Texas Section
ABSTRACTS FOR FACULTY CONTRIBUTED
PRESENTATIONS
Friday Afternoon, April 13, 2007
Mathematics and General Classrooms
Building (MAGC)
(alphabetically
by author)
Yuliya Babenko and Andras Kroo
Sam Houston State University
Markov-type
inequalities for homogeneous polynomials on non-symmetric star-like domains
Abstract: Let us consider the set of homogeneous polynomials of degree n in d variables. It was proved by Harris that if K is a 0-symmetric convex body in d-dimensional Euclidean space, then for every homogeneous polynomial h with uniform norm bounded by 1 we have that the uniform norm of the derivative of the polynomial h in direction u is bounded by a constant multiple of n*logn. In this talk we shall discuss the extension of Harris' result for non-symmetric star-like domains.
Ananda Bandulasiri
Sam Houston State University
Texas NExT Fellow
Applications of
Statistical Shape Analysis in Medical Imaging
Abstract: Statistical shape analysis plays an important role in medical imaging. In this talk, I will give a brief introduction to statistical shape analysis and will discuss two applications, one with glaucoma detection and the other with the detection of apert syndrome. Statistical methods discussed here are mainly nonparametric methods such as bootstrap and permutation method.
Brian Beavers
Stephen F. Austin State University
Texas NExT Fellow
Sequential
Matroids
Abstract: A matroid is an abstract structure that captures the properties of dependence common to graph theory, geometry, and vector spaces. In this talk we will discuss the full closure operator for matroids and graphs, equivalence of separations, and structural results for sequential matroids and graphs.
Jeremy J. Becnel
Stephen F. Austin State University
CAT Scan in
Infinite Dimensions
Abstract: The Radon Transform is tool of Functional Analysis which relates a function to its integral over a plane. It has proven useful in areas such as tomography and medicine, most notably in medical CAT scans. In this talk we introduce the Radon Transform and discuss some of its applications. We close by discussing how these notions can be extended to infinite dimensional spaces.
Andrew Borden
Palo Alto College
The Mathematical
Signature of Deception
Abstract: When performing classification by Bayesian methods, it may happen that a conditional probability distribution based on the observation of a new parameter or descriptor will be in conflict with the current assessment of probabilities. We find this when we use a very efficient Bayesian classifier that we have developed. When this apparent conflict occurs, it could be a random event or it could suggest the presence of corrupted data, even intentional deception. We have found that the use of coefficients of alienation based on probabilities very often produces false positives. On the other hand, the Shafer-Dempster mathematical theory of evidence and belief, by explicitly eliminating the ÒUnknownÓ factor, is more conservative and more robust in identifying genuine corruption of data. It produces fewer false positives as can be shown by a simulation using random generation of probability distributions. Using ShannonÕs entropy as a measure of the ÒunknownÓ factor, we map probabilities into Shafer-Dempster beliefs and compute the coefficient of alienation from there. The presentation will show how we map probabilities into Shafer-Dempster beliefs and explain why the result is more reliable.
Paul F Bracken
University of Texas
The Generalized
Weierstrass System in R^3 and Application to the Study of Deformations of
Surfaces by Means of Integrable Hierarchies
Abstract: One of the main reasons for studying GW representations
is that they can be used to investigate the deformation of surfaces under the
action of various integrable hierarchies. Here we will introduce the mNV
system, mKdV system and then apply the latter to the study of surfaces of revolution.
In particular, we study the hierarchy of Modified KdV equations and study
deformation of Tori of Revolution by means of mKdV flows.
Minerva
Cordero-Epperson
University of Texas at Arlington
Fields without associativity? Oh!, it is a
semifield!
Abstract: A (finite) semifield is a non-associative division ring; the associated projective plane is called a semifield plane. The first semifields were constructed by Dickson in the early 1900s; in the 1960s several new classes were introduced including the twisted fields of Albert. In this talk we will give a historical development of finite semifields. We will present some new semifields constructed in the last decade including a new semifield recently constructed by the author.
Kumer Pial Das
Lamar University
Texas NExT Fellow
Infinite
Divisibility under Collective Risk Model
Abstract: The concept of infinite divisibility arises in different ways in philosophy, economics, physics, order theory and probability theory. Under collective risk model, the actuary is concerned with the question of which families of frequency distribution are most appropriate. Distribution with the property of infinite divisibility responds well to changes in the number of contracts in the portfolio or to changes in the period of time over which the portfolio is under observation. In this study several properties of infinitely divisible distributions have been expressed in terms of characteristic functions.
Kumer Pial Das
Lamar University
Reading and Mathematics
connection of an ELL (English Language Learner) student
Abstract: The integration of reading and mathematics in the school curriculum has been acknowledged from different frontiers. None can deny the fact that reading provides both context and motivation for the mathematics students. In the case of ELL students this integration of mathematics and reading is more important than ever before. The goal of this study is to find out how the reading performance affects the mathematics performance. Using the latest TAKS data the Pearson correlation coefficient has been calculated for this relationship.
Charles Dorsett
Texas A&M University - Commerce
The Rhind Papyrus
Deciphered
Abstract: Most of our knowledge of ancient Egyptian mathematics is derived from two sizable papyri, the Rhind Papyrus and the Golenischev Papyrus. A. Henry Rhind purchased the Rhind Papyrus in 1858 in Luxor, Egypt. The paprus was written in about 1650 B.C. and reportedly contained work dating to the Twelfth Dynasty, 1849 - 1801 B.C. Within the papyrus is a table giving unit fraction decompositions of fractions of the form 2/n, where n is an odd natural number from 5 to 101. Nowhere within the papyrus is there an inkling as to how the decompositions were obtained. Ever since the first translation of the papyrus, mathematicians have tried to understand and explain the construction of the table. Within this talk, the mystery is ended.
James Epperson
The University of Texas at Arlington
Mathematical
Understanding Secondary Teachers Need to Create Technology-enhanced Mathematics
Lessons
Abstract: The author highlights teacher-task investigations on GeometerÕs Sketchpad¨ involving the creation of technology-enhanced lessons. These tasks were designed for the course ÒMathematics-specific Technologies,Ó which is a core requirement for a Master of Arts in Mathematics degree for inservice teachers at UT-Arlington. The course includes the study of many mathematics-teaching-related freeware programs, graphing calculators, Mathematica, and Sketchpad¨. The mathematical content knowledge necessary to create these lessons will be explored as well as questions raised regarding the use of technology in this manner to investigate the secondary teachersÕ conceptual understanding of mathematics they teach.
Jerry D. Frazee
Austin Community College (retired)
The Genesis of the
Maxwell-Heaviside Equations
Abstract: By what insight did James Clerk Maxwell postulate the displacement current term in the generalized Ampere Law? How did Maxwell's equations evolve into the set of four Maxwell-Heaviside equations that underlie the description of electromagnetic behaviour? What forms do these equations take in modern circuit analysis?
Bill Harding
The University of Mary Hardin-Baylor
The Real Y2K
Problem A Mathematical Retrospective
Abstract: The original concept of the "Year 2000 ( Y2K ) Problem" had to do essentially with the inate inabilityof most computers and computer systems to differentiate between the year 2000 AD and the year 1900AD. The basic trouble hinged on the the timing structure upon which many computer systems and application programs were based. This problem never seriously materialized having been mostly resolved ahead of time due to a massive response by the general business community. The response of the Federal Reserve in increasing the money supply prior to the onset of the year 2000 and then decreasing it relatively rapidly within the year 2000 as the Y2K threat was perceived as receding is another matter. The Federal Reserve monetary response is analyzed both graphically and from a mathematical perspective. It is further posited from the mathematical results that some of the gross effects seen in the " Dot Com Bubble" as illustrated by a specific stock index may be mathematically obtained as a ripple effect resulting from those very Federal Reserve monetary actions.
Doug Harley and George Tintera
Texas A&M University-Corpus Christi
Effective Teaching
of Self-Paced Computer Assisted Mathematics Courses.
Abstract: This talk is on the results of a study on effective teaching of
self-paced computer assisted mathematics courses. The courses are developmental courses. Topics addressed are the ability of students to do independent study of the material under appropriate supervision, the extent and nature of supervision required, the role of homework in such classes and the variety of activities used by the instructor during class.
Jacqueline Jensen
Sam Houston State University
An Honors Liberal Arts Mathematics Course
Abstract: During Fall 2006, an honors section of the liberal arts
mathematics course at Sam Houston State University was offered. The
semester was committed to a discussion of knot theory for non-mathematics majors.
The course was very well received by the students, and similar courses will
continue to be offered in the future at SHSU. We will discuss the structure of
the course, as well as lessons learned from this first attempt at teaching such
a course, and provide some advice in designing similar courses.
Cong Kang
Texas A & M University at Galveston
Classifying the Convergence Behaviors of fa (x)=(1+1/x)x+a
Abstract: We classify the convergence behaviors of the one-parameter family fa (x)=(1+1/x)x+a, a in R, which converges to the natural logarithmic base e, using nothing more than what is taught in introductory calculus courses.
Jim Kirby
Tarleton State University
Are the Hyperbolic Functions Really Correctly Named?
Abstract: When the hyperbolic functions are introduced, textbooks typically state that they are analogous to the trigonometric functions in that they are derived from the unit hyperbola as the circular functions are derived from the unit circle. But rarely (if ever) is the derivation included. The hyperbolic functions are next defined in terms of the exponential, identities are derived, and then the inverse hyperbolic functions are obtained by appealing to the inverse. In this talk, the inverse hyperbolic functions will be derived from the unit hyperbola, and then the hyperbolic functions will be obtained from them by appealing to the inverse.
Rick Kreminski
Texas A&M University - Commerce
Finding pi to hundreds of thousands of digits from a 400-year-old formula Special
Abstract: Vieta's venerable infinite product formula for pi, using nested radicals of 2, has been around since the late 16th century, when Vieta himself used it to deduce pi to 9 digits past the decimal. Surprisingly, its convergence can be dramatically accelerated; this may not have been known before.
Perhaps this is simply because it appears in the form of an infinite product, something rarely encountered. We first show what Vieta's formula is, and how it can be used to compute pi to several hundred thousand digits (on a typical PC, using just square roots and products). The prerequisites for this talk are the half-angle formulas from trigonometry, and knowledge of the Taylor series for the sine function - the material is fully accessible to first-year students. If time allows, we will discuss briefly how theta functions can also be computed using the same acceleration approach.
John F. Lamb, Jr.
Texas A&M at Commerce
The 1089 Puzzle
Abstract: No, this is not a talk about a puzzling IRS form. It concerns a numerical puzzle using a three-digit number. The digits are reversed, subtracted, reversed and added to reveal a surprising result. Properties of the base 10 place value number system are used to prove the result is always the same.
Frank Mathis
Baylor University
Locating Discontinuities
in the Coefficients of Certain Differential Equations
Abstract: We consider differential equations containing coefficients that are discontinuous with respect to the independent variable and investigate numerical methods to solve the inverse problem of identifying the location of the discontinuity if a partial solution is known.
Jennifer
McLoud-Mann and Ramona Ranalli
University of Texas at Tyler
Initiating A Sonya
Kovelevsky Day
Abstract: In this talk we will address key issues in preparing and running a successful Sonya Kovelevsky Day, in the first year and beyond. This is just a day when high school girls are invited to campus for a day of mathematical fun. The objective is to encourage them to consider mathematical careers. We will discuss how we recruited students to participate, how we involved undergrauate math majors, and the activities that worked (and the ones that didn't) on our campus as well as options in both local and national support.
Chris Monico
Texas Tech University
Newton's Method
Fractals
Abstract: It is well known that convergence plots of Newton's method applied to many complex-valued functions on C give rise to fractal images. It is also well known that Newton's method itself is easily applied to situations of several functions in several unknowns. In this talk, we will review how Newton's Method is applied to a simultaneous system of two functions f1(x,y) and f2(x,y) in two variables and show how the convergence plots for some particular choices of real valued functions generate some very interesting fractals.
Samuel Obara
Texas State University, San Marcos
Texas NExT Fellow
Curriculum Materials implementation of the Performance
Standards in Mathematics
Abstract: A qualitative case study
research was conducted to investigate the process of implementation of a
standard-based textbook by three sixth grade teachers and the mathematics
coach. The data suggest that teachersÕ mathematics knowledge and beliefs
influence on how the textbook was implemented. Findings from the study
highlights importance of providing of sufficient time and other resources to
enable teachers understand facts, reflect on student work, and try new
approaches of teaching.
Ye-Lin Ou
Texas A & M University-Commerce
The Geometry of
Soap Bubbles
Abstract: The study of minimal surfaces (like soap bubbles) has a long and rich history and many beautiful applications in mathematics and physics (it is recently found to be "extremely useful in nanotechnology"). The work related to the study of minimal surfaces has lead to two Fields Medals (what is often considered the "Nobel Prize of Mathematics") whilst there are still many interesting problems remain to be explored. In this talk, I will start with surfaces and surface area learnt in Calculus III, reviewing some interesting history and applications of the minimal surfaces, then go into some of my research work in the study of minimal surfaces in Riemannian manifolds.
Ann Petrus
Our Lady of the Lake University
When does (f(x))-1
= f -1(x)?
Abstract:Beginning students can easily confuse the reciprocal of the element f(x) with the values of the function f-1. This confusion raises the question of the existence of a function f for which (f(x))-1 = f -1(x) for every x in the domain. There are finite sets on which it is not difficult to define such a function. What must the domain of this type of function be, and do there exist intervals on which such a function can be defined?
Kent Riggs
Stephen F. Austin State University
Texas NExT Fellow
A Note of Caution
on Interval Estimation of a Proportion and Difference of Two Proportions
Abstract: The standard Wald confidence interval is used extensively in elementary statistics classes to estimate a binomial proportion as well as the difference of two binomial proportions. Unfortunately, it turns out that the actual confidence level of these intervals is often significantly less than the nominal confidence level. We demonstrate the shortcomings of these intervals, and recommend a score confidence interval or adjusted Wald confidence interval, which simple adds two successes and two failures. These findings are a result of Alan Agresti's work and simply a warning call to those who encounter or teach elementary statistics.
Hilary Risser
Texas WomanÕs University
Texas NExT Fellow
Numerical methods
for singularly perturbed BVPs
Abstract: Singularly perturbed ordinary differential equation boundary value problems occur in mechanics and the physical sciences. These problems are difficult to solve numerically when the value of the parameter is small. In order to increase the efficiency and accuracy of the numeric solvers, a first order approximation to the solution is found through perturbation analysis. This perturbation solution is used to form a more efficient initial mesh, to provide an approximate initial solution, and to serve as a check on the qualitative behavior of the solution.
Carl Seaquist
Texas Tech University
Long Division in
Cultural and Historical Perspective
Abstract: We examine two algorithms for performing long division: the first one is known to most American elementary school students while the second one is more familiar to French, Latin American, and Spanish students. In an attempt to find the origins of these different approaches and to better understand their cultural significance, we analyze the earliest printed arithmetic books in the United States and in Europe. We show that the two contemporary methods used to perform long division, as well as, a third method that was popular in the late Middle Ages and Renaissance have a long geographic history of intercultural influences and are based on three different algorithms for performing subtraction.
Therese Shelton
Southwestern University
Simulating Simple Disease or Rumor Spread
Abstract: Some diseases and some rumors are spread through simple
contact. They can be modeled with random number generation, resulting in
a sigmoidal (S-shaped) curve. Numerical and graphical results will be presented
along with the algorithm. A logical explanation for why the results should be
sigmoidal will be given.
Barbara Shipman
The University of Texas at Arlington
Highlights from a
course on real analysis for in-service teachers
Abstract: This talk highlights materials developed for the course Concepts and Techniques in Real Analysis, which is a core requirement for a Master of Arts in Mathematics degree for in-service teachers at UT-Arlington. The purpose of the program is to broaden and deepen teachersÕ understanding of the mathematics that they teach and to enable them to lead stimulating and interactive mathematical activities with their students. Specific lessons on real analysis will be presented with a view toward how these lessons achieve the goals of the program and how the teachers in the course have responded to the lessons.
Dwayne Snider
Tarleton State University
Faculty
to Faculty Learning - A Distance Model
Abstract: A look at some things we can learn at a distance about student preparation, modes of instruction, types of technology, etc. from faculty departmental meetings. The talk will stress common threads within the mathematics profession as illustrated by Mathematics Department meetings at Tarleton. The historic elements will be stressed over both the theoretic or pedalogical components. Some mention of Tarleton faculty's planning to attend a past Texas Section meeting at SMU will be included.
Selina
V‡squez-Mireles and Sandra West
Texas State University-San Marcos
Parallel Concepts
in Math and Science
Abstract: Correlating Math and Science extends the traditional idea of integrating in at least three ways: 1) highlighting parallel concepts; 2) addressing language inconsistencies; and 3) co-teaching. What constitutes parallel math and science concepts and the types of language inconsistencies that may occur as well as several examples of each will be presented.
Pamela Webster and Heather Burkham
Texas A&M University Ð Commerce
Workshops for
Intermediate Algebra Classes
Abstract: Texas A&M University-Commerce has implemented mandatory workshops as part of their developmental-level (non-credit) Intermediate Algebra course. An overview of the program will be given. The presentation will consist of data gathered over a 2.5 semester period of time concerning pass rates for workshop participants versus non-workshop participants. Also, some qualitative and quantitative data have been gathered concerning students' perceptions of the workshops. These data will also be presented.
Note: This talk is presented over two time slots.
Kenneth Word
Central Texas College
Using An Online
Learning System To Assess Student Learning IN Calculus I
Abstract: An online learning system will be used to demonstrate the assessment of student learning using homework, quizzes, and a chapter examination in a traditional Calculus I lecture course. A lesson on the numerical and graphical methods of finding the limit will be the focus of the presentation.
Connie Yarema and David Hendricks
Abilene Christian University
Increasing Content
Knowledge of Middle School Mathematics Teachers through Lesson Study
Abstract: This presentation will give a quick overview of lesson study used by the speakers in their Teacher Quality Grants. Lesson study presents the opportunity for in-service teachers to reflect on their studentsÕ learning of mathematical topics and, as a result, to increase their own content knowledge of the mathematics they teach. Examples of issues that arose while observing middle school studentsÕ learning of counting techniques as well as teachersÕ views of the content they were teaching will be discussed.