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The Mathematical Association of America

North Central Section

Fall 2004 Meeting

October 29-30, 2004

North Dakota State University

Fargo, ND

Preliminary Program

Friday, October 29, 2004 

7:00-8:00  Registration, Minard Extension Lobby

7:00-8:00  Book Sales, Minard Extension

Evening Session    Bill Martin presiding,    Minard 138

8:00          Welcome by Dr. Craig Schnell, Provost and Vice President for Academic Affairs, Minard 138

8:05-9:00  "What do Kant, Feldman, and the GRE have in common?"

                 Professor Jason Douma, University of Sioux Falls

Abstract:  What does it mean to “know” something mathematical?  While the question itself is rather esoteric and in some ways unanswerable, the struggle to resolve it provides applications for how we would teach mathematics, and yields insight into those strange and paradoxical truths that seem to pervade the field.  This talk will examine our experiences in teaching mathematics as well as a few celebrated results from pure mathematics to create a “tapas-style” introduction to questions about “truth” and “knowledge” in mathematics.

9:00-9:30  Book Sales, Minard Extension

9:00-?       Reception, Minard Extension Lobby

Saturday, October 30, 2004

8:15-10:30     Registration, Minard Extension Lobby


8:15-2:45       Book Sales, Minard Extension

Morning Session    Joe Brennan presiding,    Minard 138

9:00                Welcome by Professor Warren Shreve, Chair, NDSU Mathematics Department

9:05  Stability of Discrete-time Recurrent Neural Networks, Nikita E. Barabanov, North Dakota State University
9:25  Example of a Solvable 3-body Problem, Cody Nitsche, University of North Dakota
9:45  Hedged Betting on Tournaments: A Way to Play the World Series and the Presidential Election, Ralph Carr, St. Cloud State University

10:15-10:30  Break

10:30-11:30  "Dirty Children, Unfaithful Husbands and Similar Problems"

                     Professor Marty Isaacs, University of Wisconsin Madison

Abstract:  How can children playing in the mud deduce that they have dirty foreheads?  This talk will discuss this and similar “brain teasers” and some underlying mathematics including the Conway-Paterson-Moscow Theorem.

 

11:30-12:30  Lunch, Dining Commons

 

12:30-1:00  Business Meeting, President Jennifer Galovich presiding,    Minard 138
                 

Afternoon Session      Jennifer Galovich presiding,    Minard 138

1:00  Working Backward to Construct Examples of DE's with Known Symmetries, William Schwalm, University of North Dakota
1:20  Section NExT's--What are they?  Should We Have One?, Michael Hvidsten, Gustavus Adolphus College

1:40  The Configuration Doctrine of Nicole Oresme, William Branson, St. Cloud State University

2:00  New Proofs of Some Fibonacci Identities, Danrun Huang, St. Cloud State University

2:20  Something New Concerning Indo-Arabic Numerals, Wally Sizer, Minnesota State University Moorhead

 

 

Abstracts

Evening Session

Jason Douma, “What Do Kant, Feldman, and the GRE Have in Common?”

What does it mean to “know” something mathematical?  While the question itself is rather esoteric and in some ways unanswerable, the struggle to resolve it provides applications for how we would teach mathematics, and yields insight into those strange and paradoxical truths that seem to pervade the field.  This talk will examine our experiences in teaching mathematics as well as a few celebrated results from pure mathematics to create a “tapas-style” introduction to questions about “truth” and “knowledge” in mathematics.

 

Morning Session

Nikita E. Barabanov, “Stability of Discrete-time Recurrent Neural Networks”

The problem of global Lyapunov stability of discrete-time recurrent multi-layered neural networks (RMLNN) in the unforced (unperturbed) setting is addressed.  The weights of RMLNN are assumed to be fixed to some values, for example, obtained after training.  Frequency domain and LMI-based criteria for absolute stability of such nonlinear systems are presented and discussed.  A new method of reduction of attractor estimate is introduced and analyzed.  This method is applicable to any nonlinear dynamical system, and it is shown to be efficient for RMLNN.  Examples illustrate the results.

Cody Nitschke, “Example of a Solvable 3-body Problem”

An important discovery in classical physics is that, in general, the 3-body problem has no closed-form solution.  The most famous of the 3-body problems involves three planetary objects interacting by gravity (an inverse square-law force).  However, there is a class of completely solvable n-body problems.  In these problems the objects interact by harmonic forces.  I present an interesting solution in the language of Lie algebras.

Ralph Carr, “Hedged Betting on Tournaments:  A Way to Play the World Series and the Presidential Election”

The World Series and the upcoming presidential election are examples of tournaments in which two players, A and B, compete in a series of individual matches to determine an overall winner.  We will look at some betting games and strategies in which a group of people who want to bet on the outcome of the tournament select a probability that A will prevail over B in each individual match, and in which the payoff is connected to a savvy estimate of those probabilities and some knowledge of mathematics.

 

Afternoon Session

Marty Isaacs, “Dirty Children, Unfaithful Husbands and Similar Problems”

How can children playing in the mud deduce that they have dirty foreheads?  This talk will discuss this and similar “brain teasers” and some underlying mathematics including the Conway-Paterson-Moscow Theorem.

William Schwalm, “Working Backward to construct Examples of DE’s with Known Symnmetries”

Sophus Lie found that the known methods of solving ODE’s really amount to using symmetry groups.  It is nice to be able to generate examples of second order ODE’s for which the general solution, a set of first integrals, and two symmetry groups are known.  I show by some examples how to do this working backward from the two-parameter family of functions that is the general solution to the DE.

Mike Hvidsten, “Section NExT’s—What Are They?  Should We Have One?”

A Section NeXT is a program like the national NExT Project, but specifically serving the members of a given MAA Section.  In this talk we will learn how other sections have created Section NeXT’s, discuss possible programs and activities, review resources at the regional and national level, and then open up the floor for a discussion of starting a section NeXT for our North Central Section.

William Branson, “The Configuration Doctrine of Nicole Oresme”

Nicole Oresme was a French cleric in the 1300’s.  His configuration doctrine was a graphical representation of the changes in certain quantities.  His arguments are similar to those developed by Galileo 250 years later.  I’ll discuss the basic idea of the configuration doctrine, why Oresme was interested in it, and its influence on later mathematics.

Danrun Huang, “New Proofs of Some Fibonacci Identities”

We prove some well-known Fibonacci identities by using matrices or graphs.  In particular we answer an open question recently posed by Professor Richard Askey.  Much of this talk is based on the paper “Fibonacci Identities, Matrices and Graphs”, which is to appear in Mathematics Teacher (NCTM).

Wally Sizer, “Something New Concerning Indo-Arabic Numerals”

So you think you know your Indo-Arabic Numerals?  I’ll start with a quiz or two on numeration just to check, go into the history of positional base ten notation for numbers, and look at various Indo-Arabic systems.  Answer keys provided.