Spring 2010 Program

Abstracts are listed at the end of the page. (link)

Friday, April 23

3:30-5:30 Section NExT Writing Workshop by Ivars Peterson
Owens Science Hall Room 257
More information can be found at http://sites.google.com/site/ivarspeterson/home.
Open to **ALL**
6:30-8:00 Registration - Foyer Owens Science Hall
$10; Students, first time attendees and speakers free;
$5 for MAA-NCS Section NExT members.
6:30-10:30 Book Sales - O'Shaughnessy Science Hall 235-236
Evening Session - Owens Science Hall 150, Dr. Cheri Shakiban, Presiding
7:00-7:05 Welcome/Introduction
7:05-7:25 Prof. Walter Sizer, Minnesota State University, Moorhead
Periodicity in May's Host Parasitoid Equation
7:30-7:50 Prof. Lisl Gaal, University of Minnesota (retired)
A Mathematical Gallery
8:00-9:00 Invited Lecture

Professor Danrun Huang, St. Cloud State University
Many Phases of the Strogatz Dyadic Love-Hate Model
9:00-10:30 Reception - O'Shaughnessy Science Hall 235-237

Saturday, April 24

8:15-11:00 Registration - Owens Science Hall Foyer
Book Sales - O'Shaughnessy Science Hall 235-236
Morning Session - Owens Science Hall l50, Dr. Eric Rawdon, Presiding
9:00-9:05 Greetings, Dr. Kurt Scholz
Mathematics Department Chair, University of St. Thomas
9:05-9:25 Prof. Roger B. Kirchner, Carleton College (Emeritus)
Exploring the Crease Length Problem and other Wolfram Demonstrations
9:30-9:45 Prof. Thomas Q. Sibley, St. John's University/College of St. Benedict
Groups of Graphs of Groups
9:45-10:10 Break-Owens Science Hall Foyer
Student Poster Session-Owens Science Hall Foyer
Student Session - Owens Science Hall l50, Dr. Eric Rawdon, Presiding
10:10-10:30 Anne Dillon, Univeristy of Minnesota, Morris
Convergence and Stability of Matrices in Google's PageRank Algorithm
10:35-10:55 Benjamin Harste, Minnesota State University, Mankato
Calculus of Variations and Renewable Harvesting
11:00-12:00 Invited Lecture - Owens Science Hall l50, Dr. Eric Rawdon, Presiding

Ivars Peterson, Mathematical Association of America
Newton's Clock: Chaos in the Solar System
12:00-1:00 Luncheon Owens Science Hall 275
1:00-1:30 Business Meeting Owens Science Hall 150, Dr. John Holte, Presiding
Afternoon Session A - Owens Science Hall 250, Dr. John Holte, Presiding
1:30-1:50 Prof. William Schwalm, University of North Dakota, Dept. of Physics
Walks on Fractals
1:55-2:15 Prof. Bret Benesh, College of St. Benedict/St. John's University
Symmetric Groups that are Maximal Subgroups of Symmetric Groups
2:20-2:35 Prof. Ioannis Souldatis, Minnesota State University, Mankato
Some Random Graph Constructions
Afternoon Session B - Owens Science Hall 251, Dr. Misha Shvartsman, Presiding
1:30-1:50 Prof. Lisa Rezac, University of St. Thomas
A Capstone Course for Math Education Majors at the University of St. Thomas
1:55-2:15 H. Vic Dannon (retired)
Ordering of the Reals, Equality of all Infinities and the Continuum Hypothesis
2:20-2:35 Prof. Dale Buske, St. Cloud State University
On the Vector Triple Product


Invited Addresses

Danrun Huang, Many Phases of the Strogatz Dyadic Love-Hate Model

In addition to classical applications, this semester, I was looking for a class project that not only links the basic “dots” of a typical ODE course, but also contains room for imagination and further developments; a project in which one uses both theory and technology and that is fun even to math-apathetic students. Finally, I found the Romeo-Juliet love-hate model initiated by Steven Strogatz and a play written by McDill and Felsager. By analyzing and generalizing this model in different directions, the project has brought students many expected and unexpected benefits. People might be amazed by the students’ creativity in this project, such as how do the moons (yes, more than one), or drugs affect the relationship, and how to we design a love affair that is more chaotic than Tiger Woods’, ….

Ivars Peterson, Newton's Clock: Chaos in the Solar System

With astronomical questions inspiring new mathematics, the remarkable insights of Johannes Kepler, Isaac Newton, and Henri Poincaré paved the way to celestial mechanics and modern notions of chaotic dynamics. The result is a new picture of a solar system less placid and predictable that its venerable clockwork image would suggest.

Undergraduate Poster Session

Nisha Singh,Macalester College, Optimizing Citizen Effectiveness: An Alternative to Taagepera’s Cube Root Law for Assembly Size

Continued population growth raises questions about the size of representative bodies. Yet Rein Taagepera is the only author to propose an ideal size for bicameral legislative assemblies. The distinctive feature of his study is that assembly size is not considered a solely dependent variable, but an independent variable with potential to optimize legislative function. However, while Taagepera isolates system capacity as the sole criteria of optimality, I explore citizen effectiveness as an alternative. Results suggest that excluding citizen preference from his definition of ‘optimality’ limits the prescriptive applicability of Taagepera’s model for today’s diverse bicameral legislatures.

Molly Leonard, University of Minnesota, Numbers of Inequality: Mathematics of Conquest

For the past three years I have been researching the mathematics of the Incan civilization. Just recently I have compared this math system to the math practices emerging from Spain in the 16th century. When these two groups met for the first time on the Andean coast of South America in 1532, numbers greatly determined the outcome of the encounter. For the Incans, numbers were social and were only used to rectify societal imbalances; in this way the calculations helped distribute material goods. For the Spaniards, math practices were attached to the notions of accumulation, maximization, and domination. The numbers and how they were used very differently by two different groups has had startling consequences.

Contributed Student Talks

Anne Dillon, Convergence and Stability of Matrices in Google's PageRank Algorithm

Search engines are essential to the World Wide Web, yet most people are unaware of how they operate. This talk will examine Google’s PageRank algorithm, which ranks the pages returned in a search. Basically, PageRank assigns an importance score to each page on the Web using its hyperlinked structure. We will explore the linear algebra and graph theory behind the algorithm as used by Google and introduce our research, namely testing a possible modification to the algorithm. We will show the results of implementing this modification in terms of time-efficiency of convergence and accuracy of the resulting importance scores.

Benjamin Harste, Calculus of Variations and Renewable Harvesting

The Euler-Lagrange equation is developed by using the calculus of variations. This developed equation is then used to create a reasonable mathematical model simulating the operations and revenue of a sustainable harvesting business venture. The model is used to analyze the feasibility of operating such a business profitably. We analyze how profitable such a venture can be and consider how volatile the market is, based on the variability of a number of environmental and economic factors. Finally, it is concluded that sustainable harvesting for profit is possible for both short-term and long-term business ventures.

Contributed Talks

Bret Benesh, Symmetric Groups that are Maximal Subgroups of Symmetric Groups

Problem 12.82 of the Kourovka Notebook asks for all ordered pairs (n,m) such that the symmetric group Sym(m) has a maximal subgroup isomorphic to Sym(n). One family of such pairs is obtained when m = n+1. Kaluznin, Klin, and Halberstadt provided an additional infinite family. This paper answers the Kourovka question by producing a third infinite family and showing that no other pairs exist.

Dale Buske, On the Vector Triple Product

One of the fundamental properties of the vector triple product says that a × (b × c) = (a • c)b - (a • b)c. Through this identity, this talk aims to provide a better geometric understanding of the triple product.

H. Vic Dannon, Well-Ordering of the Reals, Equality of all Infinities and the Comtinuum Hypothesis

By the Well-Ordering Theorem, the Natural Numbers are ordered in such a way that every subset of them has a first element. The Well-Ordering Axiom is the guess that every infinite set of numbers can be well-ordered like the Natural Numbers. The Well-Ordering Axiom is equivalent to the Axiom of Choice. In 1963, Cohen claimed that it is impossible to prove that the real numbers can be well-ordered. In fact, the Dictionary Listing of the real numbers in [0,1] as infinite binary sequences, orders the real numbers with repetitions. When the repetitions are eliminated, we obtain the Midpoints Set, which is well ordered. This Well-Ordering, sequences the Real Numbers, and renders them countable.

Lisl Gaal, A Mathematical Gallery

Many mathematical ideas - from ancient geometry to more recent times can be represented pictorially. This is a collection of hand-printed lithographs of some of them.

Roger B. Kirchner, Exploring the Crease Length Problem and other Wolfram Demonstrations

Results presented here last year were published as a Wolfram Demonstration. Other demonstrations to be described include problems of rigor champion J. L. Walsh (“Tin Box with Maximum Volume”, “Swim, Swim and Walk, or Walk?”, “The Corner Wall Problem”), along with “Bounce Time for a Bouncing Ball”, “Coconuts, Sailors and a Monkey”, “Automatic Differentiation”, “Recursive Extended Euclidean Algorithm” and “Limits of A Rational Function of Two Variables”. See http://demonstrations.wolfram.com/kirchner.

Lisa Rezac, A Capstone Course for Math Education Majors at the University of St. Thomas

We will briefly discuss the content of the capstone course for math education majors at the University of St. Thomas. Our course covers the following Minnesota Board of Teaching Licensure requirements: discrete math, math history, and oral and written presentation of mathematics. We also follow recommendations from the CBMS MET document regarding connections to high school and undergraduate courses. I would like to hear from colleagues at schools offering related courses. In particular I would like to see if nearby institutions would like to pool students in order to offer the course more often.

William Schwalm, Walks on Fractals

The walk generating functions for a Michigan graph count the number of walks of a given length between two specified vertices. They also relate to the spectrum of the graph’s adjacency matrix. By a fractal graph I mean a sequence of graphs, each of which is formed by bonding together several copies of the previous graph in the sequence. (So I guess for me a fractal graph isn’t a graph.) It is easy to obtain recursions for the walk generating functions. This so-called renormalization technique, whereby you get the recursions, is used to find interesting results for several examples.

Thomas Q. Sibley, Groups of Graphs of Groups

I have investigated symmetry groups of edge-colored graphs for some time. In this talk I’ll explore the relationship between a group and the symmetry group of the graph I derive from the group. (These graphs are related to Cayley digraphs but differ in important ways.) The symmetry group always contains a copy of the original group, but some groups have additional symmetries leading to several interesting questions. I have classified the symmetry groups for abelian groups, but non-abelian groups present a continuing challenge.

Walter Sizer, Periodicity in May's Host Parasitoid Equation

May’s Host Parasitoid Equation is the difference equation x(n+1) = [c(x(n))2]/(x(n-1))(1 + x(n)). We are interested in the case c > 1 and having positive initial conditions. We consider the general situation and give some periodicity results.

Ioannis Souldatis, Some Random Graph Constructions

We will explain how Fraisse’s method can be used to construct random graphs that satisfy various properties. We will give examples of properties which no random graph satisfies, as well as examples of properties with a (unique) random graph.

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