Department

The Mathematics Department had an active and successful spring. Excellence in the classroom was particularly evident at the college-wide Spring Convocation. At the awards ceremony, mathematics professors received both of the faculty awards for teaching. Dr. John Swallow received the Omicron Delta Kappa (national leadership honor society) Teaching Award. John was noted for "his passion for sharing knowledge" and making "the learning environment supportive and interesting. He demands much from his students, but his excitement and devotion are so encouraging that students learn never to settle for less than expected." Dr. Robert Whitton won the Student Government Association Faculty Award. Rob was noted as "a great teacher in and out of the classroom. . . . He cares so much about the students and this school." Rob was also noted for his "tireless commitment and dedication to the lives of Davidson students." What a wonderful celebration of John and Rob's exemplary teaching in the classroom!

           A year ago, the department embarked hours after graduation into the North Carolina mountains for a departmental retreat. A year later, the department's curriculum changes have been approved and put in place for next year. These include a revised of the calculus sequence, new courses in computer science, and more flexible paths through the major. The revisions have received very positive reactions from students and faculty alike. Such quick affirmation confirms the value of the time the department took this year to work out all of the details!

           The semester began with the department attending the Joint Mathematics Meeting in San Francisco, primarily to interview candidates for the open tenure-track position. Hours of work and deliberation by department members in advance had narrowed the hundreds of applications down to a manageable number to interview at the meeting, and after these interviews the department prepared a list of ten and then a final list of three to bring to campus. The process led us to Carl Yerger who works in the areas of combinatorics and graph theory. We look forward to all he will offer this fall. For more information on Carl, read more below.

           Mikael Goldmann from the school of Computer Science and Communication at the KTH Royal Institute of Technology in Stockholm, Sweden will be a visiting STINT professor this coming fall. To prepare for his time in Davidson, Mikael traveled to North Carolina in April. Students and faculty enjoyed his visit, which was extended by one week due to the volcanic eruption in Iceland!

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

The annual department awards were presented at the spring convocation. Ben Altman ’10 received the William G. McGavock Mathematics Award. Ben has excelled with a "combination of talent and determination . . . in a mathematics classroom as well as on a wrestling mat." Paul Britton ’12 received the William Vinson Mathematics Award and was noted particularly for his "careful attention to detail and deep appreciation for the big picture."

           This spring two seniors, Ben Altman and Sarah Oberst, successfully completed honors in mathematics. Under the direction of Professor Molinek, Sarah completed her thesis entitled A Mathematical Model of Malaria. This project grew from studying the modeling of disease with Dr. Molinek in Mathematical Modeling (MAT 210) and a trip to Ghana in which Sarah saw firsthand the effects of the illness. Under the direction of Professor Neidinger, Ben Altman completed a thesis entitled Higher-Order Automatic Differentiation of Multivariate Functions in MATLAB. This thesis utilized MATLAB to implement four alternative methods for this massive AD problem and to compare them according to efficiency and accuracy. Techniques employed ranged from theoretical interpolation to object-oriented programming and arrays of all kinds. Ben's project grew from studying AD with Dr. Neidinger in numerical analysis (CSC 325) and Dr. Neidinger's own research advancements over his 2008-2009 sabbatical.

           In February, five 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. All five participating teams received recognition among the 2254 teams—of which only 16% were from the U.S. Three Davidson teams were awarded Meritorious distinction, given to the top 20%: Daniel Martin’11, Lake Trask ’11, and Louisa Williams ’12; Amanda Flink ’11, Sydney Owen ’11, and Greg Macnamara ’12; and Val Lee ’10, Alexander Griswold ’10, and Mali Zhang ’11. The other two teams received Honorable Mention distinction (in the next 24%): Jennings Boley ’10, Carter Eggleston ’11, and Annie Temmink ’11; and Christina Blackwood ’12, Brian Sachtjen ’12, and Stephen Streb ’12.

           In the live Math Jeopardy Competition at the MAA Southeastern Section meeting at Elon University, the Davidson team of Ben Altman ’10, Shashank Suresh ’12, Colin Thomson ’13, and Mali Zhang ’11 earned fourth place in a field of 32 college and university teams from the southeastern U.S. One highlight from the match was Shashank buzzing in to score 1000 points for Davidson by computing the surface area of a torus, which was described as a surface of revolution for a particular circle given parametrically. That's not a frequently trodden corner of calculus! Also at the meeting, this same team's T-shirt entry was named co-winner in the math T-shirt contest! Ben Altman spearheaded this effort, with assistance from Professor Chartier. The T-shirt had the Davidson Wildcat emblem, drawn by a program that found an approximate solution to a traveling salesman problem on a network of cities laid out in such a way that when the cities were connected with the path the Davidson Wildcat appeared! This design can be seen in the picture heading this section. Click the image to see a larger version of the image.

Pedagogy

With the aid of the Community Service Office, the Mathematical Modeling class partnered with four nonprofit organizations on six modeling projects. In the end, the students' work and recommendations were presented in a poster session that was attended by the community partners, other students and college faculty. To read more about the projects and students who participated read a DavidsonNews.net article or an article that appeared through College Communications.

        Professor Molinek began teaching in the Charlotte Teachers Institute. She led a seminar entitled Mathematics in Art, in which CTI Fellows study the mathematics behind several types of art and produce a curriculum unit for their own classrooms.

        Professor Chartier was selected by the graduate students at Iowa State University to visit their Math Department and present to the department on teaching. In his talk Engaging students mathematically - pitch by pitch, Tim discussed ideas on connecting with students outside the classroom in their areas of interest.

        This winter, Dr. Mossinghoff created a course, Mathematics and Politics, to be offered this fall. Aimed for a general audience, this course will examine different voting methods and some paradoxes that can occur with them, as well as other topics like how to divide a resource among several parties, such as methods for allocating seats to states in congress.

         Finally, Professor Ben Klein taught Complex Analysis, which will probably be the last regular Davidson College course he will teach. (The students in July Experience will enjoy his expertise as he leads a class this summer.) We all wish Ben and Rosemary the happiest of times and thank Ben for his service to Davidson both before and as he began his retirement.

Outreach  

Drs. Molinek, Heyer, Mossinghoff and Chartier participated in Davidson's March MATHness event, which was organized by HHMI outreach coordinator Tiffany Scheff. Geared for middle and high school students and their teachers, the event was well-attended and the audience quite energetic. Middle-schoolers added their own ambience to the presentations: after Laurie's talk on biological computing, one sixth-grader wanted to know where he could score some of those bioluminescent proteins, just because they sounded pretty cool! Mike's talk discussed some problems in plane geometry: if you place a finite number of points in the plane, not all on the same line, must there always exist at least one line that connects exactly two of the points? Donna opened the day with a talk on topology complete with a square morphing into a circle in sync with background music about the topic. Tim and his wife Tanya presented Mime-matics at the end of the day. A number of students who have studied math presented or aided in workshops throughout the event. The activities varied and were well-received. Drs. Bruce and Eve Torrence of Randolph Macon College visited and each contributed in fun ways to the day—Bruce giving a talk and Eve teaching everyone to construct a ball of fire based on a stellated dodecahedron. You can read more about the event in the DavidsonNews.net article.

          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—and their families (parents and siblings)! Parents and children watched Tim Chartier's Mime-matics performance and rotated through activities including building 3D figures with ZomeTools, which was led by several Davidson math majors.

          In March, Tim and Tanya Chartier presented Mime-matics at UNCC's Julia Robinson Math Day for middle school girls. The event drew over 200 girls. Earlier in the day, Austin Totty ’12 led an activity on the Euler characteristic while Katie Richeson ’11 and Linda Kleist, visiting student from Germany, worked with the youth as they explored origami.

Professor Laurie Heyer and her coauthors—a faculty colleague and a student from Missouri Western State University, Phillip Compeau ’08, Jim Dickson ’09 and Lance Harden ’10—were featured on the cover of the February 2010 issue of Math Horizons (pages 5-10) for their paper in that edition, titled Bacterial Computing: Using E. coli to Solve the Burnt Pancake Problem.

           Professor Irl Bivens presented The Median Value of a Continuous Function at the MAA Southeastern Section meeting. This work, developed with Professor Klein, considers a continuous function f(x) on a closed interval [a, b] that is partitioned into n equal subintervals. The talk discusses the median of the n values of f at the midpoints of the subintervals and proves the existence of a limiting median value as the number of subintervals approaches infinity.

          At the same meeting, a number of Davidson undergraduates presented their work. Ben Altman ’10 and Sarah Oberst ’10 spoke on the results of their honors theses. Mali Zhang ’11 presented on her work on a graph theory approach to scramble square puzzles. Shashank Suresh ’12 presented a poster on his summer work with the iGEM team on exploring patterns in boolean satisfiability. Professor Chartier co-organized a special session on Ranking and Clustering in which the following students presented: Jennings Boley ’10, on information gleaned from clustering data from friendships on Facebook; Mark Trawick ’10, on the use of the free software Cluto for clustering; and Colin Thomson ’13, on a method he created for computing the best weight to predict the outcome of the NCAA Division I Men's basketball tournament.

          Even while interviewing job candidates, the department was active at the Joint Mathematics Meetings in San Francisco. Professor Stephen Davis served as a panelist in a session, co-organized by Professor Chartier, entitled Teaching Calculus to Students who Have Had AP Calc: Challenges and Solutions. Erich Kreutzer ’10 presented his results on studying clustering and recommendation systems in his talk Movie Recommendation Systems. Adam Lewicki ’11 discussed results studied with Dr. Whitton in his talk Well Behaved Rotation About Planar Non-linear Curves: An Analysis of the Volume and Uniqueness of a Solid Swept Out by Rotation about a Non-linear Axis. Mali Zhang ’11 presented a poster on her work on scramble squares. Tim Chartier motivated some of the mathematical ideas behind Google's web ranking in his talk Google-opoly.

          Dr. Davis presented at the T³ (Teachers Teaching with Technology) 2010 International Conference in Atlanta. His talk Challenges in Writing AP Calculus Exams was part of a panel on Technology Issues in Advanced Placement Calculus.

          Math and Sports was the theme selected for this year's Math Awareness Month (MAM). Dr. Chartier's recent work in this area led to a number of opportunities to contribute. Two essays appeared on the MAM web page. Tim authored an article Bending a soccer ball with math that discusses the use of math to model the trajectory of a free kick in soccer. This article inspired one of the posters. Another article, Bracketology: How can math help? was coauthored with Erich Kreutzer ’10 and Amy Langville and her graduate student Kathryn Pedings of the College of Charleston. The article discussed their work and new methods in sports ranking, particularly integrating weighting of games into ranking methods that utilize linear algebra. Seeing Professor Chartier's varied involvement led Princeton University Press to interview Tim regarding sports and mathematics.

          Professor Chartier, Amy Langville and Peter Simov ’08 published the article March Madness to Movies (pages 16-19) in the April 2010 issue of Math Horizons. The article uses sports ranking methods to decide the best movie over a decade.

           Tim presented A pretty mathematical face at Kalamazoo College in which linear algebra is utilized for facial recognition. That evening, Tim presented Mime-matics for the George Kitchen Memorial Lecture series at Kalamazoo College. In the same trip, Tim presented Mime-matics and a banquet talk on sports ranking at the MAA-Michigan Section and MichMATYC spring meeting. Tim and Tanya also jointly presented Mime-matics at Virginia Commonwealth University. In the duet version of the show, a 25 foot "slinky" tube motivates ideas of topology.

Professor Michael Mossinghoff organized the Southeast Regional Meeting on Numbers ("SERMON"), held at Davidson College the weekend of April 16-18. About thirty visitors attended the conference, mostly from colleges and universities in the southeast, but also including participants from Illinois, Pennsylvania, and New York. The plenary speaker was Dr. Kevin Hare from the University of Waterloo, who gave a special math coffee for Davidson students on that Friday about perfect numbers. A number is perfect if it equals the sum of all its proper positive divisors, like 28 = 1 + 2 + 4 + 7 + 14. A very old unsolved problem in math is to determine if any odd perfect numbers exist, and Dr. Hare showed how computers have been used in recent years to determine several kinds bounds on any odd perfect numbers. For example, it is now known that if an odd perfect number exists, then it has more than 300 digits, and more than 75 prime factors. The talk included a live proof using a computer algebra system that an odd perfect number must have at least 33 prime factors!

Algebra:
         Professor John Swallow’s paper Hilbert 90 for Galois cohomology with Nicole Lemire (Western Ontario), Ján Mináč (Western Ontario) and Andrew Schultz (Illinois; Davidson ’02) appeared in the Communications in Algebra as 38 (2010), 361-372. John is excited by his long-term Galois cohomology project and plans to continue visiting his various collaborators—and he'll need to visit Andy next at Wellesley College, where Andy begins an assistant professorship this fall

Discrete geometry and number theory:
         Professor Mossinghoff's article Lower bounds for heights in cyclotomic extensions with M.I.M. Ishak, Christopher Pinner, and Benjamin Wiles of Kansas State University appeared in the Journal of Number Theory as 130 (2010) no. 6, 1408-1424. Reflecting our modern times, the journal now offers authors the chance to post a video abstract summarizing their results on a special YouTube channel for the journal. While the authors brainstormed ideas, they eventually passed on the video option.

Dynamical systems:
          Professor Donna Molinek gave the keynote address, Modeling the Progression of HIV in the Lymph System with 2-D Stochastic Cellular Automata, at the Francis Marion Undergraduate Mathematics Conference at Francis Marion University in Florence, South Carolina. Steph Meador ’12 also gave a talk at the meeting on her work with Dr. Chartier on the adaptation of sports ranking methods to search engine rankings.

         This summer, Donna will work with Beth Peters ’11 under a Davidson Research Initiative grant to create a module on graph theory and its applications for middle school students. A student from North Carolina A&T will work with Beth and Donna.

Mathematical and computational biology: 
          Drs. Heyer and Campbell's synthetic biology research group learned that their paper Solving a Hamiltonian Path Problem with a bacterial computer was named "Outstanding publication of 2009 in the Journal of Biological Engineering." Math major Jim Dickson ’09 and four other Davidson students were co-authors on this paper. Note that their paper Engineering bacteria to solve the Burnt Pancake Problem received this recognition in 2008.

          Katie Richeson ’11, a center major in Computational Biology, and Linda Kleist, visiting student from Germany, did research during a spring independent study in Math, DNA and Origami. Katie and Linda developed ideas for using DNA structural information to solve the Scramble Squares problem. They presented their work in a math coffee during the term.

          The iGEM team has been selected, and began training and brainstorming research project ideas during weekly meetings of Bio-Math Connections. Math majors Steph Meador ’12, Eugene Shiu ’12 and Stephen Streb ’12, along with Keila Alfred from North Carolina A&T, are the mathematical part of the team that will work throughout the summer. Shashank Suresh ’11 and Annie Temmink ’11 presented a math coffee on their work from last summer.

Numerical analysis and scientific computation:
          Professor Chartier continued his research in ranking and clustering. Erich Kreutzer ’10 presented their research results in his talk When a win is not a win - Inducing Ties in Sports Ranking at the SIAM Southeastern-Atlantic Section Conference. As part of the research in ranking, Tim Chartier's team of students and Amy Langville's group at the College of Charleston coordinated their work in creating mathematically generated brackets for the NCAA Division I Men's basketball tournament. Erich, Colin Thomson ’13 and Steph Meador ’12 designed their methods.

          Tim also taught a one-week unit on sports ranking in the Mathematical Modeling class. The students learned to create their own mathematically-generated brackets. They submitted their brackets to the ESPN Tournament Challenge and competed against each other and the close to 5 million other brackets! The bracket that received the most points was created by Daniel Martin ’11, predicted Duke as the winner, and was in the top 99.9th percentile. Also notable was a bracket by Steph Meador that predicted Butler's appearance in the finals. This work, in an area that receives such national focus, caught the eye of the media. Derek James of Fox Charlotte interviewed Tim, Colin and Erich in his story Breaking Down Brackets. In another television interview, Aaron Mesmer of News 14 Carolina interviewed Tim, Erich and Jennings Boley ’10 as part of his story Math meets March Madness at Davidson College. The work was also covered in two stories on DavidsonNews.net.

         During the spring semester, Chartier used funding from his Alfred P. Sloan Research Fellowship to support North Carolina State University doctoral student Chuck Wessell. Chuck came to campus for four weeks and participated in the life of the department and college in a variety of ways. Chuck visited the Mathematical Modeling class and taught a unit on clustering methods. He also helped guide the independent study on clustering financial data with Jennings Boley ’10 and Mark Trawick ’10. Chuck also aided in clustering research with Erich Kreutzer and his independent study. This work included clustering political data supplied by Professor Pat Sellers of the Political Science Department at Davidson. The visit allowed Chuck to experience life at a liberal arts college firsthand and for the department to be enriched by Chuck's gifts and knowledge.

          Professor Chartier continues his research in multigrid and presented on the topic at Florida Institute of Technology in March.

Professor Tim Chartier accepted an invitation to join the Museum of Mathematics' Advisory Council, which will offer intellectual guidance to the Board of Trustees. Soon after submitting spring grades, Tim travels to New York City, the eventual home of the nation's first mathematics museum, to aid in the planning of the interactive exhibits. The museum's traveling exhibit called Math Midway is already appearing at locations around the country.

          Professor Laurie Heyer was elected to a second 3-year term as Student Activities coordinator for the Southeastern Section of the MAA. In her first term in this role, she organized the Graduate School and Career Fair, and coordinated volunteers for all the student events (paper and poster sessions, treasure hunt, math jeopardy and a T-shirt contest) at the annual MAA-SE Section meeting.

          Professor Stephen Davis continued his leadership with the Charlotte Mathematics Club. In addition to monthly meetings, he took 17 students to the College of Charleston Math Meet in February; the group returned with several individual and team trophies.

This fall, Carl Yerger will join the department as an assistant professor. Currently, Carl is completing a doctorate at the Georgia Institute of Technology in combinatorics and optimization. He holds a Certificate of Advanced Study in Mathematics from the University of Cambridge and a B.S. in Mathematics with a humanities concentration in Economics from Harvey Mudd College. Yerger’s research, which has included an internship at the National Institute for Informatics in Tokyo Japan, has produced a number of papers in his field. Among his awards include a Barry M. Goldwater scholarship and a Winston Churchill Foundation scholarship. When not in the classroom, Carl enjoys tennis, bowling and korfball. Carl will have much to offer in and out of the classroom. We look forward to his presence on campus.

A fond farewell to our many Bernard Society members from the class of 2010! Several students reported definite plans:

Ben Altman will attend New York University in pursuit of a Master of Mathematics in Finance degree. Ananta Bangdiwala has received a Fulbright Teaching Assistantship Grant to teach and study in Madrid, Spain. Bryant Barr be working for Mercer, a Human Resources consulting firm, in their retirement group as an actuarial analyst in downtown Chicago. Abi Johnson will receive an officer's commission in the Navy.

          Val Lee will join Deloitte Consulting in Atlanta as a business analyst. Sarah Oberst will work in the Philippines as a Project Associate for Innovations for Poverty Action on a project dealing with credit scoring and the impact of microcredit. Sara Page Waugh will teach Math and French at St. Margaret's School, which is an all-girls boarding school in Tapphannock, Virginia. Nathalia Paulinelli will work for Wells Fargo in their High Grade Debt Capital Market division.

          Zana Shaban has received a fellowship to attend the M.A. program in accounting at Wake Forest University. Ben Thompson has received a full scholarship to pursue a Ph.D. in economics at the University of Michigan. Max Win will move to Arlington, Virginia to work as a software engineer with Simplicity Corporation.

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.