Department

Sarah Mason joins the Department this fall as assistant professor of mathematics.  An NSF postdoctoral fellow at the University of California, Berkeley, Sarah is an algebraic and enumerative combinatorialist.  This spring she enjoyed living in Montréal as part of the thematic semester “Recent Advances in Combinatorics” at the Centre de Recherches Mathématiques. Sarah received her doctorate from Penn in 2006 after undergraduate years at Chapel Hill and Georgia, and her interests include service learning, environmental studies, and triathalons.
           
            Professors Tim Chartier and Mike Mossinghoff received word of national awards, for teaching and high-level exposition, respectively.  See the Pedagogy and Exposition sections below for the exciting details.
 
            In the national competition for Goldwater Scholarships, Adam Topaz ’08 was named a winner and Daniel Orr ’08 earned an honorable mention.  This year the competition, among U. S. sophomores and juniors majoring in mathematics, science, or engineering, involved 1,110 applicants and 317 winners.  Only 28 winners are mathematics majors.

            Fourteen majors and eleven minors graduated from the Department, and two majors, Nick Dovidio and John Helms, earned departmental honors.  (See the Envoi section below for their plans after graduation.) Tim Rankin '07 was the recipient of the McGavock Award, and Kent Ford '09 received the Vinson Award. The Bernard Society elected officers Phillip Compeau ’08 (president), Katie Daves ’08, Adam Topaz ’08, and Don Williams ’08.

            A number of students engaged in mathematical contests this semester.  At the MAA’s southeastern sectional meeting, the Davidson Math Jeopardy team finished second out of fifteen schools  Our team consisted of John Helms ’07, Tim Rankin ’07, Andrew Ruth ’07, Peter Simov ’08, and Adam Topaz ’08, and was coached by professor Irl Bivens.  Several three-person teams from the Department also participated in the international Mathematical Contest in Modeling, and one team earned an honorable mention.

            This spring’s Math Coffee series included students Nick Dovidio ’07, on web ranking algorithms; John Helms ’07, on the algebra behind the Rubik’s Cube; Mallory Nobles ’07, on analyzing police contacts; and Tim Rankin ’07 and Andrew Ruth ’07, on threshold probabilities and optimal betting strategies.  We also heard from alumni Bill Beckmann ’72, on rethinking income tax deductions, and David Bell ’67, on modeling computer security, as well as several speakers from other institutions. 

            The Department’s lineup changes a bit each year as faculty take time for other projects, and next year will be no different.  Professor Chartier will be on leave during 2007—2008, spending a month at the Los Alamos National Lab and the remainder of the year at the University of Washington, Seattle.  Professor Heyer will be teaching again after her year’s leave in Davidson.  Professor Molinek will be returning to Davidson from her year’s leave at Chapel Hill.  Professor Swallow, recently promoted from associate professor to professor, will be teaching both semesters of first-year Humanities next year.

Pedagogy

Professor Chartier received the thrilling news that he will receive one of three Alder Awards at 2007 MathFest in San Jose this summer.  Each year up to three Alder Awards are given in recognition of exceptional teaching by an early-career mathematician.  The Department celebrated Tim’s achievement at a party at the Neidingers’.
 
            This spring Tim published several papers on teaching. Math bends it like Beckham, a note on how fluid dynamics determine the trajectories of soccer balls,appeared as Math Horizons, February 2007, 2; Using the Force: Star Wars in the classroom, about digitally representing Yoda, as PRIMUS 17 (2007), no. 1, 8—23;  and Mathematically entertained, summarizing talks from the “Entertaining with Math” session at the Joint Mathematics Meetings in New Orleans, appeared as FOCUS 27 (2007), no. 3, 18—19. Tim also publicized two web pages. The first, on mathematical murder mysteries, was created by Lesley Attkisson '06, Nick Cain '06, Bridget Cook '06, Michael Flake '06, and Martha Shott '06, and has received over 300 unique visitors thus far. The other, Tim's page on Yoda, has received over 800 and was the subject of a press release by MapleSoft.  Tim also gave a brief presentation at the 10th annual Legacy of R. L. Moore Conference.

            Professor Laurie Heyer accepted an invitation by the editors of a special issue of PRIMUS to submit a paper, and A mathematical optimization problem in bioinformatics is now awaiting comments. Laurie’s proposal for a new two-semester sequence Calculus and Modeling I and II was approved by the College, and she will offer the first instance of the sequence next year. 

            Professor Donna Molinek’s proposal for a new course Exploring Mathematics in Art was also approved, and she will offer the first instance this fall.

            The Department’s investments in the AP Calculus program remain significant.  At the reading this summer, Professor Stephen Davis will serve as the Alternate Exam Leader and professor Ben Klein as a Question Leader.

            Several from Davidson spoke in MAA sessions on teaching at the Joint Mathematics Meetings in New Orleans. Professor Chartier spoke on Mathematics in mime in the session “Entertaining with Math,” which he also organized.  Nick Dovidio ’07 described A Mathlet to interactively explore ordinary differential equation solver in “Mathlets for Teaching and Learning Mathematics.”  Professor Heyer gave a preliminary report, Computing with bacteria: the new wave of synthetic biology, in “Integrating mathematics and biology in undergraduate education.”  Finally, Professor Klein spoke on a panel entitled “What mathematical content should future mathematics majors learn while in high school?”

           This spring the Department also sponsored several independent study courses.   Professors Richie King, Mike Mossinghoff, Rich Neidinger, and Robert Whitton led independent study courses this semester, on, respectively, algebraic topology, theory of computation, dynamical systems, and algorithms for graphics.

Outreach  

Professors Bivens and Klein wrote the questions for the N. C. State Mathematics Contest.  The test, administered at the North Carolina School for Science and Mathematics, is given to the top 100 scorers on regional tests given throughout the state.  One such test took place at UNCC’s Super Competition on March 5, and professor Neidinger delivered a featured presentation, Counting on infinity, to over 100 high school students attending the event.

Exposition

Professor Mossinghoff received the wonderful news that he will receive a Ford Award at the 2007 MathFest in San Jose.  Each year several Ford Awards are given for expository excellence in articles published in the American Mathematical Monthly, and Mike will earn an award for his first paper in the journal.

            Professor Swallow gave the Section Lecture, Circular irrationalities: From Galois to Kummer and back again, at the MAA’s southeastern sectional meeting.  He also gave a variant of the talk as the keynote address at the Sewanee-Hendrix-Rhodes Undergraduate Mathematics Symposium, held in Sewanee, Tennessee, and he was glad to return to a conference he attended as an undergraduate.

            At the same southeastern sectional meeting, John Helms ’08 spoke on Exploring the Rubik’s Cube, professor Klein on Multiple representations of functions using a touchscreen calculator, and Tim Rankin ’08  and Andrew Ruth ’08 on Determining threshold probabilities.  Ben also spoke on representation of functions at the national NCTM meeting in Atlanta and on graph theory at High Point University.

           Professor Bivens’ work with Andrew Simoson (King’s College) on rotating shoreline beacons, originally published in 1998, gained new life in Simoson’s recent book Hesiod's anvil: Falling and spinning through heaven and earth (MAA, 2007).  The book christens several mathematical objects with Irl’s name—now look out for the “Bivens parameterization” and the “Bivens transform”!

Research

Algebra: 
           Professor Swallow gave a talk entitled Galois module structure of square classes in Klein 4-group extensions in the AMS special session “Cohomology and representation theory” at the Joint Meetings in New Orleans.  John has begun working with Adam Topaz ’08 this summer under the auspices of the Davidson College Research Program, initiated by a grant from the Duke Endowment.

Discrete geometry and number theory:
            Professor Mossinghoff’s paper Generalizations of Gonçalves’ inequality with Peter Borwein (Simon Fraser University) and Jeffrey Vaaler (Texas) appeared as Proc. Amer. Math. Soc. 135 (2007), no. 1, 253—261.  Gonçalves’ inequality states that the Mahler measure of a polynomial cannot get too close to the L₂-norm of the polynomial, and the paper extends the result to the L_p-norm.  Another paper, Barker sequences and flat polynomials with Peter Borwein, has been accepted to the proceedings of the conference “Number Theory and Polynomials” (Bristol, 2006).

            A third paper, Lower bounds for Z-numbers with A. Dubickas (Vilnius), was recently submitted. For a rational noninteger r > 1, a Z_r-number is positive real number l with the fractional parts of l rⁿ poorly distributed in the unit interval [0,1].  Mike and Dubickas establish results used in searching for Z_r numbers and show, for instance, that if a Z_3/2 number exists, then it exceeds 2⁵⁷. 

            At the MAA southeastern section meeting, Mike spoke on Large counterexamples in number theory, and at the New Orleans Joint Meetings, Mike spoke on Isodiametric problems for polygons in the AMS special session “Experimental mathematics in action.” Approached by an organizer of the AMS session to submit a result for a volume of related papers, he wrote and submitted An isodiametric problem for equilateral polygons.  In place of arbitrary polygons, the article considers equilateral convex polygons, finding their maximal perimeters among those with fixed diameter. 

Dynamical systems:
           Professor Molinek’s article One-dimensional stochastic cellular automata with Jane Hawkins (Chapel Hill) was accepted to Topology Proceedings.  Donna and Jane continue to work evaluating the topological and asymptotic properties of stochastic cellular automata in biological models.  Donna also gave a lecture in Chapel Hill’s ergodic theory and dynamical systems seminar.

Mathematical and computational biology: 
            Professor Heyer submitted Computing with living hardware with fifteen other co-authors—including three Davidson students and two other Davidson faculty.  Even while on sabbatical this year, her projects with students continue to expand.  This year Laurie worked with several students, including Michael Gordon ’08, Andrew Martens ’08, and Adam Topaz ’08, on improving MAGIC Tool, and this summer Nick Dovidio ’07 and Michael Gordon will work on the project.  At the same time Laurie will be working with Phillip Compeau ’08 (Davidson College Research Program) on graph theory aspects of the pancake problem, and Jim Dickson ’09 on modeling questions in synthetic biology. 

Numerical analysis and scientific computation:
            Professor Chartier and Tim Rankin ’07 submitted Efficiency of multigrid algorithms for head models on electroencephalography simulations with Ceon Ramon (Washington).  Their algorithmic improvements for producing simulations of slices of the human brain range from 20 to 66 times faster than previous methods.

            Tim also spoke on work he completed with Daniel Orr ’08, Preconditioning with adaptive multigrid via subcycling on complementary grids, at the 13th Copper Mountain conference on multigrid methods.

 Off-campus summer research experiences:
            This summer Michael Duncan ’08 joins a Research Experiences for Undergraduates (REU) program at LSU, and A. J. Hergenroeder ’08 joins an REU program at Texas A&M.  Madeline Parra ’09 will participate at the Summer Institute for Training in Biostatistics at North Carolina State University.

Leadership

Professor Heyer was elected to the newly-created position of Student Activities Coordinator of the MAA’s southeastern section.  Laurie’s other roles this year have included service on the Faculty Advisory Board for the Woodlawn School (Davidson), interviewing for the Knowles Science Teaching Foundation Fellowships, and reviewing, with Tim Elgren (Hamilton), the HHMI program at Trinity University.

            Professor Davis was appointed the chair of the AP Calculus Test Development Committee.

            Professor Swallow was appointed an associate editor of the Notices of the AMS, “the world’s most widely read magazine aimed at professional mathematicians.”  John was also accepted by the Salzburg Seminar for its “Young Leaders Summit” in December.

            Professor Klein continues his service on the editorial board of the MAA book series Dolciani Mathematical Expositions as well as on the MAA Investment Committee.

Events

On March 3 and 4, Davidson hosted its first-ever AMS meeting.   The 2¹⁰th meeting of the AMS included over 300 registered participants, 14 parallel sessions, and the Erdős Memorial Lecture, delivered by Andrew Granville (Montréal). 

 
           Professor Chartier organized the special session “Recent applications of numerical linear algebra” with Amy Langville (College of Charleston); professor Molinek the special session “Dynamical systems” with Emily Gamber (Santa Fe Institute) and Jim Wiseman (Agnes Scott College); and professor Swallow the special session “Representation theory and Galois cohomology in number theory” with Ján Mináč (Western Ontario).  Professors Mossinghoff, Neidinger, and Swallow handled many of the local arrangements during the weekend.     

            Save the date! The 2007—2008 Bernard Lecture is scheduled for September 30, 2007.  Professor Francis Su (Harvey Mudd College) will be this year’s lecturer.

Envoi           

A fond farewell to our many mathematics majors and minors from the class of 2007!

Faris Al Mazrui will enroll in the London School of Economics’ master’s program in economics.  Jeb Coleman will be a property and casualty actuary for Mercer Oliver Wyman.  Nick Dovidio will enroll in the Stanford master’s program in computer science, and Andrew Edelman will work at Banc of America Securities as an investment banking analyst. 

            John Helms will enroll in Chapel Hill’s doctoral program in mathematics after he works for the Duke Talent Identification Program Precollege Program during the summer.  Mimi Hobart will teach at Episcopal High School in Alexandria, Virginia, and Thomas Lodato will teach at Rabun Gap-Nacoochee School in Dillard, Georgia. Wilson McCrory will be with McKinsey and Company as a business analyst.  Jared McKiernan will join the Segal Company in Chicago as an actuarial analyst in the retiree medical practice. 

           Mallory Nobles will be a research assistant in the Trade and Quantitative Studies Department, International Economics Division, of the Federal Reserve Board, and Tim Rankin will begin a Ph.D. program in mathematics at Duke. Linda Russell will begin a premedical program and medical school at Columbia College and the University of South Carolina.  Andrew Ruth will be on staff with Young Life, working in Davidson. David Sartorio will enroll at Chapel Hill’s law school, and Amanda Traver will work as an economic valuation services analyst with KPMG.  James Wells will begin a graduate program in physics at the Univeristy of Connecticut, and Walter Wiggins will begin medical school at Wake Forest.

Alumni News

           Bernard Society alumni: please send us news that may be of interest to readers of the Review. General-interest news should be sent to the Davidson Journal, but we would be pleased to include more detail about any projects including mathematics, computer science, or related fields. Email us at this address, which we check periodically: mathdept@davidson.edu.

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.