David Abrahamson and Rebecca Sparks, Rhode Island College 
"A Linear Programming Approach to Predicting Award Winners  (or, Who needs baseball writers when we know how they'll vote?)

Abstract:  When a voter casts an award ballot, he often uses numerical criteria in his decision.  While no one voter may consciously assign specific weights to such criteria, the results of the balloting may coincide with scoring based on a weighted average of those criteria.  We illustrate the process of finding the appropriate weights by studying baseball's Cy Young Award voting over the last decade.

Bios:  Dave Abrahamson received his Ph.D. in Applied Mathematics in 1981 from Brown University, specializing in differential equataions under the direction of E. F. Infante.  He taught at Brown University and The Lincoln School before coming to Rhode Island College in 1986. 
Rebecca Sparks received her Ph.D. in 2001 from the University of Rhode Island, specializing in optimization and control systems under the direction of Orlando Merino.  She is currently in her third year at Rhode Island College.  Dave and Rebecca have combined their research interests and pursue topics in optimization, mathematics in sports, and pedagogy. 

William Barker, Bowdoin College
 

"Taking the Erlangen Program Seriously: A Modern Approach to Undergraduate Geometry"
Abstract:  An exciting and beautiful approach to undergraduate geometry can be built on Felix Klein's philosophy that geometry is the study of invariants under a group of transformations. Change the group of transformations --- the "symmetries" --- and one produces a new geometry. Much of the development can be done without coordinates, leading to an elegant blending of classical geometry and group theory. This lecture will present an outline of such a course, ending with applications to relativistic space-time and connections to the theory of Lie groups and Lie algebras.
 

"The CUPM Curriculum Guide 2004 and the Curriculum Foundations Project"
Abstract:  For four years the MAA Committee on the Undergraduate Program in Mathematics (CUPM) has labored to produce its Curriculum Guide 2004, a set of recommendations designed to guide Mathematics Departments in designing and revising their programs for undergraduates. One difference from past Guides has been the reliance on information collected from the partner disciplines. This was done via a series of eleven workshops held across the country with representatives of the other disciplines. Organized by the CUPM subcommittee on Curriculum Renewal Across the First Two Years (CRAFTY) under the title the Curriculum Foundations Project, mathematicians learned what other disciplines need from the mathematics instruction given to their students. This lecture will present the major themes and findings of both the CUPM Curriculum Guide 2004 and the companion Curriculum Foundations Project and indicate how they can be used by departments to improve their programs. The lecturer was heavily involved with both efforts: he was a member of the seven person writing team for the Curriculum Guide and was the Chair of the Steering Committee for the Curriculum Foundations Project.

Donna Beers, Simmons College,
"Guidelines, Timelines, and Tools for Self-Assessment: Students Get Set for a Mathematics Conference" 

Abstract:  At many colleges and universities, undergraduates who major in mathematics must fulfill an independent study or capstone project requirement. In this talk we will describe our work this past semester in guiding team-based projects. Topics covered will include: setting goals and expectations, identifying project stages from planning through implementation, introducing students to research tools and information resources in mathematics, enhancing writing and presentation skills, and developing tools for self-assessment and peer assessment. We will report on lessons learned and consider ways of refining this work for the future.

Bio:  Donna Beers is Professor of Mathematics at Simmons College. She did her undergraduate and graduate work at the University of Connecticut where she earned her Ph.D. in commutative algebras. At Simmons she has served as chair of the Mathematics and Computer Science Department, director of the Honors Program, and director of the Information Technology program. Her teaching interests include the preparation of prospective teachers and an interdisciplinary Honors seminar on patterns. Donna has served as chair and governor of the NES/MAA. She has also served on the editorial boards of The American Mathematical Monthly and Mathematics Magazine. She presently serves on the Dolciani Mathematical Expositions editorial board and on the steering committee of the MAA PREP Workshop: Leading the Academic Department: A Workshop for Chairs of Mathematical Sciences Departments.

Robert Benedetto, Amherst College
"The Uniform Boundedness Conjecture for Dynamics over Number Fields"

Abstract:  A polynomial f with rational coefficients maps rational numbers to rational numbers.  If we repeatedly compose f with itself, we see that some rational numbers are preperiodic under f.  That is, some numbers are eventually mapped to a periodic cycle of points under repeated application of the function.  In 1950, Northcott proved that for any fixed f of degree at least two, there are only finitely many rational preperiodic points.  In 1994, Morton and Silverman formulated a broad conjecture stating that in the above context, the number of such rational preperiodic points is bounded by a constant depending only on the degree of f.  In this talk, we'll discuss their uniform boundedness conjecture, including the evidence and various results surrounding it.
 

Bio:  Rob Benedetto received his Ph.D. from Brown University, was a Visiting Assistant Professor at the University of Rochester, and did an NSF Postdoc at Boston University.  He is currently an Assistant Professor of Mathematics at Amherst College, where he studies p-adic and number theoretic dynamics.

Robert Bradley, Adelphi University
"The Curious Case of the Bird's Beak"

Abstract:  The Marquis de l'Hôpital (1661-1704) wrote the first calculus book in 1696, where l'Hôpital's Rule was first published.  Among the many other topics covered, l'Hôpital studied cusps, where continuous curves fail to have a derivative.  He classified these points as being of two types: the more ordinary type, such as you would find in the “semi-cubic” equation, and a more exotic type, which resembles the shape of a bird's beak.  L'Hôpital gave a mechanical argument to show that curves with cuspidal points of this second kind must exist, but did not produce the equation of any such curve.  Almost half a century later, Gua de Malves (1712-1785) gave a proof that no algebraic curve could make the shape of a bird's beak.  His argument involving infinitesimals was persuasive, and even Leonhard Euler (1707-1783) initially accepted it as valid.  However, in the late 1740's, both Euler and Jean d'Alembert (1717-1783) fashioned counterexamples to Gua de Malves’ claim.  In this talk, I will trace the development of this curious episode in the history of the theory of equations, which is of interest in its own right, as well as for the light it sheds on the developing concept of function in the 18th century.
 

Bio:  Rob Bradley is the president of the Euler Society, the vice-president of the Canadian Society for History and Philosophy of Mathematics, and a professor at Adelphi University on Long Island. He attended college at Concordia University in Montreal, his native city. He went to Oxford on a Rhodes Scholarship, where he studied mathematics and philosophy. After working for two years as a computer geek, he did a Ph.D. at the University of Toronto and a postdoc at Northwestern University. His professional interests include the history of mathematics, probability and ergodic theory, and the preparation of future math teachers. He is an avid flatpicker, and plays the double bass with the Wickers Creek Band.

Rick Cleary, Bentley College
"An Overview of Benford's Law with Applications to Auditing"

Abstract:  Benford's law proposes a distribution of digits, most notably first digits, in measurements that span many orders of magnitude. Auditors have begun using Benford's law as part of fraud detection schemes in a variety of settings. It is well known, however, that Benford's law does not apply in certain conditions, such as when the data is all of the same order of magnitude. In this presentation we give an overview of Benford's law and some ways to use it as a teaching tool.  We discuss how the related output from popular auditing software raises interesting statistical questions for the accounting community.  (This work is being done jointly with Prof. Jay Thibodeau, Bentley College Department of Accountancy.)

Bio:  Rick Cleary is Associate Professor and Chair of the Department of Mathematical Sciences at Bentley, a business university in Waltham, MA.  He specializes in applied statistical analyses.  He enjoys finding ways to use his knowledge of statistics and the research process to work with people in a variety of fields.  In the past few years he has worked on problems in sports, biomechanics, market research, and plant pathology, among others.  At Bentley since 2001, he is now learning the ways in which statistical tools are applied in accounting, economics and finance.  He previously taught at Saint Michael's College in Vermont (1980-1997) and Cornell University (1997-2001).  Prof. Cleary's interests outside the classroom tend to athletics, especially running, golf, baseball and basketball.  He was an undergraduate at Oneonta State College in New York, and earned his Ph. D. in Statistics at Cornell.  

Frank Farris, Santa Clara University
The Battles Lecture
"Forbidden Symmetry--Relaxing the Crystallographic Restriction"

Abstract:  If you look at enough swatches of wallpaper, you will see centers of 2-fold, 3-fold, 4-fold, and 6-fold rotation. Why not 5-fold centers?  They cannot occur, according to the Crystallographic Restriction, a fundamental result about wallpaper patterns, which are defined to be invariant under two linearly independent translations.  Even so,  we offer convincing pictures that appear to show wallpapers with 5-fold symmetry. The talk is intended to be accessible to students who know something about level curves in the plane and linear algebra. 
(Here is an example of 5-fold symmetry.  Click on the image for a larger image.)

    
Bio:   Frank Farris serves as editor of Mathematics Magazine through 2005.  He hopes to continue its tradition of inspiring and challenging teachers and students of mathematics at the undergraduate level.  Awards include a Trevor Evans Award for his article "The Edge of the Universe" in Math Horizons and the David E. Logothetti Teaching Award at Santa Clara University, where he has taught since 1984. 
 

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