Carol Gibbons, Salve Regina University
Equations which Eat Their Young: A Look at Difference Equations 

We will discuss some basic ideas which are helpful in getting started on work with difference equations.  Some nonlinear rational difference equations will be used to explore such topics as periodicity, boundedness, and convergence of solutions of equations.

Carol Gibbons has been a member of the mathematical sciences department at Salve Regina University, in Newport, Rhode Island, since 1989.  She received her Ph.D. in applied mathematics from the University of Rhode Island and has worked recently with nonlinear rational difference equations.  She has been a member of the Rhode Island Calculus Consortium, a consultant for the Children's Television Workshop, and has been a speaker at local and regional conferences sponsored by NCTM.

We might think of model railroad train tracks, dominoes, the game Tetris, and the plastic Tangle toy (which has been popularized as a “cosmic guide” as well as “a folded protein model”) as little more than unrelated hobbies, games, and recreational trinkets.  Yet they share critical structural connections that unite them into a close mathematical family.  Exploring the relationships that bind these objects together introduces several wonderfully rich mathematical problems – easily stated problems that are simultaneously deep and complex – which bring knot theory, topology, geometry, and combinatorics together in exciting ways.  Moreover, this exploration provides a compelling metaphor for mathematical discovery and the unity of mathematics.

In this introductory talk we well illustrate some of these wonderful connections, introduce some of the mathematical problems that naturally arise from the study of these connections, and (hopefully) leave the audience Tangled in the wonderful web of mathematical intrigue woven together by these remarkable “children’s” “toys”.
 

For over 50 years the Mathematical Association of America has sponsored the American Mathematics Competitions for high school students.  It’s now a sequence of competitions at several levels that lead to the selection of the team of students representing the USA at the International Mathematical Olympiads.  I’ll review some of the problems from the contests with an emphasis on “easy” problems, “hard” problems, and what makes the difference.  In the process, I’ll mention some interesting bits of history, look at some trends in the contests, note some remarkable participants, and make some comments on the nature of problem posing and solving and its connections to mathematics.

Steven is currently the MAA Director for K-12 Programs, managing the American Mathematics Competitions at the University of Nebraska-Lincoln, where he is also on the faculty in the Department of Mathematics.  He is interested in nonlinear differential equations and applied dynamical systems, as well as issues of mathematical education.  Steve has received several teaching awards including the Nebraska-Southeastern South Dakota Section of the MAA Award for Distinguished Teaching of Mathematics at the University or College Level, 1997; and the College of Arts and Sciences Distinguished Teaching Award, 1991.

Over the past three years, we have been developing interdisciplinary projects for our freshman mathematics sequence in the honors program.  An overview of project development from the idea to the realization will be presented along with details of three or four projects.

Karen received a BA degree in mathematics from Emmanuel College and did her graduate work at Boston College.  She is currently a Senior Lecturer in the Mathematical Sciences Department at Bentley College where she is involved in developing interdisciplinary projects in mathematics for the honors program.  She is a former Chair and Governor of the Northeastern Section of the MAA.

David was recently appointed as the Wilder professor of Mathematical Sciences at Bentley College, where he is also Director of the Honors Program.  He received his DBA and MBA in operations research from The George Washington University and a BA in chemistry from the University of North Carolina at Chapel Hill.  His current teaching and research efforts are concentrated on the application of mathematical models in the business world.  Additional research deals with the use of information technology in the mathematics classroom and the role of discontinuous models in the social sciences.  His recent consulting experience has been with the Commonwealth of Massachusetts and the U.S. Small Business Administration.

There are many challenges facing our African American female mathematicians that differ in degree and type from our colleagues who do not share the distinction of being Black and being a female.  These challenges, which at times may seem insurmountable, are faced each day as African American females strive to make a name for themselves in the mathematical sciences.  A brief outline will be given in the form of an algorithm which provides systematic solutions to the problems facing our next generation of female mathematicians of color.

Dawn is an Assistant Professor of Applied Mathematics at the New Jersey Institute of Technology.  She graduated from Michigan State with a MS degree in Applied Mathematics in 1989.  In June 1994, she earned a Ph.D. in Engineering Sciences and Applied Mathematics from Northwestern University.  Her professional career began with a postdoctoral research position at the University of Maryland at College Park.  Dawn is in her sixth year at NJIT and enjoys research in the area of biomathematics and biomechanics and spends a great deal of her time determining optimal patterns for suturing wounds in human skin, and modeling applications in the field of mathematical physiology.

There are many connections between mathematics and music.  This survey will focus on the links between music and areas of mathematics such as rational and irrational numbers, trigonometry, geometry, permutations, and group theory.  Other connections include the Fibonacci sequence, the golden mean, fractals, and continued fractions, as well as historical notes regarding famous mathematicians.  The talk will feature both live and recorded music.

Lisa is an Associate Professor of Mathematics and Computer Science.  She received her B.S. degree from Western Michigan University in 1990, her Masters from Michigan State University in 1992, and the returned to Western Michigan U. to complete her Ph.D. under the supervision of Gary Chartrand.  Her research interests include graph theory, algorithms and computation theory, as well as connections between mathematics and music.  Both she and her husband are mathematicians and musicians (otherwise known as “mathemusicians”) and they share a love for teaching mathematics, for sharing their gifts of music with their church, and for parenting their 8-year old son, Joshua.

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