North Central Section

 

Mathematical

Association of America

 

 

 

Fall Meeting Ÿ October 17-18, 2008

Concordia College

Moorhead, Minnesota

 

 


 

Friday, October 17

 


7:00 – 8:00       Registration – Knutson Campus Center, Lounge outside Jones Conference Center A&B (2nd

                               floor)

    $10 registration fee;

    $5 for MAA-NCS section NExT members; Students, first time attendees and speakers free.               

 

7:00 – 8:00       Book Sales – Jones Conference Center C&D

                           

8:00 – 9:00       Invited Lecture  Jones Conference Center A&B, Dr. Dan Biebighauser, presiding

                            Dr. Karen Saxe, Macalester College

                            Mathematics and Politics

 

9:00 –10:30      Reception:  Lounge outside Jones Conference Center A&B

9:00 –10:30      Student Reception Area: Jones Conference Center B

 

 

Saturday, October 18

 

 


8:15 – 11:00     Registration - Lounge outside Jones Conference Center A&B

8:15 – 11:00, 12:00-3:05  Book Sales – Jones Conference Center C&D.

 

Morning Session                 Jones Conference Center A&B, Dr. Jessie Lenarz, presiding

 

9:00                        Greetings, Dr. Heidi Manning, Chair of the Division of Science and Mathematics

 

Morning Session A              Jones Conference Center A, Dr. Jessie Lenarz, presiding

 

9:10 – 9:30           Prof. Joel Iiams, University of North Dakota

                                Paradoxes from Poker with Low and/or Hole Card Wild

 

9:35 – 9:55           Prof. Michael C. Mangini, Concordia College

When Will I Ever Use Math? A Few Answers from this Cognitive Psychologist

 

10:00 – 10:20      Prof. Din Chen, South Dakota State University

                                A generalized Nonlinear Mixed Model for Binomial Dose-response Modeling

 

10:20-10:40         Prof. Daniel P. Biebighauser,  Concordia College, Moorhead

Burnside’s Lemma and Color Cycling

 

Morning Session B             Jones Conference Center B, Dr. Jerry Heuer, presiding

 

9:10 – 9:30           Prof. In-Jae Kim,  Minnesota State University, Mankato

                                On Fiedler - and Parter-vertices of Trees

 

9:35 – 9:55           Prof.  Doug Anderson, Concordia College Moorhead

                                Global Attractivity for Nonlinear Delay Dynamic Equations

 

10:00 – 10:20      William Hall, Concordia College (undergraduate student)

                                Oscillation Criteria for Systems of First-Order Equations

 

10:20 – 10:40      David Mathisen, Minnesota State University Moorhead, (undergraduate student)

                                Permutation Statistics and q-Fibonacci Numbers

 

10:45 – 11:00      Break

 

11:00 – 12:00      Invited Lecture   Jones Conference Center A&B, Dr. Su Doree, presiding

Dr. Betty Mayfield, Hood College

Women and Mathematics at the Time of Euler

 

12:00 – 1:00         Luncheon, Anderson Commons (1st floor)

 

 1:00 – 1:30          Business Meeting   Jones Conference Center A&B, President Su Doree, presiding

 

Afternoon Session A          Jones Conference Center A, Tim Peil, presiding

 

1:30-1:50              Prof. Sarah Jahn, Concordia University- St. Paul

Why Not Transform the Axes Instead of the Graph?

 

1:55-2:10              Prof.  Dan Kemp, South Dakota State University

Triangle Area Ratios: An Undergraduate Research Project

 

2:15-2:35              Prof. William Schwalm, University of North Dakota

                                Eigenvalues and Eigenvectors of Certain Pretty Matrices

 

2:40-3:00              Prof. Co Livingston, Prof. Randy Westhoff, Bemidji State University

                                STEM Camp

 

3:05-3:25              Prof. Wojciech Komornicki, Hamline University

Another Look at the Exponential Function

 

 

Afternoon Session B          Jones Conference Center B, Xueqi Zeng, presiding

 

1:30-1:50              Prof. Mike Weimerskirch, St. Olaf College

                                An Algorithmic Approach to Nim-like Games

 

1:55-2:10              Prof. Sri Pudipeddi, Augsburg College

                                Radial Solutions to a Superlinear Dirichlet Problem Using Bessel Functions

 

2:15-2:35              Prof. Lisa Rezac, University of St. Thomas

                                An Introduction to Measure Theory with a Special Application: What was Feynman                                                 Conjecturing?

 

2:40-3:00              Prof. Eric Errthum, Winona State College

                                Finding Minimal Polynomials with a Norm Calculator

                 

3:05-3:25              Prof. Byungik Kahng, University of Minnesota Morris

                                The Invariant Set Theory of Discrete Time Control Dynamical Systems with                                                       Deterministic Disturbance

 

 

Student Session                   Anderson Commons private room (1st floor), Dr. Peh Ng, presiding

               

1:35-2:20              Flatland: The Movie 

 

2:15-3:15              Prof. Aaron Wangberg, Winona State University 

The Mathematics Behind Constructing - and Viewing - Four-dimensional Shapes.

 


 

Abstracts

 


Invited Speakers

 

Dr. Betty Mayfield, Women and Mathematics at the Time of Euler

In 2007 mathematicians around the world focused on All Things Euler: his life, his work, his legacy. We were treated to special conferences, books, papers, posters, a study tour, and sessions at national meetings. We will examine a slightly different topic: female contemporaries of Leonhard Euler (1707 - 1783), some famous, some not so famous. We will look at their lives and their work, at mathematics that was written by and – surprisingly – for women in the time of Euler.   This talk grew out of an experimental summer research project with a group of undergraduate students in the history of mathematics.

 

  Dr. Karen Saxe, Mathematics and Politics

"...democracy is the worst form of government except all those other forms that have been tried from time to time." -- Winston Churchill 

 

The cornerstone for a democracy is, arguably, the electoral system chosen. How do we elect our president? Are there better alternatives? We will consider mathematical approaches to these questions, and discuss the advantages and disadvantages of the many different electoral systems that are used by democratic countries around the world.

 

Morning Session A

 

Joel Iiams, Paradoxes from Poker with Low and/or Hole Card Wild

It’s been known for some time that introducing wild cards into the game of poker skews the frequencies of hands which may lead to paradoxes. Yet there is a well-educated acquaintance of mine who refuses to stop playing poker with wild cards. His refuge is a game called seven-card stud low hole card wild. We consider this and several related games. In each case we produce a paradox. There is also an interesting surprise!

 

Michael C. Mangini, When Will I Ever Use Math? A Few Answers from this Cognitive Psychologist

Cognitive Psychology, the study of how humans and animals process information, has set for itself the difficult task of learning the representations and operations that occur in the mind.  I will discuss two ways in which mathematics has influenced my work.  First, a group of researchers suggest that the brain is essentially a machine for capturing the natural statistics of its sensory world.  In this context, I will discuss my research showing vector space representations are predictive for human face recognition.  Second, I will discuss how a simple method of statistical inference makes explicit the ineffable qualities of visual decision-making.

 

● Din Chen, A generalized Nonlinear Mixed Model for Binomial Dose-response Modeling

The Limit of detection (LOD) has attracted wide attention in the literature of environmental protection and from various regulatory agencies.  Bioassays are often used to estimate LOD as a measure of the sensitivity using dose-response modeling. In this talk, a nonlinear mixed model is proposed to model this dose-response relationship for binomial mortality data to incorporate various random effects due to the characteristics of the living organism etc. An extended quasi-likelihood method is used to estimate the model parameters along with the investigation of over-dispersion with simulation studies and real data to demonstrate the applicability of this approach.

 

  Daniel P. Biebighauser,  Burnside’s Lemma and Color Cycling

A standard application of Burnside’s Counting Lemma is to count the number of indistinguishable colorings of the vertices of a geometric object, where two colorings of the object are indistinguishable if there is a permutation from the group of symmetries of the object that sends one coloring to the other coloring.  In this talk, we explore the indistinguishable colorings that arise from symmetries and from permuting the colors themselves.  In addition to discussing the general case, we use technology to display the indistinguishable colorings for specific objects and specific color permutations.

 

Morning Session B

In-Jae Kim,  On Fiedler - and Parter-vertices of Trees

Fiedler- and Parter-vertices are defined in terms of multiplicities of an eigenvalue of an n by n symmetric matrix and its principal submatrix of order n-1.  In this talk we provide geometric characterizations of Fiedler- and Parter-vertices of acyclic matrices.  Furthermore, we describe a structure of an acyclic matrix by those vertices, which enables us to construct an acyclic matrix of a desired form according to the locations of Fiedler- and Parter-vertices.  This is a joint work with Bryan Shader at University of Wyoming.

 

  Doug Anderson, Global Attractivity for Nonlinear Delay Dynamic Equations

Conditions under which solutions of a first-order nonlinear variable-delay dynamic equation go to zero at infinity are given, for arbitrary time scales that are unbounded above. In two examples, we apply our techniques to dynamic equations on isolated, unbounded time scales, including a logistic model and a food-limited model.

 

William Hall (student), Oscillation Criteria for Systems of First-Order Equations

Oscillation criteria for two-dimensional difference systems of first-order linear difference equations are generalized and extended to arbitrary dynamic equations on time scales. This unifies under one theory corresponding results from differential systems, and includes second-order self-adjoint differential, difference, and q-difference equations within its scope. Examples are given illustrating a key theorem.

 David Mathisen (student), Permutation Statistics and q-Fibonacci Numbers

We consider the distributions of permutation statistics of restricted sets of permutations.  We shall focus on the distribution of the inv statistic over reverse layered permutations.  This distribution will give us a q-analogue of the Fibonacci numbers, Fn(q).  We will use these q-Fibonacci numbers to bijectively prove q-analogues of Fibonacci identities.

 

Afternoon Session A

● Sarah Jahn, Why Not Transform the Axes Instead of the Graph?

Once students know the shape of basic graphs we typically teach them how to transform these basic graphs.  Most students memorize rules about how to transform the graphs without any clear understanding of which order they should perform the transformations or why the rules for horizontal transformations are the opposite of the rules for vertical transformations.  Would students understand better if we looked at the equation in terms of linear transformations on x and y and transformed the axes instead of the graph?

 

Dan Kemp, Triangle Area Ratios: An Undergraduate Research Project

 In an attempt to do some undergraduate research at SDSU a group of four students was assembled.  They discovered the following:  In triangle ABC if points D, E, and F are chosen on the sides such that 

DA/BA = EB/CB = CF/CA = k and the cevians AE, BF, CD intersect to form triangle GHI, then area(GHI)/area(ABC) is constant.  A proof was found using some geometrical interpretations of complex numbers.  This will be a report of their accomplishments.

 

William Schwalm, Eigenvalues and Eigenvectors of Certain Pretty Matrices

Usually when I want a problem in which the students should find eigenvectors or eigenvalues, either the matrix is pretty to start with, in which case the solution is ugly, or else I make a problem with a pretty solution, in which case the problem is ugly.  There is a way around this dilemma.  I present a strategy for making interesting looking problems with nice solutions.  Several examples are given.

 

Co Livingston, Randy Westhoff, STEM Çamp

In June 2008, we conducted a one-week STEM Camp for high school students, with support from a TENSOR-SUMMA grant and a MnSCU IPESL Grant.   We will discuss recruitment, curriculum, and activities.

 

Wojciech Komornicki, Another Look at the Exponential Function

We investigate the definition of the exponential function as a function which agrees with exponentiation when exponents are integers.  The development is via the inverse of the natural log function and uses only elementary differential and integral calculus. As a generalization we look at functions f satisfying the functional equation f(xy) = f(x) + f(y) and show the uniqueness of the solutions under very mild conditions.  In particular, if f is continuous at a point, the only such functions are multiples of the natural log function.

 

Afternoon Session B

 

Mike Weimerskirch, An Algorithmic Approach to Nim-like Games

The winning strategy for the ancient Indian game of Nim has been known for a century in both the normal play (unable to move loses) and misere play (unable to move wins) versions.  Nim is one of a larger class of games called impartial games, for which the generalized normal play strategy was discovered in the 1930s.  This talk describes an algorithmic approach to finding strategies for certain impartial misere games.  This algorithm was implemented by three students in a computer algorithms course at St. Olaf, which lead to an award winning paper at the 2008 MICS symposium.

 

Sri Pudipeddi,  Radial Solutions to a Superlinear Dirichlet Problem Using Bessel Functions

We look for radial solutions of a superlinear dirichlet problem in a ball. We show that for if n is a suciently large nonnegative integer, then there is a solution u which has exactly n interior

zeroes.

 

Lisa Rezac, An Introduction to Measure Theory with a Special Application: What was Feynman Conjecturing?

We introduce the idea of measure on the real line and abstraction to measures on other spaces.  We will consider some “ideal” properties of a measure, and compare the development of Lebesgue measure on the real line with Wiener measure on the space of continuous functions on a closed interval: C[a,b].  We close by highlighting a (perhaps) surprising result about C[a,b] and some implications for making Feynman’s proposed path integral mathematically rigorous. 

 

Eric Errthum, Finding Minimal Polynomials with a Norm Calculator

Given an algorithm that outputs norms of algebraic numbers, is it possible to reconstruct these numbers’ minimal polynomials? This talk will demonstrate a technique that does so using some basic Galois theory, special information about when the numbers are rational, and a little bit of brute force. This method is applied to the situation of singular moduli on Shimura curves, though no prior knowledge of such structures is required.

 

Byungik Kahng, The Invariant Set Theory of Discrete Time Control Dynamical Systems with Deterministic Disturbance

Invariant set theory is an important tool in control and automation theory.  In this talk, we focus upon the invariant set theory of discrete time control dynamical systems with deterministic disturbance and explain how it gives rise to the invariant set theory of multiple valued iterative dynamical systems.  Time permitting, the controllability problems of the maximal invariant sets will also be discussed.

 

Afternoon Student Session

 

Flatland: the Movie

This is an animated film inspired by Edwin A. Abbott's classic novel, Flatland. Set in a world of only two dimensions inhabited by sentient geometrical shapes, the story follows Arthur Square and his ever-curious granddaughter Hex. When a mysterious visitor arrives from Spaceland, Arthur and Hex must come to terms with the truth of the third dimension, risking dire consequences from the evil Circles that have ruled Flatland for a thousand years.

 

Aaron Wangberg, The Mathematics Behind Constructing - and Viewing - Four-dimensional Shapes.

When Arthur Square is visited by a being from the third dimension in Edwin A. Abbot's "Flatland", he realizes there are higher-dimensional shapes which he can partially view in two dimensions.  What would a

four-dimensional shape look like?  In this session, we'll explore this question and use mathematics to construct 4-dimensional shapes. We'll also explore the mathematical techniques which will allow us to "see" these objects as they pass through our 3-dimensional world. This interactive session will be accessible to all undergraduate students.