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Page 13.1
School of Mathematics & Statistics
Head of School ProfessorEFRobertson
Degree ProgrammesSingleHonoursDegrees(BSc,MAorMSci): AppliedMathematics Mathematics PureMathematics StatisticsSingleHonoursDegrees(BSc) QuantitativeEcologyJointHonoursDegrees(BSc): Mathematicsand Chemistry,Computer Science,Economics,Geography,Logic&
PhilosophyofScience,ManagementScience,Physics,Psychology,Statistics.
Statisticsand ComputerScience,Economics,Geography,Logic&Philosophyof
Science,ManagementScience,Mathematics.JointHonoursDegrees(MSci): MathematicsandStatistics MathematicsandTheoreticalPhysicsJointHonoursDegrees(MA) Mathematicsand AncientHistory,ArtHistory,Economics,Hebrew,Latin,Mediaeval
History A,Philosophy,ScottishHistory,Statistics,TheologicalStudies. Statisticsand Economics,Mathematics,Philosophy.MajorDegreeProgrammes(BSc): MathematicswithFrench WorGeographyorGerman W
StatisticswithFrench WorGerman W
Wavailablealsoas‘withIntegratedYearAbroadDegrees’ATimetableclashexists,thereforeonlyAppliedMathematicscanbestudiedinthiscombination
BSc Programme PrerequisitesApplied Mathematics
Apassat11orbetterinbothMT2001andMT2003
Mathematics
Mathematics: Apass at 11or better inMT2001orMT2101 and in oneofMT2002or MT2003
MathematicsandPhysics: Passesat11orbetterineither(MT2001andMT2003)orMT2101plusthe Physicsrequirements
AllotherProgrammes: Apass at 11or better inMT2001orMT2101 and in oneofMT2002or MT2003
MathematicswithFrench: AsforMathematicsandalsoapassinFR2011andapassat11orbetterin FR2012
MathematicswithGerman: AsforMathematicsandalsoGM2005andapassat11orbetterinGM2006
MathematicsandStatistics: Passesat11orbetterinboth(MT2001orMT2101)andMT2004andalso inoneofMT2002,MT2003orMT2005
Chemistry and Mathematics
Passesat11orbetterinCH2101,eitherCH2102orCH2103,eitherMT2001or MT2101,andoneofMT2002andMT2003
Pure Mathematics
Passesat11orbetterinboth(MT2001orMT2101)andMT2002
Mathematics & Statistics - pathways
Page 13.2
Mathematics & Statistics - pathways
Quantitative Ecology
Passesat11orbetterinMT1006,MT2001,MT2004,BI2001andeitherBI2004orBI2005.ItisrecommendedthatstudentstakeBI2005.
Statistics
Passesat11orbetterinboth(MT2001orMT2101)andMT2004
StatisticswithFrench: AsforStatisticsandalsowithapassinFR2011andapassat11orbetterinFR2012
StatisticswithGerman: AsforStatisticsandalsoGM2005andapassat11orbetterinGM2006
BSc Programme RequirementsApplied Mathematics
SingleHonoursDegree: 240credits,ofwhichatleast210creditsmustbefromMT3501-MT3999including:
(i) MT3501-MT3504
(ii) MT3601,MT3602
(iii) atleastoneofMT3611,MT3612
(iv) MT3999
Mathematics
SingleHonoursDegree: 240credits,ofwhichatleast210creditsmustbefromMT3501-MT3999including:
(i) MT3501-MT3504
(ii) atleasttwoofMT3601,MT3602,MT3603,MT3604
(iii) atleastoneofMT3611,MT3612
(iv) MT3999
MathematicswithFrenchorGerman: 240credits,ofwhichatleast180creditsmustbefromMT3501-MT3999,including:
(i) atleastthreeofMT3501-MT3504
(ii) atleastoneofMT3601-MT3604
(iii) atleastoneofMT3611,MT3612
(iv) MT3999
MathematicsandPhysics: 240credits,ofwhichatleast120creditsmustbefromMT3501-MT3999,excludingMT3805,butincluding:
(i) atleasttwoofMT3501-MT3504
(ii) atleastoneofMT3601-MT3604
(iii) atleastoneofMT3611andMT3612
(iv) MT3999
MathematicsandStatistics: 240credits,ofwhichatleast210mustbefromMT3501-MT3999including:
(i) MT3501andatleastoneofMT3502-MT3504
(ii) MT3701andatleasttwoofMT3702-MT3706
(iii) atleastoneofMT3601-MT3604
(iv) AtleastoneofMT3611,MT3612
(v) MT3999
Mathematicsandanyothersubject:240credits,ofwhichatleast120creditsmustbefromMT3501-MT3999including:
(i) atleasttwoofMT3501-MT3504
(ii) atleastoneofMT3601-MT3604
(iii) atleastoneofMT3611,MT3612
(iv) MT3999
Pure Mathematics: 240credits,ofwhichatleast210creditsmustbefromMT3501-MT3999including:
Page 13.3
Mathematics & Statistics - pathways
(i) MT3501-MT3504
(ii) MT3603,MT3604
(iii) atleastoneofMT3611,MT3612
(iv) MT3999
Quantitative Ecology: 240creditsincluding:
(i) 60creditsfromMT3702,MT3834,MT3999
(ii) 40creditsfromBE3001andBE3002
(iii) At least 90 credits fromMT3501,MT3504,MT3602,MT3611,MT3704,MT3705,MT3706,MT3802,MT3803,MT3808,MT3813,MT3828,MT3830,MT3835,MT3838
(iv) Atleast40creditsfromBE3004,BE3005,BE3006,BE3102,BE3105
Statistics
SingleHonoursDegree: 240credits,ofwhichatleast210mustbefromMT3501-MT3999including:
(i) MT3501
(ii) MT3701-MT3706
(iii) MT3999
JointHonoursDegree: 240credits,ofwhich120mustbefromMT3501-MT3999including:
(i) MT3501
(ii) MT3701andatleasttwofromMT3702-MT3706
(iii) MT3999
InthecaseofJointHonoursinManagementScienceandStatisticsatleast45creditsarerequiredfromMN3006-MN3056.
StatisticswithFrenchorGerman: 180creditsfromMT3501-MT3999including:
(i) MT3501
(ii) MT3701andatleastthreefromMT3702-MT3706
(iii) MT3999
InthecaseofstudentswhospendpartoftheHonoursProgrammeabroadonarecognisedExchangeScheme,theProgrammeRequirementswillbeamendedtotakeintoaccountcoursestakenwhileabroad
MSci Programme PrerequisitesApplied Mathematics
Apassat17orbetterinbothMT2001andMT2003
Mathematics
Mathematics: Passesat17orbetterin(MT2001orMT2101)andoneofMT2002or MT2003
MathematicsandTheoreticalPhysics: PassesineitherMT2101or(MT2001andMT2003)plusthePhysics requirements,theMathematicspassesbeingat17orbetterandthePhysics passesbeingat15orbetter
MathematicsandStatistics: Passesat17orbetterinboth(MT2001orMT2101)andMT2004andalso inoneofMT2002,MT2003orMT2005
Pure Mathematics
Passesat17orbetterinboth(MT2001orMT2101)andMT2002
Statistics
Passesat17orbetterinboth(MT2001orMT2101)andMT2004
MSci Programme Requirements
Page 13.4
Mathematics & Statistics - pathways
Applied Mathematics300creditsfromMT3501-MT4999including:
(i) MT3501-MT3504
(ii) MT3601,MT3602
(iii) atleastoneofMT4611andMT4612
(iv) MT4999
(v) atleast120creditsfromMT4801-MT4881
Mathematics300creditsfromMT3501-MT4999including:
(i) MT3501-MT3504
(ii) atleasttwoofMT3601,MT3602,MT3603,MT3604
(iii) atleastoneofMT4611,MT4612
(iv) MT4999
(v) atleast120creditsfromMT4801-MT4881
Mathematics and Statistics300creditsfromMT3501-MT4999including:
(i) MT3501andatleastoneofMT3502-MT3504 (ii) oneofMT3601-MT3604 (iii) (MT3701orMT4701)andatleasttwoof(MT3702orMT4702),MT3706,(MT3704or MT4704),(MT3705orMT4705) (iv) atleastoneofMT4611orMT4612
(v) MT4999
(vi) atleast120creditsfromMT4701-MT4881Mathematics and Theoretical Physics305creditscomprising:
(i) MT3501andMT3504
(ii) atleasttwomodulesfromMT3501-MT3837otherthanMT3805andthosespecifiedin(i)
(iii) atleastfourmodulesfromMT4611-MT4882otherthanMT4805
(iv) eitherMT4998orPH4102
(v) thetheoreticalphysicsrequirementsPure Mathematics300creditsfromMT3501-MT4999including:
(i) MT3501-MT3504
(ii) MT3603,MT3604
(iii) atleastoneofMT4611andMT4612
(iv) MT4999
(v) atleast120creditsfromMT4801-MT4881
Statistics 300creditsfromMT3501-MT4999including:
(i) MT3501
(ii) (MT3701 orMT4701), (MT3702 orMT4702),MT3706, (MT3704 orMT4704),(MT3705 orMT4705)
(iii) MT4999
(iv) atleast140creditsfromMT4701-MT4881
Page 13.5
Mathematics & Statistics - 1000 Level modules
ModulesMT1001 Introductory MathematicsCredits: 20.0 Semester: 1
Prerequisites: Higher/A-LevelMathematics.StudentswithAatHighersandBatPaperIofCSYSoraCatA- levelmaybypassthismoduleandproceedtoMT1002.
Anti-requisite: MT1003
Description: Thismodule isdesigned togivestudentsasecurebase inelementarycalculus toallowthemtotacklethemathematicsneededinothersciences.StudentswishingtodomoremathematicswillbegivenagoodfoundationfromwhichtheycanproceedtoMT1002.SomeoftheworkcoveredisarevisionandreinforcementofmaterialintheScottishHighersandmanyA-levelsyllabuses.
ClassHour: 9.00am
Teaching: Fivelectures,onetutorialandonelaboratory.
Assessment: ContinuousAssessment=30%,2HourExamination=70%
Re-Assessment: 2HourExamination=100%
MT1002 MathematicsCredits: 20.0 Semester: Either
Prerequisites: MT1001orHigher/A-levelMathematics(AatHigherandBatPaperIofCSYS,orCatA-level).
Description: Thismoduleisdesignedtointroducestudentstotheideas,methodsandtechniqueswhichtheywillneedforapplyingmathematicsinthephysicalsciencesorfortakingthestudyofmathematicsfurther.Itaimstoextendandenhancetheirskillsinalgebraicmanipulationandindifferentialandintegralcalculus,todeveloptheirgeometricinsightandtheirunderstandingoflimitingprocesses,andtointroducethemtocomplexnumbersandmatrices.
ClassHour: 9.00am
Teaching: Fivelectures,onetutorialandonelaboratory.
Assessment: ContinuousAssessment=30%,2HourExamination=70%
Re-Assessment: 2HourExamination=100%
MT1003 Pure and Applied MathematicsCredits: 20.0 Semester: 2
Prerequisite: MT1002
Description: Theaimofthismoduleistoprovidestudentswithatasteofbothpureandappliedmathematics,togivetheminsightintoareasavailableforstudyinlateryearsandtoprovidethemwiththeopportunitytobroadentheirmathematicalexperience.
ClassHour: 9.00am
Teaching: Fivelectures,onetutorialandonelaboratory.
Assessment: ContinuousAssessment=30%,2HourExamination=70%
Re-Assessment: 2HourExamination=100%
MT1006 Statistical Data AnalysisCredits: 20.0 Semester: 1
Prerequisites: Pass inMathematicsatSCE‘O’GradeorStandardGradeatGrade1or2 (CreditLevel)orGCSE atGradeA,BorC.
Description: Thismodulewillcoverthefollowingthreemaintopics:(i)graphicalandstatisticaldatasummary:introduction tostatistics,waysofrepresenting,viewingandsummarisingdata,graphicalfallaciesandpitfalls. (ii)randomizationandMonteCarlomethods:theideaofrandomizationtests,non-parametrictestsbasedonthisparadigm,MonteCarlotestsandthebootstrap.(iii)linearmodels:fittingstraightlinestodata,uncertaintyinmodelparameters,analysisofvariance,goodnessoffit,multipleregression.
ClassHour: 11.00am
Teaching: Fourlectures,onetutorialandonelaboratory.
Assessment: ContinuousAssessment=34%,2HourExamination=66%
Re-Assessment: ContinuousAssessment=17%,3HourExamination=83%
Page 13.6
Mathematics & Statatistics - 1000 & 2000 Level modules
MT1007 Statistics in Practice
Credits: 20.0 Semester: 2
Prerequisites: MT1001orHigher/A-levelMathematics(AatHighersandBatPaperIofCSYS,orCatA-level)
Description: Theaimsofthemodulearetodemonstratebymeansoftopicalcasestudiestherelevanceofstatisticsinprovidinganswerstoquestionssuchas:shouldsoftwaterhaveagovernmenthealthwarning?;areAntarcticwhalesheadingforrecoveryorextinction?;istheuniverseevolving?;canyoutellbutterfrommarge?;wasQuintusCurtisSnodgrassreallyMarkTwain?;howcanweforecastfutureUKpopulationsize?;doesalargebrainindicateintelligence?;howcanwediscoverwhatpeoplethink?;isonegameofRussianroulettepreferabletoalifetimeofoffshorefishing?
ClassHour: 11.00am
Teaching: Fourlectures,onetutorialandonelaboratory.
Assessment: ContinuousAssessment=50%,2HourExamination=50%
Re-Assessment: ContinuousAssessment=25%,2HourExamination=75%
MT2001 Mathematics
Credits: 30.0 Semester: 1
Prerequisite: MT1002
Anti-requisite: MT2101
Description: TheaimsofthismodulearetoextendtheknowledgeandskillsgainedbystudentsinthemoduleMathematicsMT1002,andinparticulartoenhancetheirskillsinthetheoryandapplicationof:differentialandintegralcalculusofseveralrealvariables;limitingprocesses;linearmathematics.
ClassHour: 12.00noon.
Teaching: Fivelectures,onetutorialandonepractical.
Assessment: ContinuousAssessment=30%,3HourExamination=70%
Re-Assessment: 3HourExamination=100%
MT2002 Algebra and Analysis
Credits: 30.0 Semester: 1
Prerequisite: MT1002
Description: Theaimsof thismoduleare to encourage students’understandingof the logical structureofmathematicsandthenatureofproof,andtointroducestudentstosomefundamentalconceptsofabstractalgebraandofanalysis.
ClassHour: 11.00am
Teaching: Fivelectures,onetutorialandonepractical.
Assessment: ContinuousAssessment=30%,3HourExamination=70%
Re-Assessment: 3HourExamination=100%
MT2003 Applied Mathematics
Credits: 30.0 Semester: 2
Prerequisite: MT1002
Anti-requisite: MT2101
Description: Thismoduleintroducesstudentstoappliedmathematicsthroughtheconstruction,analysisandinterpretationofmathematicalmodels,andtothetechniquesofanalysisusedinmathematicalmodelling.
ClassHour: 12.00noon.
Teaching: Fivelectures,onetutorialandonepractical.
Assessment: ContinuousAssessment=30%,3HourExamination=70%
Re-Assessment: 3HourExamination=100%
Page 13.7
Mathematics & Statistics - 2000 Level modules
MT2004 Statistics
Credits: 30.0 Semester: 2
Prerequisites: MT1002andMT1004[From2001-02onlyMT1002]
Description: Thismodule introduces students to themathematicalmodels of randomness used as part ofstatisticalmodellingandanalysis.Themoduleisamixoffundamentalmathematicalstatisticsandappliedstatisticalanalysisandprovidesthebackgroundnecessaryforthe3000levelmodulesinstatistics.
ClassHour: 10.00am
Teaching: Fivelectures,onetutorialandonepractical.
Assessment: ContinuousAssessment=30%,3HourExamination=70%
Re-Assessment: 3HourExamination=100%
MT2005 Discrete Mathematics
Credits: 30.0 Semester: 2
Prerequisites: MT1002
Description: Thismoduleaimstointroducestudentstotechniquesandideasindiscretemathematics,andtoreinforcetheideaofproofinmathematics.
ClassHour: 11.00am
Teaching: Fivelectures,onetutorialandonepractical.
Assessment: ContinuousAssessment=30%,3HourExamination=70%
Re-Assessment: 3HourExamination=100%
MT2006 Project in Statistics
Credits: 10.0 Semester: Either
Prerequisites: Agradeof11orhigherisrequiredinoneofMT1004,MT1006,MT1007
Description: Thestudentwillchooseaprojectfromalistpublishedannually.Atopicoutwiththislistmaybeapproved.Weeklysessionswiththesupervisorwillbescheduled,andareportmustbesubmittedbytheendofweek10ofthesemester.
Assessment: Project=100%
Re-Assessment: ResubmissionofprojectandOralExamination.
MT2101 Mathematical Methods
Credits: 30.0 Semester: 1
Prerequisite: MT1002
Anti-requisites: MT2001,MT2003
Description: TheaimsofthismodulearetoextendtheknowledgeandskillsgainedbystudentsinthemoduleMT1002,andinparticularenhancetheirskillsinthetheoryandapplicationof:limitingprocessesanddifferentialandintegralcalculusinseveralrealvariables,methodsofFourierseriesandLaplacetransforms,andvectorcalculus.TheneedsofHonoursstudentsinPhysicsandAstronomyareaddressed.ThemoduleMT2101may,withthepermissionoftheHeadofSchool,beacceptableasaalternativetoMT2001intheentryrequirementsforHonourscoursesinvolvingmathematicsorstatistics.However,studentswishingtoretaintheoptionofentrytoHonoursMathematicsorStatisticsshouldnormallytakeMT2001.
ClassHour: 12.00noon
Teaching: Fivelectures,onetutorial,onepractical.
Assessment: ContinuousAssessment=30%,3HourExamination=70%
Re-Assessment: 3HourExamination=100%
Page 13.8
Mathematics & Statistics - 2000 Level modules
The prerequisite for each of the following Honours modules is entry to the Honours Programme(s) for which they are specified, save where a specific prerequisite is given.MT3501 Linear Mathematics
Credits: 15.0 Semester: 1
Prerequisite: MT1002
Description: Thismoduleaimstoshowtheimportanceoflinearityinmanyareasofmathematicsrangingfromlinearalgebrathroughtogeometricapplicationstolinearoperatorsandspecialfunctions.Themaintopicscoveredare:lineardependenceandindependence;changeofbasis;innerproductspaces;inequalities;convergenceinEuclideanspaces;Fourierseriesandadjointandself-adjointoperators.
ClassHour: 9.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3502 Foundations of Calculus
Credits: 15.0 Semester: 2
Prerequisite: MT2001orMT2101
Description: Thismodulegivesarigorous treatmentof topics in thecalculus,someofwhichwillalreadyhavebeenencounteredfromthepointofviewofcalculationandapplicationwithoutconsideringquestionsofvalidity.Topics,whichwillbeillustratedbymanyexamplesandcounter-examples,mayinclude:convergenceofsequencesandseries,continuity,differentiabilityandapplicationstoTaylorseries,analysisinndimensions,partialderivatives,theinversefunctiontheorem.
ClassHour: 9.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3503 Complex Analysis
Credits: 15.0 Semester: 1
Prerequisite: MT2001orMT2101
Description: Thismoduleaimstointroducestudentstoanalyticfunctiontheoryandapplications.Thetopicscoveredinclude:analyticfunctions;Cauchy-Riemannequations;harmonicfunctions;multivaluedfunctionsandthecutplane;singularities;Cauchy’stheorem;Laurentseries;evaluationofcontourintegrals;fundamentaltheoremofalgebra;conformalmappings.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3504 Differential Equations
Credits: 15.0 Semester: 1
Prerequisite: MT2001orMT2101
Description: Theobjectofthismoduleistoprovideabroadintroductiontoanalyticalmethodsforsolvingordinaryandpartialdifferentialequationsand todevelopstudents’understandingand technicalskills in thisarea.Thismoduleisaprerequisiteforseveralotherhonoursoptions.Thesyllabusincludes:existenceanduniquenessofsolutions to initial-valueproblems; series solutionsof second-ordero.d.e.’s;examples includingBessel,LegendreandAiryequations;nonlinearo.d.e.’s;classificationofsecondorderlinearp.d.e.’s;methodofseparationofvariables;eigenvaluesforboundaryconditionsofmixedtype;characteristicsandreductiontocanonicalform.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
Page 13.9
Mathematics & Statistics - 3000 Level modules
MT3601 Fundamentals of Applied Mathematics
Credits: 15.0 Semester: 1
Pre(Co)requisites: MT2001orMT2003orMT2101
Description: Theobjectofthemoduleistointroducestudentstobasicappliedmathematicalmethodswhichcanbeappliedtoproblemsinfluiddynamics,plasmadynamicsandsolarmagnetohydrodynamics.Themodulewillinclude:arevisionofthebasictechniquesofvectorcalculus;thebasicequationsoffluidmechanics,includingtheequationsofcontinuity,EulerandBernoulli;fluidmotionsacceleratedbypressuregradients;generalpropertiesofincompressibleflow;Maxwell’sequations;solarMHD(observationsandequations);equilibria;solutionofLaplace’sequationbyseparationofvariables;thewaveequation;characteristics;separablesolutions;theheatdiffusionequation;similaritysolutions;linearperturbations;small-amplitudeanalysis;examples-soundwaves;MHDwaves.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3602 Applied Mathematical Methods
Credits: 15.0 Semester: 1
Prerequisites: MT2003,MT2001orMT2101
Description:Theaimofthismoduleistogivestudentsamodernanalyticalbasisinthetheoryofordinaryandpartialdifferentialequationsarisinginappliedmathematics.Themodulewillinclude:phaseplanemethodsforlinearandnonlineardifferentialequations;thenonlinearpendulum;systemsofequations;limitcycles;stability;chaosandstrangeattractors;theLorenzequations;theRiccatiequations,anintroductiontononlinearevolutionequations:themethodofcharacteristicsinpartialdifferentialequations;theadvectionequations;diffusiveanddispersivebalance;Burger’sequation;theKorteweg-deVriesequation;solitonsandrelatedequations.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial
Assessment: 2HourExamination=100%
MT3603 Groups
Credits: 15.0 Semester: 1
Prerequisite: MT2002
Description: Thismoduleintroducesstudentstogrouptheory,whichisoneofthecentralfieldsofthe20thcenturymathematics.Themainthemeofthemoduleisclassifyinggroupswithvariousadditionalproperties,andthedevelopmentoftoolsnecessaryinthisclassification.Inparticular,thestudentswillmeetthestandardalgebraicnotions,suchassubstructures,homomorphisms,quotientsandproducts,andalsovariousconceptspeculiartogroups,suchasnormality,conjugationandSylowtheory.Theimportanceofgroupsinmathematics,arisingfromthefactthatgroupsmaybeusedtodescribesymmetriesofanymathematicalobject,willbeemphasisedthroughoutthemodule.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3604 Real Analysis
Credits: 15.0 Semester: 1
Prerequisite: MT2002
Description: ThismodulecontinuesthedevelopmentofrealanalysisstartedinMT2002.Topicsthatwillbetreatedfromarigorouspointofviewmayinclude:differentiation,Riemannintegration,uniformconvergence,functionspaces.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3611 Symbolic Computation
Page 13.10
Mathematics & Statistics - 3000 Level modules
Credits: 15.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2001orMT2101
Description: ThismoduleaimstoenablestudentstouseMapleasatoolintheirothermodulesandtoturnnaturallytosuchapackagewhensolvingmathematicalproblems.Themoduleaimstoillustratethefollowingpoints:asymboliccomputationpackageallowsonetoconductmathematicalexperiments;asymboliccomputationpackageallowsonetocollectdataaboutaproblembeingstudied.Thisissimilartothewayotherscientistswork.Itiseasiertotryseveraldifferentapproachestoaproblemandseewhichworks.Themachineisstupid.Intelligencecomesfromtheuser.Theuserthinks,theuserinterprets,thecomputercalculates.
ClassHour: 9.00am
Teaching: Twolecturesandonetutorial.
Assessment: ContinuousAssessment=30%,2HourExamination=70%
MT3612 Computing in Mathematics
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisites: (MT2001orMT2101),MT2003
Anti-requisite: HonoursorJointHonoursProgrammeinComputerScience.
Description: ThismoduleisintendedtointroducestudentstoFORTRANandthewritingofcomputercodestoimplementmathematicalalgorithms.ThemoduleincludesabasicintroductiontoFORTRAN,andtheimplementationofmathematicalalgorithmsinawell-documentedFORTRANprogram.Studentsarerequiredtocompleteaprojectinadditiontosittingtheexamination.
ClassHour: 9.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=30%,2HourExamination=70%
MT3701 Statistical Inference
Credits: 15.0 Semester: 1
Prerequisites: (MT2001orMT2101),MT2004
Description: Thismoduleaimstoshowhowthemethodsofestimationandhypothesistestingmetinfirstandsecondyearcanbejustifiedandderived;toextendthosemethodstoawidervarietyofsituations;toshowhowdifferentpointestimatorscanbecompared; toprovidean introductionto theBayesianapproachto inference.Thesyllabusincludes:distributiontheory;pointestimation;meansquareerror;unbiasedness;Fisherinformation;theCramer-Raolowerbound;maximumlikelihoodestimation;hypothesis-testing;Bayesianinference.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3702 Generalized Linear Models and Data Analysis
Credits: 15.0 Semester: 1
Prerequisite: MT2004
Co-(orpre-)requisite:MT3501
Description: Thismoduleaimstodemonstratethepowerandeleganceofunifyingalargenumberofsimplestatisticalmodelswithinthegeneralframeworkofthegeneralizedlinearmodel.Itwilltrainstudentsintheinterpretation,analysisandreportingofdata,whenasingleresponsemeasurementisinterpretedintermsofoneoranumberofothervariables.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorialandpracticalclasses.
Assessment: Project=20%,2HourExamination=80%
MT3704 Sampling Theory
Page 13.11
Mathematics & Statistics - 3000 Level modules
Credits: 15.0 Semester: 2
Availability: 2000-01
Prerequisite: MT1004orMT1007
Description: Theaimsofthismodulearetointroducestudentstoandinterestthemintheprinciplesandmethodsofdesign-basedinference,toconvincethemoftherelevanceandutilityofthemethodsinawidevarietyofreal-worldproblems,andtogivethemexperienceinapplyingtheprinciplesandmethodsthemselves.Bytheendofthemodulestudentsshouldbeabletorecognisegoodandpoorsurveydesignandanalysis,todecideuponandimplementthemaintypesofsurveydesigninrelativelystraightforwardsettings,andanalysetheresultingsurveydataappropriately.Thesyllabusincludesfundamentalsofdesignbasedvs model-basedinference,simplerandomsampling,samplingwithreplacement,ratioandregressionestimators,stratifiedsampling,clustersampling,unequalprobabilitysamplingandquestionnairedesign.
ClassHour: 12.00noon
Teaching: Twolectures,onetutorialandpracticalclasses.
Assessment: Project=15%,2HourExamination=85%
MT3705 Multivariate Analysis
Credits: 15.0 Semester: 1
Availability: 2000-01
Prerequisites: MT2004and(MT2001orMT3501)
Description: Thismoduleaims to introducestudents to the ideasand techniquesofmultivariatestatisticalanalysis.Thesyllabusincludesmeanvectors,covariancematrices,correlationmatrices;basicpropertiesofmultivariatenormal distributions; checkingmultivariate normality; the likelihood ratio and union-intersection principles forconstructingmultivariatetests;theone-sampleandtwo-sampleHotelling’sT-squaredtests;testsoncovariancematrices,testsofindependence;lineardiscriminantanalysis;principalcomponentsanalysis;canonicalcorrelation.
ClassHour: 9.00am
Teaching: Twolectures,onetutorialandpracticalclasses.
Assessment: 2HourExamination=100%
MT3706 Markov Chains and Processes
Credits: 15.0 Semester: 1
Availability: 2001-02
Prerequisite: MT2004
Description: Thismoduleprovidesanintroductiontothetheoryofstochasticprocessesandtotheiruseasmodels,includingapplicationstopopulationprocessesandqueues.ThesyllabusincludestheMarkovproperty,theChapman-Kolmogorov equations, classification of states ofMarkov chains, decomposition of chains, stationarydistributions,randomwalks,branchingprocesses,thePoissonprocess,birth-and-deathprocessesandtheirtransientbehaviour,embeddedchains,Markovianqueues.
ClassHour: 9.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3801 Topics in the History of Mathematics
Credits: 15.0 Semester: 2
Prerequisite: MT1002
Description: Theaimofthismoduleistogivestudentsaninsightintothehistoricaldevelopmentofmathematics.Topics tobecoveredmayincludesomeof: thedevelopmentofalgebra, theoriginsof thecalculus, thehistoryoflogarithms,theworkofsomeindividualmathematicians.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3802 Numerical Analysis
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Mathematics & Statistics - 3000 Level modules
Credits: 15.0 Semester: 1
Prerequisites: MT2001orMT2101
Description: Themodulewillintroducestudentstosometopicsinnumericalanalysis,includinginterpolation,bestapproximation,numericalintegration,thenumericalsolutionofordinarydifferentialequations,solutionofsystemsoflinearequationsbyeliminationandbyiterativemethods.
ClassHours: 9.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3803 Interpolation and Approximation
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2001orMT2101
Description: Thismoduleaimstopresentsomeofthekeyideasininterpolationandapproximation.TopicsmayincludeChebyshevpolynomialsandoptimalinterpolationpoints;Peano’stheorem;BernsteinpolynomialsandBernstein’sproofoftheWeierstrasstheorem,rationalapproximationandGaussianquadrature.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3804 The Sun
Credits: 15.0 Semester: 1
Prerequisites: MT2003,MT3601
Description: Thismoduleisintendedtointroducethebasicobservationsandtheoriesofsolarphysics,payingparticular attention to solarmagnetohydrodynamics.The syllabus includes: anoutlineof observational propertiesrangingfromthesolar interiortotheSun’souteratmosphere; theoreticalaspectsofsolarmagnetohydrodynamics;magneticequilibria;MHDwaves;coronalheating.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3805 Electromagnetism
Credits: 15.0 Semester: 2
Availability: 2000-01
Prerequisite: MT3601
Description: Thismoduleisintendedtointroducestudentstothepropertiesofelectromagneticwaves,includingthepropagationofplanewavesandguidedwaves,andthegenerationofwavesbyantennas,andtogiveanintroductiontothemotionofchargedparticlesinelectricandmagneticfieldsandsomeapplicationstoplasmaphysics.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3806 Numerical Solution to Partial Differential Equations
Credits: 15.0 Semester: 2
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Mathematics & Statistics - 3000 Level modules
Availability: 2000-01
Prerequisite: MT3504orMT3602
Description: Thismoduleisintendedtointroducestudentstosomeoftheideas,techniquesandconstraintsthatunderpinmodernapproachestothenumericalmodellingofphysicalprocessesthatmaybedescribedbypartialdifferentialequations.Themodulewillinclude:convergenceandstabilityofstandardfinite-differenceschemes;theapplicationofstandardmethodstotwospacedimensionalproblems;ADImethods;theCFLcondition;dispersion,dissipationandstability;theLaxWendroffmethod.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3807 Classical Mechanics
Credits: 15.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2003
Description: TheobjectofthismoduleistointroducestudentstosomeoftheideasandmathematicaltechniquesusedinunderstandingthebehaviourofdynamicalsystemsthatobeyNewton’sLaws.Thesenotionsarearguablythefoundationsofphysicsandappliedmathematics.Themodulewillinclude:Newton’slawsofmotion;conservativeforces;centralforces;non-inertial/acceleratingframesofreference;dynamicsofasystemofparticles;mechanicsofarigidbody;Euler’sequations;Lagrange’sequations;Hamilton’sequations.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3808 Dynamical Systems
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3504
Description: Thismoduleaimstointroducestudentstothebasicideasofthemoderntheoryofdynamicalsystemsandtotheconceptsofchaosandstrangeattractors.Themodulewillinclude:perioddoubling;intermittencyandchaos;geometricalapproachtodifferentialequations;homoclinicandheteroclinicorbits;Poincarésections;theSmalehorseshoemapping;centremanifoldtheory.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3809 Fluid Dynamics
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3601
Description: Thismoduleaims todevelopanunderstandingoffluidmovement through theapplicationofrelevantmathematicaltechniquestovarioussituations.Themodulewillinclude:theworkingsofPitottubesandVenturimeters;theconceptsofFroudeandReynoldsnumbers;howtosolveLaplace’sequationforvariousvelocitypotentialproblems;Navier-Stokesequations;aerofoiltheory;waterwavetheory.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3811 Aysmptotic Analysis and Perturbation Theory
Credits: 15.0 Semester: 2
Page 13.14
Mathematics & Statistics - 3000 Level modules
Availability: 2000-01
Prerequisite: MT3504
Description: Thismoduleisdesignedtointroducestudentstoasymptoticandperturbationmethodsthatgiveanalyticalapproximationstointegralsandsolutionsofdifferentialequations.Themodulewillinclude:definitionsofasymptoticseriesandexpansions;proofofWatson’slemma;Laplace’smethod;methodofstationaryphase;regularandsingularperturbationmethodsfordifferentialequations;boundarylayerequationsandthemethodofmatchedasymptoticexpansions;WKBmethod.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3812 Nonlinear Partial Differential Equations
Credits: 15.0 Semester: 2
Availability: 2001-02
Pre(Co)requisite: MT3504
Description: Theaimofthismoduleistogiveaninsightintotheroleofnonlinearpartialdifferentialequationsoftheevolutiontypeinmodernappliedmathematics.Afteranintroductiontomethodsforlinearequations,themodulewilldealwithtechniquesfortheanalysisofapplicationsinsuchareasascompressiblefluidflowandtheformationofshockwaves,travellingwaves,spreadofthinfilms,solitons,trafficflowandotherareasofthephysicalandbiologicalsciences.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3813 Fractal Geometry
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2001orMT2101
Description: Theaimofthismoduleistointroducethemathematicsusedtodescribeandanalysefractalsandtoshowhowthetheorymaybeappliedtoexamplesdrawnfromacrossmathematicsandscience.Themodulediscussesthephilosophyandscopeoffractalgeometry;andmayincludetopicssuchasdimension,representationoffractalsbyiteratedfunctionsystems,fractalsinotherareasofmathematicssuchasdynamicalsystemsandnumbertheory,JuliasetsandtheMandelbrotset.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3814 Graph Theory
Credits: 15.0 Semester: 2
Availability: 2000-01
Prerequisite: MT1002
Description: The aimof thismodule is to introduce students to the studyofGraphTheory as a tool forrepresentingconnectionsbetweendata.Topicstobecoveredmayinclude:basictheoryandapplications,Euleriangraphs,Hamiltoniangraphs,planargraphs,spanningtreesandapplications,networks,matchingproblems.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3815 Functional Analysis
Credits: 15.0 Semester: 2
Page 13.15
Mathematics & Statistics - 3000 Level modules
Availability: 2000-01
Prerequisite: MT2002
Description: Thisobjectofthismoduleistofamiliarisestudentswiththebasicnotionsoffunctionalanalysis,thatisanalysisonnormedspacesandHilbertspace.Themodulewillcovernormedspaces,convergenceandcompleteness,operators,HilbertspacesandmayincludetopicssuchasspectraltheoryandtheHahn-Banachtheorem.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3816 Finite Mathematics
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT1002
Description: Theaimofthismoduleistointroducestudentstosometopicsinthemathematicsofcombinatorialstructures.Thistheoryhaswideapplications,bothinclassicalmathematicsandintheoreticalcomputerscience.Topicstobecoveredmayinclude:codingtheory,finitegeometries,Latinsquares,designs.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3817 Rings and Fields
Credits: 15.0 Semester: 1
Availability: 2000-01
Prerequisite: MT2002
Description: Historically,ringshaveappearedasgeneralisationsofnumbersystems(integers,inparticular)withtheintentionofgainingdeeperinsightintonumbersystemsthemselves.Thiswillbereflectedinthismodule,wherestudentswillstudyfamiliarconcepts,suchasfactorisation,primeness,divisibilityetc.,inanew,moregeneral,settingofcommutativerings.Inaddition,themodulemayincludetopicsfrom:ringsofquotients,finitefieldsandextensionsoffields.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3818 Topics in Geometry
Credits: 15.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2002
Description: Theaimof thismodule is to introducestudents to thefieldofGeometryand inparticular tousetheknowledgetheyhavegainedofModernAlgebrainothermodulestoelucidateboththeareasofEuclideanandnon-Euclideangeometry.TheaxiomaticapproachtogeometryoriginallyintroducedbytheAncientGreekswasmodifiedinthe19thCenturyfollowingthediscoveryofnon-Euclideangeometries.Ageometrycanberegardedasbeingdeterminedbyitsgroupofallowabletransformationsandinthismodulewewillemphasisethisapproach.Topicstobecoveredmayinclude:EuclideangeometryandtheEuclideangroupinR2andR3,Projectivegeometry,Ellipticgeometry,Hyperbolicgeometry,anintroductiontothetopologyofsurfaces.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3819 Number Theory
Credits: 15.0 Semester: 2
Page 13.16
Mathematics & Statistics - 3000 Level modules
Availability: 2000-01
Prerequisite: MT2002
Description: Theaimof thismodule is to introducestudents tosometopics inelementarynumber theory,rangingfromproblemsfirstconsideredinancienttimestoworkstimulatedbyrecentadvancesincomputers.Topicstobecoveredmayinclude:primenumbers,cryptography,continuedfractions,Pell’sequation,theGaussianintegersandwritingnumbersassumsofsquares.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3820 Linear Algebra
Credits: 15.0 Semester: 1
Availability: 2001-02
Prerequisite: MT2002
Description: Thismoduleextendsthetheoryofvectorspacesandlinearmappings. Thesyllabusincludesbases,thedimensiontheorem,eigenvaluesandeigenvectors,theCayley-Hamiltontheorem,minimumpolynomials,sumsanddirectsumsofsubspaces,theprimarydecompositiontheorem,diagonalisation,similarity,variouscanonicalforms.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3821 Modules and Categories
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3820
Description: Thebasicideaofacategoryandthefundamentalnotionsoffunctionandnaturaltransformationareintroducedwithparticularreferencetotheabeliancategoryofmodules.Universalconstructionsareusedthroughout.Thesyllabusincludesmorphisms,exactsequences,quotientmodules,isomorphismtheorems,freemodules,productsandcoproducts,kernelsandcokernels,binormalcategories,groupsofmorphisms,additivecategories,abeliancategories,equivalentcategories,adjointfunctors.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3822 Metric and Topological Spaces
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2002
Description: Thismoduleextendsideasofconvergenceandcontinuitytotheverygeneralsettingsofmetricspacesandtopologicalspaces.Topicstobecoveredmayincludecompletemetricspacesandthecontractionmappingtheorem,compactnessinmetricspaces,topologicalspacesaxiomatizedviaopensets,compactnessandconnectednessintopologicalspaces.Manyexamplesandapplicationswillbegiven.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3823 Semigroups
Credits: 15.0 Semester: 2
Availability: 2000-01
Page 13.17
Mathematics & Statistics - 3000 Level modules
Prerequisite: MT2002
Description: Semigrouptheoryisoneoftheneweralgebraicdisciplines,andisrelatedtoanumberoffieldsofmathematicssuchasgroups,theoreticalcomputerscienceanduniversalalgebra.Inthefirstpartofthemodulethestudentswilllearnfundamentalconceptsofsemigrouptheory,includingthoseofsubsemigroups,homomorphisms,congruences,aswellasGreen’sstructuretheory.Inthesecondpartofthemodulethistheorywillbeappliedtostudyvariouskindsofsemigroupssuchas:simplesemigroups, inversesemigroups, regularsemigroups,etc.SemigrouptheoryisoneoftheactiveresearchareasintheSchool,andthechoiceoftopicswillreflectthis.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3824 Topics in Groups
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3603
Description: ThismodulecontinuesthestudyofgroupsbeguninMT3603.Themainaimofthismoduleisforstudentstogetadeeperunderstandingoftheinternalstructureofgroups,andofdifferentwaysthegroupsmayappear.Themodulemayincludetopicsfrom:thetheoryofpermutationgroups,representationsofgroupsbymatrices,solubleandnilpotentgroups,grouppresentationsandcomputationalgrouptheory.GrouptheoryisoneoftheactiveresearchareasintheSchool,andthechoiceoftopicswillreflectthis.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3825 Topics in Modern Analysis
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3604
Description: Thismodule introduces someof thepowerful techniques and ideas ofmodernmathematicalanalysisthatareimportantbothinanalysisinitsownrightandinitsmanyapplicationsinmathematicsandscience.Topicstobecoveredmayinclude:measuretheory,theergodictheorem,martingaletheory,Fuchsiangroups.AnalysisisoneoftheactiveresearchareasintheSchool,andthechoiceoftopicswillreflectthis.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3827 Forecasting
Credits: 15.0 Semester: 1
Availability: 2000-01
Prerequisite: MT2004
Description: Thismodule is intended to compare the relativemerits of ‘classical’moving average andexponentialsmoothingtechniquesandtheBox-Jenkinsapproachtoforecastingtimeseries.Thesyllabusincludes:introductiontotimeseriesmodels;simplemodels;exponentialsmoothing;lineartrendprocesses;seasonalmodels;momentsforstochasticprocesses;stationaryprocesses;whitenoiseprocesses;mixedmodels;non-stationarymodels;partialautocorrelation(PACF);theestimationstageofARMAmodelling;diagnosticcheckingusingresiduals;pointandintervalpredictions.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3828 Classification
Credits: 15.0 Semester: 2
Availability: 2000-01
Page 13.18
Mathematics & Statistics - 3000 Level modules
Prerequisite: MT2001orMT3501
Description: Theaimofthismoduleistointroducestudentstothebasicideasofclusteranalysisandgraphicalproceduresforsummarisinganddisplayingrelationshipsinmultivariatedatasets.ItwillillustratetheseproceduresbyuseoftheCLUSTANcomputerpackage.Thesyllabusincludes:typesofdata;dissimilaritymeasures;partitioningalgorithms;hierarchicalclassifications;principalcoordinatesanalysis;non-metricmultidimensionalscaling;stagesinanumericalclassification;theCLUSTANpackage.
ClassHour: 11.00am
Teaching: Twolectures,onetutorialandpracticalclasses.
Assessment: 2HourExamination=100%
MT3830 Population Genetics
Credits: 15.0 Semester: 1
Availability: 2001-02
Prerequisite: MT1004orMT2004
Description: Thismoduleaims to showhowmathematicalmodelsmaybeused to study theevolutionofpopulations and how statistical techniquesmaybe used to investigatemodel validity.The syllabus includes: anintroductiontoMendeliangenetics;dominance;pairsofalleles;theHardy-Weinbergprinciple;non-randommatingpopulations;selfing;selection;mutation.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3831 Bayesian Inference
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3701
Description: Thismoduleisintendedtoofferare-examinationofstandardstatisticalproblemsfromaBayesianviewpointandanintroductiontoareas,suchassequentialestimationandsequentialhypothesistesting,towhichtheBayesiandecisiontheoreticapproachisideallysuited.Thesyllabusincludes:Bayestheorem(discreteandcontinuouscases);inferencebasedonthenormaldistribution;statisticaldecisiontheory;BayesactionsandBayesrules;SequentialProbabilityRatioTest(SPRT).
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3832 Mathematical Programming
Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT1001orMT1002
Description: Theaimofthismoduleistointroducestudentstotheformulationandsolutionofvariouslinearprogrammingproblems.Thesubjectmatterwillbeillustratedbyapplyingthemethodsofsolutiontorealexamples.Thesyllabusincludes:formulationoflinearproblems;solutiongraphicallyandbysimplexalgorithm;sensitivityanalysis;duality;transportationandtransshipment;theassignmentproblem;non-linearprogramming;integerprogramming.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3833 Utilities, Decisions and InventoriesCredits: 15.0 Semester: 2
Availability: 2000-01
Prerequisite: MT1004orMT2004
Page 13.19
Mathematics & Statistics - 3000 Level modules
Description: Thismoduleisintendedtoprovideanintroductiontotheformulationandsolutionofproblemsofdecision-takingandproblemsinthemanagementofinventorysystemsforasingleitem,tomotivatetheneedforutilityfunctions,andtoexplainhowtheyareassessedandemployed.Thesyllabusincludes:decisiontheory;maximumandBayesianapproaches;Bayestheorem;Bellman’soptimalityprinciple;utilitytheory;utilityfunctions;inventorytheory.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3834 Ecological Modelling Credits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2001orMT2101
Description: Thismoduleisintendedtointroducethekeyconceptsintheoreticalpopulationbiologythroughaseriesofcasestudies,inordertogivestudentsthetoolswithwhichtobuildandanalysetheirownmodels.Topicswill be drawn from: differential equations,matrixmodels, individual-basedmodels, cellular automata; equilibriaandstability;linearisation;non-lineardynamicsandchaos;modelformulation;parameterestimation;validationandprediction;sensitivityanalysis;inverseproblems;demographicandenvironmentalstochasticity;structuredpopulations;spatiallyexplicitmodels.
ClassHour: 10.00am
Teaching: Twolecturesandonelaboratory.
Assessment: Essay=10%,2HourExamination=90%
MT3835 Wildlife Population AssessmentCredits: 15.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2004
Description: Thismoduleisintendedtoenablestudentstodesignappropriatesurveysforassessingabundanceofananimalpopulation,toformulatesimplestatisticalmodelsforsurveydataandderiveestimators,toanalysedatacompetently,andtoconductasmallsurveyfromconceptiontofinalreport.Thesyllabusincludes:liklihoodframeworkfor distance sampling; general estimating equation; line and point transects; hazard-rate formulations; clusteredpopulationsandsize-biasedsampling;stratificationandcovariates;varianceandintervalestimation;thebootstrap;estimationwhendetectionatthelineorpointisnotcertain;surveydesign;fieldmethods;relatedmethods;includingstriptransects,quadratcounts;cue-counting,trappingwebsandmigrationcounts;monitoringtrendsinabundance;mark-recaptureandrecoverymethods;removalmethods;catchperuniteffort;change-in-ratio.
ClassHour: 11.00am
Teaching: Twolecturesandonelaboratory.
Assessment: ProjectReport=25%,2HourExamination=75%
MT3838 Robust Statistical MethodsCredits: 15.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2004
Description: Classicalandmodernrobustmethodsfordataanalysisaredescribed.PermutationtestsandintervalsandMonteCarlotests,whichspanbothclassicalmethodsandmodern,computer-intensivemethods,arecovered,asaresomemorerecentcomputer-intensivemethods,notablythebootstrap.Illustrationsaregivenoftheapplicationofmodernmethodstostandardstatisticalproblems;theemphasisforclassicalmethodsisonorderstatisticsandrankingmethods.
ClassHour: 11.00am
Teaching: Twolecturesandonelaboratory.
Assessment: ContinuousAssessment=30%,2HourExamination=70%
MT3850 Lattice Theory
Credits: 15.0 Semester: 2
Availability: 2000-01
Page 13.20
Mathematics & Statistics - 3000 & 4000 Level modules
Prerequisite: MT2002
Anti-requisite: MT4850
Description: Theaimofthemoduleistointroducestudentstothebasicideasoforderedsetsandlattices,withparticularemphasisonvarioustypesofdistributivelattices.Thesyllabuscomprises:orderedsetsandisotonemappings;infimaandsuprema;latticesandlatticemorphisms;completelattices;modularlattices,distributivelattices,andtheirBirkhoffcharacterisations;representationofadistributivelatticeasaringofsets;join-irreducibleelementsandfiniteduality; complementation andBoolean algebras; coonectionwithboolean rings; theLindenbaum-Tarski theorem;congruences;principalcongruences,thelatticeofcongruences;implicativelatticesandpseudocomplementedlattices.
ClassHour: Tobearranged.
Teaching: Twolecturesandonetutorial.
Assessment: 2HourExamination=100%
MT3999 Project in Mathematics/Statistics
Credits: 15.0 Semester: WholeYear
Description: Thestudentwillchooseaprojectfromalistpublishedannuallyalthoughatopicoutwiththelistmaybeapproved.Studentswillberequiredtoreportregularlytotheirsupervisorandareportofnomorethan5,000wordsmustbesubmittedbytheendofthesecondsemester.
Assessment: Project=100%
The Prerequisite for each of the following 4000 modules is entry to the MSci Programme(s) for which they are specified, save where an additional prerequisite is given. The anti-requisite for each module is the corresponding 3000 module.MT4611 Advanced Symbolic Computation
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2001orMT2101
Description: ThismoduleaimstoenablestudentstouseMapleasatoolintheirothermodulesandtoturnnaturallytosuchapackagewhensolvingmathematicalproblems.Themoduleaimstoillustratethefollowingpoints:asymboliccomputationpackageallowsonetoconductmathematicalexperiments;asymboliccomputationpackageallowsonetocollectdataaboutaproblembeingstudied.Thisissimilartothewayotherscientistswork.Itiseasiertotryseveraldifferentapproachestoaproblemandseewhichworks.Themachineisstupid.Intelligencecomesfromtheuser.Theuserthinks,theuserinterprets,thecomputercalculates.StudentswillundertakeamoresubstantialprojectthanthatrequiredforMT3611.
ClassHour: 9.00am
Teaching: Twolectures,onetutorial
Assessment: Project=45%,2HourExamination=55%
MT4612 Advanced Computing in Mathematics
Credits: 20.0 Semester: 2
Availability: 2001-02
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Mathematics & Statistics - 4000 Level modules
Prerequisites: (MT2001orMT2101),MT2003
Description: ThismoduleconsistsofMT3612withtheadditionofdirectedstudyonmoreadvancedtopicsnotcoveredinMT3612,forexample,theuseofNAGlibrariesandgraphicspackagesplusaspectsofFortran90likedynamicallocatablearrays.Inaddition,thecomputingprojectwillbemoredemandingthantheprojectforMT3612.The syllabus includes: an introduction to goodprogramming style through examples; the construction of awelldocumentedFortranprogramthatimplementsanumericalalgorithm;useoftheadvancedfeaturesofFortranto,forexample,(i)manipulatematrices,(ii)readandwritetodatafiles,(iii)implementlibraryroutinesand(iv)usegraphicspackages.Thestudentswillalsocompleteanadvancedprojectthatcontributesupto35%ofthefinalmarksforthemodule.
ClassHour: 9.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=35%,2HourExamination=65%
MT4701 Advanced Statistical Inference
Credits: 20.0 Semester: 1
Prerequisites: (MT2001orMT2101),MT2004
Description: ThismoduleconsistsofMT3701withtheadditionofdirectedreadingonmoreadvancedaspectsofthesubjectandarequirementtowriteareviewessayonanaspectofthesubject.Thesyllabuswillinclude:distributiontheory–negativebinomial,multinomial,gamma,beta,tandFdistributions;pointestimation–Meansquareerror;unbiasedness;sufficiency;theefficientscore;FisherInformation;theCramér-Raolowerbound;exponentialfamilies;attainmentoftheCramér-Raolowerbound;multi-dimensionalCramér-Raoinequality;maximumlikelihoodestimation;consistencyandasymptoticefficiency;hypothesistesting–Neyman-PearsonLemma;uniformlymostpowerfultests;likelihoodratio tests;confidencesets–Pivotalquantities;BayesianInference–BayesTheorem;highestposteriordensityintervals;Bayesestimators;priordistributionsandsubjectiveprobability;conjugatepriors.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4702 Advanced Generalized Linear Models and Data Analysis
Credits: 20.0 Semester: 1
Prerequisite: MT2004
Co-requisite: MT3501
Description: Thismoduleaimstodemonstratethepowerandeleganceofunifyingalargenumberofsimplestatisticalmodelswithintheframeworkofthegeneralizedlinearmodel.Itwilltrainstudentsintheinterpretation,analysisandreportingofdata,whenasingleresponsemeasurementisinterpretedintermsofoneoranumberofothervariables.AswellasstudyingthematerialcoveredinMT3702,studentswillundertakeasubstantialpieceofprojectwork.
ClassHour: 11.00am
Teaching: 2lectures,1tutorial,practicalclassesandprojectrelatedtutorials.
Assessment: Project=40%,2HourExamination=60%
MT4704 Advanced Sampling Theory
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT1004orMT1007
Page 13.22
Mathematics & Statistics - 4000 Level modules
Description: ThismodulecomprisesMT3704butwithamoreadvancedprojectwhichwillrequiresomeorallofthefollowing:supplementaryreading,aliteraturereview,acritiqueofasurvey,questionnaireandsurveydesign,surveyimplementation,anddataanalysis.TheprimarygoaloftheadvancedprojectwillbetohavestudentsinvestigateingreaterdepthoneormorespecifictopicsencounteredinMT3704.
ClassHour: 12.00noon
Teaching: Twolectures,onetutorialandpracticalclasses.
Assessment: Project=25%,2HourExamination=75%
MT4705 Advanced Multivariate Analysis
Credits: 20.0 Semester: 1
Availability: 2000-01
Prerequisites: MT2004,(MT2001orMT3501)
Description: ThismoduleconsistsofMT3705withtheadditionofdirectedreadingonmoreadvancedaspectsofthesubjectandtherequirementforstudentstoanalyseadataset.Thesyllabusincludes:propertiesofthemutlivariatenormaldistribution;checkingmutlivariatenormality;hypothesistesting;thelikelihoodratioandunion-intersectionprinciples; one-sample and two-sampleHotellingT2 tests; tests on covariancematrices; tests of independence;discriminantanalysis;principalcomponentsanalysis;canonicalcorrelation;analysisofdatausingacomputerpackage.
ClassHour: 9.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4803 Advanced Interpolation and Approximation
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2001orMT2101
Description: ThismodulecoversthematerialofMT3803,withtheadditionoftopics,coveredbydirectedreadingand/oradditionallectures,requiringamuchmorematureunderstandingofanalysis.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4804 Advanced - The Sun
Credits: 20.0 Semester: 1
Prerequisite: MT2003orMT3601
Description: ThismoduleconsistsofMT3804withtheadditionofdirectedreadingonmoreadvancedaspectsofthesubjectandarequirementforstudentstocarryoutadetailedanalyticalinvestigationofaparticularsystemoradetailedliteraturesurveyofaspecificarea.Thesyllabusincludes:observationsoftheSunanditsmagneticphenomena;theequationsofmagnetohydrodynamics,theirpropertiesandapplicationtosolarmagnetism;convectionanddiffusionofmagneticfield;magneticequilibria,force-freefields,magneticfluxtubes;MHDwaves;wavesinmagneticfluxtubes,intensetubes,sunspots,coronalloops;coronalheating;prominences;Solarwind;helioseismology.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4805 Advanced Electromagnetism
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT3601
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Mathematics & Statistics - 4000 Level modules
Description: ThismoduleisanextensionofMT3805toinclude(i)theapplicationofparticleorbittheorytoplasmas, (ii) thepropagationofwavesinplasmas.Thesyllabusalsoincludes:electricandmagneticfieldsandpolarisation;Maxwell’sequations;waveequationforfields,propertiesofplanewavesandFresnel’srelations;Poynting’stheoremandenergyflow;scalarandvectorpotentialandtheinhomogeneonswaveequation;Green’sfunctionsolutionandretardedpotentials;radiationfromdipoleandhalfwaveantennas,andarraysofantennas;waveguides;motionofchargedparticles,adiabaticinvariantsandguidingcentredrifts;particleorbittheoryanditsuseinplasmaphysics;wavepropagationinplasmas,coldplasmdispersionrelation,cut-offsandresonances,CMAdiagram,warmplasmamodificationsofcoldplasmatheory.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4806 Advanced Numerical Solution of Partial Differential Equations
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT3504orMT3602
Description: ThismoduleconsistsofMT3806withtheadditionthatstudentswillberequiredtogainexpertiseinaprogramminglanguageandundertakecomputationalprojects.Thesyllabusincludes:convergenceandstabilityoffinite-differenceapproximationstoinitialvalueproblemsinoneandtwospacedimensions;theinvestigationofdispersionanddissipationintheapproximationofconservativelaws.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4807 Advanced Classical Mechanics
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2003
Description: ThemoduleconsistsofMT3807withtheadditionofdirectedreadingonadvancedtopics.Thestudentswillbeaskedtocompleteextratutorialsheetscoveringtheadvancedmaterial.Thefollowingmaterialwillalsobecovered:Newton’slawsofmotion–dynamicsofaparticle;momentumandenergy;conservativeforces–energyconservation;centralforces–angularmomentumconservation–planetaryorbits;non-inertial/acceleratingframesofreference,principleofequivalence,coriolisandcentrifugalforces;dynamicsofasystemofparticles;mechanicsofarigidbody,momentsandproductsofinertia,principalaxes,impulsiveforces,Euler’sequations;Lagrange’sequations,principleofleastaction,generalisedco-ordinates,Euler’sangles,Hamilton’sequations.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4808 Advanced Dynamical Systems
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3504
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Mathematics & Statistics - 4000 Level modules
Description: ThismoduleconsistsofMT3808withtheadditionofdirectedreadingonmoreadvancedortechnicalaspectsofthesubjectandarequirementforstudentstocarryoutadetailedanalyticandnumericalinvestigationofaparticularsystem.Thesyllabusincludes:discreteandcontinuousdynamicalsystems;perioddoubling,intermittency,bifurcationsandchaosinmappingsanddifferentialsystems;homoclinicandheteroclinicpointsandorbitsandtheirroleinthedevelopmentofchaos;theSmalehorseshoemappingandsymbolicdynamics;thebifurcationsofcodimensiononeandtheuseofcentremanifoldtheory;Melnikov’smethod;Strangeattractors,dimensionandLyapunovexponents;HamiltoniandynamicsandtheKolmogorov-Arnold-Mosertheorem.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4809 Advanced Fluid Dynamics
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3601
Description: ThismoduleconsistsofMT3809withtheadditionofdirectedreadingonmoreadvancedaspectsofthesubject.Bytheendofthemodulestudentsareexpectedtounderstandthevariousphysicalpropertiesoffluids;theworkingsofPitottubesandVenturimeters;theconceptsofFroudeandReynoldsnumber;gasbubblesoscillations;howtosolveLaplace’sequationforvariousvelocitypotentialproblems;theconceptofastreamfunction;Navier-Stokesequationsandtheirsolutioninsimplesituations;applicationofcomplexvariabletheorytofluidflowsanditsuseinpredictingliftanddragroundrotatingbodies;aerofoiltheory;waterwavetheory;comprehensiblefluidtheories;Machnumberandshocklines;Prandtl-Meyrexpansions;Rankine-Huguneotrelationships.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4811 Advanced Asymptotic Analysis and Perturbation Theory
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisites: MT3503,MT3504
Description: ThismoduleconsistsofMT3811withtheadditionofdirectedreadingonmoreadvancedtopicsinbothAsymptoticAnalysisandPerturbationTheory.Theadvancedtopicsmayinclude,forexample,themethodofsteepestdescents,advancedboundarylayermethodsandtheLangertransformationfortwoturningpointproblemsinWKBtheory.Studentswillbeaskedtocompletemoredemandingtutorialsheetsandcarryoutdetailedcalculationsusingthesemoreadvancedtechniques. Thesyllabuswill includethatforMT3811plusadvancedasymptoticandperturbationmethods.Forexample,additionalmethodscouldbechosenfrom(i)themethodofsteepestdescents,(ii)advancedboundarylayermethodsand(iii)Langertransformationsforturningpointproblems.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4812 Advanced Partial Differential Equations
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3504
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Mathematics & Statistics - 4000 Level modules
Description: Theaimofthismoduleistogiveaninsightintotheroleofnonlinearpartialdifferentialequationsoftheevolutiontypeinmodernappliedmathematics.Afteranintroductiontomethodsforlinearequations,themodulewilldealwithtechniquesfortheanalysisofapplicationsinsuchareasascompressiblefluidflowandtheformationofshockwaves,travellingwaves,spreadofthinfilms,solitons,trafficflowandotherareasofthephysicalandbiologicalsciences.TheparticularfocusofthismodulewillbeadescriptionoftheinversescatteringmethodforthesolutionoftheKorteweg-deVriesequation.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4813 Advanced Fractal Geometry
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisites: MT2001orMT2101
Description: ThismoduleconsistsofMT3813withtheadditionoftutorialsanddirectedreadingonextensionsofthesubjectandmoresophisticatedmathematicalanalysis.Theaimofthismoduleistointroducethemathematicsusedtodescribeandanalysefractalsandtoshowhowthetheorymaybeappliedtoexamplesdrawnfromacrossmathematicsandscience.Themodulediscussesthephilosophyandscopeoffractalgeometry;andcoversconceptssuchasdimension,representationoffractalsbyiteratedfunctionsystems,fractalsinotherareasofmathematicssuchasdynamicalsystemsandnumbertheory,JuliasetsandtheMandelbrotset.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4814 Advanced Graph Theory
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT1002
Description: ThismoduleincludesandextendsthecontentsofMT3814.Additionaltopicstobecoveredmayinclude:applicationsofgraphstogroupsandotheralgebraicstructures,automorphismgroups,furtheralgorithms,complexityofalgorithms.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4815 Advanced Functional Analysis
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2002
Description: ThismoduleconsistsofMT3815withadditionaladvancedmaterialleadingtoaproject.Themodulewillfamiliarisestudentswiththebasicnotionsoffunctionalanalysis,thatisanalysisonnormedspacesandHilbertspace.Themodulewillcovernormedspaces,convergenceandcompleteness,operators,HilbertspacesandtopicssuchasspectraltheoryandtheHahn-Banachtheorem.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4816 Advanced Finite Mathematics
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT1002
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Mathematics & Statistics - 4000 Level modules
Description: ThismoduleincludesandextendsthecontentsofMT3816.Additionaltopicstobecoveredmayinclude:Booleanalgebras,furthercombinatorialstructures.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4817 Advanced Rings and Fields
Credits: 20.0 Semester: 1
Availability: 2000-01
Prerequisite: MT2002
Description: ThismoduleconsistsofMT3817togetherwithadditionaladvancedmaterial,whichisdesignedtogivestudentsadeeperunderstandingofthestructureofringsandfieldsandtheirapplications.Itmayincludetopicsfromradicaltheory,semisimplicity,Galoistheoryandprimaryidealsanddecompositions.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4818 Advanced Topics in Geometry
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2002
Description: ThismoduleincludesandextendsthecontentsofMT3818.Additionaltopicstobecoveredmayinclude:crystallographicandfriezegroupsandtheirclassification,anintroductiontoalgebraictopology.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfhourexamination=100%
MT4819 Advanced Number Theory
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2002
Description: ThismoduleincludesandextendsthecontentsofMT3819.Additionaltopicstobecoveredmayinclude:quadraticreciprocity,quadraticforms,arithmeticfunctions,furtherDiophantineequations.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfhourexamination=100%
MT4820 Advanced Linear Algebra
Credits: 20.0 Semester: 1
Availability: 2001-02
Prerequisite: MT2001
Page 13.27
Mathematics & Statistics - 4000 Level modules
Description: ThismoduleconsistsofMT3820withtheadditionofmoreadvancedmaterial.Thesyllabusincludesbases, thedimensiontheorem,eigenvaluesandeigenvectors, theCaley-Hamiltontheorem,minimumpolynomials,sumsanddirectsumsofsubspaces,theprimarydecompositiontheorem,diagonalisation,similarity,variouscanonicalforms.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4821 Advanced Modules and Categories
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3820orMT4820
Description: ThismoduleconsistsofMT3821withtheadditionofmoreadvancedmaterial.Thebasicideaofacategoryandthefundamentalnotionsoffunctorandnaturaltransformationareintroducedwithparticularreferencetotheabeliancategoryofmodules.Universalconstructionsareusedthroughout.Thesyllabusincludesmorphisms,exact sequences, quotientmodules, isomorphism theorems, freemodules, products and coproducts, kernels andcokernels,binormalcategories,groupsofmorphisms,additivecategories,abeliancategories,equivalentcategories,adjointfunctors.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: Two-and-a-halfHourExamination=100%
MT4822 Advanced Metric and Topological Spaces
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2002
Description: ThismoduleconsistsofMT3822withadditionaladvancedmaterialleadingtoaproject.Thismoduleextendsideasofconvergenceandcontinuitytoverygeneralsettings.Topicsincludemetricspaces,completenessandthecontractionmappingtheorem,compactness,topologicalspacesaxiomatizedviaopensets,compactnessandconnectedness.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4823 Advanced Semigroups
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2002
Description: ThismodulewillconsistofMT3823,togetherwithadditionaladvancedmaterial,designedtotakestudentstothefrontiersofcurrentresearchinsemigrouptheory.Itmaycontaintopicsfrom:semigrouppresentations,decidabilityproblems,finitenessconditions,amalgamation,matrixsemigroupsandsemigroupvarieties.
ClassHour: 12.00noon
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4824 Advanced Topics in GroupsCredits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3603
Page 13.28
Mathematics & Statistics - 4000 Level modules
Description: ThismodulewillconsistofMT3824togetherwithadditionaladvancedmaterial,inwhichtheresultsfromthebasicpartofthemodulewillbeusedtoobtaindeeperinformationaboutfinitegroupsofsmallorders,simplegroups,solubilityproblemsforfinitelypresentedgroupsandBurnsidetypeproblems.Thisadditionalpartofthemodulewillbedesignedsoastogivestudentsatasteofthecurrentresearchingrouptheory.
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4825 Advanced Topics in Modern AnalysisCredits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3604
Description: ThismoduleconsistsofMT3825withadditionaladvancedmaterialleadingtoaproject.Thismoduleintroducessomeofthepowerfultechniquesandideasofmodernmathematicalanalysisthatareimportantbothinanalysisinitsownrightandinitsmanyapplicationsinmathematicsandscience.Themodulewillincludetopicssuchas:measuretheory,theergodictheorem,martingaletheory,Fuchsiangroups.Analysisisoneoftheactiveresearchareasattheschool,andthechoiceoftopicswillreflectthis.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4828 Advanced ClassificationCredits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2001orMT3501
Description: ThismoduleconsistsofMT3828with theadditionofdirected readingonmoreadvancedortechnicalaspectsofthesubjectandarequirementforstudentstoapplythemethodologyinadetailedexaminationofdata.Thesyllabusincludes:typesofdataandclassifications;constructionofdissimilaritymeasures;partitioningalgorithms;hierarchicalclassifications;principalco-ordinatesanalysis;non-metricmultidimensionalscaling;stagesinnumericalclassification;analysisofdatausingtheCLUSTANpackage.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4831 Advanced Bayesian InferenceCredits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT3701
Description: ThismoduleconsistsofMT3813withanadditionalprojectwhichwillgiveconsiderationtosomemoreadvancedaspectsofthetheoryortotheapplicationofBayesiantechniques.Thismayinvolveeitherdirectedreadingortheuseofthecomputerforsimulationordata-basedanalyses.Foundationsinclude:Bayestheorem(discreteandcontinuouscases);summarisingposteriordistributions;prediction;sufficiency;non-informativepriors.InferencebasedontheNormaldistributionincludes: inferenceandpredictionforaNormalsample;inversegammaandNormal-gammadistributions;univariateNormallinearregression;predictionofobservationssatisfyingafittedlinearmodel.StatisticalDecisionTheoryincludes:BayesactionsandBayesrules;samplingcosts;initialdeterminationofsamplesize;one-step-look-aheadrules;optimalboundedsequentialprocedures;unboundeddecisionproblems;approximationofoptimalproceduresbyboundedprocedures;sequentialProbabilityRatioTest(SPRT).
ClassHour: 10.00am
Teaching: Twolecturesandonetutorial.
Assessment: Project=25%,2HourExamination=75%
MT4832 Advanced Mathematical ProgrammingCredits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT1001orMT1002
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Mathematics & Statistics - 4000 Level modules
Description: ThismoduleconsistsofMT3832withtheadditionofdirectedreadingonmoreadvancedaspectsofthesubjectandarequirementforstudentstocarryoutaproject.Thesyllabusincludes:formulationoflinearprogrammingproblems;solutiongraphicallyandbyuseofthesimplexalgorithm;sensitivityanalysis;thedualproblemanditsrelationtotheprimalproblem;thetransportationproblemanditssolutionusingtheNorthWestCornermethodandVogel’srule;theassignmentproblemanditssolution;transshipment;nonlinearprogramming;integerprogramming.
ClassHour: 12.00noon
Assessment: Project=25%,2HourExamination=75%
MT4834 Advanced Ecological Modelling
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2001orMT2101
Description: Thismodule consistsofMT3834with the additionof an advancedproject, in the formof aliteraturerevieworaprojectonsomeaspectofmodelling.
ClassHour: 10.00am
Teaching: Twolecturesandonelaboratory.
Assessment: Essay=10%,AdvancedProjectReport=25%,2HourExamination=65%
MT4835 Advanced Wildlife Population Assessment
Credits: 20.0 Semester: 2
Availability: 2001-02
Prerequisite: MT2004
Description: ThismoduleconsistsofMT3835withtheadditionofanadvancedproject,whichmightcoveranyaspectofthemodule.
ClassHour: 11.00am
Teaching: Twolecturesandonelaboratory.
Assessment: AdvancedProjectReport=45%,2HourExamination=55%
MT4838 Advanced Robust Statistical Methods
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisite: MT2004
Description: ThismoduleconsistsofMT3838withtheadditionofanadvancedproject,whichmightcoveranyaspectofthemodule.
ClassHour: 11.00am
Teaching: Twolecturesandonetutorial.
Assessment: ContinuousAssessment=20%,AdvancedProject=25%,2HourExamination=55%
MT4850 Advanced Lattice Theory
Credits: 20.0 Semester: 2
Availability: 2000-01
Prerequisites: MT2002
Page 13.30
Mathematics & Statistics - 4000 Level modules
Description: ThismoduleconsistsofMT3850withtheadditionofmoreadvancedmaterial.Theaimofthemoduleistointroducestudentstothebasicideasoforderedsetsandlattices,withparticularemphasisonvarioustypesofdistributivelattices.Thesyllabusincludes:orderedsetsandisotonemappings;infimaandsuprema;latticesandlatticemorphisms;complete,modular,anddistributivelatticesandtheirBirkhoffcharacterisations;representationofadistributivelatticeasaringofsets;join-irreducibleelementsandfiniteduality;complementationandBooleanalgebras;connectionwithbooleanrings;theLindenbaum-TarskiTheorem;congruences,principalcongruences,thelatticeofcongruences;implicativeandpseudo-complementedlattices;introductiontoOckhamalgebras.
ClassHour: Tobearranged.
Teaching: Twolecturesandonetutorial.
Assessment: TwoHourExamination=100%
MT4998 Advanced Project in Mathematics/Statistics
Credits: 30.0 Semester: WholeYear
Prerequisite: EntrytotheMScidegreeinMathematicsandTheoreticalPhysics
Anti-requisite: MT4999
Description: Theprojectwillbechosenfromanapprovedlistoftopicsandthecreditratingwillreflectthecontentanddepthofaninvestigationinvolved.
Assessment: Project=100%
MT4999 Advanced Project in Mathematics/Statistics
Credits: 40.0 Semester: WholeYear
Anti-requisite: MT4998
Description: Thisisamoresubstantialprojectwhich,forM.Sci.studentswillreplacetheexistingHonoursproject.Theprojectwillbechosenfromanapprovedlistoftopics.Thestudentmayberequiredtoreviewcurrentliteratureandinvestigateatopicinsomedepth.
Assessment: Project=100%