Announcements

Organizing Committee Dawn Lott, New Jersey Institute of Technology; Theresa C. Michnowicz, New Jersey City University; Revathi Narasimhan, Kean University;

Program Committee Carol Avelsgaard, Middlesex County College; Amy Cohen, Rutgers University; Lawrence D'Antonio, Ramapo College; Bonnie Gold, Monmouth University; Mark Korlie, Montclair State University; Cathy Liebars, The College of New Jersey; Reginald Luke, Middlesex County College; Matthew Haines, New Jersey City University; Judith Schick-Lenk, Ocean County College; Pablo Zafra, Kean University

Hosting Committee Abdul Hassen, Paul Laumakis, Ming Sun-Li, Hieu Nguyen, Rowan University

Acknowledgements The MAA-NJ thanks Bette Counsellor, Terry Magliocco, and the faculty volunteers of Rowan University for their assistance and the College of Liberal Arts and the Department of Mathematics at Rowan University for their financial support.

High level mathematical functions, such as Airy, beta and gamma functions, are important for solving many problems in the mathematical and physical sciences. Although visualization can help one gain a deeper understanding of these ``special functions'', the singularities, poles and other complexities which make their computational domains irregular, discontinuous, or multi-connected can make the creation of effective visualizations quite difficult. The author will examine the use of numerical grid generation techniques to tackle this problem and show how this research is being used to create dynamic interactive 3D visualizations for a massive project at the National Institute of Standards and Technology (NIST) called the NIST Digital Library of Mathematical Functions (DLMF).

Bonita V. Saunders is a research mathematician in the Mathematical and

Computational Sciences Division at the National Institute of Standards and

Technology (NIST) in Gaithersburg, Maryland. She received her Ph.D. in

mathematics from Old Dominion University in Norfolk, Virginia. Her areas of research include numerical grid generation, the numerical solution of partial differential equations and the visualization of special functions. Currently, she is managing the design and development of graphics and visualization for the NIST DLMF Project. (http://math.nist.gov/~BSaunders)

Mathematics is called the `Queen of the Sciences' because it is widely believed to be a DEDUCTIVE science, concerned with A PRIORI, UNIVERSAL Truths, as opposed to the `Natural Sciences' that are INDUCTIVE, EMPIRICAL, and EXPERIMENTAL. But thanks to that great equalizer, the computer, Mathematics will soon have to resign her Queenship, and become yet another empirical science.

Doron Zeilberger is trying to harness the vast, and largely untapped, potential of the computer to do mathematics, in particular in combinatorics and special functions. He is the inventor of the Zeilberger algorithm and the co-inventor of Wilf-Zeilberger Pairs, and the prover of the Alternating Sign Matrix Conjecture, among many other accomplishments. (http://www.math.temple.edu/~zeilberg/)

We'll report on the 2000 proof of the Double Soap Bubble Conjecture and

some later breaking news. The show will include a guessing contest with

prizes.

Frank Morgan, Third Century Professor of Mathematics at Williams College and Second Vice-President of the Mathematical Association of America, is part of the international team of mathematicians who recently proved the Double Bubble Conjecture. In January, 1993, he received one of the first MAA national awards for distinguished teaching. He has written textbooks on Riemannian Geometry, Geometric Measure Theory, and Calculus Lite, and The Math Chat Book, based on his live, call-in Math Chat TV show and Math Chat column, both available at MathChat.org.

(http://www.williams.edu/Mathematics/fmorgan)

Explore ways to involve students more actively in the learning of mathematics

through use of projects, concrete materials, and technology. Examples will be

drawn from a variety of courses, including those for preservice elementary

teachers.

Janet Caldwell is well known in the field of mathematics education and is a past winner of the MAA-NJ Distinguished Teaching Award. She has taught an interesting array of courses incorporating active learning strategies, including one on patterns in nature (Fall 2000).

(http://www.rowan.edu/mars/depts/math/caldwell/caldwellweb.html)

A Pair (G,A) consisting of a group G and a finite generating set A is a Cannon Pair if the language of all geodesics in the associated CayleyGraph is regular. This property is preserved by graph products and leads to applications to the spherical and geodesic growth series for graph products.

Joseph Loeffler is a senior math major at TCNJ. The talk is based on his research at the Lafayette College Summer 2000 REU program with John Meier (Lafayette College) and James Worthington (student, Binghamton University) in geometric group theory. This work has been accepted for publication in The International Journal of Algebra and Computation (IJAC).

Organized by Theresa C. Michnowicz, New Jersey City University

Session 1 (Bosshart 118)

Presider: Ronald Czochor, Rowan University

11:15-11:30

Christopher Jay Lacke, Rowan University, lacke@rowan.edu

Sensitivity Analysis of Colorectal Cancer Screening

Regimens to Expert Aggregation Methodology

A copula is a function that allows the formation of a multivariate distribution function from any set of univariate distributions and encodes dependence information in what is referred to as the copula density. We will examine a sensitivity analysis of various copula models used in expert aggregation through an application to colorectal cancer screening.

Hieu D. Nguyen, Rowan University

nguyen@rowan.edu, http://www.rowan.edu/math/nguyen

Limits of KdV Solitons

We discuss limits of N-soliton solutions for the Korteweg-deVries (KdV) equation and mention some results related to their bounds and their convergence.

Gregory E. Coxson, Lockheed Martin NE&SS � Moorestown

gregory.e.coxson@lmco.com

Using PSL-Preserving Symmetries to Improve the

Search for Minimal-PSL Binary Codes

Binary pulse compression finds wide use in radar detection processing. The best codes for radar resolution are those with lowest autocorrelation peak sidelobe level (PSL). PSL-preserving symmetries can improve the search for best codes for a given length.

Thomas Osler, Rowan University

Osler@rowan.edu

An Unusual Approach to Kepler's First Law

Kepler's first law of planetary motion states that the orbits of planets are elliptical, with the sun at one focus. We present an unusual verification of this law for use in classes in calculus and mechanics

Presider: Abdul Hassen, Rowan University

11:15-11:30

Cathy Liebars, The College of New Jersey

liebars@tcnj.edu

New Courses for Elementary Teachers

Recently, the Conference Board of Mathematical Sciences

recommended that "Prospective teachers need mathematics courses that develop a deep understanding of the mathematics they will teach." I will present courses that meet this recommendation.

Jay Schiffman, Rowan University, Camden

schiffman@camden.rowan.edu

Utilizing the TI-89 in Mathematics Courses

The TI-89 graphics calculator will be employed to explore such aspects as creating mathematical induction problems and recursive sequences. I will also demonstrate its capacity to determine the primality or compositeness of large positive integers.

Applications to graphs and matrices will be considered

Dexter C. Whittinghill, Rowan University

Whittinghill@rowan.edu

The SIGMAA on Statistics Education: Past, Present and Future

The MAA has recently created the 'structure' of formal 'special interest groups,' and the Isolated Teachers of Statistics became the SIGMAA on Statistics Education. We will briefly recount the history of the 'SIGMAA on Stat Ed' from its creation to the very productive inaugural business meeting in New Orleans. Finally, the real payoffs of becoming a member will be discussed.

Mike Morelli, Lockheed Martin NE&SS � Moorestown

mike.morelli@lmco.com

Interesting Geometry from Archimedes

There are many interesting ideas and theorems from the mathematics of other cultures and eras that can be used in today's classroom. We will look at several theorems from Archimedes' work that will enhance courses in calculus, multivariable calculus, and geometry.

Presider: Ming-Sun Li, Rowan University

11:15-11:30

Javad Namazi, Fairleigh Dickinson University

namazi@mailbox.fdu.edu

A Property of Symmetric Matrices

An  matrix A is called non-negative, denoted by ,if  for every  vector X. We prove that a real symmetric matrix A may be written as A= M-N, where M,N0. Moreover, the representation is unique.

Beimnet Teclezghi, New Jersey City University

bteclezghi@njcu.edu

Endomorphisms of Finite Symmetric Semigroups

We characterize the proper endomorphisms (endomorphisms which are not automorphisms) of finite full transformation semigroups and find their numbers.

Christopher S. Simons, Rowan University

simons@rowan.edu

Curious Presentations for Curious Finite Groups

We consider certain finite groups obtained by "deflating" certain Coxeter presentations. Of particular interest is the Bimonster group (the wreath square of the celebrated sporadic Monster group). This talk provides what is perhaps the most elementary approach to a difficult area of group theory.

Presider: Xiaoming (Jim) Zeng, Rowan University

11:15-11:30

Marcus Wright, Rowan University

Wright@groupwise.rowan.edu

A Tale of Two Series

In this paper we use integration by parts to produce two infinite series, one convergent and the other divergent, and show how both of them are useful for computing  the tail integral of the normal distribution, where z is large.

Melkamu Zeleke, William Paterson University zelekeM@wpunj.edu

Skew Diagrams and Ordered Trees

We introduce a new combinatorial bijection to prove that among all ordered trees the ratio of the total number of vertices to leaves is two. Ordered trees are then enumerated by number of leaves, total path length, and number of vertices to obtain q-analogs of Catalan numbers.

John Snygg, Upsala College (retired ) jsnygg@earthlink.net

The NJ Proficiency Assessment exams may be harmful to the main curricula

STUDENT CONTRIBUTED PAPER SESSION (Bosshart 316)

Presider: Diana Thomas, Montclair State University

11:15-11:30

Jae Hattrick-Simpers, Rowan University

Mutations of the Mandelbrot Set

In this paper we show how to write Quick BASIC and Visual BASIC programs for the classical Mandelbrot set. We then show that tinkering with one line of the program is like altering the proteins that make up the creatures DNA.

David W. Thibault Jr., Rowan University

A Simple Ephemeris

An ephemeris is a table of the locations of the sun, moon and planets at various times. We show how to do the calculations assuming the orbits are circular.

Carmen Lefever, The College of New Jersey

Supercrossing Number and the Crossing Map

The supercrossing number, first developed by Colin Adams, is a new knot invariant in the class of "super-invariants." Basically, crossing number measures the minimum number of crossing over a knot type, or an equivalence class of knots, while supercrossing number measures the maximum number of crossings over a knot type.

Jennifer Scancella, Ramapo College of New Jersey

London Graph is Falling Down

Representing a network as a rooted graph, the research investigated the expected number of vertices, which will remain connected to the root after some catastrophic event. The research has also shown by means of suitable examples the difficulty of determining the best root placement for the root in a pre-existing graph.

Mathematical Preparation of Teachers, led by Janet H. Caldwell, Rowan University

Projects and Research for Undergraduates, led by Frank Morgan, Williams College

Discussion Table for Department Chairs, led by Ronald Czochor, Rowan University

Mathematics Outside of Academia, TBA

Program authored by Revathi Narasimhan