This page describes the tentative program for the 2007 annual meeting of the Mathematical Association of America's Texas section, which will occur April 12-14, 2007 at the University of Texas – Pan-American and Echo Hotel and Conference Center. The hotel may be found at 1903 S. Closner, Edinburg, TX 78539 and reached via telephone (toll-free) at (800)422-0336 or (locally) at (956)383-3823, or via telefacsimile (fax) at (956)381-5913.
Through this page, the author attempts to offer a more concise and user-friendly presentation of information published on the official site for the meeting, which is located at < http://www.math.utpa.edu/maa_texas_section_07 >. Though considerable effort has been made to assure the accuracy of the information herein, that site is the authoritative source. Reports of errors on this this page and any other comments will be gratefully accepted and promptly reviewed if submitted via the Syncopated Systems contact page.
This document consists of these major parts:
| date | deadline for |
|---|---|
| 2007/02/15 (original) 2007/03/02 (extended) |
Online Abstract Submission |
| 2007/03/31 | Registration by mail or telefacsimile using PDF form |
| 2007/04/12 2007/04/13 |
On-site registration |
| 2007/04/14 | Last day of meeting |
Evening sessions will be held at the Echo Hotel and Conference Center.
| time | lobby | Vista | Hidalgo |
|---|---|---|---|
| 15:00 | registration | (none) | (none) |
| 16:00 | executive committee | ||
| 17:00 | |||
| 18:00 | (none) | ||
| 19:00 | short course: "Fractional Calculus, Theory and Applications" by Lokenath Debnath and Dambaru Bhatta, University of Texas – Pan-American |
student competition | |
| 20:00 | (none) | ||
| 21:00 | (none) | (none) |
Daytime sessions will be held at the University of Texas – Pan-American Mathematics and General Classrooms Building (MAGC) and Student Union (STUN), followed by evening sessions at the Echo Hotel and Conference Center.
| time | shuttle | MAGC foyer | MAGC multimedia classroom | MAGC 1.208 | MAGC [TBD] | MAGC 1.320, 1.324, 1.410, 1.414, 1.422 | STUN 1.102 (theater) |
|---|---|---|---|---|---|---|---|
| 07:30 | shuttle from Echo Hotel | registration | (none) | (none) | (none) | (none) | (none) |
| 08:00 | undergraduate and graduate student-contributed papers sessions | ||||||
| 08:30 | (none) | Texas NexT | |||||
| 10:30 | (none) | TAAAMS | |||||
| 11:00 | student forum | (none) | |||||
| 11:30 | (none) | ||||||
| 11:50 | (none) | Texas NexT luncheon | TAAAMS luncheon | ||||
| 12:00 | |||||||
| 12:50 | (none) | (none) | |||||
| 13:00 | welcome and opening remarks by Paul Sale, Provost, University of Texas – Pan-American |
||||||
| 13:10 | invited address: "Some Interesting Examples from Ring Theory" by Efraim Armendariz, University of Texas at Austin |
||||||
| 14:30 | professional and faculty-contributed papers sessions | (none) | |||||
| 17:00 | shuttle to Echo Hotel | (none) | TCMJ Advisory Board and Editors | (none) |
| time | patio (if raining: Vista) |
Ming | Hidalgo hallway | Hidalgo |
|---|---|---|---|---|
| 17:30 | student pizza and puzzle party followed by music |
TexMATYC Meeting | (none) | (none) |
| 18:00 | cocktail reception | |||
| 18:15 | (none) | |||
| 18:45 | ||||
| 19:00 | (none) | Texas section banquet | ||
| 20:30 | (none) |
Daytime sessions will be held at the Echo Hotel and Conference Center.
| Vista | Chevron | Hidalgo hallway | Hidalgo |
|---|---|---|---|
| 06:45 | MAA student chapter advisors and student representatives breakfast | (none) | (none) |
| 07:45 | (none) | ||
| 08:00 | MAA book exhibit | ||
| 08:30 | invited address: "Teaching and the 3x + 1 Problem" by Stuart Anderson, Texas A&M University – Commerce; Texas Section Distinguished College or University Teaching of Mathematics Award |
||
| 09:00 | (none) | ||
| 09:10 | panel discussion: "Mathematics Professional Development for Faculty: Why? How?" with John E. Bernard, University of Texas – Pan-American; Karron Lewis, University of Texas at Austin Center for Teaching Excellence; Cristina Villalobos, University of Texas – Pan American (moderator) |
||
| 10:00 | (none) | ||
| 10:30 | invited address: "My Favorite Problems" by Tina H. Straley, Executive Director of the MAA | ||
| 11:20 | section business meeting: section chair Randall Hoppens, Blinn College | ||
| 12:00 | (none) | (none) |
| time | Undergraduate Student Session I: MAGC 1.410 |
Undergraduate Student Session II: MAGC 1.414 |
Undergraduate Student Session III: MAGC 1.422 |
Graduate Student Session I: MAGC 1.320 |
Graduate Student Session II: MAGC 1.324 |
|---|---|---|---|---|---|
| 08:00 - 08:15 | Candace Andrews, University of Texas at Tyler: "Finite C-Groups" |
Bobby Grizzard, Saint Edward's University: "What Does Sperner's Lemma Tell Us About Positive Matrices?" |
Christopher A. Sams, Lamar University: "Gender and Race in Actuarial Career" |
Arnab Bose, University of Texas – Pan-American: "The Radon Transform and its Applications to Medical Imaging" |
Aditi Ghosh, University of Texas – Pan-American: "A Characterization of Compact Metric Spaces via the Closed Graph Theorem" |
| 08:20 - 08:35 | Andrew Beck, Saint Edwards University: "Much Ado about Nothing: Zeroes of Nth Partial Sums of the Complex Exponential Series" |
Sarah Hall, Lamar University: "Checkmate in Infinity: Variations on the Angel Problem" |
Amanda Seitz, Sam Houston State University: "Bunnies, Bees, and Pineapples – Oh, My!: An Exploration of the Fibonacci Sequence" |
Jason La Corte, Texas State University – San Marcos: "Brouwer's Fixed-Point Theorem for Rn" |
Carl H. Price, Jr., Stephen F. Austin State University: "Sober Topological Spaces" |
| 08:40 - 08:55 | Heather Bruch, Saint Edward's University: "Bringing the Symmetries of String Theory to Live: The Geometric Action of Courant and Kac-Moody Algebras" |
Luke Harrison, Sam Houston State University: "How Not to Be Like Cortez" |
Hilari Celeste Tiedeman, Southwestern University: "A Note on Weighted Identric and Logarithmic Means" |
Gustavo Cruz, University of Texas – Pan-American: "Wave Propagation Phenomenon and Differential Equations with Periodic Coefficient" |
Darrel A. Silva, Sam Houston State University: "Order Dimension of the Joining of Special Classes of Poset" |
| 09:00 - 09:15 | Betsy Childs, Stephen F. Austin State University: "Circular Logic on Triangles" |
Amalia M. Hunter, Our Lady of the Lake University: "Investigating the Quartic" |
Ashley Weatherwax, University of Texas at Dallas: "A Game of Wymsical Mathematics" |
Reid M. Etheridge, University of Texas – Pan-American: "Generalized Gronwall Inequality with Nonintegrable Singular Kernel" |
Patrick Sugrue, Stephen F. Austin State University: "Harmonic Mappings in the Plane" |
| 09:20 - 09:35 | Jason Michel Dolloff, Southwestern University: "Fourier Analysis and Baroque Counterpoint: Modeling a Bach Fugue" |
William Jaramillo, Saint Edward's University: "RSA Cryptography" |
Daniel Wennersten, University of Texas at Arlington: "Engage, Discover, Formalize, Apply: A Coherent Teaching Method that Integrates Successful Teaching Strategies" |
Aditi Ghosh, The University of Texas Pan-American: "Mathematical Modeling of Electrospinning" |
Min Sun, Sam Houston State University: "Comparing Two Imputation Methods for Continuous Data" |
| 09:40 - 09:55 | James Doughman, Sam Houston State University: "Simulating One-Day International Cricket Scores" |
Justin Jander, Stephen F. Austin State University: "Predicting Salaries of Athletes using Regression Models" |
Dana G. Wheaton, Sam Houston State University: "Rack 'em" |
Garrett Hicks, Tarleton State University: "Statistical Analysis of Heart Rate Variability" |
Charles Obare, University of Texas – Pan-American: "Buoyant Flow Around Growing Protein Crystal" |
| 10:00 - 10:15 | Angie Forgas, Lamar University: "Granites of Central Texas" |
Daliah Maurer, Saint Edward's University: "Mathematical Analysis of HIV" |
Catherine Whitehead, Lamar University: "The Improbable Dream" |
Mark Lane, Sam Houston State University: "Algebraic Combinatorics and Magic n-Circles" |
(none) |
| 10:20 - 10:35 | Tiffany L. Gatchel, Sam Houston State University: "In the Blink of an Eye" |
Mitchell Blake, Lamar University: "The Crossing Probability Knot Energy" |
Shaun Williams, University of Texas at Tyler: "n-Colorings of Twist Knots" |
(none) | (none) |
| 10:40 - 10:55 | Steven Ayala, Saint Edwards University: "Nice Polynomials" |
(none) | Catherine Whitehead, Lamar University: "The Relationship Between Students' Background Characteristics and Their Academic Library Use" |
(none) | (none) |
|
|
(alphabetically by author)
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.
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.
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.
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.
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!
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Abstract: The crossing probability energy Ecp 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. Ecp is found to be asymptotically finite, but not asymptotically smooth. An algorithm is presented to compute Ecp as well as minimize the energy using a gradient flow. Through the development we find that Ecp is essentially the crossing number expressed as a unique knot energy.
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.
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.
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.
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.
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 1990s, 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.
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.
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.
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.
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.
(alphabetically by author)
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.
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.
Abstract: We consider differential equations with periodic coefficients and the wave propagation phenomena, described by such equations.
Abstract: This presentation will examine a Generalized Gronwall Inequality with nonintegrable singular kernal, which has several applications to the Cauchy Problem for Partial Diffrential Equations with Multiple Characteristcs. We investigate Fractional Order operators with such kernals.
Abstract: The goal of the present note is to provide a characterization of compact metric spaces in terms of the closed graph theorem
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.
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.
Abstract: It is known that a one-to-one correspondence exists between the set of all n []~n magic squares and the set of all magic labelings of the complete bipartite graph [](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 sum s. We report our progress in computing the generating function, which counts the number of magic n-circles with magic sum s. Finally, we present the Franklin magic 8-circle.
Abstract: []
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.
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.
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.
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.
(alphabetically by author)
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.
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.
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.
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.
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 unknown 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 Shannon's entropy as a measure of the unknown 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.
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.
Abstract: A (finite) semifield is a non-associative division ring; the associated projective plane is called a semifield plane. The first semifields wereconstructed by Dickson in the early 1900s; in the 1960s several new classes were introduced including the twisted fields of Albert. In thistalk we will give a historical development of finite semifields. We willpresent some new semifields constructed in the last decade including a new semifield recently constructed by the author.
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.
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.
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.
Abstract: The author highlights teacher-task investigations on Geometer's Sketchpad involving the creation of technology-enhanced lessons. These tasks were designed for the course "Mathematics-specific Technologies," 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 teachers' conceptual understanding of mathematics they teach.
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 behavior? What forms do these equations take in modern circuit analysis?
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 timedue toa 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 Y2Kthreat was perceived as receding is another matter. The Federal Reserve monetary response is analyzed both graphically andfrom 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 mathematicallyobtained as a ripple effectresulting from those very Federal Reserve monetary actions.
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.
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.
Abstract: We classify the convergence behaviors of the one-parameter family fα(x)=(1 + 1/x)(x+ α), α in R, which converges to the natural logarithmic base e, using nothing more than what is taught in introductory calculus courses.
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.
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.
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.
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.
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.
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 f_1(x,y) and f_2(x,y) in two variables and show how the convergence plots for some particular choices of real valued functions generate some very interesting fractals.
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 teachers' 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.
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.
Abstract:Beginning students can easily confuse thereciprocal 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?
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.
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.
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.
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.
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 teachers' 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.
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.
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.
Note: This talk is presented over two time slots.
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.
Abstract: An online learning system will be used to demonstrate the assessment of student learning using homework, quizzes, anda 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.
Abstract: Mathematics may well be the most versatile degree currently offerred by universities. A degree in mathematics can lead to careers as diverse as: medicine, physiology, physical chemistry, cell biology, nuclear engineering, chemical engineering, mechanical engineering, applied physics, investment banking, and national security. This paper shows how a degree in mathematics prepares an individual for a possible career in anyone of the above opportunities.
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 students 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 students learning of counting techniques as well as teachers views of the content they were teaching will be discussed.