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Using Mathematics
Starting points
Course Guide
MST121
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Contents1 Introduction 22 Courselearningoutcomes 23 Thecoursecomponents 44 Assessment 75 Studysupport 9
1 Introduction
WelcometoMST121UsingMathematics. We hope that you will find the courseenjoyableandrewarding!ThisCourseGuidegivesyouanoverviewofthelearningoutcomesofthiscourse,thecoursecomponents,assessmentandstudysupport,tohelpyoutoplanyourstudy.Youshouldbegin,now,tomakesomepreparationforstudyingMST121.Inthismailingyouwillfindpreparatorymaterials, includingtheGuide toPreparationandtheRevisionPack,tohelpyoutorefreshyourmathematicalskills. Youshouldalsohave,orbemakingarrangementstoobtain,anappropriatecomputerrunningWindows,andbefamiliarwiththebasicWindowsprocedures inSection2oftheGuide toPreparation.OnsuccessfulcompletionofMST121,youwillhavethemathematicalknowledgeandskillstostudyothercoursesthatusemathematics. Youwillalsohavegainedexperience inusingmathematicalandstatisticalsoftware,andshouldhavedevelopedgeneralskillsforlearningandcommunicatingmathematics. IfyougoontostudyMS221,thenyouwillbewellpreparedtotakefurthermathematicscourses.
2 Course lear ning outcomes
Thefollowing listofoutcomes indicateswhatyoushouldbeabletodobytheendofthecourse.
Knowledge and under standing
Youshouldbeableto: Recogniseandworkwithbasicmathematical language,andobjects
suchassequences,series,functionsandgraphs. Understandtheuseofcoordinategeometry,matrices,calculusand
statisticsinsimplesituations. Performelementarydifferentiationand integration. Describetheneedforjustificationandproof.
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Cognitive skills
Youshouldgainanappreciationof: Mathematicalideasandwaysofthinkingmathematically. Theneedforjustificationandproof. Themathematicalmodellingprocess.Key skills
Youshould: Improveyourlearningandperformanceskills(e.g.yourabilityto
organisestudytime,tostudyindependently,to learnfromfeedback,andtomeetdeadlines).
Developyourskillsforcommunicatingmathematical ideas includingtheuseofmathematical languageandterminology insentences.
Beabletoappreciatemathematicalmodelsofsimplesituations. Developskillsforusingacomputeralgebrapackage(Mathcad) in connectionwithmathematicalproblems.
Practical and/or professional skills
Youshouldgainanabilityto: Developlogicalandmathematicalargument. Useacomputeralgebrapackage(Mathcad)foralgebraicmanipulation,
differentiationand integration. Useappropriatestatisticaltechniqueswhenhandlingdata, includingacomputerpackage(OUStats). Interpretstatisticaldata. Provideappropriatediagramsandchartstosupportstatistical
information.Yourunderstandingofthesemathematical ideasisassessedthroughtutor-markedassignment(TMA)andcomputer-markedassignment(CMA)questions. SomeTMAquestions involvemakingcriticalobservationsabouttheiranswers.Yourwrittencommunication isassessed intheTMAs. Inmanycases,creditisgivenfortheclarityofyourpresentation.Improvingyourownperformance is implicit inthecourseandnotexplicitlyassessed. EvidenceofyourabilitytoworkwithacomputerwillformpartofyourTMAanswers.
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3 The cour se components
ThemainMST121coursecomponentsaredescribedbelow.
Study textsMST121 ismadeupofthefollowingfourblocksofstudy.
BlockA MathematicsandmodellingBlockB DiscretemodelsBlockC ContinuousmodelsBlockD Modellinguncertainty
Eachblock isdivided intoseveralindividuallyboundchapters,andhasassociatedwith itanexercise bookletcontainingexercisesandsolutions,andacomputer bookcontainingsoftware-basedactivities.MostchaptersinMST121containthefollowingelements: astudy guide,whichgives informationonthestructureofthe
chapter,andanintroduction; severalsections, with examples,activitiesandcommentsonthose
activities,asection summary, and exercisestoprovidepractice; achapter summary, includingastatementoflearning outcomes; solutionstoactivitiesandexercises.Somechaptersincludeablock introductionorablock summary, and somecontainanappendixrelatedtoparticularteachingsections.Yourstudywillbeguidedbythechapters,andmuchofyourstudytimewillbespentworkingdirectlyfromthem. Youwillgainmostbenefitfromyourstudyifyouworkwithapencilandpapertohand,readingthe Youshouldalsohaveyourchapters,annotatingthemandmakingyourownnotes. Weadviseyouto calculatorandthecoursekeepthesenotes,andothersthatyoumake(forexample,notesfrom Handbook available.tutorialsandyourroughdraftsofassignments),inaringbinderornotebook,foreaseofreference.Somesectionsandtheiractivitiesrequiretheuseofresourcesbeyondthechaptersthemselves. Theseresourcesarespecified inthechapterstudyguides,andtheirassociated icons(seebelow)appearatthebeginningoftheappropriatesections.
indicatesthatyouwillneedyourcomputer
indicatesthatyouwillneedaudioCDplaybackequipment
indicatesthatyouwillneedDVDplaybackequipmentInaddition,theremaybetimesotherthanthosespecifiedwhenyouwishtouseyourcomputertochecksomething. Whenusingyourcomputer,doavoidsittingatthescreenfor longperiodswithoutabreak,andkeepapencilandpapertohandforanynotesthatyouneedtomake.4
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Onaverage,moststudentsareabletostudyachapterfromthecourse inabout15hours, includingworkingthroughtheassociatedcomputerwork,audio-visualmaterialandtherelevantassignmentquestions. Towardsthebeginningofthecourse,youmayfindthatyourstudytakesalittle longer,particularly ifMST121 isyourfirstOpenUniversitycourse. However,manystudentsdofindthematerial inBlockAtobedemanding,soyoumayfindthatthepressureofstudyisreducedwhenyoureachBlockB.Youmayfindthattheweeksinwhichassignmentsareduedemandmoreofyourtimetoo. Thereisalotofmaterial inBlockC, includinganintroductiontocalculus;this isoneofthemost importantareasofmathematics,particularly forapplicationsofmathematics,and it isdeveloped inanumberofhigher-levelcourses. Accordingly,youmayneedtoreservealittlemoretimetostudyBlockC,particularly ifyouaregoingontoothercourses inmathematics,physicsorelectronics. Moststudentsfindthestatistics inBlockDfairlystraightforward,butthis isfollowedbythefinalassignments,coveringthewholecourse,forwhichyouarelikelytoneedtoreviewyourworkfromthroughoutthecourse.
Calculator
Youneedascientificorgraphicscalculator forpartsofthecourse. Thegraphicscalculatorused inthecourseMU120 issuitable,butanyscientificcalculatorshouldbesufficient. Ifyouarenotfamiliarwithyourcalculator,thenyoushouldpractiseusingitwiththehelpof itsmanual,preferablybeforethecoursebegins. Someguidance isgivenintheGuide toPreparation,andtherearefurtheropportunitiesforpracticeintheRevisionPack.
Computer software
ThesoftwarepackageMathcadandassociatedcoursefilesaresuppliedontheCD-ROM inthesamemailingasthisCourseGuide. TheprocessofinstallingMathcadandthecoursefiles isdescribed inChapterA0. Theactivitiesassociatedwiththesecoursefilesaregiveninthecomputerbooks. ThedocumentAGuide toMathcadprovidesasourceofreferencetothefeaturesofMathcadusedinthecourse. AnothersoftwarepackagecalledOUStats isused laterinthecourse.
Audio bands
Audiobandsareused insomepartsofthecourse,usuallytotalkyouthroughmaterialprinted inthetext,andoccasionally inconjunctionwithyourcomputer. Dostop,startandreplaythesebandsasoftenasnecessary.
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Video bands
TheDVDincludesvideobandsofvarioustypes. Someofthebandsarelinkeddirectlytothemaincoursetexts,andshouldbeusedwhenindicatedbythesetextsandontheStudyCalendar. The AlgebraworkoutbandsforBlocksA,BandCcovermoregeneraltechniquesinalgebra,takingyouthroughthebasicsstep-by-step.BandA(i) AthomewithMST121: in thisband, twoformerMST121
studentsanda tutordescribe theirexperienceswith thecourseandgivesomeusefuladvice.
BandA(ii) Algebraworkout: SimultaneousequationsBandA(iii) VisualisingcirclesBandA(iv) Algebraworkout: QuadraticequationsBandA(v) Algebraworkout: Powersand logarithmsBandB(i) Algebraworkout: SigmanotationBandB(ii) NetworksandmatricesBandB(iii) Algebraworkout: ArithmeticwithmatricesBandB(iv) Algebraworkout: WorkingwithvectorsBandC(i) Algebraworkout: DifferentiationBandC(ii) Visualising thederivativeBandC(iii) Algebraworkout: IntegrationBandC(iv) Algebraworkout: DifferentialequationsBandD Samplingdistributions
Supplementar y video material
AseriesoffifteenvideobandsontwoDVDsisassociatedwiththethreecoursesMU120,MST121andMS221. Youare likelytofindalloftheseprogrammes interestingandenrichingasyoustudy,butsomearemoreexplicitlyassociatedwithMST121coursechapters. ThefirstDVDcompriseseightbandsassociatedwithMU120,andthesecondhasfourbandsforMST121andthreeforMS221.
Study Calendar s
There isaStudyCalendar forMST121thatgivesthestartingdateforyourstudyofeachchapterandthedateswhentheassignmentsaredue. Italsogivesschedulesfortheaudioandvideobands.Handbook
TheMST121Handbook containsa listofnotationandaglossaryoftechnicalterms,arrangedalphabetically,togetherwithkeyresultsandformulas,organisedaccordingtothechapterinwhichtheyappear.TheHandbook isakeysourceofreferencethroughoutthecourseandyoushouldaddyourpersonalannotationstoit. Intheory,therefore,thereisno It isagoodideaeithertouseneedtomemorisematerialfromthecourse. However,themorenotation apencilortousePost-itandterminologyyoucanrememberandunderstand,theeasieryouwill stickers for your annotations untilyouareconfidentwhichfindittostudythecoursematerialsandtodoassessmentquestions typesuitsyoubest.confidently. Also,manyresultsandtechniquesfromMST121willbeusedinMS221andinothersecond- andthird-levelmathematicscourses.6
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Stop Presses
TheStopPresses,printedonpinkpaper,actascoursenewsletterscontainingusefulandoftenessentialinformation,suchaserrata,howtoreportothererrors,whattodo ifyouneedhelp,andmoredetaileddescriptionsofthevideobands.It is important to read each Stop Press as soon as it arrives, andto make a note of any points which affect you.
Course website
Any last-minutenewsaboutthecourse,suchaslateerrata,willbepostedonthecoursewebsite. Thecoursewebsitealsocontainsotherusefulresources,suchaselectroniccopiesofthecoursematerials.
4 AssessmentTheassessmentforMST121consistsoffivetutor-marked assignments(TMAs),towhichyouprovidewrittenanswers,andthreecomputer-marked assignments(CMAs),whichcontainmultiple-choicequestions. Theseassessmentsarecontained inthreeassignmentbooklets.Theassessmentonthecourse issummarised inthistable.Assignmentnumber Weighting Material covered NotesTMA10 0% Preparatory; formative
RevisionPackCMA51 0% Preparatory; formative
RevisionPackTMA01 20% BlockA substitutableTMA02 20% BlockB substitutableTMA03 20% BlockC substitutableCMA41 10% BlockD non-substitutableTMA04 20% BlocksA,B,C,D non-substitutableCMA42 10% BlocksA,B,C,D non-substitutable
TMA10andCMA51areformative,whichmeansthatyourresultsforthemdonotcounttowardsyourfinalcourseresult. Thesearepracticeassignmentstohelpwithyourpreparationforthecourse,andtogiveyouearlyfeedbackonyourmathematicalworkand, inthecaseofTMA10,onhowyoupresentyourmathematics.Thedatesbywhicheachassignmentshouldbesubmittedaregiven intheStudyCalendar. Thecut-offdateforeachofTMA01,02and03 isthelastdateonwhichyourtutormayacceptyourworkformarking,unlessheorshe
feels
that
there
are
exceptional
reasons
why
you
should
be
allowed
to
submit late. NosuchextensionsarepossiblefortheCMAsorforTMA04. InstructionsforsubmittingTMAsandCMAsaregiven intheassignmentbooklets.
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Itisimportanttoplanyourstudyto includetimetoworkontheassignments,allowingtimetorefineandcheckwhatyouwriteandperhapstoactonanyadvicethatyoumightseekfromyourtutor. Youwillprobablyfinditbesttodotheappropriateassignmentquestionsattheendofstudyingeachchapter inthecourse,andthenreviewthewholeassignmentjustbeforeyousubmit itinadvanceofthecut-offdate.InTMA04youwillbeaskedtoattemptfour longerquestionsonthecourse. TMA04 issubjecttoathreshold: youmustobtainaminimumoverallgradeof30%onthisassignment inordertopassthecourse.
Your overall grade
TopassMST121,youwillneedtohaveperformedsatisfactorily intheassessmentcomponentasawholethiswouldnormallymeanobtaininganoverallscoreofat least40%acrossalltheassignments(exceptTMA10andCMA51),andachievingat least30%onTMA04. Youroverallscorewillbecomputed inlinewiththeprocedureoutlined intheAssessmentHandbook,taking intoaccounttheweightingforeachassignmentasgiveninthetableabove.If,forwhateverreason,youdonotsubmitorachieveonlya lowmarkononeofTMA01,02or03,youroverallscoremaybe improvedbyasystemknownassubstitution. ThismeansthatyourscoreforoneofTMA01,02or03canbesubstitutedbyyouroverallcoursescore(ifthisishigher),whenthat iscalculatedattheendofthecourse. Ifsubstitutionwouldbenefityouroverallscore,theprocessiscarriedoutautomatically. Theeffectsofthesubstitutionsystemarethat: youarenotpenalisedtooseverelyforalowmarkononeofTMA01,
02or03; it isadvantageoustosubmitalltheTMAs,evenifyouarenotableto Youwillalsoreceiveuseful
doyourselfjusticeonsomeparts. feedback.MST121 isaLevel1course,andthusattheendofthecourseyouwillbeawardedeitherapassorfailgrade.Ifyouhaveachievedsatisfactorymarksacrosstheassessmentoverall,andmadeareasonableattemptatTMA04butnotachievedthethreshold,thenyoumaybeofferedtheopportunitytoattemptthenewversionsofTMA04andCMA42inthenextpresentationofthecourse. Ifyouaccepttheoffer,thenyourfinalcourseresultwillbebasedonyourscoresforthese
two
assignments
and
on
the
scores
you
obtained
for
TMA
01,
TMA02,TMA03andCMA41.
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5 Study suppor t
Your tutor
YourRegionalCentrewillsendyouthenameandaddressofyourtutor,whowillsupportyouracademicstudyandprovidefeedbackonyourwork.EveryTMAthatyousubmitontimeshouldbereturnedmarkedbyyourtutor,withcomments. Thesecommentsshouldpointoutwhatyouhavedonewell,while indicatinganymisunderstandingsanderrorsandgivingadviceonhowtoavoidthese. TMAsarethebasisforcorrespondencetuition,andshouldenableyoutoestablishadialoguewithyourtutor.Youwillreceivedetailsofotherwaysinwhichyourtutormayofferyousupport, forinstancewithface-to-facetutorialsorcomputerconferences.Youwillbeabletoobtaindetailsofface-to-facetutorialsprovidedbyothertutors,whichyouareentitledtoattend. Youarestronglyencouragedtoattendface-to-facetutorials, if itisfeasibleforyoutodoso,astheyprovideanopportunitytoreceivefocusedtuition,toworkwithotherstudents,andtodiscussyourownquestions.If itis impossible foryoutotakepart inorganisedactivities,pleasemakecontactwithyourtutor,andmaintaincontactthroughtelephone,email,lettersorfax.
Other students
Talkingwithfellowstudentsaboutthemathematicsyouarestudying isavaluablewayofenhancingyour learning. Thereareopportunitiesforthisattutorials,andyoucanarrangefurthercontactbyexchangingaddresses,emailaddressesortelephonenumberswithotherstudentsinyourarea,perhapsforminga self-helpgroup. Itmaybepossibletobookaroomatastudycentreforself-helpgroupmeetings; ifso,yourRegionalCentrewillbeabletosupplydetails. Inadditiontoanylocalarrangementsthatyoumaymakewithyourtutorandfellowstudents,theOpenUniversityStudentsAssociation(OUSA)supportsanonlinecourseforumforMST121students.
Telephone help-lines
Asmentionedabove,youmaychoosetocontactyourtutorandfellowstudentsbytelephone. Youmayalsowishtousetelephonehelp-lines. Forexample,thereisatelephone tutorial servicerunonavoluntarybasisbymembersoftheFacultyofMathematicsandComputingwhoendeavourtoansweryourqueries. Thereisalsoacomputing help-linetosupportstudentsoncourseswhichinvolvetheuseofapersonalcomputer(likeMST121).Detailsabouttheseservicesaregiven inStopPresses.
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Other suppor t
RegionalCentresprovideallstudentswithstudysupportforproblemsthatarenotdirectlyrelatedtothecoursematerials. NewstudentsstudyingMST121willusuallyreceivethissupportfromtheirtutor. Ifyouhaveanynon-academicproblemsaffectingyourOpenUniversitystudiesyoushouldconsulttheLearner Support TeamatyourRegionalCentre.DetailsabouttheLearnerSupportTeamaregiven intheliteraturesentfromyourRegionalCentre.
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cPrinted in theUnitedKingdom Copyright2008 TheOpenUniversitySUP002610 6.1
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CourseGuide
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121CourseGuide
121UsingMathematics
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