Department

As the calendar moved from July to August, the Department of Mathematics underwent a seamless transition marking the end of Professor Richard Neidinger's tenure as chair and the beginning of Professor Donna Molinek's years of leadership. Molinek's plate would soon be full with administrative responsibilities as the school year fast approached.

           The department delighted in the news that the college's Athletics Hall of Fame will soon include Erin Lang Breunig ’94. Receiving each of the following honors three of her four years at Davidson, Lang was a Deep South All-Star, Deep South Academic Honor Roll member, and member of the Southeast All-Star team and National Tournament Team. Lang also excelled in the classroom with her perfect grade point average in her mathematics major. This work led to the following honors during her senior year: Academic All-America At-Large Third Team and an NCAA postgraduate scholarship.

            Professor Keith Devlin of Stanford University (a.k.a. NPR's Math Guy) delivered the 2008 Bernard Lecture, When Mathematics Changed the World. He discussed three distinct stages in the development of modern society when a mathematical development changed - in a fundamental, dramatic, and revolutionary way - how people understand the world and live their lives. The lecture was based on Devlin's latest book The Unfinished Game: Pascal, Fermat and the Seventeenth Century Letter that Made the World Modern, Basic Books 2008. During his two-day visit, Devlin also presented a lecture Scientific Heat about Cold Hits, which discussed a major and ongoing debate regarding how to calculate the significance of a DNA profile match in a "Cold Hit" case, where the match is the result of a search through a DNA database. Devlin also presented a BBC documentary, never seen before in the United States, that discussed the real story behind the movie 21 in which MIT students used mathematics to win large sums of money at blackjack in casinos.

         At the Bernard dinner, a new and talented group of juniors and seniors joined the Bernard Society of Mathematics. Also, joining the society were Keith Devlin, the Bernard lecturer, and Jason Parsley (Wake Forest), newlywed to Professor Sarah Mason. (See the Community section below for more details.) The department also honored Benjamin Altman ’10 with the R. Bruce Jackson Award, which is given to an outstanding junior. Jean Jackson was in attendance.

           This fall’s Math Coffee series included current and former students Dr. Joe Rusinko ’01 (Winthrop University) on string theory, Greg Marcil ’11 on hyperbolic tilings, Kristi Muscalino ’09 on the geostrophic equations, and Peter Simov ’08 on data mining. The series also included speakers from other institutions as well as a Math Murder Mystery and an evening of Mathematical Taboo. 

         The new academic year offered sabbatical leave to Professors Rich Neidinger and Mike Mossinghoff. Rich will spend the year largely in Davidson as he works on several writing projects. Mike is spending the academic year at the University of South Carolina in Columbia, to interact with research groups there in number theory and combinatorics. Professor Chartier returned from his sabbatical on the west coast and was pleased to be back at the college and community.

The Anton-Bivens-Davis Calculus textbooks appeared in their ninth edition. The work, as always, represents significant effort. The new edition offers new exercises and some reorganization of topics. The second edition of Combinatorics and Graph Theory, authored by John Harris (Furman), Jeff Hirst (Appalachian State) and professor Mike Mossinghoff, was also released this fall. Some of the new material contributed by Mike was developed through his teaching Math 221 at Davidson.

         Professors Stephen Davis and Ben Klein served as an Alternate Exam Leader and a Question Leader, respectively, at the AP Calculus exam Reading in Kansas City in early June. Stephen, who also serves as chair on the Test Development Committee, led an evening session at the Reading to discus test development with AP exam readers. Both Stephen and Ben presented at the annual meeting of the North Carolina Association of AP Mathematics Teachers.

         This summer at California State University, Fullerton, Professor Laurie Heyer presented at the Genome Consortium for Active Teaching (GCAT) Microarray Workshop. Participants of the hands-on workshop for faculty who conduct research with undergraduate students and/or teach undergraduate courses learned about gene expression analysis via microarrays and to use the public domain and open source MAGIC Tool spot-finding and analysis software written and maintained by Davidson students. This fall, Laurie traveled to Boston to aid in the development of secondary classroom modules in biology and mathematics for the Consortium for Mathematics and Its Applications.

         This summer, Dr. Donna Molinek taught a workshop entitled Graphs, surfaces, and knots as part of Davidson College's July Experience. The students used crayons, twizzlers and bubbles to study topology.

         Professor Tim Chartier and Nicholas Dovidio's ’07 article Modeling a Changing World appeared as 1 (2008) in the online journal Loci. The article, suitable as a classroom supplement, contains interactive activities and questions on the topics of integrating and solving ordinary differential equations numerically.

         Although officially retiring in May after 37 years on the Davidson faculty, Professor Ben Klein taught two sections of Finite Math during the fall. Ben will also teach a section of MAT 130 in the spring.

         Professor Rob Whitton and Schell Bressler ’09 studied topics in differential geometry in an independent study this fall. During his intermediate calculus class with Rob, Adam Lewicki ’11 became fascinated with the idea of revolving one curve around another curve as a generalization of a solid of rotation. The two probed the idea all summer using the Frenet Apparatus from differential geometry, constructive methods from computer graphics, and Mathematica's three dimensional rendering strengths. Each learned from the other.

         
Outreach  

Professor Sarah Mason served as a judge for the Carolina Panthers' Numbers Crunch competition. Area high schools participated in the competition and used calculus, physics, and geometry to solve football related math exercises. The participants and judges were treated to the Panthers game against the Arizona Cardinals, which followed their pre-game appearance on the field when their images were projected on the Jumbotron.

         
Exposition

Professor emeritus J. B. Stroud published an article entitled Crockett Johnson's geometric paintings in the Journal of Mathematics and the Arts 2 (2008), 77--99. Over a sabbatical leave from Davidson, J. B. began studying Crockett's mathematical artistry as a Smithsonian Fellow in Residence from August 1979 to August 1980. J. B. notes, "The most interesting thing that I did was to unravel Johnson's 'one mark' construction of the regular heptagon. (Johnson called a straightedge and compass construction in which it is permitted to put one mark on the straightedge, a 'one mark' construction. A more accurate description of this procedure is the 'insertion principle'.)" J. B. provided proofs of two assertions by Johnson. Johnson's painting of this construction appears to the left and is among 16 additional paintings in the article.

           Professor Mike Mossinghoff offered the opening address at the Shenandoah Undergraduate Mathematics and Statistics Conference at James Madison University, which features research by undergraduate students in math. Mike's talk, entitled Sufferin' Succotash! A problem of Sylvester's, presented some problems in plane geometry, where the history includes a number of important contributions by undergraduates.

          Professors Irl Bivens and Ben Klein's article Wazir Circuits on an Obstructed Chessboard appeared in Mathematics Magazine 81 (2008), 276--284. The third author of the paper was Arthur Holshouser, an amateur (in the best sense of the word) mathematician in Charlotte with whom Ben has worked for over thirty years. A 'wazir' is a now obsolete chess piece that moves exactly one square at a time vertically or horizontally. The article studies the moves of the wazir on chess boards of arbitrary size and allows for obstructed squares.

           Professor Tim Chartier published two book reviews. The review on Computational Methods of Linear Algebra by Sewell appeared in SIAM Review 50 (2008), 808--809 while the review on Google's PageRank and Beyond: The Science of Search Engine Rankings by Langville and Meyer was published in Computing in Science & Engineering (November/December 2008), 11--12. The online article An Integer Programming Model for the Sudoku Problem authored by Bartlett and Langville (College of Charleston) with Tim Rankin ’07 and Tim appeared in the Journal of Online Mathematics and its Applications 8 (2008).

The Davidson-Missouri Western synthetic biology team continued their research in the intersection of math and biology. This year, they designed, modeled, and constructed a bacterial computer that uses XOR logic to compute a cryptographic hash function, used to authenticate documents. This work led by professors Laurie Heyer and Malcolm Campbell along with Todd Eckdahl and Jeff Poet (Missouri Western State), resulted in a provisional patent on their invention of the XOR logic built in DNA. (See below for more details on the activities of this group.)

Algebra:
         Professor John Swallow co-authored two papers in the New York Journal of Mathematics. Galois module structure of Milnor K-theory mod p^s in characteristic p, with Ján Mináč (University of Western Ontario) and Andrew Schultz (University of Illinois, Urbana-Champaign and Davidson ’02) extended work from Schultz's honors thesis as an undergraduate in the department and appeared as 14 (2008), 225--233. Galois module structure of Milnor K-theory in characteristic p with Ganesh Bhandari (Mount Royal College), Nicole Lemire (University of Western Ontario), and Ján Mináč was published as 14 (2008), 215--224.

           Under National Science Foundation funding, John worked with Jason Ferguson (Duke ’09) for six weeks during the summer on Galois cohomology.

Combinatorics:
         The four-person team of professor Sarah Mason and colleagues Jim Haglund (University of Pennsylvania), Kurt Luoto (University of Washington), and Stephanie van Willigenburg (University of British Columbia) continued research on Quasisymmetric Schur functions at their Research in Teams week at the Banff International Research Station this summer.

         Sarah gave several presentations over the summer and fall: Refinements of Littlewood-Richardson Rule at the AMS Western Sectional Special Session on Combinatorial Representation Theory in Vancouver, British Columbia, the poster Quasisymmetric Schur Functions at the 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics in Valparaiso, Chile, Quasisymmetric Schur functions and refinements of the Littlewood-Richardson Rule for the MIT's combinatorics seminar in Cambridge, Massachusetts, and Permutations, partitions, and 'jeu de taquin' for the Bryn Mawr Mathematics Colloquium in Bryn Mawr, Pennsylvania.

Discrete geometry and number theory:
         Professor Mossinghoff's paper Lower bounds for Z-numbers with Artüras Dubickas (Vilnius University, Lithuania) was accepted for publication in Mathematics of Computation. This article studies some old problems regarding the distribution of the fractional parts of particular sequences of real numbers. "Z-numbers" exhibit highly skewed distributions, and it is suspected that none exists. Their study involves ideas in number theory and dynamical systems.

           The article Minimal Mahler measures, written with Georges Rhin (Université de Metz, France) and Qiang Wu (Southwest University of China), is scheduled to appear in Experimental Mathematics. The paper reports on some substantial calculations on the Mahler measure of polynomials with integer coefficients. (The Mahler measure is a kind of a mean value for a polynomial over the unit circle in the complex plane, and occurs widely in analysis.) The paper finds the smallest nontrivial measure for each degree up to 54.

         Mike was invited to present at the Canadian Number Theory Conference in July at the University of Waterloo. This is the largest number theory meeting in North America, held every two years. He was also invited to speak on a combinatorial problem concerning polygons at a conference on Discrete Mathematics and Algorithms at Clemson University, and talked about the results of a very large computation (almost 2 CPU-years) at the Palmetto Number Theory Conference in Columbia, South Carolina. Mike has also presented in both the number theory and combinatorics seminars at the University of South Carolina this year.

Dynamical systems:
          Professor Donna Molinek's paper A Dynamical Study of a Cellular Automata Model of the Spread of HIV in a Lymph Node was accepted for publication in the Bulletin of Mathematical Biology. It was co-authored with Emily Burkhead (Meredith College) and Jane Hawkins (University of North Carolina at Chapel Hill). It appeared in the online version in August and will appear in the printed journal January 2009.

          Donna also presented Modeling the progression of HIV with cellular automata at The Pines in Davidson. The lecture was part of the Learning in Retirement series, headed by the late Louise Nelson. The Math Department mourns the death while celebrating the life of professor emerita Nelson.

Mathematical and computational biology: 
          Professor Laurie Heyer continued collaborative research between Davidson and Missouri Western State (MWSU) as discussed above. This was the third year of iGEM collaboration and the first time for the group to work shoulder-to-shoulder as the team spent one week visiting each other's campuses. The Davidson portion of the team consisted of math majors Kristi Muscalino ’09 and Madeline Parra ’09 as well as Kelly Davis ’11, Erin Feeney ’11, Pallavi Penumetcha ’11. In addition, bioinformatics center major Max Win ’10 developed software for visualizing the extensive catalog of biological parts that iGEM teams use in their projects. See the team's web page for more information. James Barron from Hampton University and Karlesha Roland from Spelman College also participated on campus under Davidson Research Initiative funding. The work resulted in another impressive Gold Medal from the 2008 iGEM (International Genetically Engineered Machine) Jamboree at MIT, an event that included 84 teams from 21 countries.

Numerical analysis and scientific computation:
         Professor Richard Neidinger spent part of his fall semester on sabbatical developing algorithms for multivariable interpolating polynomials in Newton forms. He also continued his research in automatic differentiation and his object-oriented programming Matlab package. This summer Rich traveled to Germany to attended AD 2008, the 5th International Conference on Automatic Differentiation, which is held every four years.

          Professor Tim Chartier's article Efficiency of Multigrid Algorithms for Head Models on Electroencephalography Simulations, which was co-authored with Tim Rankin ’07 and Ceon Ramon (University of Washington), appeared as International Journal of Pure and Applied Mathematics 45 (2008), 349--357. Tim co-organized the minisymposium Adaptive Algebraic Multigrid Methods for the SIAM Annual Meeting and presented on multigrid methods for the Department of Mathematics Colloquium at Wake Forest University.

          This summer, Daniel Orr ’08 worked with Tim on integrating recent research into an open-source multigrid code of Los Alamos National Laboratory. Meanwhile, Peter Simov ’08 and Tim analyzed Netflix ratings data with matrix clusters and adapting sports ranking methods. During the fall, Erich Kreutzer ’10 continued Peter's work with Tim. Erich presented a poster When Movies Compete at the Southeastern Atlantic Mathematical Sciences Workshop in Chapel Hill and a talk by the same title at the Shenandoah Undergraduate Mathematics and Statistics Conference. During the fall semester, Tim also worked with Nathalia Paulinelli ’10 on implementing and testing algebraic block smoothers within larger multigrid codes. Max Win ’10 studied the robustness and efficiency of block smoothers to compute PageRank.

Off-campus programs:
         Greg Marcil ’11 participated in the summer research program Groups, graphs, and geometry at the University of North Carolina-Asheville. He worked principally with Dr. Sam Kaplan studying closed hyperbolic tilings, which was the topic of his fall Math Coffee.

         
Leadership

Professor John Swallow was appointed chair of the Ad Hoc Faculty Advisory Committee on Curriculum Development (CCD), to recommend goals for Davidson's curricular strategic plan in 2009. Professor Laurie Heyer is also a member of the CCD. John is also a member of the steering committee, which coordinates the strategic planning process of the Principal Executive Staff and the CCD.

          Professor Stephen Davis continued his leadership roles with the Advanced Placement Program. He presented a one-day workshop (mostly on differential equations) at the Advanced Topics Summer Institute for Calculus at Rice University in June, and co-presented From Story to Differential Equation with Ruth Dover (Illinois Math & Science Academy) at the AP Annual Conference in Seattle, Washington in July. Stephen also co-organized the AP National Faculty Colloquium with Gail Burrill (Michigan State) in Chicago. The event drew representatives from college and university math departments around the country with the intent of exposing these faculty to the AP Calculus course, the exam, and invite their input for the newly formed Review Commission. Stephen also attended AP Test Development Committee meetings in Princeton, NJ and New York City, NY.

          Professor Tim Chartier accepted an invitation from the Mathematical of Association of America to serve a three year term on the Committee on the Henry L. Alder Awards for Distinguished Teaching.

         
Community

Professors of mathematics Sarah Mason and Jason Parsley (Wake Forest) married in Winston-Salem in August. Friends, family and a large contingent of mathematicians from both colleges witnessed the outdoor ceremony. Of special note, a wedding cake in the shape of the symbol for infinity was among the highlights of the reception. The cake appeared again, although in digital form the second time, on the Found Math portion of the Mathematical Association of America's homepage.

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.