Fall 2010 Program

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

Friday, October 22

6:30-8:00 Registration - Salsbury Science Center Atrium
$10; Students, first time attendees and speakers free;
$5 for MAA-NCS Section NExT members.
6:30-10:30 Book Sales - Salsbury Science Center Room 214
Evening Session - Salsbury Science Center Room 120, Chad Birger, Presiding
7:00-7:05 Welcome/Introduction - Dr. Bill Soeffing, Chair of Natural Sciences Area
7:05-7:25 Prof. Douglas Anderson, Concordia College
Prof. Michael Hvidsten, Gustavus Adolphus College

Teaching Computer Science and Math in China through the MPCC
7:30-7:50 Prof. Timothy Prescott, University of North Dakota
Shape Theorems for Evolving Sets on Two Dimensional Lattices
8:00-9:00 Invited Lecture

Prof. Timothy Peil, Minnesota State University-Moorhead
Am I Smarter than a Fifth Grader?
9:00-10:30 Reception - Salsbury Science Center Atrium

Saturday, October 23

8:15-11:00 Registration - Salsbury Science Center Atrium
Book Sales - Salsbury Science Center Room 214
Morning Session A - Salsbury Science Center Room 120, Dr. Dennis Roark, Presiding
9:00-9:20 Matthew Brorby, University of North Dakota (physics graduate student)
Elliptic Functions in General Relativity
9:25-9:45 Jonathan E. Rue, Minnesota State University - Moorhead (undergraduate student)
k-Gibonacci Numbers and Permutation Statistics
9:45-10:10 Break-Salsbury Science Center Atrium
10:10-10:30 Darren D. Row, Iowa State University (graduate student)
Zero Forcing Number of a Graph
10:35-10:55 Timothee W. Bryan, University of Sioux Falls (undergraduate student)
Further Classification of Groups of Graphs of Groups
Morning Session B - Salsbury Science Center Room 118, Dr. Joy Lind, Presiding
9:00-9:20 Prof. Marshall Hampton, University of Minnesota - Duluth
Sage: a free and open-source platform for mathematical teaching and writing
9:25-9:45 Knute Thorsgard, MD
Flat Light, Relativistically Curved, Quantized Space-Times
9:45-10:10 Break-Salsbury Science Center Atrium
10:10-10:30 Prof. William Schwalm, University of North Dakota, Dept. of Physics
Replacing parameters with conserved quantities in discrete dynamical systems
10:35-10:55 Prof. Shawn Chiappetta, University of Sioux Falls
Prof. Kris Nairn, St. John's University/College of St. Benedict

Upcoming Section NExT Activities
11:00-12:00 Invited Lecture - Salsbury Science Center Room 120, Dr. Dennis Roark, Presiding

Prof. Stacey Brook, University of Iowa, Dept. of Economics
Who is the Best NCAA Football Team?
A Production Model for the NCAA Football Bowl Subdivision
12:00-1:00 Luncheon McDonald Center Dining Room
1:00-1:30 Business Meeting Salsbury Science Center Room 120, Dr. Jason Douma, Presiding
Afternoon Session - Salsbury Science Center Room120, Dr. Jason Douma, Presiding
1:30-1:50 Prof. Thomas Q. Sibley, St. John's University/College of St. Benedict
When the Trivial is Non-Trivial: Abelian Groups with only one Multiplication
1:55-2:10 Prof. Ioannis Souldatos, Minnesota State University - Mankato
Some Random Graph Constructions
2:15-2:30 Prof. Ron Rietz, Gustavus Adolphus College
An Elementary Proof of ℵn·ℵn=ℵn
2:35-2:55 Prof. Walter Sizer, Minnesota State University - Moorhead
Similarity of Sets of Matrices
3:00-3:20 Prof. John Holte, Gustavus Adolphus College
Coping with Random Interest Rates


Invited Addresses

Who is the Best NCAA Football Team? A Production Model for the NCAA Football Bowl Subdivision, Stacey Brook, University of Iowa (Economics)

Each year pundits across the NCAA football landscape debate the validity of various NCAA football teams’ relative worthiness to play for the national championship. Given this debate seems to revolve around which team is the best in terms of production, I have created an NCAA football bowl subdivision production model to measure the performance of both the offense and defense, and created a ranking of the top 25 NCAA football bowl subdivision teams for the 2009 season.

Am I Smarter than a Fifth Grader?, Tim Peil, Minnesota State University-Moorhead

Recently, I participated in a grant where I worked with the teachers and students in grades 2 through 6 in a school system on the White Earth Reservation. For 2.5 years, I spent one day each week in the elementary school. The other four days I taught college courses from developmental mathematics through analysis for the majors. The talk will consist of interesting experiences and observations from this broad spectrum of mathematics and mathematics students. What level do I present at today?

Contributed Student Talks

Matthew Brorby, Elliptic Functions in General Relativity, University of North Dakota (physics graduate student)

It is thought that 96% of the universe comprises dark energy and dark matter about which little is known. The standard geometrical theory of gravity is general relativity. This suggests studying solutions to Einstein’s differential equations for a gravitational point source and a model of a cloud of dark matter dust. To this end, one wants to study the general solution to (y')2=a + by + cy2 + dy3 in terms of Jacobi elliptic functions. In the talk I hope to show how to do this treating separately several different regions of the parameter space.

Timothee W. Bryan, Further Classification of Groups of Graphs of Groups, University of Sioux Falls, (undergraduate)

In April 2010, Thomas Sibley from St. John's University gave a talk entitled “Groups of Graphs of Groups” in which he defined a new system of graph isometries based upon what he called “colorings.” His presentation classified the groups of graphs of groups for all Abelian and several indecomposable non-Abelian groups. This presentation extends Sibley's work by classifying 10 new graphs of groups generated by groups with non-trivial direct and central product structures. Conjugacy classes will be used to prove a sufficient condition for the isometry group of a graph of a group to be isomorphic to the group itself.

Darren D. Row, Zero forcing number of a graph, Iowa State University, (graduate student)

For a graph with each vertex initially colored either black or white, apply the rule that if a black vertex is adjacent to exactly one white vertex then that white vertex changes color to black. The zero forcing number of a graph is the smallest number of vertices needed to be initially colored black so that repeated applications of the rule will result in all vertices being black. This parameter is important to mathematicians studying the minimum rank/maximum nullity problem and to physicists studying quantum systems control. Results for some graph families will be presented.

Jonathan E. Rue, k-Gibonacci Numbers and Permutation Statistics, Minnesota State University- Moorhead (undergraduate)

Sagan, Goyt, and Mathisen studied the distribution of statistics over the pattern-restricted sets of set partitions and permutations, respectively. In their work, they determined identities that involved q-analogs of Fibonacci numbers. We generalize their work by studying a set of pattern restricted permutations counted by generalized Fibonacci numbers, which we call k-Gibonacci numbers. Let Ln;k be the set of layered permutations of length n where each layer is of length at most k. We will show Ln;k is counted by the k-Gibonacci number Fn(k). Further, we will give a recursion for counting the distribution of the inversion number over Ln;k. Finally, we will discuss a q-analogue of an identity involving k-Gibonacci numbers.

Contributed Talks

Douglas Anderson, Concordia College and Michael Hvidsten, Gustavus Adolphus College, Teaching Computer Science and Math in China Through the MPCC

The Minnesota Private College Council (MPCC) recently set up a faculty exchange with United International College (UIC) in Zhuhai, Guangdong Province, China. UIC, sponsored by Hong Kong Baptist University, is China’s first English-language liberal arts college, with a science division that includes computer science and statistics departments. The presenters recently completed sabbaticals that included significant teaching at UIC. We will share briefly some of our experiences.

Shawn Chiappetta, University of Sioux Falls and Kris Nairn, St, John’s University, Upcoming Section NExT Activities

This is a vetting session for future Section NExT activities. We especially invite people who can’t come to the early afternoon Friday session to participate. We want to get a gauge of overall interest as we move forward.

Marshall Hampton, Sage: A free and open-source platform for mathematical teaching and research, University of Minnesota-Duluth

Sage is a relatively new computational platform with the mission of providing a viable free and open-source alternative to Mathematica, Matlab, Magma, and Maple. This talk will introduce Sage and overview some of its capabilities, focusing on topics relevant to teaching undergraduate courses.

John Holte, Coping with Random Interest Rates, Gustavus Adolphus College

If future rates of interest vary randomly, how will the present value of an annuity (a stream of future payments) be affected? Undergraduate probability theory—together with techniques for elementary recurrence relations—can be used to obtain formulas for the mean and variance. The solution of this problem and some related problems will be presented, together with an application to the problem of maintaining constant purchasing power by combining an annuity with a sinking fund.

Timothy Prescott, Shape Theorems for Evolving Sets on Two Dimensional Lattices, University of North Dakota

Evolving sets are dual to random walks on a lattice, allowing the underlying geometry to aid intuition about the original walk. Local limit laws show that two dimensional random walks have transition probabilities that are eventually circular, leading one to expect a two dimensional evolving set to be eventually circular as well. We prove, however, that on three common lattices, the shape is always a semi-regular polygon, and we show that the limiting law defining this polygon is given by a two parameter stochastic diffusion.

Ron Rietz, An Elementary Proof of ℵn·ℵn=ℵn, Gustavus Adolphus College

In Naïve Set Theory, Halmos gives a proof, using Zorn’s Lemma, that a a = a for all infinite cardinals a. This amounts to showing that AxA and A have the same cardinality, for any set A of cardinality a. In the special case a = ℵn, n any non-negative integer, here is an elementary proof.

William Schwalm, Replacing parameters with conserved quantities in discrete dynamical systems, University of North Dakota (physics)

In a recent letter on discrete dynamical systems
xn+1 = F(xn,a), (1)
which have a conserved quantity
ψ(xn+1,a)=ψ(xn,a), (2)
where xn+1, xn are vectors and a is a parameter set, Roberts et al. point out that under certain conditions one can create a new dynamical system, replacing a parameter in Eq.(1) by ψ(xn,a) such that the same substitution in ψ(xn,a) gives a conserved quantity for the new system. They also show how this procedure can create new systems with more parameters, in each case having known invariants. I illustrate these constructions with simple examples and show an application to a family of dynamical systems generated from birational maps.

Thomas Q. Sibley, When the Trivial is Non-Trivial: Abelian Groups with only one Multiplication, St. John’s University

Any abelian group (G,+) with identity 0 becomes a ring with the trivial multiplication of a*b = 0 for all a and b in G. We investigate groups whose only possible multiplication is this boring multiplication. Fortunately, the mathematics involved is neither boring nor trivial. This talk is based on joint work with my student William Capecchi (who is now a graduate student).

Walter Sizer, Similarity of Sets of Matrices, Minnesota State University - Moorhead

Five theorems on simultaneously upper triangularizing a set of matrices will be presented, with a proof of one if time permits.

Ioannis Souldatis, Some Random Graph Constructions, Minnesota State University - Mankato

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.

Knute Thorsgard MD, Flat Light, Relativistically Curved, Quantized Space-Times

Although celeritas, C, is a signless and directionless vector; direction can be assigned by convention. Direction can be reversed by mirrors. The sudden reversal does not ruin relativity. A geometry exists which allows acceleration to act like a mirror: catching and reversing light all at once as an all or none quantum phenomenon.

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