Abstracts/Biographies

Title: Blogging by Numb3rs

Speaker: Mark Bridger, Northeastern University

Abstract: The CBS TV show Numb3rs features a mathematician who uses his skills to help his FBI brother solve crimes. It's network TV fare, but it's all we've got, so Mark Bridger decided to write a web-log or "blog" to explain in relatively non-technical terms the mathematics referred to in each episode. In writing nearly 100 installments, Mark has learned a lot of math, gotten some interesting e-mail, and become an unpaid -- the story of his life -- consultant to the show. His wife Maxine, also a mathematician, works with him, and she doesn't get paid either, though they both got nice hats and tee-shirts.

Biography: Mark Bridger has had an eclectic math career. He received his Ph.D. under Maurice Auslander (Brandeis, 1967) in homological algebra and published a bit in that field. Around 1980 he got involved in computing and its applications to math education. He wrote some of the first math-plotting software for the then new IBM PC, and he and his wife Maxine peddled it through their small company, Bridge Software. He also did a bit of consulting in image and data analysis.

Gabe Stolzenberg, his colleague at Northeastern University, got him interested in constructive analysis. They wrote a Monthly paper, and Mark is about to publish a text in that field. Blogging the Numb3rs show has allowed him to look into a lot of math he never had gotten around to learning -- He's just making a dent, but having a lot of fun.

Mark likes biking, gardening, crosswords and carpentry, and he played in a bluegrass band for 12 years until he hung up his mandolin by popular demand. Maxine, an expert, has not been able to convince him to do more than 1 sudoku.

Title: Serendipity and Partitions with Initial Repetitions

Speaker: George Andrews, Penn State University

Abstract:  An inquiry by an engineer led by a circuitous route to the topic of this talk. A variety of interesting connections with modular forms, mock theta functions and Rogers-Ramanujan type identities arise in consideration of partitions in which the smaller integers are repeated as summands more often than the larger summands. In particular, this concept leads to new interpretations of the Rogers-Selberg identities and Bailey's modulus 9 identities. This latter interpretation suggests some thoughts on the Borwein Conjecture.

Biography: George Andrews is Evan Pugh Professor of Mathematics at Penn State University and an expert on the theory of partitions. He has a long-term interest in the work of S. Ramanujan, whose last notebook he unearthed in 1976. He is now collaborating with Bruce Berndt on a series of volumes explicating the brilliant and sometimes enigmatic ideas in this notebook. Andrews was elected to the National Academy of Sciences in 2003. Penn State has given us permission to post this article about George Andrews. It appeared in their departmental newsletter when he was elected to the National Academy of Sciences in 2003.

Title: An equation runs through it: River running on the Colorado River in the Grand Canyon---history, current practice, and the role of a mathematician

Speaker: Catherine A. Roberts, College of the Holy Cross

Abstract: This talk will discuss the development of a model for white water rafting on the Colorado River in the Grand Canyon National Park. The speaker will discuss the challenges faced by the National Park Service as it seeks to manage, both responsively and responsibly, this important natural resource. How a mathematician came to play a part in these efforts will round out the presentation.

Biography: Catherine Roberts majored in math and art history at Bowdoin College. She then earned her doctorate in applied mathematics from Northwestern University in 1992 and is now an associate professor at the College of the Holy Cross in Worcester, MA. Prior to her move back to New England (she grew up in Chatham on Cape Cod), she taught at Northern Arizona University near the Grand Canyon. Her research took a dramatic turn away from nonlinear integral equations towards mathematical modeling when she got involved in the project that is the subject of her talk. She is the editor in chief of an interdisciplinary journal called Natural Resource Modeling. Catherine has been very involved with the Association for Women in Mathematics, helping organize their workshops and recently serving on their board. She is an associate editor of the UMAP journal, and serves on the board of the Resource Modeling Association and the Regional Environmental Council. Catherine's husband is a chemist at W.P.I. and they have two sons.

Title: Standards in the Teaching of Mathematics in the First Two Years

Speaker: Philip Mahler, Middlesex Community College

Abstract: The National Council of Teachers of Mathematics (NCTM) has “standards” for teaching K-12 mathematics, the American Mathematical Association of Two-Year Colleges (AMATYC) has the same for teaching mathematics in the two-year college, and the MAA has them for is math intensive, and now service, courses. This will present what AMATYC has to say, and compare these to the MAA’s CUPM recommendations, as well as discuss what is driving “standards-based” efforts.

Biography: Philip Mahler has a BA in Modern Languages from Assumption College and an MAT in Mathematics from the University of Florida. He was a co-Chair of the Michigan MAA section, and for the Northeast Section has served as newsletter editor and program chair. He is a past president of the New England Mathematical Association of Two-Year Colleges, and of AMATYC. He has participated in activities at the national level on quantitative literacy and college algebra reform, and is co-PI on grants related to the recent updating of the AMATYC standards.

Title: Teaching Statistics by Example

Speaker: Lisa M Sullivan, Boston University

Abstract: Many undergraduates across a range of major fields of study are required to take statistics. While statistics can be difficult for students with little mathematical background, introductory statistics courses that include real and relevant applied examples make the material more accessible and interesting to the students. Increasing students’ interest can positively affect their efforts to grasp the material. This talk will present examples, projects and exercises that might be useful for teachers of introductory statistics courses.

Biography: Lisa M. Sullivan Ph.D. is Associate Professor and Associate Chair of Biostatistics at the Boston University School of Public Health, Associate Professor of Mathematics and Statistics at the Boston University College of Arts and Sciences and Assistant Dean for Undergraduate Education at the Boston University School of Public Health. She has received numerous awards for excellence in teaching for courses in Introductory Biostatistics and Statistics I and II at Boston University. She is the Principal Investigator of the Boston University Summer Institute in Biostatistics, funded by the National Heart, Lung, and Blood Institute, designed to introduce undergraduate students to the field of biostatistics. She co-authored a popular textbook entitled Introductory Applied Biostatistics, she has published extensively in the medical arena and serves as a statistical consultant to the American Heart Association’s journal Circulation. Her research interests focus primarily on the Framingham Heart Study where she is involved in developing and evaluating health risk appraisal functions. These functions are used by practicing clinicians to assess, for example, a patient’s risk of developing coronary heart disease over the next ten years. She worked recently with other Framingham investigators on new risk functions for coronary heart disease which feature prominently in the National Cholesterol Education Program’s Adult Treatment Panel III. She is also actively involved in a number of projects centered on infant and child health including a clinical trial evaluating the effectiveness of pharmacologic treatments for children with autism and an epidemiological study to assess the association between alcohol exposure during pregnancy and the incidence of sudden infant death syndrome.

Title: When Numerical Methods Fail but Undergraduates Succeed

Speaker: Gareth Roberts, College of the Holy Cross

Abstract:  Numerical methods don't always work. For example, Newton's method applied to a quadratic polynomial with complex roots alpha and beta will fail to find a root starting from any initial seed on the perpendicular bisector of the line segment joining alpha and beta. This is usually dealt with by making a small perturbation of the initial guess, but what if the method fails to work on an open set of initial seeds?

This question is explored from a dynamical systems perspective. Taking a given numerical method and applying it to a particular family of complex polynomials leads to some fascinating dynamical systems. Such an investigation is quite accessible to a motivated undergraduate researcher. Some specific examples using Newton's and Halley's method will be discussed including the impressive contributions of some recent undergraduates.

Biography:  Gareth Roberts received his B.A. in 1992 from Oberlin College where he studied mathematics, music and ultimate frisbee. After receiving his Ph.D. from Boston University in 1999 under the guidance of Dick Hall, he spent two beautiful years in Boulder at the University of Colorado as an NSF Vigre postdoc. He is now an assistant professor at the College of the Holy Cross in the even more beautiful city of Worcester (pronounced Woostaah) and is happy to have found some outstanding undergraduate researchers to collaborate with.

Title: Canonical forms: A mathematician's view of musical canons

Speaker: Noam D. Elkies, Harvard University

Abstract:  Musical canons, from simple rounds like “Three Blind Mice” to the compendium of canons Bach compiled in his Musical Offering, have a history almost as long as that of Western music itself, and continue to fascinate musical composers, performers and listeners. In a canon the same melody is played or sung in two or more parts at once; this melody must therefore make musical sense both as a tune and in harmony with a delayed or otherwise modified copy of itself. How does one go about constructing such a melody? This challenge has a mathematical flavor. It turns out that some kinds of canons are so easy to create that they can be improvised in real time, while other kinds are more demanding, and in some cases only a handful of examples are known. The talk will be illustrated with both abstract diagrams and specific musical examples, and may also digress into generalizations of canons (the forms known collectively as “invertible counterpoint'”) and the reasons--besides showing off -- that so many composers incorporate canons into their music.

Biography:  Noam D. Elkies earned his doctorate in mathematics from Harvard in 1987 under the guidance of Benedict Gross and Barry Mazur. He has been at Harvard since then; beginning as a Junior Fellow, he joined the Mathematics department in 1990 and was tenured in 1993. His work on elliptic curves, lattices and other aspects of the theory of numbers has been recognized by prizes and awards such as the Presidential Young Investigator Award of the NSF, a Packard Fellowship, and the Prix Peccot of the College de France; his expository papers won the MAA's Ford Prize and the AMS's Conant Prize.

Elkies' main interest outside mathematics is music, mainly classical composition and keyboard performance. His compositions, often but not always in styles that recognizably flow from traditional idioms, include an opera staged in 1999, and the "Brandenburg Concerto #7" premiered in 2004. Naturally there are various canons to be found in that concerto; he will try to resist the temptation of drawing on them for examples in his presentation.

Noam Elkies is also known as a chess problemist: a number of the studies and problems he composed earned awards in international contests; he won the 1996 world championship for solving chess problems, and earned the Solving Grandmaster title five years later.

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