The Mathematical Associationof America

Louisiana/Mississippi Section

90th annual meetingHattiesburg, Mississippi

February 28th – March 2nd, 2013

Plenary SessionPutting a Spring in Yoda's Step

Tim Chartier, Davidson CollegeFriday, March 1st, 1 – 2.15p

Cochran Ballroom II

When the character Yoda first appeared on the silver screen, his movements were due to the efforts of famed muppeteer Frank Oz. In Star Wars Episode II: Attack of the Clones, Yoda returned to the movies but this time the character was not a puppet but a digital image within a computer. This talk will discuss the role, or more aptly the force, of mathematics behind a few aspects of movie special effects. Armed with differential equations, animators can create a believable flow to Yoda's robe or a convincing digital stunt person.

Banquet and 4th Annual R.D. Anderson LectureThe Fractal Geometry of the Mandelbrot Set

Robert Devaney, Boston UniversityFriday, March 1st, 6 – 9p

Oddfellows Gallery, Downtown Hattiesburg*

In this lecture we describe several folk theorems concerning the Mandelbrot set. While this set is extremely complicated from a geometric point of view, we will show that, as long as you know how to add and how to count, you can understand its geometry completely. We will encounter many famous mathematical objects in the Mandelbrot set, like the Farey tree and the Fibonacci sequence. And we will find many soon-to-be-famous objects as well, like the “Devaney” sequence. There might even be a joke or two in the talk.

*Directions to Oddfellows: Follow Hardy Street east, into the downtown area. After passing a stoplight with an obelisk on the left and a VFW on the right, Hardy turns into Front Street. Oddfellows is located at 119 East Front Street. Abundant parking lies around the side and back.

Outstanding Teacher AddressNever Stop Learning: The teachers and lessons of

my lifeJudith Covington, Louisiana State University in Shreveport

Saturday, March 2nd, 11a-12pCochran Ballroom II

In this talk I will share my memories and experiences as a child, student and faculty member who has spent her entire life in the Louisiana Mississippi Section of the MAA. As part of this talk, I will remember the mathematicians that have influenced me and the lessons that I have learned.

Section NexT WorkshopEngaging students mathematically – pitch by pitch

Tim Chartier, Davidson CollegeFriday, March 1st, 8.30 – 9.45a

Walker Science Building, Room 132

Pitching can play an important role in engaging students – pitching ideas, that is. This talk will reflect on my experiences (both successful and challenging) in presenting students with ideas that engage them in and out of the classroom. We will discuss student work that includes scholarly research, expository writing and service to the community.

Teaching and Technology WorkshopTechnology Tools for Effective Learning

John Travis, Mississippi CollegeFriday, March 1st, 10 – 11a

Chain Technology Building, Room 207

Technologically savvy students have discovered that much of their homework can be competed using the built-in capabilities of their graphing calculators. When this won’t work, they have discovered resources such as Wolfram Alpha can fill in the gap. As teachers, we often want students to solve problems using critical thinking skills without having these electronic tools. In this workshop, the participants will focus on possible ways to ask questions to get around these issues. In doing so, we will utilize open-source technology (Sage and WeBWorK) to pose the problems and to assess student progress.

Student LuncheonChaos Games and Fractal Images

Robert Devaney, Boston UniversityFriday, March 1st, 11.15a – 12.30p

Cochran Ballroom II

In this lecture we will describe some of the beautiful images that arise from the “Chaos Game.” We will show how the simple steps of this game produce, when iterated millions of times, the intricate images known as fractals. We will describe some of the applications of this technique used in data compression as well as in Hollywood. We will also challenge students present to “Beat the Professor” at the chaos game and maybe win his computer.

Textbook exhibitors:

Student PresentationsFriday, March 1st, 2.30 – 5p

Walker Science Building, Room 227

2·30pSurfaces of Revolution with

Constant Mean Curvaturein Hyperbolic 3-Space

Kinsey Zarske, Undergraduate, University of Southern Mississippi

In this talk, we discuss how to obtain the differential equation of the profile curve for a surface of revolution with constant mean curvature H = c in hyperbolic 3-space ℍ3(−c2) of constant curvature −c2. By solving the differential equation, we are able to construct surfaces of revolution with constant mean curvature H = c in ℍ3(−c2). Intriguingly, as ℍ3(−c2) flattens out to �3, Euclidean 3-space with c → 0, the limit of the surfaces of revolution with H = c in ℍ3(−c2) becomes a catenoid, the minimal surface of revolution in �3.

2·45pA Study of I-Groups

Dustin McPhate, Undergraduate, Northwestern State University

This paper is an investigation of I-groups. An I-group is a group which is isomorphic to a proper subgroup of itself. A few simple examples are presented. Then the paper works through the methods needed for and the proof that ℝ is an I-group.

3pSimultaneously Tangent Lines to

a Pair of ParabolasNick Collins, Undergraduate, Louisiana

Tech University

Given any two distinct parabolas, we use elementary algebraic techniques to find all lines simultaneously tangent to both parabolas. We then examine under what conditions simultaneously tangent lines to distinct parabolas exist.

3·15pFixed Points of Families of Matrices and their SpectraAmal de Alwis, Undergraduate,

Southeastern Louisiana University

In this paper, we first investigate the behavior of the characteristic polynomials of several families of matrices. For a 2×2 family of one-parameter matrices, the characteristic polynomials pass through a fixed point on the plane; we generalize this to n×n and discover a connection between the fixed points and the eigenvalues of certain submatrices.

Afterwards, we consider the locus of the critical points of the characteristic polynomials for 2×2 and 3×3 matrices. Depending on the specific linear entries, the characteristic polynomials could have a parabolic envelope, a linear envelope, a fixed point, or were simply vertical translations of each other. We also consider the fixed points of 2×2 families whose entries are arbitrary functions, such as polynomial, trigonometric, and exponential functions. We used Mathematica®, a computer algebra system, to discover and illustrate our results through animations.

3·30pQuaternions and Reflections in

R 4

Bimal Kunwor, Undergraduate, Southeastern Louisiana University

Let H be the real algebra of quaternions, and let S3 be the set of unit quaternions. For a, b ε S3, define Ba,b(x) = axb for x ε H . We show that Ba,b is a product of an even number of reflections. Let O(4) be the orthogonal group, and let PSp(2) be a projective symplectic group. The results in this paper extend work of Canlubo and Reyes, wherein a group homomorphism ξ: O(4) → PSp(2) is defined from the reflections of S3. In this paper, we evaluate the differential of ξ.

3·45 – 4p Break

Student Presentations (continued)4p

Estimation of the Real Space Error for Dispersion in

Molecular Dynamics SimulationsWayne Mitchell, Undergraduate,

Loyola University

When using Molecular Dynamics (MD) simulations to study dispersion potentials, it is necessary to use a cutoff radius when calculating the forces between particles in order to reduce the required computational overhead. In order to reduce the amount of error introduced by this cutoff we employ the Ewald sum technique. This technique splits the potential and the error into real space and Fourier space terms. Our goal is to produce a reliable estimator for the real space error. After testing an existing estimate, we found that it worked well for simulations with randomly distributed particles, but failed in simulations with interfaces. This suggests the need for a new estimate that can be applied when studying the dynamics of interfaces.

4·15pChaos in a two-stage ecological

model with strong nonlinearities

Logan Perry, Undergraduate, University of Louisiana at Lafayette

A discrete juvenile-adult model with Ricker-type survivorship functions is developed. The initial examination of the system’s dynamics focuses on showing stability of the extinction equilibrium, or trivial equilibrium. Given the inherent complexity, several numerical methods are used to convey the rich chaotic behavior exhibited. Bifurcation diagrams are used to explore the effect on our system of birth rate. From these diagrams, it can be seen that for certain birth rates the system exhibits chaotic behavior. Phase portraits are then used to better illustrate the presence of a discrete Hopf bifurcation. Finally, numerical approximations of the Lyapunov exponents show that sensitivity to initial conditions is indeed present for certain birth rates.

4·30pSymbolic Dynamics and

Substitutions from a to bSvetlana Mokhnach, Guest, University

of West Florida

The area of symbolic dynamics is an active and fast-growing part of dynamical systems. We generate infinite binary strings over the alphabet {a,b} using a variety of substitution mappings and explore patterns that arise. We will discuss the famous Fibonacci, Thue-Morse, and Cantor substitutions, and we will make connections to the 2∞ sequence.

4·45pA Combinatorial Exploration of

Sequences Through TilingsKathryn Dowden, Graduate, McNeese

State University

In this presentation, Fibonacci identities will be established through a combinatorial approach. The Fibonacci sequence will be illustrated by tiling n-boards using squares and dominos. Circular n-boards, known as bracelets, will be used to demonstrate how the Fibonacci numbers give rise to another sequence known as the Lucas sequence. Tilings that incorporate n-boards and bracelets will unveil remarkable identities in which Fibonacci and Lucas numbers combine harmoniously.

Funding for the Integration Bee, the Student Luncheon, and the Undergraduate Student Paper Competition is graciously provided by NSF grant DMS-0846477 through the MAA Regional Undergraduate Mathematics Conferences program.

Faculty Presentations: Session IFriday, March 1st, 2.30 – 5p

Walker Science Building, Room 120

2·30pMathematics, the Queen of Sciences: A Summer Camp

Vijaya L. Gompa, Troy University

Troy University Dothan Campus successfully hosted an all-girl five-day commuter summer camp with the theme Mathematics, the Queen of Sciences (MaQS). Twenty-five rising seventh, eighth, and nineth grade girls participated in the camp and a follow- up meeting. MaQS provided an opportunity for these girls to sharpen core academic skills in a relaxed environment and caring professionals that helped them to have a serious look at careers in STEM areas. In this paper, we discuss the ideas, implementation, minor setbacks and triumphs, pre- and post-survey results in the camp. We also discuss improvements from the lessons learned for the next camp.

2·50pUsing WeBWorK to Develop

Learning CommunitiesRaghu Gompa, Jackson State

University

WeBWorK is an internet-based method for delivering homework problems to students over the internet. It gives students instant feedback as to whether or not their answers are correct. A new feature of WeBWorK that promotes discussions among students by providing a means through a perl program, initially developed by Davide Cervone (from Union College), will be presented. This program, later modified by the present author, lets the instructor participate in the discussions, monitor their mathematical validity, and provide key points in solving a problem. Availability to all other students eliminates repetitive lecturing and promotes further clarification. The development, implementation, and impact on student learning and satisfaction will also be presented.

3·10pFlipping the Calculus Sequence

Bernd Schröder, Louisiana Tech University

This talk summarizes the presenter’s observations about teaching the calculus sequence in the “flipped” format that recently has gained positive press. The experience was positive, and the format appears to be a valid option for students who choose it. The main challenge is traditional: Getting students to prepare for class.

3·30pStatistics Examples Based On

Wilkinson & Pickett's The Spir it Level

David Gurney, Southeastern Louisiana University

Wilkinson and Pickett’s book, The Spirit Level, uses many graphs to show the relation between income, income inequality, and various measures of human well-being. Constructing similar examples using data available on the internet is a good way to demonstrate basic statistical concepts.

3·50-4p Break

4·pTeachers as Mathematical

Thinkers:Designing Effective Professional

DevelopmentTracie McLemore Salinas, Appalachian

State University

The Appalachian Mathematics Partnership provides mathematics professional development that explores mathematical habits of mind combined with pedagogical and leadership frameworks. This talk presents a set of geometry activities that expose teachers' use of definition and mathematical reasoning and their implications for professional development for the Common Core.

Faculty Presentations: Session I (continued)4·20p

A New Freshman Quantitative Reasoning Course

at UL LafayetteKathleen Lopez, University of

Louisiana at Lafayette

In this presentation, we will describe a new course for freshman in non-technical fields. Philosophy, content, and sample questions will be discussed.

4·40pApplication of Calculus to Drug

TherapyHaiyan Tian, University of Southern

MississippiThe study of the way in which a drug loses its concentration in the blood of a patient is fundamental to pharmacology. Calculus concepts will be presented to model how a drug is administered in order for the concentration to stay within the therapeutic range.

Faculty Presentations: Session IIFriday, March 1st, 2.30 – 5p

Location: Walker Science Building, Room 132

2·30pSystems of Islands

Zsolt Lengvarszky, Louisiana State University Shreveport

Systems of islands have been defined recently in a combinatorial context, later followed by more general definitions. Problems of interest include maximal systems of islands and their cardinalities. We give an introduction/ overview of the topic.

2·50pUsing Automatic Differentiation

to Compute Directional Derivatives in Matlab

Julie Roy, University of Louisiana at Lafayette

A forward mode automatic differentiation package is presented for computing first-order and second-order directional derivatives in Matlab. The motivation for creating this package came from a need to compute interval enclosures for directional derivatives used in global optimization methods. Illustrative examples are given, and limitations are discussed.

3·10pMATLAB function fsolve() failed to converge for dimension 4≥

Delin Tan, Southern University at New Orleans

Function fsolve() is the most important tool to solve the solution of nonlinear equation system. However, when the dimension of equations is 4, it failed to convergent for some≥ equation system. In this paper, we redesign fsolve() such that it would be convergent for any high dimensional equation system.

3·30pSolving the Yang-Baxter Matrix

EquationJiu Ding, University of Southern

Mississippi

Let A be an n × n matrix. The equation AXA = XAX is called the Yang-Baxter matrix equation, which is similar in format to the classic parameter-free Yang-Baxter equation in statistical mechanics. I shall present some results on the solutions of the equation for several classes of the matrix A, collaborated with a graduate student of our department and some internal and external colleagues. The talk will be elementary and college students with basic matrix theory can follow.

3·50-4p Break

Faculty Presentations: Session II (continued)4p

Iterative Matrix InversionEowyn Cenek, University of Southern

Mississippi

We solve the matrix equation Ax = b with unknown x, using an iterative approach that has the potential to solve the problem efficiently and accurately in O(n2) operations. The proposed iterative method uses an initial guess that approximates A-1, and then calculates x = A-1b using a polynomial expansion of the iteration operator. This approach lets us solve for x by matrix-vector multiplications rather than matrix-matrix multiplications, reducing the operation count from O(n3) to O(n2)for each iteration. The approach is particularly attractive for dense or full diagonally dominant matrices, providing a competitive alternative fast method for solving problems involving Toeplitz type matrices.

4·20pNon-Relativistic Quantum

Mechanics as a Gauge TheorySungwook Lee, University of Southern

Mississippi

I propose a new approach to a gauge theoretic treatment of quantum mechanics. In this model, state functions are the lifts of ordinary

ℂn-valued state functions to the holomorphic tangent bundle T+(ℂn), where we regard ℂn as an n-dimensional Hermitian manifold. When an external field is introduced, the unique Hermitian connection on the holomorphic tangent bundle T+(ℂn) gives rise to the energy and momentum operators for a particle influenced by the presence of the external field. This obtains the Schrödinger equation that describes the motion of a particle under the influence of an external field.

In this talk, I discuss the lifted quantum mechanics model for the abelian case i.e. when the external field is electromagnetic field.

4·40pThe Math in Data MiningVipin Menon, McNeese State

University

Data Mining goes on around us all the time, yet we seldom realize its presence. For a CS Professor who is a self-professed lover of mathematics, teaching Data Mining can be intimidating; students are often ill-equipped to deal with its math pre-requisites. It can be particularly hard to teach because it is a new field. We discuss the basic requirements in linear algebra, probability and statistics, regression, and optimization necessary for success in a Data Mining course.

Faculty Presentations: Session IIISaturday, March 2nd, 9 – 11a

Walker Science Building, Room 1209a

Generalized Primary IdealsChristine Gorton, McNeese State

University

An exploration of primary ideals and the generalization of this concept to a noncommutative ring setting.

9·20aSome Brunnian links associated

with Venn diagramsRick Mabry, LSU Shreveport

Laura McCormick, University of South Carolina

Venn diagrams on N sets can be viewed as plane projections of N-component (three-dimensional) links. Such links can be Brunnian, as with the Borromean Rings (N=3). We explore other Brunnian Venn diagrams, and present a Brunnian link with N=7 whose projection is a symmetric Venn diagram.

Faculty Presentations: Session III (continued)

9·40aGeometric Function Theory and

PrecalculusLenny Ornas, McNeese State

University

We will give a brief overview of the author’s current research projects in Function Theory and the number of places freshman calculus and precalculus come up again and again.

10aCoexistence and Competitive

Exclusionin a Discrete Juvenile-Adult

ModelRoss Chiquet, University of Louisiana

at Lafayette

We develop a general discrete juvenile-adult population model that describes two competing species. We consider species in which the juveniles only compete with other juveniles, and the adults only compete with other adults, i.e. juveniles and adults of either species do not compete. Assuming competition efficiencies of the two species are similar, we analyze the cases where reproduction is either continuous or seasonal. In both cases, we develop conditions on the invasion net reproductive numbers of the two species that will lead to competitive exclusion. We also show that coexistence and bistability are possible outcomes when competition efficiencies of the two species are different.

10·20aSolids of Revolution – An

Effective Teaching PerspectiveTilak de Alwis, Southeastern Louisiana

University

When teaching the topic of volumes of solids of revolution in a traditional Calculus II class, the average student has a difficult time visualizing the corresponding three-dimensional solid. In this talk, the author proposes several methods of alleviating the difficulty. One method is to create these solids by a computer algebra system (CAS) such as Mathematica, allowing them to rotate the object in real time. Such a CAS also enables the user to create disks and shells to illustrate the Disk and Shell Methods, as well as create animations. Another method is to construct the actual solid using everyday household items such as paper, cardboard, and tape. These kinds of visualization methods will make the instruction more lively compared to the traditional method of instruction.

10·40aNimfinity

John Perry, University of Southern Mississippi

While trying to explain my research to students, I invented a game that turned out to be a generalization of the game of Nim, whose mathematical implications are well known. We review some of these implications, and explore how “Nimfinity” distills fundamental ideas of commutative algebra into a challenging game.

Institutional Partners

Louisiana School forMath, Science, and the Arts

Louisiana State University - Baton Rouge

McNeese State University

Mississippi College

Mississippi State University

Northwestern State University of Louisiana

University of Louisiana – Lafayette

University of Southern Mississippi

William Carey University

Insitutional Partners' Membership Fees help fundstudent activities. Thank you for your support!

BiographiesTim Chartier is an Associate Professor of Mathematics at Davidson College. A recipient of the Mathematical Association of America's Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member, he coauthored Princeton University Press' Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms . He has worked with both Lawrence Livermore and Los Alamos National Laboratories on the development and analysis of computational methods to increase efficiency and robustness of numerical simulation on the lab's supercomputers, among the fastest in the world. This research was recognized with an Alfred P. Sloan Research Fellowship. Tim serves on the Editorial Board for Math Horizons, and chairs the Advisory Council for the National Museum of Mathematics, which opened in December 2012 as the first museum of mathematics in the United States. Tim fields questions for ESPN's Sports Science program, and writes for the Huffington Post's Science blog.

As an artist, Tim has trained at Le Centre du Silence mime school, Dell’Arte School of International Physical Theater, and with Marcel Marceau. He has taught and performed mime throughout the United States and in national and international settings.

In his time apart from academia, Tim enjoys the performing arts, mountain biking, nature walks and hikes, and spending time with his family.

Judith Covington is an Associate Professor of Mathematics at Louisiana State University Shreveport. She received a B.S. in Mathematics Education from Northwestern State University of Louisiana in 1985 and a Ph.D. In Mathematics from the University of Louisiana Lafayette in 1993. She began at LSUS in the fall semester of 1993. One of her main roles in the LSUS mathematics department is in educating future teachers. She regularly teaches the mathematics courses required for K-5 teachers and also teaches the Geometry course required for 7-12 grades teachers.

In addition to her work in teaching undergraduates, she has an extensive background in providing professional development for in-service teachers. In the 1990's she worked with the Louisiana Systemic Initiative Program. She has conducted many in-service workshops for local parishes. Recently she began the North Louisiana Math Teachers' Circle which is a group of middle school teachers that get together to work on problem solving. This group started during summer 2011 with a four day workshop and conducts six meetings during the academic year. She has been invigorated by the number of teachers that have chosen to participate and is deeply indebted to them for making this such an exciting group to be a part of.

A native of Methuen, Massachusetts, Dr. Robert L. Devaney is currently Professor of Mathematics at Boston University, 2013–2014 President of the MAA, and a Fellow of the American Mathematical Society. He received his PhD from the University of California at Berkeley under the direction of Stephen Smale. Working primarily in dynamical systems, he is the author of over one hundred research papers, a dozen pedagogial papers, and (co)-author or editor of fourteen books. He is involved with Paul Blanchard and Glen R. Hall in the Boston University Ordinary Differential Equations Project. This National Science Foundation project is an attempt to revitalize the sophomore level ordinary differential equations course by including material from dynamical systems theory. In 2005 he received the Trevor Evans Award from the Mathematical Association of America for an article in Math Horizons titled “Chaos Rules”.

For the last twenty years, Professor Devaney has been the principal organizer and speaker at the Boston University Math Field Days. These events bring over 1,000 high school students and their teachers from all around New England to the campus of Boston University for a day of activities aimed at acquainting them with what's new and exciting in mathematics. He has received the MAA's Deborah and Franklin Tepper Haimo Award for Distinguished University Teaching, the National Science Foundation Director's Award for Distinguished Teaching Scholars, and the ICTCM Award for Excellence and Innovation with the Use of Technology in Collegiate Mathematics. In 2004 he was named the Carnegie/CASE Massachusetts Professor of the Year. In 2009 he was inducted into the Massachusetts Mathematics Educators Hall of Fame.

Like the cartoon character Dilbert, he has an artistic side: he collects a coffee mug from each College or University he speaks at.

Maps

Special thanks to:

Schedule of EventsMaps of most event locations appear on the reverse side.

Thursday, February 28 th

Registration 6 – 8p Third floor, Cochran Center

Exhibits 6 – 8p Third floor, Cochran Center

Integration Bee 6·30 – 9p Cochran Ballroom I

Video and Pizza 7·30 – 8p Cochran Ballroom I

“Fractals: Hunting the Hidden Dimension”

Friday, March 1 st

Registration 8a – 4p Third floor, Cochran Center

Team Competition 8·30 – 11a Cochran Ballroom II

Section NeXT 8·30 – 9·45a Walker Science Building, Room 132

Workshop 10 – 11a Chain Technology Building, Room 207

Exhibits 10a – 4p Third floor, Cochran Center

Student Luncheon 11·15a – 12·30p Cochran Ballroom II

Plenary Session 1 – 2·15p Cochran Ballroom I

Student Papers 2·30-5p Walker Science Building, Room 227

Contributed Papers I 2·30-5p Walker Science Building, Room 120

Contributed Papers II 2·30-5p Walker Science Building, Room 132

Banquet and 6-9p Oddfellows Gallery

R.D. Anderson Lecture

Saturday, March 2 nd

Registration 8 – 11a Third floor, Cochran Center

Exhibits 8 – 11a Third floor, Cochran Center

MAA Liaison Breakfast 8 – 9a Chain Technology Building, Room 102

Contributed Papers III 9 – 10·45a Walker Science Building, Room 120

Outstanding Teacher 11a – 12p Cochran Ballroom IAddress

Business Meeting 12 – 1p Cochran Ballroom I

The Business Meeting must end at 1p for a later group!

Executive Committee 1 – 2p Cochran Ballroom IMeeting

Coffee and exhibits are located by the registration desk.