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The Mathematical Association of America - New Jersey Section

Spring Meeting

Saturday, April 4 1998

Ocean County College

Toms River, NJ


8:30-9:15      Registration and Coffee
               College Center Cafeteria

8:30-1:00      Book Exhibits
               College Center Cafeteria

9:15-9:20      Welcome by Dr. Judith Icklen,
               Vice President, Academic Affairs, Ocean County College
               Lecture Hall

9:20-9:35      "On the Probabilities of Mendel's Experimental Results Being
               So Close to His Theoretical Predictions"
               Stephanie Rebain, The College of New Jersey

               Presider: Chamont Wang, The College of New Jersey

9:35-9:50      Nathan Carter, University of Scranton

10:00-10:50    "The Prince of Problem Solvers and the Absolute Monarch of
               Problem Posers: Paul Erdos (1913-1996)"
               László Babai, University of Chicago

               Presider: William Rickert, Ocean County College

10:50-11:45    Intermission - College Center Cafeteria

11:45-12:35    "Real Estate in Hyperbolic Space: Investment Opportunities
               for the Next Millenium, by Mel Slugbate, Real Estate Broker
               with Slugbate and Mossbutter Real Estate Agency,
               Williamstown, MA"
               Colin Adams, Williams College

               Presider: Amy Boyd, Union County College

12:35-12:50    Presentation of the 1998 MAA-NJ Distinguished College or
               University Teaching Award

12:50-1:00     Remarks by Governor of MAA-NJ,
               Theresa C. Michnowicz, Jersey City State College

1:00-2:10      Lunch - College Center Cafeteria

2:10-3:00      "Automatic Differentiation: Computing Derivative Values
               Without Derivative Formulas"
               Dan Kalman, American University

               Presider: William Scott, Ocean County College

3:10-4:20      Contributed Papers Sessions

4:20-4:35      Drawing of Door Prizes and Announcement of Silent Auction
               Winners (You must be present to win)

5:00           Dinner honoring the Distinguished Award Recepient and the
               Invited Speakers; see announcements for details

Program Organizers:
Lawrence D'Antonio, Kay Gura, Ramapo College of New Jersey; Jean Lane, Union County Colleg; Theresa C. Michnowicz, Jersey City State College; Naomi Shapiro, Georgian Court College; Judith Schick-Lenk, Evan Alderfer, Ocean County College.

Program Committee:
Shirley Grone, Linda Atanasio, William Rickert, William Scott, Yuan Xu, Ocean County College, Matthew Haines, Jersey City State College.


"The Prince of Problem Solvers and the Absolute Monarch of Problem Posers: Paul Erdös (1913-1996)" by László Babai, University of Chicago

Paul Erdös wrote over 1500 papers, including joint work with 460 mathematicians. He maintained no permanent home and traveled from conference to conference with a small suitcase. We shall present a widely accessible sampling from Paul Erdös's mathematics, touching upon questions in number theory, geometry, probability theory, and combinatorics. A biographical sketch will conclude this brief account of the extraordinary life and work of the most prolific mathematician of our time.

László Babai is a professor in the Department of Computer Science and Mathematics at the University of Chicago. He received his degrees in mathematics at Eötvös University, Budapest Hungary where he subsequently became a professor. In 1990 he was elected a member of the Hungarian Academy of Science. He joined the University of Chicago in 1987.

Dr. Babai is the author of well over 100 papers. he is on the editorial board of many journals. He is one of the founders of the journal Combinatorica, one of the leading journals in discrete mathematics. He is also one of the founders of the highly acclaimed "Budapest Semesters in Mathematics" program for American undergraduates, established in 1985.

Dr. Babai was one of the recepients of the first Gödel prize in 1993, given for outstanding papers in theoretical computer science. He has given numerous invited talks, including plenary lectures at the First European Congress of Mathematics in Paris in 1992 and the International Congress of Mathematicians in Zürich in 1994. He is the 1996-1998 Pólya Lecturer of the Mathematical Association of America.

Dr. Babai considers himself a mathematical grandchild of Paul Erdös, since most of Babai's mentors were close associates of Erdös. Babai was first introduced to Erdös at the age of 15. They wrote three joint papers and were associated in many other ways. Dr. Babai is the author of a recent 90-page bibliographical study of Erdös.


"Real Estate in Hyperbolic Space: Investment Opportunities for the Next Millenium, by Mel Slugbate, Real Estate Broker with Slugbate and Mossbutter Real Estate Agency, Williamstown, MA", (Mel's brother-in-law is Colin Adams, Williams College)

The sky-high stock market got you nervous? What goes up must come down? Antsy about stocks, bonds, and mutual funds? Afraid of risky investments in Euclidean space? Then real estate in hyperbolic space is for you.

We will discuss the enormous potential of this new investment opportunity and describe the many fascinating properties of hyperbolic space that make it such an attractive place to live. This is the financial equivalent of the 1980's junk bond. No previous mathe or real estate background assumed! Recommended for faculty and students alike! Siskel and Ebert say, "Two fingers up!"

Colin Adams is head of the Mathematics Department of Williams College. He received his Ph.D. in 1983 from the University of Wisconsin, Madison. His research has focused on knot theory and hyperbolic 3-manifold theory. He has written numerous articles and several books, including the "Knot Book", which is an elementary introduction to the mathematical theory of knots and "How to Ace Calculus: the Streetwise Guide", a tounge-in-cheek supplement for calculus co-authored with Joel Hass and Abagail Thompson and due out in March, 1998. In addition to giving numerous talks, he also appears in several videos and is the co-author and co=performer, with Edward Burger, of the mathematical play "Casting About: About Casting", which was performed at the last two Mathfests. He received the Haimo Distinguished Teaching Award from the MAA in 1998.


"Automatic Differentiation: Computing Derivative Values Without Derivative Formulas" by Dan Kalman, American University

Automatic differentiation is a technique for computing derivatives of expressions which appear in scientific programming languages such as C or FORTRAN. In these languages, simple declaritive commands are automatically translated in the computational steps necessary to evaluate complicated functions. It is possible to extend this translation to compute derivatives of the functions, as well. That is the idea of automatic differentiation. It computes derivatives of expressions by performing essentially the same computations as evaluating symbolic derivatives formulas, but without ever obtaining or referring to those symbolic formulas. This talk will describe the general idea of automatic differentiation, and present some of the mathematics behind one approach to the subject.

Dan Kalman has a B.S. from Harvey Mudd College 1974, M.A. and Ph.D. from the University of Wisconsin, Madison, 1975, 1980 respectively. He has taught at University of Wisconsin, Green Bay, Lawrence University, Augustana College, and California State University at Northridge. Dr. Kalman worked for eight years at the Aerospace Corporation (where he first got involved with automatic differentiation) and served one year as Associate Executive Director of the MAA. At American University Dr. Kalman has been deeply involved with curriculum development at the entry level (roughly college algebra) for several years, culminating in a textbook just published by the MAA. He has won two writing awards from the MAA, a Pó in 1994 for an article in the College Math Journal, and a Trevor Evens in 1997 for an article in Math Horizon.


"On The Probabilities Of Mendel's Experimental Results Being So Close To His Theoretical Predictions" by Stephanie Rebain, The College of New Jersey

In 1865, Gregor Mendel proposed a genetic model to account for the results of his garden pea experiments. The model unlocked a great mystery in life and ranks one of the most important discoveries in science. In 1936, R.A. Fisher compared Mendel's data with the theoretical predictions and concluded that the probability of having data this close to expectation is 3/100,000. Fisher's calculation is widely accepted by statisticians but has drawn continuing protests from biologists as reflected in articles published in 1965-1967 and in a series of papers (1985-1987) in the Journal of Heredity.

This talk will first review the debate. We will also discuss other inconsistent interpretations of Mendel's experiments as presented in Freedman et al. (1997), Spiegel (1997), and Hogg and Cragg (1995). The talk will then present a variety of new results that are extensions of the articles by Edwards (1986) and Noviski (1995).

Specifically, our findings indicate that in 69 sets of Mendels experiments, the observed values are not as close to expectation as what Fishers paper or Freedmans 1997 book concluded; however, the 69 sets of the data are too similar to each other and the probability for that to happen is about 2/100,000.

Stephanie Rebain is a student at The College of New Jersey.


"Chaotic Attractors with Discrete Planar Symmetries" by Nathan Carter, University of Scranton

Chaotic behavior is known to be compatible with symmetry and illustrations are constructed using functions equivariant with respect to the desired symmetries. Earlier investigations determined families of equivariant functions for a few of the discrete symmetry groups in the plane; those results are extended to all the discrete symmetry groups of the plane. This includes consideration of the all the frieze and two-dimensional crystallographic groups.

Nathan Carter majors in mathematics and computer science at the University of Scranton. Theoretical computer science, chaos, and topology have been his most enjoyable areas of academic experience thus far, rivaled only by music performance in bands, choirs, or small ensembles. Future plans include undergraduate research at his home school followed by graduate school for mathematics.



Session I
Presider: William Rickert, Ocean County College

Carol Avelsgaard, Middlesex County College, "Ratio of Evenescent Quantities"

Deborah Bennett, Jersey City State College, "Random Number Generators---Too Important to be Left to Chance"

Carolyn Manigault, Felician College, "Probing Reality: Developing a Math History Course"

John Snygg, Felician College, "Why you oughta wanna learn some Clifford Algebra"

Session II
Presider: William Scott, Ocean County College

Donald Forbes, Chase Manhattan Bank (retired), "Mathematics of Esthetics"

Yi Ding, Jersey City State College, "Laboratories in Mathematical Experimentation"

R. Gregory Taylor, Jersey City State College, "On Symmetry and Categoricity"

Yuan Zhong Xy, Ocean County College, "A Class of Q-Hypoelliptic Systems of Differential Equations with Constant Coefficients"

Session III - Student Papers
Presider: Chamont Wang, College of New Jersey

Jim Tarlau, College of New Jersey, "A Critical Review Of A Case That Uses Statistics On Investment and Financial Decisions"

Jeff Cortez, College of New Jersey, "Fair Division: From Cake-Cutting to Dispute Resolution"

Susan Smallman, Andrea Johnson, and Neeraj Udashi, College of New Jersey, "On the Predictive Power of Certain Regression Models"

Greg Litkey, College of New Jersey, "Pilot Fatigue and Instrumental Disputes"


From the North or South

Use Exit 82 from the Garden State Parkway. Proceed east on Route 37 towards Toms River/Seaside Heights. Go about one mile (2 traffic lights) following signs to Laurelton. Turn at jughandle to Route 549 north (Hooper Avenue). Proceed 3 miles to jughandle leading to Ocean County College campus in Toms River. Security guard in booth in Parking Lot #1 will assist with campus directions if necessary.

Access Road From the West

From Route 9 north or south, take Church Road east. Proceed across New Hampshire Avenue. Proceed 1½ miles to access road (H. George Buckwald Drive) intersection. Turn right onto Buckwald Drive. The drive ends at College Drive near Lot #2.

From the West

Use Route 70 to Lakehurst; then take Route 37 east to Toms River/Seaside Heights. Follow signs to Laurelton. Turn at jughandle to Route 549 north (Hooper Avenue). Proceed 3 miles to jughandle leading to Ocean County College campus in Toms River. Security guard in booth in Parking Lot #1 will assist with campus directions if necessary.


To preregister and/or reserve a place for lunch, return a copy of this form (with a check made payable to MAA-NJ) by April 1, 1998 to Linda Atanasio at:

             Ocean County College
             Mathematics Department
             College Drive
             Toms River, NJ 08754



Address: Home________________________________________________________


Business Phone___________________ Home Phone_________________________

E-Mail Address_______________________________________________________

________I am enclosing $12 preregistration fee

________I am a student (no registration fee)

Lunch Reservation ____Yes, I will be attending the luncheon (enclosed is the $12 fee)

____No, I will not attend the luncheon

____I am interested in becoming a committee member or officer of MAA-NJ

____My college/company is interested in hosting a future meeting of MAA-NJ

Reminder: The dinner to honor the invited speakers and the award recepient will be at Tommy D's immediately following the meeting: To make reservations contact Linda Atanasio at 732-255-0368 or check the following:

____Yes, I plan on attending the dutch-treat dinner after the meeting at Tommy D's.

For futher information send mail to Larry D'Antonio ldant@ramapo.edu

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