Mathematical themes in a first-year seminar

379 Pages·2021·7.012 MB·English

by  Jennifer Lynne Bowen (editor), Mark Kozek (editor), Pamela B. Pierce (editor), (Professor of mathematics) Jennifer Schaefer (editor)

Mathematical Themes
in a First-Year Seminar
(cid:13)c 2021by
TheMathematicalAssociationofAmerica(Incorporated)
LibraryofCongressControlNumber:2021937676
PrintISBN978-0-88385-210-1
ElectronicISBN978-1-61444-327-8
PrintedintheUnitedStatesofAmerica
CurrentPrinting(lastdigit):
10987654321
Mathematical Themes
in a First-Year Seminar
Edited by
Jennifer Schaefer
Dickinson College
Jennifer Bowen
The College of Wooster
Mark Kozek
Whittier College
and
Pamela Pierce
The College of Wooster
PublishedandDistributedby
TheMathematicalAssociationofAmerica
The MAA Notes Series, started in 1982, addresses a broad range of topics and themes of interest to all who are involved with
undergraduatemathematics.Thevolumesinthisseriesarereadable,informative,anduseful,andhelpthemathematicalcommunity
keepupwithdevelopmentsofimportancetomathematics.
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SusanG.Staples,Chair
NotesEditorialBoard
ElizabethW.McMahon,Editor
CristaL.Arangala
VinodhKumarChellamuthu
SuzanneHamon
HeatherA.Hulett
DavidR.Mazur
EileenMurray
LisaRezac
JohnM.Zobitz
MAANotes
14. MathematicalWriting,byDonaldE.Knuth,TracyLarrabee,andPaulM.Roberts.
16. UsingWritingtoTeachMathematics,AndrewSterrett,Editor.
17. PrimingtheCalculusPump:InnovationsandResources,CommitteeonCalculusReformandtheFirstTwoYears,asubcomit-
teeoftheCommitteeontheUndergraduatePrograminMathematics,ThomasW.Tucker,Editor.
18. ModelsforUndergraduateResearchinMathematics,LesterSenechal,Editor.
19. VisualizationinTeachingandLearningMathematics,CommitteeonComputersinMathematicsEducation,SteveCunning-
hamandWalterS.Zimmermann,Editors.
20. TheLaboratoryApproachtoTeachingCalculus,L.CarlLeinbachetal.,Editors.
21. PerspectivesonContemporaryStatistics,DavidC.HoaglinandDavidS.Moore,Editors.
22. HeedingtheCallforChange:SuggestionsforCurricularAction,LynnA.Steen,Editor.
24. SymbolicComputationinUndergraduateMathematicsEducation,ZavenA.Karian,Editor.
25. TheConceptofFunction:AspectsofEpistemologyandPedagogy,GuershonHarelandEdDubinsky,Editors.
26. StatisticsfortheTwenty-FirstCentury,FlorenceandSheldonGordon,Editors.
27. ResourcesforCalculusCollection,Volume1:LearningbyDiscovery:ALabManualforCalculus,AnitaE.Solow,Editor.
28. ResourcesforCalculusCollection,Volume2:CalculusProblemsforaNewCentury,RobertFraga,Editor.
29. ResourcesforCalculusCollection,Volume3:ApplicationsofCalculus,PhilipStraffin,Editor.
30. ResourcesforCalculusCollection,Volume4:ProblemsforStudentInvestigation,MichaelB.JacksonandJohnR.Ramsay,
Editors.
31. ResourcesforCalculusCollection,Volume5:ReadingsforCalculus,UnderwoodDudley,Editor.
32. EssaysinHumanisticMathematics,AlvinWhite,Editor.
33. ResearchIssuesinUndergraduateMathematicsLearning:PreliminaryAnalysesandResults,JamesJ.KaputandEdDubinsky,
Editors.
34. InEves’Circles,JobyMiloAnthony,Editor.
35. You’retheProfessor,WhatNext?IdeasandResourcesforPreparingCollegeTeachers,TheCommitteeonPreparationfor
CollegeTeaching,BettyeAnneCase,Editor.
36. PreparingforaNewCalculus:ConferenceProceedings,AnitaE.Solow,Editor.
37. APracticalGuidetoCooperativeLearninginCollegiateMathematics,NancyL.Hagelgans,BarbaraE.Reynolds,SDS,Keith
Schwingendorf,DragaVidakovic,EdDubinsky,MazenShahin,G.JosephWimbish,Jr.
38. ModelsThatWork:CaseStudiesinEffectiveUndergraduateMathematicsPrograms,AlanC.Tucker,Editor.
39. Calculus:TheDynamicsofChange,CUPMSubcommitteeonCalculusReformandtheFirstTwoYears,A.WayneRoberts,
Editor.
40. VitaMathematica:HistoricalResearchandIntegrationwithTeaching,RonaldCalinger,Editor.
41. GeometryTurnedOn:DynamicSoftwareinLearning,Teaching,andResearch,JamesR.KingandDorisSchattschneider,
Editors.
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WilliamWatkins,Editors.
43. StudentAssessmentinCalculus:AReportoftheNSFWorkingGrouponAssessmentinCalculus,AlanSchoenfeld,Editor.
44. ReadingsinCooperativeLearningforUndergraduateMathematics,EdDubinsky,DavidMathews,andBarbaraE.Reynolds,
Editors.
45. ConfrontingtheCoreCurriculum:ConsideringChangeintheUndergraduateMathematicsMajor,JohnA.Dossey,Editor.
46. WomeninMathematics:ScalingtheHeights,DeborahNolan,Editor.
47. ExemplaryProgramsinIntroductoryCollegeMathematics:InnovativeProgramsUsingTechnology,SusanLenker,Editor.
48. WritingintheTeachingandLearningofMathematics,JohnMeierandThomasRishel.
49. AssessmentPracticesinUndergraduateMathematics,BonnieGold,Editor.
50. RevolutionsinDifferentialEquations:ExploringODEswithModernTechnology,MichaelJ.Kallaher,Editor.
51. UsingHistorytoTeachMathematics:AnInternationalPerspective,VictorJ.Katz,Editor.
52. TeachingStatistics:ResourcesforUndergraduateInstructors,ThomasL.Moore,Editor.
53. GeometryatWork:PapersinAppliedGeometry,CatherineA.Gorini,Editor.
54. TeachingFirst:AGuideforNewMathematicians,ThomasW.Rishel.
55. Cooperative Learning in Undergraduate Mathematics: Issues That Matter and Strategies That Work, Elizabeth C. Rogers,
BarbaraE.Reynolds,NeilA.Davidson,andAnthonyD.Thomas,Editors.
56. ChangingCalculus:AReportonEvaluationEffortsandNationalImpactfrom1988to1998,SusanL.Ganter.
57. LearningtoTeachandTeachingtoLearnMathematics:ResourcesforProfessionalDevelopment,MatthewDelongandDale
Winter.
58. Fractals,Graphics,andMathematicsEducation,BenoitMandelbrotandMichaelFrame,Editors.
59. Linear Algebra Gems: Assets for Undergraduate Mathematics, David Carlson, Charles R. Johnson, David C. Lay, and A.
DuanePorter,Editors.
60. InnovationsinTeachingAbstractAlgebra,AllenC.HibbardandEllenJ.Maycock,Editors.
61. ChangingCoreMathematics,ChrisArneyandDonaldSmall,Editors.
62. AchievingQuantitativeLiteracy:AnUrgentChallengeforHigherEducation,LynnArthurSteen.
64. LeadingtheMathematicalSciencesDepartment:AResourceforChairs,TinaH.Straley,MarciaP.Sward,andJonW.Scott,
Editors.
65. InnovationsinTeachingStatistics,JoanB.Garfield,Editor.
66. MathematicsinServicetotheCommunity:Conceptsandmodelsforservice-learninginthemathematicalsciences,Charles
R.Hadlock,Editor.
67. InnovativeApproachestoUndergraduateMathematicsCoursesBeyondCalculus,RichardJ.Maher,Editor.
68. FromCalculustoComputers:Usingthelast200yearsofmathematicshistoryintheclassroom,AmyShell-GellaschandDick
Jardine,Editors.
69. AFreshStartforCollegiateMathematics:RethinkingtheCoursesbelowCalculus,NancyBaxterHastings,Editor.
70. CurrentPracticesinQuantitativeLiteracy,RickGillman,Editor.
71. WarStoriesfromAppliedMath:UndergraduateConsultancyProjects,RobertFraga,Editor.
72. HandsOnHistory:AResourceforTeachingMathematics,AmyShell-Gellasch,Editor.
73. Making the Connection: Research and Teaching in Undergraduate Mathematics Education, Marilyn P. Carlson and Chris
Rasmussen,Editors.
74. ResourcesforTeachingDiscreteMathematics:ClassroomProjects,HistoryModules,andArticles,BrianHopkins,Editor.
75. TheMooreMethod:APathwaytoLearner-CenteredInstruction,CharlesA.Coppin,W.TedMahavier,E.LeeMay,andG.
EdgarParker.
76. TheBeautyofFractals:SixDifferentViews,DennyGulickandJonScott,Editors.
77. Mathematical Time Capsules: Historical Modules for the Mathematics Classroom, Dick Jardine and Amy Shell-Gellasch,
Editors.
78. RecentDevelopmentsonIntroducingaHistoricalDimensioninMathematicsEducation,VictorJ.KatzandCostasTzanakis,
Editors.
79. TeachingMathematicswithClassroomVoting:WithandWithoutClickers,KellyClineandHollyZullo,Editors.
80. ResourcesforPreparingMiddleSchoolMathematicsTeachers,CherylBeaver,LaurieBurton,MariaFung,andKlayKruczek,
Editors.
81. UndergraduateMathematicsfortheLifeSciences:Models,Processes,andDirections,GlennLedder,JennaP.Carpenter,and
TimothyD.Comar,Editors.
82. ApplicationsofMathematicsinEconomics,WarrenPage,Editor.
83. DoingtheScholarshipofTeachingandLearninginMathematics,JacquelineM.DewarandCurtisD.Bennett,Editors.
84. InsightsandRecommendationsfromtheMAANationalStudyofCollegeCalculus,DavidBressoud,VilmaMesa,andChris
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Simons,Editors.
87. TheCoursesofHistory:IdeasforDevelopingaHistoryofMathematicsCourse,AmyShell-GellaschandDickJardine,Editors.
88. Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education, Luke Tunstall, Gizem Karaali, and
VictorPiercey,Editors.
89. MAA Instructional Practices Guide, Martha L. Abell, Linda Braddy, Doug Ensley, Lewis Ludwig, Hortensia Soto, Project
LeadershipTeam.
90. WhatCouldTheyPossiblyBeThinking!?!Understandingyourcollegemathstudents,DaveKungandNatashaSpeer.
91. MathematicalThemesinaFirst-YearSeminar,JenniferSchaefer,JenniferBowen,MarkKozek,andPamelaPierce,Editors.
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Contents
QuickReferenceGuide ix
Introduction xiii
AdviceforFirst-YearSeminarInstructors xvii
I Cryptography 1
1 DevelopingResearch,Writing,andSpeakingSkillsThroughaSeminarinCryptology,
RandallD.HelmstutlerandKeithE.Mellinger 3
2 SecrecyandSecurity,LiviaHummel 11
II Gambling,GameShows,andGameTheory 21
3 TheMathematicsandImpactsofGambling,LesleyW.Wiglesworth 23
4 WheelsandDeals:AFirst-YearSeminarBasedonGameShows,AlisonMarr 31
5 GameTheoryinPopularCulture:AFirst-YearWritingSeminar,JenniferFirkinsNordstrom 41
6 AFirst-YearSeminaronDecisionMaking,PamelaB.Pierce 53
7 “ISignedUpForAFirst-YearSeminar,ButIGotAMathClass”:TheChallengesofChance,
MarkBollman 61
III MathematicalModelingandData 69
8 MeasuringSustainability,AmandaBeecher 71
9 AnInterdisciplinaryCoursetoEngageFirst-YearStudentsinBiomathematicalResearch,
ClintonK.MeyerandHeidiBerger 79
10 AFirst-YearSeminarExploringtheMathematicsofSportsRankings,JasonParsley 87
11 IntroducingGraphTheoryinaFirst-YearSeminaronNetworkScience,BrittneyMiller 99
IV MathematicsinPolitics,Equity,andSocialJustice 111
12 MathandPolitics:AnInterdisciplinaryFirst-YearSeminar,JacquelineAnderson 113
13 Mathematopia:AHumanisticMath-ThemedFreshmanSeminar,MichaelP.Saclolo 123
14 AFirst-SeminarCourseontheMathematicsofEquity,KarenE.Clark 133
vii
viii Contents
15 ExploringImmigrationThroughStatisticsandExperientialLearning,KathrynCerrone 141
16 ACivilRight:MathAnxietytoMathLiteracy,GretchenWilkeWhipple 149
V MathematicsinPopCultureandHistory 163
17 MathematicalIdentities:DivergingfromtheStereotypes,JenniferB.Schaefer 165
18 MathematicsandthePursuitofHappiness,MeghanSleezer 175
19 MathinPopCulture:AFirst-YearWritingSeminaronMathematics,MarkKozek 185
20 AFirst-YearSeminaronSTEMBreakthroughsandControversies,SarahJ.Greenwald 195
21 UncoveringtheHiddenFigures,CynthiaFarthing 207
22 Culture,Science,andMathematicsinthepre-ColumbianAmericas,XimenaCatepilla´n 219
VI Mathematics,Art,andtheNaturalWorld 227
23 TheArtofMathematicsasaFirst-YearSeminar,DebraL.Hydorn 229
24 TheMagicofChaos,RolandMinton 239
25 AFirst-YearSeminaronSymmetry,fromaMathematicalandInterdisciplinaryPointofView,
TamaraJ.Lakins 249
26 TheMathematicsofChaosasaFirst-YearSeminar,SuzanneSumner 259
27 The Intersection of Mathematics, Art, Technology, and Teaching the Value of a Liberal Education,
CherylJ.McAllisterandLaurieWernOvermann 269
VII ProofsandProblemSolving 283
28 MathWithoutMath:UnravelingRiddlesandSolvingProblems,RyanHigginbottom 285
29 MathematicsasaCreativeArt:ASeven-WeekSeminar,JenniferEarlesSzydlik 293
30 AWriting-IntensiveFYSCourseonRecreationalMathematics,EnriqueTrevin˜o 301
31 TechnicalWriting:AMathematicalApproach,NathanShank 307
VIII QuantitativeLiteracy 319
32 NineOutofTenSeniorsRecommendthisFirst-YearSeminar:StatisticsintheRealWorld,
JohannaHardin 321
33 AFirst-YearSeminaronLies,DamnedLies,andStatistics,AaronM.Montgomery 327
34 WhyDoWeChoosetoDoWhatWeDo?UsingStatisticstoInvestigateOurActions,
TriciaMuldoonBrown 335
35 TheSignalandtheNoise:WhyNumeracyReallyMatters,JenniferR.Bowen 345
36 MyHometownExplorationUnitinaFirst-YearSeminar,MariaG.Fung 353
Quick Reference Guide
QuickReferenceGuide
U:university;LA:smallliberalartscollege
AssessmentTools ClassActivities CourseSchedule andGuestLectures LinkedCourse Projects ReadingsandFilms StudentHelpers WritingAssignments
s
p
Tri
d
el
Fi
1:DevelopingResearch,Writing,andSpeaking X X X X
SkillsThroughaSeminarinCryptology
RandallHelmstutlerandKeithMellingerU
2:SecrecyandSecurity X X X X X X
LiviaHummelU
3:TheMathematicsandImpactsofGambling X X X X X
LesleyWiglesworthLA
4:WheelsandDeals:AFirst-YearSeminarBased X X X X X
onGameShows
AlisonMarrLA
5:GameTheoryinPopularCulture:AFirst-Year X X X X
WritingSeminar
JenniferFirkinsNordstromLA
6:AFirst-YearSeminaronDecisionMaking X X X X
PamelaPierceLA
7:“ISignedUpForaFirst-YearSeminar,ButIGot X X X
aMathClass”:TheChallengesofChance
MarkBollmanLA
8:MeasuringSustainability X X X X
AmandaBeecherU
9:AnInterdisciplinaryCoursetoEngageFirst-Year X X X
StudentsinBiomathematicalResearch
HeidiBergerandClintonK.MeyerLA
10:AFirst-YearSeminarExploringtheMathematics X X X X
ofSportsRankings
JasonParsleyU
ix