi• dation, Exxon Education Foundation, of creative ways. In conjunction with the sual Mathematics, will be launched in the Matilda R. Wilson Fund, National Secu• San Diego meeting, with support from the fall under the editorship of Tom Banchoff rity Agency, National Science Foundation, National Science Foundation, SUMMA and David P. Cervone. A prototype is up Office of Naval Research, and the Tensor hosted a very special event for students on MAA Online (www.maa.org) to give Foundation. from intervention programs around the readers the opportunity for input into the country. For most students, this was their final design. We are also grateful for the support the very first professional meeting-talk about MAA has received from over one thou• excitement! IMO USA 2001 sand individual donors. A special insert in Books This spring, we officially established a new FOCUS, Solutions, will highlight the hu• corporation, IMO USA 2001, Inc., to host man side of the many projects which the During 1996, we published an impressive the IMO (International Mathematical Greater MAA Fund helps to support. list of titles, including: Olympiad) in the United States in 2001. A Watch for it! A Primer of Real Functions, by Ralph five-year grant from the U.S. Department Our Planned Giving program is also con• Boas, Jr.; the fourth edition of the classic of Education will help at each stage of tinuing to grow. In the fall we received a Carns Monograph. planning and development. IMO 2001, $25,000 bequest from G. Cleaves Byers, which will involve teams from about one Julia: A Life in Mathematics, by Constance a professor at Michigan Tech and a mem• hundred countries, is certain to be a very Reid; a touching tribute to Julia Bow• ber of the MAA for over thirty -three years. special event in the life ofthe United States man Robinson by her sister, Constance Several other generous members have also mathematics community. Reid. declared the MAA as a beneficiary in their Liaisons Program insurance policies. These gifts play an im• Vita Mathematica, Ronald Calinger, Edi• portant role in helping to assure a strong The Liaisons Program, launched only a tor; a fascinating addition to MAA's MAA in the future. growing list of titles on the history of year ago, already shows every sign of mathematics. becoming a vital link between the MAA

8 August 1997 FOCUS

ing things both on-line and on paper. That ing nicely and we should have good news President's Report will be expensive. On the positive side, to announce soon. We have additional good we are already eagerly anticipating the first news about Project NExT: it has received Gerald L. Alexanderson regular issue of our new electronic jour• funding from the Exxon Foundation for A report from this president is, my friends nal, Communications in VisualMathemat• an additional three years. ics. The sample issue was just full of good tell me, overdue. I agree. But before I begin And talking about exciting projects, I ideas. a report on the state of the Association, let should say that at our May Executive and me make a personal comment. I picked up Before I leave publications-and it's very Finance Committees meetings, we ex• the May Monthly the other day and hard for me to move away from publica• plored ways of keeping our SUMMA couldn't put it down. There was Judy tions-I would like to report that a long• project active in continuing its work. in Grabiner's fascinating article on time reader and admirer of the Monthly, encouraging participation in mathematics Maclaurin's Treatise on Fluxions, Marvin Schaefer, and his wife, Mary Alice by underrepresented groups, even in a time Laczkovich's note on Lambert's proof of Schaefer, recently made the Association when funding is increasingly difficult to the irrationality of n, Grant's review of one of the beneficiaries of a charitable find and when the Association's own bud• Vita Mathematica. Instead of writing an remainder trust that will in time result in a get makes significant direct support un• overdue President's Report, Ijust sat there very significant bequest, one that will likely. reading the Monthly. And reading it made enhance the Association's endowment That brings me to the question of the me proud to be associated with the MAA. considerably. I met with these donors on a MAA's finances, the cause of some ru• Of course, that experience was not new. recent trip to Washington and we had a mors following the San Diego Board of Earlier this year in the Monthly there was great time exchanging stories about math• Governors meeting. While the long-term Karen Parshall's article on Sylvester. And ematicians and talking mathematics. This financial outlook is very good-a nearly in the CM] there was the Abbott and Richey good news, along with reports of signifi• paid off mortgage on the Washington article on Monopoly and in the Magazine cantly increased contributions to the building, the prospects for increased book Don Saari's fascinating piece on individual Greater MAA Fund, is very encouraging sales, a good fundraising record-the cur• rights. Is any mathematical organization and an indication that our members and rent period is one of belt-tightening, and anywhere in the world publishing mate• friends are willing to contribute more than that's always painful and unsettling to rial as interesting and as accessible as that their time and energy to further the work those who care a lot about the MAA. But which appears in our journals? It's a good of the Association. thing I'm not on any of our prize commit• let me reassure our members that rumors tees on publications-I don 'tthink I could When it became clear a couple of years notwithstanding, the MAA is strong, with make the difficult choices to decide just ago that Seattle would be the site of our a devoted Washington staff, many enthu• which article is deserving of a prize. I like last joint AMS-MAA MathFest, at least siastic volunteers on our over one hun• them all. in this century, many of us were concerned dred committees, and a role in the over whether the MAA could organize a American mathematical scene that is not And then there are those new books: an• successful MathFest on its own. Well, of like any other and a role many of us see as other Ross Honsberger volume, a new course we could! There have been prob• extremely important. book by Ed Barbeau, one by Martin lems in going it alone, but of one thing I won't expound here on the many and Gardner, the Resources for Teaching Lin• there is no doubt-we can certainly put diverse activities of the MAA (you can ear Algebra, the student assessment vol• together a superb program on our own, read about them elsewhere )-the planned ume edited by Alan Schoenfeld, and a with a first-class short course on epidemi- IMO 2001, the NCTM Standards review brand new contest problem book, with 010gy modeling (cosponsored by the Cen• being chaired by Ken Ross, professional many more on the way. No wonder I have ters for Disease Control headquartered development programs, student chapters, so little time. I even have trouble keeping right there in Atlanta), the Erdos tribute and Math Horizons. (Where else do you up with what is on MAA Online, which is with a lineup of stars, an impressive series get a "new" Tom Lehrer song these days, full of interesting material. of talks by our Hedrick Lecturer, Elliot and with a line like "How much gold can Lieb, of Princeton, and on and on. Our In December I attended, as part of a three• one hold/in an elephant's ear?lWhen it's program committee, chaired by Barbara day meeting of the Council of Scientific noon on the moonffhen what time is it Osofsky, our Associate Secretary Donovan Society Presidents, a symposium on the here?" Pure Tom Lehrer.) The list goes on Van Osdol, and our Associate Executive future of electronic vs. print publishing. and on. As more and more serials move on-line, Director Dan Kalman, who handled ar• the question naturally arises, how long can rangements in the Washington office, all But here I am, back on publications. Per• we continue to issue journals on paper? deserve kudos. haps it is not inappropriate that the President's Report take on the form of a Of course, expository journals such as ours One of the most effective activities spon• rondo. I'll get back to some of those other are read differently from the way research sored by the MAA, Project NExT, joined lively themes (MAA projects) at a later journals are used, so the experience of us in Atlanta for another set of meetings time. others is not necessarily directly applicable held in conjunction with a summer to our situation. But the general advice MathFest. Right now, though we're not Professor A lexanderson teaches at Santa was that for the indefinite future, scien• quite ready to announce something, plans Clara University. His e-mail address is tific organizations can expect to be issu- for a 1998 summer MathFest are progress- galexanderso@ scuacc. scu.edu. 9 I' R [ ;'\ C [ I' L E S "/ SOL;'\ [) R E [ [ R E ,\\ E :\ C[ [;'\ \' E S C[ [ ;'\ C OVER ONE MIIJLION OF THE BEST MINDS IN AMERICA HAVE ALREADY CHOSEN THE BEST RETIREMENT SYSTEM. TIAA-CREF.

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°Based on a survey conducted in 1995 by an independent organization in which 96% of respondents expressed overall satisfaction with TIAA-CREF. oOTIAA is one of only a handful of companies that currently hold the highest marks from the nation's leading independent rating agencies for stability, sound investments, claims-paying ability. and overall financial strength: A++ (Superior), AM. Best Co.; AAA Duff & Phelps; AM, Moody's Investors Service; AAA, Standard and Poor's. TIAA's guarantees are backed by its claims-paying ability. These ratings of TIAA as an insurance company do not apply to CREF. CREF certificates are distributed by TIAA-CREF Individual and Institutional Services, Inc. For more complete information, including charges and expenses. call 1 BOO 842-2733. extension 5509. for a prospectus. Read the prospectus carefully before you invest or send money. August 1997 FOCUS New Members of the Board of Governors Martha Siegel The Mathematical Association ofAmerica prides itself on the work of sections and the governance system that engages rep• resentatives of the sections in the essen• tial decisions of the organization. It has been an honor to serve on the Board of Governors with those section governors who completed their three-year term at the Jalll"s R,C. u: il~'" Richard S, R"lIIfle/ end of June. All have been active mem• bers of the Board. They have contributed their wisdom, asked good questions, and helped us to make informed decisions on all facets of the Association's activities. Although we will miss their contributions .. ~ " ," to the Board, we have no intention of al• ( ;.." lowing any of them to retire from the work of the committees and councils of the MAA. Now that we know their many . 1," strengths, we are ready to tap them for other jobs! David Stone has already been . '". elected chair of the Committee on Sec• ~ tions, and is serving, in that capacity, an• Roger II, //0,." other three-year term on the Board and its Executive Committee. Thanks to Willard A. Parker (Kansas), Lanny C. Morley (Missouri), Barbara L. Osofsky (New Jersey), Karen J. Schroeder .A..- (Northeastern), David E. Kullman (Ohio), , ~ Harvey J. Schmidt, Jr. (Pacific Northwest), , , Stephen R. Cavior (Seaway), David R. Stone (Southeastern), and Richard B. Th• I ompson (Southwestern). Your service to the MAA is deeply appreciated. It is a pleasure to congratulate and wel• '\ OOllllhl II! Ji""'/It'r I Oill/glll\ Ftli,..·\ come the new Iy elected section governors: Richard S. Rempel, Bethel College (Kan• sas), Alvin R. Tinsley, Central Missouri State University (Missouri), Theresa C. Michnowicz, Jersey City State College (New Jersey), Dennis M. Luciano, West• ern New England College (Northeastern), J. Douglas Faires, Youngstown State Uni• versity (Ohio), Yves Nievergelt, Eastern Washington University (Pacific North• west), Donald W. Trasher, SUNY College at Geneseo (Seaway), Sylvia T. Bozeman, Joanne V. Peeples Spelman College (Southeastern), and Alvin R, Tinsley Joanne V. Peeples, EI Paso Community College (Southwestern). New governors• and Roger A. Hom, University of Utah seated on the Board. They are members of at-large are James R.C. Leitzel, Univer• (ex-officio). different sections, though they live in the same house! (Hint: Only one is a section sity of New Hampshire (teacher As a note for historians, at the August governor!) education), Jeffery C. Lagarias, AT&T meeting of the Board, and for the first time, Labs (mathematicians outside academia), governors married to each other will be Not pictured: Jeffery C. Lagarias

11 FOCUS August 1997 Teaching Students with Learning Disabilities

The following articles, by Randy Schwartz, are reprinted from The Right Angle, newsletter of the Schoolcraft College Mathematics Department, volume 2, January 1995. Many of us have begun to notice a more of the psychological processes involved "prove" that their invisible disabilities are diverse, more interesting body of students in understanding or in using language indeed handicaps. Conversely, they may on campus. With passage of the Ameri• spoken or written, which may manifest be made to feel the social stigma that often cans with Disabilities Act of 1992 (ADA), itself in an imperfect ability to listen, think, attaches itself to handicaps. we are now seeing more learning disabled speak, read, write, spell, or to do math• In a number of classic experiments, it was and other handicapped students, includ• ematical calculations. The term includes shown that conscious or unconscious ing in our math classrooms. such conditions as perceptual handicaps, teacher expectation of students' perfor• brain injury, minimal brain dysfunction, In the "old days," learning disabled stu• mance exerts a large influence on their dyslexia, developmental aphasia. The term dents were pulled out of regular classrooms success or failure. There is a tendency for does not include children who have learn• and herded into special education "ghet• us to shape the students we expect to do ing problems which are primarily the re• tos." Horror stories were legion, and it is well into successes, and to shape the stu• sult of visual, hearing, or motor handicaps, now generally agreed that this dual educa• dents we expect to do poorly into failures. of mental retardation, of emotional distur• tional system was a disservice both to This shaping phenomenon has been bance, or of environmental, cultural, or "regular" and "special" students. dubbed "Pygmalion in the Classroom," economic disadvantage." after the ancient myth in which Pygmalion The new concept of "least restrictive en• Some of the most common types of learn• shaped into clay his idea of the perfect vironment" for learning disabled and other ing disabilities include perceptual prob• woman, then brought her to life. handicapped students, popularly known lems of various forms; sensorimotor as main streaming , was mandated by the Evidence suggests that people with learn• difficulties; various memory disorders; Education for All Handicapped Children ing disabilities have significant aphasia, a deficiency in the reception, as• Act (Public Law 94-142) enacted in 1975. psychoneurological and information pro• sociation, or expression oflanguage; dys• This law requires that such students be cessing difficulties-so it would be too lexia, a reading disorder characterized by educated within regular classrooms or simplistic to blame their problems purely symbol confusion; dyscalculia, a numeri• educational environments that are as close on bad teaching. Nevertheless, it has been cal ability disorder; dysgraphia, a hand• to normal as possible. The ADA extends shown that poor instruction is a primary writing disorder; attention deficit disorder and reinforces main streaming by directly cause of problems encountered by many of various types; and hyperactivity. opening to such students the doors of col• LD students in math and other subjects. In leges and other institutions. Learning disabilities may vary, but they this sense, we as educators will either be almost always affect the ability to learn part of the problem or part of the solution. These policies open up new opportunities mathematics. Four of the most common not only for individuals, but for educa• Perhaps worst of all are instructors who LD symptoms seen in math classrooms tional institutions as well. Most impor• are unwilling to muster the extra time, are incomplete mastery of arithmetic and tantly, all of society benefits when more effort, or patience that may be vital in other basic facts; difficulty understanding of its members are well educated. Of helping persons with LDs to succeed. or retaining abstract mathematical con• course, teaching a learning disabled stu• When students are written off as failures, cepts; difficulty recalling the necessary dent does require special care. It can be it is a prediction that is self-fulfilling. steps in a problem-solving process; and frustrating, both for the students and for difficulty comprehending work problems. the instructor-especially if inappropri• Learning Disabilities: A "High Suggestions for addressing these types of ate attitudes or techniques are brought to difficulty are included in the following Tech" Challenge bear. article "How Do I Teach a Learning Dis• With the enactment ofAD A, those of us in What is a Learning Disability? abled Student?" the teaching profession should take the opportunity to ask ourselves: how skillful A learning disability (LD) is a permanent Why Do Our Own Attitudes are we in actually figuring out teaching disorder that affects the way people with Matter? techniques that work for a diverse student normal or above-average intelligence take body? in, retain, or express information. Data As if the direct obstacles posed by their inside the brain can be lost-like in a faded learning disabilities were not difficult The "easy" thing would be to regard these newspaper---or become scrambled-like enough, persons with LDs also confront people as "hopeless," and watch them be radio static or a fuzzy TV picture-as it socially imposed handicaps-the tossed away like so much refuse. What a makes its way to or from the eyes, ears, manmade obstacles that can frustrate their waste! The alternative is to use all of our mouth, or hands. efforts in the classroom and elsewhere. ingenuity and all of the means at our dis• They may be made to feel they have to posal to help these students attain the suc• Public Law 94-142 defines specific learn• cess they are indeed capable of attaining. ing disability as "a disorder in one or more

12 August 1997 FOCUS How Do I Teach a Learning Disabled Student? Ideas from Some Recent Research Say: Decide how many steps and op• unknown problems. Such strategies are Below is a sample of ideas culled from erations are needed. Write the opera• helpful organizing tools to students strug• journals dealing with research and prac• tion symbols (+, -, x, I). gling with mathematics. tice in learning-disabled instruction. Space Ask: If I do ... , what will I get? If I Goal strategies entail setting and reach• here permits only the barest summary of a do ... , then what do I need to do next? ing target levels of performance. In one few key ideas. The articles themselves How many steps are needed? technique, the instructor provides the stu• provide much greater detail and all-around dent with a graph of performance (score Check: That the plan makes sense. information. or percent) versus time (day, week, test One cluster of techniques that has been of S. Estimate (predict the answer) number, etc.). On this graph, a positively sloped goal line has been drawn. As the use in LD instruction are the cognitive Say: Round the numbers, do the prob• student completes tests and retests, the strategies, designed to help students ap• lem in my head, and write the estimate. ply existing skills across different situa• scores are plotted as points on the same tions and settings. A cognitive strategy that Ask: Did I round both up and down? graph, and the resulting curve is drawn. has been successfully used to teach LD Did I write the estimate? This helps instructor and student, on any students the skill of solving mathematical given day, to discuss the progress being Check: That I used the important informa• word problems was described in the jour• made toward the final goal and to set the tion. nal Learning Disabilities Research and next day's goal. (See Whinnery and Fuchs, Practice (see Montague, Applegate, and 6. Compute (do the arithmetic) "Effects of Goal and Test-Taking Strate• Marquard, "Cognitive Strategy Instruction gies on the Computation Performance of Say: Do the operations in the right or• and Mathematical Problem-Solving Per• Students With Learning Disabilities," der. formances of Students with Learning Dis• LDR&P 8, Fall 1993.) abilities," 8, Fall 1993). The Ask: How does my answer compare LDR&P Much LD research has built upon tried• strategy involves a seven-step solution with my estimate? Does my answer and-true techniques. One that has proven make sense? Are the decimals and plan. Students are asked to memorize the to be effective in presenting a wide variety names of the seven steps, and with de• money signs in the right places? of mathematical ideas is to move from the tailed examples they are taught how to Check: That all the operations were done concrete to the semiconcrete to the abstract carry out each step in a "say, ask, check" in the right order. (i.e., from objects to pictures to symbols). fashion, as follows: Many of us recall being taught this way 7. Check (make sure that everything is about the basic facts of arithmetic (say 1. Read (for understanding) right) eight plus three, oreighttimes three). First Say: Read the problem. Ifl don't un• Say: Check the computation. such facts can be illustrated with a succes• derstand, read it again. sion of manipulative objects, such as but• Ask: Havelcheckedeverystep?Have Ask: Have I read and understood the tons, coins, checkers, popsicle sticks, etc. I checked the computation? Is my an• problem? When students can get at least 80% of their swer right? arithmetic problems correct with the aid Check: For understanding as I solve the Check: That everything is right. If not, go of these objects, they move on to pictorial problem. back. Then ask for help if I need it. problems, first using sketches of the ob• 2. Paraphrase (your own words) jects, and then tallies. When they have Two cognitive strategies that have been mastered these, they move on to symbolic Say: Put the problem in my own especially studied as aids in mastering rote representations, such as 8 + 3 =11 or 8 X words. computations are test-taking strategies and 3 =24. This basic technique can be adapted goal strategies. Ask: Have I underlined the important to many different situations. (See Miller information. What is the question? Test-taking strategies guide students to and Mercer, "Using Data to Learn About What am I looking for? approach and take tests in a systematic Concrete-Semiconcrete-Abstract Instruc• and efficient manner. In one technique, tion for Students with Math Disabilities," Check: That the information goes with the students approach their tests with a three• LDR&P 8, Spring 1993.) question. step process. First, they prepare by review• Students with learning disabilities often ing their most recently completed test on 3. Visualize (a picture or a diagram) have a hard time memorizing basic facts this skill. Second, in taking the current test, Say: Make a drawing or diagram. of arithmetic. Without this automatic pro• students start at the top and immediately ficiency, further progress in math will be Ask: Does the picture fit the problem? answer questions they are sure of (Le., the stunted. The teaching strategy of constant sure problems) and circle the questions Check: That the information goes with the time delay is useful with arithmetic or they are less sure of (i.e., the kinda sure other rote calculations. A series of prob• question. problems). Third, they return to answer lems is presented on flashcards, on a com- 4. Hypothesize (a plan to solve the prob• kinda sure problems before attempting lem) 13 FOCUS August 1997 puter screen, or whatever is available. The student is given a constant time delay of Just Who Is It That's "Dumb?" either 3, 4, or 5 seconds (as appropriate) to state, type, or write the answer. The delay The lack of understanding and compassion toward disabled people is sometimes as• provides the student with the opportunity tounding. The article "Disadvantaging the Advantaged" in the business magazine Forbes to "beat the teacher" (or tutor or class• (November 21,1994) posed the question, "Does it make sense to spend more money on mate). These sessions are continued daily dumb kids than on smart kids? Would any management worth a damn put most of its until the student gets 100% correct on one, dollars into its weakest divisions and starve the promising ones of capital?" The article two, or three consecutive sessions. (See goes on to rail against the federal spending levels for the education of learning disabled Kocinski and Hoy, "Teaching Multiplica• and other handicapped and disadvantaged children, all of whom it lumps together under tion Facts to Students With Learning Dis• the label "dumb." Contrast this with the attitude of a group of people who have made abilities: The Promise of Constant Time some real contributions to learning. For the past fifteen years, the American Association Delay Procedures," LDR&P8,FallI993.) for the Advancement of Science has included a Luncheon for Students with Disabilities at its annual meeting. Many who once attended the luncheon as kids now return to speak Some LD research in mathematics has as professional scientists. The 1994 luncheon in San Francisco invited thirty students focused on developing positive attitudes with learning disabilities, thirty with mobility impairments, twenty deaf or hearing• toward math and reducing math anxiety. impaired, and fifteen blind or vision-impaired students. Kent Cullers, a signal detection For example, one article lists six questions scientist with the Search for Extraterrestrial Intelligence project, NASA Ames Research that can be asked of test-anxious algebra Center, encouraged the youngsters to pursue their thirst for science-just as he did at students before giving an exam. The ques• their age-and not get derailed by the sneers of society. tions are designed to help the students discuss their emotional, cognitive, and historic experiences with algebra. Ques• tion 5 reads "Have you ever had any experiences where a teacher, parent, or other significant per• Letter to the Editor son: (a) said or implied that you were 'dumb' or could not learn this subject; (b) pressured you to master math; (c) grew Editor, impatient when trying to help you with math? Describe these." Congratulations to FOCUS and the authors on the incisive article on page 17 of the April issue, attacking the use of the question, "How do you rate the instructor?" The It was found that test-anxious students who article mentions that minorities and women may be downgraded because of prejudice. were given this opportunity to explore their I believe two other considerations may·inspire students to denigrate their professor: feelings about algebra outperformed simi• lar students not given the opportunity. (See 1. Instructors who give C's, D's, and F's for low achievement. If an instructor gives only Hirsch, "Helping Students Overcome the A's and B's, ratings tend to be higher. Effects of Difficult Learning Histories," 2. Science and mathematics. Instructors in other fields tend to get higher ratings (see Journal of Developmental Education 18, point 1). College algebra is especially unpopUlar. Winter 1994.) Sometimes I feel that colleges would like to give students a choice: they could (a) learn Additional steps used to reduce math anxi• mathematics or (b) write an essay titled "How Terrible Teaching Prevented Me From ety include ensuring that all prerequisites Ever Learning Mathematics." are firmly in place before new material is attempted; working to reduce the sense Some students are projecting their own weaknesses on their professors. Colleges should that math is divorced from real life; clearly encourage students to take responsibility for their own learning. If students have a communicating that students who attend problem with an instructor, they should not wait until the end of the course to release to the lesson will be able to master the bile. They should talk privately with the instructor early in the course and try to come material; and refusing to accept hopeless• to an understanding. ness. (See Burton and Meyers, "Teaching Unfortunately there is a lot of bad teaching in mathematics, beginning in grade school. Mathematics to Learning Disabled Stu• In my college mathematics classes, I ask the students to write a mathematical autobi• dents in the Secondary Classroom," Math• ography. I discuss these writings and tell them, "I realize you have been through an ematics Teacher, December 1987.) ordeal with mathematics. 1 ask you to put that behind you and learn what you can with me." If the instructor can show compassion for the student's feelings, sometimes a Randy Schwartz is editor of The Right lifetime of ineffective learning can be overcome. Angle and chair of the Department of Mathematics at Schoolcraft College in Elizabeth Berman Appelbaum, Ph.D. Livonia, Michigan. Shawnee Mission, Kansas

14 August 1997 FOCUS

der, Margaret & Lyman Aldrich, Howard Anton Jim Freeman 0 James D. Gates, Hugh Gordon, o Donald Batman, Lynne A. Baur, Kathleen The Greater MAA Ronald Gove, Adonis Gray, Dewey M. Griffith, Baxter, Gerald E. Bergum, Manuel & Maria Peter A. Gutterman 0 Adam O. Hausknecht, Jerry Berriozabal (In Honor of Arnold Ross), Martin M. Hawn, Katherine Heinrich, Fritz Herzog, Fund Billik, Harold R. Bishop, Peter Bjorklund, John GeraidA. Heuer, Aaron M. Hexamer, J. G. Home, D. Bradburn, Robert L. Bryant, Milo F. Bryn 0 John M. Horvath, V. Dwight House, Laurence G. Below are listed the generous supporters Stephen R. Cavior, Nathaniel Chafee, Jean Bee Hoye, Jiannshiun Huang, Ruth E. Hubbard, James of the Greater MAA Fund for 1996 and Chan (In Gratitude and Admiration for Professor F. Hurley 0 Franklin T. Iha, Lloyd K. Jackson, thefirstquarterof1997. The Board of Gov• Frederick Valentine, Emeritus Professor of UCLA Carl G. Jockusch, Jr., Russell E. Jones 0 Steve and my Doctoral Thesis), Jack D. Clayton 0 Jan emors thanks you for contributing to the Karpinos, John B. Kelly, Thomas C. Kipps, Rob• Dash, M. Hilary Davies (Wick), Guy De Primo, MAA programs and projects that enrich ert C. Knapp, Ralph M. Krause, Kenneth KUnen Robert L. Devaney, G. Diantonio, James A. the entire mathematics community and o Kathy Layton (In Honor of William T. Puckett), Donaldson, William E. Dorion, Thomas Drucker Jack Y. Lee, M. A. Linton, Nicholas J. Lord, profession. The special programs develop (In Memory ofLloydA. Walker), RobertL. Druet Norman W. Lord (In Memory of Estella C. Lord) and support new mathematicians and in• o David M. Einstein, Edward T. Esty, John Ewing, oJ. J. Malone, Heinrich Mantel, Walter crease the skills and opportunities for those Lawrence E. Freeman 0 Pedro J. Geraldo, Maurice Markowitch, Jr. , Arthur Mattuck, Farley Mawyer, working in mathematics education. Gilmore, Richard P. Goblirsch, Samuel Goldberg, Douglas B. Meade, David Merriell (In Honor of Robert Graves 0 Samuel W. Hahn, John L. Hank, Paul J. Kelly), Sandra Ann Mertes, Alice & Rob• Grand Benefactors Gloria C. Hewitt, Shirley A. Hill, Patricia Hokman ert T. Mertz, Arthur F. Miller, Peter E. Moore, Richard D. Anderson, Tom & JaneApostol,Alice (In Memory of William W. Hokman), Cdr. Jo• Richard A. Moore, Ronald G. Mosier, Benjamin C. Beckenbach (In Memory ofD.R. Curtiss &A. seph A. Hughes 0 Richard E. Johnson 0 Dan N.Moyls,JohnMuth,WinMyintoTogoNishiura, W. Tucker), Mary L. Boas, Malcolm K. Brachman Kalman, Wilfred Kaplan, John T. Kearns, Jr., Anne F. O'Neill, Philip Oppenheimer, Michael (In Honor of Deborah Tepper Haimo), Jean E. de Donald Keenan, Daniel Kennedy, Genevieve M. L. Oristaglio, Robert Osserman, Robert W. Owens Valpine (In Honor of S. Ulam), Andrew Gleason, Knight, Donald Kreider, David E. Kullman (In oHung-Ming Pan, Diego Pareja, Paul M. Perdew, Anna S. Henriques (In Memory of C. R. Wylie, Honor ofG. Baley Price) 0 Jeanne Laduke, Charles Juanita J. Peterson, Alan G. Poorman, Marjorie Jr.), RichardA. Hord, Robert G. Maule, Everett Livingston, Clifford A. Long, Graham Lord 0 E. Poorman, Jean Porte, Wilbur Pritchard, George Pitcher, John W. & Susan Poduska, Anonymous William D. Maness, C. E. & Nimfa Mannix, May Pryjma 0 Albert L. Rabenstein, Russell L. Ralph, (1) H. Maria,Andrew J. Matchett, GeraldA. Mischke, John Rawson, Irma M. Reiner (In Memory of W.O. Murray 0 Ivan Niven, Calvin I. Owens 0 Irving Reiner), Annabel & Charles E. Rickart, Charles E. Pagano, Jr., Hiram Paley, John W. & Benefactors WilliamM. Rodgers, Jr., Jean-Louis Roque, N.J. Alfred & Dorothee Aeppli, Gerald L. Joyce M. Petro, Vaughan R. Pratt 0 Gregory Rose, Wilson Ruiz-Torres, C. Peter Rydell 0 Rajewski, Janet Ray, RobertR. Reitano, Franklin Alexanderson, Alliance Capital Management L.P. Patrick A. Sandoz, Diran Sarafyan, Donald E. B. Richards, William G. Rosen, Sharon Ross, (as a Matching Gift), Edward & Rosemary Baker, Sarason, John J. Schiller, Ernest C. Schlesinger, Shepley Ross 0 Priscilla Cehelsky & Jeffrey Raymond A. Barnett, Barbara J. Beechler, Will• Marshall P. Scott, Edward Shapiro, Bonnie Sachs, Hans Samelson, Doris Schattschneider, iam G. Chinn (In Honor of Ken Ross), William L. Sherwood (For the Education Fund), Martha J. Joel E. Schneider, John A. Schumaker, Norman Duren, Jr., Joan & Jim Leitzel, Morris Newman, Siegel (In Honor of the Hood College Chapter of E. Sexauer, Melvin & Florence Shader, Artha J. Robert A. Rosenbaum, Michael M. Rubenstein, Pi Mu Epsilon), Louise A. Simon, Donald Small, Snyder (In Memory of Richard S. Burington), Andrew & Kaarina Sterrett, Marcia P. Sward, P. DavidA. Smith, RichardA. Smith, Sidney Smith, Bernard Sohmer, Louis Solomon, Olaf P. Uri Treisman, George C. & Claudine Watson, Robin N. Soloway, Linda R. Sons, David R. Stackelberg, Kevin Stinson, David R. Stone 0 Anonymous (l) Spharler, Michael Stecher, Marjorie Stein, Kevin William J. Terrell, John A. Thorpe, Dirck Stinson, D. Derk Swain 0 J. D. Tarwater, Brad Uptegrove, Sr. PaulJ. Villemure 0 JoeF. Wampler, Grand Patrons Tashenberg, Laurence R. Taylor, Elizabeth Teles, Elizabeth & Robert Weinstock (In Honor of Paul Ronald M. Davis, C. G. "Tino" & Mary Ann Jaime Terrazas, Robert H. Thompson, Roseanna Bateman), Alex Weintraub, Maurice D. Weir, Mendez (In Memory of Professor S. M. Ulam), Torretto, Henry S. Tropp, Carolyn C. Tucker, Tho• Allyn Washington,AlfredB. & Shirley B. Willcox James G. Wendel, Robert B. & Lena M. Wenger, mas W. Tucker 0 Visutdhi Upatisringa, Robert Izaak Wirszup, Ling-Erl E. Wu, Alun Wyn-Jones Valadez, John P. Van Alstyne 0 Frank W. Warner, o Paul J. & Eleanor Zwier, Anonymous (3) Patrons Michael Yanowitch, Lee Shuk Yee 0 Marilyn J. CaroleA. Bauer, StewartE. Boden, J.H. & Roma Contributors Zweng, Anonymous (2) Butchart (In Honor of Harry Levy) 0 Gregory M. 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Skocik, Josiah Slack, Stephanie Sloyan, A. Cohen, Michael P. Cohen, Samuel D. Conte, Irwin K. Feinstein, Michele M. Ferland, Daniel Geraldine D. Smith (In Memory of Mary P. Samuel G. Councilman, James P. Crawford, Ann C. Fielder, Holland C. Filgo, Sandra Fillebrown, Doiciani), James L. Smith, Kerry D. Smith, M. Curran, James L. Current, Philip C. Curtis' AA Finco, Benjamin Fine, William M. Finlay, Virgina Snell, Michael J. Sormani, Roger A. George Decker, Charles R. Diminnie, Kotaro Kenneth E. Fitzgerald, Mary E. Flahive, Richard Stafford, Blair Sterbaboatwright, Richard S. Dokeh, Joseph L. Doob, Ivan Doszpoly SJ, J. Fleming, RobertA. Fontenot, Karen S. Frank, Stevens, A.D. Stewart, Thomas N. Strickland, Wiliam H. Durfee' Alexander S. Elder, Joanne Edgar A. Franz, Susan Fredine, E. Clare Fried• Charles S. Stuckey· Lajos F. Takacs, Steve Elliott, George W. Ellis, J ulieA. England· Cecilia man, Ben A. Fusaro' Robert O. Gamble, Regina Taniguchi, Edward C. Thoele, James W. 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Robinson, Stanley Sarawathi S. Magill, Rosemary Mahoney, Den• Dezur, Roberto Diaz-Fernandez, Robert S. Doran, J. Rocko, James W. Roth, Edouard Ryser· David nis R. Maim, Giles W. Maloof, Margaret O. Reuben C. Drake, Lincoln K. Durst· Frank M. Sanders, E. W. Sanders, Blin B. Scatterday, Marchand, William Marion, Richard W. Marsh, Eccles, Earl F. Ecklund, Jr., HaroldP. Edmundson, Murray M. Schacher, John Scharf, Anne J. Mario U. Martelli, Joseph T. Mason, Gus William I Eggers, James W. Ellis, Gerard G. Schimmel, Charles M. Schneeberger, John R. Mavrigian, John S. Maybee, Byron L. McAllister, Emch, Jessie A. Engle' Frank Farris, Farhad Schue, Chantal M. Shafroth, Charles M. Shenitz, Mary McCammon, Janet McDonald, O. C. Farzad, George F. Feeman, Solomon Feferman, Dale A. Siegel, David A. Singer, John & Nancy McGehee, John McGuire, Roy H. McLeod, Rob-

16 August 1997 FOCUS ert F. McNaughton, Jr., J.G. McPhail, Robert C. Ron Rietz, James S. Robertson, David W. Roeder, E. Taylor, Loretta Thielman, Kirk J. Thieroff, Meacham, William Mech, Morris Meisner, Joseph C. Rogers, Bob Rosenfeld, George M. Owen P. Thomas, Shirley W. Thompson, Tho• Carolyn L. Meitler, Burnett C. Meyer, Herman Rosenstein, Arthur J. Rosenthal, Haskell P. mas Thorsen, Wolfgang J. Thron, Ronald F. Meyer, EdwardA. Meyers, Tixier Michel, Tatiana Rosenthal, EmilioO. Roxin, Dorothy S. Rutledge, Thurston, Douglas Tisdahl, Charles R. Traina, Mihnea, Shirley G. Miller, Jan Minac, Judith A. Peter M. Ryan, Charles J. Rykken • John C. Sa• James E. Trefzger, John J. Tremmel, Goetz Mings, Charles W. Mitchell, Jr., Robert B. Mollo, ber, David Sachs, Saturnino L. Salas, Valerie F. Trenkler, Theodora L. Tsakiris • Yasushi Unai, Ted R. Monroe, Robert H. Moore, Tetsuro Sand, Sarwan S. Sandhu, Mayra Alonso Richard J. Vance, W. Van der Meiden, RichardA. Motoyama, Orville B. Mott, Michael L. Motto, San Roman, Richard L. Schauer, Stephen Vandervelde, Andrew H. Van Tuyl, Argelia L. Marvin G. Mundt, H. Bernice Munro, H. Deon Schecter, Irene V. Schensted, Renato M. Castro Velez-Rodriguez, Justin M. Verst· Gretchen B. Murphy, Michael G. Murphy, William H. Myers Scher, Hans Schneider, Gregory A. Schou, George Wagner, Philip Wagreich, Michael C. Ward, John • Charles W. Neville, Lloyd C. Nietling, Scott R. R. Schriro, Mark L. Seligman, Jean T. Sells, C. Weaver, CarrollA. Webber, Volker Weber, John Nollet, Ronald D. Notestine, William Novinger, Arthur G. Settle, Joe! Shapiro, Louis W. Shapiro, Weibel, Anthony A. Weidner, Lawrence R. Weill, John J. Nowakowski, Teruo Nushiro • Brian Henry Sharp, Jr., Jack V. Shaw, John M. Shaw, Joan Weiss,Julian Weissglass, RobertA. Welker, Olerich, Rene E. Olivares, John A. Oman, John Albert D. Sheffer, Ching-Kuang Shene, David M. Wells, Aubrey D. Wentworth, Willes Oosterhout, Pedro Julio Ortiz, Harold Ox sen • Alexander L. Shklyarevsky, PJ Short, Stuart J. L. Werner, Robert W. Wettingfeld, Edward C. Joseph W. Paciorek, David L. Pagni, Helen L. Sidney, Jack Silber, Allan Silberger, Roger W. White, Jr., Raymond E. Whitney, Elaine Paisner, Mark D. Pankin, Elwood G. Parker, Simond, Robert C. Simonsen, Mary E. Sinamon, Whittlesy, Agnes J. Wieschenberg, John V. Gordon Parker, Susan R. Patterson, Painadath E. S. Judson (Jud) Sinton, Muriel Skoug, Bruce F. Wiggins, John F. Wilkinson, Robert S. Williams, Paulose, Paul S. Peck, William H. Peirce, Dennis Sloan, Lloyd B. Smith Jr., Rubin Smulin, Charles Patricia S. Willis, George W. Wimbush, Fred S. D. Pence, David E. Penney, John W. Pennisten, E. Snygg, Jimmy Solomon, Heidi A. Staebler, Wintrobe, William Wolz, Bing Wong, Robert H. Marvin Perlman, Lars D. Peterson, G. Edric Alfred T. Steele, Michael Stein, EnidM. Steinbart, Wood, George V. Woodrow III, David J. Wright Phillips, James C. Piza, Vera S. Pless, John Charles I. Steinhorn, Frank Stenger, Robert J. • George Xenakis, Donald J. Ying, David M. Polking, Richard Pollack, Peter R. Pomeroy, Stem, Rudolph M. Sternheimer, T. Christine Young, Gail Young, Paul M. Young, Bernard J. Marian B. Pour-e!, Stanley Preiser, K. David Stevens, Phillip P. Stich, Jurgen O. Stigter, Allen Yozwiak· Radu Zaharopol, Michael E. Zeidler, Prince, George D. Pryjma • Richard Quint, Gor• H. Stix, Emmanuel Stogiannis, Elmer L. Stone, Joel Zeitlin, Ben F. Zirkle, David E. Zitarelli, don Raisbeck, Jeffrey K. Raloff, John Rausen, Jeffrey L. Stuart, Pete J. Stuckey, Charles S. Paul M. Zorn, Anonymous (5) Maxwell Reade, James C. Reber, Mike Reekie, Sutton, Ronald Sverdlove, Stewart G. Swerdlow, Total of 1092 donors giving $63,900. James E. Reiland, Richard B. Remington, Bruce Robin Symonds, H. E. Syrett, Peter P. Szabaga, A. Reznick, Steve J. Ricci, Robert M. Richardson, Bogdan Szafraniec· Jeanette H. Tanaka, Angus MAA Publications Order Form Sale Books listed on pages 18 & 19 Shipping and Handling Postage and handling are charged as follows: USA orders (shipped via UPS): $2.95 for the first book, and $1.00 for each additional book. Allow 2-3 weeks for delivery. (Please note that UPS will not deliver to a P.O. Box). RUSH SERVICE, you will be charged actual postage plus a $7.00 handling fee. Canadian orders: $4.50 for the first book and $1.50 for each additional book. Canadian orders will be shipped within 2-3 weeks of receipt of order via the fastest available route. We do not ship via UPS into Canada unless the customer specially requests this service. Canadian customers who request UPS shipment will be billed an additional 7% of their total order. Overseas orders: $3.50 per item ordered for books sent surface mail. Airmail service is available at a rate of $7.00 per book. Foreign orders must be paid in US dollars through a US bank or clearing• house. Credit Card orders are accepted for all customers. ()rdcr Forlll

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Mathematical Carnival Lore of Large Numbers Series: Spectrum Series: New Mathematical Library MARTIN GARDNER PHILIP J. DAVIS A collectio n of nineteen tantalizing What notations and techniques are used puzzles taken from Martin Gardner's col• to deal with numbers, large and small? umn in SCientific American. Includes a What is the historical background for Foreword by John Horton Conway, M• calculations? These questions and many terthoughts, a Postscript, and a new Bib• more are answered in this volume. liography by Martin Gardner, and Catalog Code: NML-06/FOC97 Backtalk from the readers of Gardner's 165 pp., Paperbound, 1961 columns. ISBN 0-88385-606-9 Catalog Code: MCR/ FOC97 List:~ Sale: $4.99 320 pp., Paperbound, 1988 ISBN 0-88385-448-1 List: $+5-:00 Sale: $4.99 You're The Professor, What Next? , . The Life of Stefan Banach Series: MAA Notes BETIYE ANNE CAsE ROMAN KALUZA The theme of the book is simple: Young 4x.j TRANSLATED AND EDITED By mathematicians ought to receive some ANN KOSTANT AND WOJBOR WOYClYNSKI organized professional training in graduate The author presents engaging descrip• school. We ought to teach mathematicians how tions of Banach's personality and the to be mathematicians. usual milieu in which he worked. This -John Ewing biography is accessible to anyone with an interest in mathematics, and can be Catalog Code: NTE-35/FOC97 read by teachers as well as students at 362 pp., Paperbound, 1994 both the high school and undergradu• ISBN 0-88385-091-5 ate level. List: $29.95 Sale: $9.99 Catalog Code: BANACH/FOC97 200 pp., Hardbound, 1996 ISBN 0-8176-3884-9 List: $24:5e Sale: $ 9.99 Hungarian Problem Book I (Eotvos Competitions) Riddles of the Sphinx The Trisectors Book 1,1894-1905 Series: New Mathematical Library Series: Spectrum Series: New Mathematical Library MARTIN GARDNER UNDERWOOD D UDLEY J. KURCHAK, TRANSlATED BY The material in this book was drawn from A companion to Mathematical Cranks the ELVIRA RAPAPORT STRASSER Gardner's column in Isaac Asimov's Sci• MAA is happy to offer its readers This volume contains the Eotvos com• ence Fiction Magazine. The riddles pre• Underwood Dudley'S The Trisectors. This petitions from 1894-1905. Included in sented here incorporate the responses book is also about mathematical cranks• this volume are nonroutine problems of his initial readers, along with addi• angle trisectors. which are solvable by elementary means. tions suggested by the editors of this se• ries. Catalog Code: TRI/FOC97 Catalog Code: NML-ll /FOC97 176 pp., Paperbound, 1994 III pp., Paperbound, 1963 Catalog Code: NML-32/FOC97 ISBN 0-88385-514-3 ISBN 0-88385-611-5 184 pp., Paperbound, 1987 List: $t&.95 Sale: $9.99 List: $t&.OO- Sale: $4.99 ISBN 0-88385-632-8 List: $+5-:00 Sale: $4.99

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In Eves' Circles The High School Contest Stories about Maxima Series: MAA Notes Problem Books and Minima jOBY ANTHONY The two problem books listed below con• Series: MAA/AMS Mathematical World Ifyour interest is history of mathematics, ge• tain the problems and solutions to the V.M. TIKHOMIROV ometry, or pedagogy, then this is the book for Annual High School Mathematics Exami• TRANSLATED BY ABE SHENITZER you. A valuable sampler. . .for a mathematics nations (AHSME) given from 1961 to The author familiarizes readers with educator, particularly one with a strong in• 1972. There are challenging problems in concrete problems that lead to discussion terest in the history of mathematics. the areas ofalgebra, geometry, trigonom• of the work of some of the greatest - The Mathematics Teacher etry, logic, number theory, and combina• mathematicians of all time in the solution Catalog Code: NTE-34/FOC97 torics. of maxima and minima problems. 220 pp., Paperbound, 1994 Catalog Code: MAXIM/FOC97 ISBN 0-88385-088-5 Contest Problem Book II 187 pp., Paperbound, 1991 List:-$2+.95 Sale: $9.99 AHSME 1961-1965 ISBN 0-8128-0165-1 Series: New Mathematical Library List: ~ Sale: $9.99 COMPILATION AND SOLUTIONS BY C.T. SALKIND Catalog Code: NML-17/FOC97 112 pp., Paperbound, 1966 ISBN 0-88385-617-4 Fixed Points List: $t&.-OO Sale: $4.99 Series: MAA/AMS Mathematical World Yu A. SHASHKIN Contest Problem Book III TRANSLATED FROM THE RUSSIAN BY VIKTOR MINACHIN AHSME 1966-1972 This book presents readable exposition Series: New Mathematical Library offixed point theory. The author focuses COMPILATION AND SOLUTIONS BY on the problem of whether a closed in• C.T. SALKIND AND J.M. EARL terval, square, disk or sphere has the Catalog Code: NML-25/FOC97 fixed point property. 186 pp., Paperbound, 1973 Catalog Code: FIX/FOC97 ISBN 0-88385-625-5 88 pp., Paper• Shaping Space List: $t3:OO Sale: $4.99 bound,1991 Series: Spectrum ISBN 0-8218- 9000-X FIXed Points GEORGE FLECK & MARJORIE SENECHAL Mathematics: Queen and Shaping Space is an exuberant, richly il• List: $2+.e9 Sale: lustrated, interdisciplinary guide to Servant of Science $9.99 three-dimensional forms, focusing on Series: Spectrum E.T. BELL the surprisingly diverse world of polyhe• An absorbing account of pure and dra. applied mathematics from the geometry Catalog Code: SPACE/FOC97 of Euclid to that of Riemann and its 312 pp., Hardbound, 1988 application in Einstein's theory of ISBN 0-8176-3351-0 relativity. List: $+5:-95- Sale: $9.99 Catalog Code: QAS/FOC97 454 pp., Paperbound, 1987 ISBN 0-88385-447-3 Studies in the History List: $t+.99 Sale: $4.99 of Mathematics Series: Studies in Mathematics ESTHER R. PHILLIPS, EDITOR The material covers a wide range of current research topics: algebraic Use order form on page 17 number theory, geometry, topology, logic, the relationship between mathematics and computing, partial differential equations, and algebraic or geometry. Catalog Code: MAS-26/FOC97 320 pp., Hardbound, 1987 call 1-800-331-1622 ISBN 0-88385-128-8 List: $t5:OO Sale: $4.99 19 FOCUS August 1997 One-day STATS Workshop Harvard Supported by the National Science Foun• • make effective use of technology in their Mathemati cian dation, the Mathematical Association of statistics courses America is conducting a series of faculty • use authentic assessment practices in Awarded National development workshops designed for evaluating the work of their statistics mathematicians who teach courses in in• students troductory statistics but have little formal • discover a myriad of print and electronic Medal of Science training in the subject. resources for teaching statistics Shing-tung Yau, professor of mathemat• • engender lasting collegial relationships A one-day STATS workshop will be held ics at Harvard University, is among the among mathematicians who teach sta• at Estrella Mountain Community College nine scientists who have just been in Avondale, Arizona on October 25, 1997. tistics awarded the National Medal of Science. The application deadline is September 17, Support from the NSF provides lunch and Awarded by President Bill Clinton, the 1997. You may apply from the STATS web a variety of workshop materials related to medal recognizes exemplary work in such teaching statistics. There is no registra• site athttp://stats.dickinson.edu/ or by re• diverse fields as human genetics, math• questing an application form from Jane tion fee for the workshops. Workshop ematics, physical science, and cognition Heckler, STATS Project Registrar, Math• participants or their institutions are ex• and learning. It is widely regarded as the ematical Association of America, 1529 pected to cover travel costs, and partici• U.S. equivalent of the Nobel prize. Eighteenth St., NW, Washington, DC pants must have e-mail accounts. 20036-1385; (202)387-5200; fax President Clinton cited Yau for profound Goals of the workshop are to help faculty (202)483-5450; e-mail: jheckler@maa. contributions to mathematics that have participants to: org had a great impact on fields as diverse as topology, algebraic geometry, general • teach statistical thinking with more data You may also direct questions to project relativity and string theory. His work and concepts, less theory and fewerreci• directors Allan Rossman (rossman@ insightfully combines two different math• pes dickinson.edu) and Tom Short (short@ ematical approaches and has resulted in • explore active learning alternatives to monet. vill.edu). the solution of several longstanding and the lecture method in their teaching of important problems in mathematics. statistics

Numerical Linear Algebra Applied Numerical Linear Algebra Lloyd N. Trefethen and David Bau, III James W. Demmel "A beautifully written textbook offering a " ... a wonderful text blending together the distinctive and original treatment. It will be of mathematical basis, good numerical software, use to all who teach or study the subject." and practical knowledge for solving real problems . .. , - Nicholas]. Higham, destined to be a classic." University of Manchester. - Jack Dongarra, University of Tennessee, Knoxville. Designed for use as a stand-alone textbook Designed for use by first-year graduate students from a variety in a one-semester, graduate-level course in of engineering and scientific disciplines, this comprehensive the topic, Numerical Linear Algebra is a textbook covers the solution of linear systems, lea t squares timeless presentation that provides a concise, insightful, and problems, eigenvalue problems, and the singular value decom• elegant introduction to the fie ld of numerical linear algebra. position. Includes state-of-the-art developments. 1997/ xii + 361 pages • Softcover • ISB 0-89871-361-7 August 1997 . Approx. 450 pages . Softcover • ISB 0-89871-389-7 List Price $34.50 • SIAM Member Price $27.60 • Order OT50 List Price $45.00 • SIAM Member Price $36.00 • Order OT56

TO ORDER Shipping and Handling Use your credit card (AM EX, MasterCard, and VISA): Call toll free in USA: USA: Add $2.75 for the first book and $.50 for each additional book. 800-447-SIAM; Outside USAcaU: 215-382-9800; Fax: 215-386-7999; [email protected] Canada: Add $4.50 for the first book and $1.50 for each additional book. Or send check or money order to: SIAM, Dept. BKF097, P.O. Box 7260 Phila• Outside USA/Canada: Add $4.50 per book. All overseas delivery is via airmail. delphia, PA 19101-7260 . • http://www.siam.org • SCIENCE AND IND UST RY ADVANCE WITH MATHEMATICS 51 a nt.. Society for Industrial and Applied Mathematics

20 Baltimore Advance Registration/Housing Form Membership Name v' all that apply Mailing Address ______~ AMS 0 ASL 0 AWM Telephone Fax ______0 CMS PI .... compl.t. this Email Address 0 form .nd return It to: MAA 0 Mathematics Meetings B.dge Service Bureau (MMSB) Information: Name to appear on badge NAM 0 P. O. Box 6887 Affiliation for badge SMM 0 Providence, RI 02940-6887 FAX: 401-455-4004 Nonmathematician Guest Badge QuestlonS/chang.s c.lI: (please note charge below) 401-455-4143 or 1-800-321-4267 x4143 If you do not wish your program and badge to be mailed to you on 12110197, check this box. 0 Registration Fees Events .Iolnt M_tlngs by Dec 19 at mtg Events with Tickets Price Per Total D Member AMS, ASL, CMS, MAA $155 $202 AMS Banquet #_Regular #_Veg #_Kosher $32 D Nonmember $240 $312 MER Banquet #_~Regular #_~Veg #_~Kosher $32 D Graduate Student $ 35 $ 45 NAM Banquet #_~Regular #_~Veg #_~Kosher $32 D Undergraduate $ 20 $ 26 D High School Student $ 2 $ 5 Total D Unemployed $ 35 $ 45 Student Activities D Temporarily Employed $105 $125 D Mathchats (no charge) D Developing Countries Special Rate $ 35 $ 45 D MAA Student Workshop (no charge) D Emeritus Member of AMS or MAA $ 35 $ 45 D High School Teacher $ 35 $ 45 D Librarian $ 35 $ 45 Statistical/Other Infonnation D Nonmathematician Guest $ 5 $ 5 Mathematical Reviews field of interest # D One-day Member $121 D I am a mathematics department chair. D One-day Nonmember $172 How did you hear about this meeting? Check one: AMS Short Course on Slngu'ar Perturbation Concepts lor D Notices D Focus D WWW D Colleague(s) D Special Mailing Dltte.. ntla. Equations. D Please do not include my name on any mailing list used for promotional Registration for the Joint Meetings is not required for the Short Course. purposes. D Member, Nonmember $75 $ 90 D Please v' this box if you have a disability that requires D Student, Unemployed, Emeritus $35 $ 45 special services.

Employment Register Registration for the Joint Meetings is required for participation. Applicant Deadlines resume forms and employer job listing forms will be on e-MATH in Room lottery November 7, 1997 September and in the October issues of Notices and Focus. Housing reservations, listing of resumes/job D Employer--First Table $200 $250 descriptions in the Winter Lists November 20, 1997 D Regular D Self-scheduled Housing reservation changes/cancellations D Employer--Second Table $ 50 $ 75 through MMSB December 8, 1997 Regular Self-scheduled D D Advance registration, Employment Register, D Employer--Posting Only $ 50 $ 50 Short Course, banquets December 19, 1997 D Applicant $ 40 $ 75 50% Refund on banquets December19,1997* 50% Refund on advance registration .Ianuary 2, 1998* Payment *no refunds after this date Category Total Method of Payment D Check. Make checks payable to the AMS. Checks drawn on foreign banks Joint Meetings fee(s) must be in equivalent foreign currency at current exchange rates. AMS Short Course D Credit Card. VISA, MasterCard, AMEX, Discover. (no others accepted) Employment Register Card Number: ______

Event tickets Exp. Date: ____ Zipcode of credit card billing address: ______Hotel deposit (only if paying by check) Signature: ______Total amount paid $ Nameoncard: ______(Please note that a $5 processing fee will be charged for D Purchase Order # ______(please enclose copy) each returned check or invalid credit card.) Hotel Reservations

Below is the non-descriptive list 01 hotels at which reservations can be made through the Mathematics Meetings Service Bureau (MMSB) this lall. A more detailed list including rates lor these hotels and a list of lower-priced hotels/motels that can be called directly will be published in the October issues 01 Notices and Focus and at www.ams.org/amsmtgs/2014jntro.html. Reservations at the following hotels must be made through the MMSB to receive the convention rates listed. All rates are subject to a 12.5% sales occupancy tax. Ouarant_ requirement.: First night deposit by check (... rev..... of form, or • credit c.rd guar.nt_. D Y•• , I w.nt to re_rv •• room now ba•• d on the inform.tlon glv.n. I und.r.t.nd th.t my requ•• t m.y not be proc•• sed until I.t. Sept.mb.r 1997. D Deposit enclosed D Hold with my credit card number Exp. Date Signature ______D.t •• nd Tim. of Arriv.I ______D.t •• nd Tim. of Departure ______N.m. of Other Room Occup.nt ______Arrlv.1 D.t. Departure D.t. Spouse D Child __ (glv•• g.'

Order Hotel Single Double Double of choice 1 bed 2 beds Renaissance Harborplace (hdqtrs) $102 $112 $112 Students $82 $92 $92 Hyatt Regency Baltimore $102 $112 $112 Students $95 $95 $95 Omni Inner Harbor Hotel $92 $92 $92 Students $86 $86 $86 Days Inn Inner Harbor $80 $80 $80 Students $70 $70 $70 Marriott Inner Harbor $96 $106 $106 Students $86 $86 $86 Sheraton Inner Harbor $95 $95 $95 Students $85 $85 $85 $82 Clarion Hotel (Mt Vernon Square) $82 $82 r Students $72 $72 $72 71f r Baltimore Hilton & Towers $86 $86 $86 Students $77 $77 $77 f I Holiday Inn $79 $79 $79 e'· Tremont Hotel (all suites) $65 $65 $65 Ie 11H~ Tremont Plaza (all suites) $75 $75 $75

In' 10lil arI.~ 1H" Students $65 $65 $65 1..... 'L"dtrn"-.n•• .,. ._ .. 'l''''"'. I I I I •• '•• rll'llla'-""',,", .. lll

Specl.1 Hou.lng Requ•• t.:. D I have disabilities as defined by the ADA that require a sleeping room that is handicap accessible. If you .re not m.klng • re•• rv.tion, pl •••• ch.ck off on. of the following: My needs are: ______o I plan to make a reservation at a ater l date.

II you are a member 01 a hotel frequent-travel club and would like to receive appropriate credit, D Iwill be making my own reservations at a hotel not listed. Name 01 hotel: ______please include the hotel chain and card number here: ______D I live in the area or will be staying privately with family or friends. Other requests: ______D I plan to share a room with , who is making reservations. August 1997 FOCUS

MEETINGS

MD-DC-VA - November 21-22, 1997, - March 26-27, 1999, Southern Nazarene National MAA Meetings Mount St. Mary's, Emmitsburg, MD University, Bethany OK August 1-4, 1997 MathFest, Atlanta, GA -April 17-18, 1998, Virginia State Uni• ROCKY MOUNTAIN - April 17-18, January 7-10, 1998 Eighty-first Annual versity, Petersburg, VA 1998, Araphoe Community College, Littleton, CO Meeting, Baltimore, MD; Board of Go v• - Fall 1999, Towson State University, ernors Meeting January 6, 1998 Towson, MD - April 1999, Adams State College, Alamosa, CO January l3-16, 1999 Eighty-second An- MICHIGAN - October 3, 1997, Northern nual Meeting, San Antonio, TX; Board Michigan Univ, Marquette, MI - April 2000 Colorado State Univer- of Governors Meeting January 12, 1999 sity, Ft. Collins, CO - May 1-2, 1998, Western Michigan Uni• January 19-22,2000 Eighty-third Annual versity, Kalamazoo, MI SOUTHEASTERN-March 13-14, 1998, Meeting, Washington, DC; Board of College of Charleston, SC Governors Meeting January 18,2000 - May 1999, Eastern Michigan Univer• sity, Ypsilanti, MI SOUTHERN CALIFORNIA - Oct 4, January 10-l3, 2001 Eighty-fourth An- 1997, Claremont McKenna College, MISSOURI - April 17-18, 1998, South• nual Meeting, New Orleans, LA; Board Claremont, CA of Governors Meeting January 9, 2001 west Missouri State University, Spring• field, MO SOUTHWESTERN - Spring 1998, Pima Community College, Tucson, AZ Section Meetings - Spring 1999, Rockhurst College, Kan• ALLEGHENY MOUNTAIN - March 27- sas City, MO SEAWAY - November 7-8, 1997, Siena 28 1998, Clarion University of PA, College, Loudonville, NY Clarion, PA NEBRASKA-SOUTHEAST - April 1998, York University, No. York, SOUTH DAKOTA-April 1998, Wayne EASTERN PA & DELAWARE-Novem• Ontario, Canada ber 1,1997, University of Pennsylvania, State College, Wayne, NE - November 1998, Nazareth College, Philadelphia, PA NEW JERSEY - November 8, 1997, Rochester, NY - Spring 1998, Shippensburg University, Montclair St. College, Montclair, NJ TEXAS - Spring 1998, Southern Meth• Shippensburg, PA NORTHEASTERN - Nov 21-22, 1997, odist University, Dallas, TX FLORIDA - March 6-7, 1998, Florida Western New England College, Spring• Atlantic University, Boca Raton, FL field, MA - Spring 1999, Southwest Texas State University, San Marcos, TX - March 5-6, 1999, Florida Gulf Coast NORTHERN CALIFORNIA - Feb• Comm College, Panama City, FL March, 1998, Stanford University, WISCONSIN - April 24-25, 1998, Uni• Stanford, CA versity of Wisconsin-Stevens Point, ILLINOIS - March 27-28, 1998, Stevens Point, WI McKendree College, Lebanon, IL OKLAHOMA-ARKANSAS - March 27- 28, 1998, University of Arkansas-Little - April, 1999, Concordia University, INDIANA - October 18, 1997, Wabash Rock,AR Mequon, WI College, Crawfordsville, IN - March 20-21, 1998, Ball State Univer• sity, Muncie, IN DIMACS Workshop - November 7, 1998, St. Mary's College, Notre Dame, IN Networks in Distributed Computing DIMACS Center, Rutgers University, Piscataway, NJ, October 27-30, 1997 INTERMOUNTAIN-AprillO-ll,1998, Sponsored by DIMACS, the workshop is intended to bring together researchers from Brigham Young University, Provo, UT both academia and industry who specialize, as either theoreticians or practitioners, in KENTUCKY - March 27-28, 1998, the field of networks in distributed computing. Currently network-related research is Morehead State University, Morehead, quite large and active within distributed computing. Our main objective is to provide KY a snapshot of major themes of current technological significance on the design, use, influence, efficiency, and performance of networks in distributed computing. LOUISIANA-MISSISSIPPI - March 6- 7, 1998, University of New Orleans, LA For further information, contact Marios Mavronicolas, University of Cyprus; [email protected]. For local arrangements, contact Pat Pravato, DIMACS -March 5-6, 1999, Jackson State Univer• Center; (908) 445-5929; [email protected]; WWW: h11Illil sity, Jackson, MS dimacs.rutgers.eduIWorkshops/index.html

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