Department

The end of the academic year had been marked by commencement activities only hours earlier when the Math Department arrived in Montreat, North Carolina, for a retreat. The next two days would be filled with stimulating discussion on the curriculum, the mission of the department, activities, and long-term goals. While we kept a busy, focused schedule, there was time to relax and unwind from the semester’s end with department members shooting hoops, taking a hike, or for some, simply napping! The important discussions led to work throughout the summer and fall and what should emerge as exciting restructuring of the mathematics curriculum.

            Professor Joe Gallian of The University of Minnesota—Duluth delivered the 2009 Bernard Lecture, Using Mathematics to Create Symmetry Patterns. In the lecture, Gallian used video animations to illustrate the role of mathematics in transforming basic images into symmetry patterns. Such methods helped produce the image (seen to the upper left) for the 2003 Mathematics Awareness Month poster. As well as meeting with students about such topics as REU experiences, graduate school, and undergraduate research, Joe also presented his talk Breaking Driver’s License Codes in which he discussed his process of deciphering the techniques used for assigning such codes in Minnesota and Missouri.

            This fall’s Math Coffee series included a variety of talks in math and computer science, as well as a number of social activities. Among the speakers was Walter Wiggins (MD/PhD student, Wake Forest School of Medicine; Davidson ’07), who lectured on the intersection of mathematics and neuroscience. Daniel Kaplan (Macalester College) presented innovative ways of untangling causation in complex systems. Chuck Wessell (North Carolina State University) presented on clustering, specifically in the context of North Carolina county-by-county election data. Greg Newman ’12 presented on his internship at MTV that involved computer science. Erich Kreutzer ’10, Mark Trawick ’10, and Mali Zhang ’11 presented coffees on their summer research with talks on sports ranking, software updates to MAGIC Tool, and mathematical approaches to solving Scramble Square puzzles, respectively.

            The new academic year offered a fall semester sabbatical leave to Professor Stephen Davis, who kept quite busy with his varied activities, including the AP Calculus Development Committee. He also maintains his active participation and leadership in the Charlotte Math Club, which received the 2009 NCCTM Innovator Award at the annual meeting of the North Carolina Council of Teachers of Mathematics in October. Professors Rich Neidinger and Mike Mossinghoff both returned from sabbatical, the Mossinghoffs from a year away in South Carolina.

            As summer became fall, applications began arriving for the tenure-track position vacated by Professor Sarah Mason’s departure. The large number of applicants looks to lead to a most promising pool of candidates who will be interviewed at the Joint Mathematics Meetings in January. Look for more details on what transpires in the spring Bernard Review!

Professors Stephen Davis, Ben Klein, and Rob Whitton joined about 900 other college and secondary mathematics teachers to grade the over 300,000 Advanced Placement Calculus exams in June in Kansas City, MO. Stephen directed the grading of the Alternate (make-up) Exam and Ben oversaw the grading of a problem on the regular ("operational") exam. Stephen Davis and Michael Boardman (Pacific University) presented Results from the 2009 AP Calculus AB/Calculus BC Exam Administrations at the AP Annual Conference in San Antonio, TX.

            Professors Davis and Chartier attended MathFest, the summer meeting of the Mathematical Association of America, in Portland, Oregon. Stephen teamed again with Michael Boardman for a presentation on AP Calculus: What Faculty Need to Know. Tim served on two panels at a workshop sponsored by Project NExT, a professional development program for new Ph.D.s in the mathematical sciences. He spoke about Reflecting on Our Own Teaching and The Faculty Member as Teacher and Scholar. He also gave a talk, Google Power, offering suggestions for how to include the science behind Google’s rankings in a variety of math classes.

            Professor Laurie Heyer taught a weeklong Bioinformatics Workshop for Mathematics, Computer Science, and Biology faculty at Muhlenberg College in May. Laurie also hosted two high school teachers (a biology teacher from Hinsdale, Ill, and a math teacher from Atlanta) for a four-day curriculum writers’ meeting in June. The team wrote a bio-math module on microarrays, entitled Array of Hope, now being pilot tested in high schools nationally and soon to be published by COMAP in a book of such modules.

            Laurie was the lead instructor of analysis techniques and MAGIC Tool software at the Genome Consortium for Active Teaching microarray workshop held in July at Morehouse College and attended by 40 faculty from around the country. Mark Trawick ’10 worked on the software for 9 weeks during the summer and served as a teaching assistant at the workshop. Laurie was also invited to participate in the Transforming Undergraduate Education in Biology: Mobilizing the Community for Change conference in Washington, DC, in July. Professor Chris Paradise (biology) and Laurie presented a poster on their biology major textbook project, joint with Malcolm Campbell, titled Integrated Systems Biology.

            Professor Donna Molinek was recently selected to lead a Charlotte Teachers Institute seminar for the fall of 2010, entitled Mathematics in Art. This summer, Donna used crayons, twizzlers and bubbles to teach topology in her July experience workshop entitled Graphs, surfaces, and knots.

            Tim served as a keynote speaker at the annual Legacy of R. L. Moore Conference, a national conference on mathematical instruction focused largely on the inquiry-based methods developed by Dr. R. L. Moore in his years of teaching at the University of Texas at Austin. Tim’s talk, Exploring Mathematical Ideas with Mime, discussed uses of mime to introduce and teach mathematical ideas both in the college classroom and in Tim’s mime and math shows for children, youth and college audiences.

            Sarah Oberst ’10 and Ben Altman ’10 conducted their fall research as each pursues honors. Under the direction of Professor Molinek, Sarah is researching models which predict the spread of malaria; she studies both populations undergoing no medical intervention as well as populations with the option for intervention. Ben’s research, under the direction of Professor Neidinger, studies multidimensional higher-order automatic differentiation, extending beyond the material covered in Rich’s article to appear in SIAM Review. (See the Exposition section of the newsletter.) Erich Kreutzer ’10 conducted two independent studies in computer science: with Professor Mossinghoff, he studied Theory of Computation, a mathematical study of the fundamental capabilities and limitations of computers, and with Professor Chartier, Erich studied topics in ranking and clustering specifically as they apply to recommendation systems.

            To aid with the teaching needs of the department due to Sarah Mason’s departure, Ben Klein—who did indeed retire in 2008!—taught a section of Calculus I in the fall and will teach another course this spring. The department is grateful to Ben for delaying his full transition from teaching duties and for the care and dedication he puts into his classes and students.
         
Exposition

Professor John Swallow published a how-to article in the Notices of the American Mathematical Society, the world’s most widely read magazine aimed at professional mathematicians. Titled Proving Yourself: How to Develop an Interview Lecture 56 (2009), 948-951, the article offers advice to graduate students preparing for job interviews at colleges and universities. Candidates are often asked to deliver a lecture, and jobs can be won or lost based on that performance. The article provides guidance on telling a compelling mathematical story, handling technology, presenting oneself as a teacher and future colleague, fielding questions, and employing rhetorical strategies.

            Professor Richard Neidinger’s sabbatical writing was well received this fall. His article Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming was accepted into SIAM Review and will constitute the first article about OOP, or the implementation of algorithms in computational algebra, in the journal’s Education Section.

            Many Davidson students have attended Professor emeritus J.B. Stroud’s presentations on math in the work of artist Crockett Johnson, titled Barnaby and the Purple Heptagon. Of particular note, Harold and the Purple Heptagon was the title of the cover article in September’s Math Horizons magazine. The Math Horizons article by Stephanie Cawthorne and Judy Green stems from collaborative research by Stroud, Green, and Uta Merzbach in preparation for a 1980 exhibition of Johnson’s artwork at the Smithsonian Institution.

            Professor Tim Chartier and Erich Kreutzer ’10 published How easy is Easy Java Simulations programming? in the online journal Loci. The article reviews the Easy Java Simulation software developed by Davidson physics professor Wolfgang Christian and a colleague in Spain. Erich and Tim specifically discuss the software’s suitability for creating applets for mathematical instruction. Tim and Erich also co-authored with Amy Langville (College of Charleston) and Kathryn Pedings (College of Charleston) the article Google-opoly that also appeared in Loci. This article uses a game, called Google-opoly, played on a small directed graph to describe and model the Google PageRank algorithm. This work was one of two subcontracts Tim received under Langville’s NSF CAREER grant to develop interactive math modules. Tim published a piece entitled A Mathematical Circus as the cover article in MAA FOCUS 29 (Dec 2009/Jan 2010) no. 6, 16-17. The article discusses an interactive traveling math exhibit, Math Midway, that debuted this past summer. The exhibit is part of a larger effort to create the first interactive math museum in the U.S.

            As the banquet speaker at the fall meeting of the Maryland-District of Columbia-Virginia Section of the MAA, Tim presented his talk Putting a Spring in Yoda’s Step. Tim also gave this talk as a keynote speaker at the 5th Annual Texas Undergraduate Research Conference in Huntsville, Texas.

Professor Tim Chartier’s article Envisioning the Invisible appeared in Notices of the AMS as 57 (January 2010) no. 1, 24-28. The issue of the magazine, themed creativity in mathematics, included articles by Michael F. Barnsley on fractals and an article by Don, Muir, Volk, and Walker on music and mathematics. Tim’s article discusses his use of mime to introduce mathematical ideas and also as a teaching tool in the college classroom. The picture to the left is from the version of the show that includes Tanya Chartier, who has also studied mime including master classes with Marcel Marceau. Tim is inside the tube in a sketch that motivates ideas from topology. In preparation for the release of the issue, the American Mathematical Society prepared a press release on the magazine which made its way into national online news and a variety of blogs. Tim additionally performed his show Mime-matics at Wingate University, the Children’s Community School of Davidson, and Mint Hill (NC) Public Library since the last Bernard Review.

            Professor Rob Whitton 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. Winning teams and judges are treated to a Panthers game at which the judges were introduced to the crowd before the game; Rob reports that the crowd’s response was modest. Of particular note, Rob is now in charge of the contest and welcomes ideas for good contest problems!

         
Research

Professor Laurie Heyer and the collaborative research team between Davidson and Missouri Western State University had a big week in July. The team recently learned that their article Engineering bacteria to solve the Burnt Pancake Problem was named the The Journal of Biological Engineering’s top article of the year, having been accessed by readers more than 10,000 times. On July 20, the online journal PLoS ONE published the article, Evaluation of Three Automated Genome Annotations for Halorhabdus utahensis, co-authored by ten Davidson students, that has important implications for all genomic research. Then, the Journal of Biological Engineering published the team’s article Solving a Hamiltonian Path Problem with a bacterial computer, and wide interest in this work became quickly apparent. In its first five days online, the research paper was close to surpassing the Burnt Pancake Problem paper for the number of hits, which was again the top article of 2008 with over 10,000 hits. Such interest also led to the article ’Bacterial Computers’: Genetically Engineered Bacteria have Potential to Solve Complicated Mathematical Problems, which appeared in July in ScienceDaily. (See below for more details on the activities of this group.)

Algebra:
            Professor John Swallow lectured at the conference Linear Algebraic Groups and Related Structures at the Banff International Research Station, together with Andy Schultz (Illinois; Davidson ’02). John’s talk was entitled Galois cohomology groups as Galois modules, and applications.

Graph Theory:
            Under Davidson’s Duke Research Initiative funding, Mali Zhang ’11 spent her summer exploring mathematical approaches to solving Scramble Square puzzles. This NP-complete problem is inherently difficult to solve. Mali’s research, directed by Professor Sarah Mason in her last summer at Davidson, discovered techniques utilizing graph theory to solve puzzles. Her theorem can help solve a 2-by-2 puzzle, or spot a lack of solutions in a puzzle, in a more efficient way.

Discrete geometry and number theory:
            Professor Mike Mossinghoff’s paper Wieferich pairs and Barker sequences appeared in the journal Designs, Codes and Cryptography as 53 (2009), no. 3, 149-163. A Barker sequence is a sequence of +1’s and -1’s possessing a number of special arithmetic properties. The longest such sequence known has length 13, and it is thought that no more exist. The paper proves that if another Barker sequence exists, then its length n satisfies either n = 189, 260, 468, 001, 034, 441, 522, 766, 781, 604, or n > 2 * 10³⁰.

            Another paper of Mike’s was accepted for publication in a collection on experimental mathematics, which, broadly defined, is mathematical research performed using substantial computation to detect patterns and form hypotheses, which in turn guide directions in proof. The paper, entitled The distance to an irreducible polynomial, studies a problem first posed by the Hungarian mathematician Paul Turán.

            In September, Mike gave a plenary talk at the Workshop on Discovery and Experimentation in Number Theory, held simultaneously at the IRMACS Centre at Simon Fraser University in Vancouver and the Fields Institute in Toronto. Lectures were simulcast in a fully interactive way between the two sites and were streamed on the web as well. Mike also gave a talk in a special session on analytic number theory at the AMS Eastern Section meeting at Penn State. Mike spoke about a problem about the density of irreducible polynomials with integer coefficients. While the math was certainly the highlight of the trip, it didn’t hurt that the meeting occurred quite near the Penn State Creamery, a University-run ice cream manufacturer, where you can sample local favorites like the "Peachy Paterno."

Mathematical and computational biology: 
            The synthetic biology research group led by professors Laurie Heyer and Malcolm Campbell (biology) continued its collaboration with students and faculty at Missouri Western State University, hosting them at Davidson for a week at the beginning of the summer, and visiting them at MWSU for a week at the end of the summer. The team spent ten weeks designing, modeling, and building a biological implementation of the 3-SAT logic problem, the first problem to be proved NP-complete.

            In November, the students on the joint Davidson and Missouri Western team presented their project, called Can’t Get No SATisfaction, in a wiki page, a talk and a poster at the 2009 international Genetically Engineered Machines (iGEM) competition at MIT. Teams from 115 colleges and universities worldwide entered this year’s competition to use biological parts to build DNA-based systems that function in living cells. This year’s Davidson group, in collaboration with colleagues from Missouri Western State University, received a gold medal. Davidsonians participating on the team include Romina Clemente ’12, Mary Gearing ’11, A. J. Grant ’10, Olivia Ho-Shing ’10, Shamita Punjabi ’12, Sam Snell ’10, Shashank Suresh ’12, Leland Taylor ’12, Annie Temmink ’11, and Alyndria Thompson ’10. The research group continued to meet once a week during the fall semester to begin recruiting and training next summer’s team.

            Laurie and Malcolm attended the NIMBioS Undergraduate Research Conference at the Interface of Biology and Mathematics, held in Knoxville in October, along with Kin Lau ’10, who gave a talk, and Leland Taylor ’12, who gave a poster.

Numerical analysis and scientific computation:
            This summer, Jim Dickson ’09 worked with Professor Tim Chartier on research projects in multigrid under funding from the Department of Energy. Specifically, Jim analyzed the use of algebraic block smoothing methods as clustering algorithms and also the use of clustering methods to form algebraic blocks for iterative relaxation. Later in the summer, Jim explored the use of a measure of algebraic strength from research in algebraic block smoothers in coarse grid correction in classical AMG. Jim’s work led to a talk on Fiedler’s method at the Southeastern Ranking and Clustering Workshop in Charleston, South Carolina. Finally, Tim co-organized the minisymposium Adaptive Algebraic Multigrid Methods for the SIAM Annual Meeting and presented on multigrid methods at Appalachian State University.

            During the summer, Tim and Erich Kreutzer ’10 continued research in collaboration with Amy Langville and her graduate student Kathryn Pedings of the College of Charleston. The group continued analysis and development of sports ranking algorithms and studied sensitivity of Colley, Massey, and Markov rankings. The group also applied clustering algorithms to datasets from Netflix, Facebook, and public health applications; they studied the effectiveness of their new algorithm that aggregates the results from multiple clustering algorithms. The work in sports ranking led to a talk by Erich at the Southeastern Ranking and Clustering Workshop. For the workshop, Erich developed an online, password-protected network web tool, www.RankandCluster.com, for participants. This fall, Erich gave an invited talk at the South Eastern Atlantic Mathematical Sciences Workshop in Orlando, Florida, on his recent research for including ties into sports ranking.

            Tim also began research with Steph Meador ’12 on applying sports ranking methods in the context of web page ranking. The work has produced promising results. Tim continued work with Max Win ’10 on the effectiveness of using cosine similarity to cluster movies from Netflix ratings data.

         
Leadership

Professor Michael Mossinghoff has been named an associate editor of Mathematics of Computation, a research journal published by the American Mathematical Society, with a four-year term beginning in February. This journal is devoted to research articles in computational mathematics that cover such areas as numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods.

            Professor Donna Molinek was recently named to the Board of Advisors for the Charlotte Community School for Girls. This new school in Charlotte, opening in August of 2010, will be a tuition free private middle school for girls from low-income families. Donna will work on extracurricular mathematics activities.

            Professor Laurie Heyer was appointed to a 3-year term on the Mathematics Across the Disciplines subcommittee of the Committee on the Undergraduate Program in Mathematics, a national committee of the MAA.

            Professor Irl Bivens accepted an invitation from the Mathematical of Association of America to serve on the committee for the Carl B. Allendoerfer Award, granted to authors of excellent expository articles published in Mathematics Magazine.

         
Community

Bryant Barr ’10 was featured in a the college-produced video Davidson College - A Place Students Call Home in which students describe why they chose Davidson and what makes Davidson unique. The video includes nice segments of Bryant studying with friends, talking with Professor Heyer in her office, and even attending a computer science class with Professor Chartier.

            Bill and Laurie Heyer traveled to Australia July 30 - August 20 with funding from Davidson’s Matthews Travel Endowment Award. They sailed and snorkeled the Great Barrier Reef, took a crocodile cruise on the Daintree river in the rain forest, hiked and drove 4-wheel drive roads in the desert near the monuments of Uluru and Kata Tjuta, and toured the cities of Brisbane and Sydney. It was a phenomenal experience; Laurie is deeply grateful for the generous gift from the Matthews family that made the trip possible.

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.