Abstract: Nonlinear oscillators play a fundamental role in the analysis and understanding of many systems in the natural and engineering sciences. Mathematically, they are modeled by differential equations which have the frustrating property of having solutions not expressible in terms of a finite number of elementary functions. This talk will demonstrate that certain classes of "truly nonlinear" oscillators provide differential equations for which essentially all the qualitative properties of the solutions can be determined. Further, an easy to implement iteration method allows for the easy calculation of analytic approximations to the periodic solutions. The mathematical background needed to understand and appreciate these topics is that given in a standard introductory course in differential equations.

Biography: Ronald E. Mickens is the Distinguished Fuller E. Callaway Professor of Physics at Clark Atlanta University. He received his Ph.D. in theoretical physics from Vanderbilt University and has held postdoctoral positions at the Center for Theoretical Physics-MIT, The Joint Institute for Laboratory Astrophysics, and Vanderbilt University. His current research interests include nonlinear oscillations, difference equations, and numerical integration of differential equations using nonstandard finite difference schemes, mathematical modeling of periodic diseases, and the history/sociology of African Americans in science. He has published more than 250 research papers, authored 240 abstracts, written six books, and edited eight volumes. Professor Mickens serves on the editorial boards of several research journals, including the Journal of Difference Equations and Applications. His professional memberships include AAAS, the American Mathematical Society, the American Physical Society (for which he is an elected Fellow), the Society for Mathematical Biology, and the History of Science Society.

Abstract: "Change is Possible: Stories of Women and Minorities in Mathematics" will relate anecdotes in the lives of female and minority mathematicians and reveal remarkable trends in their acceptance into the mathematical community and society. It will be illustrated by interesting photographs.

Biography: Pat Kenschaft is Professor Emerita of Mathematics at Montclair State University and Distinguished Visiting Professor at Bloomfield College. She has been author or editor of nine books, most recently CHANGE IS POSSIBLE STORIES OF WOMEN AND MINORITIES IN MATHEMATICS, published by the American Mathematical Society in 2005. She is the 2006 winner of the Louise Hay Award for outstanding achievements in mathematics education.

Abstract: In 1751 Euler discovered that any polyhedron with V vertices, E edges, and F faces satisfies V-E+F=2, but the proof he gave was flawed. Many rigorous proofs followed, but it took 150 years for mathematicians to fully understand this simple formula. Today Euler's formula is held aloft as one of the most beautiful theorems in all of mathematics and the first great theorem of topology. In this talk we will give the history of Euler's theorem and give a sampling of its many surprising applications.

Biography: Dave Richeson is an Associate Professor of Mathematics at Dickinson College. He received an A.B. in mathematics from Hamilton College and an M.S. and Ph.D. in mathematics at Northwestern University under the direction of John Franks. He came to Dickinson College after a postdoctoral position at Michigan State University. His research focusses on dynamical systems, topology, and the interplay between the two. He has become increasingly fascinated by the history of mathematics. He is in the final stages of writing a book on the history and applications of Euler's formula for polyhedra (The Gem of Mathematics, Princeton University Press). It is written for a general audience and should appear later this year. Currently he sits on the MAA Committee on Minicourses.

When not working on mathematics Dave enjoys spending time with his wife and two young children, playing squash, spinning tunes on his weekly radio show, and looking for new mind-benders for Dickinson's Puzzle of the Month competition.

Abstract: Recent questions in theoretical ecology on the global stability of periodically forced discrete population models led to the author and his collaborators to develop a theory of periodic difference equations. We extend Elaydi and Yakubu theorem to continuous maps acting on nonconnected metric spaces and then to periodic discrete dynamical systems / difference equations. In this talk we will introduce the notion of skew-product dynamical systems in its most simplified form and indicate how it would give insights into topics of current interest such as global stability and chaos. In particular, we will indicate how the recent conjectures by Henson and Cushing on the Beverton-Holt model can be settled. Open problems and conjectures will be presented at the end of the talk.

Biography: Professor Saber N Elaydi is the author of the two best-seller books:

1. An Introduction to Difference Equations, Third Edition, Springer, 2005
2. Discrete Chaos, Taylor & Francis CRC Press, 2000