A Review of The Art of Mathematics: Coffee Time in Memphis by Béla Bollobás. xvi + 359 pp. Cambridge University Press, 2006. BY JAMES PROPP Here is one of my favorites: This proof exhibits economy Thanks For the Suppose 10 chairs are arranged (the chief idea is contained in Tangents he mathematician Tangents in a circle, half of them occupied the five-word hint), surprise Contributions! News from the Department of Mathematical Sciences Fall 2007 T and puzzle-connois- University of Massachusetts Lowell seur Peter Winkler by students. Show that there (who would think to bring ran- once joked, with a exists some whole number n domness and probability into Our thanks to all who have nod to Isaac Newton, between 1 and 9 such that if solving a problem like this?) contributed to the Department “If I have seen far- each of the 5 students moves n and fecundity (the probabilistic of Mathematical Sciences over ther than others, it is because chairs clockwise in the circle, or method has been an enormously the past few years. Your more of them will end up sitting powerful tool in the hands of I have stood on the shoulders generosity has allowed us in a previously occupied chair. Erdös and others). Bollobás’s 2007 Alumni-Awards Banquet A review of of Hungarians.” One of these to make purchases, award Hungarians is the late Paul This is not how Bollobás book is full of tasty little morsels scholarships, and engage in Next Banquet set for April 25, 2008 God Created Erdös, famous within mathemat- actually poses the problem in his like this one, puzzles whose ics for his contributions to num- book; in problem 3 (in a series solution requires attacking them activities that would otherwise the Integers of 157 problems), he asks the from some unexpected angle. have been impossible. he 2007 Alumni- _Stephen ber theory and combinatorics Awards Banquet at Giardini and famed more broadly for his reader to consider a more gener- The ability to come up with Many of you have T the Brewery by Stephen Hawking, 2005, unique lifestyle and lingo (chil- al situation. But the key idea that creative approaches to problems responded generously to • Shapiro Scholar 1162 pages, $29.95 Exchange on April dren are “epsilons,” God is the solves Bollobás’ problem can be can be cultivated, but it cannot UML phonathon and other (outstanding discovered by thinking about the be taught; it is more of an art 20 was well attend- math major):_ “Supreme Fascist”, God’s collec- fundraising contacts. These special case I’ve described—and than a craft. Hence the first half ed by the college Jennifer Cole BY GUNTRAM MUELLER tion of the best mathematical requests can benefit the proofs is “The Book”, and so by following the clue that of the book’s title. dean, current and emeritus * Outstanding o you mean that Department of Mathematical forth). Many of Erdös’ collabora- Bollobás helpfully provides in a I prefer Bollobás’s original faculty, adjuncts and stu- Graduate D Stephen Hawking? tors and successors are also separate section devoted to title, Coffee Time in Memphis Sciences directly if you specify dents. Some forty people Student:_Drew Yes, that Stephen Hungarian, and others have hints. (If you want to think (which his editor convinced him that you wish to have your in all came to wine, dine Lazar Hawking! What about this problem on your to lengthen); it bears more of the adopted what might be called gift directed to Mathematics. and congratulate our 2007 This year was business is it of a own, now would be a good time stamp of Bollobás’s personal Prof. Tom Kudzma and Stephen Giardini. “the Hungarian style,” with an Otherwise it will provide scholarship winners, each the first time the physicist to edit a to put aside this book review!) style. This is a book that emphasis on snappy problems valuable assistance to the of whom was given a book Shapiro Scholarship was and once again our team per- book of mathematics, select- and clever solutions. I can think Bollobás’s clue is a short ques- developed in the author’s mind prize and certificate in formed extremely well, earn- ing at his personal whim tion that at first seems like a non through the course of conversa- University at the College level. awarded and we are very of no better way to get acquaint- addition to any stipend. ing a Meritorious ranking what he considers to be the sequitur: “What about a random tions with students and col- grateful to Bernie and Yana ed with these people and their The awardees were Shapiro for their dedication which put them in the top brightest jewels of mathemat- work than to spend a few rotation?” leagues, sometimes in offices or to the department and gener- 15% of the 800 or so partici- ical thought through these months periodically dipping into If we choose n randomly, classrooms but just as often in • Arthur S. Zamankos then each student has a 4-out- departmental lounges or cafes. ous support of our students. pants worldwide. A copy of last 2500 years? The nerve! Béla Bollobás’s new collection of Scholarship (for outstand- of-9 chance of ending up in a Mathematicians love to find Thank you both. this year’s problems and other The gall! Where’s the griev- mathematical puzzles, titled The ing juniors and information can be found at ance committee? Well for Art of Mathematics: Coffee Time previously occupied chair. So on elegant solutions to their The Department of seniors):_Alan Bartlett, http://www.comap.com and one thing, he is the Lucasian in Memphis. average, the number of students research problems, but they can’t Mathematical Sciences Keith McElroy, Michael their final report is at Professor of Mathematics at Bollobás (the name is pro- sitting in previously occupied always be sure that the chal- entered a team in the Williams, Michelle Polys Cambridge, Newton’s old gig, nounced “bowl o’ bosh”) is one chairs will be 4/9 + 4/9 + 4/9 + lenges they set for themselves Mathematical Competition in http://faculty.uml.edu/ of the most ardent keepers of the 4/9 + 4/9, or 20/9, which is have sweet answers. It can be a • The Richardson Bedell Modeling hosted by the jgrahameagle/mcm2007.doc. and for another, he did just Erdös flame. Since Erdös died - slightly greater than 2. Now great relief from these uncertain- Scholarship (for outstand- Consortium for Mathematics A book prize was awarded to an absolutely excellent job of or, as Erdös would say, “left”—in comes the punch line: The only ties to work on a problem secure ing juniors and and its Applications. The the three team members it. Did his interest in physics 1996, Bollobás has organized a way the average value of an inte- in the knowledge that it has a seniors):_Ryan Beaven department has a strong tra- 2007 class valedictorian color his choice of pieces to conference in his honor every ger-valued quantity can exceed 2 pleasing solution, which the • The Mary Hall Prize (for dition in this competition Chris Evans, Jason Percival include? Well, the selection year at the University of is if it sometimes is 3 or greater. Continued on page 3 the outstanding freshman): stretching back over a decade and Michael Williams. is very strong in analysis, Memphis. (Full disclosure: I Congratulations to the team weak in algebra except for spoke at the 2006 conference.) members and their coach, Gauss, nonexistent in topolo- Bollobás, a professor who Tangents Non-Profit Org Kiwi. gy, but it includes some divides his time between Trinity Department of Mathematical Sciences U.S. Postage The Alumni-Awards 20th century foundations University of Massachusetts Lowell PAID College (Cambridge) and the Olney Hall Lowell, MA Banquet is an annual event and logic. University of Memphis, has UML North Permit No. 69 and we would be delighted Each of these pieces or worked for decades in functional Lowell, MA 01854 to see more people there. excerpts is preceded by an analysis, combinatorics and If you have not been interesting biographical graph theory. In the course of informed of this event in sketch and several pages of years of teaching and research, the past then please contact mathematical mis-en-scene, he has devised (or learned of) Prof Ken Levasseur explaining the context and many easily stated problems ([email protected]) the main results of that par- whose solutions possess one or to make sure you are on our ticular entry. Let’s face it: more of the hallmarks that mailing list. Continued on page 3 mathematicians prize, such as Drew Lazar and Prof. Charlie Byrne. economy, surprise and fecundity. Fall 2007 ➝ Tangents What Are You Up To? Steve’s Want to keep your classmates up to date on what you’re doing and where you are? Take a few moments to tell us Continued from back page Continued from page 1 ? Fall 2007—From the Chair where you are, and whatever else you might like to share. We’ll add it to the UML Math Alumni page, A review of God Created the Integers http://www.uml.edu/dept/math/alumni.htm. A Review of The Art of Mathematics: Editorial Note: Although we are happy that Steve Pennell has agreed to We can be contacted by mail at Department of Coffee Time in Memphis reading all these introduc- What holds the planets in Mathematical Sciences, North Campus, UMass Lowell, serve as chair, his name doesn’t lend it to as catchy a column title as problem-poser will, if pressed, Who are the right readers tions provides an excellent place? Does God do it? “Kiwi’s Korner.” We’ve wrestled with ideas for Steve’s but have decided to Lowell MA 01854.