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Union, New Jersey

Note: All talks will take place in Hutchinson Hall

 8:30- 9:15            Registration and coffee

 8:30- 1:00            Book Exhibits

 9:15- 9:20            Welcome by Betty Barber, Dean of the School of Natural
                       Sciences, Nursing, and Mathematics, Kean College of
                       New Jersey

 *9:20- 9:35           Music Recognition Using Fourier Techniques
                       Kyle Jamieson, Hopewell Valley Central High School

                       Presider: Chamont Wang, Trenton State College

 *9:35- 9:50           Calculating the Capillary Forces Exerted by a Drop
                       Between Two Cylinders
                       Karen Almgren, Princeton High School

                       Presider: Jean Taylor, Rutgers University

 9:50- 10:00           Remarks by the Chair of MAA-NJ
                       Kay Gura, Ramapo College of New Jersey

 10:00- 10:50          What's Happening in Knot Theory
                       Joan S. Birman, Barnard College, Columbia University
                       Presider: Carol Avelsgaard, Middlesex County College

 10:50- 11:35          Intermission (coffee and book exhibits)

 11:35- 12:25          T-Colorings of Graphs and the Channel Assignment
                       Fred S. Roberts, DIMACS and Rutgers University

                       Presider: Sara Kuplinsky, Ramapo College of New Jersey

 12:25- 12:40          Presentation of 1996 MAA-NJ Award for Distinguished
                       College or University Teaching of Mathematics

 12:40- 2:00           Lunch in the Green Lane Facility
                       (Book exhibits end at 1:00)

 2:00- 2:50            Mathematical Webology -
                             A Presentation on the World Wide Web
                       Cipher Deavours and Cathy Hannan, Kean College of New

                       Presider: Francine Abeles, Kean College of New Jersey

 2:50- 3:00            Intermission

 3:00- 4:00            Contributed Papers
                       (Titles and Rooms to be Announced)

 4:00- 4:15            Drawing of Door Prizes and
                       Announcement of Silent Auction Winners
                       (Must be present to win)

 5:30                  Dinner honoring distinguished teaching award recipient
                       and invited speakers. See Announcements for details.

* Student speaker

Program Organizers: Lawrence D'Antonio, Kay Gura, Ramapo College of New Jersey; Theresa C. Michnowicz, Jersey City State College; and Barry Arnow, Kean College of New Jersey; Judith Lenk, Ocean County College.

Program Committee: Francine Abeles, Isali Asina, and Pablo Zafra, Kean College of New Jersey; May Hamdan, Jersey City State College; Issam El-Achkar, Hudson County College.


What's Happening in Knot Theory

This talk will describe the knot problem and what it means to find a "knot invariant". There will be an exploration of the meaning of "finite type" invariants of knots, of why they work, and how they are computed.

Joan S. Birman is currently Professor of Mathematics at Barnard College, Columbia University. She earned a B.A. from Barnard, an M.A. (in physics) from Columbia. After a long interlude to raise three children she obtained her Ph.D. from the Courant Institute, New York University. Her research is in topology and knot theory. Professor Birman has received many awards including an honorary doctorate from the Technion (Israel Institute of Technology), a Sloan Foundation Fellowship, and a Guggenheim Fellowship. A recent highlight in her distinguished career was receiving the MAA Chauvenet Prize for her article "New points of view in knot theory" (Bulletin of the American Mathematical Society 28 (April 1993), p. 253-287). ProfessorBirman has held appointments at the Stevens Institute of Technology, Princeton University, the Technion, Hebrew University, and the Institute for Advanced Study.

Music Recognition Using Fourier Techniques

The purpose of this study was to convert a series of sound samples to musical notes using a PC. This conversion was accomplished in several steps. In the first phase, the Fast Fourier Transform (FFT) was applied to small sections of a sound file, yielding many small (1024 point) spectra. The frequency with the highest amplitude was chosen to represent each spectrum, and all these were packed into an array in computer memory. By a "harmonic-cancellation" algorithm, array values that represented overtones of a musical instrument were deleted. Next, the samples were matched to the real musical notes closest in time and pitch. Parts of this process were optimized for fast execution on a computer. Finally, the musical notes were outputted to the user on the screen.

Kyle Jamieson is a senior at Hopewell Valley Central High School. His interests include playing the cello in several different orchestras and quartets, rollerblading, and tennis. Active in both the school and the community, he has been involved in the spring musical, the Model United Nations Club, and the mathematics and science leagues.

Calculating the Capillary Forces Exerted by a Drop Between Two Cylinders

The Surface Evolver program was used to compute the surface energy of a drop of water placed between two touching cylinders, for a range of angles between the axes of the cylinders. At each angle, the numerical derivative of the energy with respect to angle was taken to get the torque exerted by the drop to make the cylinders line up. This was done for several different volumes to see how volume affects the torque. The mean curvature was measured by differentiating the energy with respect to volume. The force exerted by the drop to hold the cylinders together was calculated by computing energies for cylinders that do not quite touch and taking the numerical derivative with distance apart. This work was done under the direction of W. Craig Carter at the National Institute for Standards and Technology.

Karen Almgren is a senior at Princeton High School. She has received early admission to MIT (but may instead choose Stanford). She has taken several mathematics courses at Princeton University. In eighth grade she was a member of the New Jersey MathCounts team. She has been a candidate for the Presidential Scholars program, a semifinalist for a National Merit Scholarship, and also a volunteer for StreamWatch, Stony Brook-Millstone Watershed Association.

T-Colorings of Graphs and the Channel Assignment Problem

In assigning channels to radio or television transmitters, we try to assign different channels to transmitters that interfere. This problem is readily translated into a problem of coloring an appropriate graph. However, sometimes there are additional complications. In particular, we sometimes specify a set T of disallowed distances between channels that interfere. Then the channel assignment problem can be translated into a graph theory problem that is a generalization of ordinary graph coloring, the problem of T-coloring. This talk will describe the history of T-colorings from their introduction in the engineering literature by Hale in 1980, to the strange sets T that arose from UHF television, to the stimulus to graph theory that has led to five Ph.D. theses in recent years, and to some fascinating open questions that are easy to describe and remarkably nasty to solve.

Fred S. Roberts is currently a Professor of Mathematics at Rutgers University and a Fellow of RUTCOR (the Rutgers Center for Operations Research). He was recently made Director of DIMACS, having previously served as Associate Director. After completing his Ph.D. at Stanford University, he worked for the RAND Corporation and did postdoctoral work at the University of Pennsylvania and the Institute for Advanced Studies before joining the faculty at Rutgers. He has held visiting positions at Cornell, AT&T Bell Labs, and has been the Robert G. Stone Visiting Professor at Northeastern. His major research interests are in mathematical modeling; graph theory and combinatorics and their applications; measurement theory; utility, decision-making, and social choice; and operations research. Professor Roberts has authored four texts and numerous scientific articles. A former Vice President of SIAM, his awards and honors include being CBMS-NSF Research Conference Lecturer at Colby College, a Humboldt Fellowship, and a University Research Initiative Award from the Air Force Office of Scientific Research. MAA-NJ is very grateful to Professor Roberts for hosting two section meetings at DIMACS and for being a valuable resource person to the section.

MAA-NJ Governor:           Barbara Osofsky, Rutgers University

Chair:                     Kay Gura, Ramapo College of New Jersey

Past Chair:                Theresa C. Michnowicz, Jersey City State College

Vice Chair for
  Speakers:                Lawrence D'Antonio, Ramapo College of New Jersey
  Innovations:             Issam El-Achkar, Hudson Community College
  Two-Year Colleges:       Jeannette O'Rourke, Middlesex County College

Secretary:                 Thomas Ralston, Georgian Court College

Treasurer:                 Nancy Maulding, Raritan Valley Community College

Public Information
Officer:                   Judith Lenk, Ocean County College


The Mathematical Association of America gratefully thanks the following: