Texas Section, MAA

Midwestern State University, April 6-8, 2006

Abstracts for Contributed Paper Sessions

(alphabetically by author)

Voke Abemree
Student at Stephen F. Austin State University
"Hard" Mathematical Problems


Abstract: There are certain mathematical problems that are generally considered to be "hard" problems. In particular, the integer factorization problem and the discrete logarithm problem are at the heart of several of the most well-known cryptography schemes. It is my intention to briefly describe these problems and their significance in public key cryptography.

Stephanie Anderson
Student at St. Edward's University
Brunnian Links and Exotic Solutions to the Mu Transposase System


Abstract: Mu-transposase (or "Mu") is an enzyme that binds to three strands of DNA and aids in the transposition of the DNA strands. Biologists study how mu binds to DNA especially how the three strands of DNA are spatially related when bound by mu. Pathania, Jayaram, and Harshey conducted a series of experiments to determine the spatial relations of the DNA after the action of mu and proposed a solution (the PJH solution)[2]. They wanted to find whether more solutions were possible. Mathematicians Luecke, Vasquez, and Darcy proposed a new solution (the exotic solution).

I have completed my first research goal which was to show that the exotic solution is not isotopic to the PJH Solution. In addition, I am working on completing my second research goal of showing that there are in fact, an infinite number of solutions to the mu equations.

My first goal was to show that the exotic and PJH solutions are not isotopic. I showed this by using Kauffman's bracket polynomial. The next question was whether there are anymore solutions. A constuction of an infinite family of solutions using Brunnian links is proposed. One must show that the members of this family are not isotopic. I am studying this by using the seifert genus of links. In this talk I will describe the biological and mathematical background of this project and explain how it suffices to show that the genus of the combination of two links is greater than the maximum of either.


Eric Aurand
Faculty Member at Eastfield College
Results of Teaching Developmental Mathematics in a Manipulative Based Environment


Abstract: At Eastfield College, we have created a manipulative based environment for teaching the lower levels of our developmental mathematics sequence.  This approach will be discussed and some preliminary results that have compiled will be presented.


William F. Beard
Student at St. Edward's University
An Exploration of a Radon Relative


Abstract: Given eight points positioned randomly on the plane, form two triangles using six of the points as vertices and form a line segment between the remaining two. Is it always possible to do this such that the line intersects both triangles? This problem is known as a Radon relative, after Radon's Theorem, which states that given a finite set of points in Euclidean space, they can be partitioned into disjoint subsets whose convex hulls are also disjoint, provided that the number of points exceeds the dimension of the space by at least two. Using convexity and combinatorial arguments we study this problem by first looking simpler cases and then progressing to the more general ones.

Steven P. Bitner
Student at Texas State University, San Marcos
The Art Gallery Problem at Texas State University


Abstract:We have conducted a study of the advantages of various algorithms for the placement of guards in the art gallery problem. Comparisons were made between several methods of placement and the results were compared as they related to the Alkek Library at Texas State University, San Marcos. Research and comparison is still in progress.

William Brick
Faculty at Trinity University
Lambda Calculus: A logicians view of computer science


Abstract: The aim of this work is to explain the significance of lambda calculus to logicians and mathematicians outside of the context of computer science. This will include an explanation of the development of the basic mathematical results, as well as several examples of possible applications of lambda calculus.

Camille D. Broadus
Student at St. Edward's University
Figures of Constant Width on a Chessboard

Abstract: Finding a figure of constant width is closely related to the N-queens problem; A figure is designated as a set if squares in an n x n chessboard and it has constant width w if every row, column, and diagonal intersects with 0 or w squares.

Angela Brown
Student at Sam Houston State University
A Partial Classification of Mathematically Celtic Knots


Abstract: A mathematically Celtic knot is one that can be obtained from an alternating grid pattern by changing crossings to either vertical or horizontal uncrossings. We will show how to obtain some of these knots and prove some general results about Celtic knots.

Heather Bruch
Student at St. Edwards University
When Differential Equations Get Fishy


Abstract: Differential equations are often used to model populations. In the article, “A Bifurcation Problem in Differential Equations,” authors Duff Campbell and Samuel R Kaplan study a differential equation that models a fish population. They include a sinusoidal fishing habit function and find that the solutions become sinusoidal themselves. This project includes tow topics. The first involves substituting different fishing habit functions into the differential equation and analyzing what effect that has on the solution curves. The second topic is concerned with a more generalized version of the differential equation. It involves varying the growth rate parameter in the differential equations null cline expression and exploring the dependence of this parameter.

Elsie M. Campbell and Dionne T. Bailey
Faculty Member at Angelo State University
Solving Optimization Problems Using Precalculus Methods

Abstract: Optimization problems are traditionally solved using methods of calculus.  We will demonstrate how some of these problems can be solved in precalculus.


J. P. Coffelt
Student at Texas A&M University
Exponential Sums and Simulataneous Solutions of a Diophantine System


Abstract: For a prime $p$ and integer polynomial $f,$ define the exponential sum $S_p(f):=\sum_{x=0}^{p-1} exp( 2 \pi i f(x) / p).$ We will relate bounds on $S_p(f)$ to bounds on the number of simulataneous solutions to the system of diophantine equations $\sum_{i=1}^m x_i^{k_j} = \sum_{i=1}^m y_i^{k_j},$ for $j=1,2,...,n.$ Finally, we will demonstrate an application of these bounds on a variant of the Waring's Problem.

Kumer P. Das
Faculty at Lamar University
Texas Project NExT Research Session
The joint distribution of the surplus immediately before and after the ruin


Abstract: Risk theory considers stochastic models that may be used to study the risk of a risk enterprise, where the nature of the operation is such that expenditures may exceed receipts during some accounting periods in the normal course of operation. This study investigates in detail the surplus process of an insurance portfolio which involves the time of ruin, the surplus immediately prior to the time of ruin, and the deficit at the time of ruin. A numerical technique has been developed that allows the accurate and effective computation of the joint probability of ruin and the size of the claim that caused the ruin. Specific examples have been shown on how the programming language Fortran can be used to compute the probability of ruin for various claim distributions.

Kumer P. Das
Faculty at Lamar University
Graphical Representation of the Mathematics TAKS: A Reality Check


Abstract: The Texas State University System (TSUS) Math for English Language Learners (MELL) initiative is a multiyear effort funded by Texas Education Agency (TEA) to develop instructional resources designed to increase the effectiveness of math instruction for ELL students in PK-12 schools. As a part of this study, the statistical analysis of Mathematics TAKS data is needed to identify and develop instructional tools. Moreover, this analysis will be used to guide policymakers in the state of Texas. In this talk, a summary of the TAKS analysis will be presented.

Samuel Seth Demel
Student at Sam Houston State University
Homeomorphisms, Diffeomorphisms and Prime Numbers


Abstract: Using a construction of Kreck and Stolz, we find a 2-parameter family {W_{k,l}}_{k, l \in \mathbb{Z}} of real 8-dimensional smooth orientable manifolds with homeomorphic but not necessarily diffeomorphic boundaries. Adjusting these boundaries by the connected sum with a particular number of 8-dimensional punctured Bott manifolds, the boundaries become diffeomorphic (up to attaching a cylinder). We may then attach these manifolds at the boundary, forming a closed 8-dimensional manifold X. The A-hat-genera of these manifolds are interesting in the fact that they appear to produce very large prime numbers. We examine the distribution and characterization of these primes.

M. Fred Deutsch
Student at St. Edward's University
Optimization with Origamics: Working with Chessboards


Abstract: Mathematical Origami, or Origamics, is the mathematics of paper folding. One of the primary problems addressed in Origamics is optimization, typically maximizing paper usage. This talk will focus on the following question: given a square sheet of paper of a particular size, what is the largest k by k (k, positive integer) chessboard that can be folded? We begin with an introduction to the general subject of Origamics and other types of optimization problems. Then we explore some findings along with practical applications

Joel Douglas, Carrie St.Louis, Juan Paramo
Students at Midwestern State University
Methods of Solution for the One and Two Dimensional Heat Equation

Abstract: The Heat equation can be solved by applying theoretical procedures or numerical approximations. This study is performed to show the possible methods of solutions for the one and two dimensional Heat Equation. These equations are solved by differential methods and finite difference approximations. Neumann and Dirichlet initial and boundary conditions are applied to get theoretical particular solutions. A discrete grid method is used for the approximations. Test problems show that heat dissipates through time, which suggests that finite approximations agree with theoretical models, under certain circumstances.

Fang Duan and Ferry Butar Butar
Student at Sam Houston State University
Crossover Design

Abstract: Crossover design is a special experimental design in which all treatments are administered to the same experimental unit for a series of periods. Such design is built to avoid the confounding of time period effects and the effects that the previous treatment may carry over to the present period. In this talk, analysis of three or more treatments/periods is discussed. And particularly, two treatment two period designs are presented.


Jerry D. Frazee
Retired Faculty Member
Introducing the Fundamentals of the Calculus of Variations


Abstract: Although most four year colleges offer Calculus through Differential Equation, the Calculus of Variations is usually absent despite its increasing importance in optimization theory, mechanics and quantum theory. This situation is partly due to the opacity of available texts. A full outline is presented for a unit or semester on variational principles. With the use of a historical approach and building on basic extremal methods by way of analogy and familiar problems involving principles of economy (for example, Fermat’s Principle of Least Time), it is expected that the student will not only learn the basic concepts, but find them interesting.

Riley Gough
Student at Sam Houston State University
The Great RBI Prophecy


Abstract: This talk will include a discussion of the concepts of formulating models for baseball statistics. Ideas on a new "Runs Batted In'' model will be explored along with an analysis of Bill James' "Runs Created" formula. The error involved with these models will be emphasized.

Eunice Gray
Student at Sam Houston State University
Population Processes


Abstract: Deterministic population models describe population sizes at a particular time. However, random chance plays a large part in the growth of real life populations. In previous research, we have shown that stochastic processes have expected values that agree with the corresponding deterministic models of single and competing populations. We will seek to expand this property to an arbitrary number of populations which all interact.

Michael Gray
Graduate Student at Baylor University (in General Session)
Uniqueness Implies Existence for Nonlocal Boundary Value Problems for Third Order Ordinary Differential Equations


Abstract: It is assumed that solutions of certain nonlocal boundary value problems are unique, when they exist. Existence of unique solutions to related boundary value problems is demonstrated.

Amy Guillot
Student at Lamar University
The Effects of Vedic Mathematics


Abstract: In the Vedic system, huge sums and multiplications can often be solved immediately by the Vedic mathematics system. These beautiful methods are just a part of a complex system of mathematics, which is far more systematic than the modern system. In this study, the effect of Vedic math on modern math methods has been studied.

Roy Joe Harris
Faculty at Stephen F. Austin State University (in student session)
An Introduction to Cauchy's Theorem


Abstract: A brief overview of Cauchy's Theorem will be discussed. The use of real parameterization to evaluate complex integrals will be presented. This talk is to provide background information for the talk given by Patrick Sugrue.

Huixing He and Ferry Butar Butar
Student at Sam Houston State University
Incomplete Block Designs

Abstract:  In this talk, we consider the problem of incomplete block designs. It is sometimes necessary to block experiment units into groups smaller than a complete replication of all treatments with a randomized complete block or Latin square design. The incomplete block design is utilized to decrease experimental error variance and provide more precise comparisons among treatments than is possible with a complete block design. A general description of some major groups of incomplete block design is presented in this talk. The method of randomization and basic analysis are demostrated for balanced and partially balanced incomplete designs. The efficiency of the designs is also considered.


Amanda Hoffman
Student at Sam Houston State University
Generalizing the Power Rule

Abstract: Calculus students often think that the power rule for differentiation is the definition of the derivative and attempt to use this rule for functions to which it does not apply. In this talk, we explore the types of functions that prove these students correct. In particular, when y=f(x)^[g(x)], we ask what conditions f and g must satisfy so that y' = g(x)f(x)^[g(x)-1]. Time permitting, we will also examine other types of derivative "rules" that are not true in general, but will hold for certain classes of functions. Specific examples will be given for all cases.

Jason Holland
Faculty Member at Abilene Christian University
On the Optimal Order Ideals of a Boolean Algebra

Abstract: Typically one utilizes prime (maximal) ideals or ultrafilters in the representation theory of Boolean algebras. In this talk, we define a new object known as an optimal order ideal. Properties of optimal order ideals will be discussed as well as their similarities and differences with prime ideals. We also prove a representation reminiscent of Stone's representation theorem for Boolean algebras.

Brian Jain
Student at Baylor University
A preliminary exploration of the finite difference approximations


Abstract: Finite differences, including the forward, backward and central differences, have been used frequently for approximating derivative values. This is not only important in the theory, but also crucial in many applications. In this preliminary study, we are going to explore basic properties of the above-mentioned finite difference formulae. We tend to understand better their connections to the derivatives, and their limitations in applications within the range we can reach.

W. Max Jones and John Quintanilla
Student at University of North Texas
Convex Quadratic Programming and Gaussian Random Fields


Abstract:Excursion sets of Gaussian random fields have been frequently used in the literature to model two-phase random media. We present a novel technique which uses convex quadratic programming to find the best admissible field auto correlation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all field autocorrelation functions instead of only a predetermined parameterized family.

Tarcia Jones
Student at Stephen F. Austin State University
Elliptic Trigonometry


Abstract: Expressing the sine and cosine functions in terms of the unit circle and expressing the hyperbolic sine and cosine functions in terms of the unit hyperbola are well known to Calculus students. Julius Burkett established equations for parabolic trigonometric functions. We will show how to derive equations for elliptic trigonometric functions. Some identities for these will also be explored.

Anny-Claude Joseph
Student at Stephen F. Austin State University
Why all this fuss about the parallel postulate?


Abstract: Non-Euclidean geometry describes both hyperbolic and elliptic geometry. In this discussion we investigate the debate that led to the development of non-Euclidean geometry and the contributions of the principals including Saccheri, Gauss, Lobachevsky, Bolyai, and Riemann.

Shelly Keith
Student at Sam Houston State University
Magnetization of Cerium Ions as a Function of Temperature

Abstract: In recent temperature dependent magnetization measurements on CeCu2S2-based compounds, we found that the magnetization as a function of temperature does not follow the inverse law which is usually obeyed by cerium (Ce) ions. In this project, we build a matrix model to calculate the multiple energy levels of cerium atoms. Then we apply the Boltzman function to calculate the magnetization as a function of temperature. Mathematical approximation will be applied to this calculation for the limit cases of low temperature and high temperature ends. Finally, the theoretically calculated magnetization curve will be compared with the experimental curves.

Jim Kirby
Faculty member at Tarleton State University
Using SMART Technology in the Mathematics Classroom


Abstract: Use of smart technology allows easy posting of class notes on the internet. This talk discusses strategies for effectively doing so.

Yoshiharu Kobayashi
Student at Stephen F. Austin University
Analyzing Bargaining problems through cooperative and noncooperative Game Theory


Abstract: Bargaining problems will be presented to review the relationship between the different schools of Game Theoretical approach, noncooperative and cooperative. Part 1 of 2 will discuss the bargaining problem from the standpoint of noncooperative and review some equilibrium concepts associated with such problem.

Deborah Koslover
Faculty at Universtiy of Texas at Tyler
Bloch Electron in a Perpendicular Magnetic Field


Abstract: We study the spectral properties of a family of quasiperiodic Jacobi matrices which model an electron on a two-dimensional crystal lattice subjected to a perpendicular magnetic field. We determine how parameters related to the structure and spacing of the lattice as well as to the strength of the magnetic field affect the motion and allowed energy levels of the electron. This is done by studying eigenvalue equations associated with these parameters. The results which we obtain allow us to determine if
a) the electron's motion is localized, i.e. the spectrum is pure point,
b) the electron is free to move anywhere in the crystal, i.e. the spectrum is absolutely continuous, or
c) the motion falls in between, i.e. the spectrum is singular continuous

Curtis Kunkel
Student at Baylor University
Singular Discrete Third Order Boundary Value Problems

Abstract: We study singular discrete boundary value problems with mixed boundary conditions of the form, -D3u(t-2)+f(t,u(t),Du(t-1)D2u(t-2))=0, t in [2,T+1], D2u(0)=Du(T+2)=u(T+3)=0, where [2,T+1]={2, 3, ...,T+1} is called the discrete interval, T is a natural number, Du(t-1)=u(t)-u(t-1) is called the standard forward difference operator. We assume that f(t,x,y,z) is continuous on [2,T+1]x(0,1)XR2 and f has a singularity at x=0. We prove the existence of a positive solution by means of the lower and upper solutions method, the Brouwer fixed point theorem, an dby perturbations methods to approximate regular problems.

Mark Lane
Student at Sam Houston State University
Magic Connections Between Squares and Graphs

Abstract: There is a one-to-one correspondence between the set of all n x n magic squares and the set of all magic labelings of the complete general graph Gamma_n on n vertices. It was shown later that a one-to-one correspondence exists between the set of all n x n semi-magic squares and the set of all magic labelings of the complete bipartite graph Gamma_{n,n} on n vertices. We will discuss these relationships and present our progress toward finding a class of graphs Phi_8 that will provide a similar one-to-one correspondence between its magic labelings and the set of all 8 x 8 Franklin squares.

Michael Lecocke
Faculty at St. Mary's University
Texas Project NExT Research Session
An Empirical Study of Feature Selection in Binary Classification with DNA Microarray Data


Abstract:
Motivation: Feature subset selection (FSS) is an important aspect of performing binary classification using gene expression data from microarrays. Once feature subsets are obtained, we need to evaluate the various classifiers that are formed. We wish to see how various classifiers perform in both an internal (FSS not included) and external (FSS included) cross-validation (CV) setting for assessing the predictive accuracy of a given classifier. This research considers both univariate- and multivariate-based FSS approaches. In considering a more sophisticated multivariate approach (genetic algorithm-based), the idea is to determine whether it leads to better predictive accuracy because of its potential to consider jointly predictive subsets of genes that would likely not be easily detected by an approach combining individually predictive genes as selected by a univariate approach.

Results: A large-scale empirical comparison study is presented, in which a 10-fold CV procedure is applied internally and externally to a univariate as well as two multivariate (GA-based) FSS processes. These procedures are applied with respect to three supervised learning algorithms and six published two-class clinical microarray datasets. We find that although the more sophisticated multivariate FSS approaches in general may be able to select subsets of genes that would likely go undetected via the combination of genes from the top 100, e.g., univariately ranked gene list, neither of the two multivariate methods led to significantly better 10-fold CV error rates nor lower selection bias values across all classifiers. Ultimately, this research puts to test the more traditional implementations of the statistical learning aspects of cross-validation and feature selection and provides a solid foundation on which these issues can and should be further investigated when performing limited-sample classification studies using high-dimensional gene expression data.

Mariette Maroun
Student at Baylor University
Positive Solutions to an 3rd Order Right Focal Boundary Value Problem.

Abstract: The existence of a positive solution is obtained for the 3rd order right focal boundary value problem y''=f(x,y), x in (0,1], y(0)=y'(po)=y''(1)=0, where p in (1/2,1) is fixed and where f(x,y) is singular at x=0, y=0 and possibly at y=infinity. The method applies a fixed-point theorem for mappings that are decreasing with respect to a cone.

Frank Mathis
Faculty at Baylor University
Approximate Optimal Control of Drug Treatments


Abstract: The best strategy for the use of drugs in the treatment of certain infectious diseases may be modeled by an optimal control problem. We investigate numerical methods that approximate the solutions of such problems.

Melissa Mauck
Student at Sam Houston State University
Fingerprints: Are They Your Own?


Abstract: We will be investigating fingerprints and the accepted fact that everyone has a different set of fingerprints. We will develop a model to look at the probability that there exists more that one person with the same fingerprint. We will provide a background of the process of fingerprinting and the comparison process used in the criminal justice system.

Dr. Stefan T. Mecay, Dr. William Sliva, Dr. Eric Aurand
Professors at Schreiner University (first two) and Eastfield College (last one)
“Base”-ic Card Tricks


Abstract: We will present a card trick which can be very useful in teaching bases to students in a math for liberal arts class.

Youfeng Nie and Ferry Butar Butar
Student at Sam Houston State University
Incomplete Block Designs: Factorial Treatment Design
Abstract:  2^n and 3^n factorial experiments are just  special case of general factorial experiments in which each factor has just two or three levels (two or three treatments). We have special interest in  2^n and 3^n factorial treatment designs because they are very useful in practice. 2^n means n factors with two levels for each factor and 3^n is n factors with three levels for each factor. The effect and notations specific to factorial treatment are used to develop methods to construct incomplete block designs for factorial treatment designs is introduced. How to construct blocks for factorial treatment of incomplete block designs is discussed, which includes complete confounding and partial confounding. ANOVA is given for each design model.



Eric Overholser
Faculty at St. Mary's University of San Antonio
Texas Project NExT Research Session
Equivalence of Intrinsic Measures on Teichmuller Space


Abstract: Observing that the Teichmuller space of a Riemann surface of genus strictly larger than 1 is a bounded complete hyperbolic complex domain, we will show that the Eisenman-Kobayashi, Caratheodory, and Kahler-Einstein volume forms are equivalent on Teichmuller space.

Leslie Pacher
Student at Sam Houston State University
The Mathematical "Witch"


Abstract: We will discuss some historical and personal background related to Maria Agnesi. We will also discuss one of her great accomplishments in the field of mathematics known as the "witch" of Agnesi and some of its applications.

Fred Poage
Student at Stephen F. Austin University
Minimizing the Cost of Xigris Therapy: A Mathematical Approach


Abstract: A discussion of the cost of treating a patient suffering severe sepsis. Preparing a patient's Xigris infusion bags requires remaining within certain parameters, i.e. drug concentration, infusion time, etc. Eli Lilly and Co., the maker of Xigris (drotrecogin alpha, activated), provides a Dosing Table for preparing these infusion bags that has a certain amount of excess Xigris built into it, which will simply be discarded and unfortunately increases the cost of Xigris therapy. I will present data supporting y research on minimizing this excess production by more than 92% by using a more efficient algorithm for preparing Xigris infusion bags, while still remaining within the many parameters, thereby effectively reducing the cost of Xigris Therapy.

Carl Price
Student at Stephen F. Austin State University
The Chain Rule Revisited

Abstract: An analysis to emphasize a part of the chain rule formula.

John Quintanilla
Faculty at University of North Texas
Verifying Einstein’s’ Theory of General Relativity in a First-Semester Differential Equations Class


Abstract: In a first-semester course in differential equation, few applications of non homogeneous second-order differential equations are typically presented (besides spring displacement and electrical capacitance). In this talk, we discuss how differential equations were used to predict the precession in Mercury’s orbit, an important confirmation of Einstein’s theory of general relativity. The presenter has used this topic with success when teaching this course.

Kenneth Reddix
Student at Stephen F. Austin University
Analyzing Bargaining problems through cooperative and noncooperative Game Theory


Abstract:Bargaining problems will be presented to review the relationship between the different schools of Game Theoretical approach, noncooperative and cooperative. Part 2 of 2 will discuss the bargaining problem from the standpoint of cooperative specifically Nash?s axiomatic approach. At the end we will unveil the relationship between the schools producing a surprising result.

Clint Richardson
Faculty at Stephen F. Austin State University
The Geographic Compactness Index


Abstract: Shape indices play an important role in Geographic Spatial Analysis. This talk discusses interdisciplinary work involving a particular shape index, the compactness index (developed by one of the students), and how it reacts to some political regions as well as several types of geometric figures.

Sandra Richardson and Mary E Wilkinson
Faculty Member at Lamar University
From the Mouths of Teachers: What They Need to Improve Mathematics Instruction for English Language Learner Students

Abstract: English Language Learner (ELL) students, students whose native language is not English and who are in the process of developing English speaking and writing skills, experience significant challenges in the typical mathematics classroom. Such challenges are often coupled with limited professional development available to teachers of ELL students. This presentation outlines Texas teachers' perceived needs of available professional development that will enable teachers to better support mathematics instruction for the ELL student. Teachers' perceived training needs were ascertained through the collection and analysis of survey data and focus group findings.


Mauricio Rivas
Student at Sam Houston State University
Art and Mathematics


Abstract: In this talk we are going to explore how mathematical concepts have been used in famous artwork. We will dicuss different artists from different ages and some of the techniques they used for their work. We will also demonstrate how mathematical concepts can be seen as artistic work, and how different artistic concepts can be seen as mathematical ones.

Erik J. Robertson
Student at Sam Houston State University
Actuaries: Capitalizing Risk


Abstract: There is a highly-respected, yet little-known place in business for people with mathematics degrees. These people are called actuaries. Actuaries analyze risk, create mathematical models of it to apply to the financial world, and are compensated very well for their work. If you pay for insurance or put money into a pension plan, an actuary's work has affected you. In this presentation, we will talk about the actuarial career and what is involved in becoming an actuary, starting with a degree and culminating with the attainment of the prestigious FSA of FCAS designation.

Courtney Sanchez
Student at Sam Houston State University
A Pony's Proper Proportions


Abstract: When selecting and evaluating horses, balance is one of the most important aspects of a horse's confirmation. Using the length of the horse's head as a standard measurement, we will examine the ideal proportions found in the measurements of a horse's skeletal structure and how this ratio found in the horse compares to the Golden Ratio.

Aruna Saram and Ferry Butar Butar
Student at Sam Houston State University
Taguchi Approach to the Design of Experiment for Quality and Cost

Abstract:  During the 1960-1980 time periods, the principals of experimental design were not as widely used in the west as in Japan. Japanese engineers had much greater exposure to these concepts, and consequently, experimental design methods were more of an engineering tool in Japan than they were in the United States. Since the early 1980’s Taguchi methods to quality control have been used to optimize the process of engineering experiments. This approach has been a unique and powerful quality improvement discipline that differs from traditional practices. The general approach has far exceeded the initial quality control application and has developed in to a philosophy in its own right. This talk attempts to understand the application of Taguchi methodology to the design of experiments.

Vince Schielack
Faculty at Texas A&M University
The Mathematics of Ripley's Believe It Or Not!


Abstract: Robert L. Ripley was an incredibly popular figure in the America of the first half of hte Twentieth Century. The oddities of all types presented in his Believe It or Not! cartoons mesmerized his public, and the Ribpley's franchise is still going strong today. But from a mathematical perspective, it is rather surprising how many ofhte cartoons of this pop-culture phenomenon involved mathematics. It is clear that Ripley was quite fond of what he considered to be mathmatical oddities, involving topics that included number theory, counting, probability, algebra, and geometry. Some of his mathematical cartoons involve items true for rather transpartent reasons to the mathematically knowledgeable; others are rather surprising even today, especially in light of Ripley's lack of our modern calculuating technology; and still others of his seemingly impressive results are simply false, or at best involve Ripley twisting matheamtical language. This paper examines critically from a mathamtical standpoint examples of Ripley's craft from each of the aforementioned areas, with special regard for his errors and what have caused them, as well as an appreciation for the manner in which Ripley used his unique showcase to stimulate his readers mathamtically.

Kennon Silence
Student at Sam Houston State University
``Understanding Animal Group Movement'' or ``A Schooling Schooling''


Abstract: This talk will be an exploration of the methods used to model the movement of groups of animals, such as fish schools. The well-known works of several authors will be used to explain previous efforts toward describing how large groups of individuals may appear to act as a single-minded group.

Patrick Sugrue
Student at Stephen F. Austin State University
Cauchy's Theorem and a Proof of the Fundamental Theorem of Algebra


Abstract: An investigation of the paper, Yet Another Proof of the Fundamental Theorem of Algebra, by R. P. Boas will be presented. This paper appeared in the American Mathematical Monthly, volume 71, number 2, in 1964. Details added to this proof will include the reasons behind the assumption P(z) is real for real z and the explanation of the real parameterization of the contour integral whose integrand is 1/(izP(z+1/z)) and whose contour is |z|=1.


Jason Snyder
Student at University of North Texas
K_3,3: a Flatland Utitility Workers Workers Worst Nightmare


Abstract: Flatland Utility Workers have always had a problem connected the three utilities; Water, Electric, and Gas, to each of three houses. The problem is that the utility lines can never cross each other, as Flatlanders live in a 2-dimensional space. It will be shown that K_3,3 is not a planar graph and therefore the problem can not be resolved. It will also be shown that this situation does not pose a problem to the people of Torusland.

Min Sun and Ferry Butar Butar
Student at Sam Houston State University
Two-Level Fractional Factorial Designs


Abstract: As one of the most popular fractional designs, the two-level fractional designs are widely used in designing experiments. A two level fractional factorial design is referred to as 2^n-p fractional factorial designs. The notation indicates that the fractional factorial design is a 2^{-p}th fraction of the 2^n full factorial design and that it includes n factors each at two levels that use only 2^n-p experimental units. In this talk, both a general method for the two level fractional factorial designs and a special method for the Plackett-Burman designs are discussed. Furthermore, half replicate 2^n-1 designs are analyzed using a real-life experiment. The purpose is to design the two-level fractional experiments by approaching different methods and analyze the designs.

Yuhong Tang and Ferry Butar Butar
Student at Sam Houston State University
Comprehensive optimal design in split-plot method


Abstract: The split-plot designs have been extensively used in experiments. Different optimal methods aiming to obtain best estimation of certain parameters have been proposed.  However, in experiments, there may have multiple goals to be achieved. The single optimal criterion does not work in these cases. Thus, a function with multiple inputs needs to be designed. The optimal values of different parameters involved in the experiments are the solution of the function.  In this talk, we will propose a comprehensive optimal method, which generate the optimal combination of parameters based on goals we want to achieve.


Richard M. Thames
Student at St. Mary's Univeristy
Using Geometry Alone to Solve Jigsaw Puzzles

Abstract: I will be demonstrating a method of matching puzzle pieces together using only the shapes of the pieces by comparing their curvatures. I will show software I made that implements this technique.

Jenny Tompkins
Student at UT-Tyler
How Knot Theory and DNA Do the Tangle


Abstract: Enzymes play an important role in affecting the topology of DNA. One way an enzyme may act on DNA is by a process called site-specific recombination. This talk will begin by showing the connection between knot theory and DNA. We will then discuss more specifically how a tangle can be used to model site-specific recombination. We will then look at how tangle equations can be used to analyze enzyme mechanism during recombination.

Jing Wang and Ferry Butar Butar
Student at Sam Houston State University
Two RSM Models and the Corresponding Designs


Abstract: In this talk, we will review RSM methods, especially the first-order and the second-order models. We will discuss the mechanics of these two models, the corresponding experimental designs for these two models and the blocking methods applied to these two models respectively.


Lacey Wells
Student at Sam Houston State University
A New Look at an Old Twist


Abstract: The more information that is discovered about genetics, the more complicated it becomes. So, geneticists find themselves turning to topology (including knot thoery) to explain some of the processes that DNA undergoes. We will discuss some aspects of the fresh and exciting field of genetics through the application of century old knot thoery.


Lyndsey C. Wharton
Student at Dallas Baptist University
Fire!


Abstract: This presentation centers on the development of an algorithm for the placement of fire hydrants in a city in order to minimize costs and fulfill the necessary fire codes. A study in the math behind the codes is also a small part of the project.



Richard Wooten
Student at Lamar University
Applications and Limitations of Harmonic Functions in Modelling Wave Phenomena


Abstract: This presentation will cover a broad range of topics concerning the mathematics of waves. From how and why a harmonic function models a wave so well to the use of Fourier series and Fourier integrals to deal with nonperiodic aspects of waves. There will also be a focus given to the concept of group velocity and it's physical implications.

Kenneth J Word
Faculty at Central Texas College
Using Online Learning Systems in Precalculus and Calculus to Assess Student Homework and Quizzes


Abstract: Showing how online learning systems can be used in lecture classes to asses student homework, quizzes and exams.  Process used in college algebra, precalculus and calculus I, II, and III.

Connie H. Yarema
Faculty at Abilene Christian University
A Model for a Content Course for Pre-service Math Teachers

Abstract: This presentation will present a model for a mathematics course for pre-service middle school and high school teachers. The model will be illustrated by discussing the philosophy, content, and pedagogy of a junior level course designed for future math teachers. Sources for materials used in this course will be given.

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Document last modified January 20, 2006.