Fall 2009 Program

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

Friday, October 23

7:00-8:00 Registration - Second Floor Clifford Hall
$10; Students, first time attendees and speakers free;
$5 for MAA-NCS Section NExT members.
7:00-8:00 Book Sales - Clifford Hall 264
8:00-9:00 Invited Lecture Clifford Hall 210, Dr. Ryan Zerr, Presiding

Dr. Brett Goodwin, University of North Dakota (Department of Biology)
Math, Moths and Mice: Using Math to Help Solve a Biological Riddle
9:00-10:30 Reception - Norm Skalicky Tech Incubator Atrium

Saturday, October 24

8:15-11:00 Registration - Second Floor Clifford Hall
Book Sales - Clifford Hall 264
Morning Session - Clifford Hall 210, Dr. Timothy Prescott, Presiding
9:00-9:05 Greetings, Dr. John LaDuke,
Associate Dean of the College of Arts and Sciences
Morning Session A - Clifford Hall 210, Dr. Timothy Prescott, Presiding
9:05-9:25 Prof. William Schwalm, University of North Dakota
Some Second Order DEs that Admit Two-Parameter Groups
9:30-9:50 Ron Rietz, Gustavus Adolphus College
An Intersection Property of Uncountable Collections of Open Intervals
9:55-10:15 Prof. John Holte, Gustavus Adolphus College
Discrete Calculus and Gronwall's Lemma
10:20-10:40 Prof. Jody Sorenson, Augsburg College
Waiting to Turn Left
Morning Session B - Odegard Hall 114, Dr. Richard Millspaugh, Presiding
9:05-9:45 Prof. Peh Ng, University of Minnesota, Morris
Panel Discussion on Effective Math Clubs
Co Livingston, Bemidji State University
Shawn Chiappetta, University of Sioux Falls
Jody Sorenson, Augsburg College
Thomas Q. Sibly, St. John's University
9:45-10:05 Prof. Suzanne Dorée, Augsburg College
I'd Rather Be Approximately Right Than Precisely Wrong
10:05-10:45 Prof. Suzanne Dorée, Augsburg College
Discussion on the Instruction of College Algebra
10:45-11:00 BREAK
11:00-12:00 Invited Lecture - Clifford Hall 210, Dr. Timothy Prescott, Presiding

Francis Edward Su, Harvey Mudd College
Voting in Agreeable Societies
12:00-1:00 Luncheon Norm Skalicky Tech Incubator 211
12:00-1:00 Math Jeopardy (undergraduates only) Odegard Hall 114
1:00-1:30 Business Meeting Clifford Hall 210, Dr. John Holte, Presiding
Afternoon Session - Clifford Hall 210, Dr. John Holte, Presiding
1:30-1:50 Phil Napeieralski, Bemidji State University (undergraduate)
Ego-motion, HCI and You
1:50-2:10 Kirsten Hogenson, University of North Dakota (undergraduate)
Minimum Ranks of Ciclos and Estrellas Graph Families
2:10-2:30 Jason M. Lutz, College of St. Benedict/St. John's University (undergraduate)
An Analog for a Basis in a Finite Group
2:30-2:50 Danica Belanus, University of North Dakota (undergraduate)
Generalized Ducci Sequences
2:50-3:10 Nicole Haugen, Bemidji State University (undergraduate)
The Geometry and Motion of Nematode Sperm Cells


Invited Addresses

Francis Edward Su, Voting in Agreeable Societies

When do majorities exist? How does the geometry of the political spectrum influence the outcome? What does mathematics have to say about how people behave? When mathematical objects have a social interpretation, the associated theorems have social applications. We give examples of situations where sets model preferences, and show how extensions of classical theorems on convex sets can be used in the analysis of voting in "agreeable" societies. This talk also features research with undergraduates.

Brett Goodwin, Math, Moths and Mice:
Using Math to Help Solve a Biological Riddle

It is increasingly being argued that the interaction between math and biology will have a huge impact on both fields. As an example of how math can inform a biological investigation I will describe a recent ecological investigation that was only possible via mathematical tools. Gypsy moths are an invasive species in North America that have persisted and spread over the last century or so. During part of their life cycle gypsy moths are preyed upon by white-footed mice to such an extent that mice should drive the moths extinct. Hence, the riddle of how moths persist in the face of ferocious mouse predation. Piecing together biological information using computer simulations and mathematical models my collaborators and I have demonstrated how spatial patterns of mouse predation and details of moth movements can lead to an intrinsically unstable species interaction persisting.

Undergraduate Presentations

Danica Belanus, Generalized Ducci Sequences

A problem dating back to the 1930s considers what happens when a sequence of vectors is formed by taking each vector in the sequence and forming the next term by taking differences of adjacent entries. The map whose iterates form such a sequence is called the Ducci map. One can view this as using a permutation to determine which terms are adjacent to each other. We generalized how random permutations affect the Ducci sequence.

Nicole Haugen, The Geometry and Motion of Nematode Sperm Cells

The crawling movement of Ascaris suum sperm cells is caused by protrusive, adhesive and contractile forces that result from the polymerization and recycling of major sperm protein (MSP) dimers within the lamillipod of the cell. This presentation describes a 2-D geometric model of the forward motion and turning of these cells. The general assumption used is that the internal pH level of the lamellipod is responsible for regulating the amount of polymerization of MSP and therefore motility. This model focuses mainly on protrusion of the front boundary of the cell, although contractile and adhesive forces are present in the model.

Kirsten Hogenson, Minimum ranks of Ciclos and Estrellas Graph Families

The minimum rank of a (simple) graph over a field F is the smallest rank over all symmetric matrices over F whose i,j th entry (for i ≠ j ) is nonzero whenever {i, j} is an edge in G and is zero otherwise. The maximum nullity of G is the largest possible nullity of the same set of matrices. We define two new graph families: ciclos Ct(G) and estrellas St(G). Our primary objective is to identify the minimum ranks of four specific families of these graphs.

Jason M. Lutz, An Analog for a Basis in Finite Groups

In linear algebra, a basis of a vector space is a linearly independent spanning set. Here, we will discuss some cases when we can find an analog for a basis in a finite group. This talk is suitable for anyone with a background in undergraduate algebra.

Phil Napieralski, Ego-Motion, HCI and You

How can we estimate the motion of a camera given just the images that it produces? Moreover, can we use this information to create a unique input device similar to an accelerometer? The first problem is called Ego-motion, the second is related to Human-computer Interaction (HCI). I participated in a Research Experience for Undergraduates (REU) at the University of Central Florida this summer and I will show how mathematics can be used to find solutions to both problems.

Contributed Talks/Panel Discussions

Suzanne Dorée, I'd Rather Be Approximately Right Than Precisely Wrong

In my opinion, too much of what we teach in a traditional college algebra course is base on our obsession with exact answers. But realistic problems based on real data and using simplified models are, at best, approximate by their nature. In such settings, not only are graphical and numerical methods now sufficient, but how we work symbolically must change as well. This talk will give concrete examples when the goal is a good approximation of the solution. This work is based on our 14-year record of teaching a highly successful, 100% contextual, modeling-based "Applied Algebra" course to diverse learners.

John Holte, Discrete Calculus and Gronwall's Lemma

I have long been interested in the parallels between "continuous" calculus and discrete calculus. Finite difference formulas look a lot like familiar derivative formulas--with the right tweaking--and summation formulas likewise resemble familiar integration formulas. Recently I wondered whether there might be a nice discrete counterpart of Gronwall's Lemma, a tool in the theory of differential equations, particularly nonlinear differential equations. The "obvious" parallel turns out to be not quite right. I'll present the "right" discrete Gronwall's Lemma, and I'll give an application to systems of difference equations.

Peh Ng, Panel Discussion on Effective Math Clubs

Panelists will share/discuss ideas on how to sustain a vibrant and functional math club on campus, and which types of activities have worked or not worked.

Ron Rietz, An Intersection Property of Uncountable Collections of Open Intervals

While there exist many obvious examples of Countable collections of open intervals which are pairwise disjoint, it is easy to show that no Uncountable collection of open intervals is pairwise disjoint, or even "c-wise" disjoint: that is, every such collection contains an uncountable subset which has nonempty intersection. This suggests looking at the set consisting of the union of all intersections of uncountable subcollections of the original collection. We will show that this set is always a (nonempty) open set, and conversely, every nonempty open set can be obtained in this way.

William Schwalm, Some Second Order DEs That Admit Two-Parameter Groups

It is instructive to start from a two-parameter family of functions (complete primitive) and work backward to get a second order DE by eliminating the parameters. Starting thus from general solution, it should also be easy to find symmetry groups of the DE. I discovered that exactly how to do this was not, in fact, obvious to me. The trick turns out to be in how the primitive or general solution is written; that is, it depends on its functional form. Armed with this insight, one can find interesting cases where neither the DE or the solution is particularly ugly.

Jody Sorenson, Waiting to Turn Left

How does the Department of Transportation determine whether a specific intersection warrants a left-turn arrow? The State of Pennsylvania uses a mathematical rule to calculate a conflict factor. Intersections with a high enough conflict factor receive left-turn arrows. I will explain this rule, and show how it leads to a natural application of the (second) Fundamental Theorem of Calculus. I have used this example to create an activity for my Calculus 2 class.

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