Table Of ContentAbstracts of Papers
Presented in
Washington, D.C.
Abstracts of Papers
Presented at
MathFest 2015
Washington, D.C.
August 5 – 8, 2015
Published and Distributed by
The MathematicalAssociation of America
Contents
InvitedAddresses 1
EarleRaymondHedrickLectureSeries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
HendrickLecture1
Wednesday,August5,9:30AM-10:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
HendrickLecture2
Friday,August7,9:30AM-10:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
HendrickLecture3
Saturday,August8,9:30AM-10:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
MAACentennialLectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Lecture1:Replicators,Transformers,andRobotSwarms:ScienceFictionthroughGeometricAlgorithms
Wednesday,August5,8:20AM-9:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Lecture2:NetworkScience:FromtheOnlineWorldtoCancerGenomics
Wednesday,August5,10:30AM-11:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . 1
Lecture3:MathematicsforArtInvestigation
Thursday,August6,8:30AM-9:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Lecture4:TheRoleandFunctionofMathematicalModelsinInterdisciplinaryMentorshipthroughResearch:
LessonsfromtheWorldofEpidemics
Thursday,August5,10:30AM-11:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Lecture 5:CSHPM Kenneth O. May Lecture “We Are Evidentlyon theVerge ofImportantSteps Forward”:
TheAmericanMathematicalCommunity,1915–1950
Friday,August7,10:30AM-11:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Lecture6:RecentResultsTowardtheBirchandSwinnerton-DyerConjecture
Saturday,August8,10:30AM-11:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
AMS-MAAJointInvitedAddress
Thursday,August6,9:30AM-10:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
MAAJamesR.C.LeitzelLecture
Saturday,August8,8:30AM-9:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
AWM-MAAEttaZ.FalconerLecture
Friday,August7,8:30AM-9:20AM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
MAAChanStanekLectureforStudents
Wednesday,August5,1:00PM-1:50PM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
PiMuEpsilonJ.SutherlandFrameLecture
Friday,August7,8:00PM-8:50PM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
NAMDavidHaroldBlackwellLecture
Friday,August7,1:00PM-1:50PM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
AlderAwards 3
AlderAwards
Friday,August7,2:00PM-3:20PM,Salon2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
InvitedPaperSessions 4
MAAInvitedPaperSession:GenerationsofMonthlyGems
Wednesday,August5,1:00PM-3:50PM,Salon1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
MAAInvitedPaperSession:TheNon-Traditional“TraditionalNSAMathematician”
Wednesday,August5,1:00PM-3:45PM,DelawareB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
iii
iv Contents
MAAInvitedPaperSession:ImprovingAccesstoMathematicalModelingResearch
Thursday,August6,1:00PM-4:20PM,DelawareB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
MAAInvitedPaperSession:AlgebraicStructuresMotivatedbyKnotTheory
Friday,August7,9:00AM-11:20AMand1:00PM-5:00PM,DelawareA . . . . . . . . . . . . . . . . . . 6
MAAInvitedPaperSession:ConcreteComputationsinAlgebraandAlgebraicGeometry
Friday,August7,1:00PM-3:20PM,DelawareB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
AMS-MAAInvitedPaperSession:TheArithmeticoftheSpheres
Thursday,August6,1:00PM-3:50PM,DelawareA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
SpecialInvitedSession:TheGeometryofTriangles
Saturday,August8,1:00PM-2:50PM,Salon1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
SpecialSession:“NotesofaNativeSon”:TheLegacyofDr.AbdulalimA.Shabazz(1927–2014)
Saturday,August8,1:00PM-4:50PM,DelawareB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Themed Contributed PaperSessions 9
TCPS1A-HistoryofMathematics
Wednesday,August5,10:30AM-11:55AM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
TCPS1B-HistoryofMathematics
Wednesday,August5,10:30AM-11:55AM,Washington5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
TCPS1C-HistoryandPhilosophyofMathematics
Wednesday,August5,1:00PM-2:55PM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
TCPS1D-HistoryandPhilosophyofMathematics
Wednesday,August5,1:30PM-3:55PM,Washington5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
TCPS1E-TheMathematicsofEuler
Wednesday,August5,3:00PM-5:55PM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
TCPS1F-SpecialSessioninMemoryofJackieStedall
Thursday,August6,8:30AM-11:25AM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
TCPS1G-HistoryandPhilosophyofMathematics
Thursday,August6,1:00PM-2:25PM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
TCPS1H-HistoryandPhilosophyofMathematics
Thursday,August6,1:00PM-2:25PM,Washington5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
TCPS1J-SpecialSessiononPhilosophyofMathematics
Thursday,August6,2:30PM-4:55PM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
TCPS1K-SpecialSessiononMathematicalCommunities
Friday,August7,8:00AM-10:25AM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
TCPS1M-SpecialSessioninHonorofKarenParshall
Friday,August7,2:00PM-4:55PM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
TCPS1N-HistoryandPhilosophyofMathematics
Saturday,August8,8:30AM-11:55AM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
TCPS1P-HistoryandPhilosophyofMathematics
Saturday,August8,8:30AM-11:55AM,Washington5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
TCPS1Q-SpecialSessioninMemoryofIvorGrattan-Guinness
Saturday,August8,1:00PM-3:25PM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
TCPS1R-HistoryofMathematics
Saturday,August8,3:30PM-5:25PM,Washington4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
TCPS2A-TheContributionsofWomentoMathematics:100YearsandCounting
Friday,August7,1:00PM-3:55PM,Washington2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
TCPS2B-TheContributionsofWomentoMathematics:100YearsandCounting
Saturday,August8,1:00PM-3:15PM,Washington2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
TCPS3-MathCircleProblemsInvolvingtheNumber100inHonoroftheMAA’s100thAnniversary
Friday,August7,8:30AM-11:05AM,Washington6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
TCPS4-UndergraduateResearchActivitiesinMathematicalandComputationalBiology
Friday,August7,1:20PM-4:15PM,Washington5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
TCPS5A-RecreationalMathematics:NewProblemsandNewSolutions
Friday,August7,1:00PM-4:55PM,Washington1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Contents v
TCPS5B-RecreationalMathematics:NewProblemsandNewSolutions
Saturday,August8,1:00PM-3:15PM,Washington1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
TCPS6A-MathematicsandArt
Wednesday,August5,1:00PM-4:55PM,MarylandA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
TCPS6B-MathematicsandArt
Thursday,August6,8:50AM-11:25AM,MarylandA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
TCPS7-FinancialMathematics
Wednesday,August5,1:00PM-2:35PM,Washington6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
TCPS8-MathematicsinVideoGames
Saturday,August8,3:00PM-4:55PM,Washington3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
TCPS9-WhatCanaMathematicianDowitha3DPrinter?
Saturday,August8,1:00PM-4:55PM,VirginiaB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
TCPS10-TheScholarshipofTeachingandLearninginCollegiateMathematics
Wednesday,August5,1:00PM-5:35PM,Washington2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
TCPS11A-CultivatingCriticalThinkingthroughActiveLearninginMathematics
Thursday,August6,8:30AM-11:25AM,Washington1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
TCPS11B-CultivatingCriticalThinkingthroughActiveLearninginMathematics
Thursday,August6,1:00PM-5:15PM,Washington1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
TCPS12-ImprovingUndergraduateMathWriting
Wednesday,August5,1:00PM-5:15PM,VirginiaA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
TCPS13-SuccessfulSTEMProgramsforElementaryEducationMajors
Thursday,August6,1:00PM-3:15PM,Washington2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
TCPS 14- Projects, Applicationsand Demonstrationsto Enhance a Numerical Analysis orComputationalMathe-
maticsCourse
Saturday,August8,1:00PM-2:35PM,Washington3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
TCPS15-DemocratizingAccesstoAuthenticMathematicalActivity
Friday,August7,1:20PM-3:35PM,MarylandA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
TCPS16-CurriculumDevelopmenttoSupportFirstYearGeneralEducationMathematicsStudents
Wednesday,August5,1:00PM-3:35PM,Washington3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
TCPS17-CurriculumandCourseDevelopmenttoSupportFirstYearSTEMStudents
Friday,August7,1:00PM-2:55PM,Washington3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
TCPS18-UsingModelingforTeachingDifferentialEquations:Before,During,After
Saturday,August8,1:00PM-4:35PM,VirginiaA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
TCPS19A-InnovativeApproachesintheCalculusSequence
Friday,August7,1:00PM-3:35PM,Washington6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
TCPS19B-InnovativeApproachesintheCalculusSequence
Saturday,August8,1:00PM-3:35PM,Washington6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
TCPS20-Evidence-BasedApproachestotheMathematicalPreparationofSecondaryTeachers
Wednesday,August5,1:00PM-1:55PM,Washington1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
TCPS21-ShowMeGeometry:GeometrySoftwareandTabletDemonstrations
Wednesday,August5,1:00PM-2:55PM,VirginiaC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
GeneralContributed PaperSessions 36
AlgebraandLinearAlgebra
Wednesday,August5,1:00PM-3:40PM,VirginiaB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
AnalysisandOther
Friday,August7,8:30AM-11:10AM,Salon1,BalconyB . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
AppliedMathematics
Thursday,August6,1:00PM-4:55PM,Washington3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Geometry
Thursday,August6,1:00PM-4:40PM,Salon1,BalconyB . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
GraphTheory
Thursday,August6,8:30AM-11:25AM,Washington3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
HistoryorPhilosophyofMathematics
Thursday,August6,9:15AM-11:25AM,Salon1,BalconyA . . . . . . . . . . . . . . . . . . . . . . . . . . 40
vi Contents
InterdisciplinaryTopicsinMathematicsandModelingorApplications
Friday,August7,1:00PM-4:25PM,MarylandB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
MathematicsandTechnology
Saturday,August8,8:45AM-11:25AM,Salon1,BalconyA . . . . . . . . . . . . . . . . . . . . . . . . . . 42
MentoringandOutreach
Thursday,August6,8:15AM-11:10AM,MarylandB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
NumberTheoryandLogicorFoundations
Saturday,August8,1:00PM-4:55PM,Salon1,BalconyB . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
ProbabilityorStatistics
Friday,August7,9:15AM-11:25AM,MarylandB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
TeachingorLearningAdvancedMathematics
Friday,August7,1:00PM-3:10PM,Salon1,BalconyB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
TeachingorLearningCalculus
Thursday,August6,9:15AM-11:25AM,Salon1,BalconyB . . . . . . . . . . . . . . . . . . . . . . . . . . 46
TeachingorLearningDevelopmentalMathematicsandAssessment
Friday,August7,9:15AM-11:25AM,Salon1,BalconyA . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
TeachingorLearningIntroductoryMathematics,PartA
Wednesday,August5,1:00PM-2:55PM,MarylandB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
TeachingorLearningIntroductoryMathematics,PartB
Thursday,August6,1:00PM-4:40PM,MarylandB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Graduate StudentSession 50
GreatTalksforaGeneralAudience:CoachedPresentationsbyGraduateStudents,PartA
Saturday,August8,1:00PM-5:00PM,VirginiaC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
GreatTalksforaGeneralAudience:CoachedPresentationsbyGraduateStudents,PartB
Saturday,August8,1:00PM-5:00PM,MarylandC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
GreatTalksforaGeneralAudience:CoachedPresentationsbyGraduateStudents,PartC
Saturday,August8,1:00PM-5:00PM,Salon1Salon1,BalconyA . . . . . . . . . . . . . . . . . . . . . . . 51
PosterFest2015 52
APosterSessionofScholarshipbyEarlyCareerMathematiciansandGraduateStudents
Friday,August7,3:30PM-5:00PM,ExhibitHallA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
HighlightsfromAWMStudentChapters
Wednesday,August5,3:30PM-5:00PM,MarriottFoyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
AbstractsAlphabetizedbyAuthor’sLastName 56
A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Q. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
U. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Contents vii
V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
IndexofSpeakers 196
Invited Addresses
Earle Raymond Hedrick Lecture Series
KarenSmith,UniversityofMichigan
Wednesday,August5,9:30AM-10:20AM, Salon2/3
HedrickLecture1
Friday,August7,9:30AM-10:20AM, Salon2/3
HedrickLecture2
Saturday,August8,9:30AM-10:20AM, Salon2/3
HedrickLecture3
MAA Centennial Lectures
Wednesday,August5,8:20AM-9:20AM, Salon2/3
MAA CentennialLecture 1: Replicators, Transformers, and Robot Swarms: Science FictionthroughGeo-
metricAlgorithms
ErikDemaine,MassachusettsInstituteofTechnology
Wednesday,August5,10:30AM-11:20AM,Salon2/3
MAACentennialLecture2:NetworkScience:FromtheOnlineWorldtoCancerGenomics
JenniferChayes,MicrosoftResearch
Thursday,August6,8:30AM-9:20AM,Salon2/3
MAACentennialLecture3:MathematicsforArtInvestigation
IngridDaubechies,DukeUniversity
Thursday,August5,10:30AM-11:20AM, Salon2/3
MAACentennialLecture4:TheRoleandFunctionofMathematicalModelsinInterdisciplinaryMentorship
throughResearch:LessonsfromtheWorldofEpidemics
CarlosCastillo-Chavez,ArizonaStateUniversity
Friday,August7,10:30AM-11:20AM,Salon2/3
MAACentennialLecture5:CSHPMKennethO.MayLecture“WeAreEvidentlyontheVergeofImportant
StepsForward”:TheAmericanMathematicalCommunity,1915–1950
KarenParshall,UniversityofVirginia
Saturday,August8,10:30AM-11:20AM,Salon2/3
MAACentennialLecture6:RecentResultsTowardtheBirchandSwinnerton-DyerConjecture
ManjulBhargava,PrincetonUniversity
1
Description:MAA Invited Paper Session: Algebraic Structures Motivated by Knot Theory. Friday . TCPS 3 - Math Circle Problems Involving the Number 100 in Honor of the MAA's 100th Anniversary TCPS 14 - Projects, Applications and Demonstrations to Enhance a Numerical Analysis or Computational Mathe-.
