







Program
for the Fall 2003 Meeting
University of Sioux Falls Sioux Falls, South Dakota October 2425
Friday, October 24
7:008:00 Registration, Salsbury Science Center
Evening Session, Prof. Mark Yarbrough presiding 8:009:00 Lecture Karen Saxe, Macalester College “A Nobel Prize, an Oscar, and the Mathematics of the Game of Hex” Zbornik Lecture Hall, Salsbury Science Center
9:00? Book Sales, Cleveland Center Room 221 9:00? Reception, Cleveland Center Atrium
Saturday, October 25
8:1510:55 Registration, Salsbury Science Center 8:153:30 Book Sales, Cleveland Center Room 221
Morning Session, Prof. Wally Klawiter presiding, Zbornik Lecture Hall, Salsbury Science Center 9:00 Welcome, Dr. Kirby Wilcoxson, Senior Vice President for Academic Affairs 9:10 Jason Douma, University of Sioux Falls, “Old Group Decompositions in a New Light” 9:30 Namyong Lee, Minnesota State University, Mankato, “Mathematical Understanding of ALS” 9:50 William Schwalm, University of North Dakota, “Using Scale Invariance” 10:10 Kristen Nairn, College of Saint Benedict, “Graver Complexity of the Twisted Cubic Curve”
10:3010:45 Break
10:4512:00 Assessment Forum Bill Martin, NDSU, organizer Zbornik Lecture Hall, Salsbury Science Center
12:001:00 Lunch, Salsbury Student Union Dining Room
Afternoon Session, Matt Richey, section president, presiding, Zbornik Lecture Hall, Salsbury Science Center 1:001:30 Business meeting 1:302:30 Lecture Underwood Dudley, DePauw University “Formulas for Primes”
Concurrent Sessions Session I, Matt Richey presiding, Cleveland Center Room 206 2:403:00 Tina DeJong and Michael Simpkins (presenter), University of Sioux Falls, “The Behavior of Central Generators within pGroup Minimal Central Product Decompositions” 3:003:20 Adam Duffy, Garrett Kolpin (presenter), and David Wolfe, Gustavus Adolphus College, “Games Played in Tall Warehouses”
Session II, Shawn Chiappetta, presiding, Cleveland Center Building Room 207 2:403:00 Nicholas McClure, St. John’s University, “A Competing Population Model for Mosquitoes” 3:003:20 Walter S. Sizer, Minnesota State University Moorhead, “Periodic Solutions of a Difference Equation”
ABSTRACTS
Karen Saxe, “A Nobel Prize, an Oscar, and the Mathematics of the Game of Hex” During this talk, we will play Hex and see how this remarkably simple game has connections to some relatively deep mathematics. No mathematical background is necessary; all are welcome!
Jason Douma, “Old Group Decompositions in a New Light” In the world of group decompositions, the venerable direct product usually grabs the headlines. However, a generalization of the direct product—the central product—is particularly well equipped to answer certain types of questions about group structure (especially automorphism group structure). This talk will explore conditions in the central product structure of pgroups that predicate a desirable automorphism group structure.
Namyong Lee, “Mathematical Understanding of ALS” Amyotrophic Laterral Sclerosis (ALS) is a motor neuron disease also popularly known as Lou Gehrig’s disease. In this presentation we briefly introduce ALS through mathematical modeling of the neurophysiological system. The HodgkinHuxley equation (1952) and its simplified versions, such as the FitzHughNagumo (196162) and MorrisLecar (1981) equations, will be explained. Current results of mathematical analysis and computer simulation for blocking and echoing of neuronal signal cases will be shown.
William Schwalm, “Using Scale Invariance” Equations of physics are dimensionally consistent, meaning that they admit scaling transformations as symmetries. Thus they can be written in terms of characteristic variables of the scaling subgroups (which are Buckingham’s dimensionless “Π” variables). I review the generalized scaling concept for a physical relation F(w,x,y,z)=0 where there are exponents a, b, c and d such that for any k, F(k^{a}w,k^{b}x,k^{c}y,k^{d}z)=kF(w,x,y,z). We note that Buckingham’s theorem, Every physical relation can be expressed as a relation between dimensionless variables, follows. Such scaling also reduces the order of isobaric (or generalized homogeneous) ODE’s, and gives similarity solutions of PDE’s.
Kristen Nairn, “Graver Complexity of the Twisted cubic Curve” The Graver complexity of a curve is defined in terms of the higher Lawrence lifting. We will restrict our attention to finding the Graver complexity for the twisted cubic curve and will demonstrate some geometric properties of the Graver basis that are related to toric varieties.
Assessment Forum, Bill Martin, organizer This forum has three goals: (a) To provide information about the MAA Project SAUM (Supporting Assessment in Undergraduate Mathematics), (b) to provide specific information and practical examples of assessment practices in selected mathematics departments, and (c) provide an opportunity for members of the section to meet and interact with colleagues who are working on assessment in mathematics departments. Participants will leave the session with information about national mathematics assessment activities, individuals in the section already working on assessment, and resources available to help departments initiate, develop, and refine assessment activities.
Underwood Dudley, “Formulas for Primes” A survey, with a moral lesson (not all theorems are equally good) in which exactly one theorem is proved.
Tina DeJong and Michael Simpkins, “The Behavior of Central Generators within pGroup Minimal Central Product Decompositions” In this presentation, we explore the central product structures within nonAbelian pgroups. Using GAP software to assist in our analysis, we develop the theorem that for any group containing a central generator, the group can be expressed as a central product decomposition. In addition, we note that central generators of central product factors stay home or move to the join in any automorphism of a given group expressed as a central product decomposition.
Adam Duffy, Garrett Kolpin, and David Wolfe, “Games Played in Tall Warehouses” Partizan End Nim is a variation of the classical game known as Nim. It is played by two players called Left and Right. Initially there are n stacks of boxes in a row, each stack containing at least one box. Players take turns removing boxes from the stacks on their respective sides (Left removes from the leftmost stack, while Right removes from the rightmost stack). The first player that cannot move loses. One added twist is that the piles can be of any ordinal height. An efficient recursive method is given to compute the outcome of (and winning moves from) any position.
Nicholas McClure, “A Competing Population Model for Mosquitoes” We built a differential equation model of competing mosquito populations that incorporates logistic growth, the mosquito lifecycle stages, and seasonal influences. A parameter sensitivity analysis suggests that the modified birth and survival rates and death rates would best enable a modified population to win under competition against another population.
Walter S. Sizer, “Periodic Solutions of a Difference Equation” We show how to deduce the periodicity of some solutions to the Lyness difference equation, x(n + 1) = (a + x(n))/x(n1). 







Correspondence should be sent to
Jason Douma at Jason.Douma@usiouxfalls.edu 