**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. Johns 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, Ill 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

**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 Abels 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.