Texas Section

Mathematical Association of America

ABSTRACTS FOR STUDENT PRESENTATIONS

Friday Morning, April 13, 2007

Mathematics and General Classrooms Building (MAGC)

(alphabetically by author)

Candace Andrews

University of Texas at Tyler

Finite C-Groups

Abstract: In this talk, discussion will focus on known results concerning the characterization of Finite C-Groups. Methods for determining C-Groups will be explained and terminology will be introduced.

Steven Ayala

St. Edwards University

Nice Polynomials

Abstract: A nice polynomial is a polynomial that has integer roots, and all of its derivatives must have integer roots. We would like to find a formula to generate all of these polynomials. The form for the cubic nice polynomials has been found. It has also been speculated that no nice polynomials exist in a degree above 3. However, a form of "decent" polynomials has been found for degree 4. A "decent" polynomial is a nice polynomial that only requires the first and second derivatives to follow the nice polynomial rules. A problem that arises from this is the possible leading coefficients of these decent polynomials. There are decent polynomials of degree 5 that have different leading coefficients. We couldn't find any decent polynomials for any degree higher than 5, but we could calculate the possible leading coefficients of such polynomials. We found an algorithm that would produce all of the possible leading coefficients up to degree 100. After some analysis, we found a general form for when a prime number will or will not be a possible leading coefficient.

Andrew Beck

St. Edwards University

Much Ado about Nothing - Zeroes of Nth Partial Sums of the Complex Exponential Series

Abstract: This lecture first discusses the location of zeroes of Nth partial sums of the exponential series in the complex plane, then moves on to show ways of finding and displaying the zeroes. For N< 5, the equations can be solved exactly, and zeroes plotted. For all other N, we can use intersecting level curves to approximate the location. Since it is impossible to show every partial sum, proven theories about the locations of the zeroes of Nth partial sums are given and explained. One question of interest is whether the zeroes lie on an expanding wavefront, which is contingent on the zeroes being vertices of their closed convex hull.

Heather Bruch

St. Edward's University

Bringing the Symmetries of String Theory to Live:  The Geometric Action of Courant and Kac-Moody Algebras

Abstract: String Theory needs 10 dimensions in order to be mathematically consistent.  The familiar, space-time provides 4 dimensions, so one can consider 6 dimensional compact manifolds to make up the ten dimensions. Calabi-Yau manifolds satisfy the constraints for the allowed manifolds, but more general structures are possible. Compactifications with fluxes are called generalized Calabi-Yau manifolds and can be understood in terms of the Courant bracket which generalizes the Lie derivative. This particular generalization naturally includes fluxes. My project explores the semi-direct product of the Courant algebra and the Kac-Moody algebra as a further generalization to see if the electromagnetic field and fluxes can simultaneously be considered. The first goal is to build a geometric action from this construction. String theorists might be able to use this to understand the many string vacua.

Betsy Childs

Stephen F. Austin State University

Circular Logic on Triangles

Abstract: Certainly one can draw a circle using the three midpoints of the sides of a triangle. But when does that circle go through the bases of the altitudes of the triangle? And when does that circle bisect the segments between the orthocenter and the triangle's vertices? The answer to both questions is always! Come and see why!

Jason Michel Dolloff

Southwestern University

Fourier Analysis and Baroque Counterpoint: Modeling a Bach Fugue

Abstract:For this math modeling project, a fugue and its subject (main theme) by J. S. Bach will be examined. In particular, Fourier analysis will be used to model the occurrences of the fugue subject in its varying forms as it occurs throughout the piece. A model that demonstrates the structure of the fugue and provides a mathematical visualization representation of different note patterns will be the result.

James Doughman

Sam Houston State University

Simulating One-Day-International Cricket Scores

Abstract: One day international (ODI) cricket is the most popular type of cricket in the world. Started from the United Kingdom, now it is becoming popular even in the United States. Winning a one day international (ODI) cricket match, could depend on various factors related to the strengths of the two teams. While some of these factors have been analyzed and well documented in the literature, some are yet to be investigated. In this kind of analyses, the data collection is the most tedious part as usual in other cases. We present here a way of simulating cricket scores using simple statistical methods; so that researchers can use simulated data for statistical model building for cricket scores.

Angie Forgas

Lamar University

Granites of Central Texas

Abstract: The grain size distribution of three common minerals found in granite (quartz, orthoclase feldspar, and plagioclase feldspar) was determined by calculating the mean, variance, median, mode and standard deviation. The percentages of the minerals quartz, orthoclase feldspar, and plagioclase feldspar were then used in order to distinguish between the particular rock types of the granite.

Tiffany L. Gatchel

Sam Houston State University

In the Blink of an Eye

Abstract: In efforts to assimilate vision-related knowledge of the neural substrate into an organized and comprehensible working model, many theorists have urged the use of a modular schematic. By mapping out parts of the brain into familiar categories (ie: face recognition, scene processing, body-part recognition), some have sought to develop a conceptual framework of various groupings of visual stimuli and the pathways by which they are processed. Yet, why should neurons inherently structure their electrochemical mechanisms around such intuitive and semantic distinctions? What is obviously sought after and increasingly incorporated in neural sciences is a more robust and precise language for description – namely, mathematics. Without disregarding the need for a conceptual interface, this presentation will consider a more logical-positivistic perspective. It is upon us to examine the descriptive or predictive power of a mathematical model as it relates to neurological properties and mechanisms. An exciting glance is made at a variety of innovative mathematical methods and tools that lead us to the cutting edge of visual-cortical research. New paradigms in statistics, algorithmic dynamical models, quantum physics, and topology are facilitated by rapid advancements in related technologies. Recent breakthroughs are discussed, and expectations for future mathematical solutions in visual neuroscience are revealed.

Bobby Grizzard

St. Edward's University

What Does Sperner's Lemma Tell Us About Positive Matrices?

Abstract: The Perron-Frobenius Theorem is often proved using Brouwer's Fixed-Point Theorem. The proof of the latter relies on ideas from analysis and topology. We prove one of the main results of the Perron-Frobenius Theorem - that a positive matrix has a real and positive eigenvalue - using Sperner's lemma, which is a result proved by employing simple counting techniques. We construct a generalized Sperner labeling of a space transformed linearly by a positive matrix and show that there is some vector whose image has the same direction under the transformation. Hence the matrix must have a positive eigenvalue.

Sarah Hall

Lamar University

Checkmate in Infinity: Variations on the Angel Problem

Abstract: The Angel problem is a mathematical conundrum that attempts to relate the finite and infinite through a series of moves on a chessboard, wherein an angel that may only move up to a certain, fixed amount of spaces is challenged to evade capture by a devil that may move an infinite number. In my presentation, I will be illustrating numerous variations and the mathematical methods I have used to predict the outcomes to each variation, as well as delving into the question of how to maximize each character's ability to achieve success through using geometrical forms, functions, and a variation on bubble sorting.

Luke Harrison

Sam Houston State University

How Not To Be Like Cortez

Abstract: Before modern artillery there were trebuchets, a form of catapult.  A large trebuchet could hurl most objects with amazing precision. Trebuchets are aimed with

precise calculations.  Although no longer an effective tool for war, the trebuchet teaches us a great deal about release velocity and release angles. In this talk we will explore the calculations needed to accurately aim a trebuchet.

Amalia M. Hunter

Our Lady of the Lake University

Investigating the Quartic

Abstract: This investigation reveals new parameters for the quartic that have never been published. By using these new parameters, the reader will gain the understanding of graphing a quartic polynomial without a graphing calculator. Professors will find this useful especially because until now there has not been a tool to graph the quartic polynomial by hand.

William Jaramillo

Saint Edward’s University

RSA Cryptography

Abstract: RSA cryptography, named after Rivest, Shamir, and Adlemen, has been a classic and efficient cryptosystem due to its tremendous difficulty of factoring. A receiver chooses two large, distinct prime integers, and through specific algorithms obtains the public and private keys. The public keys are released to a specific party so that this party may apply an encryption algorithm to the original message. This encrypted message is then sent to the receiver so that the receiver may decrypt the scrambled message. Throughout the beginning course of my research on this public-key cryptosystem, my goal was to investigate various attacks on the system. For example, repeated encryption is a method that allows a user to continue repeated compositions of the encrypted message to obtain the original message, or one may take the risk of selecting elements of small order. Although these are methods of attacking the cryptosystem, these methods are highly complicated and often inefficient, especially if the public keys and primes are chosen properly. The final goal of my research is to show that if it is possible to find an algorithm that breaks Rabin’s cryptosystem, there is then a probabilistic algorithm for obtaining the two distinct primes.

Justin Jander

Stephen F. Austin State University

Predicting Salaries of  Athletes using Regression Models

Abstract: This talk will use methods of statistical regression to predict salaries of athletes using a variety of variables.  It will include the success and failures of the models, as well as reasons a person would want to use it.  There will also be a discussion on the method that the sample was taken to make the model as well as the purpose of variables chosen.

Daliah Maurer

St. Edward’s University

Mathematical Analysis of HIV

Abstract: Mathematical models of HIV dynamics provide an important link to numerous assumptions and improve our understanding of the interplay between the various parameters. We examine linked differential equations that monitor the changes in viral load, infected and uninfected T-cells, and analyze the subsequent modifications with respect to the current treatment strategies available today. By calculating the nullcline steady-states of the system we establish a relationship between the parameters in order to maintain critical level of T-cell counts. Further, we evaluate the Jacobian matrix near the nontrivial equilibrium points to determine the behavior of the solutions to the system. Our analysis concludes with an experimental model that incorporates a viral coevolution model and accounts for the immune response. This analysis allows us to better fit the data and investigate the crucial links between the parameters in more detail.

Stephanie Meyer

Sam Houston State University

A Complex History

Abstract: We will explore the evolution of the number i. The discovery of the square root of negative one had repercussions on many aspects of mathematics. We will examine some of these effects.

Blake Mitchell

Lamar University

The Crossing Probability Knot Energy

Abstract: The crossing probability energy E_cp is defined and properties are explored. The energy is based upon the probability that non-adjacent edge pairings of a polygonal knot do not cross. E_cp is found to be asymptotically finite, but not asymptotically smooth. An algorithm is presented to compute E_cp as well as minimize the energy using a gradient flow. Through the development we find that E_cp is essentially the crossing number expressed as a unique knot energy.

Christopher A. Sams

Lamar University

Gender and Race in actuarial career

Abstract: Actuary has been rated one of the best jobs in America almost every year the report has been published. In this study few demographic factors has been used to analyze the distribution of this profession.

Amanda Seitz

Sam Houston State University

Bunnies, Bees, and Pineapples - Oh, my! An exploration of the Fibonacci Sequence

Abstract: In the year 1202, Leonardo Fibonacci introduced the numerical pattern known as the Fibonacci sequence. In this talk, we will discus the history of the Fibonacci sequence, its occurrence in nature and the mathematics behind this numerical pattern.

Hilari Celeste Tiedeman

Southwestern University

A Note on Weighted Identric and Logarithmic Means

Abstract: It is well known that the classical inequality relating bivariate forms of the arithmetic and geometric means can be refined via the logarithmic (L) and identric (I) means. Moreover, sharp power mean bounds are known that separate L and I. Using properties of the Gaussian hypergeometric function, generalizations of these inequalities involving weighted versions of L and I will be presented.

Ashley Weatherwax

University of Texas at Dallas

A Game of Wymsical Mathematics

Abstract: The game of Wym is a combinatorial game created by a UT Dallas professor from the merging of two other combinatorial games: Nim and Wythoff’s Game. In short, the game begins with random piles of tokens, and each player removes tokens on their turn. The object of the game is to remove the last token. The complete winning strategy is not yet known, but there are many interesting patterns and theorems that have been thus far discovered.

Daniel Wennersten

University of Texas at Arlington

Engage, Discover, Formalize, Apply:  A Coherent Teaching Method that Integrates Successful Teaching Strategies

Abstract: A recently conducted international study, PISA 2003, shows that students in the United States are outperformed by students in other countries on tests requiring the application of mathematical knowledge.  Educational organizations such as the National Council of Teachers of Mathematics have, since before the 1990’s, made suggestions for schools to focus their curricula more on the application of mathematics rather than only on the performance of calculations.  Despite these recommendations and state adoptions of stricter standards, PISA 2003 shows that the United States still needs improvement in mathematics education.  To move towards this improvement, educators have discovered through research that the following learning strategies improve student ability to apply and comprehend mathematics:  collaboration, motivation, discovery, communication, and technology.  This paper presents research supporting each of these learning strategies, and it supports the claim that, although these strategies improve comprehension, they lack an integrated method of implementation.  To allow better implementation of these learning strategies, this paper suggests a lesson-plan that integrates them into one complete system and supplies examples with suggestions for further implementation.  Each of the four components of this plan: engage, discover, formalize, and apply, uses one or more of the learning strategies mentioned above.

Dana G. Wheaton 
Sam Houston State University

Rack’em

Abstract: During this talk, we will conduct a geometric look into billiards. We will study the angles required for shots and where error can occur. This examination will include not only error gotten from the table, but from the ball and cue as well.

Catherine Whitehead

Lamar University

The Improbable Dream

Abstract: Everyone wants to be a millionaire, but what are the chances that someone can actually become a millionaire by spending a dollar on a lottery ticket. I hope to let everyone know what the odds are for someone to hit it big with Texas Lotto.

Catherine Whitehead

Lamar University

The relationship between student's background characteristics and their academic Library use

Abstract: In this study we examine the factors that influence student's academic library use. Random sampling has been used to choose a sample from all the students enrolled during this semester (Spring 2007) at Lamar University. In this talk the findings of the survey will be presented.

Shaun Williams
University of Texas at Tyler
n-Colorings of Twist Knots

Abstract: In this talk we give necessary and sufficient conditions on n for the twist knot (2k+1)1 to be n-colorable.  In addition, if the knot (2k + 1)1 is n-colorable, then all solutions for such a coloring are found.

Graduate Contributed Papers

Arnab Bose

The University of Texas-Pan American

The Radon Transform and its Applications to Medical Imaging

Abstract: One of the most significant and non-trivial applications of Mathematics to seek out solutions to real life problems in the recent past has been the use of The Radon transform and its inverse in the field of medicine. The transform which was discovered by the Austrian mathematician Johann Radon in 1917 purely with mathematical intentions proved to be a key factor in medicine. In the 1960s, a physicist, Allan M.Cormack used the transform to solve what is called as The Reconstruction Problem. For this work, he shared the Nobel Prize in 1979 with Godfrey N. Hounsfield who was the first person to design a diagnostic technique of CT (Computerized Tomography) scan.

The main objective of this talk is to present an introduction to The Radon Transform and how it is used to solve The Reconstruction Problem along with its applications to medical imaging. We discuss the historical background of Radon’s work and how it led Cormack to solve the Reconstruction Problem. Next we mention how it is used in Computerized Tomography (CT Scan) using X-rays. We illustrate the reconstruction by taking a simple example in three-dimensions and then by reconstructing it from its image using the dual of The Radon Transform, concluding the talk with some pictures of CT scan images of the human brain.

Jason La Corte
Texas State University - San Marcos
Brouwer's fixed point theorem for Rⁿ

Abstract: The statement of Brouwer's theorem is that a continuous function of an n-dimensional closed ball into itself must have a fixed point.  This theorem may be proven in several different ways.  We present a short, illustrated proof using the Sperner's lemma and the Knaster-Kuratowski-Mazurkiewicz lemma.  As time permits, we will introduce two important tools of algebraic topology, homotopies and homology, and outline a proof based on these ideas.

Gustavo Cruz

University of Texas-Pan american

Wave Propagation Phenomenon and Differential Equations with Periodic Coefficients

Abstract: We consider differential equations with periodic coefficients and the wave propagation phenomena, described by such equations.

Reid M. Etheridge

University of Texas - Pan American

Generalized Gronwall Inequality with Nonintegrable Singular Kernal

Abstract: This presentation will examine a Generalized Gronwall Inequality with nonintegrable singular kernel, which has several applications to the Cauchy Problem for Partial Differential Equations with Multiple Characteristics. We investigate Fractional Order operators with such kernels.

Aditi Ghosh

The University of Texas - Pan American

A Characterization of Compact Metric Spaces via the Closed Graph Theorem

Abstract: The goal of the present note is to provide a characterization of compact metric spaces in terms of the closed graph theorem

Aditi Ghosh

The University of Texas Pan American

Mathematical modeling of electrospinning

Abstract: Electrospinning is a process that can produce nano-scale fibers from a polymeric fluid solution or melt. In this talk we present a mathematical model for electrospinning and electrically forced jets and explain the resulting linear stability and instabilities of an electrified jet under different operating parameters. In electrospinning process, a meso scale fluid jet is forced through a nozzle under the influence of high electric (1,000 Volt/cm) field. This leads to the formation of so-called “Taylor Cone’ and jet instability. Further, the jet undergoes phase changes (liquid to solid) within milliseconds. Understanding this complex electro-hydrodynamic instability is the key to successful applications of these polymeric nanofibers in as diverse fields as defense, aerospace, biotechnology, and health care. In this presentation, we present a set of differential equations that represent free flow jet that interacts with the electrically charged environment. While phase change is not included in this investigation, inclusion of the non-uniform electrical filed is the significant departure from the existing literature. Presently, we are in the process of numerically solving these equations. Numerical results will be validated with the experimental results that are being collected from the Instrumented, Controlled Environment Electro-Spinning (ICEES) equipment of the Manufacturing Engineering Department.

Garrett Hicks

Tarleton State University

Statistical Analysis of Heart Rate Variability

Abstract: The aim of this study is to evaluate the differences of male and female heart rate variability (HRV) as related to cross-country athletes. In this study, HRV is defined as the time fluctuation between R waves or variation in duration of RR intervals. To gather HRV data of actual heart beats, a resting EKG in the supine position was conducted on seven male and female cross-country athletes at Tarleton State University for a consistent time period. After analyzing the data using SAS, there was evidence to support that HRV in male and female cross-country athletes is statistically the same.

Mark Lane

Sam Houston State University

Algebraic Combinatorics and Magic n-Circles

Abstract: It is known that a one-to-one correspondence exists between the set of all n-by-n magic squares and the set of all magic labelings of the complete bipartite graph ƒ¡(n,n) on 2n vertices. We give a one-to-one correspondence between the set of all magic n-circles and the set of all magic labelings of the complete bipartite multigraph M(n,n) on 2n vertices. We discuss the methods used in algebraic combinatorics that allow us to compute the minimal Hilbert basis used to construct any magic n-circle with magic sums. We report our progress in computing the generating function, which counts the number of magic n-circles with magic sums. Finally, we present the Franklin magic 8-circle.

Charles Obare
University of Texas - Pan American
Buoyant flow around growing protein crystal

Abstract: Higher quality protein crystals are those which, in particular, are more structurally uniform and free of impurities. Convective flow which can exist during protein crystal growth can carry perturbations and transport impurities to the crystal growth interface and, thus, can reduce the quality of the grown protein crystal. In this talk we present a relevant buoyant flow system and discuss the resulting flow effect around a growing protein crystal.

Carl H Price Jr.

Stephen F. Austin State University

Sober Topological Spaces

Abstract: A topological space is said to be sober if every irreducible closed subset of X is the closure of exactly on singleton of X. An irreducible closed subset of X is a nonempty closed subset of X that is not the union of any two of its proper closed subsets. We show that sober spaces fit in the hierarchy of the separation axioms between T2 and T0, yet are not related to the T1 condition.

Darrel A. Silva

Sam Houston State University

Order Dimension of the Joining of Special Classes of Posets

Abstract: The order dimension is an invariant on partially ordered sets (posets) introduced by Dushnik and Miller in 1941. Known algorithms for computing order dimension are NP-complex for general posets. We will present a family of posets known as generalized crowns whose order dimension is easily determined by a formula. We will introduce a binary operation, called layering, which produces a larger poset Q from two compatible posets P and P'. We will discuss layering of generalized crowns and their order dimension. We also will introduce an additional binary operation called coadunation and discuss the order dimension of the coadunation of any two posets with known order dimension.

Patrick Sugrue

Stephen F. Austin State University

Harmonic mappings in the plane

Abstract: This presentation will be an overview of my thesis research, harmonic mappings in the plane.   The talk will cover basics of definitions, classification of regions, normalization, the analytic inheritance of geometric properties, and examples to illustrate all.

Min Sun

Sam Houston State University

Comparing Two Imputation Methods for Continuous Data

Abstract: The problem of nonresponse is an important one and is difficult to handle in sample surveys. Multiple imputation provides a useful strategy for dealing with data sets with missing values. Among their methods, fully normal (FN) imputation and Imputation adjusted for uncertainty in the mean and variance (MV) are used for continuous data. The purpose of this paper is to display and compare the FN and MV methods, which include the normal-based analysis of a multiple imputed data set and confidence interval for population mean after multiple imputation.