99th annual meeting of the texas section of the ... · 99th annual meeting of the texas section of...

99th Annual Meeting of the Texas Section of theMathematical Association of America

Tarleton State UniversityStephenville, TX

March 28 – 30, 2019

2019 Texas MAA

TABLE OF CONTENTS

CONFERENCE OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Conference Events at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

WELCOME & SPECIAL THANKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

INVITED LECTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Shortcourse: Dr William ‘Bus’ Jaco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Invited Address: Dr William ‘Bus’ Jaco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Student Forum: Dr Brandilyn Stigler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Plenary Address: Dr Suzanne Doree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Banquet Speaker: Dr Edward Burger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Invited Address: Dr Bryant Wyatt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Invited Address: Mr Eli Luberoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

OVERVIEW OF SESSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Friday Morning Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Friday Afternoon Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

MATHEMATICAL ART DISPLAYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Selected Photos of the Mathematica Art Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

FULL SESSION DESCRIPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Friday Morning Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Friday Afternoon Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

PRESENTERS INDEX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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Conference Overview

2019 Texas MAA

Conference Events at a Glance:

Thursday, March 28

12:00 PM - 3:00 PM Registration open in the Mathematics Building Lobby

3:00 PM - 7:00 PM Registration open in the Thompson Student Center Lobby

12:30 PM - 4:00 PM Gerrymandering Symposium in Math 227

4:00 PM - 6:00 PM Executive Committee Meeting in Thompson Student Center 130

1:00 PM - 5:00 PM Student Activities in Thompson Student Center Ballrooms

5:00 PM - 5:30 PM Magic show with Dr Jim Kirby in Thompson Student Center Ballrooms

5:00 PM - 6:30 PM T3AMS in Thompson Student Center 027

6:00 PM - 6:30 PM Pizza in Thompson Student Center Ballrooms

6:30 PM - 9:30 PM Math Bowl in Thompson Student Center Ballrooms

7:00 PM - 9:00 PM Shortcourse - Dr William ‘Bus’ Jaco in Math 113

“Building a Regional Community to Support Mathematics Learning by Inquiry”

Friday, March 29

7:30 AM - 11:00 AM Registration in the Mathematics Building Lobby

8:00 AM - 10:45 AM Student Breakouts in the Mathematics Building

8:00 AM - 10:45 AM Texas NExT in Math 310

8:00 AM - 9:00 AM T3AMS “Workshop on transition to math majors” in Math 315

11:00 AM - 12:00 PM Student Forum - Dr Brandilyn Stigler in the Thompson Student Center Ballrooms

“Is Math Really Everywhere?”

11:00 AM - 12:00 PM Faculty Panel on Bylaws in the Thompson Student Center 027

12:00 PM - 1:00 PM Texas NExT and Departmental Liaison Luncheon in the Thompson Student Center 027

12:00 PM - 1:00 PM T3AMS Luncheon in the Thompson Student Center 130

12:00 PM - 1:00 PM Lunch on your own or in Dining Hall

1:15 PM - 1:30 PM Official Welcome by President Dottavio in the Thompson Student Center Ballrooms

1:30 PM - 2:30 PM Plenary Address - Dr Suzanne Doree in the Thompson Student Center Ballrooms

“The Curious Case of 2s and 3s: Dynamics on Weak Compositions”

2:30 PM - 6:00 PM Exhibits in Math 125

2:45 PM - 4:45 PM Faculty contributed papers in the Mathematics Building

5:00 PM - 6:00 PM Math Circles by Dr Jane Long in Math 310

5:00 PM - 6:00 PM Book signing with Dr Edward Burger in Math 125

6:30 PM - 9:00 PM Banquet - Dr Edward Burger in the Thompson Student Center Ballrooms

“Making Up Your Own Mind through Practices of (Mathematical) Effective Thinking”

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2019 Texas MAA

Conference Overview

Saturday, March 30

8:00 AM - 8:30 AM Business Meeting in the Tarleton Student Center Ballrooms

8:30 AM - 9:25 AM Invited Address - Dr Bryant Wyatt in the Thompson Student Center Ballrooms

“Thor onto Democritus: A Topological Isomorphism on Atoms and the Void”

9:30 AM - 10:25 AM Invited Address - Dr William ‘Bus’ Jaco in the Thompson Student Center Ballrooms

“The Study of Three-manifolds using Triangulations”

10:30 AM - 11:25 AM Invited Address - Mr Eli Luberoff in the Thompson Student Center Ballrooms

“Knocking Down Barriers with Technology”

11:30 AM - 11:45 AM Conference Resolution - Dr John Sieben in the Thompson Student Center Ballrooms

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2019 Texas MAA

Welcome & Special Thanks

Welcome!

Welcome to the 99th Annual Meeting of the Texas Section of the Mathematical Association of America! We would

like to thank all of the speakers, attendees, and contributors to the conference. We hope you enjoy all of the sessions

and receive valuable information that you can share with your colleagues. We welcome you to Tarleton State University,

and Stephenville, TX. We anticipate that you will have a wonderful experience. Please let us know if we can assist you

in any way.

Dr. Eileen Faulkenberry

Local Arrangements Chair

Mr. Michael Warren

Student Activities Chair

Special Thanks!

Program Layout: A special thank you to Dr. Keith Emmert for his hard work preparing the layout and contents

of the program booklet.

Student Activities Committee: Mr. Joey McMahan, Mrs. Courtney Holland, Mr. John Robinett, and Mr. Ed

Smith.

Local Arrangements Committee: Dr. Kathy Horak Smith, Dr. Scott Cook, Dr. Beth Riggs, Mrs. Nancy

Summer, Mrs. Rose Ann Jackson, Mrs. Colleen Seaman, Mrs. Janice Groseclose, Mrs. Imelda Salinas, and Mrs. Diane

Casey.

Exceptional Thanks go to all the faculty and staff of the Tarleton State Mathematics Department, who have

contributed in many ways, great and small, to ensure the success of this conference.

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Shortcourse as well as Invited Address

2019 Texas MAA

Dr William ‘Bus’ Jaco - Regents Professor and Grayce B. Kerr Chair, Department of Mathematics, OklahomaState University and Executive Director of the Initiative for Mathematics Learning by Inquiry

Short Course: Thursday March 28th, 7:00 PM - 9:00 PM, Thompson Student Center 219Building a Regional Community to Support Inquiry Learning in Mathematics

Abstract: The Initiative for Mathematics Learning by Inquiry (MLI) has provided seed funding to establish five(5) Regional Inquiry Learning Communities in Texas. The Short Course will be set up for active engagement; there willbe five areas representing each of the five regions so that discussions can take place on the organizational aspects of aRegional Community. We will discuss a protocol that has worked: expanding seed money into more substantial funding,enhancing and scaling the community, the role of mentorship and cultural change, and sustaining the community throughviable partnerships and collaborations.

Invited Address: Saturday March 30th, 9:30 AM - 10:25 AM, Thompson Student Center BallroomsThe Study of Three-manifolds using Triangulations

Abstract: We will introduce the notion of using triangulations for a combinatorial (discrete) approach in the studyand understanding of three-manifolds. In particular, we introduce a combinatorial deformation theory for an algorithmicconstruction of the prime decomposition for any given closed three-manifold. We will provide a concurrent and analogouscombinatorial deformation theory for surfaces that gives complete visualization of such combinatorial deformations andresults in an alternative method for the classification of closed two-manifolds.

Biography: William ‘Bus’ Jaco is Regents Professor and Grayce B. Kerr Chair,Department of Mathematics, Oklahoma State University and Executive Director ofthe Initiative for Mathematics Learning by Inquiry. He holds degrees from Fair-mont State University (B.A. magna cum laude), Penn State University (M.A.), andUniversity of Wisconsin-Madison (Ph.D.). He held faculty positions at University ofMichigan and Rice University before joining the faculty at Oklahoma State Universityas Head in 1982. He is a Fellow of the American Mathematical Society, a Fellow ofthe American Association for the Advancement of Science, an Honorary Life Mem-ber of the American Mathematical Society, an Honorary Associate Member of theMoscow Mathematical Society and received Honorary Recognition for Service to St.Petersburg and Russian Mathematics and Mathematicians. He was recognized as the2017 Eminent Faculty Member at Oklahoma State University and is an outstandingalumnus of Fairmont State University. He served as Head, Department of Mathemat-

ics at OSU, 1982-87, as Executive Director and CEO of the American Mathematical Society (Providence, RI), 1988-95,and again became Head of Mathematics at OSU, 2011-2018. He served as Chair-elect, Chair, and Retiring Chair ofthe Mathematics Section of the American Association for the Advancement of Science, serves on the Advisory Boardof the American Institute of Mathematics, served on the Board of Mathematical Sciences at the National ResearchCouncil/National Academy of Sciences, served on the Joint Policy Board for Mathematics, and was an elected memberof the Board of Trustees of the American Mathematical Society serving as Chair of the Board of Trustees, 2014-15. Hismathematical research is in Geometry and Topology where he studies low-dimensional manifolds, decision problems,algorithms, and complexity theory. Recently he has participated as co-chair of the Oklahoma State Regents for HigherEducation Math Task Force, recommending statewide adoption in public higher education of Math Pathways to Com-pletion and Co-Requisite Instruction at Scale. He is PI on a number of funded projects, the largest, The MathematicalInquiry Project, is a statewide five-year project bringing mathematics learning by inquiry pedagogy in all entry-levelcollege mathematics courses.

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2019 Texas MAA

Student Forum as well as Plenary Address

Dr Brandilyn Stigler - Associate Professor of Mathematics at Southern Methodist University

Student Forum: Friday March 29th, 11:00 AM - 12:00 PM, Thompson Student Center BallroomsIs Math Really Everywhere?

Abstract: We have all heard the expression “math is everywhere.” Sometimesit can be hard to see that. In this talk we will see where mathematics arises in somecommon applications as well as in some interesting ones. Throughout I will highlightsoft skills that are developed when studying mathematics and share how math hasshaped certain aspects of my life.

Biography: Dr. Brandilyn Stigler is an Associate Professor in the Departmentof Mathematics at Southern Methodist University. She earned a PhD in mathematicsat Virginia Tech in 2005 and then held a postdoctoral fellowship at the MathematicalBiosciences Institute at the Ohio State University. Her research focus is algebraicbiology, in which she uses computational algebraic geometry to model biological pro-cesses, such as metabolism and tissue development. In 2018 she received an Altshuler

Distinguished Teaching Professor Award at SMU.

Dr Suzanne Doree - Augsburg University in Minnesota

Plenary Address: Friday March 29th, 1:30 PM - 2:30 PM, Thompson Student Center BallroomsThe Curious Case of 2s and 3s: Dynamics on Weak Compositions

Abstract: The “Boltzman Game” begins with N students who each have $1. Ateach turn, two students are randomly selected and the first student gives $1 to thesecond, if possible. In the long run, how often does a student have $0, $1, $2, etc.?The answer uses Markov Chains, elementary counting, and other tools from discretemathematics and uncovers a curious coincidence about $2s and $3s. We will alsotake a quick look at the state graph on these weak compositions, the induced dynam-ical system on partitions, and describe the Boltzman Distribution from StatisticalMechanics that motivated the game.

Biography: Dr. Suzanne Doree is the on the Board of Directors for the Math-ematical Association of America and teaches mathematics at Augsburg University inMinnesota.


Banquet Speaker

2019 Texas MAA

Dr Edward Burger - President of Southwestern University

Banquet Speaker: Friday March 29th, 6:30 PM - 9:00 PM, Thompson Student Center BallroomsMaking Up Your Own Mind through Practices of (Mathematical) Effective Thinking

Abstract: Here’s a Puzzle: How can we impactfully engage and uplift our stu-dents to thrive in their math courses and beyond? How can we inspire our students tosee the beauty and power of mathematical thinking? Here we will offer some practicalstrategies of thinking that will allow our students to not only make greater meaning ofmathematics, but apply those mindful practices beyond their math classes to enhancethe rest of their lives. We will illustrate these mindful strategies of effective thinkingthrough some illustrative puzzles.

Biography: Dr. Edward Burger is President of Southwestern University as wellas an educational and business consultant on thinking, innovation, and creativity.He has delivered over 700 addresses worldwide at venues including The SmithsonianInstitution, Microsoft Corporation, The World Bank, The International MonetaryFund, the U.S. Department of the Interior, The New York Public Library, and theNational Academy of Sciences. He is the author of over 70 research articles, books,and video series (starring in over 4,000 on-line videos). His most recent book, Mak-ing Up Your Own Mind: Thinking Effectively through Creative Puzzle-Solving, wasjust published by Princeton University Press. Burger was awarded the 2001 MAADeborah and Franklin Tepper Haimo National Award for Distinguished Teaching of

Mathematics. The MAA also named him their 2001-2003 Polya Lecturer. In 2004 he was awarded the MAA ChauvenetPrize, and in 2006 he was a recipient of the MAA Lester R. Ford Prize. In 2006, Reader’s Digest listed Burger in theirannual “100 Best of America” as America’s Best Math Teacher. In 2010 he was named the winner of the Robert FosterCherry Award for Great Teaching - the largest prize in higher education teaching across all disciplines in the Englishspeaking world. Also in 2010, he starred in a mathematics segment for NBC-TV on the Today Show ; that appearanceearned him a 2010 Telly Award. The Huffington Post named him one of their 2010 Game Changers: HuffPost’s GameChangers salutes 100 innovators, visionaries, mavericks, and leaders who are reshaping their fields and changing theworld. In 2012, Microsoft Worldwide Education selected him as one of their “Global Heroes in Education.” In 2013,Burger was inducted as an inaugural Fellow of the American Mathematical Society. In 2014, Burger was elected to ThePhilosophical Society of Texas. Today he has a weekly, lively program on higher education and thinking produced byNPR’s Austin affiliate KUT. The series is aptly called Higher ED, and the episodes are available on KUT’s website oron iTunes.


https://www.kut.org/topic/higher-ed

2019 Texas MAA

Invited Address

Dr Bryant Wyatt - Professor of Mathematics, Tarleton State University

Invited Address: Saturday March 30th, 8:30 AM - 9:25 AM, Thompson Student Center BallroomsThor onto Democritus: A topological isomorphism on atoms and the void

Abstract: Today, more than ever, the world needs inspiring mentors and teach-ers. This is a look into my journey as an educator. Though I may never know exactlywhere I am on this road, NVIDIA GPUs and undergraduate research has made mytime at Tarleton an exciting trip.

Biography: Dr. Bryant Wyatt received his Ph.D. in Applied Mathematics fromthe University of Texas at Arlington and enjoys teaching applied mathematics.

Mr Eli Luberoff - CEO of Desmos

Invited Address: Saturday March 30th, 9:30 AM - 10:25 AM, Thompson Student Center BallroomsKnocking Down Barriers with Technology

Abstract: One-to-one. Accessibility. Personalization. Internationalization. Lowfloor. High ceiling. What do these all have in common? Each is intended to makemathematics work for every student. Not just the confident students, not just thestruggling students, every student. We’ll explore the technology and techniques thatcan open doors, challenge the bored, empower the disempowered, enable the disabled,and turn every student into a mathematics student.

Biography: Eli Luberoff is the CEO of Desmos, a company with a mission “tohelp every student learn math and love learning math.”


https://www.desmos.com/https://www.desmos.com/

2019 Texas MAA


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Overview of Friday Morning SessionsRoom 8:20 - 8:35 AM 8:40 - 8:55 AM 9:00 - 9:15 AM 9:20 - 9:35 AM

109Calculus: Putting the “C” in CSIKeegan WinchesterHardin-Simmons University

Can the Practice of Religion beConsidered Contagious?: ADynamical Systems Approach toModeling the Practice of Religionin the Twentieth Century.Jocelyn BacaSt. Mary’s University

Rocket ProjectionsClaire Harding, Maddie GodleskiSouthwestern University

Connecting Number Theory andSatellite ConstellationsAyesha GonzalesSt. Edward’s University

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Lagrangian formalism for Besselequations and its auxiliaryconditionsNiyousha DavachiUniversity of Texas at Arlington

Indexing and its Possibility inMultiple Number RealmsDaeyoung SonMiddle Georgia State University

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Role of Internal Calcium PoolsDuring AcuteMethylmercury-Induced CellDeath in the C57BL6J MouseAndrea AldazSt. Mary’s University

Intervening in ClostridiumDifficile Infections in CaliforniaHospitalsErik BoonstraStephen F. Austin StateUniversity

Using Systems FactorialTechnology to Classify NumericalCognition with PythonSabrina HetzelTarleton State University

A Nurse with a Pie ChartJosie ChavezHardin-Simmons University

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Classifying p-adic Fields ofDegree p2

Alex JennyMidwestern State University

Integer Values for GeneratingFunctions of Gibonacci SequencesIvan MotaSaint Edward’s

A Different CountdownConundrumShania RobertsMidwestern State University

On a Family of GeneralizedDivisibility RelationsOtto Osterman, Joseph BurnettThe University of Texas at Dallas

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A Toy Problem and it’s TwistedSolutionNicholas Petela, Jaryd DomineTarleton State University

N-Body Approach to theTraveling Salesman ProblemJohnny SeayTarleton State University

Charting the SET UniverseAdrian Silva Jr.St. Edward’s University

Properties and Parameters ofCodes from Line Graphs ofCirculant GraphsJennifer Melendez, AlexanderWestbrooksTexas A&M University -Commerce

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On Critical Dipoles inDimensions n ≥ 3Blake AllanBaylor University

Complex Analysis on theIntersection of Two Disks on thePlaneCristo Sanchez, Micalyn RoweTexas A&M University -Commerce

The History and Development ofthe Saccheri QuadrilateralSamantha AtkinsHardin-Simmons University

Hausdorf DimensionCorina HuetherStephen F. Austin StateUniversity

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Overview of Friday Morning SessionsRoom 9:40 - 9:55 AM 10:00 - 10:15 AM 10:20 - 10:35 AM

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Modeling the Interaction Between TwoPhytoplankton SpeciesIxtaccihuatl ObregonUniversity of the Incarnate Word

Project Santé: Battery Storage ManagementApplicationEmmanuel Alvizo, Hector LeducUniversity of the Incarnate Word

Parameter Estimation and Simulation ofBacteriophage Infection ModelDavid Kiker, Shey Andrews,Michaela Aguirre, Keith Emmert, DustinEdwardsTarleton State University

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N-body Adaptive Optimization of LatticeTowersHakiem Grant, Wyatt Young, Jaryd DomineTarleton State University

N-body Simulation of Binary Star MassTransfer using Nvidia GPUsMason McCallumTarleton State University

Math V GerrymanderingPreston Ward, Maria Tovar, DianaDinh-Andrus, Tyra BuchananTarleton State University

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On Some Flexible Statistical DistributionsTo Model Lifetime DataTom Overman, Henry Alvarez, SummerZeigman, Angela AvilaUniversity of Texas at Arlington

Women’s Golf: An NCAA Comparison usingMathematical ModelingKatie DyoSouthwestern University

Racial Gerrymandering and Convex HullsOmar DominguezSt. Edward’s University

209Magic Squares of SquaresPreston WardTarleton State University

Discovering New BasesRebecca DesrochersHardin-Simmons University

A Mathematically “Sound” AnalysisWritam Nanda, Chris TalleyCollin College

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Progress on the Earth-Moon Problem forGraphsZachary NadeauAngelo State University

A k-medoids Approach to ExploringDistricting PlansAnthony PizzimentiThe University of Iowa

Obtaining Integer Outputs From SquareNonnegative Integer MatricesAndrew RogersStephen F. Austin State University

213On the Homology of the Logistic FunctionLogan WillhoiteStephen F. Austin State University

Keeping PIECE in the FamilyLacey ScottStephen F. Austin State University

The Five Platonic SolidsKaty YarbroughHardin-Simmons University

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Overview of Friday Afternoon SessionsRoom 2:40 - 2:55 PM 3:00 - 3:15 PM 3:20 - 3:35 PM

108Growth Minded GradingJohn SnowUniversity of Mary Hardin-Baylor

HB 2223 Implementation at SFASUSarah StovallStephen F. Austin State University

The Co-Requisite Model at TAMUCPamela WebsterTexas A&M University - Commerce

109Online Courses: Tips & TricksHanan KuzatTexas A&M University-Commerce

Are online classes truly better thantraditional for most students?Anna LurieSt. Mary’s University

The Datasaurus and Persistent HomologyRyan JensenStephen F. Austin State University

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Mathematics and Culture: An ExperimentalCourseMichael OrtizSul Ross State University Rio Grande

Bad Math Clubs Borrow...Sarah Cobb, Marcos LopezMidwestern State University

Quantitative Consulting: My PIC MathExperience (So Far)Catie PattersonAustin College

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A Comparison of Methods for Calculationsthe Basic Reproductive Number for PeriodicEpidemic SystemsChristopher MitchellTarleton State

DE and Social Justice: A Cholera Modelwith Bacterial ReservoirTherese SheltonSouthwestern University

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The M/M/1 Queue with Unreliable Serviceand a Working Vacation.Joshua PattersonUniversity of Texas at Arlington

Chaos in Generalized Inverse LimitsLinda PhamLamar University

Surfaces containing double conicsFazle RabbyTexas Christian University

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Identifying the Influential: Using thePD4SDG database as a proxy for regimeformationTu NguyenTarleton State University

Mix Mix RevolutionClayton BooneTarleton State University

New evidence of persistent periodicity incertain no-slip billiards in dimension twoBishwas GhimireTarleton State University

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Bayesian model selection for informativehypotheses: A comparison of data-basedversus default encompassing priorsTom Faulkenberry, Bryanna ScheulerTarleton State University

High Performance Computations forRandom Network Models of ParentalVaccine Acceptance and Disease SpreadAndras BaloghUniversity of Texas Rio Grande Valley

Mathmagic: Self Working Card TricksJason SnyderCollin College

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Overview of Friday Afternoon SessionsRoom 3:40 - 3:55 PM 4:00 - 4:15 PM 4:20 - 4:35 PM

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Corequesites and Non-STEM DevelopmentalMathematics CurriculumRebecca StewardTexas A&M University-Commerce

Teaching College Algebra throughApplicationsKristofer JorgensonSul Ross State University

Enhancing Instruction of Linear Algebrausing Dynamic VisualizationsRichard ChandlerUniversity of North Texas at Dallas

109Unavoidable Minors for HypergraphsDennis HallAngelo State University

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Advancing Careers in Mathematics throughMentoring & CollaborationTimothy HuberUniversity of Texas Rio Grande Valley

Who really teaches? The untold story of whoactually teaches math in Texas and how itworks out for themKeith HubbardStephen F. Austin State University

Finding an Assessment Style that Fits theModern Mathematics CourseJohn EhrkeAbilene Christian University

208Approximating a Nonholonomic SystemChris CoxTarleton State University

Investigating Deep Euler-Lagrange-PoissonSegmentation Learning for ImageSegmentationAdam Bowden, Nikolay SirakovTexas A&M University - Commerce

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Enigma: Breaking Down the GermanEncryption MachineEdward SmithTarleton State University

Using group structure and transformationsto connect abstract algebra with secondaryschool content to address the needs ofpreservice secondary mathematics teachersin an abstract algebra courseAndrew Kercher, James AlvarezUniversity of Texas at Arlington

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Math, the engine of the autonomous vehiclesraceTu NguyenTarleton State University

Electrophysiological markers forMild-Cognitive Impairment in Older AdultsJulio Cesar Enciso AlvaUniversity of Texas at Arlington

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Using Scripting Tasks in UndergraduateCourses to Examine ConceptualUnderstandingJanessa Beach, Theresa Jorgensen, James A.

Mendoza ÁlvarezThe University of Texas at Arlington

The Impact of Reflection on DevelopmentalMathematics StudentsHannah GrantTarleton State University

Essential Trigonometry Without GeometryBryant Wyatt, John Gresham, JesseCrawfordTarleton State University

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Mathematical Art Displays

Celtic Link PatternsTime: All Day Mathematics Art Room: 113

Angela Brown Sul Ross State UniversityIncluded are a number of Celtic Patterns made from rectangular grids. The pieces are mixed media.

The Power of Colors and SymbolismTime: All Day Mathematics Art Room: 113

Erika Balogh University of Texas Rio Grande ValleyThrough my artworks, I explore the power of colors and symbolism. The five-pointed star, the pentagram, is a well-recognized symbol all around the world. It has been used by many companies as a trademark or as a symbol onnumerous national flags. Symbol associations are common to all people. However, symbols have different meaningsto each individual. Some symbols have universal meaning while others can vary dramatically between cultures. Forexample, the five-pointed star is often connected with the human body. In my artwork, this symbol represents the unionof opposites, generally expressed as male and female, in order to generate a greater whole – a unity. But there is noperfect unity, as it is not possible to form a tiling using pentagons.

Round, Recursive, and BlueTime: All Day Mathematics Art Room: 113

John Snow University of Mary Hardin-BaylorWe use a recursive algorithm to generate a random function on [−1, 1]× [−1, 1] using functions from precalculus. Valuesof the function are interpreted as colors between two complementary RGB colors. We then use spherical coordinates tomap the colors to the surface of a sphere and project this mapping onto a the faces of a truncated icosahedron.


Selected Photos of the Mathematica Art Displays

2019 Texas MAA

Round, Recursive, and BlueJphn Snow The Power of Colors and

SymbolismErika Balogh

The Power of Colors andSymbolism

Erika Balogh


Erika Balogh


Erika Balogh


Erika Balogh


Erika Balogh


Erika Balogh


Erika Balogh


2019 Texas MAA

Selected Photos of the Mathematica Art Displays

Celtic Link PatternsAngela Brown


Friday Morning Sessions

2019 Texas MAA

Calculus: Putting the “C” in CSITime: 8:20-8:35 Applied Mathematics Room: 109

Keegan Winchester Hardin-Simmons UniversityNewton’s Law of Cooling can be used to model the temperature of an object over time. Using differential equations,Newton’s Law of Cooling can be utilized in the forensic sphere. In this presentation, Calculus will be used to solve amurder.

Role of Internal Calcium Pools During Acute Methylmercury-Induced Cell Death in the C57BL6JMouse

Time: 8:20-8:35 Probability and Statistics Room: 208

Andrea Aldaz St. Mary’s UniversityMethylmercury (MeHg) is an environmental neurotoxicant of contemporary concern that causes a cascade of cellulareffects leading to cell death. MeHg targets a-motor neurons (aMNs) located in the lumbar region of the spinal cord. aMNsare important for skeletal movement; their degeneration is a key feature of amyotrophic lateral sclerosis. MeHg-inducedcell death results from uncontrolled increase in internal calcium concentration ([Ca2+]i). The initial effect is release ofCa2+ from internal organelles (mitochondria and smooth endoplasmic reticulum (SER)) followed by extracellular Ca2+entry. Our purpose was to elucidate the immediate and delayed contribution that mitochondria and SER provide duringMeHg-induced cell death. This was being performed using lumbar spinal cord slices isolated from C57BL6J mice, andcalcein-AM, a fluorophore that label viable cells green. Cell viability was determined following a 15min [20µM] MeHgexposure in the absence and presence of chemicals that modulate internal Ca2+ pools: Carbonyl cyanide m-chlorophenylhydrazone (CCCP) and thapsigargin. CCCP depolarizes the inner mitochondrial membrane increasing cytosolic Ca2+.Thapsigargin blocks the SER Ca2+-ATPase (SERCA), preventing uptake of cytosolic Ca2+. We hypothesized thatCCCP + thapsigargin treatment would increase [Ca2+]i increasing further incidence of MeHg-induced cell death. MeHgalone significantly decreases viability from baseline at 3hrs post-MeHg by 0.65 relative change. To assess the significanceof MeHg-induced cell death occurring at delayed timepoints, statistics were performed by a 1-way analysis of variancefollowed by Tukey’s multiple comparison test. Internal Ca2+ stores contribute to MeHg-induced cell death since theMeHg + CCCP + thapsigargin shows a significant viability loss by 0.52 relative change from MeHg control group.Statistics were performed by a 2-way analysis of variance followed by Sidak’s multiple comparison test. This projectsheds light on the role of Ca2+i organelles to MeHg-induced neuronal death. This research is important because it shedslight on the role of Ca2+i-containing organelles, mitochondria and SER, to MeHg-induced motor neuronal death.

Classifying p-adic Fields of Degree p2

Time: 8:20-8:35 Algebra and Number Theory Room: 209

Alex Jenny Midwestern State UniversityThere are only a finite number of extensions of Qp for a given degree, making a complete classification of these extensionspossible. The case where p does not divide the degree of the extension is understood. For all other degrees divisible byp, the only known cases are when n ≤ 15. The motivating idea behind this project was to classify p-adic fields of degreep2 by classifying the generating polynomials and classifying the ramification polygons.

A Toy Problem and it’s Twisted SolutionTime: 8:20-8:35 Discrete Mathematics Room: 212

Nicholas Petela Tarleton State UniversityJaryd Domine Tarleton State University

In the shadow of the Rubik’s Cube lay the Rubik’s Snake, a twistable chain of triangular prisms. The Snake presents us acombinatoric conundrum: Each segment can turn four ways, but the Snake fills space as it goes and cannot pass throughitself. While commercial versions of the snakes tout “endless possibilities”, can this be true? Of course not! We presenthere our search for the number of “legal” configurations and explore the problem’s relation to the self-avoiding walks onthe cubic lattice and string restrictions involving self-similarity and symmetry. Patterns, algorithms, and visualizationshave been found in twisting corners of our path as we continue to shed light on the Rubik’s Snake.


2019 Texas MAA


On Critical Dipoles in Dimensions n ≥ 3Time: 8:20-8:35 Analysis Room: 213

Blake Allan Baylor UniversityWe consider generalizations of Hardy’s inequality corresponding to the case of dipole potentials to extend Fermi andTeller’s 1946 result concerning bound states in the electric dipole. We (implicitly) determine the critical constants(critical dipole moments) for which this inequality holds. In addition, we extend this inequality to the case of finitelymany and countably many (but suitably screened w.r.t. their support) dipole potentials whose singularities are uniformlyspaced apart. This is based on joint work with F. Gesztesy

Can the Practice of Religion be Considered Contagious?: A Dynamical Systems Approach to Modelingthe Practice of Religion in the Twentieth Century.

Time: 8:40-8:55 Applied Mathematics Room: 109

Jocelyn Baca St. Mary’s UniversityReligious affiliation within a population tends to increase or decrease at various times as living conditions changebetween peaceful or troublesome periods in civic circumstances. This project models the dynamics of the practice ofCatholicism within a population that has been subdivided into Non-Catholic, Catholic, and Clerical/Professed Religioussub-categories using a dynamical systems approach and treating the practice of Catholicism as an infectious disease.Mathematical analysis of this nonlinear system of differential equations then compares the model projections with realhistorical data gathered from the twentieth century regarding the practice of Catholicism. This mathematical model ofthe dynamics of the practice of Catholicism, once formed and validated, can be used to project trends of Catholicismtoday by making adjustments to the parameters of the model and the distribution of the population amongst the variouscategories. Further, the model can determine the shift in the number of people in each category according to the civiccircumstance. Computer simulations of the model and an analysis of such simulations will be explored.

Lagrangian formalism for Bessel equations and its auxiliary conditionsTime: 8:40-8:55 Applied Mathematics Room: 112

Niyousha Davachi University of Texas at ArlingtonLagrangian formalism is established for differential equations whose solutions are given by Bessel functions. The for-malism is based on standard and non-standard Lagrangians, and it is shown that the latter required the calculus ofvariations to be amended by auxiliary conditions, which is a novel phenomenon. The obtained results are applied todifferent Bessel equations.

Intervening in Clostridium Difficile Infections in California HospitalsTime: 8:40-8:55 Probability and Statistics Room: 208

Erik Boonstra Stephen F. Austin State UniversityClostridium difficile infection (CDI) poses a serious health threat for hospitalized patients. For an example in 2015there were approximately 500,000 infections and 29,000 deaths in the United States. Individual risk factors includeadvanced age, prolonged antibiotic use, and severe illness. Environmental risk factors of CDI include bathroom sharingwith infected patients, patient transfers, and seasonal trends. Despite several clinical trials testing various strategies forreducing CDI rates, most have been unsuccessful or provided short-term success. So, what we aim to do is effectivelychoose hospitals within a region to include in a clinical study with the goal of maximizing the reduction of CDI casesfor a fixed treatment efficacy rate. To achieve this we used a linear mixed effects model to predict CDI rates 24 monthsout. Using this prediction model, we test various selection strategies such as targeting hospitals with high CDI rates,larger proportions of patients over 65, and high levels of centrality within the hospital network. Then using the selectionmethods we simulated interventions to determine which selection strategy resulted in the maximum reduction of CDIcases over 24 months. This work was done in correlation with the University of Iowa Department of Biostatistics througha program called ISIB, which was funded by National Heart, Lung, and Blood Institute.



2019 Texas MAA

Integer Values for Generating Functions of Gibonacci SequencesTime: 8:40-8:55 Algebra and Number Theory Room: 209

Ivan Mota Saint Edward’sThe generating functions F (x) and G(x) for the Fibonacci and Lucas sequences will produce integers if and only if xis a ratio of consecutive terms from their respective sequences. Similar results have been extended to sequences Rnwith initial terms 0 and 1 and recursion Rn+1 = aRn + bRn−1 for positive integers a and b. We present analogousresults for certain generating functions of Gibonacci numbers, sequences Gn of nonnegative integers that follow thesame recursion as the Fibonacci numbers with initial terms G0 and G1 with G0 > G1. We show that the generatingfunction for these Gibonacci sequences also produce integers when x is either a ratio of consecutive Fibonacci numbersor a ratio of consecutive Gibonacci numbers Hn with initial terms H0 = G0, H1 = G0−G1. One key aspect of the proofinvolves using fundamental solutions of the generalized Pell’s equation of the form, x2 − 5y2 = 4N , where x, y, and Nare integers, to generate Pell multiples which are additional solutions to the generalized Pell equation.

N-Body Approach to the Traveling Salesman ProblemTime: 8:40-8:55 Discrete Mathematics Room: 212

Johnny Seay Tarleton State UniversityIn the Traveling Salesman Problem (TSP), you are generally given a list of cities and the distances between each pair ofcities. The goal is to find the shortest possible route that visits each city exactly once and returns to the original city. Ithas been studied informally for centuries, and more formally for decades. The TSP has become one of the most popularproblems in the fields of mathematics and computer science. Numerous approximation techniques have been studied,ranging from linear programming methods to nature-inspired models. Here, we present a novel n-body approach to theTSP.

Complex Analysis on the Intersection of Two Disks on the PlaneTime: 8:40-8:55 Analysis Room: 213

Cristo Sanchez Texas A&M University - CommerceMicalyn Rowe Texas A&M University - Commerce

Many problems in STEM require working on regions with inconvenient geometries such as the outside region of across-sectional shape of a wing or a blade (of a propeller, rotor, or turbine). Special types of complex functions, calledconformal mappings, make these problems simpler to work on. In this project, we study an analytic property of a regionof intersection between two disks (with varying radiuses and centers). We first create a conformal mapping between theregion of intersection and the unit disk. Then, we explore some integrability properties for different derivative orders ofthe conformal map on the region of intersection with respect to the angle of intersection between the two disks.

Rocket ProjectionsTime: 9:00-9:15 Applied Mathematics Room: 109

Claire Harding Southwestern UniversityMaddie Godleski Southwestern University

We built and launched a rocket, with an altimeter inside of it, measuring the maximum altitude. Using a thrust curveprovided by the engine manufacturers, calculations were done to find a graphs of the theoretical values of the rocketlaunch. This was done by writing code on MATLAB as well as calculating by hand.

Indexing and its Possibility in Multiple Number RealmsTime: 9:00-9:15 Applied Mathematics Room: 112

Daeyoung Son Middle Georgia State UniversityThis paper explores a new topic of indexing and its possibility among multiple number realms. After defining basicequalities and terminology of sequence, the paper defines indexing and classifies the topics. The paper also includesthe proof of impossibility of indexing in the real number realm and function analysis done to this point in integers andnatural numbers.


2019 Texas MAA


Using Systems Factorial Technology to Classify Numerical Cognition with PythonTime: 9:00-9:15 Probability and Statistics Room: 208

Sabrina Hetzel Tarleton State UniversityThe way a cognitive processing system handles multiple information sources can be classified in two ways. The firstis the system’s processing order. There are two main types of processing order: serial, where information is processedsequentially, and parallel, where information is processed simultaneously. The second classification type is stopping rule,which asks whether the system stops after sufficient information is processed, or whether the system processed all sourcesof information until completion. The first of these is called self-terminating whereas the second is called exhaustive. Thecombination of processing order and stopping rule is known as an individual’s architecture. Systems Factorial Technology(SFT) is a mathematical technique for classifying architecture from response time data in human cognitive tasks. Weapply SFT to analyze how people process numerical information from the numerator and denominator when doing taskswith fractions. Using Python, we compute two processing signatures for 7 different observers: the survivor interactioncontrast and capacity curve. These curves both point to a serial self-terminating system, implying two things. First,people process fraction components one at a time, and second, people process only the necessary parts of the fractionthat are needed for the task.

A Different Countdown ConundrumTime: 9:00-9:15 Algebra and Number Theory Room: 209

Shania Roberts Midwestern State UniversityThe Countdown is a British game show which consists of word and number puzzles. In the numbers part of the game,players attempt to reach a target number by performing basic arithmetic operations on a set of six “large” and “small”numbers. The target numbers range from 100 to 999; the “large numbers” are chosen from 25, 50, 75, and 100; the“small numbers” from 1-10. Since the numbers are chosen at random, not every configuration of numbers is solvable.This talk explores how the game changes when exponentiation is allowed in addition to the basic arithmetic operations.The pool of numbers was also reduced to only include the small numbers. We attempted to find the smallest set ofnumbers which can generate every target number with these modifications.

Charting the SET UniverseTime: 9:00-9:15 Discrete Mathematics Room: 212

Adrian Silva Jr. St. Edward’s UniversitySET is an addictive game with many hidden mathematical properties still being discovered. We explore the structure,relationships, and geometry within the SET Universe, which is the entire deck of 81 cards in the game SET, where mostrules of geometry remain but some are altered due to the structure of the game. A variation of the game introduces theconcepts of “planets” and “comets” within the SET Universe. We explore the properties of planets and comets to countthem, compute the probabilities of drawing them at random, and discover the relationships between them.

The History and Development of the Saccheri QuadrilateralTime: 9:00-9:15 Geometry and Topology Room: 213

Samantha Atkins Hardin-Simmons UniversityThis presentation will include a brief introduction to Giovanni Saccheri and evaluate the development and history of theSaccheri quadrilateral.

Connecting Number Theory and Satellite ConstellationsTime: 9:20-9:35 Applied Mathematics Room: 109

Ayesha Gonzales St. Edward’s UniversitySatellite constellations are unique to their mission. Some missions aim to provide coverage to a limited region, whileothers may need many satellites to reduce the number of ground connections per satellite. Thus, there is no one-size-fitsall constellation. Design theory had led to the creation of 2D Necklace Flower Constellations (FCs), a generalizationthat allows for simpler design and optimization of constellations. In this talk, we discuss this Necklace FC theory, showan example with interesting geometry, and connect number theory to constellation design.



2019 Texas MAA

A Nurse with a Pie ChartTime: 9:20-9:35 Probability and Statistics Room: 208

Josie Chavez Hardin-Simmons UniversityFlorence Nightingale did not just contribute to the nursing field, but also made the biggest contribution to Statistics.She made a pie chart that helped with data observation. In this presentation, we will dive into the history of the piechart.

On a Family of Generalized Divisibility RelationsTime: 9:20-9:35 Algebra and Number Theory Room: 209

Otto Osterman The University of Texas at DallasJoseph Burnett The University of Texas at Dallas

We consider a generalized class of divisibility relations corresponding to unique factorizations of integers via a restrictionon the exponents appearing in their prime factorizations. To each of these divisibility relations we may associate amultiplicativity condition for arithmetical functions. We show that the set of arithmetical functions satisfying thesemultiplicativity conditions form a group under the corresponding convolutions, in direct analogy to the group of mul-tiplicative arithmetical functions under Dirichlet convolution. We also present asymptotics for functions pertainingto analogues of classical number theoretic functions, including the totient function, summatory totient function, anddivisor functions. Finally, we may present results on analogs of the Mertens function in connection with the RiemannHypothesis.

Properties and Parameters of Codes from Line Graphs of Circulant GraphsTime: 9:20-9:35 Discrete Mathematics Room: 212

Jennifer Melendez Texas A&M University - CommerceAlexander Westbrooks Texas A&M University - Commerce

Paley, lattice and triangular graphs are some examples of strongly regular graphs that produce linear codes from theirneighborhood designs. Most of these families of graphs are line graphs of a much larger class known as circulant graphs,Gn(S). In this project, we utilize prior results to obtain properties and parameters of binary codes Cn(S) that comefrom neighborhood designs of line graphs of circulant graphs.

Hausdorf DimensionTime: 9:20-9:35 Geometry and Topology Room: 213

Corina Huether Stephen F. Austin State UniversityUndergraduate mathematics students become familiar with numerous shapes that live in the first three integer dimen-sions. However, not all shapes fit so perfectly into 1D, 2D, or even 3D spaces. Fractals, for example, are objects thatcan exhibit non-integer dimension, which is its Hausdorf dimension. In this presentation, we will discuss the Hausdorfdimension of a variety of shapes, including the Koch snowflake and the Sierpinski gasket. The discussion will also includethe formation of these shapes as well as their interesting properties (such as area and perimeter).

Modeling the Interaction Between Two Phytoplankton SpeciesTime: 9:40-9:55 Applied Mathematics Room: 109

Ixtaccihuatl Obregon University of the Incarnate WordWe will be looking at modeling the interaction of two types of phytoplankton species within the same environment.Algae is the main component of the environment, serving as the main source of nourishment for plankton development.We will focus on the interaction between plankton that create toxic particle versus plankton that generate non-toxicparticles. The model we will be looking at is composed of three differential equations representing the evolution ofresources allocated to the plankton, the non-toxic plankton population, and the toxic plankton population. It will beshown that competitive interactions and initial conditions have the biggest impact on the model’s dynamic.


2019 Texas MAA


N-body Adaptive Optimization of Lattice TowersTime: 9:40-9:55 Applied Mathematics Room: 112

Hakiem Grant Tarleton State UniversityWyatt Young Tarleton State UniversityJaryd Domine Tarleton State University

A lattice tower is a structure comprising many beams connected at joints, and a key dilemma in their design is that thethickness of a beam is proportional to both its strength and cost. We want to minimize cost by making beams thinner,without compromising safety; Low cost is the goal and allowable strain, a proportional change in beam length, is theconstraint. This problem is force-based, differential in nature and heavily dependent on tower geometry, lending it to acomputational approach. We present here our n-body spring-based model, and an optimization algorithm inspired bythe atrophy and hypertrophy of muscles.

On Some Flexible Statistical Distributions To Model Lifetime DataTime: 9:40-9:55 Probability and Statistics Room: 208

Tom Overman University of Texas at ArlingtonHenry Alvarez University of Texas at ArlingtonSummer Zeigman University of Texas at ArlingtonAngela Avila University of Texas at Arlington

In this presentation, we will present different parametric distributions under the family of generalized gamma distribu-tions that can be used to model survival data that are subject to right censoring. The goal is to introduce a bigger classof parametric distributions that contain the commonly used parametric distributions as special cases. The estimatesof the model parameters are obtained through maximum likelihood technique and comparison of different candidatemodels are done through likelihood-based methods. A real clinical data application is provided for illustrative purposes.

Magic Squares of SquaresTime: 9:40-9:55 Algebra and Number Theory Room: 209

Preston Ward Tarleton State UniversityMagic Squares are square matrices with a special arrangement of numbers in them. These numbers are special becauseevery row, column and diagonal adds up to the same number. What is not known is if you can construct a 3x3 magicsquare of squares, in which each element of the matrix is itself a square, and the rules for the sums still holds. In thistalk I will show our efforts to find these magic squares, and make a conjecture that they don’t exist.

Progress on the Earth-Moon Problem for GraphsTime: 9:40-9:55 Discrete Mathematics Room: 212

Zachary Nadeau Angelo State UniversityImagine being a cartographer in a world where every country on Earth is advanced enough to own a colony on the moon.Now, imagine being tasked with coloring a map of the earth and a map of the moon so that the color of every countryon Earth matches the color of its corresponding colony on the moon. If we wish for no two adjacent regions on eithermap to share the same color, what is the minimum number of colors required to color any configuration of Earth-Moonmaps? In this talk, we will explore this Earth-Moon problem in terms of vertex coloring on graphs, and discuss howthis situation differs from that of the famous four-color theorem. Additionally, we will give some partial results whenthe graphs have certain restrictions. This talk is intended for a general audience.

On the Homology of the Logistic FunctionTime: 9:40-9:55 Geometry and Topology Room: 213

Logan Willhoite Stephen F. Austin State UniversityThe Logistic Function, defined as L(x) = ax(1 − x) , is often analyzed through the use of Cobweb Plots. I will presentmy research on the Logistic Function and its iterates from a more topological approach where I develop first persistenthomology bar codes. I will also show how these bar codes change as the value of a in the Logistic Function varies from1 to 4.



2019 Texas MAA

Project Santé: Battery Storage Management ApplicationTime: 10:00-10:15 Applied Mathematics Room: 109

Emmanuel Alvizo University of the Incarnate WordHector Leduc University of Incarnate Word

Solar energy is one of the best renewable energy sources, however, once the sun goes down there is no energy to betransformed and used. Energy companies are looking into battery storage units so during the hours of the day when thesun is not prevalent, the battery storage units can use up the stored energy to release into the grid. In the process, batterystorage units can be exposed to overheating, humidity, charging/discharging cycles, and other environmental issues. Theobjective of Project Santé: Battery Storage Management Application is to design a Micro Supervisory Control and DataAcquisition (SCADA) system to manage battery storage and increase the efficiency of the battery life. Using ArduinoBoards, Temperature Sensors, XBee’s, MATLAB, and ThingSpeak, the system senses, analyzes, and makes decisionswith the help of human regulation on how to control a fan in charge of keeping temperature, humidity, and pressurefor batteries at appropriate levels. The system will be semi-autonomous; meaning it will be running autonomously,however, in case of an emergency, human interaction would be accessible. Our system is applicable to what currentsystems are doing and would improve upon their reliability, management, and effectiveness. Although this research isinspired by battery storage units for energy companies, this study can also be applied to anything using batteries inorder to increase the efficiency and prolong their life.

N-body Simulation of Binary Star Mass Transfer using Nvidia GPUsTime: 10:00-10:15 Applied Mathematics Room: 112

Mason McCallum Tarleton State UniversityBinary stars are system of two stars that orbit around a common center of mass. Among the various types of binaries, theW UMa systems are among the most interesting. These are examples of contact binaries where the two main sequencestars are in physical contact and share a common envelope. The structure and evolution of single stars depend on theinitial mass of the stars, but because mass transfer can occur in contact binaries, their structure and evolution are verydifferent from single stars. In this study our goal is to develop an N-body model of a W UMa system. Given the initialmasses of the two components, the model will allow us to compare results with well studied W UMa systems. Giventhe initial parameters, does binary mass transfer play any role in the formation of A- or W-subtype and can our modelgenerate statistics that can be used for comparison with observations?

Women’s Golf: An NCAA Comparison using Mathematical ModelingTime: 10:00-10:15 Probability and Statistics Room: 208

Katie Dyo Southwestern UniversityWe present a preliminary report of applying statistical analysis to compare the performances of individual women’sgolfers. Data on the three National Collegiate Athletic Association (NCAA) divisions is obtained from Golfstat. Wecreate stochastic models based on probability of injury to model having a full roster for the season in order to be ranked.

Discovering New BasesTime: 10:00-10:15 Mathematics Education Room: 209

Rebecca Desrochers Hardin-Simmons UniversityDuring this presentation, we will explore many bases within mathematics including 5, 6, 10, and 20. We will learn aboutwhen and how these bases came about and how they were applied in the past. Also, we will solve problems applyingthe bases we talk about throughout the presentation.

A k-medoids Approach to Exploring Districting PlansTime: 10:00-10:15 Discrete Mathematics Room: 212

Anthony Pizzimenti The University of IowaAs the fight against unconstitutional partisan gerrymandering mounts, researchers and legislators alike continue thesearch for methods of drawing fair districting plans. A districting plan is a partition of a state’s subdivisions (e.g.counties, voting precincts, etc.) and by modeling these districting plans as graphs, they are easier to create, store, andoperate on. Here, we present a variant on the k-medoids algorithm where, given a set of initial medoids, we find anoptimal partition of the graph such that each set in the partition is connected and of similar population to each otherset. Then, this partition admits a districting plan.


2019 Texas MAA


Keeping PIECE in the FamilyTime: 10:00-10:15 Geometry and Topology Room: 213

Lacey Scott Stephen F. Austin State UniversityDetermining a minimum distance under a given constraint is always an intriguing question. I will discuss solutions tothe following question: A farmer owns a one mile by one mile patch of land that is fenced around its perimeter. Hewants to split the land equally between his three daughters. To do this, he will add interior fencing and he wants to usethe least amount of fencing possible. How could he do it?

Parameter Estimation and Simulation of Bacteriophage Infection ModelTime: 10:20-10:35 Applied Mathematics Room: 109

David Kiker Tarleton State UniversityShey Andrews Tarleton State UniversityMichaela Aguirre Tarleton State UniversityKeith Emmert Tarleton State UniversityDustin Edwards Tarleton State University

Bacteriophages are an emerging focus in research due to their potential use in treating antibiotic resistant bacterialinfections. Tarleton State University, as part of the international HHMI SEA-PHAGES bacteriophage discovery program,is working on an interdepartmental project between the biology and mathematics departments to create a mathematicalmodel for the complexity of bacteriophage infection of host cells. We constructed a Compartmental Diagram using4n+ 1 differential equations to model interactions between bacterial cells and bacteriophage, in which n different typesof phages are capable of infecting a cell. Susceptible cells are represented as Class S. Class Cj represents those bacteriawhich have become infected with the jth phage where the bacteriophage are circularizing. Bacteria in Class Cj will thenmove to either a lytic or lysogenic cycle. Class Ij represents the cells infected by the j

th bacteriophage and are currentlyfollowing a lytic cycle. Class Rj represents the cells infected by the j

th bacteriophage which are currently following alysogenic cycle and exhibiting bacteriophage homoimmunity. We assume it possible to move from Class Rj to Class

j when suitable environmental stress occurs. The Classes Cj , Ij , and Rj are considered immune to infection by adifferent virus. Finally, Class Vj represents j

th virus in the environment produced from lysis of infected cells. A simplemass-action interaction term, αjSVj , controls the creation of newly infected susceptible bacteria and removes spent virus.A single, constant carrying capacity is used to control the growth of all classes of bacteria. Local asymptotic stabilitycriteria for selected equilibria are then derived. Currently, we are designing experiments to evaluate and verify themodel that has been created. Microbacterium foliorum will be used as a host for bacteriophages to establish parameterswhich that can be used to verify the model. Other collaborators from Tarleton State University: Abigail Ballard, SheyAndrews, Michaela Aguirre, Matthew Bristerpostma

Math V GerrymanderingTime: 10:20-10:35 Applied Mathematics Room: 112

Preston Ward Tarleton State UniversityMaria Tovar Tarleton State UniversityDiana Dinh-Andrus Tarleton State UniversityTyra Buchanan Tarleton State University

Courts at all levels are struggling with the increasingly pressing and complex issue of political gerrymandering. Deadlinesfor the post-2020 census redistricting are quickly approaching. At the heart of our difficulties to fairly divide ourselvesin voting district lies a math problem – how do we measure fairness? How can we use that measure to draw fair districtboundaries? Our project is part of nationwide collaboration of mathematicians, demographers, lawyers, mapmakers,political leaders, and citizens attempting to develop tools for this purpose. We will survey Markov Chain Monte Carlomethods used in the PA Supreme Court case and our recent work to improve and apply it to more states. We willdiscuss several commonly used compactness metrics and present a new idea called transit time compactness that aimsto sue the Google Maps API to measure cohesiveness of people, not just land.



2019 Texas MAA

Racial Gerrymandering and Convex HullsTime: 10:20-10:35 Probability and Statistics Room: 208

Omar Dominguez St. Edward’s UniversityRacial gerrymandering is drawing political maps to dilute the voting power of groups based on race. Texas CongressionalDistrict maps were recently contested at the Supreme Court on the basis of racial gerrymandering. Specifically, evidencesuggests that Texas Congressional District 35 was packed with a greater percent of Hispanic/Latinos than that of itssurrounding area to dilute their voting power in neighboring districts such as 21, which is less Hispanic/Latino thanits surrounding area. To investigate this, we compare the percent of Hispanic/Latinos in each district to that of thedistrict’s convex hull, which is the smallest convex region from which the district was drawn. We find that the percent ofHispanic/Latinos in District 35 and two other districts are significantly greater than that of their convex hulls, suggestingthat these districts were packed, and that the percent of Hispanic/Latinos in several neighboring districts including 21are significantly less than that of their convex hulls, suggesting that these districts were cracked.

A Mathematically “Sound” AnalysisTime: 10:20-10:35 Analysis Room: 209

Writam Nanda Collin CollegeChris Talley Collin College

In an airplane, our ears are bombarded by multiple sources of sound, from the roaring engine to babies crying. How is itthat our minds can turn this cacophony into white noise that lulls us to sleep? Enter Fourier analysis, the mathematicalreason for the comfort experienced during our travels. The process of breaking down a wave step by step is calledFourier transformation. In this mathematical analysis we delve deep into the fundamental aspects of Fourier transform.Real world applications derived from everyday situations (a walk in a park, a college library etc.) will be visualizedthrough animated graphs. Soundscapes are broken into singular waves of sound using FFT (Fast Fourier Transform),then filtered to eliminate unwanted noise. We will discover relationships between waves modeled by a diverse set ofmathematical equations using Fourier Series. Along with this, the center of mass of an object moving within a periodwill be manipulated by adding sound waves. The animations present throughout this presentation are created usingmanim, an open source python library.

Obtaining Integer Outputs From Square Nonnegative Integer MatricesTime: 10:20-10:35 Discrete Mathematics Room: 212

Andrew Rogers Stephen F. Austin State UniversityLet A be a square nonnegative integer matrix. The main question of this project is to determine all vectors v suchthat Anv is a vector of integers for some natural number n. The entries of v do not necessarily need to be integers;

consider the example A =

(4 12 3

), v =

(1/4−1/2

). This problem is a component of a question in dynamical systems,

a branch of mathematics that investigates and describes change over time. We obtain partial results using eigenvaluesand eigenvectors.

The Five Platonic SolidsTime: 10:20-10:35 Geometry and Topology Room: 213

Katy Yarbrough Hardin-Simmons UniversityThis presentation examines the Five Platonic Solids. By definition, Platonic solids must have faces that are all identical,are regular polygons meeting at the same three-dimensional angles. These solids include the cube, tetrahedron, hexa-hedron, octahedron, dodecahedron, and icosahedron. The first study of the solids was by the Pythagoreans and laterelaborated by Plato. Finally, they were proven in the last book of Euclid’s Elements and was later used by JohannesKepler to explain the geometry of the universe.


2019 Texas MAA

Friday Afternoon Sessions

Growth Minded GradingTime: 2:40-2:55 Mathematics Education Room: 108

John Snow University of Mary Hardin-BaylorMastery-based grading is a grading system in which students only receive credit for correct work and in which studentsare given the opportunity to demonstrate mastery of topics on which they may not have performed well when first tested.There is a growing community of college professors employing some form of master-based grading in mathematics. Iwill discuss my experiences using adaptations of mastery-based grading in upper and lower level college mathematicsclasses.

Online Courses: Tips & TricksTime: 2:40-2:55 Mathematics Education Room: 109

Hanan Kuzat Texas A&M University-CommerceHow can we implement enjoyment and success in online courses? The choices of designing online courses are to preparea piecemeal approach of educational materials and integrate them into an interesting and exciting existing curriculumto attract our viewers. In this presentation some techniques in designing online courses will be implemented to fastenand ease the process of delivering instructional materials in an online environment.

Mathematics and Culture: An Experimental CourseTime: 2:40-2:55 Mathematics Education Room: 112

Michael Ortiz Sul Ross State University Rio GrandeStudents from underrepresented groups or nontraditional backgrounds often face setbacks in becoming attuned to themathematical style of discourse. In this talk, I’ll describe an experimental course designed to give students at a regionalborder college a passport to the culture of mathematics, in which students read texts about and involving mathematics,from George Polya’s How to Solve It to the stories of Jorge Luis Borges, from the painter Paul Klee’s theories of abstrac-tion to the life of Srinivasa Ramanujan, working on concrete problems while reflecting on the history and philosophy ofmathematics and grappling with questions about gender, ethnicity, and forms of privilege.

The M/M/1 Queue with Unreliable Service and a Working Vacation.Time: 2:40-2:55 Probability and Statistics Room: 209

Joshua Patterson University of Texas at ArlingtonWe define a new term ’unreliable service’ where the service itself is unreliable (i.e. may fail). We will define thisphenomena, discuss how it differs from the current literature, and discover how common this phenomena is in manyreal-world scenarios. We first consider the classic M/M/1 queue with unreliable service and find some similarities withan M/PH/1 queue but with some noteworthy differences as well. Next, we consider the M/M/1 queue with unreliableservice and a working vacation. In both cases, surprising explicit results can be found including positive recurrenceconditions, the stationary distribution, and in some cases a decomposition of both the queue length and waiting timerandom variables.

Identifying the Influential: Using the PD4SDG database as a proxy for regime formationTime: 2:40-2:55 Applied Mathematics Room: 212

Tu Nguyen Tarleton State UniversityThis project examines the geospatial coverage and network connectivity of entities that have registered voluntary com-mitments to the United Nations Sustainable Development Goals as published in the Partnership Data for the SustainableDevelopment Goals (PD4SDGs) database. We seek to measure support for the sustainable development paradigm. Weassume that the projects registered in PD4SDGs represent good faith efforts to support the values, norms, and beliefsof sustainable development. However, merely registering a project in a database is not sufficient for regime formation.We will present mathematical models that attempt to quantify the efficacy of these projects toward regime formationand identify factors that inhibit it. We first look at the geographical coverage of the projects and the entities con-ducting them. We then perform a network analysis of the topology of the network where two nodes are connected byan edge if they are partners on the same PD4SDGs project. We identify connected components of entities connected(directly or indirectly) through such collaboration. Then, we apply mathematical connectivity metrics such as degreerank, betweenness centrality, cut degree, and pagerank to identify the most important entities in the network.



2019 Texas MAA

Bayesian model selection for informative hypotheses: A comparison of data-based versus defaultencompassing priors


Tom Faulkenberry Tarleton State UniversityBryanna Scheuler Tarleton State University

Though analysis of variance (ANOVA) is the statistical workhorse of the behavioral sciences, the typical action of“rejecting the null” leaves support for a rather diffuse, noninformative hypothesis about the underlying group means. Onthe other hand, informative hypotheses specify equality and/or inequality constraints among the group means, allowingthe researcher to make specific predictions about directions, effect sizes, etc. Within a Bayesian framework, one canconfront observed data with several such models and measure evidence for each. In this talk, we will describe a recentframework for such model comparison (the encompassing prior approach of Klugkist et al., 2005) and discuss some recentsimulation work comparing two methods of prior specification: a data-based prior versus a default prior.

HB 2223 Implementation at SFASUTime: 3:00-3:15 Mathematics Education Room: 108

Sarah Stovall Stephen F. Austin State UniversityWe will give a brief summary of our planning and implementation of co-requisite mathematics courses to meet require-ments of House Bill 2223. We will also report results from Fall 2018 and our plan for going forward.

Are online classes truly better than traditional for most students?Time: 3:00-3:15 Mathematics Education Room: 109

Anna Lurie St. Mary’s UniversityWith technology surrounding us everywhere we turn, and seemingly unending list of possible innovations in the classroom,we take a look at what works and what does not. The results of a pilot study in the Fall 2018 semester of convertingface-to-face classes to a blended/online format are presented. Our study was conducted in a primarily Hispanic-servinginstitution with a big percentage of students in need of financial aid/first generation college. In spite of the wide useof the internet and social media by students, we found that they had considerable difficulties studying online. Theypreferred face-to-face format to boring recorded lectures, resisted online discussions and did not want to solve homeworkproblems in class instead of at home. Their class performance was also worse than that of a face-to-face class. Theresults of similar studies are also presented and discussed.

Bad Math Clubs Borrow...Time: 3:00-3:15 Mathematics Education Room: 112

Sarah Cobb Midwestern State UniversityMarcos Lopez Midwestern State University

Undergraduate math clubs provide a venue for students to encounter a variety of mathematical ideas outside of theircoursework. It can also serve to build a sense of community among students (and faculty) interested in mathematics.This talk will review how the math club at Midwestern State University comes up with activities that promote thesegoals. We will discuss specific resources we have used as well as practices we have found helpful in running our club.


2019 Texas MAA


A Comparison of Methods for Calculations the Basic Reproductive Number for Periodic EpidemicSystems

Time: 3:00-3:15 Applied Mathematics Room: 208

Christopher Mitchell Tarleton StateWhen using mathematics to study epidemics, often the goal is to determine when an infection can invade & persist withina population. The most common way to do so uses threshold quantities called reproductive numbers.An infection’sbasic reproductive number (BRN), typically denoted R0, measures the infection’s initial ability to reproduce in a naivepopulation, & is tied mathematically to the stability of the disease-free equilibrium.Next-generation methods have longbeen used to derive R0 for autonomous continuous-time systems; however many diseases exhibit seasonal behavior.Incorporating seasonality into models may improve accuracy in important ways, but the resulting nonautonomoussystems are much more difficult to analyze. In the literature, two principal methods have been used to derive BRNsfor periodic epidemic models. One, based on time averages is simple to apply but does not always describe the correctthreshold behavior. The other, based on linear operator theory, is more general but also more complicated, & no detailedexplanations of the necessary computations have yet been laid out. This paper reconciles the two methods by laying outan explicit procedure for the second & then identifying conditions (& some important classes of models) under whichthe two methods agree.This allows the use of the simpler method, which yields interpretable closed-form expressions,when appropriate, & illustrates in detail the simplest possible case where they disagree.

Chaos in Generalized Inverse LimitsTime: 3:00-3:15 Geometry and Topology Room: 209

Linda Pham Lamar UniversityWilliam S. Mahavier and W. T. Ingram have greatly contributed to the realm of mathematics through their workconcerning inverse limits, a subset of dynamics and topology. This subject is still relatively new. In fact, Mahavier wasa pioneer of generalized inverse limits not even two decades ago. We will explore the behavior of inverse limits with set-valued functions with the restriction of using only two lines in the unit interval [0,1] x [0,1]. We have considered a varietyof different situations and examples and our methods involve the use of the Mahavier product and the examination ofvarious intersection points and their influence on the dynamics of the system.

Mix Mix RevolutionTime: 3:00-3:15 Applied Mathematics Room: 212

Clayton Boone Tarleton State UniversityWe will take an in-depth look at the ergodicity (ability to fully mix) of billiards with cusps that contain low curvaturesand use specular collisions. We are interested in the mixing rates of these billiards and will use numerical methods toinvestigate their true mixing power. We will also take a step into the world of no-slip billiards and will investigate theergodicity of these billiards under no-slip conditions. Our quest is to become the ultimate mix masters.

High Performance Computations for Random Network Models of Parental Vaccine Acceptance andDisease Spread


Andras Balogh University of Texas Rio Grande ValleyHouseholds with parents and children are connected to each other through different layers of social networks. Childrenmake face-to-face contacts biological (physical) networks and pediatric disease transmission occur. Parents’ decisionsare shaped through social networks through which information and opinions about vaccination diffuse. We establishedstochastic models for two different types of networks: the Erdos-Rényi network model and the Barabási-Albert networkmodel. The models also include birth process. High performance parallel computations were carried out in order tounderstand the mutual influence emerging on the multiplex network model.



2019 Texas MAA

The Co-Requisite Model at TAMUCTime: 3:20-3:35 Mathematics Education Room: 108

Pamela Webster Texas A&M University - CommerceTexas A&M University - Commerce was awarded the CRSM 2018 grant in an effort to support our current co-requisitemodel and efforts to meet the new standards from HB 2223 as related to delivering Developmental Education. Thispresentation will discuss our current implementation, as well as tweaks to the program for Fall 2019. Data, thus far,will be presented, along with lessons learned.

The Datasaurus and Persistent HomologyTime: 3:20-3:35 Geometry and Topology Room: 109

Ryan Jensen Stephen F. Austin State UniversityThe datasaurus dozen is a generalization of Anscombe’s quartet. It is a collection of 12 data-sets in R2, all of whichhave essentially the same statistics (X-mean, Y -mean, X-standard deviation and Y -standard deviation), but whichare visually very different. For example the titular data-set is in the shape of a Tyrannosaurus rex, another in theshape of an oval and another in the shape of an “X.” The datasaurs dozen was designed to urge people to “nevertrust summary statistics alone; always visualize your data.”1 In this talk, we will give a brief introduction to persistenthomology, a tool from algebraic topology which is used to describe the shape of topological spaces. We will then showhow persistent homology can differentiate between the some of the data-sets in the datasaurus dozen. 1https://www.autodeskresearch.com/publications/samestats

Quantitative Consulting: My PIC Math Experience (So Far)Time: 3:20-3:35 Mathematics Education Room: 112

Catie Patterson Austin CollegeStudents of mathematics are often told that there are many ways they can use their skills outside of academia. However,these same students frequently struggle to understand exactly how these skills are used in the “real world.” To givemy students a taste of how mathematics can be used beyond the classroom, I am currently teaching a course throughthe MAA’s Preparation for Industrial Careers in Mathematics (PIC Math) program. In this talk, I will describe myexperience so far with PIC Math. I will also explain the structure of the course, which is centered around semester-long,group projects for a specific client, Meals on Wheels of Tarrant County. Finally, I will describe the kinds of projects mystudents are working on for their client and the skills they are gaining through these projects.

DE and Social Justice: A Cholera Model with Bacterial ReservoirTime: 3:20-3:35 Applied Mathematics Room: 208

Therese Shelton Southwestern UniversityWe present a system of differential equations that models the level of bacteria in the water for an SIRB model. Parametervalues can distinguish severity of infection. We describe how cholera is intimately linked to issues of social justice.

Surfaces containing double conicsTime: 3:20-3:35 Geometry and Topology Room: 209

Fazle Rabby Texas Christian UniversityA conic in P 3 is a nondegenerate hyperplane section of a quadric cone. A double conic in P 3 is a curve that is supportedon a conic with multiplicity two at each points. Such curves have always embedding dimension two and therefore aresingular all through its support. In this talk I will describe degrees and singularities of surfaces containing a doubleconic.


https://www.autodeskresearch.com/publications/samestatshttps://www.autodeskresearch.com/publications/samestats

2019 Texas MAA


New evidence of persistent periodicity in certain no-slip billiards in dimension twoTime: 3:20-3:35 Applied Mathematics Room: 212

Bishwas Ghimire Tarleton State UniversityNo-slip billiards are dynamical systems where linear and angular momentum can be exchanged on collisions at theboundary with total energy conserved. The nature of exchange depends upon the spin and mass distribution of thecolliding particle. We investigate the dynamics and periodicity of no-slip billiards for the 2D plane strip and certainregular polygons. We show that on the 2D strip, for every natural number n, there is a mass distribution such that allnon-degenerate orbits have period 2n. It is known that no-slip equilateral triangles with uniform mass distribution arepersistently periodic (with periods two, three, four, or six) regardless of the starting location, linear velocity, or spin.We present evidence that a no-slip square is persistently periodic with period eight, ten, or twelve when the mass isconcentrated on the rim.

Mathmagic: Self Working Card TricksTime: 3:20-3:35 Algebra and Number Theory Room: 213

Jason Snyder Collin CollegeSelf working card trick are a classification of card tricks that do not require sleight of hand and very little setup. In thistalk/demonstration, I will be performing two maybe three self working card tricks and show, using concepts of numbertheory, why these tricks work. I will also be providing the audience with instructions on how to perform these seeminglymiraculous feats of card magic.

Corequesites and Non-STEM Developmental Mathematics CurriculumTime: 3:40-3:55 Mathematics Education Room: 108

Rebecca Steward Texas A&M University-CommerceThe curriculum and format of the Non-Stem developmental mathematics class will be discussed. The discussion willinclude how the curriculum flows with the college level corequisite class that students are required to take at the sametime through HB 2223. Projects and activities used within the class will be discussed as well.

Unavoidable Minors for HypergraphsTime: 3:40-3:55 Discrete Mathematics Room: 109

Dennis Hall Angelo State UniversityIt is well know that, for any integer n greater than one, there is a number r such that every 2-connected simple graphwith at least r edges has a minor isomorphic to an n-edge cycle or K2,n. This result was extended to matroids byLovasz, Schrijver, and Seymour who proved that every sufficiently large connected matroid has an n-element circuitor an n-element cocircuit as a minor. An analogous result for k-polymatroids has been partially developed, but lacksan explicit description of the minors in all cases except for when k = 2. However, an explicit description is possiblefor 2-connected k-hypergraphs. In this talk, we use results on polymatroids to provide a list of unavoidable minors for2-connected k-hypergraphs.

Advancing Careers in Mathematics through Mentoring & CollaborationTime: 3:40-3:55 Mathematics Education Room: 112

Timothy Huber University of Texas Rio Grande ValleyThe University of Texas Rio Grande Valley is completing the 4th year of a 5-year National Science Foundation S-STEMgrant that provides students in an accelerated BS/MS with financial and academic support, integrated with mentoringand research advisement. This talk will feature key aspects of the program and its role in building a community ofengaged student scholars. The S-STEM dovetails with another NSF initiative called IMPACT (Increasing MathematicsPotential across Texas). IMPACT involves synchronous teaching of advanced math courses at UTRGV and UT Dallas.Students at each institution attend active learning sessions linked through videoconferencing and connect in personeach summer with industry leaders in Dallas. The combined initiatives significantly increase student access to doctoralprograms and industry careers in mathematics.

99th Annual Meeting of the Texas Section o

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