FOCUS November 2004
FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, FOCUS August/September, October, November, and December. Volume 24 Issue 8 Editor: Fernando Gouvêa, Colby College; [email protected] Inside Managing Editor: Carol Baxter, MAA 4Master of Recreational Mathematics—and Much More [email protected] An Interview with Martin Gardner Senior Writer: Harry Waldman, MAA By Don Albers [email protected] 8Low Down Triple Dealing Please address advertising inquiries to: By Colm Mulcahy Frank Peterson, 10 Science Policy at the MAA [email protected] By David Lutzer President: Ronald L. Graham 12 New MathDL President-Elect: Carl C. Cowen By Lang Moore First Vice-President: Barbara T. Faires, 13 MAA Around the World and in the Classroom Second Vice-President: Jean Bee Chan, By Joel Haack Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: John 14 The Changing Face of Calculus: W. Kenelly First-and Second-Semester Calculus as College Courses By David M. Bressoud Executive Director: Tina H. Straley 17 First Annual Embry-Riddle Undergraduate Mathematics Conference Associate Executive Director and Director By Greg Spradlin of Publications: Donald J. Albers 19 MathFest 2004 FOCUS Editorial Board: Rob Bradley; J. Kevin Colligan; Sharon Cutler Ross; Joe 20 MathFest in Photos Gallian; Jackie Giles; Maeve McCarthy; Colm 22 The August 2004 Board of Governors Meeting: Mulcahy; Peter Renz; Annie Selden; Hortensia Soto-Johnson; Ravi Vakil. A Graduate Student’s Perspective By Michael Lauzon Letters to the editor should be addressed to Fernando Gouvêa, Colby College, Dept. of 24 NSF Beat Mathematics, Waterville, ME 04901, or by By Sharon Cutler-Ross email to [email protected]. 25 Freshmen Can Offer Mathematical Solutions to Real-World Issues Subscription and membership questions By Joseph Kirtland and Pau-San Hoh should be directed to the MAA Customer Service Center, 800-331-1622; e-mail: 26 ICME Study 16 [email protected]; (301) 617-7800 (outside 27 Research Experiences for Minority Undergraduates: U.S. and Canada); fax: (301) 206-9789. MAA SUMMA’s National REU Program Headquarters: (202) 387-5200. By Robert E. Megginson Copyright © 2004 by the Mathematical 29 SAUM Offers On-line Guide for Assessment of Student Learning Association of America (Incorporated). Educational institutions may reproduce 30 Archives of American Mathematics Spotlight: articles for their own use, but not for sale, The Mathematical Association of America’s Records provided that the following citation is used: By Kristy Sorensen “Reprinted with permission of FOCUS, the newsletter of the Mathematical Association 31 Undergraduate Poster Session at the 2005 Joint Meetings of America (Incorporated).” 32 In Memoriam Periodicals postage paid at Washington, DC 34 Wisconsin’s NPrime Project and additional mailing offices. Postmaster: By Linda Thompson and Margaret Wilsman Send address changes to FOCUS, Mathematical Association of America, P.O. 35 Employment Opportunities Box 90973, Washington, DC 20090-0973. On the cover: Martin Gardner sitting on the Alice statue in Central Park. See pages 4-9 for ISSN: 0731-2040; Printed in the United States our tribute to Gardner on the occasion of his 90th birthday. Photograph courtesy of Jim of America. Gardner.
2 November 2004 FOCUS Math Gateway: An NSDL Pathway to Undergraduate Mathematics
The National Science Foundation has Math Forum Duke Connected awarded the Mathematical Association (http://www.mathforum.org) The Math Curriculum of America a Pathways Grant as part of Forum is one of the oldest online re- Project (http:// the National STEM (STEM is NSF-speak sources in mathematics with a particu- www.math.duke.edu/ for Science, Technology, Engineering, lar emphasis on K-12 mathematics. education/ccp) and Mathematics) Digital Library This site has online materials for lab ac- (NSDL) Program. This four-year grant iLumina tivities for undergraduate mathematics will support the creation of a portal, The (http://www.ilumina-dlib.org) The courses from precalculus through linear Math Gateway, for undergraduate math- iLumina site, hosted at the University of algebra, differential equations, and en- ematics materials within NSDL. This North Carolina at Wilmington, is one of gineering mathematics. Lang Moore and project will bring together collections the oldest collections in the NSDL. David Smith edit the site. with significant mathematical content and services of particular importance to College Board webODE Project the delivery and use of mathematics on (http://apcentral.collegeboard.com) At This project is just getting underway the Web. The Association will use a new their AP Central site the College Board under the direction of Paul Blanchard at version of the content management sys- has a wealth of resources directed toward Boston University. tem currently supporting the Math- AP high school teachers. The Math Gate- ematical Sciences Digital Library way would link to their resources for cal- Eduworks (MathDL) to support the portal to these culus and statistics. (http://www.eduworks.com) The MAA collections and services. and MathDL are cooperating with Geoff CAUSE Collier and Robby Robson of Eduworks The Math Gateway project is an out- (http://causeweb.org) The Consortium on their NSDL project to improve growth of the Mathematical Sciences for the Advancement of Undergraduate interoperability and reusability. Conference Group on Digital Educa- Statistics Education is a project of the tional Resources. This group of individu- American Statistical Association. WeBWork als with an interest in online mathemat- (http://webwork.math.rochester.edu) ics has met each year for the past four Demos with Positive Impact WeBWork, founded by Arnie Pizer and years at MAA headquarters. Many of the (http://mathdemos.gcsu.edu) This project Mike Gage of Rochester, is one of the organizations represented at these meet- is managed by Lila Roberts of Georgia most useful online homework systems ings will participate in the Math Gate- College and State University and Dave for mathematics. MathDL will provide way. The initial participating organiza- Hill of Temple University. The site pro- some services for WeBWork. tions/collections are listed below. vides teachers with demos and accom- panying information on how these Some of these collections include mate- MERLOT demos might be used. rials related to many disciplines. In that (http://www.merlot.org) MERLOT pro- case, the Math Gateway will only link to vides access to National Curve Bank the mathematics items. an extensive (http://curvebank.calstatela.edu) This site, collection of directed by Shirley Gray at Cal State Los The new grant will support the publica- resources and Angeles, has a wide range of online math- tion of a regular Math in the News col- services over ematical resources including an audio file umn on the Math Gateway portal. In many different disciplines. Flora of Tom Lehrer singing New Math. addition to support of the portal, the new McMartin of MERLOT is supervising the grant will provide resources for the con- evaluation program for the Gateway Virtual Laboratories in Probability tinuing support of MathDL. Perhaps the Project. and Statistics most important of these will be funds to (http://www.math.uah.edu/stat)This site enable the hiring of a full-time web mas- Eisenhower National Clearinghouse was developed by Kyle Siegrist at the ter to support both MathDL and the (http://www.enc.org) The Eisenhower University of Alabama at Huntsville. Math Gateway. The grant also will sup- National Clear- port an extensive system of workshops inghouse is an Ethnomathematics Digital Library at the section meetings of the MAA to extensive (http://www.ethnomath.org) The encourage the mathematical public to online resource Ethnomathematics Digital Library is a explore the learning opportunities af- for K-12 sci- project of Pacific Resources for Educa- forded by The Math Gateway and, more ence and math tion and Learning. The Library has links generally, by the NSDL. teachers. ENC is playing a central role in to relevant websites worldwide. the NSDL outreach to middle schools.
3 FOCUS November 2004 Master of Recreational Mathematics — and Much More An Interview with Martin Gardner
By Don Albers
On October 21, Martin Gardner cel- he has produced more than 60 books, a few local magicians in Tulsa, Logan ebrated his ninetieth birthday. For 25 of most still in print; many have been Waite and Wabash Hughes, who worked his 90 years, Gardner wrote the monthly bestsellers. His Annotated Alice has sold for the Wabash Railroad. “Mathematical Games “ column for Sci- over a million copies, and the 15 volumes entific American. His columns have in- collecting his “Mathematical Games” DA: At what age did this occur? spired thousands of readers to learn columns have gone through several more about the mathematics that he printings. All 15 volumes have been digi- MG: I was a high school student at the loved to explore and explain. Among his tized and will soon be published by the time. I’ve never performed magic; it’s just column correspondents were several dis- MAA on a single CD entitled Martin been a hobby. The only time I got paid tinguished mathematicians and scien- Gardner’s Mathematical Games. for doing magic was when I was a stu- tists, including John Horton Conway, dent at The University of Chicago; I used Persi Diaconis, Ron Graham, Douglas In his ninetieth year, he has returned to to work at the Marshall Field’s depart- Hofstadter, Richard Guy, Don Knuth, Sol Oklahoma, where he was born. He is in ment store during the Christmas season Golomb, and Roger Penrose. good health and full of energy. We look demonstrating Gilbert magic sets. I forward to more from him as he begins learned a lot from the experience. That Gardner’s columns have earned him a his second 90 years. What follows is a was the first time I realized that you’re place of honor in the mathematical com- small portion of an interview done at really not doing a magic trick well until munity, which has given him many Gardner’s home in Hendersonville, NC you’ve done it in front of an audience awards. But he has always declined invi- in the fall of 1990 and spring of 1991.
Martin reading on his front porch at age Martin at age 10, 1925. Martin and his younger brother 15, 1929 Jim, 1920. about a hundred times. Then it becomes tations to accept awards in person, on the Don Albers: As a high school student you second nature, and you know what to say. grounds that he is not a mathematician. were already writing articles for The “I’m strictly a journalist,” he insists. “I Sphinx, a magazine devoted to magic. DA: What are the elements of a success- just write about what other people are Does your interest in magic go back to ful magic trick? doing in the field.” His modesty is admi- your father? rable, but we insist that he is far more MG: The most important thing is to than a journalist. Martin Gardner: Magic wasn’t a special startle people, and have them wonder hobby of his, but he did show me some how it’s done. Close-up magic that you In addition to his massive contributions magic tricks when I was a little boy. I do on a table right in front of people is to mathematics, Gardner has written learned my first tricks from him, in par- very different from the stage illusions about magic, philosophy, literature, and ticular one with a knife and little pieces that David Copperfield does. It’s close- pseudoscience. Over his first ninety years, of paper on it. I then got acquainted with up magic that most intrigues me, espe-
4 November 2004 FOCUS cially when it has a mathematical flavor. to read that way. It was very embarrass- MG: I was very good at math in high I did a book on mathematical tricks that ing when I was in first grade, because the school. In fact, it and physics were the has, for example, a chapter on topologi- teacher would hold up cards that said ‘cat’ only subjects in which I got good grades. cal tricks. I did two massive books for the and ‘dog’ and I was always the first to call I was bored to death by the other classes. magic profession: The Encyclopedia of out the word. She had to tell me to shut I flunked a class in Latin and had to take Impromptu Magic and Martin Gardner it over. I just don’t have a good ear for Presents. The first book covers tricks that languages. don’t require any special equipment. A lot of them are just jokes and gags of the DA: You got your B.A. in 1936, then type ‘bet you can’t do this.’ worked briefly for the Tulsa Tribune as a reporter, and then came back to The DA: Your book Mathematics, Magic, and University of Chicago to the PR office Mystery has been a bestseller for many writing news releases (primarily science years. releases), and took a graduate course from Carnap. What else did you do until MG: I waste a lot of time on magic. Dai the outbreak of World War II? Vernon was one of the great inventors of magic. He was a great influence on Persi MG: I had various jobs. I worked as a case Diaconis. Persi traveled with Dai for a worker for the Chicago Relief Adminis- long time. I knew Vernon very well. I tration, I had to visit 140 families regu- knew Persi when he was a student at larly in what was called the Black Belt. I NYU. You probably heard the story how also had several odd jobs: waiter, soda he got into Harvard. jerk, etc. Remember, this was at the height of the Great Depression. DA: As I recall, he gave you some credit for writing a letter of recommendation DA: In December of 1941, the U.S. en- Gardner as a navy sailor, 1941. to Fred Mosteller, the Harvard statisti- tered World War II and you enlisted in Gardner as a navy sailor, 1941. cian. the Navy.
MG: Mosteller is a magic buff. When MG: I ended up serving on DE 134, a Persi said he wanted to get into Harvard, destroyer escort, in the Atlantic. I was I wrote to Fred and said that Persi can miserably seasick for about three days, do the best bottom deal and second deal and then I was never seasick again. I of anybody I know, and that got him into couldn’t wait for the war to end, but later Harvard. I talked to Fred on the phone I looked back at it as a rather pleasurable about it and he said, “Is he willing to time of my life. You’re on a ship, you major in statistics?” And Persi said sure make friends with your shipmates, you he’d major in statistics if that would get got liberties now and then, and you didn’t him into Harvard. So he went up to have to worry about anything. Harvard, and they had a session together, maybe doing card tricks. Mosteller got I’ve had migraine headaches all my life him into Harvard. that were fairly severe when I was in high school. When I enlisted in the Navy, I did DA: What did your mother do? not list my migraines because I was afraid they wouldn’t take me. I feared that I MG: She was a kindergarten teacher be- might develop migraine headaches dur- fore marriage, but then became a house- ing battle situations. We were part of a wife, caring for three children. Her hobby so-called “killer group” of six destroyers was painting, and I have a number of her looking for German submarines. During paintings hanging in the house. Both of Martin Gardner with the Mad Hatter in my four years in the Navy, I never had a my parents lived into their nineties. I had Central Park, New York City. migraine headache. I’m convinced that a brother and sister, both younger, who they’re associated with periods of anxi- are deceased. up, to give the other children a chance to ety. When you’re in the Navy, you don’t learn how to read. worry about what you’re going to do to- I learned to read before I went to school. morrow, what tie to put on, etc. You just My mother read The Wizard of Oz to me DA: As a kid, do you remember other follow orders. In a way, you have a big when I was a little boy, and I looked over strong interests in addition to magic? sense of freedom. Otherwise, I have no her shoulder as she read it. I learned how other explanation.
5 FOCUS November 2004
Martin Gardner with his brother Jim and Gardner with his wife Charlotte, and Martin and grandson Martin. sister Judith. their two sons Jim, left, and Tom.
DA: At the end of the war, you promptly York City, because for writers that’s ematician who has to teach a course in went back to Chicago. where all the action is. I had a friend who mathematics, and then write. To me, it’s worked for Parents’ Institute, and who hard to imagine how a professional MG: Yes, I went back, and I could have was in charge of their periodicals for chil- mathematician would have time to even had my old job back in the public rela- dren. They were starting a new magazine write a book. I had nothing else to do, tions office at The University of Chicago called Humpty Dumpty, and were look- except research for those columns, and because there was an understanding that ing for activity features, where you fold write them up. if you enlisted in the service you could the page or stick something through the get your old job back. But the one rea- page, or cut; where you destroy the page. DA: Most people that I’ve ever talked to son I didn’t go back to the PR office was So he hired me to do the activity features about your Scientific American columns that I sold a story, my first sale, to Es- for Humpty Dumpty, as well as a short know that it was your job, but they’re still quire. The title of the story, “The Horse story for every issue and a poem of moral awed by the fact that you turned out on the Escalator,” came from a joke go- advice. something really sparkling every month. ing around at the time about a man who It’s one thing to write something every entered Marshall Fields department store DA: Your work with children’s magazines month, but that doesn’t mean that it’s on a horse, and the elevator operator told went up to about 1956. By 1957 you were going to be inspirational or great fun to him he couldn’t take the horse on the el- at Scientific American. So there was not read each time. evator. And he said, “But lady, he gets sick much of a hiatus between Humpty on the escalator!” It was a shaggy dog joke Dumpty and Scientific American. MG: I miss doing those columns, they about a horse. The story is about a man were a lot of fun, and I met many fasci- who collected horse jokes, and his wife MG: No, I stopped working for Humpty nating people while doing them. Once didn’t think any of them were funny, but Dumpty to start “Mathematical Games” the column got started I began hearing she laughed heartily every time he told at Scientific American. I couldn’t do both. from people like Sol Golomb and John one to conceal the fact. So that was my It started with the sale in December 1956, Conway, who were really doing creative first story. I decided that maybe I could of an article on Hexaflexagons. That was work that had a recreational flavor. That make a living as a freelance writer, and I not a column, but that led to the column. kept the column going. It became much very quickly sold Esquire a second story, When Gerry Piel, the publisher of Scien- more interesting after I began getting and that was the “No-Sided Professor,” tific American, called me and suggested feedback from people like Conway, Ron about topology. the column. That was when I resigned Graham, Don Knuth, and many others. from Parents. DA: That had to give you a lot of confi- Probably my most famous column was dence, helping to convince you that you DA: A lot of people are astonished that the one in which I introduced Conway’s could earn a living as a writer. anybody could turn out one of those col- game of Life. Conway had no idea when umns on mathematical games and rec- he showed it to me that it was going to MG: That’s right, but Esquire changed reations every single month for Scientific take off the way it did. He came out on a editors after I had sold them several sto- American. visit, and he asked me if I had a Go board. ries. The new editor had a different I did have one, and we played Life on the policy, and he didn’t care for the kind of MG: Perhaps they don’t realize I had no Go board. He had about 50 other things stories I was writing. So I moved to New other job. I’m not a professional math- to talk about besides that. I thought that
6 November 2004 FOCUS
Life was wonderful — a fasci- DA: You’ve read a lot of contem- nating computer game. When I porary material, and you’ve read did the first column on Life, it a lot by those who have been really took off. There was even gone a long time. Are there any an article in Time magazine of those departed people that about it. you’d like to sit down with over dinner, or sit down here in your DA: Can you tell me a little bit library and chat with them? more about how you actually approach writing? You previ- MG: I’d love to chat with Gödel ously said something about how for example. He had some you did your monthly columns strange cosmological views, and over a long period of time. You I’d like to talk to him about that, write about many other things about time travel into the past. I as well. Do you have a different never could quite understand style or a different mode when Gardner doing some table magic that. And of course he was a you write about pseudoscience? dedicated Platonist. He thought all of mathematics was out MG: I don’t think so. I’ve never there, including the transfinite worried about style. I just write as Martin Gardner regrets that it is impossible for him to: numbers. I’d enjoy talking to clearly as I can, and I suppose it’s him about that. Of course I’d improved over the years. I get in- 1. Evaluate: love to talk with Einstein and terested in a topic, and I do as Angle trisections Neils Bohr. Among puzzle mak- much research as I can on it. I have Circle squarings ers, I’d most want to talk with my library of working tools, so I Henry Dudeney and Sam Loyd. can do a lot of research right here. Proofs of Fermat’s last theorem I also would enjoy talking to I usually rough out the topic first, Proofs of the four-color theorem Bertrand Russell. He’s one of just list all the things that I have to Roulette systems my heroes. say, and then I sit down and try to 2. Give advice on, or supply references for, put it together on the typewriter. DA: Here’s an equally easy ques- It’s all kind of a sequence that is high school science or math projects. tion for you. Once you’ve de- hard to explain. It comes easy for 3. Inscribe books for strangers. parted this life, let’s suppose you me, I enjoy writing and I don’t suf- 4. Give lectures, or appear on radio or TV shows. had an opportunity to come fer from writer’s block, where I sit 5. Attend cocktail parties. back in a hundred years. What and wonder for an hour how I’m questions would you most want going to phrase the opening sen- 6. Make trips to Manhattan except under to know the answers to that tence. extreme provocation. might have been developed 7. Donate books to libraries. during that time? DA: Which of your more than sixty 8. Provide answers to old puzzles. books is in some sense a favorite? MG: I guess I’d be interested to 9. Prepare material on speculation for toy know if various famous un- MG: I think my Whys of a Philo- companies or advertising agencies. solved problems had been sophical Scrivener is my favorite be- 10. Put the reader in touch with Dr. Matrix. solved, such as the Goldbach cause it is a detailed account of ev- Conjecture. But I don’t have any erything I believe. Martin Gardner’s form letter, often sent as a response to re- great desire to come back and quests he received from readers. learn what modern mathemat- DA: Let’s move back to math for a ics is up to. You’re giving me minute. You’ve lived long enough now to credit for being more of a mathemati- see a lot of really interesting mathemati- cian than I really am. I’m strictly a jour- cal ideas hit the scene, and there are also nalist. I just write about what other some really beautiful ideas that were here physics, and in particular the develop- people are doing in the field. long before you were on the scene. First, ment of superstring theory. That came during your own lifetime, what ideas, as a complete surprise to me. It’s a beau- what discoveries just kind of knocked tiful theory of particles, and it may or your socks off? may not be true, but it’s the hottest thing in town now in particle physics. It opens MG: Well, I think the most interesting de- up the possibility that higher dimensions Thanks to Jim Gardner for supplying the velopments are mainly in mathematical are not just artifacts but actually real. photos that accompany this interview.
7 FOCUS November 2004 Low Down Triple Dealing By Colm Mulcahy
Dedicated to Martin Gardner on the occasion of his 90th birthday
Consider the following three demon- times) on a packet of thirteen cards, word being spelled out and the size of strations of mathemagic: which was then split into two piles. Draw the “quarter deck” which the spectator attention to the two cards originally se- starts with, and the fact that you must 1. A deck of cards is handed to a specta- lected. Say, “Wouldn’t it be surprising if, somehow know the identity of one card tor, who is invited to shuffle freely. She is after all that triple dealing based on the in the spectator’s hand from the begin- asked to call out her favourite ice-cream values of two randomly selected cards ning! It should come as no surprise that flavour; let’s suppose she says, “Choco- from a shuffled deck, there were cards the card in question is the bottom card: late.” Next, she is asked to cut off about a intimately related to the two you selected asking the spectator to hold the cards in quarter of the deck and hold it ready for at the bottoms of the two piles now on her hand in preparation for the spelling dealing. You take another quarter of the the table?” Have the piles on the table is just to give you an added opportunity deck and demonstrate a spelling deal, turned over: one of the cards exposed is to peek at this card, if you haven’t already dealing cards into a pile, one for each let- 9♣ and the other is 4❤. “A curious align- done that as she completed her shuffling. ter in the word “chocolate,” before drop- ment with the selected cards.” You must do whatever it takes to discover ping the rest of your quarter deck on top. that card’s identity! Set those cards aside and have the spec- 3. Have each of three volunteers in turn tator perform this spelling routine three pick a card at random, and then have the This is the scoop on the ice cream trick: times with the cards in her hands. You cards returned to anywhere in the deck. correctly name the top card in her pile at Shuffle with abandon. Ask a fourth per- Claim 1: Start with n cards, the bottom the conclusion of her triple dealing. son to name their favourite magician. one of which is known. If k cards are dealt Assume they say, “Harry Houdini.” Hold out into a pile, thus reversing their or- 2. A deck of cards is handed to two spec- the deck in the right hand, and peel cards der, and the remaining n – k cards are tators, each of whom is invited to shuffle off the bottom into a pile in the left hand, dropped on top as a unit, and this type at will and then choose a card (of not too without altering their order, one for each of deal is repeated twice more, then the low a value) and place it face up on the letter, as you spell out the whole name. known card rises like cream to the top table. Let’s suppose that 4♣ and 9❤ are Hand the stack of twelve cards to the first — provided that n ≤ 2k. selected and displayed. You run through volunteer and ask him to spell out the deck face up, tossing out all of the HOUDINI while dealing out seven cards, In the case of the nine-letter word Aces, 2s and 3s — saying, “Sorry, I should then dropping the other five on top. Now CHOCOLATE, the trick works provided have eliminated the low cards earlier.” give the cards to the second volunteer that the portion of the deck selected by Then riffle shuffle a few times. Remark, and give the same directions, and finally the volunteer contains at most eighteen “Since a 9 was selected, let’s count out to the third volunteer for one last deal of cards. If MINT CHOCOLATE CHIP nine cards,” dealing into a pile on the the same type. Take the cards behind (seventeen letters) is named, you’ll ask table. Shuffle overhand and continue, your back and immediately produce for between a third and half of the deck. “We’ll need four more,” as you peel off three cards, handing one to each volun- (If RUM is selected, try to force RUM that many cards as a single unit, without teer face down. Have the chosen cards RAISIN!) changing their order. Drop these on top named, as they are turned over, to reveal of the other nine. (The rest of the deck is that you have correctly located each one. The triple deal described is actually 75% ignored from now on.) Pick up this pile of a rather interesting quadruple deal. of thirteen cards and demonstrate a deal The same purely mathematical principle This is the real scoop: of the nine top cards into a pile, revers- underlies each of these demonstrations, ing their order, and then putting the re- with a little more magic thrown in for Claim 2: Start with n cards, and assume maining four on top. Have the first spec- good effect as we progress to the second that n ≤ 2k ≤ 2n. If k cards are dealt out tator do this deal three more times, and and third tricks. We gradually reveal this into a pile, thus reversing their order, and hand the cards to the second spectator. principle below, and discuss how each of the remaining n – k cards are dropped Have the second volunteer deal either the tricks is done as we go, before finally on top as a unit, and this deal is repeated four or nine cards into a pile, with the explaining why the principle works. three more times, the entire packet of n remainder placed beside this to form a cards is restored to its original order. second pile. Recap: the two numbers (4 Let’s start with the first effect. There are and 9) being used were determined by two secrets working behind the scenes for Now consider the second effect above. freely selected cards, and as a result a deal you here: an unadvertised but important Two cards (not Aces, 2s or 3s) are chosen of nine cards was performed done (three relationship between the length of the and set aside face up. Let’s suppose they
8 November 2004 FOCUS are 4♣ and 9❤. As you run through the Have these cards returned, one at a time, the cards). Actually, it’s easy to see in all deck face up, ostensibly to toss out the to the deck and then control them to the cases: Suppose for the sake of concrete- low valued cards, what you really focus bottom — this means that you appear to ness that n = 13 and k = 8. Let’s agree to on doing is cutting the 9♣ and 4❤ to the allow free choice of where to put the represent a pile of thirteen cards in a par- top and bottom respectively. They will cards, but you actually use elementary ticular order by a sequence of gray-scale stay there if you are panels in decreasing careful how you order of brightness, riffle shuffle. Con- from white for the tinue as described top card to black for earlier: reversing the bottom card, as nine cards into a pile depicted in the im- and then doing age. some overhand shuffling whose Then the results of purpose is to bring the four deals — each the bottom card to of eight cards into a the top. Peel four pile with the other more off the top five dropped on top without reversing — is given by the suc- them and drop on cessive images in the top of the other pictures. nine. You now have thirteen cards with Since the last image the desired two shows a fully restored cards at the top and pile, the deal in ques- bottom of that tion has period 4: af- packet. Your subse- ter four deals we are quent demonstra- always back to where tion of dealing nine we started. After Proof Without Words and dropping four is three such deals, the just the first of a series of four deals: the magic techniques (e.g., double cuts) to original bottom card (black) has risen to first spectator does the next three deals, get each card to the bottom. As a result, the top — in preparation for its final thereby restoring the packet to its initial the third volunteer’s card is at the bot- journey back to the bottom under one state. The second spectator deals (either tom of the deck, the second volunteer’s more deal. Moreover, it is clear that the four or nine) cards into a pile and then card is one up from the bottom, and the eight bottom cards become the eight top there are two piles on the table with one first volunteer’s card is two up from the cards, suitably reversed, after three deals. of the desired cards at the bottom of each bottom. Peel cards off the bottom of the There are just three portions of the packet pile. You are all set for the grand finale. deck — without altering their order — — of sizes 5, 3 and 5 here — to keep track one for each letter of the name of the of: and they move around intact, subject The third effect uses the fact that after magician called out, as you spell out both at most to some internal reversals. The three deals of the type described, not only words in full. Hand the resulting packet only relationship between 13 and 8 which does the bottom card rise to the top, the of cards to the first volunteer and ask that is needed to make this sequence of im- next to last card becomes the second card the longer of the two names (HOUDINI ages totally generalizable is the fact that from the top, the one above that becomes in our example) be spelled out as cards 8 ≥ 13/2. the third card, and so on: are dealt into a pile, before dropping the remainder on top. Now give the cards to Finally, we suggest that during all deal- This is the real triple scoop: the second volunteer and finally to the ing the cards are held low, close to the third volunteer for two more deals. The table, so as to justify fully the title of this Claim 3: If k cards from n cards are dealt three chosen cards are now on the top article. out into a pile, reversing their order, and of the packet of cards, with the order re- the remaining n – k are dropped on top versed, and you are all set to conclude in Colm Mulcahy ([email protected]) has as a unit, and this process is repeated triumph. taught at Spelman College since 1988. He twice more, then provided that n ≥ k ≥ is currently the chair of the department of n/2, the original k bottom cards become Why are all of the above claims valid for mathematics there. The number of syl- the top k cards, in reverse order. any n and k with n ≤ 2k ≤ 2n? It’s cer- lables in his first name is strictly between 1 tainly easy to see if n = k (reversing all of and 2. He is a member of the FOCUS edi- To perform the third trick, ask each of the cards each time), and almost as easy torial board and will be contributing a three volunteers to pick a card at random. to see if n = 2k (reversing exactly half of regular “Card Colm” to FOCUS Online.
9 FOCUS November 2004 Science Policy at the MAA
By David Lutzer
Many MAA members might not real- to recommend that MAA engage the ser- dated with a second MSP program al- ize that MAA is involved in national sci- vices of a professional government rela- ready in the Education Department. As ence policy — but it is. Presenting a tions firm. The Board of Governors explained below, the MAA opposes this discipline’s perspectives on research agreed, and the firm of Lewis-Burke As- proposed shift. funding issues to national policy mak- sociates (LBA) was chosen. ers has long been an activity of profes- At the end of the day on Monday, SPC sional organizations. See, for example, Among LBA’s first activities on behalf of worked with Lewis-Burke Associates the governmental affairs sections of the MAA was to organize a two-day Wash- staff to formulate a page of talking web pages of the American Institute of ington meeting of the Science Policy points. Themes were taken from sched- Physics, the American Chemical Society, Committee on March 22 and 23 of this uled congressional testimony of MAA the Society for Industrial and Applied year. The purpose of the meeting was to President Ron Graham (see pages 21–22 Mathematics, and the American Math- get SPC members to meet with congres- in the May/June 2004 issue of FOCUS) ematical Society. But Washington deci- sional and executive branch officials, to and reflected the day’s conversations sions can also affect undergraduate math- present MAA’s positions on several sci- with NSF and OMB officials. A copy of ematics, which is among MAA’s most ence funding issues in person. On Mon- the talking points page was left with each central interests. Consequently the jobs day, March 22, the SPC met senior staff staff member visited on Tuesday and is of the MAA President and the MAA Ex- members of the National Science Foun- available on the SPC website, mentioned ecutive Director include presenting dation (NSF) and the Office of Manage- above. The talking points focused on MAA policy perspectives on pending ment and Budget (OMB), the goal was mathematics as a cornerstone of the federal decisions with undergraduate to prepare committee members for meet- nation’s technical workforce preparation ramifications. ings with congressional staffers, sched- program, currently a hot issue in Wash- uled on Tuesday. ington. They urged Congress to reverse Where do MAA’s science policy positions previous years’ declines in the budget of come from? According to the MAA by- Monday’s meetings included extended the NSF Division of Undergraduate Edu- laws, only the MAA President and Ex- discussions with David Radzanowski cation, one of two NSF divisions that ecutive Director may speak for MAA on who is in charge of Science and Space support undergraduate mathematics, science policy issues. The Board of Gov- Programs in the White House OMB; with and called for increased support for the ernors can be influential in shaping MAA Rosemary Haggett, Director of the NSF VIGRE and REU programs in the NSF science policy, and the MAA also has a Division of Undergraduate Education; Division of Mathematical Sciences be- Science Policy Committee (SPC) whose and with Bill Rundell, Director of the cause of their importance to under- charge is to assist the Association “in NSF Division of Mathematical Sciences. graduate mathematics. The talking anticipating, responding to, and initiat- Both Joel Widder (of Lewis-Burke) and points also argued that the NSF Math ing changes in the educational, the finan- David Radzanowski (of OMB) made it and Sciences Partnership Program cial, and the policy environments that clear that budget times will be very bleak should not be shifted to the Department may impact the work of the MAA and in the near future. The NSF visitors of Education, because, to quote President its members.” (To see some of what SPC briefed SPC on the programs in their di- Graham’s congressional testimony, has traditionally done, go to the MAA rectorates that contribute to under- home page at http://www.maa.org and graduate mathematical education. Both The MAA believes that if transferred to the then choose “Science and Professional NSF visitors agreed with Radzanowski’s Department [of Education], MSP funds Policy” within the “Special Groups” pull- prediction of lean budgets for the next will likely be distributed via block grants, down menu.) few years and recently an important con- which could spread the money too thinly gressional appropriations subcommittee to do any real good and which will, in all The MAA President and Executive Di- has proposed a 2% budget cut for NSF likelihood, result in much of the funding rector are both ex officio members of SPC in the 2005 fiscal year, confirming being redirected at the state level to pro- and can seek committee advice whenever Radzanowski’s gloomy predictions. grams outside the scope of MSP’s original the need arises. For example, some years intent. ago the SPC formulated talking points In addition, the SPC spent a consider- that the MAA President and Executive able amount of time trying to under- On Tuesday, after some SPC members Director could use in case they were stand the intricacies of an administration visited the offices of their own senators asked for comment on what seemed to proposal to move NSF’s Mathematics and representatives, SPC met as a group be a controversial educational proposal and Sciences Partnerships (MSP) pro- with Jeff Smith who is the senior adviser from the White House. Perhaps the most gram from NSF to the Department of to Senate Minority Leader Daschle on important SPC action in recent years was Education, where it would be consoli- science policy; with Kara Haas and Jim
10 November 2004 FOCUS
Wilson from the staff of the House Sci- “bang for the buck” in terms of enhanc- multi-year task will be to build linkages ence Committee; with Tracy Locklin of ing the nation’s scientific and technical with congressional staffers and federal the Senate Health and Labor committee; workforce preparation effort. We had agency program officials who will come and with Jennifer Miller of the House VA, been warned that “Washington runs on to understand MAA’s science policy po- HUD and Independent Agencies Appro- anecdotes” and so we did our best to sitions, and to call upon MAA represen- priations Subcommittee. (In spite of its wrap our messages in stories from our tatives for advice on issues related to un- name, the Senate Health and Labor personal experiences with undergradu- dergraduate mathematical education. If Committee is the authorizing commit- ates and undergraduate teaching. you want to help in this effort, please tee for both the NSF and for the Depart- contact MAA Secretary Martha Siegel ment of Education, and the House VA, Everyone with whom the SPC met was ([email protected]) to volunteer for HUD and Independent Agencies Com- courteous and many were enthusiastic appointment to the SPC. mittee is the appropriations committee about the issues that we presented. While in charge of NSF.) With small variations, some SPC members had never visited the David Lutzer is Professor of Mathematics the message to each was (a) that, using offices of a congressman or senator be- at the College of William and Mary. He relatively small expenditures, NSF has fore, by the end of the day, all of us felt chairs the MAA Science Policy Commit- been very effective in focusing nation- that presenting MAA’s perspectives “on tee, is a member of MAA’s Committee on wide efforts of college and university the Hill” was something we could confi- the Profession, and is a member of the mathematicians on several important dently and comfortably do. Joint Policy Board for Mathematics undergraduate issues and in fostering (JPBM). He also headed the CBMS2000 educational improvement in the U.S., While members of SPC and the Lewis- national survey of the undergraduate and (b) that relatively small additional Burke staff were pleased with the efforts mathematical sciences. His website is at allocations in the 2005 budget (now in launched in March 2004, all agreed that http://www.math.wm.edu/~lutzer. the planning stage) would yield a lot of this cannot be a one-time effort. The
11 FOCUS November 2004
New MathDL online learning materials. All materials to work with the mathlet is included. All have been classroom tested and peer re- mathlets published in OSSLETS, will be By Lang Moore viewed. DCR provides instructors with reviewed and approved by an editorial a set of tools ready for implementation board directed by OSSLETS Editor, in an existing curriculum as well as an Frank Wattenberg. The MAA’s Mathematical Sciences Digi- ongoing forum for discussion of the is- tal Library (MathDL) has a new home, a sues surrounding the materials and their Early in 2005, two additional compo- new look, new material, and many forth- uses. Within this community, the library nents, MAA Reviews and Online Class- coming new features. In August, the also provides a snapshot of trends and room Capsules, will appear. MAA Reviews MAA began publishing the three com- thoughts on issues relevant to the use of will be the online successor to the Tele- ponents of MathDL, The Journal of technology in mathematics teaching and graphic Reviews that, until recently, ap- Online Mathematics and its Applications learning. Learning materials in DCR in- peared in The American Mathematical (JOMA), Digital Classroom Resources clude (but are not limited to): interac- Monthly. Fernando Gouvêa will edit this (DCR), and Convergence, using a new tive web pages; web pages enhanced with section of MathDL. The reviews will be content management system. The site is animation or streaming video; down- similar to the ones that currently appear now housed at MAA Headquarters and loadable programs that run indepen- in the Briefly Noted section of Read This!, maintained by the MAA. The web ad- dently of the web or web browser; and the MAA’s online book review column. dress has not changed: MathDL may still modules developed for commercial com- In addition to brief reviews, the site will be accessed at http://www.mathdl.org. puter algebra systems. Doug Ensley, the feature longer reviews of selected books, founding editor of DCR, continues as the a complete searchable database of books Work on MathDL began in the Fall of current editor. received, and a regularly updated Basic 2000 under a National Science Founda- Library List. tion grant in the National STEM(STEM Convergence, the newest component of stands for Science, Technology, Engineer- MathDL, first appeared last April. This Classroom Capsules will bring together ing, and Mathematics) Digital Library online magazine focuses on the use of the the best of 111 years of the short class- (NSDL) Program (see http:// history of mathematics in teaching room materials from the MAA print www.nsdl.org). MathDL was one of the mathematics. The magazine, also funded publications. It will be easily searched by first of over 171 projects supported by by an NSF grant, features articles, re- topic, author, and student level. Wayne the NSDL program. MathDL debuted in views, “Today’s Quotation,” a “problem Roberts, the editor of Classroom Cap- January 2001 with the first issue of from another time,” and “on this day.” sules, is currently assembling an edito- JOMA. It was hosted by the Math Forum Editors Victor Katz and Frank Swetz have rial board. until August of 2004. created an online magazine that is both enjoyable and instructive. The Committee on Programs in Math- All articles and other materials submit- The next component of MathDL to come ematics is developing a successor to their ted to JOMA are peer-reviewed. Since the current Illustrative Resources site at online will be OSSLETS — Open Source http:/ first year, JOMA has been published con- Sharable Mathlets. OSSLETS will feature /www.maa.org/cupm/illres_refs.html. The tinuously as accepted materials are ready short interactive online materials that are new component of MathDL will replace to be posted. Each volume after Volume the current site and will continue to be scientifically and pedagogically sound 1 represents a calendar year without sub- and that can be easily reused or named Illustrative Resources. David division into issues. repurposed. In addition, many of these Bressoud and Susanna Epp will be co- editors. CUPM is currently seeking fund- materials can produce output that is eas- JOMA takes full advantage of the Web ily cut-and-pasted into a spreadsheet or ing to support this site development. as a publication medium. Its materials a computer algebra system. The proto- contain dynamic, full-color graphics; in- type OSSLETS, called Lite Applets, was ternal and external hyperlinks to related In addition, MathDL has been develop- designed by a group headed by Frank resources; applets in Java, Flash, ing software to support online meetings Wattenberg and funded by a supplement Shockwave, or other languages; MathML, and workshops. Andrew Schretter of to the MathDL grant. These first applets SVG, and other XML markups; audio Duke has done the development work. were reported on in the article Lite and video clips; and other Web-based A preliminary version of the software was Applets by Frank Wattenberg, Bart features. David Smith, founding editor used by Lang Moore, David Smith, and Stewart, and Suzanne Alejandre which of JOMA, will retire from the editorship Frank Wattenberg to support their 2003 at the end of this calendar year. A search appeared in Volume 2 of JOMA. online PREP workshop, Authoring Online Interactive Materials in Math- is currently underway for his replace- The OSSLET site will feature mathlets ment. ematics. Information on how to use this that satisfy the following criteria: the software for committee meetings, work- mathlet and its source code are available The Digital Classroom Resources (DCR) shops, and similar activities will be avail- for reuse; two examples of use of the able soon. library is an exemplary collection of free mathlet are given; a discussion of how
12 November 2004 FOCUS
MAA Around the World and in the Classroom
By Joel Haack
My academic training was as a ring theorist. Fol- lowing a stint in administration, I have inherited the history of math- ematics courses at my institution. Consequently, the professional devel- opment that I have experienced and enjoyed through Linda Haack studying the Thompson Harmonic the first two MAA Joel and Linda Haack aboard the London Eye. Photo Analyser at the London Science Museum. mathematics study courtesy of Carol Dotseth. Photograph courtesy of Joel Haack. tours has been sig- nificant. tangible by information and photo- reinvigorating; I look forward to the next With respect to my teaching, I have been graphs about the development of science one! able to use information learned on the from the Royal Society and the British Greece and England trips in my class- Museum. Joel Haack is Professor of Mathematics at room in many ways that make the sub- University of Northern Iowa in Cedar ject more present for the students. For This year, I will make a number of pre- Falls, Iowa. just a few examples, I have been able to sentations that have been enriched by the share photographs of Miletus and Samos, MAA tours. Together with a colleague making Thales and Pythagoras come from acoustics, I will make several pre- This is a new series that will feature alive for the students. At the office of the sentations describing the use of the occasional articles by MAA Math- European Cultural Center of Delphi, we Henrici harmonic analyzer, a hundred- ematical Study Tour participants on had the opportunity to hear and play a year-old tool used to find Fourier coeffi- how they have incorporated the in- reconstruction of an ancient hydraulic cients. While I first learned of this de- formation and educational experi- organ, discussed in one of Heron of vice at the MAA’s pre-conference work- ence abroad into their classroom Alexandria’s works; the CD and accom- shop on Mathematical Technologies, I teaching, syllabi preparation, and panying booklet have let me share some had the chance to view an early model in course discussions. of this experience with my class as well. the Science Museum of London, where I I can describe the reflecting telescope that could also see Lord Kelvin’s much more Isaac Newton presented to the Royal So- massive harmonic analyzer. Another ciety, having had the chance to see a rep- presentation, to the secondary math- Found Math lica at the Royal Society in London. Our ematics teachers of Iowa, will be based visit to Bletchley Park will allow me to on what I learned about Thomas Harriot Florida Student: “What are the angles share the story of Alan Turing’s life with in a lecture Jackie Stedall delivered to our on a three-four-five-triangle?” an immediacy that would otherwise not group in London. be possible. Governor Jeb Bush: “The angles would Space limitations here keep me from ex- be ... If I was going to guess ... Three- Finally, I am now responsible for a course tolling additional professional opportu- four-five. Three-four-five. I don’t know, entitled Science, Mathematics, and Tech- nities on the tours: discussing mathemat- 125, 90 and whatever remains on 180?” nology in the Americas. Next year’s MAA ics education with Greek and English study tour to Mexico to study the Mayan colleagues, viewing an impressive math- Florida Student: “It’s 30-60-90.” civilization will be a significant learning ematics exhibit in Athens and an exhibit opportunity for me. But, perhaps sur- of JMW Turner’s lectures on perspective Reported on WFTV, July 6, 2004 Online prisingly, last year’s trip to England adds in London, and developing professional at http://www.wftv.com/education/ to this class as well, as we include a dis- friendships. The first two MAA tours 3498203/detail.html. cussion of “What is science?” that is made have been intellectually satisfying and
13 FOCUS November 2004 The Changing Face of Calculus: First- and Second-Semester Calculus as College Courses
By David M. Bressoud gral calculus, it is not a bad course. The that does not build directly on their problem is that few students take it as training and lead them into further There was a time when it made sense intended. mathematics. Calculus II should be a to teach single variable calculus as a year- course that they find challenging and long course. Most of the students who In the fall of 2000, 107,000 students took exciting, one that helps them see the po- enrolled for the first semester intended mainstream Calculus II in a 2- or 4-year tential of modern mathematics and to complete a full year. Nearly all the stu- college or university in the United States makes them want to pursue it. Those dents who began the second semester [4]. Spring enrollments were certainly colleges and universities that find that came from the first-semester course at higher. Enrollments in Calculus II have many or most of their Calculus II stu- that institution. No more. The number been flatb, so we can estimate that roughly dents come with credit for calculus taken of students who take their first calculus a quarter million students take main- in high school should assess how well course in high school is much higher stream Calculus II in college each year. their curriculum meets the needs of these than the number who take calculus for In the spring of 2004, over 150,000 high students and entices them into continu- the first time in collegea. At many colleges school students earned a score of 3 or ing their study of mathematics. and universities, the majority of students better on one of the Advanced Placement in Calculus II passed the first-semester Calculus Examsc. Many more high school The Need for a New Calculus I course somewhere else, a trend that is students obtained International Bacca- accelerating. Large and increasing num- laureate or community college credit for The movement of first-semester calcu- bers of the students who take Calculus I calculus. lus into the high school curriculum also do so with no intention of continuing on has profound implications for how we to the second semester of the course. In many colleges and universities, it is teach Calculus I in college. Students who already the case that most of the students begin calculus in college are very differ- In the CUPM Curriculum Guide 2004 who take Calculus II come with credit for ent from those of a generation ago. They [6], the first and foundational recom- Calculus I taken in high school. These are far more likely to have weakness in mendation for all departments is to “un- students are not well served by the tradi- their mathematical preparation. They are derstand the student population and tional approach to calculus in college. also far less likely to aspire to taking a evaluate courses and programs.” The They have seen an entire course of dif- second semester of calculus. The tradi- CUPM Guide encourages departments ferential and integral calculus and have tional Calculus I course was never de- to “determine the extent to which goals already studied many of the topics that signed to stand alone. Now it must. of courses and programs are aligned with will be covered in the first half of Calcu- the needs of students” and “continually lus II. It makes no sense to pretend that There are many initiatives under way to strengthen courses and programs to bet- they are barely familiar with integration. supplement Calculus I instruction with ter align with student needs.” I will ar- “just in time” refreshment or teaching of gue that the traditional year-long single On the other hand, those who have taken pre-calculus topics. These are important, variable calculus course is badly out of the AB syllabus have had the equivalent but I want to focus on a different side of alignment with student needs at most of a one-semester course, not a full col- the problem with Calculus I that is rel- institutions. lege year. There are significant gaps in evant to the needs of the students at my their knowledge. Most of these students institution, Macalester College. The larg- The Need for a New Calculus II will not have studied integration by parts, est single group of students taking our L’Hospital’s Rule, or parametrized mo- Calculus I consists of prospective majors At colleges and universities on semester tion. Many of them would benefit from in the biological sciences. They are par- systems, the traditional Calculus I is dif- more and deeper work on limits, implicit ticularly ill-served by the traditional ferential calculus with the barest intro- differentiation, differential equations, course. duction to integration in the last few and the theorems of calculus. They need weeks. Calculus II picks up where Cal- a Calculus II course, but not the one we As part of the preparation for the CUPM culus I left off, reintroducing and then traditionally offer. Curriculum Guide 2004, the subcommit- developing integral calculus for roughly tee on Curriculum Renewal Across the half a semester. It then moves on to se- The need for revising Calculus II be- First Two Years (CRAFTY) sponsored the quences and series and may touch on comes even more imperative when we Curriculum Foundations Project, a series some topics of several variable calculus remember that the students who come of eleven workshops for faculty from such as partial derivatives. Aside from the to this course directly from a high school partner disciplines such as economics, fact that the material on sequences and AP course are among our most math- engineering, and physics. These faculty series never seems to hang together with ematically promising. The last thing we came together to explain and elaborate the earlier work on differential and inte- should do is to put them into a course upon what they want their students to
14 November 2004 FOCUS learn from their mathematics coursesd. eigenvectors. Can they learn all this for and enticing them into the further The workshop for biologists, held at within the context of Calculus I? study of mathematics. This should be the Macalester College in November, 2000, goal of every mathematics course, was personally enlightening. Macalester is among a handful of colleges whether taught in high school or college. that believes the answer is “yes.” We have Biology programs face constraints. They developed a substitute for Calculus I that There are fundamental shifts now occur- usually require two semesters of math- does not attempt to duplicate the cover- ring in the needs of the students who take ematics. Some institutions require more age of the traditional course. Its empha- our mathematics courses. Macalester’s or less, but because there is so much tech- sis is on geometric and conceptual un- solution is built around the needs of this nical information that has to be taught derstanding, and its syllabus includes: college and its students. What is needed within four years, few feel they can af- at your college or university will depend ford to require more than two semesters Functions and units: linear functions, on your situation and your students. of mathematics, and most feel that one power relations, polynomials, trigono- What you cannot expect is for the cur- semester of mathematics is not sufficient. metric functions, exponential functions, ricular solutions that worked a genera- Many medical schools, a driving force in logarithms. tion ago are still best for today. the biology curriculum, require one se- Dynamical systems: simple systems of mester of calculus. It is not uncommon discrete difference equations and differ- Bibliography for biology departments to have a math- ential equations. ematics requirement of Calculus I & II. The derivative: graphically, numerically, [1] APCentral, AP Research and Data, When the biologists gathered at algebraically; Taylor polynomials to sec- http://apcentral.collegeboard.com/pro- Macalester, they were unanimous and ond degree. gram/research/. strong in the opinion that Calculus I & The integral: as anti-derivative and as II made no sense as the two mathemat- area. [2] Bressoud, David M., “The Changing ics courses their majors should take. In Functions of two variables: contours, Face of Calculus: First-Semester Calcu- their own words: “The current math- gradients, optimization via hill climbing. lus as a High School Course,” FOCUS, ematics curriculum for biology majors The linear algebra of Ax = b: vectors, September 2004. does not provide biology students with projection, least-squares, subspace, span. appropriate quantitative skills. The field Emphasis is on 3-dimensional space. [3] Ganter, Susan and William Barker, of biology is becoming much more quan- Curriculum Foundations Project: Voices of titative which will necessitate a change This is a course that stands on its own the Partner Disciplines, Mathematical in the mathematics curriculum for biol- merits. Not only our biologists, but also Association of America, 2004. ogy majors” (p. 16). Biologists need our chemists and economists have mathematics, but not what we have been praised it for meeting the needs of their [4] Lutzer, David J., James W. Maxwell, teaching. students. We have been running it experi- and Stephen B. Rodi, Statistical Abstract mentally, a program made possible by of Undergraduate Programs in the Math- There are aspects of calculus that biolo- funding from the Hughes Foundation. ematical Sciences in the United States: Fall gists do need, though they need far less That money is ending. We are too small 2000 CBMS Survey, American Math- than we teach. The topics identified at an institution to be able to afford to run ematical Society, Providence, RI, 2002. the workshop were “integration for the two distinct Calculus I courses. In view purpose of calculating areas and average of the fact that Calculus II now draws so [5] Morgan, Rick and Len Ramist, Ad- value, rates of change, optimization, and few students from Calculus I, we have vanced Placement Students in College: An gradients for the purpose of understand- decided that it is the traditional Calcu- Investigation of Course Grades at 21 Col- ing contour maps.” The most important lus I that will disappear. For us, Calculus leges, Educational Testing Service Report mathematical tools for biologists lie in I and Calculus II will become very dis- No. SR-98-13, 1998. data analysis and statistics. Here the list tinct courses. of needed topics is far richer, “descrip- [5] Pollatsek, Harriet et al, Undergradu- tive statistics, conditional probability, These courses will still be connected. Part ate Programs and Courses in the Math- regression analysis, multivariate statis- of the intention of the revised syllabus is ematical Sciences: CUPM Curriculum tics, probability distributions, simula- to show students the importance and Guide 2004, Mathematical Association of tions, significance and error analysis” (p. usefulness of mathematics and to en- America, 2004. 16). courage them to continue their pursuit of it. But our two courses in single vari- Notes The kind of statistical analysis that these able calculus will no longer be two halves students need to be able to do is deep. If of a single course. Each is being rede- a) As estimated in the first article of this they are to understand the statistical tools signed around the actual needs of the series [2], there are probably between that they will be using, then they need students who take it, moving them for- 500,000 and 600,000 high school some familiarity with the concepts of ward in their understanding of and abil- students taking calculus each year. Also gradients, linear transformations, and ity to use mathematics, preparing them as shown in that article, the numbers
15 FOCUS November 2004 taking first-semester calculus in colleges have been flat or slightly declining for the past twenty years. Total mainstream and non-mainstream Calculus I enrollments in all 2- and 4-year institutions in the fall of 2000 was 384,000 [4]. If we estimate Seventh Annual that spring enrollments in Calculus I are two-thirds of fall enrollments, then between 600,000 and 700,000 students take some form of Calculus I in college each year. Roughly half of these, perhaps more, will have taken calculus in high school. b) 111,000 in fall, 1990, 106,000 in fall, 1995 [4]. February 4 - 6, 2005 c) Not all colleges or universities give credit for a 3 on the AP Calculus exam, A national showcase for research but a study [5] of students at 21 projects of undergraduate women universities including Boston College, Carnegie Mellon, William and Mary, in the mathematical sciences. Michigan State University, Pennsylvania State University, Stanford, University of Main Program Virginia, and Yale showed that those who scored a 3 on the AP Calculus AB exam Talks by undergraduate women and started at the university with about their own research Calculus II did better in that course than did students who had completed Calculus I at that university. Plenary Speakers Susan Friedlander, d) The reports of these workshops, University of Illinois at Chicago written by faculty in the partner disciplines, are available from the MAA as Curriculum Foundations [3]. Page Margaret Wright, references that follow refer to this New York University edition. For more information David Bressoud is DeWitt Wallace Profes- or to register, request funding sor of Mathematics at Macalester College or sign up to give a talk, in St. Paul, Minnesota. He serves both as visit us on the web at Chair of the MAA’s Committee on the ∼ Undergraduate Program in Mathematics www.math.unl.edu/ ncuwm (CUPM) and as Chair of The College or write to us at Board’s AP Calculus Development Com- [email protected] mittee. He has been involved with AP Cal- culus since 1990–91 when he had the privi- Department of Mathematics lege of teaching an AB course at the State University of Nebraska-Lincoln College Area High School and of learning 203 Avery Hall how to teach calculus from some great Lincoln, NE 68588-0130 teachers, especially Annalee Henderson. Deadline for registration January 21, 2005
University of Nebraska-Lincoln An equal opportunity educator and employer with a comprehensive plan for diversity
16 November 2004 FOCUS First Annual Embry-Riddle Undergraduate Mathematics Conference
By Greg Spradlin
The first annual Embry-Riddle Under- The response of the graduate Mathematics attendees to the con- Conference, funded by ference evaluation MAA NSF Grant DMS- was overwhelmingly 0241090, was held on positive. All respon- March 27, 2004 at dents completing a Embry-Riddle Aeronau- survey thought that tical University. ERAU is the conference was a fairly small (with about well organized, and 4500 students at the indicated that they Daytona Beach campus) would attend an- university focusing on other conference. aviation and aerospace. Some respondents ERAU has no mathemat- would have liked to ics major, but does have have more breaks a large and active student between talks for in- MAA chapter, many of troductions and so- whose members partici- Jan Prokaj explaining “Multirate Numerical Techniques for Linear and cializing. Some re- pated in the conference. Nonlinear Diffusion Problems In One Spatial Dimension.” spondents would The one-day program have liked a greater included student presen- variety of talks from tations and a keynote address. Approxi- which to choose. Some complained (jus- system for interplanetary travel. 8 of the mately 70 people attended, from several 10 student talks could be classified as “ap- tifiably) about an audiovisual snafu that Florida universities. delayed the last talk by 20 minutes. We plied” mathematics, and the other 2 as “pure,” reflecting the aerospace interests will act on these suggestions at future A total number of 14 student presenters of the Embry-Riddle students. The conferences. delivered 10 talks. When registering for agenda for the conference is still online the conference, the students were given The MAA and NSF have given Embry- at http://faculty.erau.edu/spradlig/erumc/ the option of a 20-minute talk or a 50- Riddle another grant to hold a similar agenda.htm . minute talk. Two students chose the 50- conference in spring 2005. This year, the minute option. Jay Lang of Embry- The keynote address, by Erich Friedman Conference Program Director will orga- Riddle gave an enthusiastic talk about the of Stetson University in Deland, Florida, nize a committee of ERAU mathematics Golden Ratio, its mathematical proper- department members to generate ideas was about unsolved problems in plane ties, and its occurrence in art and nature. geometry. Professor Friedman presented on how to improve on our promising Uriah Tobey, also of Embry-Riddle, ex- twenty-five easily stated but unsolved start. Our primary challenge is to attract plained how he programmed a TI-89 more students to give talks, especially problems. His talk was accessible to any- calculator to compute rocket trajectories one with a high school background in from other universities. In 2004 only from Earth to Mars, given initial and ter- geometry, and drew many questions three students from outside Embry- minal positions of the trajectory. Many Riddle gave presentations. We will try to from the audience. in the audience were awestruck by the enlarge this number by speaking to area complexity of the problem and the speed Approximately 33 students attended the faculty at MAA state and regional meet- of the calculator in solving it. ings, and more persistently reminding conference. It was difficult to count them, because these included many Embry- area MAA liaisons and student chapter Other highlights of the conference in- Riddle students who happened to be in leaders about the 2005 conference. cluded an introduction by Amanda the same building, saw the signs for the Fountain (University of Western Florida) conference, and dropped in to listen to to hyperbolic geometry, Christopher some talks. Although the students were Subitch’s (University of Central Florida) not polled about their affiliation, the simulation of propagating optical waves, number of unfamiliar faces suggested Greg Spradlin is an Assistant Professor of and an Embry-Riddle team’s use of that at least half of them were from in- Mathematics at Embry-Riddle Aeronau- STELLA and Maple to design a landing tical University. stitutions other than Embry-Riddle.
17 FOCUS November 2004
18 November 2004 FOCUS MathFest 2004
The 2004 MathFest was held in Providence, RI on August 12 to 14. With over 1200 participants, it was one of the most successful MathFests ever. Peter Sarnak was the Hedrick Lecturer, giving three fascinating lectures on Ramanujan Graphs and their connections with automorphic forms and Ramanujan’s Conjecture. Alan Schoenfeld was the Leitzel Lecturer. Schoenfield’s lecture, entitled Mathematics and the Schools, was a report on his attempt, as part of a group at the University of California at Berkeley, to do some work with the local schools. Other exciting speakers included Tony DeRose of Pixar Animation on “How Computer Graphics is Changing Hollywood” and Steve Sigur on “The Mystery of the Missing Tangents.” There were many special sessions, panels, and contributed paper sessions, and of course also many social activities. Even USA Today seemed to be in on the action, carrying a front-page story on how “Algebra’s for Everyone Now — Expectations are Rising” on August 21. The following pages give a glimpse of some of what went on.
Overheard at MathFest I needed some exercise, so I rode the escalators up and down several times.
— Anonymous
Algebra is a 4000-year-old mathematical system that uses letters or other symbols to stand for relationships between numbers.
— USA Today
The USA Today forgot to mention that analysis is also useful.
— Peter Sarnak
The real macho guys do hard analysis; the clever guys do soft analysis. “Soft” means that you’ve understood it.
— Peter Sarnak
How to Get a Job at Pixar
Want to enter the high-flying world of computer animation? One way to get yourself a job at Pixar Animation is to figure out how to solve integral equations like:
Lxy(),,= Bxy()+ ∫ LxzRxyzVxzdz()( ,,,, )() zZ∈
Or at least learn to approximate a solution quickly.
Tony DeRose described how animators handle lighting today by asking his audi- A full audience in a darkened room: Tony DeRose ence to imagine a photographer setting up his lighting equipment in the dark. explains “How Computer Graphics is Changing Once everything was set up, the photographer would wait for two hours. At that Hollywood.” point, the lights would go on and he could assess the result. If he wasn’t satisfied, the lights would go out again, the equipment would be rearranged, and another two hour wait would follow.
Figuring out the effect of lighting a scene in an animated film involves solving the integral equation above. This is done numerically on (essentially) a supercomputer, and it takes several hours. So if you can do it quickly, you’ll have it made.
Photographs courtesy of Fernando Gouvêa.
19 FOCUS November 2004 MathFest in Photos
Colm Mulcahy at the FOCUS Ron Graham at the MAA Joe Gallian, Richard Guy, and Aparna Editorial Board Meeting. Business Meeting. Higgins.
An impossible object, an exhibit at Baby pictures! Ina Lindemann and Aparna Higgins Darren Glass the “Glass and Geometry” booth. Tom Grasso.
The Board of Governor’s Meeting Ken Ross signs a copy of his latest book.
Ron Bradley, fearless leader of HOM- The only person who SIGMAA. knew all that was going on: Jim Tat- tersall, Associate Secretary of the MAA.
Francis Su, one of the Stan Seltzer celebrates first winners of the Ed Burger, winner of the Chauvenet Prize. 25 years as a member Henry Alder Award. of the MAA.
John Lutts at the Silver and Gold Dan Kalman speaking at the Banquet. Opening Banquet. John Harvey, 50 Books! years with the MAA. 20 November 2004 FOCUS
More books! Placing the email center inside the More baby pictures! Jennifer Quinn, exhibits area made it particularly Doris Schattschneider, and Martha pleasant to check on news from home. Siegel.
Steve Kennedy looks closely at a Otto and Marlisa Bretscher promote dodecahedron in the “Glass and Geometry” Otto’s Linear Algebra textbook. booth. Glass and Geometry
Douglas Duncan, winner Richard K. Guy Greg Frederickson, of the Trevor Evans Emma Breedlove Smith Jim Smith, 50-year winner of the George Award. celebrates 25 years as a member. Pólya Award. member of MAA.
“Dali is the one on the right.”– Zvezdelina Stan- A slide from Tom Banchoff’s Beverly Ruedi and Carol Baxter kova, one of the first Steve Sigur of the talk at the Silver and Gold tending to the MAA booth. Henry Alder Award Paideia School, who Banquet. Tom is the one on winners. gave one of the invited the left. addresses.
21 FOCUS November 2004 The August 2004 Board of Governors Meeting: A Graduate Student’s Perspective By Michael Lauzon
A mathematician’s duties fall into three ticle, from here on the reports became that a committee’s secretary should be general categories: research, teaching, more interesting. informed immediately about any pos- and service. Most of us enjoy one or both sible conflict of interest. Finally it was of the first two, and put up with the lat- The report about upcoming book pub- decided that the MAA secretary should ter because it is necessary to do some lications was the most enjoyable of the take these suggestions into account and administrative work to organize confer- meeting. There were about a dozen new write a policy that reflects them to be ences, find new faculty or graduate stu- publications this year, and we were given voted on at the next board of governors dents to keep our mathematics depart- a summary of each book and copies of meeting. ments thriving, and, in this case, to keep the new publications were passed around the MAA running smoothly. The Board for our perusal. We were also told about Another issue that involved some discus- of Governors, while a decision making last year’s bestsellers. Two books that sion was the formation of a steering com- organization, also serves as a vehicle for caught my attention were Euler: Master mittee for the next strategic planning different parts of the MAA to commu- of Us All by Bill Dunham and Musings of process. What was proposed was that a nicate to each other what they are doing the Masters, edited by Raymond Ayoub. few section governors form a plan to put to further mathematics and mathemat- Euler: Master of Us All is about Euler’s together a statement of long-term objec- ics education. Governors fall into three life and prolific works in mathematics tives for the MAA. The committee is not broad categories, sectional governors, and has been on the MAA top ten supposed to suggest any particular long- who represent geographic regions, gov- bestseller list for five years. Musings of the term goals, but decide how such goals ernors who represent specific interests, Masters is a new book which presents will be decided upon. After some dis- such as minorities, high school teachers, informal writings of many mathemati- cussion, the governors agreed that the or certain MAA publications, and MAA cal greats (Poincaré, von Neumann, committee should be kept small (and for officers. Hardy, and many more). this reason would be unable to reflect too many diverse opinions) and should be When I arrived at the Board of Gover- Creating a conflict of interest policy was made up of sectional Governors. nors (BOG) meeting, I had a chance to the most contentious issue of the meet- talk with some of the governors before ing. While there was near universal One interesting thing about attending the meeting began. Some I knew from agreement that some conflict of interest the BOG meeting was that I heard about either my undergraduate or graduate policy was necessary (for people on many MAA activities that as a graduate institution; others I met for the first time. awards committees, for example), it was student I would otherwise not know Everyone was friendly, but they all not clear what form the policy should about. Some issues pertained to people seemed to indicate we were in for a long take. For example, the governors decided with much more money than I, such as a day. The general opinion was that the that a list of examples of conflict of in- policy requiring a minimum amount of agenda for this meeting had many re- terest as part of the MAA’s official writ- money to establish an endowed prize. ports and a few contentious issues that ten policy might turn into a laundry list Others were reports about programs for might lead to lively debates. of situations to avoid instead of serving people with a different background from as examples to suggest a general idea of me, such as the Report from the Office For the first two hours or so, the meet- what conflict of interest means. It was of Minority Participation. Still others ing consisted of dry but necessary re- decided that identifying when a conflict were programs targeted toward younger ports. For example, we heard several re- of interest arises should be left to the people, such as a report about what goes ports related to the finances of the MAA, common sense of individuals, but that on at the Math Olympiad Summer Pro- which can be summarized as follows: the MAA secretary should be contacted gram, and a report about mathematical The MAA has enough money to carry about unclear cases. There was also contests in general. While there was little out its programs, but of course more some debate about what should be done excitement or glamour in the BOG, I did money would be nice. After these re- in cases of suspected conflict of interest, come away with a better idea of how ports, the president issued a comment and whether immediately recusing one- much hard work is involved to keep the that the BOG is responsible for all ac- self should be part of official policy. It various parts of an organization as large tivities that take place in the MAA, and was decided that many discussions, such as the MAA working well together. we really should try to pay attention. At as those conducted over e-mail, move this point the governor sitting on my left slowly enough for a conflict of interest turned to me and said, “So what are you to be resolved without someone neces- Michael Lauzon is a graduate student at going to write?” Fortunately for this ar- sarily having to recuse themselves, but Brown University.
22 November 2004 FOCUS
23 FOCUS November 2004 NSF Beat fessional and undergraduate research. career are the transition points addressed Other opportunities for undergraduate by the project at the University of Ne- By Sharon Cutler-Ross students will include working in small braska (Judy Walker, PI). The central teams with undergraduate summer re- piece of the program is Nebraska Inten- searchers from other disciplines and sive Mathematics: a Mentoring, Educa- The Mentoring through Critical Tran- helping faculty mentors develop statis- tion, and Research Experience which will sition Points (MCTP) initiative of the tics modules for non-mathematics bring together students about to enter National Science Foundation made its courses. Post docs will help run the Cen- graduate school, students who have just first awards this year. The program has ter, teach undergraduate statistics finished the first year of graduate school, support from the Division of Math- courses, aid the summer research teams, graduate students close to finishing the ematical Sciences, the Division of Under- and continue their own research pro- PhD, and faculty a few years out of graduate Education, and the MPS Office grams. graduate school who teach at predomi- of Multidisciplinary Activities. The tran- nately undergraduate colleges. The key sition points of interest are those from The MCTP project at the University of piece of the various components of the high school to college, undergraduate Alabama at Birmingham (Lex Overs- project is the focus on the relationship school to graduate school, and from teegen, PI) addresses all three transition between PhD- and non-PhD-granting graduate school to a professional career points. Talented high school students institutions. in mathematics. will be able to go directly into an accel- erated program leading to a BS and an The Institute for Advanced Study will The Statistics Undergraduate Mentoring MS in four to five years. The transition sponsor a Program for Women in Math- (SUM) Project at St. Olaf College (Julie to graduate school will be smoothed by ematics (Phillip Griffiths, PI) with Legler, PI) is intended to increase the an increased focus on independent re- MCTP funding. This annual ten-day number of undergraduates from four- search in the undergraduate courses. Fi- mentoring program serves a mix of un- year colleges who concentrate on statis- nally, the mathematics doctoral program dergraduate and graduate students, and tics in graduate school and to increase will be supplemented with more empha- post-doctoral researchers. Senior the number of statistics PhDs who sis on the breadth of mathematics, ex- women mathematicians organize and choose to teach at four-year colleges. A posure to another science, and develop- present the program on a specific topic Center for Interdisciplinary Research will ment of interpersonal and communica- each year. The project goals are to en- be established where undergraduate stu- tion skills for career success. hance the mathematical education of tal- dents, post-doctoral assistants, and fac- ented women mathematicians and retain ulty mentors can work collaboratively The transitions from undergraduate to these women in the field by establishing with faculty and students in other de- graduate school and from graduate an extensive support network of other partments on statistical aspects of pro- school to the early years of an academic women mathematicians.
24 November 2004 FOCUS Freshmen Can Offer Mathematical Solutions to Real-World Issues By Joseph Kirtland and Pau-San Hoh
Many first-semester freshmen view revising the paper. To complete the = 20, which is congruent to 0 (mod 10). their education as a process of master- project successfully, students must inves- The abbreviated number 673494 (here 4 ing a collection of unrelated skills from tigate the history of their topic, be aware is the check digit) would be an invalid a variety of academic disciplines. The au- of current trends, and develop a solution number as s(6)+7+s(3)+4+s(9)+4 = thors have found this to be particularly or describe the next step that should be 3+7+6+4+9+4 = 33, which is not con- true of students who must take math- taken. By doing this, they start to make gruent to 0 (mod 10). Unknown to us ematics and writing courses as part of larger connections among different dis- until a year or so later was that the fed- their general requirements. Rather than ciplines. eral Health Care Financing Administra- seeing the practical value of solid math- tion, an agency in the Department of ematical and writing skills, these students Over the years, the students have tackled Health and Human Services, had pro- are more apt to express relief at having a variety of topics, including modern posed creating a national standard iden- “gotten through” these course require- dance, environmental science, cryptog- tifier in May of 1998. ments because they perceive that they raphy, criminal justice, and transporta- have gotten them “out of the way” of their tion engineering. Some of the more in- Another student’s proposal in the fall of college careers. To address this and other teresting projects were those in which 2003 similarly paralleled a real-world concerns, the authors have taught for the student proposals anticipated or pre- interest. To deal with the problem of last six years a mathematics-composition dicted solutions suggested or imple- underage drinking and fake IDs, a stu- course cluster (partially supported by mented later. During the fall of 1998, for dent developed an enhanced identifica- NSF–DUE 9752632) to incoming unde- example, one student decided to wade tion number system for all drivers in the cided freshmen where the same students into the world of health care with its diz- U.S. The number would be associated are enrolled in both an introductory- zying array of care providers and benefit with a person’s driver license and would level mathematics and a freshman com- management bureaucracies, coupled be unique to that person. In addition, the position class. with the constant movement of patients number included a check digit scheme through the system. In particular, he so that all establishments that sell alco- The cluster creates a unified learning wanted to make it easier for patient in- hol could scan the card and verify its au- environment where students develop formation to be maintained and insur- thenticity. This freshman’s proposal was basic skills and examine practical appli- ance claims processed as a person grows echoed in a September 2003 report by the cations of mathematics. As students write and changes physicians and insurance American Association of Motor Vehicle formal papers on the mathematics, they companies. The student’s solution was to Administrators (AAMVA). While the are compelled to demonstrate and assess develop a universal health care identifi- studen concentrated on a way to make their own understanding of the subject. cation number system and accompany- the identification number of a license a By having them write at length, the in- ing check digit scheme. more secure and unique identifier of the structors can then identify those who license holder, the AAMVA report dis- have a comprehensive understanding of The medical identification number he cusses the progress that has been made the content, those who fall somewhat designed would be assigned to a person with regards to all aspects of driver’s li- short of that, and those who have simply at birth and used by all health care pro- cense security (issuing, forgeries, unique relied on rote memorization. By the end viders, insurance companies, and em- identifiers, etc.). of the semester, all cluster students dem- ployers throughout that person’s life. onstrate understanding of the math- This involved creating a hashing process In addition to predicting or paralleling ematics and its value in the real world by that encoded the most relevant informa- current efforts, a number of students writing a research paper. In this final pa- tion that a doctor and an insurance com- have also tackled known problems. New per, the students document their inves- pany would need to know about a pa- York State, on August 16, 2000, and the tigation of a topic using the skills and tient. The identifier was a 25-character state of Washington, on April 19, 2001, knowledge presented in the mathemat- alphanumeric string. After all letters were passed laws stating that social security ics class. Whether drawing from a per- converted into digits, the check digit numbers could not be openly used by sonal experience or addressing a national scheme would apply the permutation s public or private colleges to identify stu- or global problem, the project provides = (0)(1,2,4,8,7,5)(3,6)(9) to every other dents. A number of our cluster students an avenue for students to explore the digit, add up all the resulting digits, and have proposed new methods for creat- broader impact of mathematics and to then append the check digit so that the ing a student identification number sys- see how mathematics can be used to ad- sum, with the check digit included, was tem. These methods involved elaborate dress significant issues. The instructors equal to 0 (mod 10). For example, the hashing functions that encode student give one-on-one guidance through all abbreviated number 186452 (here 2 is the information in a sophisticated and secure stages of research and writing, from de- check digit) would be a valid number as way so that no two students get assigned fining the problem to formatting and s(1)+8+s(6)+4+s(5)+2 = 2+8+3+4+1+2 the same number (which is why schools
25 FOCUS November 2004 use social security numbers). In addition, then to guide them so that they used the tracking, ciphers based on natural lan- many of the systems developed also in- most appropriate data sources. While we guage systems, etc. All of the students cluded a check digit. never pushed a student in one direction mentioned in this article were very proud or another, we did impart on them the of their work and felt a real sense of ac- Although writing is often seen as the dis- importance of strong writing and good complishment when they found out that cipline that serves mathematics in such mathematical skills. We also trained the their approaches paralleled or predicted linkages, the reverse effect is equally students in basic research methodology work done by others in the field. This fact strong in this particular cluster. The clus- and encouraged them to not be afraid to alone was the best reinforcement of the ter students have said often that writing tackle large issues. Most importantly, the importance of having solid mathemat- about mathematics has forced them to projects gave the students the sense that ics and writing skills. confront the demands of academic writ- they can do meaningful work on issues ing, such as concision, precision, coher- that have an impact on the world in Joseph Kirtland and Pau-San Hoh teach ence, and logical order. which they live. Even at the initial stage Mathematics and English, respectively, at of their projects when they were explor- Marist College in Poughkeepsie, NY. They With careful guidance, even first-semes- ing topics to investigate, we could see the would like to express their gratitude to the ter freshmen produced results where students’ excitement in considering the students who participated in the cluster mathematics was used in a meaningful options where they thought mathemati- and especially to Rich Carlson, David and practical way. The key was to have cal applications were possible: GPS, mo- Chamberlain, Melissa Long, and Elizabeth the students pick their own problems and lecular research, endangered species Camire.
ICMI Study 16
The International Commission on chaired by Ed Barbeau of the University Mathematical Instruction (ICMI) has of Toronto ([email protected]) commissioned a study on Challenging and Peter Taylor of the University of HOMSIGMAA Contest Mathematics in and beyond the Class- Canberra in Australia who is the execu- room, whose main event will be a Study tive-director of the Australian Math- The History Of Mathematics Special Conference from June 27 to July 3, 2006 ematical Trust ([email protected]). This Interest Group of the MAA is pleased at Trondheim, Norway with invited par- document defines terms, describes is- to announce its second annual Student ticipants. The scope of this study will be sues, provides sample situations, and Writing Contest in the History of wide. It will look at, for instance, the poses questions for discussion. Finally, Mathematics. impact of mathematical challenges both it indicates how to become involved in inside and outside of the classroom, the the Study Conference. Would-be partici- The deadline for submissions is March role of mathematical challenges in sup- pants will be asked to submit a brief cur- 30, 2005. Information and submission porting the curriculum for students of riculum vita and a 6-10 page document guidelines can be found on the HOM all levels of ability, vehicles for propagat- addressing matters relevant to the study SIGMAA website at http:// ing mathematical challenges and assess- no later than August 31, 2005. The com- www.maa.org/homsigmaa or by con- ment of their effectiveness. We would like mittee plans to send out invitations by tacting Amy Shell-Gellasch at to emphasize that we are interested in January 31, 2006. The Conference will [email protected] students and activities of all type, and be followed by a publication. A copy of want to go far beyond contests for tal- the discussion document can be ob- ented students. tained by going to the website http:// www.amt.canberra.edu, clicking on A discussion document has been pre- “LINKS” and then on “ICMI Study 16.” pared by an international committee
26 November 2004 FOCUS Research Experiences for Minority Undergraduates: SUMMA’s National REU Program By Robert E. Megginson Though some progress has twenty of the 47 students been made in recent years on who participated in SIMU the problem of the scarcity of in its first two summers African Americans, Hispanic had been accepted into Americans, and Native Ameri- Ph.D. programs in the cans (for brevity, these three mathematical sciences, and groups will hereinafter be re- seventeen others had been ferred to collectively as minori- accepted into other gradu- ties, with full recognition that ate programs. With the to- there are many other minority tal annual output of U.S. groups in the U.S.) in the re- Hispanic American and search mathematics commu- Native American math- nity, much remains to be done. ematics Ph.D.s averaging According to recent census fig- only about fifteen in recent ures, these three groups to- years, this single program gether now constitute about has the potential of having 27% of the U.S. population (see Student Researchers Ary Clemons, Francesca Duncan, Mariam a significant impact on that [1]), but according to [2] they Konatè, and Jeremy Smith studied protein folding and DNA production. still account for only about 6% sequencing using graph-theoretic techniques with Debra Knisley at of the mathematics Ph.D.s East Tennessee State University. One factor that almost cer- given to U.S. citizens and per- tainly contributed to manent residents each year. dents about the prospect of a research SIMU’s success is that participants inter- career in mathematics and persuade acted with a critical mass of students The under-representation of minorities them to continue their education into from backgrounds like their own, and in the ranks of Ph.D. mathematicians, mathematics graduate school. A good saw first hand that there were other and more generally in all of academe, is example is provided by the Summer In- Chicano, Latino, and Native American a well-known problem. Much of the stitute in Mathematics for Undergradu- students who shared their interest in damage has already occurred by the time ates (SIMU) conducted at the University mathematics and could succeed in the the undergraduate years are reached. For of Puerto Rico–Humacao from 1998 to field. Without a direct focus on recruit- example, minorities receive high school 2002 (see http://cuhwww.upr.clu.edu/ ing minority participants, it is difficult diplomas at rates substantially lower than ~simu/). In each of its five summers this for an REU to achieve such a critical the national average, and those minori- program engaged about two dozen His- mass. Mathematics REU sites between ties who do graduate from high school panic American and Native American 1980 and 2000 that did not explicitly fo- then enroll in college at rates lower than students, all U.S. citizens or permanent cus on recruiting minorities averaged their white counterparts with high school residents, in intensive six-week research fewer than 4% minority participants, degrees (see http://nces.ed.gov/programs/ projects designed and conducted by lead- which clearly does not contribute to the digest/d02/tables/dt012.asp). Some might ing mathematicians. Follow-up included solution of the under-representation take this as evidence that “it’s not our continuing in contact with research men- problem in the Ph.D. ranks. problem here in college,” and that the tors during the school year and presen- matter needs to be addressed somewhere tations of research at the annual confer- With all of this in mind, the MAA’s earlier in the educational pipeline. In fact, ences of the Society for Advancement of Project for Strengthening Under-repre- it makes it imperative that we, as college Chicanos and Native Americans in Sci- sented Minority Mathematics Achieve- mathematicians, encourage the minor- ence as well as in the MAA’s undergradu- ment (SUMMA) established a National ity students who do make it into our ate poster session at the January Joint Research Experience for Undergraduates mathematics undergraduate programs to Mathematics Meetings. Program (NREUP) in 2003 to provide persist through to advanced degrees to primary or supplemental funding for provide the next generation of mentors Students were not accepted into the summer REUs of substantial length en- and role models for students from simi- SIMU program just on the basis of their rolling enough minority students to have lar backgrounds. promise for graduate school in the tra- a presence in the program. It was decided ditional sense, but with much attention to require that the students be local to There is much evidence that mathemat- paid to their untapped potential and will- the program, in part to stretch program ics REUs (research experiences for un- ingness to work as described by faculty funds by eliminating travel costs but also dergraduates) can excite minority stu- recommenders. As of January 2003, to encourage program sites to develop
27 FOCUS November 2004 the talent at their own institutions rather produce interesting partial results. David tinuing the project, and received an NSF/ than recruit from talent already devel- Housman’s program at Goshen College DMS grant for doing so along with con- oped elsewhere. focuses on cooperative game theory and tinued NSA funding. With this funding, fair division, where, for example, known it was possible to expand the number of With funding in hand sites for summer 2004 to six, with from the National Secu- East Tennessee State University, rity Agency for a pilot Virginia State University, and project, SUMMA con- California Lutheran University ducted an e-mail solicita- added to the original sites. Each tion of its members for of the six sites had at least four “MAA Summer Research minority undergraduates partici- Program” sites for sum- pating, and initial indications are mer 2003. The two pri- that the students in them have mary sites selected from done exciting work that should the seventeen applications whet their appetites for a career received are programs at as a mathematician and point California State University them toward graduate school in at Chico and Texas South- the mathematical sciences. ern University. Funding was also provided to Funding for NREUP will again be Goshen College in Indiana available for summer 2005, for for adding a student to an which applications will be ac- existing REU. All three The Pebbling Team: Marlene Merchain, Modesty Briggs, Juan cepted through January 31. Up to programs received con- Zuniga, and Victor Moreno did research on graph pebbling at the six grants of up to $25,000 each tinuation funding from NREUP program at California Lutheran University. will be given. Grants are intended NREUP for summer 2004 to provide some compensation after the pilot proved successful. allocation methods fail for partially de- for a faculty researcher as well as stipends, fined cooperative games due to the diffi- room, and board for at least four under- Quite a bit of thought is needed to be culty or infeasibility of determining the graduates from minority groups under- put into the initial selection process, since coalitional worth functions, but where represented in the mathematical sciences. many more worthy proposals were re- there are several possible approaches Funding received through this program ceived than could be funded, but the ex- open to student investigation. In the pro- can be for new projects, but can also be cellence of the proposal pool showed gram on geometric graph theory and used to supplement existing projects pro- from the beginning that a larger program game theory directed by Nathaniel Dean vided the student funds are used for un- would be feasible with no loss in quality. and Tong Wu at Texas Southern Univer- dergraduates from underrepresented mi- A major criterion for selection was that sity, students work on problems such as nority groups. See http://www.maa.org/ the research in which the students would finding tight bounds for the size of the nreup for further details and application be engaged had to be intellectually sub- smallest square integer lattice that will instructions. stantial and require hard work on their realize a sphere-of-influence graph, a cer- part, with an excellent chance of devel- tain type of graph important in pattern References oping further directions of investigation, recognition and computer vision. presentations that would interest re- [1] U.S. census figures; http:// search mathematicians, and, possibly, Though it is too early to know with cer- www.census.gov/Press-Release/www/ publications. tainty how many of the students in 2003/cb03-100.html. NREUP’s 2003 pilot project will end up [2] American Mathematical Society, An- For example, in the program on knot in graduate school, initial attitudinal sur- nual Survey of the Mathematical Sciences, polynomials conducted by Thomas veys of the students are quite encourag- First Report, for 2000 through 2003; Mattman at California State University ing. For example, the four African Ameri- http://www.ams.org/employment/ at Chico, students investigated such mat- can students in the Texas Southern Uni- surveyreports.html. ters as the trip matrix of a knot and a versity program, who were tentative generalization from which the Jones about attending graduate school when polynomial of the knot can be computed the program began, reported at the end Robert E. Megginson is Professor and As- and the algebraic nature of some of the that they had become determined to do sociate Dean at the University of Michi- properties of the Jones polynomial can so. gan at Ann Arbor. The project described be deduced. There are several important in this article is being supported by the open questions arising in this investiga- With this and much other evidence of National Science Foundation under Grant tion that lend themselves to student ex- success in hand, the MAA and SUMMA No. 0353841, with other significant fund- ploration and for which the students can sought funding for expanding and con- ing received from the National Security Agency.
28 November 2004 FOCUS SAUM Offers On-line Guide for Assessment of Student Learning
Several factors continue to press for Over the past three years, a series of stronger assessment of student learning. workshops have brought together teams SAUM Self Paced On Line Guide In his recent article “The Four A’s: Ac- of faculty from mathematical sciences to Designing and Implementing countability, Accreditation, Assessment, departments with more experienced col- a Program for Assessing and Articulation,” Lynn Steen pointed leagues from a variety of institutions to Learning in the Major out that “as higher education has be- construct plans for assessment. Follow- come more important, more prevalent, up sessions have allowed the teams to and more costly, those who pay the bills receive assistance at the implementation Available through the SAUM website, — administrators, trustees, legislators, stage as well. A volume of case studies, http://www.maa.org/saum, this Guide parents — are beginning to ask for evi- Assessment Studies in Undergraduate provides easy access to materials de- dence of value.” This summer, as Con- Mathematics (MAA Notes #49), pub- signed to assist faculty develop or en- gress considers reauthorization of the lished in 1999, was distributed to all hance assessment programs in their de- Higher Education Act, connections be- mathematics departments and the full partments. The first section provides an tween accountability (and in particular text is available on the SAUM web site, overview of assessment, including an introduction to terminology, and points outcome assessment) and accreditation http://www.maa.org/saum. A second vol- are some of the most contentious issues, ume is expected sometime next year. to recent recommendations from the raising concerns among many in higher SAUM has also provided leaders for more MAA’s Committee on the Undergradu- education of federal imposition of bur- informal “assessment forums” at section ate Program in Mathematics on both densome and costly oversight. Unless the meetings for seventeen of the 29 MAA curriculum and assessment. academic community begins to take se- sections. riously the need to use assessment as a In the second section, broader readings tool for both documenting and improv- Through both the forums and work- are presented that expand on assess- ing our work, it is almost certain that shops, we have found that there is a grow- ment by looking at it from an interna- such requirements will be imposed from ing interest in the mathematics commu- tional perspective and in a larger arena the outside, either from federal or state nity for information and support for de- of program evaluation and accountabil- governments, traditional accreditation velopment of assessment plans. In order ity, where your assessment results may bodies, or (more likely) from a combi- to reach a broader audience, a self-paced be used. nation of all three. on-line guide, “Designing and Imple- menting a Program for Assessing Learn- Finally, a collection of representative With support from the National Science ing in the Major,” has now been posted case studies are presented, together with Foundation, the MAA Supporting As- on the SAUM website. Together with a pointers to ongoing projects that may sessment in Undergraduate Mathemat- range of other materials, including the provide points of contact for faculty in- ics (SAUM) project aims to assist faculty full text of the case studies volume, terested in discussing their own efforts develop effective methods of assessing SAUM offers faculty an in-depth look at with others who are pursuing similar courses, blocks of courses, or entire pro- the assessment process. Whether you are goals. A bibliography rounds out the grams within the mathematics depart- just beginning to think about assessment, Guide, offering those so inclined to con- ment, not only to answer the external or trying to refine existing mechanisms, tinue exploring the current research calls for accountability, but even more you can find the resources to help you and practice on assessment and ac- importantly, to assist faculty as they make understand and improve student learn- countability. critical decisions about course and cur- ing in your courses. ricular revision.
Tattoo Design Contest
Calling all aspiring artists! The MAA is looking for math-related designs for its new temporary tattoo, to be made available to stu- dents, student chapters, and members. The first such tattoo, which was very popular at the Phoenix Joint Mathematics Meetings, is shown right. To enter, email a four-color design, two inches square at 300 DPI, to the MAA at [email protected] by Friday, Decem- ber 10th. Designs selected for printing will be notified by email and receive 100 free tattoos. Winners will be announced in Math Horizons.The triaxial tritorus design was created by Paul Bourke of Swinburne University.
29 FOCUS November 2004 Archives of American Mathematics Spotlight: The Mathematical Association of America Records
By Kristy Sorensen
The Mathematical Association of MAA, I’d be happy to discuss your America and the Archives of American records with you. To get an idea of what Mathematics (AAM) at the Center for types of papers we currently hold, you American History have had a close rela- may be interested to learn that the tionship for many years. Building on the searching aid for the MAA Records was presence of the papers of R. L. Moore and recently mounted on the Texas Archival some of his colleagues and students, the Resources Online (TARO) website. It can AAM was established when the Math- be viewed at http://www.lib.utexas.edu/ ematical Association of America chose taro/utcah/00328/cah-00328.html. The University of Texas at Austin as its official archival repository in 1978. Since As is the case with any growing collec- then, numerous deposits of papers, pho- tion, the finding aid for the MAA Records tographs, and other records have come is a work in progress. We expect it to into the archives. The MAA records held grow, change, and become more refined at the AAM now total more than 300 lin- as new groups of papers are brought into ear feet. the archives, cataloged, and opened for research. The Mathematical Association We now have a strong foundation of of America Records is one of the core col- records in which mathematical histori- lections at the AAM, and we look forward ans, mathematicians, and members and to helping it grow and evolve to best help officers of MAA can find valuable and Annotated program from the Second our researchers in the future. unique information about the history Annual Meeting of the Mathematical and work of this professional organiza- Association of America, December 28– The Archives of American Mathematics tion. I am working to develop a more fo- 30, 1916. From the Mathematical As- is located at the Research and Collections cused appraisal strategy that can bring sociation of America Records, Archive division of the Center for American His- in the most historically relevant materi- of American Mathematics, Center for tory on the University of Texas at Austin als from all areas of the MAA. Too often American History, The University of campus. Persons interested in conduct- important records are inadvertently de- Texas at Austin. ing research or donating materials or stroyed or relegated to unopened base- who have general questions about the ment files. Alternatively, bulky day-to- In order to create an effective appraisal Archives of American Mathematics day files can take up valuable space in of- strategy, I’ll need to hear from those of should contact Kristy Sorensen, Archi- fices or archives shelves. My goal is to you who are creating potentially archi- vist, [email protected], (512) create an appraisal strategy that will be val records. If you are an officer, a com- 495-4539. Our web site is located at flexible enough to allow for a variety of mittee chair, a section leader, an editor, http://www.cah.utexas.edu/ historical records, without opening the or involved with any one of the many im- collectioncomponents/math.html. floodgates to unexamined materials. portant records-creating positions in the
In Memoriam
William Firey, Emeritus Professor at John E. Freund, longtime member of the at the age of 94. Doob taught at the Uni- Oregon State University, died on August MAA and prolific author of textbooks on versity of Illinois at Urbana-Champaign 15, 2004. Described by friends as a probability and statistics, died on August from 1935 until his retirement in “mathematician of the old school,” Firey 14, 2004 at the age of 83. A passionate 1978.He had been a member of the MAA had been part of the Putnam Questions educator, he was a member of the MAA since 1963. Committee and a member of the edito- since 1949. Brief death notices of interest to MAA rial board for the MAA’s Spectrum se- members are posted online at http:// ries. He was a member of MAA since Joseph L. Doob, a pioneer in the study www.maa.org/news/inmemoriam.html 1968. of the mathematical foundations of probability theory, died on June 7, 2004 and included in FOCUS. Send notices to Carol Baxter at [email protected].
30 November 2004 FOCUS
Undergraduate Poster Session at the 2005 Joint Meetings
The 2005 Undergraduate Student expository posters cannot be accepted. Word) to Mario Martelli at Poster Session will take place on Friday To apply, students need to supply (1) [email protected]. January 7 in Atlanta, Georgia, at the the project title, (2) an abstract, no Joint Annual Meeting of the AMS, longer than a half page, (3) names and Each poster will be evaluated by at least MAA, and AWM. Professor Mario affiliations of all authors, (4) name, three judges. Prizes will be awarded to Martelli of Claremont McKenna Col- email, and telephone number of the the best posters with money provided lege is the organizer. The MAA Com- student who will be the contact person by the AMS, MAA, AWM, CUR, PME, mittee on Undergraduate Students Ac- for the logistics of the presentation, (5) and by the Moore Foundation. The tivities and Chapters (CUSAC) spon- name(s) and affiliation(s) of the person in charge of coordinating the sors the Session. advisor(s), and (6) sources of financial accomodations of students participat- support. Send all the information to ing in the Poster Session is Prof. Diana Please apply early, since the space is lim- Professor Mario Martelli, Mathemat- Thomas of Montclair State University. ited! Posters are expected to present a ics Department, Claremont McKenna Please get in touch with her at new result, or a different proof of a College, Claremont, CA 91711 or by [email protected] if you known theorem, or an innovative solu- email (PDF format, TeX, or Microsoft are interested in this service. tion of a Putnam problem, etc. Purely
31 FOCUS November 2004 In Memoriam cepts of Mathematics. His two volume spent 1947–48 studying mathematics at Survey of Geometry was first published Carnegie-Mellon. From there, he re- by Allyn & Bacon in 1963 and has been turned as an instructor to the Polytech- Howard W. Eves, 1911–2004 reprinted in several abridged versions. nic Institute, then held positions succes- By Cindy Eves-Thomas sively at AVCO Research, SUNY-Buffalo, and Clayton W. Dodge While at the Institute for Advanced Stud- the University of Minnesota, Ford Mo- ies in Princeton, he became a friend of tor Company, the University of Water- Albert Einstein, who once pointed to an loo, and the University of Alberta, where aster growing in a crack in the sidewalk he was Chair of the Department of Math- and remarked, “Bloom where you are ematics from 1976 to 1981. Murray planted.” His MMM (My Mathematical Klamkin is best known for editing the Museum) contained a nickel that Problems columns of many journals: Einstein had owned and a pencil Oswald SIAM Review, the Pi Mu Epsilon Journal, Veblen had probably dropped, among School Science and Mathematics Journal, hundreds of other interesting curiosities. Crux Mathematicorum, the American Mathematical Monthly, Mathematics Eves was a strong spokesman for the Magazine, and most recently, Math Ho- MAA and a founder of its Northeast Sec- rizons. Klamkin is one of the three great- tion, which made him the first recipient, est contributors to the SIAM Review in 1980, of its Howard Eves Award for Problems and Solutions Section. Murray service to the Section and the Associa- also served the MAA as a visiting lecturer, Howard W. Eves, well known author tion. More importantly, he was a great a committee member, and on the Board and longtime professor at the University humanitarian. Quietly and without fan- of Governors, of Maine, died June 6, 2004, after a long fare or expectation of reward, he helped illness. He was 93. many people in need, going far beyond Not surprisingly, he was also on the the call of duty. His honorary degree Putnam Competition Committee, and Eves received his Ph.D. in mathematics from the University of Maine was there- was instrumental in starting the USA from Oregon State University. He en- fore a Doctorate of Humane Letters. His Mathematical Olympiad. The standards joyed a long and distinguished career as comment on that degree was equally he set as the Chair of the USAMO Com- a teacher, geometer, writer, editor, and modest: “They must have seen me pat- mittee from 1972–1985 and the Coach historian of mathematics. He served as ting a dog.” of the USA Team at the International associate editor for several journals. His Mathematical Olympiads from 1975– many awards included a Distinguished Murray Klamkin, 1921–2004 1984 were significant to the continued Teaching Award from the State of Maine, By Steven R. Dunbar success of the program. Under his lead- honorary doctorates from the University ership, the USA team delightfully sur- of Maine and McDaniel College, and the prised the mathematics community by George Pólya Award for mathematical doing well despite having to compete writing. Eves spent most of his career at against countries that had been partici- the University of Maine at Orono and at pating in the IMO since its beginning in Machias, and more recently at Central 1959. In Steve Olson’s recent book Count Florida University. For 25 years he ed- Down, Klamkin is quoted as saying “A lot ited the Elementary Problems section of of people were dead set against it, they the American Mathematical Monthly. He thought a US team would be crushed ...” was a member of the MAA since 1942. In the 2001 IMO in Washington DC, he returned as an Honorary Member of the Eves was the author of numerous math- Problem Selections Committee and a ematics articles and books, including In- guest lecturer at the summer training troduction to the History of Mathematics, program for the USA team. one of the most widely used texts in the Murray Klamkin, prolific mathemati- subject. His six volume Mathematical cal problem poser and solver, professor Mathematicians and students of math- Circles series, collecting humorous and of mathematics, and member of the ematics will long appreciate his creation interesting anecdotes about mathemati- MAA since 1948, passed away on August of brilliant problems and lucid solutions cians, was recently reprinted by the MAA, 6, 2004 at the age of 83. Murray Klamkin and the standards that he set. “The best who also published his two volumes of received a B. Ch. E. from the Cooper problems,” he said, “are elegant in state- Great Moments in the History of Math- School of Engineering in 1942, then ment, elegant in result, and elegant in ematics and in 2001 his Mathematical spent 4 years in the U.S. Army. After re- solution. Such problems are not easy to Reminiscences. In 1997 Dover reprinted ceiving an M.S. in Physics at the Poly- come by.” Murray found them consis- his Foundations and Fundamental Con- technic Institute of Brooklyn in 1947, he tently and shared them generously throughout his long and fruitful career. 32 November 2004 FOCUS
James E. White 1946–2004 teachers and students from around the models the physics of rockets, an activ- By Dan Kalman world, bear witness to his successful re- ity that puts students in the driver’s seat alization of this vision. of a space shuttle to achieve orbit, a beau- tifully rendered three dimensional ver- White had a long and active involvement sion of tic-tac-toe, and a physically and with the Mathematical Association of geometrically accurate simulation of America. He was co-director of the pocket billiards. Most impressive of all, MAA’s Interactive Mathematical Text perhaps, is his multimedia survey of Project, which introduced dozens of gravitation, in which the user navigates mathematicians to the development and a Myst-like virtual world, while retrac- use of interactive instructional computer ing the mathematical and physical evo- activities. He was also Principal Investi- lution of our understanding of gravity. gator for another MAA project, the Web And this is just a small sample. He re- Educators Library Collection of Math- cently completed a calculus textbook, ematical Explorations (WELCOME). integrating both traditional text lectures James E. White, founder and director of This project combined three areas of and interactive explorations. the Mathwright Library at http:// MAA concern: educational technology, www.mathwright.com, as well as princi- professional development, and increas- Those who knew him well recognized pal creative force behind the Mathwright ing access to mathematics for under-rep- both a powerful intellect and a gentle and software family, died suddenly and un- resented groups. The project, which was generous spirit. There was poetry at the expectedly July 18, 2004. He was 58 years incorporated into the MAA’s SUMMA heart of his life and work, and he saw old, and is survived by his wife, Sally, four Program, worked to bring interactive poetry and beauty in mathematics. Who children, and two grandchildren. White computer activities to students of minor- else would choose Monet’s Water Lillies received his Ph.D. at Yale University un- ity serving institutions by offering pro- as the setting for an interactive explora- der William Massey in 1972 in Algebraic fessional development opportunities and tion of buoyancy and boat construction? Topology. He held permanent and visit- mentoring to the faculty of these insti- ing faculty positions at many institutions, tutions. His final project for the MAA, Through his software and internet li- including the University of California at completed shortly before his death, in- brary, James White inspired and influ- San Diego, Carleton College, Bates Col- volved incorporating materials from the enced mathematics students and educa- lege, Kenyon College, Spelman College, WELCOME project in the MAA’s tors from all over the world. He offered California State University Monterey Bay, MathDL digital library. generous encouragement to all who met and Stetson University. His non-aca- him, and carried on correspondence with demic experience included work at Jet James White had a life-long fascination a host of collaborators, followers, and Propulsion Laboratory. Most of his work with the world of ideas. He was first a students. His memory will continue to on the Mathwright project was done dur- mathematician, with several books and inspire all who knew him. His energy, ing his tenure at the Institute for Aca- scholarly papers to his credit. He was enthusiasm, creativity, and originality demic Technology at the University of widely read in mathematics, philosophy, will be sadly missed. An invited paper North Carolina Chapel Hill. and physics, studied differential geom- session in his honor will take place at the etry and its applications to relativity, and January Joint Mathematics Meetings in White will best be remembered in the had a particular interest in foundational Atlanta. The title of the session is Worlds mathematics education community for issues in quantum mechanics. At the time of Interactive Mathematics: The Legacy of his vision, creativity, and leadership in of his death, he was deeply immersed in James E. White. See http://www.ams.org/ the applications of technology. He rec- research in these areas, and had recently amsmtgs/2091_maainvited.html for more ognized early that computers offer a completed a paper presenting an inno- information on this session. unique and powerful tool to inspire, cap- vative new link between the geometric tivate, and entrance students, and for 30 ideas of ancient Greece and the modern years devoted himself to innovative uses subject of special relativity. At the same Have You Moved? of computer technology. His philosophy time, he was fascinated by the issues of was that students will learn best when cognition and learning, and read widely The MAA makes it easy to change they ask and answer their own questions, in this area. your address. Please inform the and he understood that computer soft- MAA Service Center about your ware can create powerful environments White was also a prolific author of inter- change of address by using the elec- in which students are empowered to do active computer activities for students, tronic combined membership list at so. His dream and vision was to develop and for their teachers. The Mathwright MAA Online (www.maa.org) or call a tool with which teachers and students Library includes nearly a hundred of his (800) 331-1622, fax (301) 206-9789, could easily create these environments. contributions, displaying an amazing email: [email protected], or mail The hundreds of activities housed in the wealth of creative and inspiring lessons. to the MAA, PO Box 90973, Wash- Mathwright Library, created by scores of There is a lunar lander that accurately ington, DC 20090.
33 FOCUS November 2004 Wisconsin’s NPRIME Project
By Linda Thompson and Margaret Wilsman
The Networking Project for Improve- tations and discussion of current issues ment in Mathematics Education in the field. Materials such as selected (NPRIME) is currently in its sixth year Mathline videos, information concern- in Wisconsin. This highly successful ing NSF reform curricula, and the Wis- statewide project has used the Internet consin Department of Instruction’s Cur- and conferences to establish connections riculum Planning in Mathematics Guide between faculty involved in mathemat- have been distributed to those who at- ics education at the state’s colleges and tend or request these materials online. universities and PK-12 mathematics teachers. The Project has been funded In the past two years NPRIME has made by grants from the Eisenhower Profes- small grants available for colleges or uni- sional Development Program, the Wis- versities for Connection Projects. Eight consin Education Communications schools have received these grants for Marcia Weller Weinhold of Purdue Board, PBS Mathline, and the Wiscon- projects that involve some or all of: col- University presented the findings from sin ESEA Improving Teacher Quality lege faculty observations in PK-12 class- her dissertation. Program. A summary of five of rooms; PK-12 students’ work used as case NPRIME’s most successful programs fol- studies in college courses; PK-12 teach- lows. ers participation in college classrooms; preservice students connected online Through Student NPRIME, preservice with PK-12 mathematics teachers; col- teachers from 10 Wisconsin colleges and lege faculty connected online with PK- universities have had the opportunity 12 mathematics teachers; staff in high through an open forum to ask questions need school districts learning more online of master mathematics teachers about NPRIME and giving input into concerning the teaching and learning of future directions of NPRIME. mathematics. They are also encouraged to express their own views on questions An exciting new initiative for the group and concerns raised by other students. in the coming year will be NPRIME’s Over 250 students have participated to participation in the Institutions of date. Linda Uselmann of Edgewood College. Higher Education (IHE) Network of the Milwaukee Mathematics Partnership, a The NPRIME Online Learning Commu- National Science Foundation sponsored nity has brought some 50 mathematics award of $20 million over 5 years target- educators from state colleges and univer- ing the improvement of student learn- sities online for discussions on such top- ing in mathematics. While the award is ics as Wisconsin’s new performance- housed at University of Wisconsin–Mil- based licensing, the NCTM 2000 Prin- waukee, the Milwaukee Public Schools, ciples and Standards for School Math- and Milwaukee Area Technical College, ematics, mathematics education research, the IHE Network has been established to NSF Reform Curricula, and implications share knowledge among those institu- of the TIMSS study. tions of higher education in Southeast Wisconsin most likely to educate future Two Book Talks have been organized teachers of the Milwaukee Public online over the past couple of years. Schools. This connection with NPRIME During the summer of 2002 participants will enable this effort to engage faculty discussed Liping Ma’s Knowing and from throughout the state. The work will Teaching Elementary Mathematics. Dur- Participants explored the use of be centered on research efforts targeting ing the fall of 2003 an online discussion calculators in teaching mathematics. teacher learning through multiple mea- of the National Research Council’s Add- sures and will be based on national re- ing It Up: Helping Children Learn Math- In each year of the project two or three search and professional recommenda- ematics was facilitated by Linda Face-to-Face Meetings have been held at tions highlighted in The Mathematical Uselmann of Edgewood College. different college and university sites. Education of Teachers (CBMS, 2001) and These conferences have featured presen- Adding It Up (NRC, 2001a).
34 November 2004 FOCUS
EMPLOYMENT OPPORTUNITIES The Department may also have postdoctoral the department and for the university, and or visiting positions for the 2005-2006 aca- scholarship. Required: excellent communica- ALABAMA demic year (Ph.D. required). tion skills and a Ph.D. in math/statistics by the time of appointment. Preferred: teach- UNIVERSITY OF ALABAMA Further information about the full range of ing experience, potential for continued re- IN HUNTSVILLE the Department’s research and educational search, and ability to contribute to our newly Department of Mathematical Sciences activities may be found at http:// designed applied math program with tracks The Department of Mathematical Sciences www.math.arizona.edu. in actuarial science and statistics. Informa- at the University of Alabama in Huntsville tion about the position and the university can invites applications for a tenure track posi- Application review begins October 1, 2004 be found on the web at http:/ tion at the rank of assistant professor, begin- and continues as long as positions remain math.colstate.edu. Review of applications ning spring semester 2005 or fall semester unfilled. Applications received before Octo- begins November 329, 2004. As an AA/EEO 2005. In exceptional cases, more advanced ber 1, 2004 will receive the fullest consider- employer, CSU is committed to diversity and appointments may be considered. A Ph.D. ation; applications received after January 2, equality in education and employment. degree in mathematics or applied mathemat- 2005 are unlikely to be considered. ics is required. Applicants must have a strong GEORGIA COLLEGE commitment to teaching and show evidence Please send a letter of interest (specifying & STATE UNIVERSITY of excellent teaching ability. Applicants position(s) applied for), an AMS Cover Sheet The Mathematics/Computer Science Depart- should also show evidence of outstanding (which can be downloaded from http:// ment of Georgia College & State University research potential in an area that matches the www.ams.org/coversheet), a curriculum vi- invites applications for a tenure track Assis- interests of the department. Preference will tae with a list of publications, a statement of tant/Associate Professor position in math- be given to applicants whose research areas research interests, a statement of teaching ematics education. Employment would be- are probability/stochastic processes or nu- experiences/philosophy and a minimum of gin August 2005. For details see merical analysis. three (3) letters of recommendation (enclose www.gcsu.edu/facultyjobs. Application re- Applicants should send a curriculum vita or arrange to be sent) to: view begins December 8, 2004 and contin- with the AMS standard cover sheet, tran- ues until position is filled. GC&SU is an scripts, and three letters of recommendation Personnel Committee Equal Opportunity/Affirmative Action Em- (with at least one letter addressing teaching) Department of Mathematics ployer. INDIANA to University of Arizona P. O. BOX 210089 Chairman Tucson, Arizona 85721-0089 UNIVERSITY OF NOTRE DAME Department of Mathematical Sciences Department of Mathematics, University of University of Alabama in Huntsville The University of Arizona is an EEO/AA Notre Dame, Notre Dame, IN Huntsville, AL 35899. Employer-M/W/D/V 46556 Special Professional Faculty Positions For more information about the department, CALIFORNIA The Department of Mathematics of the Uni- visit our web site at: versity of Notre Dame invites applications for http://www.math.uah.edu. CALIFORNIA STATE POLYTECHNIC two Special Professional Faculty positions. UNIVERSITY, POMONA Candidates should have a doctorate in Math- To ensure full consideration, all materials The Mathematics Department invites appli- ematics or Mathematics Education, a passion should be received by November 1, 2004. Late cations for two tenure track positions, one for undergraduate teaching, and a record of applications will be reviewed until the posi- in Mathematics Education and one in Sta- excellence in the classroom. The starting date tion is closed. Women and minorities are tistics, both at the Assistant or Associate Pro- for these positions is August 22, 2005. Can- encouraged to apply. The University of Ala- fessor, beginning September 2005. To be con- didates at any rank will be considered. The bama in Huntsville is an Affirmative Action, sidered in the initial review, complete appli- teaching load can vary between two and three Equal Opportunity Institution. cations are due by 12/8/04 for Mathematics courses a semester, depending on class size Education and 1/20/05 for Statistics. The and other duties. These are not tenure track ARIZONA search continues until closed. For informa- positions, but they provide all usual faculty tion about qualifications or the application benefits, and have the possibility of being THE UNIVERSITY OF ARIZONA procedure, visit www.csupomona.edu/ renewed indefinitely. The salary is competi- Department of Mathematics ~math/position, or contact the Faculty tive. Applications, including a curriculum Tucson, AZ Search Committee, Mathematics Depart- vitae, a letter of application, and a completed The Department of Mathematics is seeking ment, Cal Poly Pomona, 3801 W. Temple Ave., AMS standard cover sheet, should be sent to: applications for tenure-track positions at ei- Pomona, CA 91768-4007; 909-869-4008; Fax: William G. Dwyer, Chair, at the above ad- ther the Assistant, Associate or Full Profes- 909-869-4904; [email protected]. AA/ dress. Applicants should arrange for at least sor level, which will begin in Fall 2005. By EEO. three letters of recommendation to be sent the time of appointment, candidates are ex- GEORGIA to the chair. These letters should document pected to have a Ph.D. and excellent research the applicant’s ability as a creative and effec- record or potential, as well as a strong com- COLUMBUS STATE UNIVERSITY tive teacher of undergraduate mathematics. mitment to teaching. Rank and salary de- The Mathematics Department at Columbus Notre Dame is an equal opportunity em- pend on the qualifications of the selected State University invites applications for a ten- ployer. Women and minorities are urged to candidate(s). ure track position beginning August 2005. apply. The evaluation of candidates will be- Responsibilities include teaching four courses gin December 1, 2004. Information about the per semester, academic advising, service for department is available at http:// www.math.nd.edu/. 35 FOCUS November 2004
MARYLAND Williams College is a private, residential, Mathematics and Statistics, visit http:// highly selective liberal arts college with an www.williams.edu/Mathematics. GOUCHER COLLEGE undergraduate enrollment of approximately Assistant Professor 2,000 students. The teaching load is two NEW HAMPSHIRE Department of Mathematics courses per 12-week semester and a winter and Computer Science term course every other January. In addition DARTMOUTH COLLEGE A tenure track position is available at the as- to excellence in teaching, an active and suc- John Wesley Young sistant professor level for Fall 2005, pending cessful research program is expected. Research Instructorship final approval in October 2004. Ph.D. re- The John Wesley Young Instructorship is a quired in mathematics, with a specialization To apply, please send a vita and have three post-doctoral two-year appointment in- in the fields of applied mathematics or prob- letters of recommendation on teaching and tended for promising Ph.D. graduates with ability preferred. Additional requirements: research sent to the Hiring Committee, De- strong interests in both research and teach- a commitment to excellence in teaching; the partment of Mathematics and Statistics, Wil- ing and whose research interests overlap a ability to teach a wide variety of courses and liams College, Williamstown, MA 01267. department member’s. Current research ar- conduct a research program; a commitment Teaching and research statements are also eas include applied mathematics, combina- to fostering research by undergraduates. The welcome. Evaluations of applications will torics, geometry, logic, non-commutative position also includes opportunities to de- begin on or after November 15 and will con- geometry, number theory, operator algebras, velop courses for the college’s first year pro- tinue until the position is filled. Williams probability, set theory and topology. Instruc- gram and courses with interdisciplinary and College is dedicated to providing a welcom- tors teach four ten-week courses distributed international emphases. Preference will be ing intellectual environment for all of its fac- over three terms, though one of these terms given to qualified candidates who are inter- ulty, staff and students; as an EEO/AA em- in residence may be free of teaching. The as- ested in participating in such programs. The ployer, Williams especially encourages appli- signments normally include introductory, ability to teach introductory level computer cations from women and minorities. For advanced undergraduate, and graduate science courses is a plus. Deadline for appli- more information on the Department of courses. Instructors usually teach at least one cations: January 7, 2005. Informal interviews Mathematics and Statistics, visit http:// course in their own specialty. This appoint- will be conducted at the AMS/MAA meet- www.williams.edu/Mathematics. ment is for 26 months with a monthly salary ings in January. Submit vitae, transcripts of of $4,350.00, and is not renewable. Salary in- graduate work, three letters of recommenda- WILLIAMS COLLEGE cludes two-month research stipend for In- tion (two of which must address teaching The Williams College Department of Math- structors in residence during two of the three experience or potential), and a personal state- ematics and Statistics invites applications for summer months in 2006 and 2007. To be eli- ment describing your interest in teaching at one tenure track position in statistics, begin- gible for a 2005-2007 Instructorship, candi- a small liberal arts college and also briefly ning fall 2005, at the rank of assistant pro- date must be able to complete all require- describing your research to: Human Re- fessor (in an exceptional case, a more ad- ments for the Ph.D. degree before Septem- sources, Goucher College, 1021 Dulaney Val- vanced appointment may be considered). We ber, 2005. Applications may be obtained at ley Road, Baltimore, MD 21204. Goucher are seeking a highly qualified candidate who http://www.math.dartmouth.edu/recruiting/ College is an Equal Opportunity Employer. has demonstrated excellence in teaching and . Or, submit a letter of application, curricu- research, and who will have a Ph.D. by the lum vitae, graduate school transcript, thesis U.S. NAVAL ACADEMY time of appointment. abstract, statement of research plans and in- The USNA Mathematics Department antici- terests, and at least three, preferably four, let- pates at least one tenure-track position (sub- Williams College is a private, residential, ters of recommendation to Donna Black, ject to approval and funding) at the Assis- highly selective liberal arts college with an Department of Mathematics, Dartmouth tant Professor level to start in August 2005. undergraduate enrollment of approximately College, 6188 Bradley Hall, Hanover, New See web site http://www.usna.edu/ 2,000 students. The teaching load is two Hampshire 03755-3551. At least one referee MathDept/website/Hire.htm for full infor- courses per 12-week semester and a winter should comment on applicant’s teaching abil- mation. Tel: 410-293-6701; Fax: 410-293- term course every other January. In addition ity; at least two referees should write about 4883; Email: [email protected] . The United to excellence in teaching, an active and suc- applicant’s research ability. Applications re- States Naval Academy is an Affirmative Ac- cessful research program is expected. ceived by January 5, 2005 receive first con- tion/Equal Employment Opportunity Em- sideration; applications will be accepted un- ployer and provides reasonable accommoda- To apply, please send a vita and have three til position is filled. Dartmouth College is tions to applicants with disabilities. letters of recommendation on teaching and committed to diversity and strongly encour- research sent to the Hiring Committee, De- ages applications from women and minori- MASSACHUSETTS partment of Mathematics and Statistics, Wil- ties. liams College, Williamstown, MA 01267. WILLIAMS COLLEGE Teaching and research statements are also DARTMOUTH COLLEGE The Williams College Department of Math- welcome. Evaluations of applications will The Department of Mathematics anticipates ematics and Statistics invites applications for begin on or after November 15 and will con- a tenure-track opening with initial appoint- one tenure track position in mathematics, be- tinue until the position is filled. Williams ment in the 2005-2006 academic year. The ginning fall 2005, at the rank of assistant pro- College is dedicated to providing a welcom- position is for an applied mathematician at fessor (in an exceptional case, a more ad- ing intellectual environment for all of its fac- the rank of Assistant Professor. In extraordi- vanced appointment may be considered). We ulty, staff and students; as an EEO/AA em- nary cases, an appointment at a higher rank are seeking a highly qualified candidate who ployer, Williams especially encourages appli- is possible. Successful candidate should have has demonstrated excellence in teaching and cations from women and minorities. For demonstrated ability to work across disci- research, and who will have a Ph.D. by the more information on the Department of plines; particularly, it is expected that he or time of appointment. she seek out and strike up collaborations
36 November 2004 FOCUS across campus with departments such as bi- To create an atmosphere supportive of re- Review of applications will begin November ology, physics, computer science; he/she search, Dartmouth offers new faculty mem- 15, 2004 and continue until the position is should also aggressively seek funding in his/ bers grants for research-related expenses, a filled. Send letter of application, vita, tran- her area of research. Current applied inter- quarter of sabbatical leave for each three aca- scripts, and 3 letters of recommendation (at ests include (but not limited to) imaging, sig- demic years in residence and flexible sched- least one addressing teaching potential or nal processing, computational number uling of teaching responsibilities. The teach- ability) to: Dr. Robin Sue Sanders, Chair, theory, statistical physics, stochastic pro- ing responsibility in mathematics is three Mathematics Dept., Buffalo State College, cesses, quantum computing and computa- courses spread over three of four ten-week Bishop 317, 1300 Elmwood Ave., Buffalo, NY tional biology and are receiving funding from terms. 14222-1095. For more information about the various sources including NSF and NIH. college, visit www.buffalostate.edu. Candidates for the position must be commit- To apply for the position, applications may ted to outstanding teaching and interaction be obtained at the math department website: Buffalo State is the largest four-year compre- with students at all levels of undergraduate http://www.math.dartmouth.edu/recruiting/ hensive college in the State University of New and graduate study. . Or, send a letter of application, curriculum York (SUNY) system. The campus is located vitae, and a brief statement of research re- in the museum district of Buffalo, the sec- To create an atmosphere supportive of re- sults and interests, and arrange for four let- ond largest city in New York State. The area search, Dartmouth offers new faculty mem- ters of reference, at least one of which spe- offers a variety of cultural and recreational bers grants for research-related expenses, a cifically addresses teaching, to be sent to activities. quarter of sabbatical leave for each three aca- Donna Black, Recruiting Secretary, Depart- demic years in residence and flexible sched- ment of Mathematics, Dartmouth College, Buffalo State is an affirmative action/equal uling of teaching responsibilities. The teach- 6188 Bradley Hall, Hanover, New Hampshire opportunity employer. ing responsibility in mathematics is three 03755-3551. Applications received by De- courses spread over three of four ten-week cember 15, 2004 will receive first consider- NAZARETH COLLEGE terms. ation. Tenure-track position in mathematics, begin- ning Fall 2005. Ph.D. in mathematical sci- To apply for the position, applications may Dartmouth College is committed to diversity ences, demonstrated teaching excellence, be obtained at the math department website: and strongly encourages applications from commitment to innovative teaching in a col- http://www.math.dartmouth.edu/recruiting/ women and minorities. Inquiries about the laborative environment, and use of technol- . Or, send a letter of application, curriculum progress of the selection process may be di- ogy in teaching required. Responsibilities in- vitae, and a brief statement of research re- rected to Dan Rockmore, Recruiting Chair. clude: 4 courses per semester (majors and sults and interests, and arrange for four let- non-majors), scholarship and service. Pref- ters of reference, at least one of which spe- NEW YORK erence will be given to qualified candidates cifically addresses teaching, to be sent to with an interest in teaching applied math- Donna Black, Recruiting Secretary, Depart- ematics, in particular, statistics, mathemat- ment of Mathematics, Dartmouth College, BUFFALO STATE COLLEGE Mathematics ics education, and/or directing student re- 6188 Bradley Hall, Hanover, New Hampshire search. 03755-3551. Applications received by De- Assistant/Associate Professor Buffalo State will receive applications for a cember 15, 2004 will receive first consider- Nazareth College, a thriving, independent, ation. tenure-track assistant/associate professor, Mathematics Department, to begin spring or co-educational, liberal arts college with 2000 fall 2005 semester. Salary is competitive. undergraduates and 1200 graduate students, Dartmouth College is committed to diversity is minutes from downtown Rochester, noted and strongly encourages applications from for its internationally recognized industries women and minorities. Inquiries about the Responsibilities: Effectively teach variety of undergraduate and graduate courses in and museums, and for its cultural diversity. progress of the selection process may be di- Nazareth College seeks individuals with an rected to Dan Rockmore, Recruiting Chair. mathematics and applied mathematics; grow professionally through scholarly activities; understanding of the benefits and impor- tance of ethnic and racial diversity on cam- DARTMOUTH COLLEGE participate in department and college com- mittee work; advise students. Provide lead- pus and demonstrated commitment to the The Department of Mathematics anticipates promotion of such diversity. a tenure-track opening with initial appoint- ership in developing new concentration in applied mathematics. Teaching load 9 hours/ Send letter of application, philosophy of ment in the 2005-2006 academic year. In ex- teaching, curriculum vitae, transcripts, and traordinary cases, an appointment at a higher semester. Successful graduate must have genuine interest in teaching undergraduates. three letters of reference at least two of which rank is possible. Preference given to candi- address teaching history/potential to: Profes- dates working in either set theory/logic or sor Susan Riegle, Search Committee, areas of algebra with connections to existing Required Qualifications: Ph.D. in applied mathematics or mathematics with concen- Nazareth College, 4245 East Avenue, Roch- research interests in the department includ- ester, NY 14618. E-mail: [email protected]. ing computational algebra, algebraic and tration in applied field; potential for schol- arithmetic geometry, representation theory, arly activity; effective teaching; strong com- munication skills; knowledge of computer See: http://www.naz.edu/dept/hr/postings/ coding theory and algebraic combinatorics. faculty.html EOE/AA. Candidates for the position must also be algebra systems and/or graphing calculators. committed to outstanding teaching and in- OHIO Preferred Qualifications: Operations research, teraction with students at all levels of under- BALDWIN-WALLACE COLLEGE graduate and graduate study. modeling, computational mathematics, ap- plied statistics, actualrial science, biomedi- Mathematics and Computer Science Depart- cal mathematics, or other applications to ment, Tenure-track Assistant Professor, be- natural sciences. ginning August 2005. Teaching introductory mathematics courses for education majors. 37 FOCUS November 2004
Qualifications include a Ph.D. in Mathemat- Mathematics, Clarion University, Clarion, PA regional mathematics teachers. Qualifica- ics Education with master’s level work in 16214 or e-mail to [email protected]. tions and requirements: Doctorate in Math- mathematics and K-12 teaching experience. Applications completed by December 10, ematics or Mathematics Education (ABD Candidates with a Ph.D. in Mathematics or 2004 will receive full consideration. Clarion upon hire may be considered). A terminal those who have entered a Ph.D. program in University is an EOE Empolyer. degree from an accredited institution is re- Mathematics Education will be considered. quired for tenure. The position requires ex- B-W is an equal opportunity employer, com- INDIANA UNIVERSITY cellence in teaching, as well as experience or mitted to a diverse faculty, staff and student OF PENNSYLVANIA potential in research and academic service. body. For position information and appli- Mathematics Faculty Positions A demonstration of teaching effectiveness cation instructions, see www.bw.edu/re- Indiana University of Pennsylvania’s Math- will be required as part of the interview. Can- sources/hr/jobs. ematics Department invites applications for didates will be judged on potential for teach- tenure track faculty positions in Mathemat- ing, research and university service. Prefer- THE OHIO STATE UNIVERSITY ics, Statistics, and Research in undergradu- ence will be given to candidates with two AT NEWARK ate mathematics education to begin in fall of years of K 12 teaching experience or the Assistant Professor of Mathematics 2005. A Ph. D. in the appropriate field is re- equivalent in knowledge and experience. All (Two Positions) quired. Review of applications begins De- candidates must furnish proof of eligibility The Ohio State University at Newark seeks cember 1, 2004 and continues until positions to work in the U.S. upon appointment. to fill two positions in mathematics at the are filled or closed. All applicants must be Shippensburg University is an Equal Oppor- level of assistant professor. Applicants should work eligible. For job descriptions, require- tunity Employer. Review of applications be- possess a Ph.D in Mathmatics, excellent ments, and application procedures, log on to gins November 15, 2004, and will continue teaching documentation and an active re- http://www.math.iup.edu/jobs, e-mail until the position is filled. Applicants must search program. Duties include an annual [email protected] or call 724-357-2608. send a letter of application, current curricu- teaching load of six courses on a quarterly Indiana University of Pennsylvania, a mem- lum vitae, official undergraduate and gradu- system and service to the department and ber of the State System of Higher Education, ate transcripts, three letters of recommenda- campus. Preference will be given to those is an equal opportunity employer M/F/H/V. tion, and copies of course outlines: Search applicants with a research area compatible Committee, Department of Mathematics, with current OSUN math faculty. These ar- MESSIAH COLLEGE 1871 Old Main Drive, Shippensburg Univer- eas include Algebraic Topology, Commuta- Mathematics - Tenure-Track sity, Shippensburg, PA 17257. At least one rec- tive Ring Theory, Differential Geometry and Faculty Position ommendation letter must address the Analysis. Applications are invited for a full time, term candidate’s teaching ability, and the letter of tenure-track position in the Mathematical application should address how the candi- OSUN is located 35 miles east of downtown Sciences Department to begin August 2005. date will contribute to this department. In- Columbus on a lovely campus in the scenic The position requires a doctorate in Math- complete applications and applications sent rolling hills of central Ohio. It enjoys close ematics and a commitment to teaching a full by e mail will not be considered. For addi- ties with the Columbus campus and area. range of undergraduate courses in a Chris- tional information see http://www.ship.edu/ OSUN faculty members have their primary tian College environment. ~math. Contact: Pamela A. McLaughlin, E teaching responsibilities in Newark but are Mail: [email protected], Phone: 717-477- regular faculty members of their respective For more information on Messiah College 1431, Fax: 717-477 4009 departments in Columbus. Instruction takes and the Department visit: www.messiah.edu/ place in small classes which facilitates care- acdept/depthome/mathsci/home.htm TEXAS ful attention to student needs. Send letters of interest, a statement of teach- TEXAS LUTHERAN UNIVERSITY To apply please send a cover letter, detailed ing philosophy, and a résumé to: Department of Mathematics invites applica- CV and three letters of reference to The Ohio tions for a tenure-track assistant professor- State University Newark, 1179 University J. Barry DeRoos, Chair ship beginning August 2005. Requirements Drive, Newark, OH 43055. The Ohio State Messiah College include Ph.D. in mathematics by appoint- University is a regional campus of The Ohio Department of Mathematical Sciences ment date, ability to teach a wide range of State University. To build a diverse workforce PO Box 3041 introductory and advanced undergraduate Ohio State University encourages applica- One College Avenue courses, and a commitment to mentor stu- tions from individuals with disabilities, mi- Grantham, PA 17027 dents in an undergraduate research program. norities, veterans, and women. “EEO/AA EOE Submit letter of application, cv, statement of employer”. teaching philosophy, and five references SHIPPENSBURG UNIVERSITY (names, addresses including email, tele- PENNSYLVANIA Mathematics Department phone) to: Dean John T. Sieben - College of The Mathematics Department seeks candi- Natural Science and Mathematics, Texas CLARION UNIVERSITY dates having a primary interest in mathemat- Lutheran University, 1000 W. Court St., Tenure track Assistant Professor of Math- ics teacher preparation. Responsibilities: Seguin, TX 78155; fax (830) 372-6095, phone ematics beginning August 2005. We seek an Teaching undergraduate mathematics educa- (830) 372-6007, e-mail [email protected]. outstanding teacher, who is an active scholar tion or mathematics courses, advising stu- mailto:[email protected]. Review of applica- and an excellent colleague. Doctorate in dents, supervising student teachers, conduct- tions begin November 8 and continue until mathematics or a related field preferred: ABD ing research, and contributing to the aca- the position is filled. Texas Lutheran Univer- considered. For complete details see our web demic climate of the department through sity is an equal opportunity employer and page: http://math.clarion.edu. Send to Math- writing grants, reviewing the curriculum, encourages women and minorities to apply. ematics Search Committee, Department of serving on committees, and interacting with Full position description is available at www.tlu.edu http://www.tlu.edu. 38 November 2004 FOCUS
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