The Bernard Review
Spring 2011

Department website: www.davidson.edu/math

Chair: Donna Molinek

Address changes, news of interest to readers?
email us: mathdept@davidson.edu

Department

Joint Math Meetings 2011 Logo
The spring semester began with several members of the department attending the Joint Mathematics Meeting in New Orleans. Professor Davis, along with Dr. Michael Boardman (Pacific University), presented a talk on Calculus Reform and AP Calculus in the MAA session Influences of the Calculus Reform Movement on the Teaching of Mathematics. Professor Mossinghoff co-organized an AMS-SIAM special session on Mathematics of Computation: Algebra and Number Theory. He also was coauthor of a paper presented by Kevin Hare, Pisot and Salem polynomials dividing Newman polynomials, in the Special Session he chaired. Professor Heyer spoke on Creating/improving the biomathematics/biostatistics course in a panel discussion sponsored by SIGMAA on Mathematical and Computational Biology - SIGMAA on Statistics Education - and ASA/MAA Joint Committee on Undergraduate Statistics. Professor Yerger spoke on Steinberg's Conjecture on Higher Surfaces, in the AMS session Special Session on New Topics in Graph Theory. Professor Chartier was featured as the Mathematical Association of America's Student Lecturer in which he presented Mime-matics. Tim also gave a talk in a session for undergraduates on research in numerical linear algebra. He presented another talk on his use of service-learning in the math modeling course. Students Lake Trask ’11 and Colin Thomson ’13 participated in a poster session. As a prelude to the activities, members and friends of the department enjoyed watching Stephen Curry play for the Golden State Warriors against the New Orleans Hornets on the night before the conference began.

           In other news, Professor Mossinghoff received a grant from the Simons Foundation that will support travel and future research collaborations, and help foster activities within the Bernard Society in the years to come.

           The department will miss the presence of Professor Swallow next academic year. On June 1, John will begin a one-year leave to serve as Acting Associate Provost at his alma mater, The University of the South. He will work closely with the current provost through the fall 2011 semester and assume full responsibilities as Acting Provost during the spring 2012 semester. John will report directly to the new president John McCardell, former president of Middlebury College. We wish John well and much success. For more information, you can read the College Communications story on this opportunity for John.

           It has been another year of varied, memorable, and notable activities. Read on to learn more.

Awards and Recognitions

Annie Temmink Annie Temmink ’11, an art major and math minor, was among 40 graduating seniors "of unusual promise" from across the nation who received fellowships this year from the Thomas J. Watson Foundation for a year of independent, purposeful exploration and travel. Traveling to Ghana, India and Indonesia, Annie plans to observe and work with seamstresses, designers and artisans to determine the cultural influences of their fashion, and the effect of a globalized economy on fashion in these countries.

          The annual department awards were presented at the spring convocation. Daniel Martin ’11 received the William G. McGavock Mathematics Award. He was noted for distinguishing himself "with a perfect GPA within the major and with several research activities," some of which are described in this newsletter. Kyle Yang ’13 received the William Vinson Mathematics Award and was noted particularly for his "drive and talent for finding simple solutions to complex problems."

           At the MAA Southeastern Section meeting in Tuscaloosa, Alabama, Stephen Streb ’12 presented his research with last summer and fall's iGEM team under Drs. Heyer and Campbell's direction. He was awarded one of the Patterson Prizes, recognizing his presentation as the best one in his session. At the same meeting, the Math Jeopardy team of Karen Larson ’12, Beth Peters ’11, Stephen Streb ’12 and Kyle Yang ’13 represented Davidson very well. The team won their first round easily this year, but lost in a close match in the second round after a tough final jeopardy problem. Thanks to Professor Mossinghoff for coaching the team.

          Katie Richeson ’11, a center major in computational biology, was awarded first place for the student competition at the 2011 North Carolina Nanotechnology and Commercialization Conference. She was the only undergraduate in the competition against half a dozen graduate students. Katie was also awarded high honors for her thesis, DNA-Computing: Solving The Complementary Bounded Tiling Problem Using Bionanotechnology.

          This winter, we received the results of the Putnam exam, the notoriously difficult annual math contest held at institutions across the U.S. and Canada. The big news is that the Davidson team rank this year was 74th, placing us well within the top 15%! This is our best ranking ever, topping the team rank of 88 achieved in 2007. (While each person works individually on the contest problems, a team score is obtained by summing certain individual scores.) The five Davidson students who took part were Greg Macnamara ’12, Jimmy Rountree ’11, Colin Thomson ’13, David Wang ’12, and Kyle Yang ’13. All five students had scores greater than the median with Colin and David receiving the highest scores. Thanks to Professors Mossinghoff and Yerger, who ran preparatory sessions over the fall semester to get students ready for this contest.

           In February, seven teams participated in the international Mathematical Contest in Modeling. The competition poses open-ended, applied problems requiring a busy four-day period of research and writing. In all, a total of 2775 teams participated in the MCM with 88% of the teams coming from counties other than the United States. Six teams received Honorable Mention distinction: Lejla Agic ’11, JP Craven ’11, Kelly Davis ’11, Jack DeLoach ’12, Thom Dimmock ’12, Tyler Hammett ’12, Bill Jin ’12, Matt Johnson ’12, Colin Nelson ’12, Lucy McMurry ’13, Jena Manilla ’13, Steph Meador ’12, Johnny Pav ’11, Robert Lorenzen ’13, Beth Peters ’11, Matt Ray ’12, Leland Taylor ’12, and Colin Thomson ’13. The other team, consisting of Cyrus Lala ’13, Anvi Raina ’11 and David Wang ’12, received Successful Participant.

           The International Collegiate Programming Competition is a multi-stage contest in computer programming for undergraduates all over the world. Cyrus Lala ’13, Colin Nelson ’12, Greg Newman ’12 and Jimmy Rountree ’11 joined forces to tackle a competitive programming problem to control a team of players in a virtual snowball fight. The team shared their experiences in a Math Coffee, which included demonstrating how code could be tested by entering a battle with a virtual opponent.

Pedagogy

Graph theory at CCSG Beth Peters ’11 and Professor Molinek traveled to the Charlotte Community School for Girls weekly during the spring semester and taught from the Graph Theory curriculum unit that Beth created with her Duke Research Initiative award during the summer of 2010. It was a rewarding experience for both Beth and Donna as they engaged 5th graders in mathematical learning. Beth also presented her work in a poster at the MAA Southeastern Section meeting.

        At the national meeting of the Association of American Colleges and Universities, Professor Swallow was part of a session called HEDs-Up, featuring ten-minute talks in the spirit of TED talks. His presentation was Global liberal education, participatory culture, and the intellectual habits of students. He shared a vision of networked learning that requires a paradigm shift and a change in thinking that could benefit liberal education in a digital age. John also presented a Vann Lecture, Education and Intellectual Habits, Old and New, at McCallie School in Chattanooga. The lecture addressed the intellectual habits he sees in students who have grown up with the Internet, and what these mean for the liberal arts education.

        With support from the new Davidson College Center for Civic Engagement, the Mathematical Statistics and Mathematical Modeling classes worked on problems posed by campus and community nonprofit organizations. The students' work and recommendations were presented in the inaugural community-based learning poster session, which featured over 40 student posters from courses in Biology, Economics, English, Mathematics, Sociology and the Center for Interdisciplinary Studies.

        At the MAA Southeastern Section meeting, Professor Carl Yerger presented a talk Reading Questions: Pedagogical differences between educational environments in a special session of talks by beginning faculty.

        This winter, Professor Mossinghoff taught a new computer science course on the theory of computation. This is a very mathematical course that studies the fundamental capabilities and limitations of computers, as well as the question of what problems can be solved efficiently with computers. He looks forward to developing another new course in computer science for the fall, on programming languages.

        Professor Heyer received a course development stipend from the VPAA office to redesign her bioinformatics course as an alternative first course in programming using Python. The new version of the course will be offered in the fall. Laurie also discussed her pedagogical work in an online panel discussion on modeling-based calculus, hosted by Project MOSIAC.

        Professor Chartier began teaching a seminar for the Charlotte Teachers Institute. This spring and fall he will lead a seminar, Mathematics through Popular Culture, in which CTI Fellows, who are teachers in the Charlotte-Mecklenburg school district, explore mathematical ideas that apply to a variety of topics in popular culture.

Outreach  

March MadnessProfessors Neidinger, Heyer, Mossinghoff, Yerger and Chartier presented or organized activities in Davidson's March MATHness event, which was organized by HHMI outreach coordinator Tiffany Scheff. Geared for high school students and their teachers, the day offered a variety of talks and activities. Mike opened the day discussing some of the mathematical ideas behind some "six degrees of separation" phenomena, including unexpectedly close connections that arise in chains of acquaintances, in linking movie stars to Kevin Bacon, and in connecting baseball players through the teams they played on. Laurie discussed her research with undergraduates on the Pancake Problem, a problem from genomics; she explained the pancake model for genome rearrangements, and showed how the pancake problem can be connected to graph theory and studied with Markov Chains. Rich closed the day discussing how mathematics measures the number of things in an infinite set. Starting with a toddler's understanding of numbers, he led the group to infinity and beyond! Between these presentations were numerous activities that involved Davidson student leadership. A main draw was a math competition, organized by Professor Yerger, with help from students Daniel Bernstein ’13 and Shashank Suresh ’12. The competition consisted of two rounds, with the final round deciding the overall winner. Dr. Annalisa Crannell of Franklin & Marshall College visited and contributed a talk and activity in math and art. During her visit, Annalisa led an outreach activity, also in conjunction with HHMI outreach, at the Pines at Davidson. Annalisa, with the aid of Davidson students, taught residents how to draw 3-D block letters, using some some quick-and-easy tricks from 1-point perspective drawing.

          In February, a program called MOSAIC (math, originality, science, achievement, imagination and creativity) offered an afternoon on Davidson's campus devoted to math and science activities for elementary school students in grades 3 through 5, along with their parents and siblings. Parents and children watched Tim and Tanya Chartier's Mime-matics performance and rotated through several activities led by several Davidson students, including origami, graphs, and building 3-D figures with ZomeTools.

          Beth Peters ’11, Andrew Keesler ’14 and Caroline Figgie ’13 led an activity at UNCC's Julia Robinson Math and Computing Festival for middle school girls in March. Austin Totty ’12, who is pursuing teacher certification, led an activity on Euler's formula and other ideas from combinatorial geometry at this festival, and facilitated a Charlotte Teachers Circle meeting on the same topic. He and Dr. Chartier also visited a 5th grade math class at JV Washam Elementary in Cornelius, NC. They presented a lesson on Fibonacci numbers, including a magic trick, a game of nim, and connections to the golden ratio.

Exposition

Professor Swallow wrote an opinion piece, Mathematical Community: only we can tell the story and it is time we did, in the March issue of Notices of the AMS, the world's most widely read magazine aimed at professional mathematicians. The piece discussed how mathematics, despite its common image of an isolated academic field, has increasingly become an active community of interaction and collaboration. Given this reality, mathematicians should tell their stories to reflect this culture.

          Professor Mossinghoff was the featured speaker at the North Carolina State Dinner in January at High Point University. His talk on Polygonal plates at the banquet described several problems in plane geometry, playfully phrased as questions in dinnerware design. One of the problems featured in the talk analyzes convex polygons that have large perimeter, relative to their diameter. Some of the optimal polygons in this problem form the basis for the Bernard Society math T-shirt for 2010-2011. The graphic is seen below.

           Professor Bivens presented The Mystifying, Minimizing, Median: From Geometry to Probability and Back Again at the MAA Southeastern Section meeting. This work, developed with Professor Emeritus Klein, considers minimizing the area between a fixed curve and members of a given one-parameter family of curves. This work had some unexpected implications when the results are interpreted in terms of probability. Much of Irl's sabbatical time this spring was spent collaborating with Stephen Davis to complete the upcoming new edition of their Calculus text.

         Professor Heyer's chapter, Teaching Bioinformatics and Genomics: An Interdisciplinary Approach, coauthored with Dr. Campbell of the biology department, appeared in a volume of the Dimacs Series in Discrete Mathematics and Theoretical Computer Science entitled BioMath in the Schools.

          Professor Chartier had two articles published in Math Horizons this spring. The first article, which appeared in the February 2011 issue, entitled Alumni Profiles: Math Modeling Makes for an Optimal Career, highlighted Don Williams and his use of mathematical modeling as a consultant for IBM. The second article, A Nonnegative analysis of politics, was coauthored with doctoral student Chuck Wessell, who visited Davidson in the spring of 2010. The article, which appeared in the April 2011 issue of the magazine, discussed matrix clustering, with national voting data on presidential elections as one application. Tim's 2007 article Using the Force: Star Wars in the Classroom was chosen as exemplary paper of PRIMUS, a journal on Problems, Resources, and Issues in Mathematics Undergraduate Studies.

           The Society of Industrial and Applied Mathematics' website www.whydomath.com published a module Google PageRank: The Mathematics of Google by Amy Langville (College of Charleston), two of her graduate students and Tim Chartier. The Why Do Math website contains modules that are accessible to first year college students and popular science enthusiasts. They are also meant to be accessible to advanced high school students. This module includes a video where Tim plays Randy the Random Surfer who is stuck in the infinite simulation for PageRank as he is ever computing for Google.

           The blog for Make Magazine, which shows original things people have made and often gives instructions on how to make your own versions, posted a Math Monday entry on creating candy mosaics. The entry contains a mosaic of President Obama's campaign "Hope" poster constructed with (actual) M&Ms. The applet, coded by Steph Meador ’12, that appears on Tim's blog enables you to construct mosaics with M&Ms, Jelly Bellies, Gummy Bears, Hershey Kisses, or Peeps. The algorithm was developed for the math book Tim is writing.

           Tim presented Mime-matics at Georgia College & State University and SUNY Potsdam. He discussed his work in ranking sports and social networks at Georgia College and the mathematics of digitizing Yoda in a presentation at Clarkson University. Tim visited Denison University and presented two talks on the use of service-learning in the math modeling course. Tim was also a keynote speaker at the Research Undergraduate Mathematics Conference at Catawba College.

Research

Combinatorics and graph theory:
            Professor Yerger organized a minisymposium in graph theory at the SIAM Southeastern Section Conference at UNC-Charlotte. He presented a talk Steinberg's Conjecture on Higher Surfaces in a special session on discrete mathematics at the MAA Southeastern Section Meeting. In mid-May, Carl attended the Cumberland Conference on Graph Theory, Combinatorics and Computing and presented a contributed talk on ongoing research in Ramsey Theory with Daniel Bernstein ’13 and David Grynkiewicz of Karl Franzens University of Graz, Austria.

Discrete geometry and number theory:
          Professor Mossinghoff's paper Enumerating isodiametric and isoperimetric polygons was recently published in the Journal of Combinatorial Theory (Series A). This paper develops the mathematics behind this year's Bernard Society T-shirt. Specifically, there is a theorem behind the design! Define the diameter of a polygon as the max distance between vertices of the polygon. Consider the following problem: For a fixed positive integer n, how can you design a convex polygon that has n sides, diameter 1, and perimeter as large as possible? It may be surprising that the regular polygon is often not optimal, and that there are often several different polygons that all achieve the best possible value for the perimeter. When n = 24, there are exactly 12 different polygons with diameter 1 that have the largest perimeter, taking symmetry (flips and rotations) into account. All 12 of these polygons are featured on this year's math department T-shirt.

          Mike had a paper, co-authored with a colleague at the University of South Carolina, accepted in Mathematics of Computation. Mike also spoke at the MAA Southeastern Section meeting in Tuscaloosa, and at a number theory meeting in Savannah.

Dynamical systems:
          In March, Professors Donna Molinek and Rich Neidinger traveled to Furman University for the Carolinas Dynamics Symposium. This summer, Donna will direct David Wang ’12 and a student from North Carolina A&T in research funded by the Davidson Research Initiative.

Mathematical and computational biology
          Newly approved center major in computational biology Leland Taylor ’12 has funding from the Davidson Research Initiative to work with Professor Heyer this summer on a project to assemble newly sequenced genomes. Six other students, including math majors Duke DeLoache ’12 and Lillian Wilson ’13, met several times this spring to prepare for summer research in synthetic biology with Professors Heyer and Campbell.

Numerical analysis and scientific computation:
          Professor Chartier continued his research in ranking and clustering. His papers Sensitivity of Ranking Vectors and Sports Ranking with Nonuniform Weighting were accepted for publication by the SIAM Journal on Scientific Computing and Journal of Quantitative Analysis in Sports, respectively; both papers are coauthored with Erich Kreutzer ’10, and Dr. Amy Langville and her graduate student Kathryn Pedings.

          The Mathematical Modeling class again learned to create their own mathematically-generated brackets. Prior to the tournament, Derek James, coanchor of the morning show Fox News Rising, visited the class and interviewed Kelly Davis ’11, Daniel Martin ’11 and Tim for a TV segment Bracketology 101 that aired later that day. Early in the tournament, many of the brackets were doing quite well. Vickie Kearn, Executive Editor of Princeton University Press, interviewed Lucy McMurry and Tim regarding the brackets and class. The class's brackets struggled, as did many in the country. However, they still performed as well or better than many sports analysts which brought about a follow-up interview by Vickie Kearn with Kelly Davis and Tim.

          In January, Daniel Martin ’11 and Tim advised the ESPN program Sport Science, which airs programs on the science behind sports, on the feasibility of a triple cork occurring in the X Games. The work led to a TV segment that aired during the snowboarding competition. The evening that the show aired, Torstein Horgmo completed the first ever triple cork in competition, as predicted by math and physics. The AMS produced a Math Moment Putting Another Cork in It and also a podcast on Daniel and Tim's work.

          Tim continued research in social networks. Lake Trask ’ 11 continued research within an independent study on applying sports ranking to Twitter. You can hear Lake and Tim discuss the research in a Pod'cats, The Twitter Project, with Jeff Tolly of Admissions. Daniel Martin ’11 and Tim consulted for the social gaming website Prediculous. They developed an authority and ranking algorithm that uses social interaction parameters, social game performance and content creation variables.

Leadership and Service

This April, the faculty approved the first revision of the distribution requirements as a whole since 1987. This came after extensive work by the Graduation Requirements team, which included a variety of forums for faculty input. Thanks to Professor John Swallow for his leadership and dedication to these issues.

          In March, Professor Swallow served as a Department of Mathematics reviewer at Bucknell University, a private liberal arts college. In April, Professor Molinek traveled to California to conduct an external review for the Department of Mathematics at the University of San Francisco, a private Jesuit University.

          Professors Stephen Davis and Carl Yerger continued their leadership with the Charlotte Mathematics Club. In addition to monthly meetings, they took 20 students to the College of Charleston Math Meet in February. Stephen also hosted the CMC participation in the Purple Comet! Math Meet for middle and high school students with assistance from students Austin Totty ’12, Catherine Schricker ’14 and Sam Castle ’14. Catherine and Sam led a workshop for participants on the raytracing software POV.

          Professor Tim Chartier joined the Advisory Council for the Charlotte Teachers Institute. Tim joins a number of faculty from Davidson and UNCC, including Professor Donna Molinek.

Envoi

Davidson graduates A fond farewell to our many Bernard Society members from the class of 2011! Several students reported definite plans:

Carter Braxton accepted a position as a research associate in the macroeconomics department for the Federal Reserve Bank of Kansas City. Kelly Davis will work for an AmeriCorp-affiliated organization that provides free comprehensive healthcare services to the homeless population in Washington, D.C. Amanda Flink will be teaching high school math as part of the 2011 Texas Teaching Fellows Cohort in Dallas. Adam Lewicki accepted a job doing Quantitative Analysis (programming and quant based trading) at RBC in New York City. Daniel Martin will begin work in a financial management development program for the Edens & Avant commercial real estate development company in
Columbia, S.C. Beth Peters will begin a masters program in education that will lead to teacher certification through the Stanford Teacher Education Program.

          Ali Rauh will enroll in the PhD program in Economics at the University of Chicago. Katie Richeson was awarded the Sir Keith Murdoch Fellowship from the American Australian Association to work at the Australian Institute of Engineering and Nanotechnology in Brisbane, Australia where she will be working on modeling, developing, and testing nanostructured biosensors to detect changes in DNA methylation patterns for earlier breast cancer detection. Jimmy Rountree will pursue a masters in Computer Science at The College of William and Mary. Lake Trask will begin doctoral studies in Operations Research at North Carolina State University. This summer Lake will conduct research on social networks related to cyber security at Lawrence Livermore National Laboratory.

Continuing Support

            Thank you for your continuing support of the Richard R. Bernard Society for Mathematics at Davidson College. Your gifts support outside speakers and math coffees, student travel to conferences, and other mathematical events.

            To make a contribution to the society, please specify "Bernard Society" on your check and mail it to the Office of Development, Davidson College, Box 7173, Davidson, NC 28035-7173. Gifts to the Bernard Society are separate from the Annual Fund.