These are the abstracts for the papers to be presented at the 2005 Midwest Undergraduate Mathematics Symposium.
Student Presentations, Faculty Presentations, Plenary Addresses
Evolution of Cooperation Via Kinship and Imitation
by Shikha Basnet, Simpson College
This talk will center on explaining the evolution of cooperation based on the emergence of kinship behavior in structured population of unrelated individuals. We will look at a model based on an infinite structured population in which individuals meet and interact with their neighbors, individuals learn by imitating their more successful neighbors. We will move on to discussing conditions required to support cooperative behavior.
Accept or Reject: Modeling Host Responses to Avian Brood Parasitism
by Laura Becker, Simpson College
I will present a game theory model that evaluates fitness values when hosts make the decision of whether to accept or reject an egg due to avian brood parasitism. In this model, the decision of the host to accept or reject is influenced by the level of mimicry related to egg pigmentation and the ratio of parasites to hosts in the overall population.
Axioms of Kinship
by Cindee Calton, University of Northern Iowa
Throughout the world, there are many different ways of defining our relationships with our family members. Who we choose to group together with the same kinship term reveals much about how we view those relatives. Throughout the world, there are only 6 basic ways of grouping relatives, despite the many possible ways of doing so. This talk explores how to think about human kinship axiomatically and discover why only certain patterns appear, using both mathematical and anthropological thinking. Interesting case studies of elaborate patterns of marriage are also explored briefly at the end of the talk.
For Whom The Bar Lifts
by Jean Clipperton, Casie Schmitt and Tracy Robson, Simpson College
Toll booth plazas are interesting subjects to model in terms of traffic flow and optimal number of booths for a given plaza. This paper addresses the dilemma of creating a toll plaza with the best number of booths for any given highway with respect to cost and traffic flow. Our system of equations, based on Queuing Theory, allows such variables as wait time and speed of service to dictate the formation of such plazas.
Rigor in Analysis: From Newton to Cauchy
by James Collingwood, Drake University
This paper seeks to examine the level of rigor which was present in work with the calculus from the time of its invention through Cauchy's work in the 1820s. The paper traces the changing standards of rigor which marked the work with the calculus during this period. Newton's and Leibniz's approaches to rigor are compared and it is shown how each affected the level of rigor in mathematics present in the British Isles and on the Continent, respectively. The general level of rigor used by eighteenth century mathematicians will be compared to the changing standard of rigor used in the nineteenth century by mathematicians such as Cauchy. Also, forces which may have impeded early attempts to make the calculus rigorous and forces which may have provided the impetus for later work with the calculus to become more rigorous will be examined.
Modeling Flood Damage Caused by Failure of the Lake Murray Dam
by Greg Elliott, Scott Roth and Prakash Kayastha, Simpson College
Our project models the course of a flood following a critical failure of the Lake Murray Dam near the South Carolina capitol of Columbia. We model the changes in elevation of the land around the dam through analysis of a topographic map. We divide our map into simplified geometric sections in order to calculate the area of land that is vulnerable to flooding. The model tracks the progress of the flood over different time periods. We specifically examine the ramifications of the flood on the South Carolina State Capitol Building and Rawls Creek, a tributary of the Saluda River downstream from the dam.
by Chris Fink, Nick Phillips, Om Gurung, Simpson College
We will discuss our project which models the degradation and depletion of the Earth’s freshwater supply over a long horizon. Two different models were developed for this purpose, both will be discussed. One model is very simplistic and projects depletion of freshwater supplies while keeping most variables constant. Our other model turns out to be simplistic, yet very elegant and flexible. The latter model attempts to account for changing variables, mainly demographic changes in the world's population.
University of Iowa Student Supercomputer Project
by Spencer Kuhl, University of Iowa
I plan to describe the University of Iowa Student Supercomputer Project (UISSP) and the progress that our undergraduate oriented research organization has made in the past year. The UISSP facility is a Linux (or Beowulf) cluster of 16 low-cost, off-the-self, state-of-the-art personal computers (PCs) that are configured to operate as a very high speed parallel computing platform. The cluster is currently housed in the University of Iowa physics building, Van Allen Hall. The cluster is owned and managed exclusively by the University of Iowa undergraduate student population. The cluster was designed and constructed entirely by a small group of undergraduates. The UISSP is now an official undergraduate student organization. The general purpose of the UISSP facility is to provide University of Iowa undergraduate researchers with their own high performance computing platform. I will also be touching on the projects running on the cluster as well as my own research.
Opportunities in Statistics and Bioinformatics at Iowa State University
by Tanzy Love, Iowa State University
Many exciting projects are available to students in the course of graduate work or undergraduate summer research programs in the Iowa State Statistics Department. My thesis explored the changing gene expression of maize during the process of embryogenesis. This required knowledge of complex statistical and biological methods. Preparation for these fields is helped by an interest in logical decision making and mathematics. A strong interest in biological questions with a solid background in mathematics is the natural precursor to advanced genetic and bioinformatic study. Recent graduates from our department have accepted first jobs at a wide variety of companies and institutions. Everything from the financial and manufacturing sectors to biotechnology and human health research. Statisticians are increasingly important in an economy where large amounts of data must be analyzed for safety and efficiency.
Axelrod’s Model for the Evolution of Cooperation
by Lwanda Manxodidi, Simpson College
In this talk we will discuss a model first presented in the highly acclaimed paper, “The Evolution of Cooperation”, authored by Robert Axelrod and William D. Hamilton. In this paper the authors claim the existence of an Evolutionary Stable Strategy for Iterated Prisoners Dilemma (IPD) that could potentially support the evolution of cooperation. We will first consider the requirements for a strategy to be evolutionary stable and then evaluate the merits of the model in terms of the author’s claims.
The Struggle for Cooperation
by Tracy Robson and Casie Schmidt, Simpson College
We will present a model that supports the evolution of cooperation for finite structured populations. We will consider different strategies and the conditions required via imitation for initiating cooperation. These conditions include the mutation rates for different strategies and the number of subpopulations.
Using Queuing Theory to Relieve Traffic Jams Due to Tollbooths
by Mandi White, Lindsay Saunders, Kelli Esbaum, Simpson College
This paper introduces a mathematical analysis that determines the optimal number of tollbooths for a given number of highway lanes that would minimize motorist irritation during peak traffic hours. The analysis implemented a Poisson distribution and the Erlang C function in the M/M/n queue theory. In this paper, we calculated the total mean time waiting in a tollbooth system for highways of 2 to 30 lanes.
Mathematical Modeling Provides Authentic Learning Experiences
by Murphy Waggoner, Simpson College
Mathematical modeling, especially that done in conjunction with COMAP's modeling contests, provides students with the opportunity to work on real-world problems as part of a team and under a time constraint. Students report that their participation in the modeling contest is one of the most memorable and most valuable mathematical learning experiences while in college. I will talk about how to become involved with the college or high school modeling contests, including how to select, prepare and nurture teams.
Halving Your Cake (morning address)
Dr. Deanna Haunsperger and Dr. Steve Kennedy, Carleton College