Student Talks Handout:
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Last updated:
04/11/12, 09:43 a.m.

Friday, 3:10  3:30 p.m., G219



Adam Lewis, Mercer University



Title:

Pascal to the Rescue



Abstract:

In the 17^{th} century, Blaise Pascal found himself in a pickle. No matter how hard he tried, he could not figure out how to measure lengths of parabolic arcs with Euclidean coordinates. So Pascal employed an underused problemsolving technique: he decided to view these arcs from a different perspective. Instead of using Euclidean coordinates, Pascal chose to use polar coordinates. In the spirit of Pascal, we will use this same problemsolving technique to answer questions about the hemisphere model of hyperbolic geometry. Questions such as: what would mirror images look like in the hemisphere model? What would railroad tracks look like? How does one reflect a point over a line? If you're ready to answer these questions and more, prepare to learn how changing your perspective can lead to understanding relationships among the Klein disk, the hemisphere model, and Blaise Pascal himself, as well as the answer to our questions. It's time to bend your perspective of Geometry!

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Friday, 3:10  3:30 p.m., G222



Mark Woods, Millikin University



Title:

Good or Bad: Altering Admission Standards



Abstract:

Entrance requirements for some colleges and universities have become more inclusive over the past several years. In this talk, we will analyze whether students who would not have been previously admitted to Millikin University are being retained longterm. Further, we will discuss how Millikin can predict the retention of similar students in the future.

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Friday, 3:40  4:00 p.m., G219



Scott Rexford, Northern Illinois University



Title:

To Construct a Hyperbolic Triangle...



Abstract:

In this presentation we will discuss the motivation for defining fractal dimension and construct a fractal having a two dimensional attractor and zero measure, obtained from iterations on a solid from classical geometry. We will give a brief description of Poincare's model for hyperbolic geometry and present a construction of a triangle with arbitrary centroid given three angles having sum less than pi. We will construct a parametric curve to find a region in the plane for which a presented problem from transformational geometry is solvable. We will also briefly present a derivation of a series converging to π.

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Friday, 3:40  4:00 p.m., G221



David Irwin, Miami University (Oxford, OH)



Title:

dNice Numbers



Abstract:

dNice number is what can be expressed as sum of an Arithmetic Progression (A.P) with common difference d >=1
We explored for d = 1 last year conference. We like to present results for d > 1 this time.

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Friday, 3:40  4:00 p.m., G222



Morgan Perkins, Millikin University



Title:

Predicting Retention of Marginally Admitted Students



Abstract:

It is a common debate whether there are benefits to a university by being more inclusive regarding their entrance standards. We decided to analyze the retention rate of the current senior class who were marginally admitted to Millikin University. Some of the characteristics considered were GPAs, ACT scores, and intended major.

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Friday, 4:20  4:40 p.m., G219



Matthew Harris, University of Evansville



Title:

Mercury pollution Modeling Around the A.B. Brown and Gibson Generating Stations



Abstract:

Mercury is a pollutant that can cause great damage to ecosystems, especially in larger concentrations, such as when it bioaccumulates in fish. In Southern Indiana, the amount of fish that can be eaten out of the Ohio River is limited because of the mercury found in the fish. For this reason, understanding the mercury emissions (eg. from power plants) in Southern Indiana is important. The amount of mercury deposited in the soil around two power plants (A.B. Brown and Gibson Generation Stations) was physically sampled and then modeled using AERMOD. The model took into account meteorological, land, landscape, and mercury emission data. The amount of deposition around Brown was greater than the amount of deposition around Gibson, despite the fact that Gibson emits more mercury. There are three types of mercury that naturally occur when burning coal: elemental, divalent and particulate. After modeling the emissions from the two plants, it was found that different amounts of these three types of mercury found at the two power plants caused this discrepancy. In order to estimate the speciation profile for the total mercury output of each plant, two methods were used. One method, the Linear Method, showed that the speciation must be different for each plant. The other method, the Bisection Method, was used to get the modeled data to fit better to the sampled data. The final speciation profile at Brown was 33.2% Hg(P),14.5% Hg(II), 52.3% Hg(0) and the final speciation profile at Gibson was 4% Hg(P), 25% Hg(II), 71% Hg(0). The model that used the final speciation profile and the sample data, once normalized to have both be unitless, have similar graphs for both Brown and Gibson.

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Friday, 4:20  4:40 a.m., G221



Lane Bloome, Millikin University



Title:

Connections between Central Sets and Cut Sets in ZeroDivisor Graphs of Commutative Rings



Abstract:

The zerodivisor graph of a commutative ring with unity, denoted G(R), is a graph that has a vertex for every nonzero zero divisor of R, and vertices a and b are connected by an undirected edge in the case that ab = ba = 0. These structures have been the subject of much algebraic and graph theoretic investigation for the past 15 years. Recently, there has been undergraduate research focused on investigating cutstructures in these graphs. A cut vertex of a graph is a vertex that disconnects the graph upon removal, and a cutset of a graph is a minimal set of vertices that disconnects a graph upon removal. This talk looks at the relationship between the center of G(R) and the cutsets of G(R).

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Friday, 4:20  4:40 p.m., G222



Trenton Tabor, RoseHulman Institute of Technology



Title:

Building Predictive Models in Absence of Theory: An Application of the LASSO Variable Selection Technique to Student Persistance



Abstract:

Because of the nature of some processes, it is problematic to generate a theoretical model that is complete enough to describe and predict behavior in the process. For these types of problems, building a predictive model typically involves regressing against all of the available observed characteristics of the process. However, when the number of observable characteristics is large compared to the number of observations, these models may be difficult or impossible to generate. One method of analysis in these situations is the Least Absolute Shrinkage and Selection Operator, which can be used to generate sparse and parsimonious models, this method is discussed in relation to an application of predicting student persistence rates. By analyzing past student success and failure, a model is created to relate student persistence probability to a number of easily observed characteristics.

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Friday, 4:50  5:10 p.m., G219



Trent Tabor, Chase Mathison, James Folberth, RoseHulman Institute of Technology



Title:

Hortonian scaling of maximum flow in nonidealized river basins



Abstract:

River basin flow models typically involve thousands of nonlinear, coupled ordinary differential equations. We used the results of R. Mantilla et al. to model the flow in the Clear Creek and Big Bear Creek watersheds using various assumptions about the impact of friction on the velocity of the flow. The Horton order of a link (river) in a basin is a natural number that describes how many other links feed into the link. Using our model, we empirically verified Mantilla's results that mean peak flow scales with Horton order.

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Friday, 4:50  5:10 p.m., G221



Aaron Davis, Southwest Baptist



Title:

Statistical Analysis of Prime Factors



Abstract:

This presentation will report the results of an investigation of the prime factors of the positive integers 2 through n as n gets large. Tools used in the investigation include means, variances, and standard deviations. Computer programs were used to investigate these measurements to see if they yield any discernible pattern(s) including if there is a limit associated with means, variances, or standard deviations as n gets large. This is mainly a computational approach rather than a theoretical approach.

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Friday, 4:50  5:10 p.m., G222



Jill Shuman, RoseHulman Institute of Technology



Title:

Optimizing Beam Selection in Radiotherapy



Abstract:

Radiotherapy is used in the treatment of approximately 50% of cancer patients. One of the main components of radiotherapy is the selection of angles along which the radiation is delivered to the tumor. As the tumor is treated, more dose is delivered to the target as well as the surrounding critical structures. In order to minimize the amount of damage to critical structures, and maximize the amount of damage to the tumor, we have developed an optimization technique to alleviate high doses in the critical structures. We use dynamic programming to decide if we should reoptimize the angles during the course of daily treatments.

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Saturday, 10:10  10:30 a.m., G219



Andrew Harris, RoseHulman Institute of Technology



Title:

A Mathematical Model for the Baking Process – A Phenomenological Approach



Abstract:

In this talk, I will present a mathematical model for the baking process of a cake and/or bread. The model is based on basic physical principles including diffusion, elasticity, and thermodynamics. I will explain the modeling process from these first principles to partial differential equations. The final model then consists of a coupled system of seven nonlinear partial differential equations that specify the temperature, moisture content, vapor content, pressure, and deformation in the dough. This is solved numerically to produce a reasonable representation of the baking process.

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Saturday, 10:10  10:30 a.m., G221



Meagan Ryan, Saint Mary of the Woods College



Title:

Understanding Coulomb Potential: An Unproven Array of Points



Abstract:

In this presentation, we will discuss the use of the Coulomb potential to find the minimal energy configuration of n charges located on a thin circular conductor. Some history and mathematical background will be presented, highlighting the motivation behind finding solutions for the unsolved problem. Some simple mathematical cases will be illustrated and explained, while a comparison between the energies using the Coulomb potential and logarithmic potential will be discussed.

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Saturday, 10:10  10:30 a.m., G222



Jacki Simon, RoseHulman Institute of Technology



Title:

Robustness Test for a Protein Alignment Algorithm



Abstract:

Proteins, the basic building blocks of many biological molecules, can be compared by three dimensional folds that dictate structure and function. Many efficient, accurate algorithms have been determined that take a mathematical description of a protein's folds and use dynamic programming to align its structure with that of other proteins. As proteins are not usually static molecules, a method of studying an algorithm's robustness under perturbations of the data has been developed and used to test the stability of one of the dynamic programing alignment algorithms.

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Saturday, 10:40  11:00 a.m., G219



Chelsey Barron, Saint Mary of the Woods College



Title:

Breaking Down the Riemann Hypothesis



Abstract:

The problem popularly referred to as the Riemann Hypothesis was first posed in 1859. Since then there have been many attempts to solve this problem (some "solutions" can readily be found online). This talk will examine the Riemann Hypothesis by providing a brief history of the problem, mentioning some of the mathematical stumbling blocks to completing the proof, and explaining the problem's relevance (and the solution's relevance) to presentday applications.

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Saturday, 10:40  11:00 a.m., G221



Jackie Buhrman, Millikin University



Title:

The U.S. Life Insurance Industry: Time Series Analysis



Abstract:

The life insurance industry is an important part of our financial sector, providing a variety of services to its customers, including term or permanent life insurance, investment annuities, and mutual funds. Life insurance is an integral component of many financial portfolios; about 70% of American households have some type of life insurance. However, there have been very few recent studies on the growth or health of the life insurance industry. My research attempts to answer questions such as "What is the current trend in the health of the life insurance industry, and how does that compare to the current trend in GDP?" and "Which major economic events have had an effect on the life insurance industry, and what has that effect been?", among others. To accomplish this, I have selected variables to represent the health of the industry, chosen a group of life insurance companies to represent the industry, and then used those variables to model the health of the life insurance industry over a period of time.

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Saturday, 10:40  11:00 a.m., G222



Joseph Gasper, Kent State University



Title:

An Introduction to Object Oriented Design Principles and Their Benefit to Mathematicians



Abstract:

I will be taking you through the design and evolution of an Application Programming Interface for abstract strategy board games, detailing road blocks and how they were overcome with the use of object oriented design principles, then describing the benefits of said principles to the mathematician and mathematical community with examples.

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Saturday, 11:20  12:10 p.m., G219



Michael Fitzpatrick, University of Iowa
Trenton Schirmer, University of Iowa
Greg Zynda, Indiana University,
Brian Shroud, University of Notre Dame



Title:

Graduate Student Panel



Abstract:

This new session added to this year's conference aims to be a resource for undergraduates in mathematics who are starting to ask questions about what's next? Four panelists with various mathematical backgrounds will talk about their experiences in making decisions about graduate school, and answer your questions about choosing the right school for you, selecting an advisor, obtaining funding, the graduate school application process, and anything else you've wanted to know (but have been unable to ask). After the panelists introduce themselves and talk about how they came into their current positions, they will take questions from the audience.

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Saturday, 11:20  12:10 p.m., G221



Brad Jones, Consulting Actuary, Actuarial Services, McCready and Keene, Inc.



Title:

Q&A about a Career in Actuarial Science



Abstract:

Our own RoseHulman alumnus Brad Jones (Class 2005) will answer questions related to a career in actuarial science. If you want to know more about actuarial science, Brad will tell us how he chose this career and what activities are part of his daily routine. Also, he will explain the actuarial testing process.

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Saturday, 11:20  12:10 p.m., G222



Andrew Rourke, Maplesoft



Title:

Stick With It! (Why math matters now more than ever)



Abstract:

Let's face it: studying mathematics is hard, but in today's increasingly techfilled world, mathematics is playing a larger and larger role in everyday life. At the heart of much of our modern society is mathematics, and in the coming years great rewards will go to those who possess mathematical knowledge and skills (and an ability to apply them). This talk will focus on examples from everyday life where mathematics  sometimes hidden, sometimes not  plays an important role, and how Maplesoft  through products like Maple and MapleSim  is committed to helping students both succeed in their studies today and prepare for their careers of tomorrow.

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