09年美赛优秀论文集

09年美赛优秀论文集09年美赛优秀论文集

The

Journal

PublisherCOMAP,Inc.

ExecutivePublisherSolomonA.GarfunkelILAPEditorChrisArney

AssociateDirector,

MathematicsDivisionProgramManager,

CooperativeSystemsArmyResearchOf ceP.O.Box12211

ResearchTrianglePark,

NC27709-2211

david.arney1@arl.army.mil

OnJargonEditorYvesNievergelt

Dept.ofMathematicsEasternWashingtonUniv.Cheney,WA99004

ynievergelt@ewu.edu

ReviewsEditorJamesM.CargalMathematicsDept.TroyUniversity—

MontgomeryCampus231MontgomerySt.Montgomery,AL36104

jmcargal@http://www.77cn.com.cn

ChiefOperatingOf cerLaurieW.Arag´onProductionManagerGeorgeW.WardProductionEditorJoyceBarnesDistributionJohnTomicekGraphicDesignerDaivaChauhan

Vol.30,No.2

Editor

PaulJ.CampbellBeloitCollege700CollegeSt.

Beloit,WI53511–5595campbell@beloit.eduAssociateEditorsDonAdolphsonBrighamYoungUniv.ChrisArneyArmyResearchOf ceAaronArcherAT&http://www.77cn.com.cnb.RonBarnes

U.ofHouston—DowntnArthurBenjaminHarveyMuddCollegeRobertBoschOberlinCollege

JamesM.CargalTroyU.—MontgomeryMurrayK.ClaytonU.ofWisc.—MadisonLisetteDePillisHarveyMuddCollegeJamesP.Fink

GettysburgCollegeSolomonA.GarfunkelCOMAP,Inc.

WilliamB.GearhartCalif.StateU.,FullertonWilliamC.GiauqueBrighamYoungUniv.RichardHabermanSouthernMethodistU.JonJacobsenHarveyMuddCollegeWalterMeyerAdelphiUniversityYvesNievergeltEasternWashingtonU.MichaelO’LearyTowsonUniversity

CatherineA.RobertsCollegeoftheHolyCrossJohnS.RobertsonGeorgiaMilitaryCollegePhilipD.Straf nBeloitCollege

J.T.Sutcliffe

St.Mark’sSchool,Dallas

09年美赛优秀论文集09年美赛优秀论文集

Vol.30,No.2

GuestEditorial

2009

TableofContents

DiscreteMathFirst!

ChrisArney.................................................................93

SpecialSectionontheICM

Resultsofthe2009InterdisciplinaryContestinModeling

ChrisArney.................................................................99RebalancingHuman-In uencedEcosystemsYuanSiZhang,ShuoPengWang,and

NingCui....................................................................121StrivingforBalance:WhyReintroducingMoreSpeciestoFishFarmEcosystemYieldsBiggerPro tsSeanClement,TimothyNewlin,and

JosephLucas...............................................................141Authors’Commentary:TheOutstandingCoralReefPapers

MelissaGarrenandJosephMyers................................159Judges’Commentary:TheOutstandingCoralReefPapers

SheilaMiller,MelissaGarren,andRodneySturdivant....163

OnJargon

PtolemytoFourier:Epicycles

FawazHjouj...............................................................169

Reviews...................................................................173

09年美赛优秀论文集09年美赛优秀论文集

GuestEditorial93

GuestEditorial

DiscreteMathFirst!

ChrisArney

DivisionChief,MathematicalSciencesDivisionChief,NetworkSciences

ProgramManager,CooperativeSystemsU.S.ArmyResearchOf ceP.O.Box12211

ResearchTrianglePark,NC27709–2211david.arney1@us.army.mil

Introduction

Recently,thisJournalpublishedseveralintriguingeditorialsoncalculusandmodeling.JamesCargalestablishedtheboundsofmodelingasasci-enceandthelimitationsofmathematicalproblemsolving[2007].Icertainlyagreewithhispointsontheartandscienceofmodeling.PaulCampbell[2006]andUnderwoodDudley[2008]debatedtheviabilityofthecalculuscourse.IguessIaminanagreeablemood,sinceIalsosupportCampbell’sstatementthatwereallydoneedtochangethewayweteachcalculus.IagreesomuchwithDudley’spointsmadeinrebuttalthatIwillbefoolish(hisword)andadvocatefor

discretemathematicsasthestandard rst-yearcollegemathematicscourse(vs.acrappyorevenasuperbcalculuscourse).

First,letmebeclear:Ilovecalculus(bothasaliberalartandasapro-fessionaltool).Itiswonderfulmathematicsthatcanenrichandempowerone’slife.IalsoagreewithDudleythateventhoughsomestudentsdonotfullyunderstandtheconceptsandtheoriesofcalculus,itshouldstillbetaught—andweshouldcontinuetoreform,re ne,improve,andenhanceitsteaching.AndIstronglyagreewithhimthatmathematicsisgoodforstudentsbecauseitcananddoesdevelopthinkingandproblemsolvingskills.Ibelievewe(mathematicseducators)shouldbepleasedbywhatwearedoingandcon dentwearehavingapositiveimpactonstudentsin

cCopyright2009byCOMAP,Inc.Allrightsreserved.TheUMAPJournal30(2)(2009)93–97.

Permissiontomakedigitalorhardcopiesofpartorallofthisworkforpersonalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforpro torcommercialadvantageandthatcopiesbearthisnotice.Abstractingwithcreditispermitted,butcopyrightsforcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.

09年美赛优秀论文集09年美赛优秀论文集

94TheUMAPJournal30.2(2009)

calculusandinmodelingandothermathcoursesaswell.

HereiswhereIgoastepfurtherthanDudley:Istronglybelievethatwewouldhaveevengreatersuccessifwetaughtdiscretemodelingasthestandardcoursetoour rst-yearstudents.Suchacourseshouldincludecopiousmodelingandmoderninterdisciplinaryproblemsolving.Ifwedothiswellandprepareandmotivateourstudentstotakethecalculus,thatcoursecanbemoreliketheonethatCampbelladvocates—fullofrichideasandfullerapplications,resultinginimprovedstudentunderstandingofmathematics.

BackgroundandPerspective

BeforeIprovidemycase,letmegivealittlebackgroundandperspec-tive.Mathematics,asatoolforhumans,hasalwaysbeenuseful.BenjaminFranklinhighlightedthisinhis1735essay“Oftheusefulnessofmathemat-ics”[1735]:

Therehasnotbeenanysciencesomuchesteemedandhonoredasthisofmathematics,norwithsomuchindustryandvigilancebecomethecareofgreatmen,andlaboredinbythepotentatesoftheworld,viz.emperors …… 此处隐藏：27089字，全部文档内容请下载后查看。喜欢就下载吧 ……