**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 |
Announcements |
Registration
Form |
Directions |

8:30-9:30 | Registration and Coffee |

8:30-1:30 | Book Exhibits |

9:30-9:45 | Welcome by Mel Janowitz
Associate Director, DIMACS |

9:45-10:30 |
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) |

11:30-12:15 |
Program Verification
Robert Kurshan, Bell Laboratories
Presider: Robert Clay, Georgian Court College |

12:15-1:30 | Lunch (Book Exhibits end at 1:30) |

1:30-2:15 |
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 |

2:45-3:30 |
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.

**Acknowledgments**

The MAA-NJ thanks

- Fred Roberts, Mel Janowitz, Sarah Donnelly and Christine
Houck, DIMACS, for their kind hospitality in hosting the meeting.

**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.

**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.

**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 2^{n-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.

- 1. Directing Undergraduate Research, led by Michael A. Jones, Montclair
State University.

- 2. Creating Contacts with Industry to Help Students, led by Mike Morelli,
Lockheed Martin.

- 3. Discussion for Department Chairs, led by TBA.

- 4. Math Education for Elementary Teachers, led by Kathy Safford, St.
Peter's College

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, tmichnowicz@njcu.edu, 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*