North Central Section

 

Mathematical

Association of America

 

 

 

Spring Meeting Ÿ April 25-26, 2008

College of St. Benedict

Collegeville, Minnesota

 

 


 

Friday, April 25

 


7:00 – 8:00       Registration – Gorecki Hall

    $10;  Students, first time attendees and speakers free.  

    $5 for MAA-NCS section NExT members.

 

7:00 – 8:00       Book Sales – Gorecki Hall 204B

                           

Evening Session  Gorecki Hall 204A, Dr. Gary Brown, presiding

 

8:00 – 9:00       Lecture, Dr. Paul Zorn, St. Olaf Collage

                            Revisiting Familiar Places:  What I Learned at the Magazine 

 

9:00 –10:30      Reception, Gorecki Hall 204C

 

Saturday, April 26

 

 


 8:15 – 11:00    Registration - Gorecki Hall

 8:15 – 11:00, 12:00-2:55  Book Sales – Gorecki Hall 204B

 

Morning Session  Gorecki Hall 204A, Dr. Jennifer Galovich, presiding

 

9:00                        Greeting, Dr. Joe Des Jardins, Associate Provost and Dean,

                                College of St. Benedict and St. John’s University

 

 9:05 – 9:25          Prof. Richard Järvinen, Winona State University
                                Reliability as a Field in the Space Program:  Two Examples

 

 9:30 – 9:45          Prof. Chuck Rodell, St. John’s University and College of St. Benedict

Life and Equations: A View from Biology

 

9:45   9:50          DOT Survey Instructions, Co Livingston, NCS Secretary

 

Morning Session A             Gorecki Hall 204A, Dr. Jennifer Galovich, presiding

 

9:55 – 10:10         Prof. Tom Sibley; St. John’s University and College of St. Benedict

                                Lights, Camera, Proof

 

10:15-10:35         Prof. Joel Iiams, University of North Dakota

Paradoxes from Poker with Low &/or Hole Card Wild

 

Morning Session B             Gorecki Hall 120, Dr. Kris Nairn, presiding

 

9:55 – 10:15         Prof. Aaron Luttman, Bethany Lutheran College

Nonlinear Optimization and Regularization Techniques for Astronomical Imaging

 

10:20-10:40         Prof. Ellen Hill, Minnesota State University Moorhead

                                Lessons Learned from Teaching a Writing Intensive Math Course

 

 

10:40 – 11:00      Break and DOT survey

 

Invited Lecture   Gorecki Hall 204A, Dr. Jennifer Galovich, presiding

 

11:00 – 12:00      Dr. Deanna Haunsperger, Carleton College  

                                Bright Lights on the Horizon

 

12:00 – 1:00         Luncheon, Gorecki Hall 204C

 

 1:00 – 1:30          Business Meeting, Gorecki Hall 204A,  President Tom Sibley, presiding

 

Afternoon Session A          Gorecki Hall 204A, Dr. Tom Sibley, presiding

 

1:30 – 1:50           Prof. Loren C. Larson, St. Olaf College (retired)

Rook Tours as Sliding Block Puzzles

 

1:50-2:05              Prof. Dan Kemp, South Dakota State University

                                Triangle Area Ratios: An Undergraduate Research Project

 

2:10-2:30              Prof. In-Jae Kim, Minnesota State University, Mankato

Inertias of Matrix Patterns

 

2:30-2:50              Prof. Bill Schwalm, University of North Dakota, Department of Physics

                                Eigenvalues and Eigenvectors of Certain Matrices

 

2:55-3:15              Prof. Byungik Kahng, University of Minnesota, Morris

Chaotic and Non-chaotic Singularities of Planar Piecewise Isometric Dynamics

 

3:15-3:35              Prof. Mike Melko, Northern State University

Exploring Dynamical Systems with Mathematica

 

Afternoon Session B          Gorecki Hall 120, Dr. Mike Tangredi, presiding

 

1:30 – 1:50           Prof. John Holte, Gustavus Adolphus College

The Gambler’s Ruin Online and Offline

 

1:50-2:05              Prof. Paul Weiner, Saint Mary’s, University of Minnesota

Viewing the Hamming Code in its Natural Habitat

 

Student Session                   Gorecki Hall 120, Dr. Mike Tangredi, presiding

 

2:10-2:30              Lara Brekke-Brownell, University of Minnesota (undergraduate student)

Mutually Tangential Circles Fitting in an Annulus

 

2:30-2:50              Anna Duane, Carleton College (5th year intern)

Binomial Coefficients and Kepler Walls

 

2:55-3:15              Tova Lindberg, Bethany Lutheran College (undergraduate student)

Classifying the Maximal Ideals of C(X)

 

3:15-3:35              Candyce Hecker, University of North Dakota (graduate student)

“Sublimits” in a Separable Metric Space

 


 

 

Abstracts

 


Invited Speakers

 

Ÿ Paul Zorn, Revisiting Familiar Places:  What I Learned at the Magazine 

Among the side benefits of editing Mathematics Magazine was to learn a lot of mathematics.   Much was completely new to me, but could there possibly be anything new to learn about cubic polynomials? Countable sets?  Equilateral triangles?  Bijective functions?

 

The short answer is yes.    The Magazine and other undergraduate journals are rich sources of novel --- and often surprising ---views of supposedly familiar, thoroughly understood, topics from undergraduate mathematics.     I'll give some examples that worked for me.    That such examples exist attests partly to the speaker's ignorance, but also to the depth and richness of our subject.

 

Ÿ Deanna Haunsperger, Bright Lights on the Horizon

What do a square-wheeled bicycle, a 17th-century French painting, and the Indiana legislature all have in common?  They appear among the many bright stars on the horizon of mathematics, or perhaps, more correctly, in  Math Horizons.  Math Horizons, the undergraduate magazine started by the MAA in 1994, publishes articles to introduce students to the world of mathematics outside the classroom.  Some of mathematics’ best expositors have written for MH over the years; here are some of the highlights from the first ten years of Horizons. 

 

Morning Session

 

Ÿ Richard Järvinen, Reliability as a Field in the Space Program:  Two Examples 
Dr. Jarvinen has worked as a NASA Research Scientist at the Johnson Space Center in Houston, Texas, in a dozen different years since 1995 doing risk and reliability assessments for the Space Shuttle and International Space Station.  His talk will offer insight into the field of reliability as applied to the Space Program using two (he believes interesting) examples drawn from his NASA experience.  His first example offers a surprise of valuable use for decision-making, while the second leads to an opening for research.  The talk is accessible to students and should prove to be of interest to faculty who teach them.

 

Ÿ Chuck Rodell. Life and Equations: A View from Biology

Historically, mathematical reasoning has played a major role in stimulating advancement in our understanding of the biological world.  A partial list includes the works of William Harvey, Gregor Mendel, and GH Hardy.  One lesson to be gathered from these examples is that significant insight can be gained from relatively simple mathematical reasoning.  This raises the question, why isn’t mathematical reasoning more pervasive in the biological sciences?

 

Morning Session A

 

Ÿ Tom Sibley; Lights, Camera, Proof
How can we help students improve their ability to prove propositions? Introduction to proof texts and courses can familiarize students with definitions and proof techniques.  But the art of developing a mathematical idea for a proof seems harder to teach.  I’ll discuss an approach to teaching the process of finding these ideas based on an NSF funded study.  It uses videos of students attempting proofs new to them. Students in a class work on these proofs themselves, view the videos, and discuss and reflect on the process.

Ÿ Joel Iiams, Paradoxes from Poker with Low &/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!

 

Morning Session B

 

Ÿ Aaron Luttman, Nonlinear Optimization and Regularization Techniques for Astronomical Imaging

Astronomical images taken by ground-based telescopes suffer from blurring caused by the atmosphere.  The mathematical problem of de-blurring the images can be formed as a linear operator equation which does not have unique solutions, so we try to compute an “optimal” solution in some mathematical sense.  The traditional method for computing an optimally de-blurred image is using a regularized least-squares optimization, but we will show in this presentation that using the Poisson negative log-likelihood data fidelity can be more appropriate, given the nature of the noise in the data.  The presentation will be self-contained and available to students and faculty members of all backgrounds.

 

Ÿ Ellen Hill, Lessons Learned from Teaching a Writing Intensive Math Course

The presenter will give suggestions for the specific issues in teaching a mathematics course that is either writing intensive or requires some writing.  The specific suggestions will focus on upper level mathematics courses, but some attention will be paid to lower-level, general audience mathematics courses as well.  The range of issues addressed will include suggestions on how to make it easier to manage the grading involved to what issues in mixing Math and English you should cover with your students before a paper is due.

 

Afternoon Session A

 

Ÿ Loren C. Larson, Rook Tours as Sliding Block Puzzles

Abstract:  See title.

 

Ÿ 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.

 

Ÿ In-Jae Kim, Inertias of Matrix Patterns

The inertia of a square matrix A is the ordered triple (p,q,r), recording qualitative information of the eigenvalues of A, where p (resp. q and r) is the number of eigenvalues with positive (resp. negative and zero) real part.  The inertias of matrices have been studied extensively with association to stability of dynamical systems, and it is known that partial information of matrices can often determine possible inertias of those matrices.  In this talk we discuss recent developments on the inertias of matrix patterns that are matrices with only partial information on the entries such as being zero or nonzero, or signs of entries. 

 

Ÿ Bill Schwalm, Eigenvalues and Eigenvectors of Certain Matrices

The n by n matrix with all entries +1 has eigenvectors that are easy to find, or even to guess.  This talk is about certain other matrices, with entries written in terms of the index values via simple formulas.  For these one can often find formulas for the eigenvectors and hence also for the eigenvalues.  A use of this might be to make exercises that seem perhaps less contrived (post hoc) than the ones made via sets of eigenvectors.  The author suspects he may learn something in the process of making this presentation.

 

Ÿ Byungik Kahng, Chaotic and Non-chaotic Singularities of Planar Piecewise Isometric Dynamics

The main purpose of this research is to establish the connection between the geometrical properties of the singularity and the dynamics of the system.  We classify the singularity of bounded invertible planar piecewise isometric dynamics into three types, in terms of their geometrical properties.  Among the three, we one type of the singularity can be removed by lifting up the dynamics to a suitably defined (branched) manifold.  Among the remaining two, only one generates the (weakly) chaotic dynamics, while the other does nothing. 

 

Ÿ Mike Melko, Exploring Dynamical Systems with Mathematica

Mathematica will be used to illustrate various concepts and issues that arise in dynamical systems and their discretizations. In particular, we will investigate the approximation error that results from using the Euler and Runge-Kutta methods to numerically integrate the pendulum equation. If time permits, we will briefly discuss symplectic integrators and their relevance to numerical integration. This will again be done in the context of the pendulum equation.

 

 

Afternoon Session B

 

Ÿ John Holte, The Gambler’s Ruin Online and Offline

Often it is faster to look up the answer to a problem than it is to work it out yourself. In this presentation I’ll tell how these approaches worked out for my students and me in the case of some extensions of the standard gambler’s ruin model.

 

Ÿ Paul Weiner, Viewing the Hamming Code in its Natural Habitat

The Hamming code naturally lives in a high dimensional realm, and so it is hard for us Low-D-folks to picture.  However, by being somewhat sneaky, the presenter has managed to get some candid shots of the Hamming code in its home environment.  Necessary background on the Hamming code and hypercubes will also be provided.

 

 

 

 

Afternoon Student Session

 

Ÿ Lara Brekke-Brownell, Mutually Tangential Circles Fitting in an Annulus

Suppose that two not necessarily concentric circles are given with one in the interior of the other.  Suppose that the region between these two circles contains non-overlapping circles (i.e. they share no more than one point) which are tangent to both original circles and to at most two other circles in this region.  This paper will examine the conditions which are necessary and sufficient for exactly k such circles to be in the region between the large and small circles such that each is tangent to exactly two other circles in this region.  The conditions are based on the radii of the large and small circles and the distance between their centers.  The method used treats the two given Euclidean circles as concentric circles in hyperbolic geometry.

 

Ÿ Anna Duane, Binomial Coefficients and Kepler Walls

Kepler walls are a new combinatorial object made up of stacks of rows of bricks in which no two bricks are adjacent and every brick not in the top row is  supported" by a brick immediately above, above and to its right, or above and to its left.  It turns out that the Kepler walls on n bricks with a given number of available brick spaces in their top row are counted by a certain binomial coefficient; for example, there are C(2n-1,n) Kepler walls with a single top row space and n bricks total.  In this talk, we define Kepler walls and describe a prototypical bijection from walls with one top row space to an appropriate set of lattice paths.  We also briefly mention how this technique generalizes to walls with k top row spaces. 

 

Ÿ Tova Lindberg, Classifying the Maximal Ideals of C(X)

A maximal ideal of a ring is a proper subring not contained in any other proper subring that “absorbs” elements from the ring.  If X is a closed and bounded subset of the complex plane, then we can classify all of the maximal ideals of the ring C(X), the space of all complex-valued continuous functions on X.  This is interesting as an algebraic method of exploring objects in analysis.  In this talk a brief background for the project will be given and the complete characterization of maximal ideals on C(X)

 

Ÿ Candyce Hecker, “Sublimits” in a Separable Metric Space

At the Spring 2007 MAA meeting, Dr. Thomas Q. Sibley presented a talk entitled “Sublimital Analysis” in which he addressed the limits of subsequences of a sequence in R, these were called “sublimits.”  His discussion included a look at the collection of “sublimits,” and how to construct a sequence in R for which the collection of “sublimits” is some given closed set in R.  This discussion will extend these ideas to subsequences and “sublimits” in Rn as well as to any separable metric space.