North Central Section

 

Mathematical

Association of America

 

 

 

Fall Meeting Ÿ October 19-20, 2007

Bemidji State University

Bemidji, Minnesota

 

 


 

Friday, October 19

 


7:00 – 8:00       Registration - Bridgeman Hall lower level

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

    $5 for MAA-NCS section NExT members.

 

7:00 – 8:00       Book Sales - Bridgeman Hall 105

                           

8:00                    Evening Session – Bridgeman Hall 100– Dr. Randy Westhoff, presiding

 

8:00 – 9:00       Lecture, Dr. David Appleyard, Carleton College

                            In Praise of Student Ingenuity

 

9:00 –10:30      Reception - David Park House

 

Saturday, October 20

 

 


 8:15 – 11:00    Registration - Bridgeman Hall lower level

 8:15 – 11:00, 12:00-2:40  Book Sales – Bridgeman Hall 105

 

 9:00                   Morning Session – Bridgeman Hall 100, Dr. Eric Lund, presiding

                            Greeting, Dr. Pat Rogers, Dean, College of Social and Natural Sciences

 

 9:05 – 9:25      Prof. Walter Sizer, Minnesota State University Moorhead

                            From Normal School to University:  The Mathematics Program at Minnesota State

                            Normal School/University Moorhead

                           

 9:25 – 9:45      Prof. Mark Fulton, Bemidji State University, Department of Biology

Exploring a 45-Dimensional Forest: Vector-Field Representations of Vegetation Change

 

 9:50 – 10:10    Prof. In-Jae Kim, Minnesota State University, Mankato

                            Trees with Distinct Eigenvalues for Distinct Diagonal Entries

 

10:15 – 10:35 Prof. Kenneth Kaminsky, Augsburg College

                            Odd-boiled Eggs

 

10:35 – 11:00  Break

 

11:00 – 12:00  Dr. Richard Spindler, presiding

 

                            Lecture, Dr. Jim Tattersall, Providence College

                            NUMBERS, NUMBERS, NUMBERS

 

12:00 – 1:00     Lunch, American Indian Resource Center, Great Room

 

  1:00 – 1:30     Business Meeting - Bridgeman Hall 100- President Tom Sibley, presiding

 

  1:30 – 3:30     Afternoon Session - Bridgeman Hall 100- Dr. Ryan Hutchinson, presiding

 

  1:30 – 1:50     Prof. Douglas Anderson, Concordia College-Moorhead

                            Self-adjoint Matrix Equations on Time Scales

 

  1:55 – 2:15     Prof. Bill Schwalm, University of North  Dakota, Department of Physics

                            Light Clock Proof of Time Dilation and Length Contraction


 2:20 – 2:40     Afternoon Session - Bridgeman Hall 100- Dr. Ryan Hutchinson, presiding

 

 2:20 – 2:40      Timothy Prescott, University of California, Los Angeles (graduate student)
Brownian Motion for Random Walk Among Bounded Random Conductances

 

 2:45 – 3:05      Jerry Brooks, University of North Dakota, Department of Physics (graduate student)

                            Weisner's Method for Generating Functions of Eigenfunctions of a Sturm

                            Liouville Boundary Value Problem

 

 2:20 – 2:45      Afternoon Session - Bridgeman Hall 204- Dr. Co Livingston, presiding

 

 2:20 – 2:40      Theodore C. Leonard, St. John’s University/College of St. Benedict (student)

Winning Darts: Where to Aim to Minimize Risk and Maximize Expected Values When Playing the Classic Darts Game of 501

 

 2:45 – 3:00      Shane Strasser, University of Sioux Falls (student)          

                            Methods of Calculating Fractals and Their Application to Proteins      

 

 

Abstracts

 


Ÿ David Appleyard, In Praise of Student Ingenuity

 

In my 41 years of undergraduate teaching, I rarely finished reading a set of exams without having been surprised and delighted by unexpected and correct solutions to certain problems on the exam.  In this talk, as time permits, I’ll show examples which solve problems from among calculus, differential equations, complex variables, difference equations, combinatorics, number theory, set cardinality, finite automaton theory, and algorithm analysis.

 

Ÿ Wally Sizer, From Normal School to University:  The Mathematics Program at Minnesota State Normal School/University Moorhead

 

I will trace the major steps in the evolution of the mathematics program at this institution as it changed from normal school to teachers' college to college and finally university.

 

Ÿ Mark R. Fulton, Exploring a 45-Dimensional Forest: Vector-Field Representations of Vegetation Change

 

A vector-field visualization of data from plots of vegetation observed over time field gives leverage on a number of questions of interest to ecologists.  This visualization leads naturally to an operational definition of predictability of vegetation change, and a natural decomposition of changes into ecologically interpretable components that can be separately analyzed for predictability.  The approach will be illustrated using data from a long-term study of forest dynamics in southeast Texas.

 

Ÿ In-Jae Kim, Trees with Distinct Eigenvalues for Distinct Diagonal Entries

 

It is known that each eigenvalue of a real symmetric, irreducible, tridiagonal matrix has multiplicity 1.  The graph of such a matrix is a path.  In this talk, it is shown that there are more trees requiring simple eigenvalues if the associated acyclic matrices with those trees have distinct diagonal entries. (This is a joint work with B.L. Shader)

 

Ÿ Kenneth Kaminsky, Odd-boiled Eggs

 

Observant Jews cannot eat eggs containing blood-spots.  When boiling eggs, if the majority of the eggs are free of blood-spots, the blood-free eggs may be eaten and the cooking utensil remain kosher.  Otherwise, all the eggs must be discarded and the utensil is no longer kosher.  A Dutch rabbi heard that if you add an egg to an even number being boiled, it is more likely that the majority will be blood-free.  Is this true?  What if you add an egg to an odd number?  What is this probability if you boil a really large number of eggs?

 

Ÿ Jim Tattersall, NUMBERS, NUMBERS, NUMBERS


The contents of two second century (A.D.) manuscripts, the Introduction to Arithmetic, by Nicomachus of Gerasa and Mathematics Useful for Understanding Plato by Theon of Smyrna , will be discussed. They were the main sources of knowledge of formal Greek arithmetic in the Middle Ages. The books are philosophical in nature, contain few original results and no formal proofs. They abound, however, in intriguing number theoretic observations. We will extend some of the results found in these ancient volumes and introduce several types of numbers that lend themselves naturally to undergraduate research.

 

Ÿ Douglas Anderson, Self-Adjoint Matrix Equations on Time Scales

Rudiments of time-scale calculus are introduced to unify and extend continuous, discrete, and quantum calculus. This is done via linear second-order matrix equations on time scales that are formally self-adjoint with respect to a certain inner product. Using a generalized Wronskian, a Lagrange identity and Abel’s formula are established. Two reduction-of-order theorems are given. A comprehensive roundabout theorem relating key equivalences concludes the talk.

 

Ÿ Bill Schwalm, Light Clock Proof of Time Dilation and Length Contraction

The light clock is a simple imaginary device (sort of a geometric construction) used to prove the time dilation and length contraction formulas of special relativity starting from only one postulate, that all the laws of physics are the same in any inertial frame.  The argument is simple and self-contained (not much physics) and requires only the Pythagorean theorem.  Suitable for introductory courses, for example in Precalculus.

 

Ÿ Timothy Prescott, Brownian Motion for Random Walk Among Bounded Random Conductances

Consider the nearest-neighbor simple random walk on the integer lattice with a random environment of i.i.d. nearest-neighbor conductances  (that is, the walk chooses each step in proportion to the available conductances), where we require only that the probability of a positive conductance is high enough.  We prove that, for almost every environment, the walk converges to isotropic Brownian motion.  This holds despite the fact that the local central limit theorem may fail in high dimensions due to an anomalously slow decay of the probability that the walk returns to its origin.

 

Ÿ Theodore C. Leonard, Winning Darts: Where to Aim to Minimize Risk and Maximize Expected

    Values When Playing the Classic Darts Game of 501

The standard dartboard contains regions that score different point values; generally, high value areas are adjacent to low scoring values and medium point values are near each other. The aim of this research was to determine what aiming point yielded the highest expected values. This project obtained real data to see how actual darts are distributed about an aiming point. This data was statistically analyzed and a simplistic distribution model was chosen. From this model, and actual measurements of the dartboard, we were able to numerically find the ideal aiming point for players ranging from beginner to expert.

 

Ÿ Jerry Brooks, Weisner's Method for Generating Functions of Eigenfunctions of a Sturm

    Liouville Boundary Value Problem

Some problems in quantum physics are Sturm Liouville boundary value problems.  The eigenvalues are possible values for measurements of a physical quantity, such as energy, and the eigenfunctions have to do with probabilities.  In Weisner's method a generating function for the eigenfunctions is found by solving partial differential equations, or by exponentiating a ladder operator.  The general method is illustrated in an example.

 

Ÿ Shane Strasser, Methods of Calculating Fractals and Their Application to Proteins 

Proteins can vary in their physical structure by varying the two torsion angles of each amino acid.  The non-covalent bond interactions in protein strands, however, reduce the theoretical number of degrees of freedom.  One way to determine the actual number of degrees of freedoms is by using fractal dimensions.  Using self-similar methods to calculate fractal dimension as an introduction, one can then look at more advanced methods to calculate fractal dimension.  The first method is referred to as the box-counting method.  The second method is the cluster grouping, which can deal better with proteins of higher torsions in comparison to the box-counting method.