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MathematicalAssociationofAmericaFall2019JointMeetingofthe
NewJerseyandMetroNewYorkSections
EssexCountyCollege303UniversityAvenue
Newark,NJ
Saturday,October26,2019
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MathematicalAssociationofAmericaNewJerseyandNewYorkMetroSections,Fall2019MeetingProgram
AlleventstakeplaceintheMegastructureBuilding8:30–9:30 RegistrationandCoffee;ReceptionArea9:00–1:30 BookExhibits;ReceptionArea9:30–9:40 WelcomebyDr.DenisBlackmore,ProfessorNJITand
RecipientofMAATeachingExcellenceAward;SieglerHall9:40–10:30 GroupLocomotioninFluids,JunZhang,NYU.Presider:
SatyanandSingh,CUNY;SieglerHall10:30–10:45 MAA-NJBusinessMeeting;room211510:45–11:10 IntermissionandBookExhibits;ReceptionArea11:10–12:00 CountingCurves:TalesfromtheEnumerativeCrypt, Susan
JaneColley,OberlinCollege. Presider:DawnNelson,SaintPeter’sUniversity;SieglerHall
12:00–1:30 Lunch;rooms2101B,2110,2111,2113,and21151:30–2:45 Workshop:EncouragingCreativityinMathematics,
PresentedbyMikaMunakata,AshwinVaidya,andCeireMonahan,MontclairStateUniversity;room4135
1:30–3:05 ContributedPaperSessions;rooms2101B,2110,2111,2113,and2115
3:00–3:30 IntermissionandRefreshments;ReceptionArea(Silentauctionbiddingendsat3:30)
3:35–4:25 Unsolved(andSolved)ProblemsFromTheOn-LineEncyclopediaofIntegerSequences, NeilJ.A.Sloane,RutgersandtheOEISFoundation.Presider:DavidNacin,WilliamPatersonUniversity;SieglerHall
4:30–5:00 PrizesandAwards;Doorprizesandsilentauctionwinners(mustbepresenttowin);SieglerHall
5:30 DinnerHonoringSpeakers,SpanishPavillion,31HarrisonAve.,Harrison,NJ07029
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AbstractsandBiographiesofSpeakers
GroupLocomotioninFluidsJunZhang
NYUCourantInstituteofMathematicalSciencesUnderstandinghowanimalsmoveisveryimportanttousaswetrytocomprehendtheanimalkingdomandbeinspiredbytheirstrategieswhenmovingabout.Subjecttophysicallaws,animallocomotiongaitsmaylookvastlydiverseacrossmanyspeciesbutmostofthemdosharesomeverycommonfeatures.Forexample,birdsflaptheirwingsintheairandfishflapcaudalfins(tail)inwater.Suchflappingmotionsandtheirinteractionwiththesurroundingfluidshasbeenacentralprobleminfluiddynamics.Inthistalk,Iwilldiscussafewsimpleexperimentsaswestudyhowanimalsmoveinwaterandair.Throughthesestudies,thefamiliarphenomenaofanimalswimmingandflyingmayofferafewsurprises.
JunZhanggraduatedfromWuhanUniversityinChinabeforeheearnedhisPh.D.inPhysicsattheUniversityofCopenhagen,Denmark.AfterapostdoctoralexperienceinbiophysicsatRockefellerUniversity,hecametoNYUandstartedbuildingtheAppliedMathLabattheCourantInstituteandlaterhebecameafacultymemberthere.Hisresearchinteresthasbeeninthefieldofphysicsoffluidsandcomplexsystems,whichincludesbiomechanicsorbio-locomotion(organismalswimmingandflying,andwalking),geophysicalfluids(thermalconvection,continentaldynamics,anderosion),solid-on-solidfriction,urbanheat-islandeffect,andself-organizationphenomenaatmanydifferentscales.
CountingCurves:TalesfromtheEnumerativeCryptSusanJaneColley
DepartmentofMathematics,OberlinCollegeEditorofTheAmericanMathematicalMonthly
WewillconsidertheSteinerproblem(1848)offiveconics:todeterminehowmanyconicsaresimultaneouslytangenttofiveothers.Wewillreviewsomeofthehistorysurroundingthisproblemandsomeoftheingredientsneededtosolveit.Finally,we’llspeedaheadtomoderntimesandbrieflysketchjointworkwithGaryKennedy(OhioState)andLarsErnström(Ericsson)thatusesmathematicaltechniquesinspiredbyideasintheoreticalstringtheorytoaddresssomeanalogousquestionsabout“higher-order”contactofplanecurves.
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SusanColleyistheAndrewandPaulineDelaneyProfessorofMathematicsatOberlinCollegeandcurrentlytheEditorofTheAmericanMathematicalMonthly.ShereceivedherB.S.andPh.D.degreesfromMITinthepreviouscentury.Herresearchinterestslieinalgebraicgeometryandrelatedareas;studentsmayknowherfromhertextbookVectorCalculus,4thed.(Pearson,2012)andcurseheraccordingly.
Unsolved(andSolved)ProblemsFromTheOn-LineEncyclopediaofIntegerSequences
NeilJ.A.SloaneRutgersUniversityandTheOEISFoundation
TheOEIScontains320,000sequencesandhasbeencitedby8000articles.Buteveryfewdaysanewsequenceissubmittedwhichmakesonewanttodropeverythingtotrytosolveit.Hereisacollectionofrecentandnot-so-recentexamples,mostlystillunsolved,arisingfromalgebra,geometry,andnumbertheory.Warning:thistalkmaycauseinsomnia.
NeilJ.A.SloanereceivedaPh.D.degreeinElectricalEngineeringfromCornellUniversityin1967andworkedatAT&TBellLabsuntilhisretirementin2012.HeisanAT&TFellowandaFellowoftheLearnedSocietyofWales,theAMS,andtheIEEE.Heistheauthorofbooksoncodingtheory,spherepacking,optics,integersequences,orthogonalarrays,androckclimbing.OnGoogleScholarhehas54,000citationsandanh-indexof81.HisrecentvideosonYouTubehavebeenviewedthreemilliontimes.
Workshop:EncouragingCreativityinMathematics:TheRethinkingofaGeneralEducationMathematicsCoursePresentedbyDr.MikaMunakata,Dr.AshwinVaidya,andCeire
Monahan,MontclairStateUniversityWhatiscreativity?HowisitrelevanttoundergraduateSTEMeducation?TheCreativityinScienceandMathematicsprojectatMontclairStateUniversity,fundedbytheNSF,challengesthecommonnotionthatcreativityisrelegatedtotheartisticrealm.Inanefforttochallengetraditional,lecture-styleinstructionandtochallengestudents’preconceptionsaboutthe
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natureofscienceandmathematics,wehavedevelopedcoursemodulesforundergraduateSTEMcoursesthatembracecreativeapproachestobothtraditionalandunusualquestions.Throughthesemodules,studentsarechallengedtoaskquestions,testassumptions,andtakeonnon-routineapproaches.Aspartoftheproject,wecollectedandanalyzedbothquantitativeandqualitativedatafromthestudentsandinstructors.ResultsfromYear1indicatethatthecoursemodulesandadaptedinstructiondidhaveanimpactonstudents’understandingsaboutthenatureofmathematicsandattitudestowardthelearningofmathematics.
Inthissession,wewilldescribethesecoursemodulesandtheoutcomesoftherelatedresearchandengageparticipantsinsomesampleactivities.Participantswill:1)LearnaboutamodelforincorporatingcreativityintoSTEMcourses;2)Hearaboutsignificantresultsfromourimplementation;3)Engagewithsomesamplemodules;4)GenerateideasforinstructionalinnovationsthatencouragestudentstoembraceSTEMascreativeendeavors;and5)Considerwaysinwhichtheycanparticipateintheprogram.
MikaMunakataisaprofessorofMathematicsEducationintheDepartmentofMathematicalSciencesatMontclairStateUniversity.InadditiontothisprojectoncreativityinSTEM,herresearchinterestsincludeteacherleadership,interdisciplinarySTEMteachingandlearning,andprofessionaldevelopment.
AshwinVaidyaisanAssociateProfessorinthedepartmentofMathematicalSciencesatMontclairStateUniversity.Heworksonproblemsattheinterfaceofphysicsandmathematics,onissuesofemergenceofpatternsinphysicalsystemsandisalsointerestedinfosteringconditionsintheclassroomfortheemergenceofcreativityinhisstudents.
CeireMonahanisadoctoralstudentandresearchassistantatMontclairStateUniversity.Sheisaformermiddleschoolteacherinterestedindevelopinginnovativewaystoinfusecreativityandmathematicstoimprovestudentlearningalongwithunderstandingbestpracticesinpreparingandsupportingpre-andin-serviceteacherstoteachmathematics.
AbstractsofContributedPaperSessions
Organizer:KathyTurrisi,CentenaryUniversityGeneralContributedPapers;room2101BPresider:KathyTurrisi,[email protected],CentenaryUniversity
1:30–1:50:ObamacareMeetsRealAnalysisSamFerguson,[email protected],NewYorkUniversityAbstract:Lastyear,thespeakermetanUberdriverwhowaseligibleforassistanceinpayingforhealthinsuranceundertheAffordableCareAct,butwhocouldn'tclaimitunderexistingIRSguidance.Inthistalk,wehighlighthowtheoremsandproofsinrealanalysisrevealedflaws
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inIRSguidanceandallowedthoseadverselyaffectedtoclaimassistanceusinganalternateprocedure.WerelatetheIRSguidancetolessonsandconceptswewantourstudentstolearninrealanalysiscourses,suchashowtoapplyone-sidedcontinuity,theroleofmonotonicityinprovingtheexistenceoflimits,andproofbybisection.ThisworkwasfeaturedinanarticleandvideomadeavailablebyMoneymagazineat:http://time.com/money/5237795/irs-tax-problem-obamacare/subsidy/
1:55–2:15:UsingSageMathtoExploretheMathematicsoftheLightsOutGameBoyanKostadinov,[email protected],NYCCollegeofTechnology,CityUniversityofNewYorkAbstract:Inthistalk,weuseSageMathtoexplorecomputationallythemathematicsbehindtheLightsOutgame.WeofferconcretecodingexplorationsforstudentstoinvestigatetheclassicalLightsOutgameanditsvariants,fromsimpleexercisestoopenproblems,suitableforstudentresearchprojects.WeprovidesampleSageMathcodefornumericalexplorationsandvisualizationsofLightsOut,whichoffersinsightandbuildsintuitionfordeepermathematicalunderstanding.
2:20–2:40:DiscriminantofPolynomialsYusufGurtas,[email protected],QueensboroughCommunityCollegeAbstract:Discriminantofaquadraticgivesusadefinitiveansweraboutthenatureofitsroots.Thesameisalsotrueforacubic,eventhoughit’snotsoeasytocalculateit,howeverafterthethirddegreeclassicaldiscriminantbecomesmoreandmoredifficulttocalculateandlessandlessinterestingintermsoftheinformationitcarriesaboutthenatureoftheroots.Discriminantofapolynomialofdegreenisahomogenouspolynomialofdegreenofitscoefficientsandusesallofthem.Inthissessionwewilltalkaboutadiscriminantofdegreetwothatusesonlytheleadingthreecoefficientsofagivenpolynomialofdegreenandtheinformationitcarriesaboutthepolynomial,inparticularaboutthenatureofitsroots.Wewillalsomentionotherdiscriminantsofdegreetwothataredefinedusingonlythreeconsecutivecoefficientsofthepolynomialandpointouttosomeoftheinformationthattheycarryaboutthepolynomialitself.
2:45–3:05:ModelingCarcinogenesisbyColoringGraphsJoshHiller,[email protected],AdelphiUniversityAbstract:Inthistalkwewillshowthataclassicalmodelfrommathematicaloncologyisequivalenttoacoloringproblemonhypergraphs.Weexplorethisnewperspectiveanduseittoshowseveralwaysinwhichgraphtheorycanhelpusformulatebiologicalhypothesis.
RecreationalMathematics;room2110Presider:DavidNacin,[email protected],WilliamPatersonUniversity
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1:30–1:50:Pascal,Padovan,andProofsWithoutWordsDavidNacin,[email protected], WilliamPatersonUniversity Abstract:WhathappensifwetrytoconstructtheFibonaccispiralwithtrianglesinsteadofsquares?WegetasequencewecallthePadovannumbers.WeshowhowthisconstructiondefinesthissequenceandthenfindthissamesequencehiddenagaininPascal'striangle,inawayalsosimilartothatofFibonacci.Wethenproveseveralidentitieswithouteitherwordsornumbers,byconsideringcoloringscorrespondingtosumsofentriesonPascal’striangle.
1:55–2:15:ThePlasticRatio,theMonasteryatVaals,andaNewFibonacciArrivalDavidNacin,[email protected], WilliamPatersonUniversity Abstract:Thegoldenratioisfamouspartlyfromitssimpledefinitioninvolvingtheproportionsandsinglerectangle.Weintroduceadifferentratioinvolvingproportionsofasquare,andusethatasanalternatemethodfordefiningthePadovansequence.Wethenobserveusesofthissequenceinarchitecture,andconcludewithanaturalconstructionoftheFibonaccinumbersinasequencerelatedtothePadovannumbers.
2:20–2:40:BreakfreeBarrycades BrianHopkins,[email protected],SaintPeter’sUniversityAbstract:BarryCipradevelopedabricklayer'spuzzlewhererowsofbrickswithlengths1,2,...,nareorderedtoavoidmultipleverticalbreaks.Howmanyrowscantherebe?Forwhatnhasthemaximumpotentialarrangementbeenfound?RichardGuyhasnamedtheseBreakfreeBarrycades.Wewillsurveyresultsfromanunpublishedmanuscriptandsubsequentworkfromcomputerscientists.
2:45–3:05:RainbowBarrycades BrianHopkins,[email protected],SaintPeter’sUniversityAbstract:UsingthecolorcodingofCuisenairerods,wherelength1bricksarewhite,length2bricksarered,etc.,weexploreavariantofapuzzlefromBarryCipra.ARainbowBarrycadehasrowsofbrickswithlengths1,2,...,norderedtoavoidrepeatedcolorsinanycolumn.Howmanyrowscantherebe?Forwhatnhasthemaximumpotentialarrangementbeenfound?
TeachingandLearningMathI;room2111Presiders:FarjanaShati,[email protected];JuliaRivera,[email protected];NewYorkCityCollegeofTechnology,CUNY
1:30–1:50:ReadingTablesandChartsandExtractingNecessaryInformationtoCreateaModeloftheProblemandAnalyzetheModelinDifferentialEquationTanvirPrince,[email protected],HostosCommunityCollege,CUNYAbstract:Thisprojectispartofthe“NumeracyInfusionforCollegeEducator(NICE)”program.SeveralfacultyfromdifferentcollegesofCUNYwerepartofthisprogramandwewentthroughprofessionaldevelopmentonhowwecaninfusequantitativereasoninginourcourses.Iwaspartofthistrainingandinthispresentation,IwillshowsomeoftheseQR
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outcomesthatIinfusedinmydifferentialequationclass.ThemainQRgoalthatIwantedtoachieveisforthestudentstobeabletoreadgraphs,tables,andchartsandtobeabletoextracttherelevantinformationtocreateamodeloftheproblem.Studentslaterwillbeabletoanalyzethemodeltoanswermorequestions.ThetablethatIhaveusedisthepopulation,inthousands,ofharborsealsintheWaddenSeaovertheyears1997to2012.Studentsusethegivendatatoanswersomerelevantquestions.Forexample,isthedatasetfollowapatternforlogisticgrowthmodel?Ifyes,findthelogisticmodelforthegivendataset.Studentswillalsobeabletocalculateerrorbetweenthegivenmodelandtheactualdata(erroranalysis).Studentsweretested(assessed)attheendonthreequestionstoseehowwelltheyacquiredtheknowledge.
1:55–2:15:ActiveLearningwithMath-AnxiousStudents:WhatILearnedWorkingattheMuseumofSexistObjectsAnilVenkatesh,[email protected],AdelphiUniversityAbstract:Howdoyouuseactivelearningtechniqueswithstudentswhoexperiencemathanxiety?Theheightenedlevelofengagementinsuchtechniqueshasbeenshowntosupportlearningmoreeffectivelythanlecture-basedclasses,yetstudentswhoalreadyexperiencemathanxietymayfindtheexpectationofclassroomengagementfurtheranxiety-inducing.Ihonedmyskillsinactivelearningpedagogyinasurprisingplace:theMuseumofSexistObjects(MoSO)atFerrisStateUniversity.Thismuseumseekstoraiseawarenessandinspireactivisminresponsetoeverydayitemsthatpromotesexism,genderedviolence,andfemalestereotypes.Asatourfacilitatoratthemuseum,Iregularlyworkedwithgroupsofstudentswhodisplayedcleardiscomfortwiththesubjectmatterandwerereluctanttoengageinconversation.Inthistalk,IsharesomefacilitationtechniquesIdevelopedattheMoSOthathelpedovercometheinitialhesitationtoengagewiththemuseum'scollection.Ithendiscusstheclearparallelsbetweenmuseumfacilitationonsensitivetopicsandactivelearningpedagogywithmath-anxiousstudents.
2:20–2:40:TheEffectofPeer-SupportedPrecalculusWorkshopsonWomen,Minorities,andFirst-GenerationCollegeStudentsFarjanaShati,[email protected],JanetLiou-Mark,[email protected];NewYorkCityCollegeofTechnology,CUNYAbstract:Peer-ledcollaborativeproblem-solvingsessionsareconsideredtobeaneffectivepracticeinpromotingunderstanding.TheimplementationofthePeer-LedTeamLearningworkshopmodelinaprecalculuscoursewherestudentsworkonceaweekonasetofmoduleshaveshownsignificantdifferencesbetweenresponsesprovidedmalesandfemales,minorityandnon-minoritystudents,andfirst-generationandnon-firstgenerationcollegestudents.Differencesindepartmentfinalgradesandcoursegradesbetweeneachgroupwillbediscussed.
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2:45–3:05:TheImpactsofaGeoscienceResearchProgramonGender,Ethnicity,andFirst-GenerationStatusofUndergraduatesMajoringinMathematicsandEngineeringJuliaRivera,[email protected],JanetLiou-Mark,[email protected],ReginaldBlake,[email protected];NewYorkCityCollegeofTechnology,CUNYAbstract:Ithaslongbeenrecognizedthatresearchexperiencesforundergraduatesarecriticalcatalystsforattracting,recruiting,andretainingstudents(particularlyunderrepresentedminoritystudents)inSTEMfields.Overaspanoffiveyears,astudywasconductedattheNewYorkCityCollegeofTechnologyoftheCityUniversityofNewYorktoexaminetheimpactsasummerNationalScienceFoundationResearchExperiencesforUndergraduates(NSFREU)programhadongender,ethnicity,andfirst-generationcollegestudentswhoweremathematicsandengineeringmajors.Overthecourseofanine-weekprogrameachsummer,differentcohortsofparticipantsweretrainedingeoscienceresearchusingsatelliteandground-basedremotesensingdataandapplications.Surveyresponsesregardingtheirresearchexperienceswerecollectedandanalyzed.Theseresultsshowedstatisticallysignificantgainsforunderrepresentedminorityandfirst-generationcollegestudentsintheirconfidencetoconductresearch,intheirabilitytocommunicatescience,andintheirinterestinapplyingforgraduateschool.Resultsfurthershowedthatfemalestudentsenjoyedtheresearchexperiencemorethantheirmalecounterpartsdid.Moresothantheirfemalepeers,malestudentsfoundtheresearchexperiencemorechallengingthantheyfirstexpectedittobe.ThestudywassupportedbytheNSFREUgrant#1560050.
TeachingandLearningMathII;room2115Presider:SatyanandSingh,[email protected],NewYorkCityCollegeofTechnology
1:30–1:50:ChallengesandStrategiesinaCollegeMathESLClassroomMonicaDeniMorales-Hernandez,[email protected],AdelphiUniversityAbstract:Asmathematicianswe’llprobablyagreewhenit’ssaidthatMathematicsistheuniversallanguage;asmathinstructors,weallhavefacedchallengesthathavemadeusmodifyandimproveourteachingtechniquesandthewaywecommunicatemathtothestudents.Weallhaveaskedatleastonceofthefollowingquestion:WhatshouldIdotocommunicatemathwithstudentsthathavelimitedmathexperience?Somemighthavesuccessfullyansweredthisquestionandsomeothersmightstillbelookingfortheanswer.Someinterestingquestionstoaskare:HowdowecommunicatemathwithstudentsthatnotonlyhavelimitedmathexperiencebutalsohavelimitedEnglishskills?Howdowemodifythemathcurriculumsothatthestudentscansuccessfullycompletetheclass?Inthistalk,Iwillexplorechallengesandstrategiesthatmaybeimplementedinintroductorymathclasses.
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1:55–2:15:AnEnticingSimulationinOrdinaryDifferentialEquationsthatPredictTangibleResultsSatyanandSingh,[email protected],NewYorkCityCollegeofTechnology,CUNYAbstract:InthiscasestudythedistancetraveledbyamassinanunderdampedsystemwassimulatedwiththeMaplesoftware.Thisisanimportantprobleminphysicalandquantumsystemsinmathematicsandphysics.Theresultstoucheduponaninteractionbetweencalculusanddifferentialequationsandillustrateaniceapproachforcollaborationinsmallstudentgroups.Thiscasestudychallengedstudentstoconjectureonsolutions,simulatethemandprovethemtheoreticallywhiletheyderivedunexpectedlyelegantclosedformexpressionsandgeneralizations.Thisapproachprovidedamediumforrichdiscussions,enhancedstudentsuccessandretentionandpropelledsomestudentsintograduateprograms.
2:20–2:40:BeyondtheHandout:InteractiveActivitiesthatInspireMathematicalThinkingAshleyTasy,[email protected],BrookdaleCommunityCollegeAbstract:Weallknowthatwithanything,practicinghelpsaidinprogress.Inthemathclassroom,itissoeasytofallintothepracticeofusinghandoutsfilledwithproblemstoassessstudentlearning.However,isitalwaysthebestmethod?Inthispresentation,Iwillteachyoudifferenttypesofactivitiesthatcaneasilybeintegratedintoyourlecturestoengagestudentsanddevelopmorecriticalthinkingofconcepts.
2:45–3:05:ImprovingStudentEngagementThroughOnlineMini-AssessmentsinLargeLectureClassesSheilaTabanli,[email protected],RutgersUniversityAbstract:Assessingstudentseffectivelyisavitalcomponentofeffectiveteachingandlearning.Assessingstudentlearningonadailybasisinlargelectureclassesbecomesachallengeduetolimitedopportunitiesforclosestudent-instructorinteractions.Bycreatingonlinemini-assessmentsinteacher.desmos.comwebsiteandincorporatinginteractiveactivitiestolecturesoffersimmediatefeedbacktotheinstructorandtostudentssimultaneously.AlthoughDesmosisafree,onlinegraphingcalculatorusedextensivelybystudents,thereisaDesmoscomponentthathasnotbeenwidelyutilizedbyteachers.Theteacher.desmos.comwebsiteenablesinstructorstocreateclassactivitieseasilyandfreelytoassessstudentlearning.TheseinteractiveactivitieshavebeenextensivelyusedinfourlargelecturefreshmanCalculusIclassesforlifesciencesmajorsatRutgersUniversity-NewBrunswick.Theinstructorisabletoidentifyareasofmisconception,commonmistakes,andcomparesthestudentlearningoutcomesamongthefourlargelecturesectionsthatshecurrentlyteaches.Theactivitieshavebeendesignedforanonymousstudentinputandnotforgradingpurposes.Inthisdigitalage,studentsarealreadyaccustomedtousingcellphonesforvariousdailytasks.Beyonditsfunctionasaclassroomassessmenttool,mobiletechnologyistheprimaryconduitforsomestudents’learningexperiences.Ithasbeenobservedthatstudentsaremoreinclinedtoprovidingonline,anonymousfeedbackratherthanofferingindividualorgroupfeedback
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specificallyinlargelectureclassestaughtinanauditoriumseating.Byanalyzingthecommonmistakesasawhole-classontheassignedfewproblems,thisinteractiveassessmentcontributestoamoreengagingactivelearningenvironment.
StudentResearchPaperSession;room2113Presider:AbrahamMantell,[email protected],NassauCommunityCollege,SUNY
1:30–1:45:PatternsBetweentheNumberofCeviansorCaliiansandtheRegionsthatTheyForminPolygonsCaliaKugler,HalfHallowHillsHighSchoolEast;Advisor:RobertGerver,InstituteofCreativeProblemSolvingAbstract:Thispaperisadescriptionofaninvestigationintoceviansandcaliians(ceviansinafigureotherthanatriangle).Theformulaforthenumberofregionsformedinatrianglebydrawingnceviansfromeachvertexisobtainedinseveralways.Next,formulasforthenumberofregionsformedinothersimplepolygonsbydrawingncaliiansaredeveloped.Apatternisobservedandageneralformulaforthenumberofregionsinanypolygonisdeveloped.Thisformulaisthengeneralizedtoshowthenumberofregionsformedinasimplepolygonbydrawingcaliiansnotonlytotheoppositesideofavertexbuttoothersidesaswell.AJavaprogramisdevelopedtocountthenumberofregionsinatriangleandasquareformedbyanynumberofceviansorcaliiansdrawnfromanyvertex,thusnotrequiringthesamenumberofceviansorcaliiansfromeachvertex.Somerecommendationsforfurtherresearchincludedevelopingformulasforthenumberofregionsinanysimplepolygonformedbydrawinganynumberofceviansorcaliiansfromanyvertextoanyside.Additionalfigurescanbeconsidered,includingcirclesandconvexpolygons.Aninvestigationtoextendingcaliianstocomplexpolygonsshouldbeconsideredaswell.AnextensiontotheJavaprogramtoincludeotherfiguresshouldbedeveloped.
1:46–2:01PM:AGame-TheoreticApproachtoNeuralNetworksDanielleGruber,VillageSchool(GreatNeck,NY)Abstract:Thebrainisanintricatesystemofconnectedregions,constantlyandcontinuouslyrelayingandintegratinginformation.Connectivityisanessentialfeaturewhenconsideringthedynamicsofaneuralnetwork,asitgreatlyinfluencesthepathwaysbywhichregionscommunicateandthemeansbywhichregionsactivate.Inneuroimaging,connectivityisoftendefinedanatomically,bythebiophysicalconnectionsthatactuallyexist,andfunctionally,bythestatisticaldependenciesamongregions.Here,amathematicalmodelbasedonevolutionarygametheoryonnetworks(EGN)isformulated,capturingelementsofbothanatomicalandfunctionalconnectivity,andfurtherdelineatingdifferencesbetweenabraininrestingstateandabrainengagedinaspecifictask.Themodel,basedontheworkofMadeoetal.,(2017),describestheactivationsofdifferentregionsinthenetworkasfunctionsoftime,changingbasedoninteractionswithotherregionsintermsofpayoffsforactivationand
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inactivation.Althoughtheoreticalinnature,themodelhasimplicationsforourunderstandingofneuralnetworkdynamicsandthetechniqueswhichattempttocapturesuchdynamics.
2:02–2:17PM:DerivingtheArmitageandDollModelofCarcinogenesisGabriellaSmokovich,AndrewVelasquez-Berroteran,andEleniZamagias,AdelphiUniversity;Advisor:JoshuaHillerAbstract:TheArmitageandDollmodelofcarcinogenesisisoneofthefundamentalcornerstonesofmathematicaloncology.However,this'model'isnotreallyamodelatallbutratheraframeworkthathasbeenmodifieddozensoftimesintheliterature.InthispresentationwewillexaminehowtheArmitageandDollpresentedandderivedtheiroriginalworkwithaneyetowardsexplainingwhytheirworkhasbeensowidelyinfluential.
2:18–2:33PM:AnEnticingStudyofPrimeNumbersoftheShapex2+y2XiaonaZhou,NewYorkCityCollegeofTechnology(CUNY);Advisor:SatyanandSinghWewillstudyandproveimportantresultsonprimesoftheshapex2+y2usingnumbertheoretictechniques.Ouranalysisinvolvesmaps,actionsoversets,fixedpointsandinvolutions.Thispresentationisreadilyaccessibletoanadvancedundergraduatestudentandlaysthegroundworkforfuturestudies.
2:34–2:49PM:AlgorithmsforChangeDetectioninDynamicNetworksNeilHwang,CityCollege(CUNY)Abstract:Theclusteringproblemhasbecomeapopulartopicamongresearchersinfieldsrangingfrommathematicstosocialsciences.Alsoknownasthecommunitydetectionorcommunityrecoveryproblem,itspopularityisevidencedbymanymethodsavailableintheliterature.Regardlessofthemethodchoice,oneimportantinputisthenumberofclusters.Iwillfirstreviewfivealgorithmsandthemainunderlyingtheoreticalresultsfromrecentliteratureforestimatingthenumberofcommunitiesinnetworkdata.Then,Iwillpresentanovelalgorithmthatextendsthealgorithmsintheliteraturetodetectstructuralchangesindynamicnetworks.Theperformanceofthealgorithmsiscomparedusingsimulationsandreal-lifenetworkdata.
2:50–3:05PM:SuccessiveTighteningofPinchPointsofLogisticMapsandFractalsHarryH.Xi,PrincetonUniversity;Advisor:JonathanFickenscherAbstract:Wewillexplorethedynamicstabilityofthefixedpointsofthefamilyoflogisticmapsg(x)=ax(1–x)forrealparametersa.Fromcertainvaluesofa,wewillobservethatconvergenceofiterationsofthelogisticmaptothosefixedpointsarenon-geometric.Forthesecases,wewillthenexaminehowperturbationsofgfromthezerofunctiony=0,thepositiveidentityy=x,andthenegativeidentityy=–xtranslateintoratesofconvergencetofixedpointsusingdifferentialanalysis.Becausetheresultingdifferentialanalysisprovessouseful,wewillexplorehowsuchanalysiscanpredict,particularly,thetrajectoryofthesizeoftheUniverseinthefuture.Moreover,ofconsiderableinterestarethelogisticfunctionsg
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whichhaveinitialperturbationfromthenegativeidentityy=–x.Here,addinghigherpowerperturbationsmayaffectnotonlytherateof,butalsotheconvergenceitself,ofiterationstop.Inthisrespect,wewillderiveaformulatoseewhichpowerperturbationsmayaffectconvergenceandwhichonescannot.Finally,wewillshowthatthelogisticmapsaredynamicallyconjugateuptorenormalization,andthisrenormalizationleadsintotheanalysisoftheMandelbrotSet(z0=0,zn=zn-12+c),JuliaSets,HénonMapobjects,andotherrelatedfractals.
LunchDiscussionTables
OrganizedbyKathyTurrisi,CentenaryUniversity.Therewillbeninediscussiontablesatlunch:1. DoingExperimentsinaMathEnvironment,ledbyJunZhang,NewYorkUniversity2. PublishinginMAAJournals(EspeciallytheMonthly),ledbySusanJaneColley,Oberlin
College3. UsingAItoGuessSequences,ledbyNeilJ.A.Sloane,RutgersUniversity4. EncouragingCreativityinMathematics,ledbyMikaMunakata,AshwinVaidya,andCeire
Mondhan,MontclairStateUniversity5. TopicsinGraphTheory,ledbyDeepakBal,MontclairStateUniversity6. PeerAssistedLearningMathematics,ledbyJuliaRiveraandFarjanaShati,NYCityCollege
ofTechnology,CUNY7. HowtoGetMoreHighSchoolParticipationwithLocalMAASections,ledbyAbraham
Mantell,NassauCommunityCollege,SUNY8. RetainingStudentsinMath,ledbyLindaRitchieandKathyTurrisi,CentenaryUniversity;
GraceCook,BloomfieldCollege9. TeachingtheFirstTwoYearsofCollege,ledbyJonathanWeisbrod,RowanCollegeat
BurlingtonCounty
Thosewhopre-registeredhavepriorityatthesediscussiontables.Welookforwardtoasetoflivelyandinterestingdiscussions!
ReportontheMathFest2019MAACongressMeetingByTomHagedorn
TheMAACongressmetforanall-daymeetinginCincinnationJuly31,2019,thedaybeforethe2019MathFest.ThemeetingbeganwithintroductionsandareviewoftheMAA’srevisedmissionandvisionstatements:
Mission:ThemissionoftheMathematicalAssociationofAmericaistoadvancetheunderstandingofmathematicsanditsimpactonourworld.Vision:Weenvisionasocietythatvaluesthepowerandbeautyofmathematicsandfullyrealizesitspotentialtopromotehumanflourishing
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TheCongressreviewedtheMAA’sstrategicgoalsandapprovedtwonewgoals:(1)TosustainarobustportfolioofprogramsthatexpandMAA’soutwardfacingimpact;and(2)HostingtheInternationalMathematicalOlympiadcompetitioninJuly2021.TheCongressthenheardreportsontheMAA’scurrentoperationsandprograms.Significantly,in2018,theMAAexperiencedmodestmembershipgrowthandhadabalancedbudget.TheCongresswasinformedaboutnewmembershipbenefits:
a) AccesstoPRIMUS,JournalofMathematicsandtheArts,andChanceb) DiscountedsubscriptionstoTheGreatCoursesc) AccesstotheMAAVideoLibrary.NewtotheVideoLibrarythisfallwillbethe2019MAA
MathFestSpeakerVideosTheCongressdiscussedtheendingoftheJMMin2021.Asof2022,allMAAnationalmeetingeventswilloccuratMathFest.TheMAAwillbuildonthecontinuedgrowthofMAAMathFestandwillalsodirectresourcestobettersupportMAASectionsatsectionalmeetingsandotherprogramsthatexpandaccessandservicestomoremembers.Examplesinclude:
• DigitalcommunitytoolssuchasMAAConnect• MoresupportforSectionNExT• ExpandedMAAMathFestprogram• NewSectionspeakerprograms
Themeetingconcludedwithtwodiscussionsoni)IdeasforIncreasedSupportforMAASectionMeetings;andii)howtoensurethatallareasoftheMAAcommunityarewell-representedontheCongress.Thenextmeetingwillbeatthe2020MathFestinPhiladelphia,Jul.29-Aug.1.
MathFest2019MAASectionOfficersReportByTomHagedorn
TheMAA’sSectionOfficer’sMeetingwasledbyLisaMarano(EPADEL),chairoftheMAATaskForceonSections.TheTaskForcehasbeenworkingonanumberofways,bothsmallandlarge,thattheMAAcanhelpsupportsections.Theyinclude:
a) VisitorandLecturePrograms.MAA-NJhasanEditorLecturesProgramvisitorin2019-20andwecanhostoneMAAofficersectionvisitoreachyear.
b) Communication.ThisareaisconsideredMAA’sgreatestunmetneed.MAAisunveilingMAA-Connect,anewmeetingsoftwareplatformthisfalltoenablesectionsandsectionleaderstomoreeasilyworktogether.
c) Logistics.MAAisworkingtoprovidehelpwithonlineregistration,jointmeetinglogisticsandpromotingattendanceatsectionalmeetings.
d) DiversityandInclusion.TheMAAwouldliketohelpsectionsincreasediversityandinclusioninsectionmeetings.
e) DevelopingaCommunityBeyondMeetings.TheMAAwouldliketostrengthentieswithSIGMAASoutsideofmeetingsandhavesectionalSIGMAAactivities.
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f) SupporttorunSectionElections.MuchofthemeetingwasspentbrainstormingamongsectionleadersonhowtobestutilizethenewMAA-Connectsoftware.OfficersthoughtaboutwaysthatbeingabletoconnecttothelargercommunityofSectionLeaderscouldenhanceorimprovewhatweareabletodoforourSection.
TheTaskforcealsohighlightedthemanyMAAPrograms,includingthenewTondeurBIGCareerInitiative.ThisprogramprovidesfinancialsupportforaroundofBIG(“Business,Industry,andGovernment”)CareerActivitiesatMAASectionMeetingsfromSpring2020-Fall2021.ProposalsaredueatMAAabout6monthsaheadoftime.OfficersdiscussedwaysthatsectionscanworkcollaborativelytocreatenewTondeuractivitieswhichcanworkwithinthestructureofourexistingsectionprogram.
TheTaskForceisalsoencouragingsectionstohighlightandcelebratetalentedpeopleineachsectionwhomaynotattendnationalmeeting.IthasformedaSectionBestPracticescommitteethatwillbelookingtocollectalistofbestpracticesbysectionsonavarietyoftopics.KarenStanish,KeeneStateCollege,willchairthissubcommittee.
BookSalesattheMeeting
Therewillbe25TitlesonDisplayatthemeeting,including14AMSbooksand11MAAbooks.ThediscountedmeetingpriceforMAAandAMSmembersis40%.Thediscountfornon-membersis25%;discounts,alongwithfreeshipping,arevalidthroughNovember26.DiscountsapplytoTitlesonDisplayandmostotherAMSandMAAbooks.Toplaceanorder,call1-800-321-4267or401-455-4000andaskforCustomerService.UsecodeMT262foryourdiscount.Nobookorderswillbetakenatthemeeting.
FutureMeetings
MAA-NJ.TheSpring2020MAA-NJSectionmeetingwillbeheldatRowanUniversityonSaturday,April18,2020.TheFall2020MAA-NJSectionmeetingwillbeheldatKeanUniversityonSaturdayNovember14,2020.
MAAMETRO-NY.TheMAAMetropolitanNewYorkSectionwillholditsnextmeetingonSundayMay3,2020atQueensCollege,CUNY.
GSUMC.The2020GardenStateUndergraduateMathematicsConference(GSUMC)willbeheldinconjunctionwiththeSpringMeetingoftheNJSectionatRowanUniversity.Theconferencewillincludeposterandoralpresentationsessionsforundergraduatestudents,aswellasateammathematics-problemcompetition.Therearemanyopportunitiesforfacultytoparticipateinco-organizingtheconference.Contactoneoftheco-directorsDeepakBal([email protected]),LeeCollins([email protected]),orIkJaeLee
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([email protected])tovolunteer.ForadditionaldetailsseetheGSUMCwebsite:http://sections.maa.org/newjersey/GSUMC/GSUMC.htm
NationalMAAMeeting.The2020JointMathematicsMeetingwillbeinDenver,January15–18.
MathFest.The2020MathFestwillbeinPhiladelphia,July29–August1.
CallforContributedPapersandLunchTableDiscussionTopicsfortheSpring2020MAA-NJMeeting
Therewillbetwospecialcontributedpapersessions.Allpaperswillbereviewedbytheorganizers.Pleasesubmitatitle,three-tofour-sentenceabstract,andone-pagedescriptioninMSWordformatbyJanuary24,2020tothesessionorganizer.
1. RecreationalMath.Organizer:DavidNacin,[email protected], WilliamPatersonUniversity
2. GeneralContributedPapers.Organizer:KathyTurrisi,[email protected],CentenaryUniversity
MAAmembersinterestedinleadingaLunchTableDiscussionattheSpring2020meetingareaskedtosubmittheirproposalstoKathyTurrisi,CentenaryUniversity,[email protected],2020.
CallforNominationsfortheMAA-NJAwardforDistinguishedCollegeorUniversityTeaching
TheMAA-NJSectionDistinguishedTeachingAwardSelectionCommitteeisseekingnominationsforthe2020award.Pleaseconsidernominatinganinspiring,respected,orinfluentialdeservingcolleagueforthisprestigiousaward.AnomineemusthavebeenanMAAmemberforatleasttwoyearspriortothenomination.Nominationinformationispostedathttp://www.maa.org/newjersey.ForadditionalinformationyoumaycontactZhixiongChen(Secretary,MAA-NJ)[email protected],2019.
SocialMediaInformation
AmessagefromsocialmediadirectorGraceCook,BloomfieldCollege.Checkusout!Email: [email protected]: https://www.facebook.com/maanewjerseyInstagram: https://instagram.com/maanewjerseyTwitter: https://twitter.com/maanewjersey
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MAA-NJCommittees
AwardsCommittee:TomHagedorn,CollegeofNewJersey(chair);AihuaLi(ex-officio),MontclairStateUniversity;SaritaNemani,GeorgianCourtUniversity;JonathanWeisbrod,RowanCollegeatBurlingtonCounty.
NominatingCommittee:ZhixionChen,NewJerseyCityUniversity;KarenClark,CollegeofNewJersey;ThomasHagedorn(chair),CollegeofNewJersey;AihuaLI(ex-officio),MontclairStateUniversity;HieuNguyen,RowanUniversity.
TeachingAwardCommittee:DenisL.Blackmore,NewJerseyInstituteofTechnology;KarenClark(chair),CollegeofNewJersey;AihuaLi(ex-officio),MontclairStateUniversity;DirckUptegrove,Nokia.
ContributedPaperCommittee(NJandNY):GraceCook,BloomfieldCollege;AihuaLi(ex-officio),MontclairStateUniversity;JanetLiou-Mark,NewYorkCityCollegeofTechnology,CUNY;AbrahamMantell,NassauCommunityCollege,SUNY;SatyanandSingh,NewYorkCityCollegeofTechnology,CUNY;KathyTurrisi(chair),CentenaryUniversity.
OrganizingCommittee(NJandNY):AmandaBeecher,RamapoCollege;ZhixiongChen,NewJerseyCityUniversity;GraceCook,BloomfieldCollege;ThomasHagedorn,TheCollegeofNewJersey;IkJaeLee,RowanUniversity;AihuaLi,MontclairStateUniversity;JanetLiou-Mark,NewYorkCityCollegeofTechnology,CUNY;AbrahamMantell,NassauCommunityCollege,SUNY;SusanMarshall,MonmouthUniversity;DawnNelson,SaintPeter’sUniversity;HieuNguyen,RowanUniversity;LindaRitchie,CentenaryUniversity;SatyanandSingh,NewYorkCityCollegeofTechnology,CUNY;KathyTurrisi,CentenaryUniversity;DirckUptegrove,Nokia;ElizabethUptegrove,FelicianUniversity;PaulvonDohlen,WilliamPatersonUniversity;JonathanWeisbrod,RowanCollegeatBurlingtonCounty;ChungWong,CountyCollegeofMorris.
HistoryCommittee:GraceCook,BloomfieldCollege;ThomasHagedorn,CollegeofNewJersey;AihuaLi(ex-officio),MontclairStateUniversity;HieuNguyen(chair),RowanUniversity.
HostingCommittee:DenisBlackmore,NewJerseyInstituteofTechnology;LiGuo,RutgersNewark;ChengwenWang(chair),EssexCountyCollege;MamtaVyas,EssexCountyCollege.
DinnerHonoringtheInvitedSpeakers.TheSectionwillhonortheinvitedspeakersatdinneratSpanishPavillion,31HarrisonAve.,Harrison,NJ,followingthemeeting.Everyoneiscordiallyinvited.
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Acknowledgments.WethanktheDepartmentofMathematicsatEssexCountyCollegefortheirkindhospitalityinhostingthemeeting.AndthankstotheEssexCountyCollegeMathClubstudentvolunteersforassistingatthemeeting.
WethankJacquelineBakal(FelicianUniversity),Cengage,andPrincetonUniversityPressfortheirgenerousdonationsforsilentauctionanddoorprizes.
NJAMTECallforPapers.TheNewJerseyAssociationofMathematicsTeacherEducatorsinvitescontributedpapers(15-to25-minutetalkplus10-to15-minutediscussion)atitsannualmeetingscheduledforJune5,2020atTheCollegeofNewJersey.Thethemeis:Howteacherpreparationprogramscanpreparefutureteachersofmathematicstodeveloprichunderstandingsofthecontenttheywillteachandtosupporttheprofessionaldispositiontobecomelifelonglearnersofthatcontent.However,anytalkaboutresearchresults,professionaldevelopment,orissuesofconcerntomathematicsteachereducatorswillbeconsidered.ProposalsshouldbesenttoNJAMTEPresidentJamesE.R.Beyersatbeyers@tcnj.edubyFebruary8,2020.Forfurtherdetails,contactJamesBeyers.
Announcement.Alactationroomisavailableatthismeeting.Signagedirectsthosewhoneedittotheroom.
JointheMAA!http://www.maa.org/membership/join_main.html
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MAA-NJSectionOfficers
CongressRepresentative ThomasHagedorn,TheCollegeofNewJersey
Chair AihuaLi,MontclairStateUniversityChair-elect PaulvonDohlen,WilliamPaterson
UniversitySecretary ZhixiongChen,NewJerseyCityUniversityTreasurer DirckUptegrove,NokiaVice-ChairforFallMeetings IkJaeLee,RowanUniversityVice-ChairforSpeakers AmandaBeecher,RamapoCollegeofNew
JerseyVice-ChairforSpringMeetings ElizabethUptegrove,FelicianUniversityVice-ChairforStudentActivities DeepakBal,MontclairStateUniversityGSUMCCo-directors DeepakBal,MontclairStateUniversity;Lee
Collins,RowanUniversity;IkJaeLee,RowanUniversity
Vice-ChairforTwo-YearColleges JonathanWeisbrod,RowanCollegeatBurlingtonCounty
BookSaleCoordinators DirckUptegrove,Nokia;ElizabethUptegrove,FelicianUniversity
ContributedPaperOrganizerandLunchDiscussionOrganizer
KathyTurrisi,CentenaryUniversity
DoorPrizeCoordinator LindaRitchie,CentenaryUniversityLiaisonCoordinator IkJaeLee,RowanUniversityProgramEditors DawnNelson,SaintPeter’sUniversity;
ElizabethUptegrove,FelicianUniversityProjectNJ-NExTCo-Directors SusanMarshall,MonmouthUniversity;
ChungWong,CountyCollegeofMorrisSocialMediaDirector GraceCook,BloomfieldCollegeWebmaster DirckUptegrove,Nokia
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MAAMetro-NYSectionOfficers
CongressRep.(2017–2019)
AlanTucker,StonyBrookUniversity
(631)[email protected]
Chair(2018–2021)
JanetLiou-Mark,NYCCollegeofTechnology(CUNY)
(718)[email protected]
Chair-Elect(2018–2021)
SatyanandSingh,NYCCollegeofTechnology(CUNY)
(718)[email protected]
Secretary(2018–2021)
JohannaFranklin,HofstraUniversity
(516)[email protected]
Treasurer(2018–2021)
ArmenBaderian,NassauCommunityCollege(SUNY)
(516)[email protected]
Vice-ChairforFour-YearColleges(2018–2021)
BoyanKostadinov,NYCCollegeofTechnology(CUNY)
(718)[email protected]
Vice-ChairforTwo-YearColleges(2018–2021)
OlenDias,HostosCommunityCollege(CUNY)
(718)[email protected]
Vice-ChairforHighSchools(2018–2021)
MutiaraSondjaja,NewYorkUniversity (212)998-3375
BookExhibitCoordinator
NadiaBenakli,NYCCollegeofTechnology(CUNY)
(718)[email protected]
GraphTheoryDaysLiaisons
LouisV.Quintas,PaceUniversityArmenBaderian,NassauCommunityCollege(SUNY)EdgarG.DuCasse,PaceUniversity
[email protected]@[email protected]
LiaisonCoordinator ElenaGoloubeva,WebbInstitute
(516)[email protected]
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MathFairChair–NYC
RandyJ.Asher,BrooklynTechnicalHighSchool
(718)804–[email protected]
MathFairChair–LongIsland
JosephQuartararo,Northport-EastNorthportPublicSchools
(631)[email protected]
MetroNExTCoordinators
BenjaminGaines,IonaCollegeMutiaraSondjaja,NewYorkUniversityJohannThiel,NYCCollegeofTechnology(CUNY)
(914)[email protected](212)[email protected](718)[email protected]
NewsletterEditor AbrahamS.Mantell,NassauCommunityCollege(SUNY)
(516)[email protected]
PublicRelationsChair
Xiaomeng(Vivian)Kong,NassauCommunityCollege(SUNY)
(516)[email protected]
Speaker’sBureauChair
AbrahamS.Mantell,NassauCommunityCollege(SUNY)
(516)[email protected]
StudentChapterCoordinator
DavidSeppala-Holtzman,St.Joseph’sCollege
(718)[email protected]
SectionArchivist AgnesM.Kalemaris,FarmingdaleStateCollege(SUNY)
(631)[email protected]
Webmaster EricRowland,HofstraUniversity
(516)[email protected]
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