The Bernard Review
Fall 2010

Department website: www.davidson.edu/math

Chair: Donna Molinek

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

Department

Laurie Heyer after receiving the Thomas Jefferson AwardThe 2010-2011 academic year brought many exciting changes, events and awards to the mathematics department. We welcomed two new members: Assistant Professor Dr. Carl Yerger and Visiting STINT Professor Dr. Mikael Goldman. Carl joined the department after completing his doctorate from Georgia Institute of Technology. This fall, he taught a computer science course in algorithms, and Combinatorics and Graph Theory from the newly revised math curriculum (see the Pedogogy section of the newsletter for more details on these changes). Mikael joined the department for the fall semester from KTH-Royal Institute of Technology in Stockholm, Sweden, and taught a computer science seminar on cryptography. We will greatly miss Mikael and his wife Meg when they return home to Stockholm in December.

            At Fall Convocation, Professor Laurie Heyer won Davidson College's Thomas Jefferson award. Laurie was cited as "not only a fine teacher, but a true innovator" whose work has been "transforming, on learning at Davidson College, and more broadly in the nation." The complete citation and pictures from the event are available from the math department web page.

            Students practiced throughout the fall semester to prepare for mathematics and computer science competitions. A computer programming team, consisting of Cyrus Lala ’13, Greg Newman ’12 and Jimmy Rountree ’11, held weekly practice sessions in preparation for the ACM Regional Programming competition at Chapel Hill, NC. This was Davidson's first time to compete in the ACM contest. Four Davidson students participated in the Virginia Tech Regional Mathematics Competition and five students (Greg Macnamara ’12, Jimmy Rountree ’11, Colin
Thomson ’13, David Wang ’12, and Kyle Yang ’13) took the Putnam exam, following weekly practices for these contests over the fall semester. These are very challenging tests: the median score on the Putnam is almost always less than 5 points out of 120 possible. Nearly 100 schools participated in the Virginia Tech test this year, and more than 500 institutions across the U.S. and Canada took part in the Putnam exam. Thanks to Professors Mikael Goldmann, Michael Mossinghoff and Carl Yerger for coordinating these efforts.

            The new academic year also brought a year-long sabbatical leave for Professor Irl Bivens. Irl is spending the year working with Professor Stephen Davis on the next edition of their Calculus text. He is also completing a paper with Professor Emeritus Ben Klein on some surprising behavior associated with the problem of minimizing the area between two curves.


Bernard Society Activities

Image from 2010 Bernard Lecture poster Professor Manjul Bhargava of Princeton University delivered the 2010 Bernard Lecture, "Linguistics, Poetry, and Mathematics." At the Bernard Society banquet before the lecture, the department honored Shashank Suresh’12 with the R. Bruce Jackson Award, which is given to an outstanding junior. Jean Jackson was in attendance.

In his lecture, Bhargava described patterns appearing in ancient Sanskrit poetry, and how ancient scholars discovered certain combinatorial sequences long before Pascal and Fibonacci. The image on the lecture poster seen to the left, with the logarithmic spiral over the Sanskrit text, foreshadows some of the mathematical structures that arise in the poetry. Bhargava also presented a talk "Sums of Squares and the 290-Theorem" about some surprising recent results in number theory. The 290 Theorem says that one can determine whether or not a particular type of function (a positive definite quadratic form with integer coefficients) represents every positive integer by merely checking if it represents everything up to 290. Bhargava also visited a cryptography class, where he performed a magic trick with the assistance of Travis McElroy ’13.

            This fall’s Math Coffee series included a variety of talks in math and computer science, as well as a number of social activities. Dr. Scott MacLachlan of Tufts University discussed models for viscous flows, such as convection, within the Earth's mantle. Greg Marcil ’11 described a few sample problems from his time at the Budapest Semesters in Math. Daniel Martin ’11 discussed his summer research at the North Carolina State University's REU. Beth Peters ’11 presented her summer work on a graph theory curriculum module for middle school students. Steph Meador ’12, Eugene Shui ’12 and Stephen Streb ’12 described their summer project on solving the knapsack problem with a bacterial computer. Colin Thomson ’13 presented his summer research on clustering. Professor Goldmann closed the semester's math coffees with a talk on computer security.


Pedagogy

Fall 2010 Geometry classThis fall's courses reflected the department's recent curriculum revision, in which students may learn proof technique in any one of three courses: Sets and Proofs, Number Theory, or Combinatorics and Graph Theory. Sets and Proofs is similar to the previously labelled proofs course, MAT 300. Students also have more flexibility at the upper level of the major. At the lower level, Calculus I now emphasizes modeling (except for students with no previous exposure to calculus, who can take a standard Calculus I course). Visit the department's page Transition to 2010 Curriculum Revision for further details on curricular changes. Another change in the department's classes was enabled by the new outdoor classroom space in front of the E. H. Little Library. Professor John Swallow's geometry class, shown in the picture to the left, made extensive use of the classroom during the fall semester.

            Professor Mike Mossinghoff developed and taught a new course on Mathematics and Politics. This is the second offshoot from the department's popular course on "Exploring Mathematical Ideas", following Professor Donna Molinek's "Mathematics and Art" version of the course. The new course discusses several mathematical topics that arise in the political arena, including various systems for running elections and their advantages and disadvantages, methods for apportioning seats in Congress, measuring the power of the President, and dividing resources in a fair way. Maybe the Bernard Society will adopt one of the election methods they studied to elect its officers next year!

            Professors Laurie Heyer and Malcolm Campbell taught the first-ever synthetic biology workshop for faculty this summer at Davidson. Fifteen teams of faculty from primarily undergraduate institutions learned how to incorporate synthetic biology into their courses and research with students. Laurie also led a breakout session for the Project NExT workshop at Mathfest on incorporating biological examples across the mathematics curriculum.

            This summer, Professors Rich Neidinger and Donna Molinek were invited to the National Science Foundation-sponsored Project MOSAIC at the Institute for Mathematics and Its Applications in Minneapolis. The project aims to improve undergraduate mathematics curriculum by integrating modeling, statistics, computation, and calculus. Rich presented on Automatic Differentiation at the workshop, a topic he regularly teaches in numerical analysis at Davidson and recently published about in SIAM Review, which is discussed more in the Exposition section of the newsletter.

            Art major and math minor Annie Temmink ’11 conducted an independent study with Professor Tim Chartier this fall on the open source programming language called processing, which teaches fundamentals of computer programming in a visual context.


Exposition

Cover of SIAM ReviewProfessor Rich Neidinger's article Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming appeared in SIAM Review 52 (Sep 2010) no. 3, 545-563. The article was prefaced by an introduction by the Education Section Editor.

Professor Stephen Davis gave a one-day workshop presentation to AP Calculus BC teachers at the Advanced Topics Summer Institute for Calculus at Rice University this summer. At MathFest, he gave a joint contributed paper session talk with Stephen Kokoska (Bloomsburg University) entitled AP Calculus: Facts, Figures, and FAQs, I & II.

            Together with biology professor Malcolm Campbell and colleagues from Missouri Western State University, Professor Laurie Heyer published papers in BIOS and Crossroads (the student magazine of the Association for Computing Machinery) on synthetic biology and computing with living cells.

            Laurie and Malcolm presented at Beyond BIO2010, a celebration of mathematical biology educational reform held at the National Research Council in Washington D.C., and Laurie gave a seminar in the biology senior session at Swarthmore College on "Engineering bacteria to solve NP-complete problems in vivo."

            Professor Mike Mossinghoff gave a talk at High Point University about the phenomenon of "Six degrees of separation," starting from the original context of connecting two people with a short chain of acquaintances (like Robert Whitton to Stephen Curry to Chris Mullen to Michael Jordan), and continuing with similar structures among actors, baseball players, and mathematicians, and introducing some ideas from graph theory along the way. Mike gave the same talk at Davidson as a Math Coffee later in the term.

            Professor Tim Chartier's article "Bracketology: How can math help?", co-authored with Erich Kreutzer ’10 and collaborators at the College of Charleston, and his article "Bending a Soccer Ball with Math" appeared in the book Mathematics and Sports edited by Joseph Gallian. Tim's articles "A Nonnegative analysis of politics" co-authored with Chuck Wessell (North Carolina State University) and a profile on Davidson mathematics alumnus Don Williams ’08 were accepted to Math Horizons.

           The article on soccer appeared just before the World Cup. As the tournament began, a query from a reporter from the Inside Science News Service contacted Tim for a subsequent article on soccer balls. ESPN's "Sport Science" show also contacted Tim to aid in an episode on the controversial new World Cup ball, and soon after about another episode on the accuracy of soccer bicycle kicks. Later in the summer, Tim also helped with a "Sport Science" episode on the home run derby.


Outreach  

Charlotte Teacher's Institute Logo Professor Donna Molinek led a Charlotte Teachers Institute seminar entitled "Mathematics and Art" that met once a week throughout the fall semester. The institute brings teachers from throughout the Charlotte Mecklenburg School system to classes at Davidson College, and culminates with each teacher developing a curriculum module to use in his or her classroom.

           Professor Emeritus Ben Klein led the July Experience course "On the Shoulders of Giants" this summer.

            After judging the Carolina Panthers’ Numbers Crunch competition for several years, Professor Rob Whitton organized the event this year. Area high schools participated in the competition and used calculus, physics, and geometry to solve football-related math exercises. The winners and judges, which included Professors Bivens and Yerger, attended the Panthers game against the 49er's on October 24, and were excited to see them win!

            On October 21, Tim and Tanya Chartier performed Mime-matics in Hance Auditorium at the college as part of a Celebration of Mind event. On that day, people from cities worldwide gathered for independent Celebrations of Mind events to honor what would have been the 96th birthday of Martin Gardner (1914-2010). Tim and Tanya additionally performed their mime and math presentation at Randolph Macon College, the University of Colorado at Boulder, Charlotte Community School for Girls, and the World Science Festival Street Fair in New York City.


Research

Iris studied in an REU at NCSUDaniel Martin ’11 had his paper "Spectral Clustering and Visualization: a Novel Clustering of Fisher's Iris Data Set," co-authored with North Carolina State University REU collaborators David Benson-Putnins, Margaret Bonfardin, and Meagan E. Magnoni, accepted for publication in SIAM Undergraduate Research Online. Their work with consensus clustering supports the existence of four clusters, instead of the generally accepted three clusters, in Fisher's Iris data set.

Algebra:
            Professor John Swallow published a paper, "Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p" in the Journal of the London Mathematical Society with N. Lemire, J. Mináč (Western Ontario) and Davidson math alumnus Andy Schultz ’02 (Wellesley College).

Combinatorics and Graph Theory:
            Professor Carl Yerger's paper "Five Coloring Graphs on the Klein Bottle," co-authored with colleagues from Georgia Tech, was accepted to the Journal of Combinatorial Theory, Series B.

           In August, Carl presented a talk entitled "Steinberg's Conjecture and Higher Surfaces" at the Second Netherlands Workshop on Graphs and Matroids. On August 19, he successfully defended his PhD thesis, entitled Color-Critical Graphs on Surfaces. Later in the fall, Carl won a competition to be the student reflection speaker at his Masters/PhD Commencement at Georgia Tech in December.

Discrete geometry and number theory:
            Professor Mike Mossinghoff attended the Canadian Number Theory Association meeting at Acadia University in Nova Scotia, where he gave a talk about some recent work on polynomials with a colleague at the University of South Carolina. Mike spoke on the same topic at the Palmetto Number Theory Series meeting in Greensboro in the fall, and gave a talk about some other work in discrete geometry regarding polygons with special properties at the AMS sectional meeting in Richmond, Virginia.

            Mike's paper "Heights of roots of polynomials with odd coefficients," co-authored with colleagues from Kansas State University, has been published in the Journal de Théorie des Nombres de Bordeaux. Another paper, "Average Mahler's measure and Lp norms of unimodular polynomials," written with K.-K. S. Choi from Simon Fraser University in British Columbia, was recently accepted into the Pacific Journal of Mathematics.

Mathematical and computational biology:
            Math majors Steph Meador ’12, Eugene Shiu ’12, and Stephen Streb ’12, along with six other students, spent ten weeks doing interdisciplinary research with Professors Laurie Heyer and Malcolm Campbell this summer. They presented their work on designing a biological computer to solve the Knapsack problem at the 2010 international Genetically Engineered Machines competition, at MIT in November, and were recognized with a gold medal for their achievements.

            Computational Biology major Katie Richeson ’11 and one-year international student Linda Kleist did research with Laurie this summer on structural DNA computing. Katie, Laurie and Malcolm traveled to Duke University this fall to use their atomic force microscope to visualize the structural elements Katie constructed in the lab.

           Laurie gave a talk entitled My Computer is Alive... and Other Tales from the Intersection, and helped lead a breakout session at the HHMI Quantitative Biology group meeting at the University of Delaware in May.

Mathematics education:
         Beth Peters ’11 worked with Professor Donna Molinek and Claire Benton (North Carolina A&T) over the summer to produce a mathematics curriculum unit for middle school students. Beth's project included learning the basics of graph theory, developing examples, and producing a module appropriate for use in the classroom. Beth plans on trying out her unit this coming spring at the Charlotte Community School for Girls, a new school for economically disadvantaged middle school girls.

Numerical analysis and scientific computation:
            This summer, Lake Trask ’11 worked with Professor Tim Chartier on a research project in sports ranking as applied to web networks. Tim and Lake focused on applying their ideas to networks of users on Twitter, leading to a provisional patent this fall to protect the idea for a year while they refine their work. This work was recently highlighted in an article by the college.

            Colin Thomson ’12 worked with Tim on applying clustering to biological datasets. Colin's work focused on visualizing the results obtained via consensus clustering. Tori Ellison and Kathryn Pedings, both pursing master's degree students at the College of Charleston, worked with Tim, Colin and Lake on clustering and ranking. This fall, Tim continued research on ranking and clustering methods with Lake and Eugene Shiu ’12.

            Tim gave talks on his research in ranking both in sports and social networks at the University of Colorado at Boulder and Randolph-Macon College. Tim's paper "Minimum violations sports ranking using evolutionary optimization and binary integer linear program approaches," co-authored with Erich Kreutzer ’10, and colleagues from the College of Charleston and Tsukuba University in Japan, appeared in the Proceedings of the Tenth Australian Conference on Mathematics and Computers in Sports. Tim, Erich, and their collaborators at the College of Charleston also had their paper "Sports Ranking with Nonuniform Weighting" accepted to the Journal of Quantitative Analysis in Sports.

Off-campus programs:
         Annie Temmink ’11 participated in the Claremont Colleges NSF Mathematics REU program. She worked principally with Dr. Johanna Hardin on clustering microarray data.

         
Leadership and Awards

Katie RichesonComputational Biology major Katie Richeson ’11 has been awarded a USA-Australia fellowship that will support her for a year of research in nanomedicine at the Australian Institute of Bioengineering and Nanotechnology, housed at the University of Queensland in Brisbane. Katie is the first Davidson student to win this fellowship.

           Professor John Swallow was elected Secretary of the Board of Regents of Sewanee: the University of the South. At Davidson, Dr. Swallow serves on the Graduation Requirements Team, Presidential Search Committee, Strategic Advisory Council, and Executive Committee. The college and department are grateful for the time and care John puts into these important responsibilities.

           Professor Stephen Davis continued his leadership with the AP Calculus program, serving as chair of the AP Development Committee. In Kansas City this summer, he served as an Alternate Exam Leader for the 8th straight year at the AP Reading.

            Professor Tim Chartier travelled to New York City in May to attend the first meeting of the Advisory Council of the Museum of Mathematics, which will be the nation's first museum of mathematics. The meeting focused on the development of exhibits that will be part of the museum which is targeted to open in Manhattan in 2012.


Community

           Congratulations to Stephen and Elisabeth Davis who welcomed grandchildren in May and September.


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.