0$$)2&86 NEWSMAGAZINE OF THE MATHEMATICAL ASSOCIATION OF AMERICA, VOL. 35, NO. 3, JUNE/JULY 2015
National Math Festival MIT Wins Putnam Call for Papers at JMM MAA National Positions Filled
0$$)2&86is published by the he MAA Officers Election ended on May 4. The officers elected are Mathematical Association of America in as follows: February/March, April/May, June/July, T August/September, October/November, and December/January. Advertising inquiries: [email protected] MAA FOCUS Staff Director of Publications: Jim Angelo Editor: Ivars Peterson, [email protected] Managing Editor & Art Director: Lois M. Baron, [email protected] Staff Writer: Alexandra Branscombe President-Elect First Vice President Second Vice President Deanna Matt Boelkins Tim Chartier MAA Officers President: Francis Edward Su Haunsperger Grand Valley State Davidson College Past President: Robert L. Devaney Carleton College University First Vice President: Jenna Carpenter Second Vice President: Karen Saxe Two new members of the nominating committee were elected: Secretary: Barbara T. Faires Treasurer: Jim Daniel Chair, Council on Publications and Communications: Jennifer J. Quinn Executive Director Michael Pearson MAA FOCUS Editorial Board Donald J. Albers, Janet L. Beery, David M. Bressoud, Susan J. Colley, Brie Finegold, Joseph A. Gallian, Jacqueline B. Giles, Fernando Q. Gouvêa, Rick Cleary Susan Jane Colley Jacqueline A. Jensen, Colm Mulcahy, Adriana J. Babson College Oberlin College Salerno, Amy Shell-Gellasch, Francis E. Su, Laura Taalman, Gerard A. Venema All terms begin February 1, 2016. The MAA congratulates the new Letters to the editor should be addressed to officers and thanks all who participated in the election. Ivars Peterson, Mathematical Association of America, 1529 18th Street, NW, Washington, DC 20036, or by email to [email protected]. Subscription and membership questions Falconer Lecturer: Nominations should be directed to the MAA Customer Service Center, 800-331-1622; email: he Association for Women in Mathematics and the Mathematical [email protected] 301-617-7800 (outside Association of America annually present the Etta Z. Falconer U.S. and Canada); fax: 301-206-9789. MAA T Headquarters: 202-387-5200. Lecture to honor women who have made distinguished contributions to the mathematical sciences or mathematics education. These one-hour Copyright © 2015 by the Mathematical expository lectures are presented at MAA MathFest each summer. Association of America (Incorporated). Nominations for the 2016 AWM-MAA Falconer Lecture are solicited Educational institutions may reproduce articles and will remain active for a total of two years (one year beyond the initial for their own use, but not for sale, provided the following citation is used: “Reprinted with nominations). The letter of nomination should include an outline of the permission of MAA FOCUS, the newsmagazine nominee’s distinguished contributions to the mathematical sciences or of the Mathematical Association of America.” mathematics education and address the nominee’s capability of delivering Periodicals postage paid at Washington, D.C., an expository lecture. The deadline for nominations is September 1. and additional mailing offices. Postmaster: Send Nomination materials for this award should be compiled into one PDF address changes to MAA FOCUS, Mathematical file and submitted online at0DWK3URJUDPVRUJ . The link to Association of America, P.O. Box 90973, MathPrograms will be available 45 days prior to deadline. Check Washington, DC 20090-0973. ISSN: 0731-2040 DZPPDWKRUJ for more details. (print). ISSN 2161-704X (online). Printed in the United States of America. 0$$)2&86 NEWSMAGAZINE OF THE MATHEMATICAL ASSOCIATION OF AMERICA v VOL. 35, NO. 3 v JUNE/JULY 2015
Features
National Math Festival Brings Math to the Mall . . . 4 Katharine Merow
To Friend or Not to Friend? Facebook for Professional Educators . . . 6 Dana C. Ernst, Matthew Leingang, and Ron Taylor
Supporting a Statistician in a Math Department . . . 8 SIGMAA Stat Ed
Distinguished Lecture: Bubbly Mathematics . . . 12 Katharine Merow
MAA Competitions Gets New Director . . . 20 Alexandra Branscombe
Interview: T. Christine Stevens . . . 22 Kenneth A. Ross 4 Call for MAA Papers at the 2016 Joint Mathematics Meetings in Seattle . . . 35
About the CoverDepartments News 18 President’s Message | 2 MAA National Positions Filled Francis Edward Su 2 Falconer Lecturer: Nominations To the Mathematical Beach 9 New SIGMAA on Undergraduate 26 Puzzle Page | Research Laura Taalman, Editor KenKen Variations 10 Tensor Foundation Grants Awarded by Robert Fuhrer to 27 Projects 28 Book Reviews | 15 Girls’ Team Places Second in European Olympiad Guided by Shanthi Math Books in the Kitchen Chandrasekar, National Math 31 MAA Books Beat | Steve Kennedy 17 MIT Wins, Sets Record at Putnam Festival attendees discovered Exploring the Heart of Calculus Competition the beautiful curved loops 33 Archives Spotlight | Carol Mead 32 Call for Nominations: Dolciani and geometric symmetry of Can You Identify These People? Award kolam, a South Indian style of SDLQWLQJXVLQJULFHpRXU Above right, a girl pulls a bubble at the festival’s 2REOHFN2O\PSLFV Photos: MSRI, National Math Festival 4
National Math Festival Brings Math to the Mall
By Katharine Merow
s he made his way to the National Mall in AWashington, D.C., on April 18, University of Maryland math professor Larry Washington worried. He worried about the weather, whether it was too nice. He worried about star power, the allure of Usher and Mary J. Blige. Would folks forsake the sunshine, he wondered, to hear a lecture about the Rubik’s cube in the subterranean depths of the Smithsonian’s Ripley Center? Could even a giant square-wheeled tricycle compete with Gwen Stefani and the other big-name artists performing in the free Earth Day concert across the Mall? Would anyone, in other words, come to the National Math Festival? Washington worried for naught. People came to the National Math Festival in droves. Official estimates put attendance upward of 10,000. Visitors young and old thronged the Smithsonian’s Enid A. Haupt Garden, the Ripley Center next door, the National Museums of Natural and American History across the lawn- turned-construction-site. They enjoyed mathematical balloon twisting, an exhibition of math-inspired art, lectures about Archimedes and Minecraft and fair lane assignment in BMX bicycle racing. Organized by the Mathematical Sciences Research Institute (MSRI) and the Institute for Advanced Study in cooperation with the Smithsonian Institution, the National Math Festival made good on its promise to “enliven the National Mall with dozens of interactive math experiences.” Ivars Peterson indicates a population distribution created by MAA at the National Math Festival the hands of people touching (and staining) a sharp corner at For its contribution to the festival, MAA coaxed its the National Gallery of Art’s East Building. onetime Director of Publications Ivars Peterson out of semi-retirement to lead a Math on the National Mall the two-foot smudge, tapered at both ends, represents tour. Decked out in several MAA monograms, Peterson all the passersby who have reached out and touched the walked grandmothers, schoolchildren, and teachers enticingly sharp corner. through the mathematical aspects of the monuments, Download Peterson’s “Field Guide to Math on the museums, and lawns at the heart of the nation’s capital. National Mall” at KWWS ELWO\,9'$.. He pointed out the wrench-proof pentagonal lug nuts on fire hydrants and the Möbius nature of the recycling Getting Students Involved symbol. He explained why his Twitter page (KWWSV The National Math Festival relied on an army of WZLWWHUFRPPDWKWRXULVW) features a photo of Kenneth volunteers to man tables inside the Ripley Center and Snelson’s Needle Tower. activity stations in the Smithsonian’s Haupt Garden, and Extending his arm to the lavender-pink marble, college students made up much of the labor force. Peterson pointed out that the discoloration on the The Society for Industrial and Applied Mathematics 19-degree corner of the National Gallery of Art’s East (SIAM) provided funding for more than 60 students
Building serves as a population distribution. He said that from eight universities to staff the 20 exhibits in the MEROW K.
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National Museum of Mathematics’s Math Midway at the Library of Congress to celebrate public and private (KWWS PDWKPLGZD\RUJ). support for basic scientific and mathematics research. Members of Eve Torrence’s Art of Mathematics class Then, on April 17, MSRI and the Children’s Book at Randolph-Macon College led activities sponsored by Council held a press conference to announce the the Bridges Organization’s MoSAIC outreach program inaugural winners of a new youth book prize, (PRVDLFPDWKDUWRUJPRVDLFSODQ . They helped visitors Mathical, that honors inspiring math-related fiction build icosahedrons and dodecahedrons decorated with and nonfiction for readers in grades pre-K through 12. The 2014 winners were Have You Seen My Dragon? by Steve Light, One Big Pair of Underwear by Laura Gehl, “The public day was bigger, Really Big Numbers by Richard Evan Schwartz, and more diverse, and had more Nearly Gone by Elle Cosimano. Read more at KWWS PDWKLFDOERRNVRUJ. excitement than I’d dreamed.” —David Eisenbud, MSRI Director More Festivals MSRI Director David Eisenbud said he could not be happier with how the first-of-its-kind festival played Persian patterns, construct the five Platonic solids from out. “The public day was bigger, more diverse, and had punch-out sheets, and make an origami octahedral more excitement than I’d dreamed,” he said. “The two skeleton. education events and the gala went off very smoothly. “The students were champs working with the public,” Given the success, we are just beginning to think about Torrence said. a repeat—possibly in 2017.” (The USA Science and Undergrads from Marymount University interacted Engineering Festival will come to D.C. in the off year, he with festival-goers, too, as they built a hyperbolic star explained.) out of Zometools in the Ripley Center concourse. In the meantime, those in need of a festival fix Marymount mathematics professor Alice Petillo sees can consider attending—or organizing—a Julia value in providing out-of-classroom opportunities for Robinson Mathematics Festival. Held throughout people to experience mathematics, and she is trying North America—in the Ripley Center in 2012 (KWWS to uncover the effect of the National Math Festival on ELWO\',(+\)—Julia Robinson Mathematics Marymount’s approximately 40 volunteers. She collected Festivals introduce kids young and old to the beauty pre- and postfestival reflection data and hopes to report of mathematics by presenting them with engaging, on her findings soon. thought-provoking problems. See a list of upcoming festivals at KWWS MUPIRUJUHJLVWHUSKS. For information Before the Fun and Games on hosting or sponsoring one, email LQIR#MUPIRUJ. However effective at deepening appreciation for the And, of course, there’s that other celebration of importance, beauty, or fun of mathematics, the day of mathematics coming to D.C. before summer’s end. Join public activities on the Mall was really the culmination MAA for its much-anticipated centennial celebration at of the National Math Festival. The meeting of minds in MAA MathFest 2015. fact began two days earlier. On April 16, a breakfast briefing on Capitol Hill Katharine Merow is a freelance writer working in brought together mathematicians, educators, Washington, D.C. and lawmakers—including Senators Harry Reid (D-Nevada), Chuck Schumer (D-New York), Al Franken 7KH1DWLRQDO0DWK)HVWLYDOZDVVSRQVRUHGE\WKHIROORZ (D-Minnesota), Patty Murray (D-Washington), and LQJ &DUQHJLH&RUSRUDWLRQRI1HZ
PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 6 7R)ULHQGRU1RWWR)ULHQG" Facebook for Professional Educators
By Dana C. Ernst, Matthew Leingang, and Ron Taylor
s educators we idealistically dream of students Open to all. At one extreme is a policy of maximum Awanting to interact with professors outside of class. openness: “Feel free to friend me on Facebook. I accept This seems to be one reason we are required to hold all friend requests from students.” office hours. But sometimes students want to interact It’s fun to see what your students are up to. You’ll find in nonacademic ways. With the rise of social media, some of your current students are friends with some of students are increasingly more interested in connecting your former students (keep that in mind as you consider with their professors on sites such as Facebook, recycling exam problems). You’ll learn which of your Google+, LinkedIn, Tumblr, and Twitter. students like to sing and who likes to race cars on the Facebook, in particular, has been a positive experience weekend. You might find out some things you wish you for all three of us authors. It has allowed us to be hadn’t known, but by and large learning more about in touch with each other and with other colleagues your students makes them easier to teach. far away. And in some cases we have developed relationships with students outside of class that have led to better interactions in class. For starters, find out if your Our aim here is to encourage faculty to think about school or department has a the ways in which they are comfortable interacting with policy regarding interaction with students outside of class. In particular, we are interested students on social media. in the question of whether to be Facebook “friends” with students. In this article we restrict our attention to Facebook, though much of what we say applies more broadly They will also find out more about you. Since you hold across social media. The main reason for this is that such enormous power over them, they may have trouble in our view Facebook provides a robust ecosystem for conceiving of you as a human being with your own interaction between several parties in more or less real family, hobbies, and interests. Seeing your life outside time. the classroom can help them identify with you. And you Additionally, although the use of FB among college can use your posts to evangelize about math every once students may be on the decline, it seems to be the most in a while. widely used of the various social media platforms. You can maintain some boundaries between you and The three of us agree that it is a bad idea to initiate your student Facebook friends using Facebook lists and friend requests to students. The power differential is too privacy settings, which we will describe below. great; the student may be uncomfortable accepting the request, but feel uneasy ignoring or rejecting it. Some Not while you’re my student. At the opposite extreme is students will inevitably see it as an intrusion into their a policy that goes something like: “I will not accept a private life. Plus, you would be showing favor toward the Facebook friend request from an individual that is or students you friend online. has the potential to be my student.” What should you do when you get a Facebook friend Once you are sure an individual will no longer be request from a student? We believe that it is important your student, you get to decide which friend requests to to have a consistent policy in place to handle fairly this accept and which to deny. This policy allows you to treat inevitability. Make your policy public by stating it on the all students equally while you are in a position of power, first day of class or including it on your syllabus. Before and later you can filter the individuals to whom you settling on a policy, we encourage you to find out if your allow access to your personal life. school and/or department has an official or unofficial A variation is to not accept friend requests until a policy regarding interaction with students on social student graduates. One disadvantage of such play-it-safe media. policies is that you forego an opportunity to deepen the student-teacher relationship. In particular, if you share Potential Policies mathematics or education-related content on Facebook Here we lay out three potential policies and discuss their (as we often do), then you give up the chance to provide merits. valuable insight into your career and craft.
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Let’s wait and see. Somewhere in the middle we have students doing, for example, you can make sure that a policy along the lines of: “I do accept friend requests your student list will not see pictures you are tagged in. from students, but not until after the semester is over You can also customize the privacy settings of any if they are currently in one of my courses for the first single post, so if you want to vent about students, you time.” can restrict them from seeing it. To be vigilant about This allows you to share the fun of the social media your Facebook privacy, consult LifeHacker’s always up- experience with your students, like the “Open to All” to-date guide at KWWS WLQ\XUOFRP/+)%3ULYDF\. policy, but the delay allows time for a course to end. On the other hand, it might behoove you to clean up This alleviates the pressure of students hoping that the your act on social media. Facebook is more open and friending process will improve their grade. We have the public than it used to be, so you should probably behave opportunity to connect with students sooner rather than on Facebook more often as you do in mixed company later, but also after we have had some time to develop a than you might among your close friends. If you are rapport with them. always on your best behavior, you do not have to worry Of course, all these policies will have exceptions about who is eavesdropping. based on the culture of your institution or the kinds of interactions you have with students (research students, Connect graders, tutors, etc.). But the central point is still to have Being friends with students on Facebook is not the same a policy and try to apply it uniformly. as being friends in real life and need not infringe on the professional relationship between teacher and student. Facebook Lists and Privacy Settings Don’t be afraid to be friends with your students. As long You can use friend lists on Facebook to create sets as you do it fairly and responsibly, it can both preserve of friends, and then set options for which lists can your authority and enhance the relationships you see which of your posts. Matthew uses a list called already have with them. “Students” and adds students to that list when he accepts their friend request. The pageIDFHERRNFRPKHOS Dana C. Ernst (dana.ernst@ nau.edu) is an assistant IULHQGVOLVWV has up-to-date documentation on how to professor at Northern Arizona University. Matthew configure these lists. Leingang ([email protected]) is a clinical associate You can also configure your privacy settings to control professor of mathematics at the NYU Courant Institute of who sees which types of automatic notifications. If you Mathematical Sciences. Ron Taylor ([email protected]) is have your students in a list and you are worried one of an associate professor at Berry College. Look for them on your high school buddies is going to tag you in a picture Facebook.
123RF doing the sort of thing you don’t want to see your
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Supporting a Statistician in a Math Department
any mathematical sciences departments are introductory statistics courses (KWWS JRRJO JI5T); Mfinding themselves responsible for teaching this statement has been endorsed by the boards of the statistics. Although statistics uses mathematical concepts MAA and the ASA. in an essential way, administrators and colleagues must recognize the important differences between the Evaluating Their Work fields, how each subject should be taught, and how a The work of statisticians is different from the work statistician should be evaluated for tenure. of most mathematicians. Thus, the evaluation of the quality of their work requires familiarity within their Professional Development field and its many nuances. For example, statisticians Mentoring and professional development are important are often involved in important interdisciplinary for all new faculty hires, but are even more important work that may be published in a journal that does not for a statistician in a mathematical include statistics (or mathematics) sciences department. Statistician in the title. Statisticians are often mentors are recommended for new listed as the third or fourth author faculty in statistics, especially if this even though their contributions are person is the only statistician in the essential. In many cases, a statistician department (KWWS JRRJO3E'&). If may consult on a project that requires there are no senior statistician mentors thoughtful and time-consuming available in the department, contact work, but may produce outcomes the Isolated Statisticians Network, a that are not statistically significant committee of the American Statistical and, consequently, may not result in a Association (ASA), for advice (KWWS publication. JRRJO)5;V(). Statistical consulting (paid and It is particularly important for new unpaid) is an important form of statistics faculty members, in a department without scholarship and professional development for many other statistics faculty, to travel to conferences and statisticians. A new statistician on campus will often workshops in order to have the opportunity to talk with receive requests for help with data from faculty, other statisticians about both their research and the students, staff, and even outside the college or university. teaching of statistics. In addition, departments should If the new statistician is expected to provide such a recognize the need for statisticians to have specialized service, then some form of reassigned/released time software for their research and their teaching. may be warranted. Otherwise, the faculty member’s Applied statistics instructors should use very performance in those areas that are most closely aligned different pedagogical approaches than teachers of pure to tenure and promotion could be adversely affected. mathematics courses (KWWS JRRJOZHYIM). Students in The American Statistical Association has endorsed the a first statistics course should learn to reason about the MAA’s “Guidelines for Programs and Departments in world through examples involving real and often-messy the Undergraduate Mathematical Sciences.” In addition, data (KWWS JRRJO/LK:). A statistics faculty member the ASA’s endorsement lists specific areas of support for must spend a lot of time searching for good real-world new statistics faculty members (KWWS JRRJO+L(E:.). data sets for examples and exercises. He or she must As the need for qualified statistics instructors continues keep abreast of a field that is rapidly and continually to grow, it is essential for mathematicians and changing; in particular, he or she must keep up with the statisticians to appreciate the distinct differences new advances in technology and statistical computing between the approaches to research and pedagogy that are having a major impact on both research and between the two fields. teaching. Thus, a statistics faculty member must devote a The ASA-MAA Joint Committee on Statistics Education significant amount of time developing the support tries to stimulate effective change in undergraduate materials for the technology in addition to developing statistics education, especially in the many institutions course content. See the recent recommendation where the department of mathematics bears primary from the MAA-ASA Joint Committee on Statistics responsibility for the teaching of statistics.Contact:
Education for a discussion of qualifications for teaching Michael Posner at [email protected]. SHUTTERSTOCK
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SIGMAA on Undergraduate Research Formed
By Dominic Klyve
ome of my most exciting and The group will also provide Chair – Dominic Klyve, Central Sprofessionally useful moments development opportunities for Washington University with colleagues in the MAA have faculty interested in beginning work Outreach Coordinator – Michael occurred by participating in in undergraduate research. Dorff, Brigham Young University SIGMAAs. These Special Interest Some members of other SIGMAAs Secretary-Treasurer – Jan Groups of the MAA bring together have reported that the most benefi- Rychtar, University of North people with shared interests, either cial aspect to membership is joining Carolina–Greensboro in person or via email discussion the email list. All members will have Program Coordinator – Christina lists. For example, SIGMAAs find the option to belong to a dedicated Eubanks-Turner, Loyola that the Joint Mathematics Meetings email list on which members can ask Marymount University provide a convenient venue to meet, questions, exchange ideas, and make exchange ideas, and generally have a connections. During the first year, however, a great time. The UR SIGMAA will provide a chair-elect will be chosen by the For these reasons, I am very useful structure around which talks membership. We are also looking for pleased to announce the formation or sessions at section or national an electronic resources coordinator. of a SIGMAA focused on under- meetings can be organized. (It’s If more than one person expresses graduate research. The new group, worth noting, however, that, like all interest in this position, we’ll hold UR SIGMAA, was officially SIGMAAs, the UR SIGMAA will an early election for this too. The incorporated this spring and is open not monopolize activity in this area. other officers will be replaced at for membership. We expect that many of the talks staggered intervals over the next and poster sessions on this subject three years. Rising Interest will continue to be run much as they The UR SIGMAA plans to expand Undergraduate research, as have been for years, whether or not and to develop even further the MAA members know, has risen the organizers join the SIGMAA.) exciting work happening in regard dramatically in its impact on the to undergraduate research mathematical community over Become a Charter Member throughout the MAA. I hope many the last decade. The MAA already At this point, I’m sure most readers MAA members will consider joining supports this activity in innumerable are wondering: Can I join now? The us as charter members and help set ways, and there has been a demand best news of all is—yes, you can the course of this new group. for a special interest group dedicated join UR SIGMAA today! Although to undergraduate research for some patient MAA members can wait Dominic Klyve is on the faculty at time. (In fact, a call sent out via until they renew their dues and Central Washington University, Project NExT lists and other sources check the “UR SIGMAA” box on Ellensburg, Washington. quickly resulted in the names of 96 the renewal form, those wishing to people who expressed interest in join sooner can call MAA customer being charter members!) service at 800-331-1622, or send an What will this new SIGMAA email to PDDVHUYLFH#PDDRUJ to do? The short answer is that this add the SIGMAA before their next decision will rest with its members. membership renewal. It’s not too late I’m expecting that the group will be to become a charter member! very active. For those who want to do more According to the charter, the than join, it’s possible to become UR SIGMAA will “promote even more involved. Four of the undergraduate research within the officer positions were filled, under MAA through greater awareness provisions of our charter, before the of the work in this area currently MAA approved the charter. Two- underway, and by encouraging thirds of the initial slate of interim
SHUTTERSTOCK members to become involved.” officers has therefore been selected:
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Tensor Foundation Grants Awarded to 27 Projects
lthough the MAA is not a for strengthening underrepresented Tensor-SUMMA Grants support Agrant-making organization, minority mathematics achievement programs that encourage pursuit we administer a variety of programs (SUMMA). and enjoyment of mathematics for public and private sources that Tensor Grants for Women and among middle school students, high fund activities that advance the Mathematics support projects school students, and/or beginning association’s goals. The MAA does designed to encourage college and college students from groups this for the Tensor Foundation, university women or high school traditionally underrepresented in which finances one program for and middle school girls to study the field of mathematics. women and mathematics and one mathematics.
Tensor-SUMMA Grants
Project Title Project Organizer Project Institution Institution City Increasing the Participation of Hispanic Students in Brian Conrey American Institute of Mathematics 6DQ-RVH&$ AIM’s Morgan Hill Math Program Enhancing Diversity: The CSU Channel Islands Geoffrey Buhl California State University Channel Camarillo, CA Mathematics REU Islands Cougar Math Advancement Project (C-MAP) 6RoD$JUHVW College of Charleston Charleston, SC Science and Technology Academy for Residence Mazen Shahin Delaware State University Dover, DE Scholars (STARS) InSTEM (Inspiring STEM in Girls) Nell Cobb DePaul University Chicago, IL Fisk University Math Club Qingxia Li Fisk University Nashville, TN Supporting Math Majors Project Aimee Tennant Huston-Tillotson University Austin, TX The Maximizing Mathematics Achievement (MaxiMA) Shenglan Yuan LaGuardia Community College, CUNY Long Island City, Project NY San Francisco Math Circle Eric Hsu San Francisco State University San Francisco, CA Navajo Nation Math Circles Tatiana Shubin 6DQ-RVH6WDWH8QLYHUVLW\ 6DQ-RVH&$ The Math Games Project: Math Games in a Youth Sports Gregory Budzban Southern Illinois University Carbondale, IL League Setting to Enhance Mathematical Learning in Minority Students CHAMP-Cougars and Houston Area Math Program Mark Tomforde University of Houston Houston, TX Maryland Mathematics Camp (Mathletics) Stephanie Timmons University of Maryland College Park, MD Brown Wellesley Emerging Scholars Initiative Stanley Chang Wellesley College Wellesley, MA Minorities in Mathematics Speaker Series (MIMSS) Alicia Youngstown State University Youngstown, OH Prieto-Langarica TROY UNIVERSITY TROY A 2013 summer commuter math and science camp (Mathematics, the Queen of Sciences) held at Troy University, Dothan Campus, Alabama, received a Tensor grant.
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Tensor Grants for Women and Mathematics
Project Title Project Organizer Institution Name City GirlsGetMath@ICERM -LOO3LSKHU Brown University Providence, RI California State University Monterey Mathematics & Mentoring Program -XGLWK&DQQHU Bay (University Corporation at Seaside, CA Monterey Bay (on behalf of the CSU Monterey Bay)) Southeastern Conference for Undergraduate Women in Sarah Schott Duke University Durham, NC Mathematics King University Women in STEM Club Wendy Traynor King University Bristol, TN “GEMS” Summer Day Camp for Middle School Girls - Linda McGuire Muhlenberg College Allentown, PA Girls Experience Muhlenberg Science :RPHQ:KR/RYH0DWKHPDWLFV 6LJQLoFDQW:ULWLQJVRQ -RDQQH6QRZ Saint Mary’s College Notre Dame, IN Women and Mathematics Girls Exploring Mathematics Meghan De Witt 6W7KRPDV$TXLQDV&ROOHJH Sparkill, NY $OO*LUOV$OO0DWK6XPPHU&DPS Westmont Encouraging Women in Mathematics Patti Hunter Westmont College Santa Barbara, CA Sonia Kovalevsky Mathematics Day -HVVLFD+DPP Winthrop University Rock Hill, SC Solutions In the April/May issue, we presented three Alcazar puzzles. The solutions are below. Easy Medium Hard PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 12 Distinguished Lecture » Bubbly Mathematics By Katharine Merow et’s test your intuition about bubbles. century B.C. that a circle is the most efficient way to L The standard “double bubble” consists of a little enclose a given area. It wasn’t until 1884, however, that sphere and a big sphere, with a surface between them. Hermann Schwarz established the analogous result in Do you think that (a) the surface is flat, (b) the big three dimensions, that a sphere has the least surface area bubble pushes into the little bubble, or (c) the little for a given volume. Area minimization is the principle bubble pushes into the big bubble? dictating soap bubble behavior, Morgan explained. Frank Morgan (Williams College) asked his “When you have a cluster of soap bubbles coming audience at the MAA Carriage House on April 28 together,” Morgan said, “they look for the least area way eight such questions. Part of the MAA’s NSA-funded to enclose and separate three . . . or more given volumes Distinguished Lecture Series, Morgan’s “Soap Bubbles of air.” and Mathematics” beguiled attendees with its gameshow Analysis of such clusters turns out to require some flavor, its displays of bubble-blowing prowess, and its sophisticated mathematics. As he indicated milestones insights into the mathematical process. in the development of strategies to understand bubbles, The answer to that double-bubble question? Morgan played video clips of the mathematicians “The little bubble pushes into the big bubble,” Morgan involved. said. “And the reason is, there’s more pressure in the One of these mathematicians was Jean Taylor, whose little bubble.” 1976 paper “The Structure of Singularities in Soap- Bubbles may seem like kid stuff, but they’re Bubble-Like and Soap-Film-Like Minimal Surfaces” everywhere: They make bread fluffy, mattresses definitively answered the hardest question Morgan supportive, fire extinguishers effective. They’re also, posed during his lecture: How many different ways can Morgan emphasized, a topic of serious mathematical soap films come together? study. Morgan considers the proof of the double-bubble “In math . . . the answer is always one, zero, or infinity,” conjecture his greatest mathematical achievement, and Morgan quipped, “but in this case the answer is two— he took pains in his talk to connect the work of both what? two!—a very unanticipated kind of answer.” 2015 Abel Prize winners—John Nash Jr. and Louis Indeed, what Taylor proved is that (1) soap bubbles Nirenberg—to soap bubble geometry. meet in threes along a curve at an angle of 120 degrees Morgan traced the history of this mathematics all and (2) these curves meet in fours at a vertex at the the way back to Zenodorus, who proved in the second tetrahedral angle of approximately 109.47 degrees. Though Morgan joked about spending the remainder of his talk “going over some of the technical details” of Taylor’s paper, after only a brief overview of her argument, he moved on to other topics, among them the double bubble. He floated some alternatives to the standard double bubble, which, until Morgan and his coauthors proved it in 2002, was merely suspected to be the most efficient way to enclose two volumes of air. Two separate bubbles are wasteful, he noted; if they come together, they can share the common wall. A bubble inside a bubble also offers no advantage, since containing the smaller bubble makes the larger bubble unnecessarily—and inefficiently—large. “So that’s why you never see a bubble inside a bubble,” Morgan said, even as he dipped a pair of wands into his bucket of soap solution and succeeded in blowing Frank Morgan used his prowess in manipulating soap films exactly that. and bubbles to illuminate questions of mathematical interest Within an instant, however, the smaller bubble popped in the study of minimal surfaces. out and glommed on to the outside of the larger one in L. McHUGH 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO Sprechen Sie MATLAB? Over one million people around the world speak MATLAB. Engineers and scientists in every field from aerospace and semiconductors to biotech, financial services, and earth and ocean sciences use it to express their ideas. Do you speak MATLAB? Morgan outlined the history of soap bubble geometry—including Image: Kim Young-Sang, Jeong Hee-Jun, Quantum Device Lab, Hanyang Univ. ©2013 The MathWorks, Inc. the inquiry into how many ways bubbles can come together. that familiar double-bubble configuration. “It prefers that shape,” Morgan said. Proof of the double-bubble conjecture established the standard double bubble as the most efficient—more efficient than, say, John Sullivan’s bubble-with-a-bubble-around- its-waist—but it leaves open the question of whether other arrangements are stable and therefore might occur in nature. “I love this question because mathematicians have no idea how to solve it, but a kindergarten student could answer it tomorrow by just blowing a different double bubble,” Morgan said. Morgan ended his talk with a championship round of sorts. Attendees who had correctly answered more than two of Morgan’s earlier questions tried to outdo one another in the identification of the best—that is, most perimeter- Modeling electric potential in efficient—planar five-bubble, six-bubble, seven-bubble, and a quantum dot. Contributed eight-bubble. by Kim Young-Sang at HYU. Even those finalists eliminated in the first round went This example available at home with prizes. “Good attempt,” Morgan said as he www.mathworks.com/ltc handed each of them a miniature jar of bubble solution. “We have little research kits so you can get better at this.” Blowing bubbles may seem a frivolous pastime, but Morgan gave listeners choice words for anyone chiding them for production of soapy spheres. “If you want to understand the universe,” he said mid-talk, The language of technical computing “you should start out by understanding the soap bubble.” Katharine Merow is a freelance writer in Washington, D.C. AMERICAN MATHEMATICAL SOCIETY Peter Lax, Mathematician An Illustrated Memoir Reuben Hersh, University of New Mexico, Albuquerque, NM Reuben Hersh, a former student of Peter Lax, has produced a wonderful account of the life and career of this remarkable man. The book is well researched and full of interesting facts, yet light-hearted and lively. It is very well written. A nice feature is the abundance of photographs, not only of Peter Lax and his family, but also of colleagues and students. Although written for mathematicians, the book will have wider appeal. Highly recommended. —Peter Duren, University of Michigan A life of Peter Lax, one of the most famous and influential mathematicians of the modern era. 2015; 253 pages; Softcover; ISBN: 978-1-4704-1708-6; List US$35; AMS members US$28; Order code MBK/88 Art in the Life of Mathematicians Anna Kepes Szemerédi, ELTE, Budapest, Hungary, Editor Mathematicians reflect on the roles that mathemat- ics and art have played in their lives. 2015; approximately 259 pages; Hardcover; ISBN: 978- 1-4704-1956-1; List US$49; AMS members US$39.20; Order code MBK/91 Really Big Numbers and You Can Count on Monsters (2-Volume Set) Richard Evan Schwartz, Brown University, Providence, RI These books are unique teaching tools that take math lovers on a journey designed to motivate kids (and kids at heart) to learn the fun of numbers. 2015; Softcover; ISBN: 978-1-4704-2294-3; List US$40; AMS members US$32; Order code MBK/84/90 Order by Phone: facebook.com/amermathsoc Order Online: (800)321-4267 (U.S. & Canada), @amermathsoc www.ams.org/bookstore (401)455-4000 (Worldwide) plus.google.com/+AmsOrg 15 Girls’ Team Places Second at European Olympiad olving a mathematical Olympiad was the U.S. team leader. Fostering this joy of creative Sproblem does not happen “You want the girls to compete problem solving is a goal of the instantaneously. It takes hours of against each other, and if it is too Olympiad. “When someone is going poking and prodding to extract an easy, half of them get high scores into a contest I say ‘have fun’ instead answer. Then there is an emotional and there is no distinguishing factor. of ‘good luck,’ ’’ says Sherry Gong rush when the problem is finally Too hard and it is demoralizing,” she (MIT), the U.S. deputy leader. solved, describes Celine Liang, says. The 2014 exam was an example Aside from solving very who won a gold medal at this year’s of a demoralizing year, where high challenging math problems, EGMO European Girls’ Mathematical scorers received medals, but not a participants can bond over more Olympiad (EGMO). single contestant made it onto the than a mutual love of mathematics. “After finishing an EGMO list of honorable mentions, says In the week the international problem, or any Olympiad problem, Iglesias. contestants were together, they I get an amazing sense of fulfillment. played card games in the dorms, Mainly because I spent many hours Finding the Fun visited markets and shopping malls, working towards a solution,” says Like many teenagers, the U.S. tried new foods, and enjoyed a Liang. “Finally finishing a problem contestants have preferences—in celebratory dance party at the end of is a definite achievement every this case, about the types of the competition. time.” problems on an exam. Some enjoy Wang says she will never forget The U.S. team claimed second solving Euclidean geometry and the last night of the competition, overall at the EGMO, which combinatorics questions; others when she realized, after receiving took place April 14–20 in Minsk, dislike algebra and number theory. a bouquet of roses for winning Belarus. Every member of the “I absolutely love geometry first place, she could not bring the U.S. team placed among the top problems because the diagrams are flowers on her flight home. scorers, winning either a gold or so beautiful,” says Liang. “There She says, “So Rachel [Zhang] and I a silver medal. On the team were are just so many relationships knocked on people’s doors and sang high school students Meghal between different lines, points, and the song ‘Finite Simple Group of Gupta (Monta Vista High School angles that are hard to see initially Order Two,’ a math love song, and in Cupertino, California), Celine but reveal themselves after some gave them roses.” Liang (Saratoga High School in searching.” —Alexandra Branscombe Saratoga, California), Danielle Wang (Andrew Hill High School in San Jose, California), and Rachel Zhang (Parkway South High in Ballwin, Missouri). The exam is made up of six proof-style problems given over two days. The U.S. team score was 116 out of a possible 168 points, behind Ukraine’s first-place 139. Wang was the only contestant in the entire event to receive a perfect score of 42 points. One of her proofs was so well done it was displayed as one of the example solutions, says Mark Saul, MAA director of competitions. In its fourth year as an inter na- tional competition, the 2015 EGMO The U.S. team visited the U.S. Embassy in Minsk, Belarus, while competing in contained problems at the perfect the European Girls’ Mathematical Olympiad. From left: Mark Saul, Jenny Iglesias, level of difficulty, says Jenny Iglesias Sherry Gong, Meghal Gupta, Rachel Zhang, Celine Liang, Danielle Wang, (Carnegie Mellon University), who and Charge’ d’Affaires Scott Rauland. PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 Join us in Washington, D.C., for our Centennial Celebration. 2015 MAA Centennial Lecturers Manjul Bhargava, Princeton University Carlos Castillo-Chavez, Arizona State University Jennifer Chayes, Microsoft Research Ingrid Daubechies, Duke University Erik Demaine, Massachusetts Institute of Technology Karen Parshall, University of Virginia Undergraduate Student Activities MAA Chan-Stanek Lecture for Students “Seventy-Five Years of MAA Mathematics Competitions” Joseph Gallian, University of Minnesota Duluth Workshop What’s the Story? A Graduate Student Workshop on Formulating a Research Presentation for a General Audience Radical Dash A daily scavenger hunt filled with math challenges and creativity for teams of undergraduates. Secrets of Mental Math Performance by Arthur Benjamin Panel Session Nonacademic Career Paths for Mathematicians MAA Student Paper Sessions Pi Mu Epsilon J. Sutherland Frame Lecture Noam Elkies, Harvard University Pi Mu Epsilon Student Paper Sessions Pi Mu Epsilon Student Banquet Industrial Math Research in the PIC Math Program Estimathon! MAA Ice Cream Social and Undergraduate Awards Ceremony “0353, part of Fire Series” Artwork and Photograph by Mathematical sessions run Wednesday morning Erik Demaine and Martin Demaine through Saturday evening (August 5–August 8) Register Today maa.org/mathfest Joint Meeting with the Canadian Society for History and Philosophy of Mathematics and the British Society for the History of Mathematics. 17 MIT Wins, Sets Record in Putnam Competition ompetitors from Massachusetts CInstitute of Technology (MIT) at the 75th annual William Lowell Putnam Mathematical Competition swept up most of the highest scores. Not only did one of MIT’s three- person teams claim first place in the competition, but MIT now holds the record for the number of individuals ranking in the top-five highest exam scores in a single year. Exactly 4,320 students from 557 colleges and universities across the (From left) MIT Junior Mitchell Lee, sophomore Bobby Shen, mathematics United States and Canada took the professor Bjorn Poonen, freshman Mark Sellke, and sophomore Lingfu Zhang. exam on December 6, 2014. This is the eighth team win for MIT, (a score of 81). The 2014 fellows, which is the highest median score which includes a $25,000 prize and in alphabetical order, are Ravi since 2002, said Joseph Gallian, additional $1,000 awards for each Jagadeesan, Zipei Nie, Mark A. professor in the Department of team member (Mitchell M. Lee, Sellke, Bobby C. Shen, David H. Mathematics and Statistics at the Zipei Nie, and David H. Yang). Yang, and Lingfu Zhang. University of Minnesota Duluth. Harvard University’s team (Calvin Five of this year’s six Putnam In addition, “34 percent of the Deng, Malcolm Granville, and fellows attend MIT—all except participants had a score of zero, the Xiaoyu He) took second place, and Jagadeesan (Harvard)—which sets a lowest percentage since 2003,” added Rensselaer Polytechnic Institute record for highest number of annual Gallian, who served as president of (Theerawat Bhudisaksang, Owen fellows to come from the same the MAA from 2007 to 2008. Goff, and Wijit Yangjit) placed third. institution. Several of these same Gallian will present more This is the first top-five finish for students have been Putnam fellows interesting facts and history about Rensselaer. more than once. This is Nie’s third the Putnam—and other MAA With an emphasis on speed, the year placing in the top five, and the competitions—in his lecture six-hour Putnam consists of 12 second for classmates Shen and “Seventy-Five Years of MAA problems designed by a Questions Yang. Mathematics Competitions” at the Committee: Hugh Montgomery The names will also be familiar 2015 MAA MathFest, which will (University of Michigan), Henry to those who follow MAA’s be held in Washington, D.C., this Cohn (Microsoft and MIT), and competitions. Of the 2014 fellows, August. David Savitt (University of Arizona). four won gold medals on a U.S. More details about the 2014 The highest exam score was 96 out team, which the MAA sponsors, at Putnam Mathematical Competition of a possible 120 points. an IMO: Jagadeesan, Sellke, Shen, will appear in the October 2015 Participants who achieve the top and Yang. American Mathematical Monthly. five overall scores on the exam A complete list of Putnam winners are named Putnam fellows and Statistically Speaking can be found at KWWS NVNHGOD\DRUJ receive a $2,500 prize each. This Looking at the statistics, the SXWQDPDUFKLYH, and past IMO year was distinctive because there 2014 Putnam competition may contestants can be found at KWWS are six Putnam fellows, thanks to appear easier than past exams. The LPRRIILFLDORUJGHIDXOWDVS[. ALLEGRA BOVERMAN ALLEGRA a three-way tie for fourth place nationwide median score was 3, —Alexandra Branscombe PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 18 To the Mathematical Beach By Francis Edward Su thought I had chosen the my connection with my students? college experiences and certain life Iright book for the occasion. How often do I take the time to get outcomes—including employee 3UHVLGHQW V On this Saturday morning, to know their backgrounds? What engagement and multiple measures 0HVVDJH I was volunteering with a are the primary experiences that of well-being (purpose, social, program called Reading to Kids that shaped them, and do those present financial, community, physical). seeks to inspire underserved youth obstacles or opportunities for In particular, those who, as in Los Angeles to enjoy reading. learning? And in what ways does the students, felt “supported” in Assembled before me was a group of mathematical beach say “open to all” college—defined as those who eager Latino and African American but still feel restricted? would affirm all three: (1) “my children from the neighborhood. These questions appear unrelated professors cared for me as a person”; The book I chose was about to mathematics, but if we ignore (2) “I had at least one professor going to the beach. It was at the their effects, some of our students who made me excited about right reading level, with playful will not flourish. learning”; and (3) “I had a mentor illustrations I thought would be We should try to know our who encouraged me to pursue my appealing. Nevertheless, after students as whole people. Even goals”—were twice as likely now to reading just a few pages in a most as I write this, a Gallup-Purdue be engaged at work (57 percent vs. spirited voice, I could tell that the survey of 30,000 college graduates 25 percent) and three times as likely kids did not share my enthusiasm. is making the news. It shows a to be thriving in all areas of well- So I asked, “How many of you have strong correlation between certain being (17 percent vs. 6 percent). ever been to the beach?” To my surprise—though this part of LA is just 15 miles from the ocean—only one of the eight children raised a hand. Wasn’t going to the beach a quintessentially Californian thing to do? Some reflection supplied potential explanations. In a low-income neighborhood, parents often work multiple jobs to make ends meet, so they may not have had the time or resources to bring their kids to the beach. And when an African American friend of mine heard this story, he said, “Black families don’t take their kids to the beach” and explained how this was a vestige of a segregated era when African Americans were not allowed in public pools and beaches. Whatever the reason, I had missed something essential for connecting with my students: the historical, cultural, and economic context they brought to the classroom. That episode helped me reflect on how I teach college students. What context am I missing that hinders 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 19 What can we as instructors do? I them to tell their own stories, you offer just a few ideas here and would empower them to make math In what ways does the love to hear yours. relevant in their cultural contexts. mathematical beach say x Show students you want to know x Open up about your own stories. their stories. A questionnaire, as What are some of the academic “open to all” part of a first assignment, could or nonacademic obstacles you have thoughtful questions such have faced? Your students will but still feel restricted? as, What’s your favorite book? appreciate them because stories of Most important person in your struggle are universal. life? A nonacademic obstacle you are facing right now? Make the We should never lose sight of questions optional or general so the fact that the ability to know that students don’t have to divulge our students, and be known, is one much if they don’t want to. of the most important aspects of teaching. Our students, especially x Use your knowledge of student the most disadvantaged ones, will stories to craft examples that feel better supported, and the extra Sadly, only a quarter of all college they can relate to. This includes effort we take will enrich our own graduates could say their professors using a variety of cultural names lives as well. cared for them as a person, and only and the pronoun “she” in generic Even a failure to connect can break 14 percent said they felt supported examples. the ice and start a conversation. In in all three ways. my case, I put down the book about x Highlight contributions from the beach and said to my kids with diverse sources. Photos or a smile, “Tell me stories about what stories from a diverse set of you like to do for fun.” mathematicians offer our students This August, MAA is celebrating multiple chances to identify its centennial MathFest in with a role model and show that Washington, D.C. Over the last the mathematical beach can be century, we have established a enjoyed by everyone, regardless of vibrant and inclusive community economic or cultural background. that nurtures the human side of mathematics and supports all x Where possible, try to keep your aspects of a faculty member’s life. course structure from placing Join us. Celebrate with us! undue barriers on various groups. For instance, I once realized that Francis Su can be by scheduling office hours only in reached at VX#PDWK the late afternoon, athletes could KPFHGX and found not come see me. Be especially on Twitter at # sensitive to disadvantaged groups, PDWK\DZS. such as students with part-time jobs or those whose weekend is consumed with family obligations. Left: The beach at Port St. Johns, South Homework announced Friday Africa, the morning after a storm and due Monday may not leave forced a partially anchored structure enough flexibility. into tracing out concentric circles on the sand. The photo, by James Metz, x Offer ample opportunities for appears in the MAA Found Math students to express mathematical galleries (KWWS ELWO\<<17). Send ideas in their own words, using your photos for possible inclusion to their own examples. By inviting IRXQGPDWK#PDDRUJ. PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 20 MAA Competitions Gets New Director By Alexandra Branscombe irector of Competitions Steve Dunbar has the director’s duties include making sure that six contest Dretired from the MAA American Mathematics exams are created on time; schools and student teams Competitions (MAA AMC). Dunbar, who divided are registered; the exams are scored; and prizes are his time between MAA AMC and being a professor awarded. The six exams are AMC 8, AMC 10, AMC in the Department of Mathematics at the University 12, American Invitational Mathematics Examination of Nebraska–Lincoln (UNL), stepped away from both (AIME), and the United States of America Mathematical positions in mid-May. He had been working vigorously Olympiad (USAMO) and Junior Mathematical to transition the AMC program from Lincoln, Olympiad (USAJMO). Nebraska, to its new base in Washington, D.C., with his replacement, Mark Saul, who took over as director on Successes June 1. Dunbar judges the success of his leadership by the Dunbar has been an MAA member for more than 40 quality of each contest and how they all contribute to years, since he joined in 1974 on a student membership. the MAA AMC’s goal: strengthening the mathematical Before joining the MAA leadership team, Dunbar was capabilities of young people. the director of an interdisciplinary computer science “I think the thing that we have been able to do is create and business program at UNL, but realized he wanted to and expand a really smoothly running program,” says find a way back into mathematics. Dunbar. “Expansion and diversification of the program A new position on a special projects assignment for are the two biggest accomplishments.” the MAA AMC, which he accepted in 2001, offered Today, more than 350,000 students in about 6,000 the perfect fit for Dunbar to get his wish. While he schools participate in the MAA AMC contests each continued to teach mathematics, his duties at MAA year. From there, about 10,000 student qualify for the grew, and in 2004 he was appointed director of AIME, and then roughly 500 students continue on to competitions. the USAMO. Since then, Dunbar has developed the AMC program His hope for the future of MAA competitions—and into what it is today: delivering high-quality math for the new director—is the continued efficiency and contests around the world. In its most basic description, growth of the program. “I would want to see Steve Dunbar (left) has retired from MAA AMC. His replacement is Mark Saul. At right, Dunbar and the 2012 L. McHUGH USAMO team. 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 21 [MAA AMC] continue to expand and that more students get an opportunity to participate,” he says. Accustomed to wearing multiple hats, Dunbar says that retirement means time to use his competition experiences to generate new projects. “One of the things I have been able to observe over 15 years is the creation of mathematical contest problems,” he says. “I’d like to think about the process of creating math questions. There are a lot of people who have written about how you solve problems, but not much written about how you pose problems,” he said. Whether he ends up writing an article or a book, he’s excited about delving into the issue as part of his future. Lifetime of Experience New director Saul has had a lifetime of experience in math competitions. He has been a contestant, acted as a math team coach, and served on MAA competitions committees to develop and distribute the contests. Outside of competitions, his experience includes being project director at the National Science Foundation and, most recently, serving as director of the Center for Mathematical Talent at the Courant Institute of Mark Saul. Mathematical Sciences. into math competitions and inspire creative problem solving. Teaching Thanks to the work Dunbar put into creating an Saul vividly remembers competing in his first MAA efficient and well-run program, Saul sees an opportunity math competition. He was 15 years old on the Bronx to grow the program and motivate more students to join High School of Science math team, a team he would the community. later return to coach. “I think we need to take a good look at who is taking “At that time, there were not that many opportunities our competitions, who is benefiting from them, and for mathematics outside the textbook,” he says. “The then widen the pool,” he says. “There are many schools kind of mathematics that actually uses your knowledge and many students against whom the deck is stacked. in creative ways—the MAA exam and local contests What is important about these contests is that it were the only things that did this.” opens students up to a different way of thinking about With a craving for challenge and problem solving, Saul mathematics.” was drawn to teaching. He taught K-12 mathematics for In addition, Saul would like to explore ways to 35 years at multiple schools, including his former high introduce new content to the system of exams, such school. Saul’s favorite classes to teach were advanced as adding questions that require proofs, a style that is honors math and remedial math. already commonly used in East European competitions. Teaching gifted students requires corralling His goal is to get young people to challenge their their creative thoughts and relating them to more misconceptions about what it means to do mathematics. conventional mathematical thinking—you have to be “Mathematical competitions expand their a mind reader, says Saul. Teaching struggling students understanding of what mathematics is . . . It is a creative is similar. It’s a matter of finding out where they went way to think from different angles,” says Saul. These wrong and getting them back on track, he added. skills are important to students because it will influence “From working with gifted kids, you can learn how to how they use math in the future, even if it is not in a reach the kids that everyone has given up on,” he says. mathematical field. “Mathematics is the heavy industry of the sciences,” he Direction says. “It’s the foundation for everything we do.” This same principle reappears when Saul discusses his L. McHUGH goals for the MAA AMC—bring more young people Alexandra Branscombe is staff writer for MAA FOCUS. PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 22 Interview ª T. Christine Stevens Professor Emeritus, Saint Louis University Associate Executive Director, American Mathematical Society Interviewed by Kenneth A. Ross Kenneth A. Ross is an emeritus material for algebra. Then, halfway professor in the Mathematics through the year, my family moved, Department at the University of and I was back in a traditional Oregon. algebra class. If I hadn’t finished the As a project for the 2015 centennial eighth-grade algebra on my own, I of the MAA, members of the would not have been able to make history subcommittee of the MAA the transition back to a traditional centennial committee have been algebra curriculum. interviewing prominent members of Earlier, in the sixth grade, a the mathematical community. The problem arose when I started full interviews will be available on the in a new school and my mother MAA website; excerpts from selected was notified that I was weak in interviews are appearing in MAA mathematics. When the teacher FOCUS. showed her my work, it turned out The excerpts here are based on an that my answers were correct, but I interview that took place January 15, had given them in a format that the 2010. teacher had not expected. Christine Stevens in the mid-1980s. When did you get interested in because it seemed to me to be the mathematics? strongest one in mathematics and I had many interests, and science. I was a chemistry major mathematics was certainly one of at first. I switched to mathematics them. I always enjoyed mathematics, because of an undergraduate and I thought about it a lot. When research experience after my I did science projects in school, sophomore year. It was a chemistry they were mathematics projects, project supported by the National involving the Klein bottle and the Science Foundation. I discovered Where did you grow up and go to Möbius strip. that I enjoyed analyzing the data school? It may also be significant that, more than collecting them. So my I was born in Maryland, but lived when I was in high school, I interest shifted from chemistry to on Long Island (in New York State) was hired to write the solutions applied mathematics. and in two cities in California, and manuals for several elementary and Between my junior and senior I graduated from high school in secondary mathematics textbooks. years at Smith, I worked at Bell Morristown, New Jersey. Except Although I didn’t realize it at the Laboratories in Whippany, New for three years, I attended public time, the books on which I worked Jersey, doing Fortran programming schools. Looking back at my had been written by some of the and working with the simplex schooling, I can see that moving leading figures in K-12 mathematics algorithm. I was doing cost-benefit around so much led to some education, such as Steve Willoughby, analyses for antiballistic missiles, problems in “articulation,” but I who would later become president and I was struck by the fact that managed to navigate the educational of NCTM [National Council of every number in the programs I system. In the eighth grade, for Teachers of Mathematics]. This was wrote represented a nuclear weapon. example, I was taught a little algebra my first paying job, and perhaps it I began to wonder whether I and then finished the material on foreshadowed my later interest in wanted to focus all my energies on my own. In the ninth grade, I started educational issues. destruction. So my interest moved in a new school that used the SMSG I chose Smith College, among to pure mathematics in my senior [School Mathematics Study Group] various good liberal arts colleges, year. 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 23 What was the special attraction of I had started out working on years, and this made a big difference mathematics? manifolds with John Mather, but because teaching at a liberal arts The logical structure of the subject Mather left Harvard for Princeton, college leads you to think about the made more sense to me. There was so I approached Gleason because role of a teacher in a different way. less memorizing, and I found the I had taken a course with him on For example, I taught a reform-style work in mathematics less frustrating topological groups, during which calculus course there long before than in the laboratory sciences. he had posed some open questions the term “calculus reform” had even Also, the science applications with that involved Lie groups. I thought been invented. But teaching per which I was familiar at that time my knowledge of manifolds might se wasn’t my entry to the MAA. In seemed to be related to weaponry. help with those questions. At first fact, my career path is much more Later, I realized that the applications I was afraid to show Gleason how complicated. of science were much more diverse little I knew, so I was a little too I should mention that I met my than that, but by that time I had eager to be independent. But when future husband, Thomas Moisan, at already chosen pure mathematics as I really needed help, Gleason gave Harvard. In fact, I recruited him to my field of study. me good advice. Now that I have work on the McGovern campaign had PhD students of my own, I can in 1972. I had already been active Was the transition from Smith College see that he provided me with a good in the antiwar movement. Tom and WR+DUYDUGGLIoFXOW" combination of encouragement and I were married in 1974. His degree I applied to Harvard, Cornell, and independence. was in English, and he obtained a Princeton and was accepted by all teaching job at Middlebury College three. However, my application to It’s clear that good teaching has in Vermont. Princeton was for their program been important to you throughout While finishing up my degree, I in the philosophy and history of your career, so it was natural for you taught at Lowell State College (now mathematics, and I realized that to get involved in the MAA. How and the University of Massachusetts I wanted a more mathematical when did that happen? I note that the Lowell). I then got a job at Mount program. I ended up choosing Missouri Section honored you with its Holyoke College in 1977, and for the Harvard over Cornell. teaching award in 1996 and that you next four years Tom and I had two The transition to Harvard was obtained the Haimo Award in 1997. apartments in two different states. difficult, though Smith had a good I had good teachers myself, and Each of us kept looking for a job that liberal arts program and my senior they were early models. I taught at would bring us geographically closer project was an extremely valuable Mount Holyoke College for four to the other, but without success. experience in which I had learned how to learn on my own. So I had a pretty good background, but still found myself on the “remedial track” at Harvard, since many of the incoming hotshots had already taken several graduate courses as undergraduates. I’ve described some of my experiences with [my thesis adviser] Andy Gleason in a memorial article that appeared in the Notices of the AMS (November 2009). Even among Harvard people, Gleason was regarded as extra bright. I didn’t realize until later how broad his interests were, which included work with the MSEB Chris Stevens (center) with others who served on the Project NExT leadership [Mathematical Sciences Education team over the years: (from left) Judith Covington (Louisiana State University Board] and with K-12 mathematics in Shreveport), Joe Gallian (University of Minnesota Duluth), Aparna Higgins L. McHUGH curricula. (University of Dayton), and Gavin LaRose (University of Michigan). PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 24 Finally, we realized that we were Mathematics Department had an issues in teaching undergraduate more marketable as a couple. In open position, and I was hired too. mathematics. 1981 we received two pairs of offers Later we were simultaneously chairs Our original objective was to bring and took the one from Arkansas of our respective departments. I new faculty up to date on changes State University in Jonesboro. They think that administrators were in curriculum and pedagogy that had agreed to an unpaid sabbatical sometimes worried by the fact that had been occurring while they were the next year, which we took in these two large departments were in graduate school. I discussed Cambridge, England. “in bed with” each other. the concept with some people at Finally, I can explain the NSF, and they thought it was a my entry into the inner good idea. When Jim Leitzel and I When I attended my first Joint workings of the MAA. computed the budget for a week- Mathematics Meetings in Biloxi, It was undoubtedly long workshop, however, we decided my experiences in that it was too expensive. Then we Mississippi, in 1979, women Washington that led had the idea of piggy-backing on mathematicians were much less to my appointment in the summer meetings, with two or the early 1990s to the three days of sessions just before the visible than they are now. MAA’s Science Policy meetings (which were still, at that Committee, which I time, joint meetings of the MAA I spent the year in Cambridge eventually chaired. While at the and the AMS). Jim and I worked working on some problems in NSF, I had participated in some of out the details and drafted a sample topological groups and also on the the deliberations of the MAA’s Task workshop program. Jim wrote up a history of Lie groups. It was my Force on Minorities in Mathematics, proposal for the MAA, but we heard first trip outside North America, which was chaired by Louise nothing back from the leaders. and it was great fun! The year in Raphael. The report of the task force During the summer, the Exxon Cambridge was a productive one for led to the establishment of SUMMA Education Foundation approached both Tom and me. [Strengthening Underrepresented Marcia Sward (who was the We returned to Arkansas State Minority Mathematics Achieve- MAA executive director) about in 1983-1984. The university’s ment] and the Committee the possibility of expanding their president at that time was Ray on Minority Participation in mathematics program to include Thornton, who had represented Mathematics, to which I was the undergraduate level. Marcia an Arkansas district in the U.S. subsequently appointed. Then in responded that there was a big House of Representatives. With 1993 Marcia Sward arranged for me need for professional development his help, I successfully applied to to be a visiting mathematician at for faculty and mentioned, as an become the 1984-85 AMS/MAA/ the MAA for a few months, while example, the conference that Jim SIAM congressional science fellow Tom had a research fellowship at the and I had proposed for new PhDs in in Washington, D.C., where I Folger Shakespeare Library. mathematics. worked as a legislative assistant to The Exxon Education Foundation Representative Ted Weiss of New This must be about the time you got liked this example and asked for a York. Meanwhile, Tom did research involved with Project NExT [New formal proposal within a month! at the Folger Shakespeare Library. Experiences in Teaching]. How did Jim and I wrote the proposal After that, we returned to Jonesboro that program get started? together, with a lot of input from for the years 1985 to 1987. From As a visiting mathematician at Marcia. Only six weeks after getting 1987 until 1989, I was at the NSF the MAA, I worked on strategic the Exxon Education Foundation’s as a program officer in teacher planning and learned a lot about request for a proposal, Marcia enhancement. During that period, the structure of the organization. received a letter telling her that they Tom taught at Mary Washington In the spring of 1993 I had would fund the program. This led College (now University of Mary several conversations with Jim to 18 years of support for Project Washington) in Fredericksburg, Leitzel, who had previously been NExT from the Exxon Education Virginia. a visiting mathematician at the Foundation and its successor, the In 1989, Tom was hired as chair MAA, and he suggested that the ExxonMobil Foundation. Our of the English Department at Saint MAA sponsor a conference for program officer was Bob Witte, Louis University. Fortunately, their new PhDs in mathematics about who was very knowledgeable about 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO We are Two Sigma. We find connections in all the world’s data. These insights guide investment strategies that support retirements, fund research, advance education and benefit philanthropic initiatives. So, if harnessing the power of math, data and technology to help people is something that excites you, let’s connect. NEW YORK HOUSTON Visit us at www.twosigma.com/careers to learn more and apply. LONDON HONG KONG mathematics education and a key advocacy for mathematics. When I research and applications. supporter of Project NExT. became chair of the MAA Science There have been changes in the When the MAA received the Policy Committee, I realized that the mathematical community, as well. request to submit a formal proposal Joint Policy Board for Mathematics When I attended my first Joint for the program that would (JPBM) focused exclusively Mathematics Meetings in Biloxi, eventually be called Project NExT, on funding for mathematical Mississippi, in January of 1979, Jim Leitzel invited me to codirect it research. I argued that funding women mathematicians were much with him. When I expressed some for undergraduate mathematics less visible than they are now. I reservations about my availability, education was also important and think that the program also paid he said that he would go it alone if managed to get a concern for it less attention to undergraduate and I declined. So I agreed to codirect voiced in JPBM’s congressional graduate education than current the program with him. Sadly, Jim testimony. programs do. died in 1998, so I then became the The meeting schedule itself was director of Project NExT. What changes have you seen in the quite demanding. There were AMS mathematics world since you became contributed paper sessions in the What other accomplishments in the involved? evening, and my talk (about my MAA are you especially proud of? I think I’ve witnessed a lot dissertation) was scheduled at 7:45 My work with Project NExT is of changes in the world of at night! undoubtedly my most significant mathematics. Substantively, it Fortunately, one thing that has not contribution to the MAA. Closely was exciting to be around for changed is the friendliness of the related to that was the role I the classification of finite simple mathematical community. Although played in helping to establish the groups and the proofs of Fermat’s I went to Biloxi knowing hardly any James R. C. Leitzel Lecture at last theorem and the Poincaré mathematicians at all, I met a lot of MathFest, which honors Jim’s many conjecture. interesting people there, and I’ve contributions to the profession. It has also been fun to observe the continued to find mathematicians I also worked to broaden the scope rapidly growing role of calculators much more outgoing that the usual of the mathematics community’s and computers in mathematical stereotype would suggest. 26 KenKen Variations By Robert Fuhrer enKen® puzzles are a familiar Puzzle 1: Standard but Challenging Ksight in many worldwide This 9 × 9 KenKen puzzle follows publications, websites, and mobile the standard rules but is a real apps, including the New challenge! York Times, NCTM’s Illuminations, the Times 3X]]OH3DJH (UK), Der Spiegel, and USA Today online. They are also used by more than 30,000 teachers in their classrooms to teach math skills, logical reasoning, problem solving, creative thinking, and perseverance. For this column, we will go one step further and explore some interesting variations of the game. The standard KenKen rules are simple: t For an n × n grid, fill each row and column with the numbers 1 through n. t Each heavily outlined set of cells, called a cage, contains a mathematical clue that consists of a number and an arithmetic operation. The numbers in the cage must combine (in any order) to produce the target number using the mathematical operation indicated. t Cages with just one cell should be filled with the target number. t Numbers can be repeated in a cage, as long as they are not repeated in any row or column. See the example in the box below. ([DPSOH 7KH[.HQ.HQSX]]OHRQWKHOHIWKDVWKHVROXWLRQVKRZQRQWKHULJKW 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 27 Puzzle 2: KenKen Twist The solutions to these three puzzles are at PDDRUJ If you’ve played a lot of KenKen puzzles, then you IRFXV]HQ]HQ and will appear in the August/September probably have certain strategies that are rooted in the issue. fact that the numbers “1 through n” are what you have At a basic level, solving KenKen puzzles requires not to work with. In KenKen Twist, we use a different set only simple arithmetic but also a combination of logic, of numbers, to spice things up a bit. The numbers to be algebra, number theory, and combinatorics. KenKen used are listed in the upper right corner of the puzzle. puzzles have also been used in the classroom to explore syllogisms and isomorphism, partitions and other topics from discrete math, and even geometry concepts. For example, see the National Council of Teachers of Mathematics article “Using KenKen to Build Reasoning Skills” (KWWS ELWO\]3V0=$). KenKen is also a good playground for undergraduate and faculty research projects in recreational mathematics. To play unlimited KenKen puzzles of virtually any size or difficulty level, visit NHQNHQSX]]OHFRP. You can also download the KenKen Classic app from the Apple App Store, the Google Play store, or the Kindle App Store. Teachers can sign up for the free KenKen Classroom Program, which provides a set of weekly puzzles of varying sizes and levels, at NHQNHQSX]]OHFRPWHDFKHUV FODVVURRP. KenKen® is a registered trademark of Nextoy, LLC, ©2015, KenKen Puzzle LLC. All rights reserved. Robert Fuhrer is the founder of Nextoy LLC and KenKen Puzzle Co.; UIXKUHU#QH[WR\FRP Laura Taalman is editor of the Puzzle 3: No-Op KenKen Puzzle Page column. To suggest puzzles for the column, In this puzzle you’re back to using the standard contact her at ODXUDWDDOPDQ#JPDLOcom. “1 through n” set of numbers, but we’ve decided not to show you any of the operations. You must determine which operation needs to be applied in each cage. Good luck! PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 28 BOOK REVIEWS ª Math Books in the Kitchen to Bake π: An Edible Exploration of tackles lots of interesting ideas from How to Bake π: An the Mathematics of Mathematics, mathematics in her book, she mostly Edible Exploration of recently published by Basic Books, does so at a pretty low level, and it the Mathematics of which is almost certainly the first is unlikely that many undergraduate Mathematics book ever written about baking and math students, let alone professional Eugenia Cheng category theory. mathematicians, will gain new Basic Books, 2015, 288 pages, Yes, you read that right. Baking mathematical insights from the Hardcover, $27.50 and category theory. Cheng is a book. category theorist by training, but And although the meta-level Reviewed by Darren Glass she is also deeply interested in the ideas about the analogies between popularization of mathematics. ideas in cooking and ideas in f you think about it, mathematics In addition to a series of YouTube mathematics— as well as the more Iis really just one big analogy. For videos that she has made that give general thoughts about abstraction one example, the very concept of a semi-technical introduction to and mathematics—were interesting, the number three is drawing an category theory for mathematicians, I think most MAA members would analogy between a pile with three Cheng has gotten attention in the think them more suited to a short rocks, a collection of three books, media for articles she has written article rather than a 250-page book. and a plate with three carrots on it. about how to use math to make a But we are not the target audience For another, the idea of a group is perfect doughnut or to optimally for Cheng’s writing. drawing an analogy between adding combine jam, clotted cream, and Each chapter begins with a recipe, real numbers, multiplying matrices, scones. which Cheng then uses to motivate and many other mathematical How to Bake π is a book for the mathematics that follows. For structures. So much of what we general audiences. Although Cheng example, a chapter that discusses do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? It therefore isn’t all that surprising that mathematicians seem fond of using analogies to describe mathematics itself. A quick Google search will show that many words have been written describing how doing mathematics is similar to playing a musical instrument, going to the gym, learning a foreign language, falling in love, climbing a ladder to the moon, and eating ice cream. My personal favorite writing on this topic is an article from a 2003 issue of The Believer, in which Jordan Ellenberg describes how mathematics is analogous to mountain climbing but is not analogous to competitive hot dog eating. Eugenia Cheng’s analogy of choice is that mathematics is similar to baking, and she has written a book about this analogy titled How 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 29 mathematical generalizations begins and is very thoughtful about her give it to as a gift) and that most with a recipe that she developed for cooking, her mathematics, and her people would rather keep their Julia a gluten-free, dairy-free, sugar-free, expository writing, and as a reader I Child separate from their Saunders paleo-diet-compatible Olive Oil enjoyed seeing where she would go Mac Lane. Plum Cake. She writes that “it’s not next. really a cake—it’s a generalization of While the first two-thirds of the Darren Glass is an associate professor book introduces many different of mathematics at Gettysburg College. This is the best book topics in mathematics and discusses Although he likes to cook Mexican Cheng’s general philosophy of food and Indian food, he has never imaginable to introduce mathematics, the last third zeroes been a very good baker. This review people who don’t think in on category theory, which appeared originally in “MAA they are interested in Cheng describes as “the process of Reviews.” working out exactly which parts of mathematics at all to math are easy, and the process of some of the deep ideas of making as many parts of math easy The Proof and the as possible.” She describes category category theory, especially Pudding: What theory as being more about the Mathematicians, Cooks, if they like to bake. relationships between objects than and You Have in Common about the objects themselves, which Jim Henle (it probably won’t surprise you to Princeton University Press learn) she compares to the idea that 2015, 176 pages, Hardcover, $26.95 a lasagna is a certain relationship a cake. It has things in common between noodles, sauces, and cheese Reviewed by Joel Haack with a cake . . . but is still somehow despite the fact that your specific not quite the same as a cake.” The sauce recipes may be different from n the delightful book The chapter goes on to discuss how mine. IProof and the Pudding: What non-Euclidean geometries are She goes on to discuss various Mathematicians, Cooks, and You generalizations of the geometry notions of sameness, structure, Have in Common, author Jim that the reader is familiar with and and universal properties, and she Henle shares exactly that. Henle how our normal notions of distance manages to do so while keeping provides evidence, directed to the can be generalized to scenarios that the book quite readable and light “you,” who is not necessarily either mathematicians might think of as in tone even as the actual content a mathematician or a cook, that Hamming distances and taxicab gets increasingly technical. Again, the disciplines of mathematics metrics. I suspect that the lack of rigorous and cooking share a number Another chapter discusses how definitions or technical depth will of common traits, as do their some mathematics is created to solve probably leave most of you reading practitioners. There is no discussion a particular problem while other this review pretty unsatisfied with of applications of mathematics mathematics is developed on its Cheng’s book, but there are still to cooking (or for that matter, of own and applications are searched some very interesting expository cooking to mathematics). for after the fact. She refers to this as and philosophical ideas in the book. The book is neither a cookbook Internal-vs-External motivation and Put another way: This is the best nor a mathematics book. Rather, leans heavily on the analogy of how book imaginable to introduce it is a book about cooking and sometimes a chef goes shopping people who don’t think they are about mathematics. Yes, there are for ingredients for the recipe they interested in mathematics at all to mathematical ideas and problems want to cook and other times a dish some of the deep ideas of category presented, and recipes as well, but is developed to use the ingredients theory, especially if they like to bake. they are there to illustrate Henle’s one has in the pantry, such as the (Yes, Basic Books, you can use that points about the commonalities Chocolate and Prune Bread Pudding quote as a blurb.) in the two pursuits. I should say, she developed, whose recipe is However, I can’t help but feel that however, that the puzzles presented included in the book. Even from the target audience for this book is (typically made up or extended by these limited descriptions you can very small (in particular, I cannot Henle) and the recipes presented probably tell that Cheng truly enjoys think of a specific person I would (typically made up or extended by PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 Celebrating a Century of Advancing Mathematics Henle) are intriguing—the reader will want to grab a pencil and some mixing bowls and play along. So, what are some of these commonalities? Here is just one example. Both mathematicians and cooks have to be arrogant, initially. Having the attitude that The Mathematical Association of America (MAA) has one can solve a problem or create a century-old tradition of publishing highly regarded a dish is critical to even making mathematical expository books and journals that the attempt—on the mathematical educate and enlighten mathematicians. side, how often have we implored a student or friend to try something, And in our centennial year, it’s time to give ourselves arguing that she or he can in fact a proper name—MAA Press. make progress on a problem or puzzle? Similarly, many people are convinced they can’t make bread. Try it! This arrogance (or mock arrogance, or confidence) should CALCULUS AND ITS ORIGINS ITS AND CALCULUS in each case then be followed by MATHEMATICS MAGAZINE HEM doubt: Am I correct? How could MA AT T I IC CS CS S SM MA MA the solution be improved; how A AG could the bread be made better? Dave Perkins THE AMERICAN MATHEMATICAL MONTHLY By my (likely incomplete) count, Henle provides 29 commonalities THE COLLEGE MATHEMATICS JOURNAL Volume 88, No. 1, February 2015 1-90 (actually, I arrived at 30, but no one H NTHL EMA would believe that was an actual A ATI TI TIC Y ICS CS CS S J JO OU O count). He also admits that one U oue1 VolumeVo 1 Volume 122, No. 3, March 2015 could similarly link mathematics 2No 22 22, No. or cooking to most fields. I doubt, Volume 46, No. 1, January 2015 1-80 March 3 3, March though, that many of the other 2015 2015 comparisons would provide the same amount of fun! Henle stresses the pleasure and sheer joy of both cooking and mathematics. He does mention the practicality of each, in two chapters, though these two chapters together occupy a mere one and one-half pages. If you too are a mathematician because of how much fun mathematics is, and you would like to share your joy with Visit us at the MAA Pavilion in the exhibit hall during others in a way they might be able 0$$0DWK)HVWRUoQGXVRQOLQHDWmaa.org/publications. to understand your pleasure, give them this book. Joel Haack is professor of mathematics at the University of Northern Iowa. This review appeared in “MAA Reviews.” 31 Exploring the Heart of Calculus By Steve Kennedy his business of of learning mathematics. With Tteaching and that exposed as my philosophical learning mathematics bias, you will have no trouble 0$$%RRNV%HDW is harder and more understanding my enthusiasm for subtle than it seems. When I was Phil Anselone and John Lee’s The younger, I thought I could lead my Heart of Calculus: Explorations students to the promised land of and Applications. This book came mathematical enlightenment by together as a collection of exercises giving crystal-clear, enthusiastic assigned to students in Oregon lectures. Gradually I came to believe State’s honors calculus sequence. that my lectures were not providing Each of the book’s 16 chapters is an 3KLOLS0$QVHORQHDQG-RKQ:/HH understanding and that the only role extended exploration of a topic in The Heart of Calculus: Explorations they served, if I did a good job with calculus. Each ends with a themed and Applications, SS them, was to motivate the students collection of problems and project +DUGERXQG /LVW3ULFH to go home and do the hard mental ideas. 0HPEHU3ULFH work needed to figure out concepts Used as a text in a senior on their own. math-major capstone course, the (Essentially, the assumption that Once I started leaning this experience would give your students pi is rational allows you to build a way—students understand only a chance to look back at the material polynomial that, when integrated those things they discover for from the beginning of their math against the sine function, provably themselves—I was faced with the major from a more advanced yields an integer greater than zero central dilemma confronting every perspective. Or, you could pick and and less than one. All you really advocate of inquiry-based learning: choose challenging exercises and need to know is integration by parts How on earth can I get my students projects to really push your current and some more or less elementary to construct for themselves several calculus or ODE students. (That’s facts about polynomials.) Your centuries’ worth of collective my plan!) students are then invited to prove mathematical progress? Some examples: In a chapter meant that e and pi2 are irrational. My answer: Asking them to solve to supplement, or amplify, the There is a nice nonstandard really hard problems. multivariable calculus discussion discussion of the error in a Taylor I admit to being influenced by my of curvature, the authors describe series approximation. There are own teachers. As an undergraduate curvature in a very natural way as chapters on Newton’s method, the student in real analysis, I was asked the rate of turning of the tangent Buffon needle problem, and simple on a take-home examination to vector. (Their description provides harmonic motion. Also, you get prove that the set of real numbers in a nice unification of the 2D and 3D extensive and detailed discussions of the unit interval with no threes in cases.) Then they derive all the usual hanging cable and optimal location their decimal expansions is closed, formulas for curves in the plane problems and three chapters perfect, and totally disconnected. and in three-space. Students are devoted to celestial mechanics We had never seen the Cantor set. invited to explore some examples culminating in vector calculus I didn’t sleep for two days working in the problems or to retrace the proofs of Kepler’s laws. Your on that problem. But, a few days steps of Newton and Huygens, students can’t possibly fail to get later, when the instructor showed who, independently, discovered the excited by this. There is much here us the middle-thirds Cantor set, notion of curvature. to enrich your calculus classes and my understanding and engagement The very next chapter contains to challenge your students. was at a level I’ve rarely achieved. a beautiful exposition of Ivan That, and similar experiences, left an Niven’s supremely clever proof Steve Kennedy is senior acquisitions impression. that pi is irrational. If you’ve never editor at MAA. Contact him if you’re Struggling with challenging seen that proof, this is the clearest interested in writing a book for the problems seems to be the essence explanation I’ve ever come across. MAA, at [email protected]. PDDRUJSXEVIRFXVKWPOv-XQH-XO\v0$$)2&86 CAREERS at the NATIONAL SECURITY AGENCY Call for Nominations: Mary P. Dolciani Award he Mary P. Dolciani Award Trecognizes a pure or applied mathematician who is making a distinguished contribution to the mathematical education of K-16 students in the United States or Canada. This award is given annually at MAA MathFest. Nominations for the 2016 award should be sent by September 1, 2015, to the MAA Secretary, Barbara Faires, at secretary@maa. org. Guidelines for nominations and a nomination form can be found at the MAA website. A nominee must have received a PhD in pure or applied mathematics, have a record of published research in pure or applied mathematics, and have a record of distinguished EXTRAORDINARYWORK contributions to K-16 mathematics education. ,QVLGHRXUZDOOV\RX¶OO¿QGWKHPRVWH[WUDRUGLQDU\SHRSOHGRLQJ WKHPRVWH[WUDRUGLQDU\ZRUN,W¶VQRWMXVW¿QLWH¿HOGWKHRU\ GLVFUHWHPDWKHPDWLFVDOJRULWKPDQDO\VLVRUWKHRSSRUWXQLW\WR MAA Awards ZRUNIRUWKHFRXQWU\¶VODUJHVWHPSOR\HURIPDWKHPDWLFLDQV $OLVWRIWKHDZDUGVJLYHQE\WKH 0$$LVDWmaa.org/awards7KH ,W¶VDOORIWKHVHDQGPRUH±UROOHGXSLQWRDQRUJDQL]DWLRQWKDW¶V GHGLFDWHGWRDQH[WUDRUGLQDU\FDXVH±WKHVDIHW\DQGVHFXULW\RI DZDUGVLQFOXGHWKHVH $OGHU$ZDUG WKH8QLWHG6WDWHVRI$PHULFD Â$OOHQGRHUIHU$ZDUGÂ%HFNHQEDFK %RRN3UL]HÂ&HUWLILFDWHRI0HULWÂ &KDXYHQHW3UL]HÂ'ROFLDQL$ZDUG U.S. citizenship is required. NSA is an Equal Opportunity Employer. All applicants for employment are considered without Â(XOHU%RRN3UL]HÂ(YDQV$ZDUG regard to race, color, religion, sex, national origin, age, marital status, disability, sexual orientation, or status as a parent. Â+DOPRV)RUG$ZDUGÂ*XQJDQG +X$ZDUGIRU'LVWLQJXLVKHG6HUYLFH Â+DVVH3UL]HÂ+DLPR$ZDUGIRU 'LVWLQJXLVKHG7HDFKLQJÂ+HGULFN /HFWXUHVÂ+LJK6FKRRO6OLIIH$ZDUGV Â-DPHV5&/HLW]HO/HFWXUHÂ-3%0 &RPPXQLFDWLRQV$ZDUGÂ0$$1$0 'DYLG%ODFNZHOO/HFWXUHVÂ0HULWRUL Search NSA to Download RXV6HUYLFHÂ0RUJDQ3UL]HÂ3yO\D WHERE INTELLIGENCE GOES TO WORK® $ZDUGÂ3yO\D/HFWXUHVÂ3XWQDPÂ 5REELQV3UL]HÂ6HOGHQ$ZDUG 33 Can You Identify These People? By Carol Mead t has been awhile since I last asked for your Carol Mead is the archivist for the Archives of American Ihelp in identifying people in photographs Mathematics, located in the Research and Collections from the Paul Halmos Photograph Collection. division of the Dolph Briscoe Center for American History $UFKLYHV6SRWOLJKW Here are four more photos of people for you to on the University of Texas at Austin campus. Contact her identify. Thank you for your responses! With your help, by email (FDUROPHDG#DXVWLQXWH[DVHGX) or by phone the collection is closer than ever to being complete. (512-495-4539). 4320: Halmos snapped this photograph in Tel Aviv in 3828: Halmos wrote “Razak” on the back as well as May 1985. He noted the man on the left as “Jakimowski” “March 1983, Bloomington.” I assume it is at the and the one on the right as Juday Eisenberg (Dean). Do University of Indiana at Bloomington. Do you recognize you know Jakimowski’s first name? the man? 3728: This is “Williams” at Oberwolfach in August 1980. 3357: One of these men is another “Williams,” while There are many people named Williams—do you know the other two are, I believe, James E. Brennan and Lee which one this is? Albert Rubel. Can you help me identify who is who? PDDRUJSXEVIRFXVKWPOv-XQH-XO\v0$$)2&86 A MERICAN MATHEMATICAL SOCIETY Search for an Executive Director for the American Mathematical Society Position The Trustees of the American Mathematical Society seek candidates for the position of Executive Director of the Society to replace Dr. Donald McClure, who plans to retire in the summer of 2016. This position offers the appropriate candidate the opportunity to have a strong positive infl uence on all activities of the Society, as well as the responsibility of overseeing a large, complex, and diverse spectrum of people, publications, and budgets. The desired starting date is July 1, 2016. Duties and terms of appointment The American Mathematical Society, with headquarters in Providence, RI, is the oldest scientifi c organization of mathe- maticians in the U.S. The Society’s activities are mainly directed toward the promotion and dissemination of mathematical research and scholarship, broadly defi ned; the improvement of mathematical education at all levels; increasing the apprecia- tion and awareness by the general public of the role of mathematics in our society; and advancing the professional status of mathematicians. These aims are pursued mainly through an active program of publications, meetings, and conferences. The Society is a major publisher of mathematical books and journals, including MathSciNet, an organizer of numerous meetings and conferences each year, and a leading provider of electronic information in the mathematical sciences. The Society maintains a Washington offi ce for purposes of advocacy and to improve interaction with federal agencies. The Executive Director is the principal executive offi cer of the Society and is responsible for the execution and adminis- tration of the policies of the Society as approved by the Board of Trustees and by the Council. The Executive Director is a full-time employee of the Society appointed by the Trustees and is responsible for the operation of the Society’s offi ces in Providence and Pawtucket, RI; Ann Arbor, MI; and Washington, DC. The Executive Director is an ex-offi cio member of the policy committees of the Society and is often called upon to represent the Society in its dealings with other scientifi c and scholarly bodies. The Society employs a staff of about 200 in the four offi ces. The directors of the various divisions report directly to the Executive Director. A major part of the Society’s budget is related to publications. Almost all operations (including the printing) of the publications program are done in-house. Information about the operations and fi nances of the Society can be found in its Annual Reports, available at www.ams.org/annual-reports. The Executive Director serves at the pleasure of the Trustees. The terms of appointment, salary, and benefi ts will be consistent with the nature and responsibilities of the position and will be determined by mutual agreement between the Trustees and the prospective appointee. Qualifi cations Candidates for the offi ce of Executive Director should have a Ph.D. (or equivalent) in mathematics, published research beyond the Ph.D., and signifi cant administrative experience. The position calls for interaction with the staff, membership, and patrons of the Society as well as leaders of other scientifi c societies and publishing houses; thus leadership, communica- tion skills, and diplomacy are prime requisites. Applications A search committee chaired by Robert Bryant ([email protected]) and Ruth Charney ([email protected]) has been formed to seek and review applications. All communication with the committee will be held in confi dence. Sugges- tions of suitable candidates are most welcome. Applicants can submit a CV and letter of interest to: Executive Director Search Committee c/o Carla D. Savage Secretary, American Mathematical Society Department of Computer Science North Carolina State University Raleigh, NC 27695-8206 [email protected] The American Mathematical Society is an Affi rmative Action/Equal Opportunity Employer. 35 Call for MAA Papers: 2016 Joint Mathematics Meetings January 6–9, Seattle, Washington he MAA Committee on Contri- Topics and Techniques for Tbuted Paper Sessions is soliciting Teaching Real Analysis contributed papers pertinent to the Wednesday (1/6) afternoon sessions listed below. Contributed Real analysis is a core component paper session presentations are of the mathematics program. It has limited to 15 minutes, except in the traditionally been considered difficult general session where they are limited for students, but is also challenging to to 10 minutes. teach since the student body can be Please note that the dates and times diverse and there are many choices scheduled for these sessions remain in subject matter. Students may end tentative. up applying their knowledge of real The deadline for submission of analysis in differential equations, abstracts is Tuesday, September 22. functional analysis, probability, even economics and physics. There are CONTRIBUTED PAPER many exciting topics that can be SESSIONS WITH THEMES covered and many possible strategies for success. Speakers at this session Experiences and Innovations in can present topics that could be Teaching Probability Theory added to real analysis courses and Wednesday (1/6) morning can discuss improved presentation We invite papers and scholarly techniques of traditional topics. presentations on improving the Organizers: Erik Talvila, University teaching of probability theory, at of the Fraser Valley; Paul Musial, the undergraduate or beginning Chicago State University; Robert graduate level, by innovative methods. Vallin, Lamar University; and James Possible topics could include Peterson, Alma College. inquiry-based learning, projects, mathematical writing, real-world Using Philosophy to Teach applications, connections to other Mathematics areas of mathematics, integration of Thursday (1/7) morning technology, or simulation. Courses in the philosophy The focus of this session will be on of mathematics are rare, but the teaching of probability theory (the philosophical questions frequently construction, analysis, and theoretical arise in the regular curriculum, often properties of probabilistic models) presenting difficulties to teachers rather than statistics or data analysis. who haven’t prepared to respond Reports on student outcomes, to them. In recent years a growing either anecdotal or empirical, are number of teachers of mathematics encouraged. are discovering that addressing Organizers: Jonathon Peterson, philosophical issues deliberately in Purdue University; and Nathaniel their courses not only eases the strain Eldredge, University of Northern but also enhances students’ ability to SEATTLE MUNICIPAL ARCHIVES MUNICIPAL SEATTLE Colorado grasp difficult mathematical concepts. An upcoming MAA Notes volume, Using the Philosophy of Mathematics in Teaching Collegiate Mathematics, PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 36 illustrates the ways a wide variety (2) Partner with K-12 educators to ODEs course; and (4) descriptions of of teachers have found to introduce focus on the implications related to applications or nonstandard topics philosophical questions as an the assessments (such as PARCC and and how such topics can lead to exciting part of presenting standard Smarter Balanced) being used; student engagement and interest. mathematical material. This session (3) Discuss changes mathematics Organizers: Christopher S. invites teachers at all levels to discuss departments have made to their Goodrich, Creighton Preparatory ways they have found to include programs implementing the CCSS School; and Beverly H. West, Cornell philosophy in the mathematics and assessments for the mathematical University classroom. Papers on other topics in education of teachers, or Sponsor: Community of Ordinary the philosophy of mathematics will be Differential Equations Educators considered as time permits. (4) Discuss departmental initiatives (CODEE) Organizers: Carl Behrens, to ensure a smooth transition from Alexandria, Virginia; and Dan school to higher education in light of Innovative and Effective Ways to Sloughter, Furman University the CCSS and associated assessments. Teach Linear Algebra Sponsor: POM SIGMAA Organizers: William Martin, North Friday (1/8) afternoon Dakota State University; Karen Linear algebra is one of the most Common Core State Standards Morgan, New Jersey City University; interesting and useful areas of (CCSS) for Mathematics Practices Gulden Karakok, University of mathematics because of its beautiful and Content: The Role of Math Northern Colorado; and James A. and multifaceted theory, as well as for Departments in Preparing Math Mendoza Epperson, University of the enormous importance it plays in Education Candidates for New Texas at Arlington understanding and solving many real- Assessments Sponsors: MAA Committee on the world problems. Consequently, many Thursday (1/7) afternoon Mathematical Education of Teachers valuable and creative ways to teach its The Common Core State Standards (COMET) and the MAA Committee rich theory and its many applications for Mathematics have been widely on Assessment are continually being developed and adopted and implemented nationally. refined. Mathematics departments share The Teaching and Learning This session will serve as a forum responsibility with teacher education of Undergraduate Ordinary in which to share and discuss new programs to prepare future teachers Differential Equations or improved teaching ideas and to meet content and, especially, Friday (1/8) morning approaches. These innovative and mathematical practices standards. The teaching of undergraduate effective ways to teach linear algebra Mathematics faculty also collaborate ordinary differential equations include, but are not necessarily limited with the K-12 system to ensure a (ODEs) provides a unique way to to: (1) hands-on, in-class demos; smooth transition from school to introduce students to the beauty (2) effective use of technology, such higher education, one of the primary and applicative power of calculus. as Matlab, Maple, Mathematica, Java purposes of the CCSS. ODEs are also rich with aesthetically Applets, or Flash; (3) interesting and This session seeks reports of pleasing theory, which often can be enlightening connections between mathematics faculty experiences with communicated visually and explored ideas that arise in linear algebra and their department’s implementation of numerically. ideas in other mathematical branches; the CCSS mathematics standards with This session will feature talks that (4) interesting and compelling a focus on the requirements of new describe innovative teaching in the examples and problems involving assessments. We invite contributed ODEs course as well as the description particular ideas being taught; papers describing efforts, including of either projects or pedagogy that (5) comparing and contrasting evidence of their impact, that can be used to engage students in visual (geometric) and more abstract (1) Investigate how well their math their study of ODEs. Successful (algebraic) explanations of specific education candidates are prepared contributions could include but ideas; (6) other novel and useful with the knowledge and skills are not limited to: (1) innovative approaches or pedagogical tools. necessary to assess that their students ways of teaching standard topics in Organizers: David Strong, meet the CCSS for mathematics the ODEs course; (2) strategies for Pepperdine University; Gil Strang, content and practices; teaching both differential equations MIT; and Megan Wawro, Virginia and linear algebra simultaneously; Tech (3) the inclusion of technology in the 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 37 Helping Students See beyond MAA; Courtney Davis, Pepperdine Teacher Educators (AMTE) created Calculus University; and Angela Spalsbury, a set of Standards for Elementary Saturday (1/9) afternoon Youngstown State University Mathematics Specialists (DPWHQHW We need more and better-educated Sponsor: SIGMAA TAHSM SXEOLFDWLRQV) to encourage states to mathematics and science students. address the urgent need to increase Too many high school and beginning Mathematics and Sports the mathematical knowledge and college students think of mathematics Saturday (1/9) morning expertise of elementary school merely as calculus and the topics The expanding availability of staff by establishing an elementary leading to it. Many talented and play-by-play statistics and video- mathematics specialist license, promising students lose interest based spatial data for professional certificate, or endorsement. in mathematics—some never take and some collegiate sports is leading Elementary mathematics specialists a single math class in college, and to innovative kinds of research, are teachers, teacher leaders, or some drop out of the math major using techniques from various areas coaches who are responsible for soon after beginning—because they of the mathematical sciences. By supporting effective mathematics are never exposed to the beauty and modeling the outcome distributions instruction and student learning at usefulness of the many other areas of in certain situations, researchers the classroom, school, district, or state mathematics. Students—and society— can develop new metrics for player level. would immensely benefit from the or team performance in various Recently some institutions have students’ being exposed to other areas aspects of a sport, comparing actual begun degree or certificate programs of mathematics before leaving high results to expected values. Such to educate these elementary school or during their first semesters work often has implications for mathematics specialists. Papers will in college. strategic game management and report on the preparation, placement, Papers submitted for this personnel evaluation. Classic areas and support of mathematics session should describe classroom of study, such as tournament design, specialists in the elementary grades as presentations and materials that ranking methodology, forecasting well as on the development of degree provide students with the exposure performance, insight into rare or or certificate programs to educate described above. Such classroom record events, and physics-based these mathematics specialists. Papers presentations and materials should be analysis, also remain of interest. may describe programs to prepare t An introduction to a specific This session will include pre-service or in-service teachers mathematical idea or application; presentations of original research to become elementary mathematics and expository talks; topics related specialists, or they may describe t Accessible to high school or early- to the use of sports applications in efforts with school districts to create college-level students; curriculum are welcome. With a t Self-contained (including broad audience in mind, all talks information on how to most are requested to be accessible to effectively use the presentation or mathematics majors. Undergraduates materials); and their mentors are particularly encouraged to submit abstracts for t Composed of PowerPoints, video consideration. or audio clips, online or printed Organizers: Drew Pasteur, College handouts, materials or tools for of Wooster; and John David, Virginia experimentation and visualization, Military Institute and so on; and t Interesting, entertaining, and Preparation, Placement, possibly captivating. and Support of Elementary The organizers hope that Mathematics Specialists speakers will make their classroom Thursday (1/7) morning presentations available online (on Over the last decade, there have their own websites) for use by other been numerous calls for the use educators. of mathematics specialists in Organizers: David Strong, elementary and middle schools. In TIM THOMPSON/VISITSEATTLE.ORG TIM Pepperdine University; James Tanton, 2013, the Association of Mathematics PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 38 positions and support for these Organizers: Timothy Comar, often-underrepresented audiences. specialists. Reports on the successful Benedictine University; and Daniel Talks are also invited that describe installation and implementation of Hrozencik, Chicago State University the lasting impact of math circles on elementary mathematics specialists Sponsor: SIGMAA BIO, the various audiences; for example, talks are also welcome. Papers should SIGMAA on Mathematical and that describe how math circles affected include evidence of success or the Computational Biology you as a young mathematician are potential for application to other welcome. institutions or districts. Mathematics and the Arts Organizers: Katherine Morrison, Organizers: Laurie J. Burton, Wednesday (1/6) morning and University of Northern Colorado; and Western Oregon University; Cheryl afternoon Philip Yasskin, Texas A&M University Beaver, Western Oregon University; Presentations exploring connections Sponsor: SIGMAA MCST, the and Klay Kruczek, Southern between mathematics and the arts SIGMAA on Math Circles for Connecticut State University are invited from any of various Students and Teachers Sponsor: MAA Committee on the perspectives, including mathematical Mathematical Education of Teachers aspects of traditional art, Mathematics Experiences and (COMET) mathematical topics represented by Projects in Business, Industry, and or incorporated into art, and artistic Government Trends in Undergraduate and aesthetic aspects of mathematical Friday (1/8) afternoon Mathematical Biology Education topics. All artistic areas are welcome: The MAA Business, Industry, and Friday (1/8) morning visual, poetical, dramatic, musical, Government Special Interest Group Several recent reports emphasize literary, dance, fiber arts, and so forth. (BIG SIGMAA) provides resources that aspects of biological research are Practitioners from anywhere along the and a forum for mathematicians becoming more quantitative and that spectrum of math and the arts, as well working in business, industry, and life science students, including premed as educators with experience at this government (BIG) to advance the students, should be introduced to intersection, are invited to report on mathematics profession by making a greater array of mathematical, their experiences, whether primarily connections, building partnerships, statistical, and computational artistic, mathematical, pedagogical, or and sharing ideas. BIG SIGMAA techniques and to the integration of blended. consists of mathematicians in BIG mathematics and biological content at Organizer: Douglas Norton, as well as faculty and students in the undergraduate level. Mathematics Villanova University academia who are working on majors also benefit from coursework Sponsor: SIGMAA ARTS, the BIG problems. Mathematicians, at the intersection of mathematics and SIGMAA on Mathematics and the including those in academia, with biology because there are interesting, Arts BIG experience are invited to present approachable research problems, papers or discuss projects involving and mathematics students need to be The Broad Impact of Math Circles the application of mathematics to BIG trained to collaborate with scientists Thursday (1/7) afternoon problems. in other disciplines, particularly A mathematics circle is an The goal of this contributed paper biology. enrichment activity for K-12 students session is to provide a venue for Topics may include scholarly work or their teachers, which brings them mathematicians with experience in addressing the issues related to the into direct contact with mathematics business, industry, and government design of effective biomathematics professionals, fostering a passion and to share projects and mathematical course content, courses, and excitement for deep mathematics in ideas in this regard. Anyone curricula; the integration of biology the participants. Math circles provide interested in learning more about BIG into mathematics courses, student a unique opportunity to reach a wide practitioners, projects, and issues will recruitment efforts, the gearing of variety of audiences and have a lasting find this session of interest. content toward premed students, impact. Organizers: Carla D. Martin, undergraduate research projects, This session is focused on how Department of Defense; and Allen effective use of technology in bio- math circles have served this Butler, Wagner Associates mathematics courses, preparation for variety of populations and the Sponsor: BIG SIGMAA, the graduate work in biomathematics and effect of this service. Talks are SIGMAA on Business, Industry, and computational biology or for medical invited that address how math Government careers, and assessment issues. circles have served nonstandard or 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 39 Incorporating the History of Mathematics into Developmental Math Courses Saturday (1/9) morning Developmental math courses and courses prerequisite to the calculus sequence such as college algebra and precalculus are challenging for many students. By incorporating the history of mathematics into these courses, a deeper level of understanding and interest may be achieved. This session seeks papers that offer ideas for incorporating the history of mathematics (generally or specifically) JMM 2015 Exhibit Hall. into these courses. Organizers: Van Herd, University The Scholarship of Teaching indicate the type of evidence that of Texas at Austin; and Amy Shell- and Learning in Collegiate has been gathered and will be Gellasch, Montgomery College Mathematics presented. For example, papers might Sponsor: HOM SIGMAA Wednesday (1/6) morning and reference student work, participation afternoon or retention data, pre/post tests, Integrating Research into the In the scholarship of teaching and interviews, surveys, think-alouds, and Undergraduate Classroom learning, faculty bring disciplinary so on. Saturday (1/9) afternoon knowledge to bear on questions Organizers: Jacqueline Dewar, Undergraduate research is a of teaching and learning and Loyola Marymount University; high-impact practice that inspires systematically gather evidence to Thomas Banchoff, Brown University; student learning, builds crucial skills, support their conclusions. Work in Curtis Bennett, Loyola Marymount boosts retention and graduation this area includes investigations of the University; Pam Crawford, rates, and particularly benefits effectiveness of pedagogical methods, Jacksonville University; and Edwin underrepresented and at-risk students. assignments, or technology, as well as Herman, University of Wisconsin– Although students often engage in probes of student understanding. Stevens Point undergraduate research outside of The goals of this session are to the classroom, incorporating research (1) feature scholarly work focused The Contributions of Minorities to projects into the classroom can bring on the teaching of postsecondary Mathematics throughout History this impactful experience to even mathematics; (2) provide a venue for Friday (1/8) morning more students. teaching mathematicians to make The history of mathematics is This session will focus on public their scholarly investigations filled with inspiring stories of incorporating research into the into teaching/learning; and (3) mathematicians. This session will undergraduate classroom, from highlight evidence-based arguments focus on the stories of minority introductory to upper-level for the value of teaching innovations mathematicians (people of color, mathematics courses. Presentations or in support of new insights into native peoples, women, and other may describe a particular research student learning. Appropriate for peoples historically underrepresented project or activity, faculty experiences this session are preliminary or final in mathematics) of the distant and in mentoring undergraduate reports of postsecondary classroom- not-so-distant past and the impact research in the classroom, or student based investigations of teaching they have had on mathematics and its experiences and feedback. All talks methods, student learning difficulties, teaching. should emphasize why the project(s) curricular assessment, or insights Organizers: Amy Shell-Gellasch, being discussed is considered into student (mis)understandings. Montgomery College; and Lloyd undergraduate research rather than Abstract submissions should have Douglas, University of North Carolina a typical assignment. Participants are a clearly stated question that was or Sponsor: HOM SIGMAA encouraged to share the impact on the L. McHUGH is under investigation and should students involved if possible. PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 COME FOR THE MATH. STAY FOR THE STORIES. Visit QuantaMagazine.org for the latest developments in mathematics, theoretical physics and the life sciences. illuminating science MAGAZINE An editorially independent publication of the Simons Foundation 41 Organizers: Shannon R. Lockard, Modeling Across the Curriculum students’ mathematical cognition Bridgewater State University; Report emphasize the value in and reasoning, teaching practice and Timothy B. Flowers, Indiana teaching mathematical modeling as in inquiry- oriented mathematics University of Pennsylvania a dynamic problem-solving process. classrooms, design of research-based In addition to courses specifically curricular materials, and professional Graduate Students Teach Too: dedicated to mathematical modeling development of mathematics teachers, Ideas and Best Practices and applied mathematics, many with intention to support and advance Saturday (1/9) morning undergraduate mathematics programs college students’ mathematical Graduate teaching assistants have made an effort to infuse thinking and activities. (GTAs) make up a nontrivial portion modeling into courses across their The presentation should report of the teaching workforce at many existing curriculum. results of completed research that universities. Though their duties vary, This session welcomes papers builds on the existing literature most are responsible for teaching concerning best practices, useful in mathematics education and introductory general education examples, or effective strategies in the employs contemporary educational courses in some capacity. In fact, design and teaching of undergraduate theories of the teaching and learning a 2010 AMS survey of four-year courses in which mathematical of mathematics. The research colleges and universities suggests that modeling makes up a significant should use well-established or roughly 8 percent of introductory activity or core learning objective. innovative methodologies (e.g., math courses (15 percent for Collectively, the papers presented in design experiment, classroom statistics) are taught fully by graduate this session will represent applications teaching experiment, and clinical students. This responsibility may of mathematics to a broad range of interview, with rigorous analytic seem straightforward at first glance; fields. methods) as they pertain to the however, there is a growing movement Organizers: Jason Douma, study of undergraduate mathematics toward accountability for general University of Sioux Falls; and Rachel education. We also welcome education outcomes in such courses. Levy, Harvey Mudd College preliminary reports on research Students in these classes deserve a Sponsors: MAA CUPM projects in early stages of development positive, engaging experience—one Mathematics across the Disciplines or execution. that not only permits them to take Subcommittee and the SIAM Organizer: Karen A. Keene, North future math courses (if desired), but Education Committee Carolina State University also fosters gains in numeracy. In light Sponsor: SIGMAA on RUME of a GTA’s workload and background, Research in Undergraduate such an experience can be challenging Mathematics Education Origami in the Mathematics K-12 to create. Thursday (1/7) morning and Classroom This session is designed to encourage afternoon Saturday (1/9) afternoon dialogue among both graduate This session presents research Programs that take advantage of programs and graduate instructors. reports on undergraduate paper folding to teach mathematics Talks might include reports on mathematics education. The session are thriving in many parts of the innovative preparation methods will feature research in a number of world. Presenters in this session will for new instructors, accountability mathematical areas including calculus, describe their innovative strategies for measures for GTAs, means for linear algebra, advanced calculus, exploring mathematics in the K-12 infusing quantitative literacy into abstract algebra, and mathematical classroom and/or with future/in- GTA-led courses, as well as novel proof. The goals of this session service teachers using paper folding/ ideas or reports from graduate are to foster high-quality research origami as the means to reach the students themselves. in undergraduate mathematics goals established by the Common Organizer: Samuel L. Tunstall, education, to disseminate well- Core. The focus of the session will be Michigan State University designed educational studies to the on rich mathematical explorations greater mathematics community, that are based on or enhanced by Mathematical Modeling in the and to transform theoretical work paper folding. Presentations are Undergraduate Curriculum into practical consequences in expected to be scholarly. Saturday (1/9) morning college mathematics. Examples Organizers: Roger Alperin, San Jose Both the MAA’s 2015 CUPM of such types of research include State University; and Perla Myers, Curriculum Guide and SIAM’s rigorous and scientific studies about University of San Diego PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 42 Contemplative Pedagogy and are coming to the forefront. This be accepted. Papers that provide Mathematics session invites presenters to describe insights on the following questions Friday (1/8) afternoon innovative methods of assessment are explicitly invited: requirements Contemplative pedagogy aims with which they have experimented for K-12 that affect collegiate-level to incorporate contemplative/ in the attempt to accurately reflect QL, QL requirements for two-year introspective practices into the the diversity of ways students learn colleges, the distinction between classroom in order to deepen the and understand course material. K-12 quantitative literacy standards educational experience. Students are Presenters should focus on practical and collegiate quantitative literacy challenged to engage more fully with issues of implementation and discuss standards, and the impact of changing the material and their experience of the level of success of the method in requirements at the K-12 and two- learning. Common techniques include the college classroom. Presenters may year schools on four-year school in-class mindfulness activities, deep also share methods to determine the curricula. listening or dialoguing, journaling, validity of their assessments, advice Organizers: Aaron Montgomery, and beholding. As more and more for others looking to implement or Central Washington University; Gary data comes in showing the efficacy create alternative assessment methods, Franchy, Southwestern Michigan and benefits of such practices in all or how these methods can help College; Gizem Karaali, Pomona aspects of life, the Contemplative instructors evaluate the effectiveness College; Andrew Miller, Belmont Education movement has been of a nontraditional classroom. University; and Victor Piercey, Ferris gaining momentum, strengthening Organizers: David Clark, Grand State University connections with established Valley State University; Jane Sponsor: SIGMAA QL good pedagogy, and expanding to Butterfield, University of Victoria; departments outside the humanities Robert Campbell, College of St. Innovative Approaches to One- and social sciences. This contributed Benedict and St. John’s University; Semester Calculus Courses paper session solicits presentations and Cassie Williams, James Madison Thursday (1/7) morning from college-level educators with University Students who major in such fields hands-on experience of contemplative as agriculture, architecture, biology, pedagogy or contemplative practices. Quantitative Literacy in the K-16 business, economics, and liberal arts We welcome reports on successful, Curriculum and human sciences often take a one- or unsuccessful, attempts at Wednesday (1/6) afternoon semester, terminal calculus course contemplative pedagogy, whether Because of its nature, quantitative with a focus on applications. One anecdotal or systematic. We also invite literacy (QL) is referenced at almost approach to these courses involves educators with personal out-of-class all levels of the educational system. focused, targeted versions of calculus, contemplative practices, to reflect on Traditional mathematical topics such such as applied calculus, business how that practice has informed their as calculus have relatively well-defined calculus, or calculus for the life teaching. prerequisites and outcomes and an sciences. Some schools cannot offer Organizers: Luke Wolcott, Lawrence established location in the traditional a wide range of calculus courses and University; and Justin Brody, Goucher mathematical curriculum sequence. must design a single course to meet College Quantitative literacy typically the needs of these students. involves the use of a wide variety of This session invites presenters to Assessing Student Learning: precollegiate mathematics to enable share innovative course designs for Alternative Approaches a deeper understanding within a a one-semester calculus course for Wednesday (1/6) morning nonmathematical context. As a result, students interested in a variety of Assessment is central to determining changing requirements for K-12 disciplines, particularly those that a student’s level of mastery, yet mathematics can have a significant involve mathematical modeling. traditional methods of assessment impact on what we do at the collegiate Presenters are expected to report their (such as exams, quizzes, and level. course design, how it meets the needs homework) may not accurately Papers in this session will focus of students, and evidence for the and robustly measure student on the interface between the K-12 effectiveness of their approach. understanding. With the recent curriculum and collegiate quantitative Organizers: Joel Kilty and Alex M. increase in the popularity of non- literacy. Given the breadth of this McAllister, Centre College lecture-based course structures, area, it is expected that papers with techniques that assess deeper learning a variety of different focuses will 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 43 Conversations with the Partner programs. Talks should identity the during a class visit; students may serve Disciplines: Collaborations research basis for curricular change as consultants to a community-based to Improve the Mathematics such as on-campus conversations, organization; or course meetings can Curriculum the Curriculum Foundations take place on-site in the community, Saturday (1/9) afternoon Project, or other professional reports to name a few. The undergraduate mathematics or guidelines. Talks illustrating Proposals for this session should curriculum is an essential component successful models for collaboration describe collaborations between of the education of future scientists, or interdisciplinary courses/programs mathematics courses (or programs) health professionals, engineers, developed from these partnerships and community members or computer scientists, business are also welcome. Projects renewing organizations. These collaborations professionals, and social scientists; and mathematics courses in the first two should be more than simple attempts it supports the quantitative education years of the undergraduate curriculum to “fix” the communities and should of all students. Understanding and are especially encouraged. Papers view communities as sources of adapting to the evolving needs of from the session may be considered knowledge rather than as deficient. the partner disciplines is critical for a special issue of PRIMUS. All proposals must provide rich to maintaining a vital and relevant Sponsors: Curriculum Renewal descriptions of the collaboration mathematics curriculum. The 2013 Across the First Two Years (CRAFTY) and the mathematics learning that NRC report The Mathematical Sciences and Mathematics Across the took place, and they should provide in 2025 revealed that “the educational Disciplines (MAD) subcommittees evidence of the impact that the offerings of typical departments in of CUPM and the journal PRIMUS: collaboration had on participants, the mathematical sciences have not Problems, Resources, and Issues in both students and community kept pace with the changes in how Undergraduate Mathematics Studies members (if applicable). Accounts of the mathematical sciences are used” Organizers: Victor Piercey, Ferris internships will also be considered. and that a “community-wide effort State University; Suzanne I. Doree, Organizer: Ksenija Simic-Muller, is needed . . . to make undergraduate Augsburg College; Jason Douma, Pacific Lutheran University courses more compelling to students University of Sioux Falls; and Susan and better aligned with the needs of Ganter, East Carolina University Innovative Targeted Solutions in user departments.” One national effort Teaching Introductory Statistics to improve such communication over Bringing the Community into the Thursday (1/7) afternoon the past decade has been the MAA’s College Mathematics Classroom Statistics is a very rapidly growing Curriculum Foundations Project: Thursday (1/7) afternoon field and enrollments in introductory Voices of the Partner Disciplines. Colleges and universities are statistics courses are expanding. This session presents successful often involved in the surrounding The 2015 MAACurriculum Guide collaborations with partner disciplines communities, typically through recommends that all math majors to revise mathematics courses or partnerships and outreach. But how learn effective data analysis. This often are communities present in is also a time of great innovation college classrooms, in particular in and change in the way Introductory mathematics classrooms? This session Statistics is taught. This session is concerned with collaborations invites papers on successful methods between universities and the used in Intro Stats. These methods communities they serve that enhance can range from an innovative full- student mathematical learning, course curriculum overhaul to a while also building stronger ties with single effective in-class activity. All individuals and organizations in these papers should provide participants communities. Such collaborations can with a clear take-away idea for use in happen in any mathematics course, Introductory Statistics. from liberal arts mathematics to the Organizers: Patti Frazer Lock, St. capstone; they can be implemented Lawrence University; Randall Pruim, at any level, of an individual course Calvin College; and Sue Schou, Idaho or program-wide; and they can take State University many forms. For example, community Sponsor: SIGMAA on Statistics JMM Employment Center. members may share their expertise Education PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 44 New Ideas in Teaching Upper- making discrete mathematics courses to Proofs–style course. This kind Level Statistics Courses more meaningful to all students of course is not currently offered in Friday (1/8) afternoon is through the use of technology, most two-year college mathematics Much attention has been paid especially as computer software programs. We invite faculty from two- recently to improving student becomes more freely available (e.g., and four-year institutions to share learning in the introductory statistics SAGE or Wolfram Alpha) and easier t*OUSPEVDUJPOUP1SPPGTBOE course. This session is focused on the to use (e.g., newer versions of Maple Mathematical Reasoning courses rest of the undergraduate statistics and Mathematica). Other approaches for students who have had a year curriculum. include meaningful projects and of calculus and intend to take We invite submissions that provide activities.For this session, we invite upper-division mathematics courses details about innovative learning proposals that describe an activity, especially as taught to students in activities, technologies, resources, problem, assignment, or project two-year colleges; or teaching methods that have that advanced the knowledge and been used effectively in Stat II, engagement of students enrolled t.FUIPETPGJOUFHSBUJOHUIF mathematical statistics, or other in a discrete mathematics course. teaching and practice of proof-writing statistics courses beyond the intro Descriptions of entire courses are also for mathematics majors into standard stat course. Submissions may range welcome. Although we are especially first- and second-year mathematics from single effective activities used interested in proposals about courses courses; or in these courses to major curricular that simultaneously serve computer t$PMMBCPSBUJWFFČPSUTCFUXFFOUXP revisions or completely new courses. science and mathematics majors by and four-year institutions to create or We welcome submissions that include implementing computer software or facilitate transfer of Introduction to partnerships with other disciplines. programming, proposals describing Proof and Mathematical Reasoning Presentations should explicitly address other innovative approaches to courses or course equivalents. the objectives and effectiveness of the teaching discrete mathematics in described activities. general will also be considered. Talks Organizers: Joanne Peeples, El Paso Organizers: Patti Frazer Lock, St. in this session should also describe Community College; Chris Oehrlein, Lawrence University; Randall Pruim, outcomes, giving evidence of the Oklahoma City Community College; Calvin College; and Sue Schou, Idaho success of the intervention. and Dean Gooch, Santa Rosa Junior State University Organizers: Ksenija Simic-Muller, College Sponsor: SIGMAA on Statistics Pacific Lutheran University; and Tom Sponsor: MAA Committee on Two- Education J. Edgar, Pacific Lutheran University Year Colleges Addressing the Needs of Proofs and Mathematical Professional Development for Mathematics and Computer Reasoning in the First Two Years Mathematicians: A Contributed Science Majors in Discrete of College Paper Session for MAA PREP Mathematics Courses Wednesday (1/6) morning Organizers and Participants Saturday (1/9) afternoon As more students begin their college Wednesday (1/6) afternoon The needs of mathematics and education at a two-year college before MAA has supported professional computer science majors in discrete transferring to a bachelor’s degree development activities that mathematics courses differ: Although program, it is increasingly important have enhanced the mathematics a proof-based approach is typically to ensure that students choosing to profession through the PRofessional desired for mathematics majors, major in mathematics are adequately Enhancement Program (MAA PREP), computer science majors need to prepared for the rigor of advanced funded by the National Science understand the connection between mathematics courses. In particular, Foundation. A variety of professional the mathematics and concepts they they will need to read, comprehend, development workshops have been encounter in computer science and write proofs. Most standard conducted under the MAA PREP coursework. Yet all students can calculus sequences do not or cannot umbrella, and it would be beneficial benefit from both approaches: provide the needed preparation for workshop organizations and computer science majors from more because they must serve a significantly participants to share their experiences mathematical rigor, and mathematics diverse set of majors. Therefore, and insights. This session will provide majors from more programming many bachelor degree programs in a venue for organizers to share their applications. One possible approach to mathematics require an Introduction ideas with one another and for 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO 45 Seattle Central Library. Submissions by undergraduates or examples of the use of the material in the undergraduate classroom are encouraged. Organizers: Paul R. Coe, Sara B. Quinn, and Marion Weedermann, Dominican University Revitalizing Complex Analysis Saturday (1/9) morning Complex analysis, despite its beauty and power, seems to have lost some of the prominence it once enjoyed in undergraduate mathematics, science, and engineering. Thanks to funding from NSF, a national dialogue has begun with the intention of remedying this situation. Two sessions at the 2015 San Antonio JMM focused on participants to share their experiences. effective and important for teaching suggestions for curricular reform from Organizers: Jon Scott, Montgomery mathematics and for fostering positive a variety of perspectives: modifying College; Barbara Edwards, Oregon attitudes toward the subject. the traditional course to include more State University; Nancy Hastings, This session invites scholarly modern ideas; including modules Dickinson College; and Stan presentations on the use of inquiry- suitable for student investigation; Yoshinobu, Cal Poly San Luis Obispo based methods for teaching and and instituting a transitions course Sponsor: MAA Committee on learning. We especially invite containing a meaty component of Professional Development presentations that include successful complex analysis. IBL activities or assignments, that Papers at this session should likewise Inquiry-Based Teaching and support observations about student be scholarly and focus on ways to Learning outcomes with evidence, or that could enliven complex analysis as taught Friday (1/8) morning help instructors who are new to IBL to to undergraduates. The table is open The goal of inquiry-based learning try new methods. to suggestions for technological (IBL) is to transform students Organizers: Brian Katz, Augustana innovation, pedagogical ideas, or from consumers to producers of College; and Victor Piercey, Ferris other innovative approaches that seem mathematics. Inquiry-based methods State University promising. aim to help students develop a deep Organizers: Russell Howell, understanding of mathematical Recreational Mathematics: Westmont College; Paul Zorn, St. Olaf concepts and the processes of doing Puzzles, Card Tricks, Games, College; and Alan Noell, Oklahoma mathematics by putting those Game Shows, and Gambling State University students in direct contact with Thursday (1/7) morning mathematical phenomena, questions, Puzzles, card tricks, games, game The Development and Adoption of and communities. Within this context, shows, and gambling provide an Open Educational Resources for IBL methods exhibit great variety. excellent laboratory for testing Teaching and Learning Activities can take place in single class mathematical strategy, probability, Friday (1/8) afternoon meetings and span entire curricula and enumeration. Pencil-and-paper This session will showcase the for students of any age; students can puzzles, board games, game shows, increasing popularity of open be guided to reinvent mathematical card tricks, and card games all provide educational resources (OER) for concepts, to explore definitions and opportunities for mathematical and courses in mathematics and the observe patterns, to justify core statistical analysis. Submissions to sciences. Examples of this may results, and to take the lead in asking this session are encouraged that include, but are not limited to, the new questions. There is a growing look at new problems as well as develop ment, enhancement, or HOWARD FRISK/VISITSEATTLE.ORG HOWARD body of evidence that IBL methods are novel approaches to old problems. adoption of open-source or PDDRUJIRFXVKWPOv-XQH-XO\v0$$)2&86 46 open-access course texts and ▶ Teaching and Learning The deadline for abstracts is related materials, the creation Developmental Mathematics Tuesday, September 22. and/or implementation of course ▶ Teaching and Learning Each participant can give only technological enhancements, Introductory Mathematics one talk in the MAA contributed such as instructional apps and paper sessions, whether it is in one video tutorials, and experiences ▶ Teaching and Learning Calculus of the themed sessions or in the with the inclusion of low- or ▶ Teaching and Learning general session. If your paper cannot no-cost homework platforms or Advanced Mathematics be accommodated in the session mathematics software systems in a ▶ Algebra in which it is submitted, it will particular course. Presenters should automatically be considered for the attempt to address the effectiveness ▶ Analysis general session. (formally or informally assessed) ▶ Applied Mathematics The organizer(s) of your session of the adoption of such resources ▶ Geometry will automatically receive a copy of in their courses. Presenters from all the abstract, so it is not necessary educational levels and STEM-related ▶ Graph Theory for you to send it directly to the fields are encouraged to submit ▶ Linear Algebra organizer. All accepted abstracts are abstracts, with preference awarded published in a book that is available to ▶ Logic and Foundations to those topics focusing on the high registered participants at the meeting. school, community college, and ▶ Number Theory Questions concerning the submission undergraduate levels. ▶ Probability and Statistics of abstracts should be addressed to Organizers: Benjamin Atchison, DEVFRRUG#DPVRUJ. ▶ Topology Framingham State University; and Jeremy Russell, College of New Jersey ▶ Other Submission Procedures for MAA GENERAL CONTRIBUTED PAPER Contributed Paper Abstracts SESSIONS Abstracts may be submitted Wednesday (1/6), Thursday (1/7), electronically at Friday (1/8) , and Saturday (1/9), KWWS MRLQWPDWKHPDWLFVPHHWLQJV morning and afternoon RUJPHHWLQJVDEVWUDFWVDEVWUDFW Organizers: Bem Cayco, San Jose SO"W\SH MPP State University; Timothy Comar, Fill in the number of authors, click Benedictine University; and T. James “New Abstract,” and then follow the Reid, University of Mississippi step-by-step instructions. The MAA’s General Contributed Paper Session accepts contributions in all areas of mathematics, curriculum, and pedagogy. When you submit your abstract, you will be asked to classify it according to the following scheme. ▶ Assessment ▶ History or Philosophy of Mathematics ▶ Interdisciplinary Topics in Mathematics ▶ Mathematics and Technology ▶Mentoring ▶ Modeling and Applications ▶ Outreach SEATTLE MUNICIPAL ARCHIVES MUNICIPAL SEATTLE 0$$)2&86v-XQH-XO\vPDDRUJIRFXVKWPO Attending MAA MathFest this August? Visit the MAA Pavilion in the exhibit hall and browse our latest books. College Calculus: A One-Term When Life is Linear: From Computer A Century of Advancing Mathematics Course for Students with Previous Graphics to Bracketology S. Kennedy, et al, Editors Calculus Experience by T. Chartier Meeting Price: $45.50 by M. Boardman and R. Nelsen Meeting Price: $38.00 Meeting Price: $45.50 TEXTBOOKS CLASSROOM RESOURCE An Invitation to Real Analysis LUIS F. MORENO of Calculus Heart The The Explorations and Applications Philip M. Anselone and John W. Lee A Mathematical Space Odyssey: The Heart of Calculus: An Invitation to Real Analysis Solid Geometry in the 21st Century Explorations and Applications by L. Moreno by C. Alsina and R. Nelsen by P. Anselone and J. Lee Meeting Price: $53.25 Price Not Yet Set Meeting Price: $45.50 I, Mathematician Release Party and Author Signing Join us on Thursday, August 6 at 3:00 p.m. in the MAA Pavilion! Meet editors Steve Krantz and Randi Ruden as well as contributors Hyman Bass, Roger Cooke, Keith Devlin, Underwood Dudley, and Sol Garfunkel. I, Mathematician To learn more about these and all our books P. Casazza, S. Krantz, visit maa.org/publications/books. and R. Ruden, Editors Meeting Price: $38.00 CELEBRATING A CENTURY OF ADVANCING MATHEMATICS The Mathematical Association of America Periodicals Postage Paid at 1529 Eighteenth Street, NW Washington, DC, and Washington, DC 20036 additional mailing offices Looking for a Job? Looking for an Employee? Look at MAA Math Classifieds Mathematics is a diverse field. Find what’s best for you. Whether you are searching for a job or ϐ ǡ ϐϐϐǤ mathclassifieds.org Explore what’s available.