The Mathematical Association of America
New Jersey Section

Fall Meeting
DIMACS, Rutgers University
Piscataway, NJ

Saturday, October 28, 2000

Fall 2000 Meeting Program

All talks will be at the first floor lecture hall of the DIMACS center

Abstracts of Main Talks
Registration Form

8:30-9:30 Registration and Coffee
8:30-1:30 Book Exhibits
9:30-9:45 Welcome by Mel Janowitz
Associate Director, DIMACS
Renewal Systems, Sharp Eyed Snakes, and Shifts of Finite Types
Aimee Johnson, Swarthmore College
Presider: Dawn A. Lott, NJIT
10:30-10:45 Remarks by Chair of MAA-NJ
Judith Lenk, Ocean County College
10:45-11:30 Intermission (Coffee and Book Exhibits)
Program Verification
Robert Kurshan, Bell Laboratories
Presider: Robert Clay, Georgian Court College
12:15-1:30 Lunch (Book Exhibits end at 1:30)
Modeling Radiation Transfer in the Human Body: A Hot Topic for Student Research
Ann K. Stehney, Cedar Crest College
Presider: Amy Cohen, Rutgers University
2:15-2:30 Remarks by Governor of MAA-NJ
Amy Cohen, Rutgers University - New Brunswick
2:30-2:45 Intermission
The Erdos Magic
Joel Spencer, Courant Institute
Presider: Reginald Luke, Middlesex County College
3:30 Drawing of door prizes and announcement of Silent Auction Winners (must be present to win)   Concurrent with
Project NeXT sessions  (Room 433 DIMACS center)
5:00 Dinner honoring invited speakers and retiring section officers

Organizing Committee Theresa C. Michnowicz, New Jersey City University; Revathi Narasimhan and Pablo Zafra, Kean University

Program Committee Carol Avelsgaard, Middlesex County College; Lawrence D'Antonio, Ramapo College; Matthew Haines, New Jersey City University; Cathy Liebars, The College of New Jersey; Judith Schick-Lenk, Ocean County College.

Hosting Committee Fred Roberts, Mel Janowitz, Sarah Donnelly and Christine Houck, DIMACS.


The MAA-NJ thanks

Abstracts and Biographies of Speakers

Renewal Systems, Sharp Eyed Snakes, and Shifts of Finite Type

Aimee Johnson, Swarthmore College

One of the basic mathematical questions is when two seemingly different objects are really the "same". In this talk we will consider sets of bi-infinite strings of symbols which arise from different types of graphs, and explore what it means for these sets to be the "same". Once we agree what it means for these objects to be the same, we will try to determine whether they actually are the same. We will finish with a partial answer to this question that leaves us with a tantalizing open problem that is the subject of active mathematical research.

Aimee Johnson was an undergraduate student at University of California, Berkeley, and attended graduate school at the University of Maryland, College Park. There she studied ergodic theory under the direction of Daniel J. Rudolph. After a 3 year position at Tufts University, she joined the faculty at Swarthmore College, where she is an assistant professor. In her research she has considered measurable, topological, and symbolic dynamics systems.

Program Verification

Robert Kurshan, Bell Laboratories

I will discuss a method for checking the correctness of certain types of computer programs. The method is based on a mathematical analysis of the program. This is in contrast with customary testing based upon program execution. The new form of analysis has been found to be more reliable than conventional testing, and is being used commercially in the development of programs implemented as integrated circuits. The same methodology is applicable to the development of ``control-intensive'' software programs as well.

An interesting part of the story is the technology transfer process: how did an idea get from research to a commercially successful product. I will spend a few minutes on this as well.

Robert Kurshan is a Distinguished Member of Technical Staff at Bell Laboratories, Murray Hill, NJ. He has worked there since receiving his Ph.D in mathematics in 1968, from the University of Washington. He spent two years as Visiting Professor at the Technion (Haifa, Israel) in the departments of Mathematics and Electrical Engineering. In addition, he has taught courses at U.C. Berkeley and N.Y.U. At Bell Labs, he did research in periodic sequences, digital filtering and approximation theory, before he began work in formal verification in 1983. He is an author of over 60 technical publications, holds eight patents in communications, digital filtering and verification, and is the author of the book Computer-Aided Verification of Coordinating Processes (Princeton Univ. Press, 1994), which is based upon courses he gave at U. C. Berkeley and the Technion. He designed and built the COSPAN verification system together with Zvi Har'El, Ronald H. Hardin, and a number of others, based upon the theory which is developed in this book. COSPAN has been in use (and continuous development) since 1986, having been applied to a number of commercial projects, as well as having been licensed to numerous universities for educational use. Currently, COSPAN is marketed for commercial use by Cadence Design Systems, Inc., under the trademark FormalCheck.

Modeling Radiation Transfer in the Human Body:

A Hot Topic for Student Research

Ann K. Stehney, Cedar Crest College

It has been some years since Chernobyl and Three Mile Island were news, but exposure to radiation is still a "hot" topic. To assess the health risks associated with accidental, occupational, or environmental exposure, the International Commission on Radiological Protection has proposed increasingly sophisticated mathematical models for the transfer and deposition of radioactive substances in the human body. We suggest a variety of related problems that can be introduced as early as a first course in linear algebra, yet are suitable for a senior seminar in which students devise and test their own models. The questions lend themselves to both continuous and discrete methods, drawn from throughout the undergraduate math curriculum. The talk includes a preliminary report on joint work with chemist A. F. Stehney, based on his study of thorium workers.

Ann Stehney obtained her Ph.D. in differential geometry from SUNY Stony Brook and joined the faculty of Wellesley College, where she became department chair and served as director of Educational Research and Development. She then spent ten years in applied mathematics at the Center for Communications Research, a government contractor in Princeton. Recently Associate Dean of Douglass College at Rutgers, she is now Vice President for Academic Affairs and Dean of Faculty at Cedar Crest College in Allentown, PA.

The Erdos Magic

Joel Spencer, Courant Institute of Mathematical Sciences

The Probabilistic Method is a lasting legacy of the late Paul Erdos. Here we examine two problems that Erdos started working on in the 1960s, both with recent improvements.

(i) Erdos showed that given any 2n-1 n-element sets there exists a two coloring of the underlying points so that no set is monochromatic. Srinivasan and Radhukrishnan (building on a 1978 result of Beck) have recently done better.

(ii) Fix 2 <= k < t (e.g.: k=3,t=5) In a universe of n elements how many t-sets can you have with no k-set contained in two (or more) of them.

C n,k/C t,k is a natural counting bound. Erdos and Hanani conjectured that this was asymptotically attainable. This was shown by Rodl in1985. Here we examine an argument of the speaker using a Random Greedy Algorithm and an analogy to Birth Processes.

Joel Spencer is a Professor of Mathematics and Computer Science at the Courant Institute, for Mathematical Sciences, New York University. His area of research is in Discrete Mathematics and Theoretical Computer Science. He obtained his Ph.D. from Harvard in 1970 under the direction of A. Gleason. He has been a visitor at M.I.T. and the Institute for Mathematics and Its Applications and has authored over 140 publications. A Sloane Foundation Fellowship, editorship of The Annals of Applied Probability and an associate editorship of the American Mathematical Monthly are among his many professional accomplishments. He was an invited speaker at the International Congress of Mathematicians at Zurich in 1994 and has lectured at an NSF-CBMS conference in Durango. The second edition of his book, The Probabilistic Method (with Noga Alon), published by Wiley, has recently appeared.


Governor for MAA-NJ

The New Jersey Section of the Mathematical Association of America is proud to announce the election of Amy Cohen, of Rutgers-New Brunswick, as the Governor of the section.

Lunch discussion tables for Fall 2000 meeting

There will be four discussion tables at lunch.

You must preregister to reserve your place at a discussion table. Reservations are on a first-come-first-served basis. Each discussion table has limited seating.

We look forward to a set of lively and interesting discussions!

MAA-NJ Spring 2001 Meeting

The Spring Meeting of the Mathematical Association of America, New Jersey Section, will be held at the Rowan University, Glassboro, NJ on April 21, 2000. Frank Morgan of Williams College will be one of thee invited speakers.

Call for contributed papers

MAA members are invited to present papers at the MAA-NJ Spring 2001 Meeting. Please submit a paper with a short abstract by February 1, 2001, to Theresa C. Michnowicz, New Jersey City University,, 201-200-3219.

Slate of candidates for election at MAA-NJ Fall 2000 Meeting

Chair-Elect: Reginald Luke, Middlesex County College

Vice Chair for Speakers: Dawn A. Lott, NJIT

Secretary: Mark Korlie, Montclair State University

Nominating Committee:

Theresa C. Michnowicz (chair), Reva Narasimhan.

Program and web page by Revathi Narasimhan, Kean University, Vice Chair for Speakers, MAA-NJ