Coulll on Controversy 20 Use and Care of Numbers 8 In this issue 5 A Student Guide to the National Math Meetings 8 The Use and Care of Numbers Math Horizons is for undergraduates and others who are interested in mathematics. 12 Internships Its purpose is to expand both the career and intellectual horizons of students. 14 Art Benjamin-Mathemagician DONALD J. ALBERS Editor BEVERLY JOY RUED1 21 Census 2000: Count on Controversy Managing Editor CAROL BAXTER 24 Exploring Moduli Spaces Associate Manapng Editor JANE D'ALELIO 26 A Dozen Questions About a Donut Art Director Math Horizons (ISSN 1072-4 1 17) is pub- Problem Section lished four times a year; September, 32 November, February, and April by the Mathematical Association of America, 1529 Eighteenth Street, NU!, Washington, DC 20036. September 1998 Volume VI, Issue 1. Periodicals postage paid at Washington, DC and additional mailing of- fices. Annual subscription rates are S20.00 for kL4A members and S33.00 for non- members and libraries. Bulk subscriptions sent to a single address are encouraged. The minimum order is 20 copies (3120.00); additional subscriptions may be ordered in units of 10 for 360.00 per unit. For advertising rates or editorial in- quiries call (202) 387-5200. Printed in the United States of America. Copyright 01998 The Mathematical Association of ,h~erica.POSTMASTER: Send address changes to Math Horizons, MAA Service Center, PO Box 91 112, Washington, DC 20090-1 112. Cower b~ Tom Mann of Mann & Mann Inc. THE MATHEMATICAL .\SSOCL.\TION OF AMERICA 1329 Eighteenth Street, r\n,V Iiashington, DC 20036 How to Reach Us e-mail: [email protected] Call: (202) 387-5200 Fax: (202) 265-2384 Write: Math Holizons, The Mathematical Association of America, 1529 Eighteenth Street, NW, Washington, DC 20036. Math Horizons November 1998 3 math HORIZONS ADVISORY BOARD GERALDL.ALEXANDERSON Fasten Your Seat Belts! Santa Cla,m University TOMAPOSTOL California Institute of Technology Math Horizons (MH) is now five years old. It has been nl\ GEOKCEBERZSEW great pleasure to serve as founding editor and to watch ir Rose-H,ftlmnn Institute of Technology ROBERTBOZEX~N develop. Thanks to the thousands of subscribers like you Morehozcse College who have given support to MH during its infancy. Special M~R\'INBRURAKER thanks to Marcia Sward, Executive Director of the MAA, Messiah College who collaborated with me on the original idea of a maga- BARBARAFAIRES Westmi~uterCollege zine for students. The backing of the MAA's Executive and DEBOM FRA~UT'L Finance Committees; the Board of Governors, the Commit- K~ctztownUniversity tee on Publications, and the MH Advisory Board has been JOEG.AI.I.IAN central to its success. Carol Baxter and Beverly Ruedi have University of Minnesota-Df~luth APARNAHIGGINS served magnificently as managing editors, and Jane University of Daj~ton D'Alelio has provided inspired designs as art director. ROBERTHOOD Editor Em.eritzls, Boys' Life I've had a wonderful time, but the MAA changes editors HAROLDJACOBS U.S. Grant High School, Van Nzqs, CA every five years and it's time now for new editors. In 1999, SANDRAKEITH Professors Deanna Haunsperger and Steve Kennedy of St. Cloud State Uniuersity Carleton College take over as co-editors. They are loaded LEONARD~LOS~NSK~ with ideas, full of energy, fine teachers, and are very Santa Clara Univer.xity JOEMALKWITCH involved with student activities. Their ideas for MH are so York College exciting that it's clear that readers are in for a great ride. CLEOPATRIAMARTINEZ So, fasten your seat belts! Phoenix College ROBERTMEGGINSON University of Michigan RICHARDNEAL University of Oklahomn HENRYPOLLAK Teachers College, Columbia University FREDAPORTER-LOCKLEAR Pembroke State University PETER RENZ Free-lc~.nceEditor V. FREDERICKRICKEY Bowling Green State University RONALDC. ROSIER Zonference Boa.rd of the Mathematical Sciences MARKSAUL Bronxville School, NY ANITASOLOJV Randolph-Macon Woman's College ASDRE!~ST ERR^, JR. The Mathematical Association of America IAN STWVARI. Wanuick University JUDITHTANUR State University of New York, Stony Brook IRVINVANCE Michigan State University PETERWALTHER Salislt-Kootenui College ANN~VATKINS California State University, Northridge ROBINWILSON TIE Open University Math Horizons November 1998 DAN KALMAN A Student Guide to the National Math Meetings he two largest professional societies for mathematics are the Mathematical Association of America (MAA) T and the American Mathematical Society (AMS). Each January, these organizations hold a joint convention, called the "national meetings" by most members of the organizations. The MAA also holds a national meeting in the summer. Attending a national meeting can be a rewarding experi- ence for college math students. You can hear interesting talks about math, meet people from around the U.S. who share an enthusiasm for the subject, and get a glimpse into the profes- sional world of mathematicians. But to get the most out of the math meetings you have to be prepared. That'swhere this guide comes in. It gives you inside information on what to expect, how to pick events, and even how to keep your expenses to a minimum. Kinds of Talks Let's start with the program. One of the main activities at the ers ~vhoare experts in the area that is the focus of the session. math meetings is attending talks. These come in three dif- A variation on a special session is a panel discussion. This ferent flavors: invited addresses (hour talks), invited special kind of session often has more closely coordinated presenta- session talks (usually on the order of 20 minutes), and con- tions, and more time for discussion with the audience. To illus- tributed papers (10 to 15 minutes). The invited addresses are trate the differences, here is an example. There might be a the main attractions for a general audience. The speakers are special session on dynamical systems (which is the mathemati- asked to choose topics that will make sense to a large audi- cal branch of chaos). The organizer would invite outstanding ence. Usually, they are nationally recognized mathematicians researchers in the field to make presentations, but would not who are known for outstanding research, for outstanding necessarily try to fit the presentations together. In contrast, for speaking skills, or both. The speakers are on the program at a panel discussion on career opportunities in industry, there the invitation of the organizers of the meetings, which is why might be one spokesperson from the aerospace industry, one they are called invited addresses. (No, they don't check for from the pharmaceutical industry, and one from a special ef- invitations at the door - anyone can go and listen.) fects company in the entertainment industry. The invited special session talks are more specialized than The contributed paper sessions feature speakers who have the invited addresses. These are arranged as part of a session volunteered to give talks, as opposed to appearing by invita- that focuses on a particular topic or theme. They invite speak- tion. These speakers want to share something they have been working on with colleagues having similar interests. Most of these sessions are organized around a theme. For example, the MAA might announce a contributed paper session on applications of mathematics to environmental science. Then, anyone who has been working in this area can send in a DAN KALMAN teaches mathematics at American University. description of a brief talk for inclusion in the program. There Math Horizons November 1998 5 are also AMS sessions of contributed papers that are not so- licited in any organized way. Rather, mathematicians simply send in a request to present a paper concerning anything they might be working on, and the AMS tries to group them according to subject and schedules sessions for them. What to Attend So now that you knowwhat the different kinds of talks are, how do you decide what to go to? One helphl resource is a list of events expected to be of interest to students. These are often available from faculty advisors for student math clubs and MAA or Pi Mu Epsilon chapters. They can also be found on the world wide web before the meetings begin. The MAA's website, MAA Online (http://~w.maa.org),has a page for student ac- tivities. Look there for information on the national meetings. There are three levels of information about almost all of ;he presentations. The first two are contained in the main pro- presentation in the session will cover, but they do give you a gram, and can be found at both the summer and winter meet- pretty good idea of the kinds of topics that can be expected. ings. The third level is published in a separate booklet,just for the winter meeting. The information from each level can help Abstracts you choose what to attend. Here are some details about what kind of information is available. That brings us to the third level of information, abstracts for The best overview of the entire meeting is the preliminary the talks. These are generally available only at the January program. It is published before the meeting in both FOCUS, meetings, in a separate abstracts booklet, usually to be found in the newsletter of the MAA, and in the Notices of tlw AMS. You the registration area. As part of your registration fee, you are should be able to find at least one of these by askingjust about entitled to pick up a copy, but you generally have to ask for it. any faculty member in your mathematics department. Another They don't give copies away just as a matter of course. The place to find the same information is on the internet through book of abstracts includes a paragraph or two prepared by each MAA Online.