Download pdf - School of Mathematics & Statistics Head of School Degree ... · Page 13.6 Mathematics & Statatistics - 1000 & 2000 Level modules MT1007 Statistics in Practice Credits: 20.0 Semester:

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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

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Quantitative Ecology

Passesat11orbetterinMT1006,MT2001,MT2004,BI2001andeitherBI2004orBI2005.ItisrecommendedthatstudentstakeBI2005.

Statistics


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


(iv) MT3999

MathematicswithFrenchorGerman: 240credits,ofwhichatleast180creditsmustbefromMT3501-MT3999,including:

(i) atleastthreeofMT3501-MT3504

(ii) atleastoneofMT3601-MT3604


(iv) MT3999

MathematicsandPhysics: 240credits,ofwhichatleast120creditsmustbefromMT3501-MT3999,excludingMT3805,butincluding:

(i) atleasttwoofMT3501-MT3504


(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



(iv) MT3999

Pure Mathematics: 240credits,ofwhichatleast210creditsmustbefromMT3501-MT3999including:

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(i) MT3501-MT3504

(ii) MT3603,MT3604


(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


Statistics


MSci Programme Requirements

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Applied Mathematics300creditsfromMT3501-MT4999including:

(i) MT3501-MT3504

(ii) MT3601,MT3602


(iv) MT4999

(v) atleast120creditsfromMT4801-MT4881

Mathematics300creditsfromMT3501-MT4999including:

(i) MT3501-MT3504

(ii) atleasttwoofMT3601,MT3602,MT3603,MT3604


(iv) MT4999


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


(iv) MT4999


Statistics 300creditsfromMT3501-MT4999including:

(i) MT3501

(ii) (MT3701 orMT4701), (MT3702 orMT4702),MT3706, (MT3704 orMT4704),(MT3705 orMT4705)

(iii) MT4999

(iv) atleast140creditsfromMT4701-MT4881

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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




MT1003 Pure and Applied MathematicsCredits: 20.0 Semester: 2

Prerequisite: MT1002

Description: Theaimofthismoduleistoprovidestudentswithatasteofbothpureandappliedmathematics,togivetheminsightintoareasavailableforstudyinlateryearsandtoprovidethemwiththeopportunitytobroadentheirmathematicalexperience.

ClassHour: 9.00am




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.


Re-Assessment: ContinuousAssessment=17%,3HourExamination=83%

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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.


Re-Assessment: ContinuousAssessment=25%,2HourExamination=75%

MT2001 Mathematics




Description: TheaimsofthismodulearetoextendtheknowledgeandskillsgainedbystudentsinthemoduleMathematicsMT1002,andinparticulartoenhancetheirskillsinthetheoryandapplicationof:differentialandintegralcalculusofseveralrealvariables;limitingprocesses;linearmathematics.

ClassHour: 12.00noon.

Teaching: Fivelectures,onetutorialandonepractical.



MT2002 Algebra and Analysis



Description: Theaimsof thismoduleare to encourage students’understandingof the logical structureofmathematicsandthenatureofproof,andtointroducestudentstosomefundamentalconceptsofabstractalgebraandofanalysis.

ClassHour: 11.00am




MT2003 Applied Mathematics




Description: Thismoduleintroducesstudentstoappliedmathematicsthroughtheconstruction,analysisandinterpretationofmathematicalmodels,andtothetechniquesofanalysisusedinmathematicalmodelling.

ClassHour: 12.00noon.




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MT2004 Statistics


Prerequisites: MT1002andMT1004[From2001-02onlyMT1002]

Description: Thismodule introduces students to themathematicalmodels of randomness used as part ofstatisticalmodellingandanalysis.Themoduleisamixoffundamentalmathematicalstatisticsandappliedstatisticalanalysisandprovidesthebackgroundnecessaryforthe3000levelmodulesinstatistics.

ClassHour: 10.00am




MT2005 Discrete Mathematics


Prerequisites: MT1002

Description: Thismoduleaimstointroducestudentstotechniquesandideasindiscretemathematics,andtoreinforcetheideaofproofinmathematics.

ClassHour: 11.00am




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



Anti-requisites: MT2001,MT2003

Description: TheaimsofthismodulearetoextendtheknowledgeandskillsgainedbystudentsinthemoduleMT1002,andinparticularenhancetheirskillsinthetheoryandapplicationof:limitingprocessesanddifferentialandintegralcalculusinseveralrealvariables,methodsofFourierseriesandLaplacetransforms,andvectorcalculus.TheneedsofHonoursstudentsinPhysicsandAstronomyareaddressed.ThemoduleMT2101may,withthepermissionoftheHeadofSchool,beacceptableasaalternativetoMT2001intheentryrequirementsforHonourscoursesinvolvingmathematicsorstatistics.However,studentswishingtoretaintheoptionofentrytoHonoursMathematicsorStatisticsshouldnormallytakeMT2001.

ClassHour: 12.00noon

Teaching: Fivelectures,onetutorial,onepractical.



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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



Description: Thismoduleaimstoshowtheimportanceoflinearityinmanyareasofmathematicsrangingfromlinearalgebrathroughtogeometricapplicationstolinearoperatorsandspecialfunctions.Themaintopicscoveredare:lineardependenceandindependence;changeofbasis;innerproductspaces;inequalities;convergenceinEuclideanspaces;Fourierseriesandadjointandself-adjointoperators.

ClassHour: 9.00am

Teaching: Twolecturesandonetutorial.

Assessment: 2HourExamination=100%

MT3502 Foundations of Calculus


Prerequisite: MT2001orMT2101

Description: Thismodulegivesarigorous treatmentof topics in thecalculus,someofwhichwillalreadyhavebeenencounteredfromthepointofviewofcalculationandapplicationwithoutconsideringquestionsofvalidity.Topics,whichwillbeillustratedbymanyexamplesandcounter-examples,mayinclude:convergenceofsequencesandseries,continuity,differentiabilityandapplicationstoTaylorseries,analysisinndimensions,partialderivatives,theinversefunctiontheorem.

ClassHour: 9.00am



MT3503 Complex Analysis



Description: Thismoduleaimstointroducestudentstoanalyticfunctiontheoryandapplications.Thetopicscoveredinclude:analyticfunctions;Cauchy-Riemannequations;harmonicfunctions;multivaluedfunctionsandthecutplane;singularities;Cauchy’stheorem;Laurentseries;evaluationofcontourintegrals;fundamentaltheoremofalgebra;conformalmappings.




MT3504 Differential Equations



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.




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MT3601 Fundamentals of Applied Mathematics


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



MT3602 Applied Mathematical Methods


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


MT3603 Groups



Description: Thismoduleintroducesstudentstogrouptheory,whichisoneofthecentralfieldsofthe20thcenturymathematics.Themainthemeofthemoduleisclassifyinggroupswithvariousadditionalproperties,andthedevelopmentoftoolsnecessaryinthisclassification.Inparticular,thestudentswillmeetthestandardalgebraicnotions,suchassubstructures,homomorphisms,quotientsandproducts,andalsovariousconceptspeculiartogroups,suchasnormality,conjugationandSylowtheory.Theimportanceofgroupsinmathematics,arisingfromthefactthatgroupsmaybeusedtodescribesymmetriesofanymathematicalobject,willbeemphasisedthroughoutthemodule.

ClassHour: 10.00am



MT3604 Real Analysis



Description: ThismodulecontinuesthedevelopmentofrealanalysisstartedinMT2002.Topicsthatwillbetreatedfromarigorouspointofviewmayinclude:differentiation,Riemannintegration,uniformconvergence,functionspaces.

ClassHour: 10.00am



MT3611 Symbolic Computation

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Availability: 2000-01


Description: ThismoduleaimstoenablestudentstouseMapleasatoolintheirothermodulesandtoturnnaturallytosuchapackagewhensolvingmathematicalproblems.Themoduleaimstoillustratethefollowingpoints:asymboliccomputationpackageallowsonetoconductmathematicalexperiments;asymboliccomputationpackageallowsonetocollectdataaboutaproblembeingstudied.Thisissimilartothewayotherscientistswork.Itiseasiertotryseveraldifferentapproachestoaproblemandseewhichworks.Themachineisstupid.Intelligencecomesfromtheuser.Theuserthinks,theuserinterprets,thecomputercalculates.

ClassHour: 9.00am



MT3612 Computing in Mathematics



Prerequisites: (MT2001orMT2101),MT2003

Anti-requisite: HonoursorJointHonoursProgrammeinComputerScience.

Description: ThismoduleisintendedtointroducestudentstoFORTRANandthewritingofcomputercodestoimplementmathematicalalgorithms.ThemoduleincludesabasicintroductiontoFORTRAN,andtheimplementationofmathematicalalgorithmsinawell-documentedFORTRANprogram.Studentsarerequiredtocompleteaprojectinadditiontosittingtheexamination.

ClassHour: 9.00am


Assessment: Project=30%,2HourExamination=70%

MT3701 Statistical Inference



Description: Thismoduleaimstoshowhowthemethodsofestimationandhypothesistestingmetinfirstandsecondyearcanbejustifiedandderived;toextendthosemethodstoawidervarietyofsituations;toshowhowdifferentpointestimatorscanbecompared; toprovidean introductionto theBayesianapproachto inference.Thesyllabusincludes:distributiontheory;pointestimation;meansquareerror;unbiasedness;Fisherinformation;theCramer-Raolowerbound;maximumlikelihoodestimation;hypothesis-testing;Bayesianinference.

ClassHour: 11.00am



MT3702 Generalized Linear Models and Data Analysis



Co-(orpre-)requisite:MT3501

Description: Thismoduleaimstodemonstratethepowerandeleganceofunifyingalargenumberofsimplestatisticalmodelswithinthegeneralframeworkofthegeneralizedlinearmodel.Itwilltrainstudentsintheinterpretation,analysisandreportingofdata,whenasingleresponsemeasurementisinterpretedintermsofoneoranumberofothervariables.

ClassHour: 11.00am

Teaching: Twolecturesandonetutorialandpracticalclasses.


MT3704 Sampling Theory

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Description: Theaimsofthismodulearetointroducestudentstoandinterestthemintheprinciplesandmethodsofdesign-basedinference,toconvincethemoftherelevanceandutilityofthemethodsinawidevarietyofreal-worldproblems,andtogivethemexperienceinapplyingtheprinciplesandmethodsthemselves.Bytheendofthemodulestudentsshouldbeabletorecognisegoodandpoorsurveydesignandanalysis,todecideuponandimplementthemaintypesofsurveydesigninrelativelystraightforwardsettings,andanalysetheresultingsurveydataappropriately.Thesyllabusincludesfundamentalsofdesignbasedvs model-basedinference,simplerandomsampling,samplingwithreplacement,ratioandregressionestimators,stratifiedsampling,clustersampling,unequalprobabilitysamplingandquestionnairedesign.


Teaching: Twolectures,onetutorialandpracticalclasses.


MT3705 Multivariate Analysis



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



MT3706 Markov Chains and Processes




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



MT3801 Topics in the History of Mathematics



Description: Theaimofthismoduleistogivestudentsaninsightintothehistoricaldevelopmentofmathematics.Topics tobecoveredmayincludesomeof: thedevelopmentofalgebra, theoriginsof thecalculus, thehistoryoflogarithms,theworkofsomeindividualmathematicians.

ClassHour: 11.00am



MT3802 Numerical Analysis

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Prerequisites: MT2001orMT2101

Description: Themodulewillintroducestudentstosometopicsinnumericalanalysis,includinginterpolation,bestapproximation,numericalintegration,thenumericalsolutionofordinarydifferentialequations,solutionofsystemsoflinearequationsbyeliminationandbyiterativemethods.

ClassHours: 9.00am



MT3803 Interpolation and Approximation




Description: Thismoduleaimstopresentsomeofthekeyideasininterpolationandapproximation.TopicsmayincludeChebyshevpolynomialsandoptimalinterpolationpoints;Peano’stheorem;BernsteinpolynomialsandBernstein’sproofoftheWeierstrasstheorem,rationalapproximationandGaussianquadrature.

ClassHour: 10.00am



MT3804 The Sun


Prerequisites: MT2003,MT3601

Description: Thismoduleisintendedtointroducethebasicobservationsandtheoriesofsolarphysics,payingparticular attention to solarmagnetohydrodynamics.The syllabus includes: anoutlineof observational propertiesrangingfromthesolar interiortotheSun’souteratmosphere; theoreticalaspectsofsolarmagnetohydrodynamics;magneticequilibria;MHDwaves;coronalheating.

ClassHour: 11.00am



MT3805 Electromagnetism




Description: Thismoduleisintendedtointroducestudentstothepropertiesofelectromagneticwaves,includingthepropagationofplanewavesandguidedwaves,andthegenerationofwavesbyantennas,andtogiveanintroductiontothemotionofchargedparticlesinelectricandmagneticfieldsandsomeapplicationstoplasmaphysics.




MT3806 Numerical Solution to Partial Differential Equations


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Description: Thismoduleisintendedtointroducestudentstosomeoftheideas,techniquesandconstraintsthatunderpinmodernapproachestothenumericalmodellingofphysicalprocessesthatmaybedescribedbypartialdifferentialequations.Themodulewillinclude:convergenceandstabilityofstandardfinite-differenceschemes;theapplicationofstandardmethodstotwospacedimensionalproblems;ADImethods;theCFLcondition;dispersion,dissipationandstability;theLaxWendroffmethod.




MT3807 Classical Mechanics




Description: TheobjectofthismoduleistointroducestudentstosomeoftheideasandmathematicaltechniquesusedinunderstandingthebehaviourofdynamicalsystemsthatobeyNewton’sLaws.Thesenotionsarearguablythefoundationsofphysicsandappliedmathematics.Themodulewillinclude:Newton’slawsofmotion;conservativeforces;centralforces;non-inertial/acceleratingframesofreference;dynamicsofasystemofparticles;mechanicsofarigidbody;Euler’sequations;Lagrange’sequations;Hamilton’sequations.

ClassHour: 10.00am



MT3808 Dynamical Systems




Description: Thismoduleaimstointroducestudentstothebasicideasofthemoderntheoryofdynamicalsystemsandtotheconceptsofchaosandstrangeattractors.Themodulewillinclude:perioddoubling;intermittencyandchaos;geometricalapproachtodifferentialequations;homoclinicandheteroclinicorbits;Poincarésections;theSmalehorseshoemapping;centremanifoldtheory.

ClassHour: 10.00am



MT3809 Fluid Dynamics




Description: Thismoduleaims todevelopanunderstandingoffluidmovement through theapplicationofrelevantmathematicaltechniquestovarioussituations.Themodulewillinclude:theworkingsofPitottubesandVenturimeters;theconceptsofFroudeandReynoldsnumbers;howtosolveLaplace’sequationforvariousvelocitypotentialproblems;Navier-Stokesequations;aerofoiltheory;waterwavetheory.




MT3811 Aysmptotic Analysis and Perturbation Theory


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Description: Thismoduleisdesignedtointroducestudentstoasymptoticandperturbationmethodsthatgiveanalyticalapproximationstointegralsandsolutionsofdifferentialequations.Themodulewillinclude:definitionsofasymptoticseriesandexpansions;proofofWatson’slemma;Laplace’smethod;methodofstationaryphase;regularandsingularperturbationmethodsfordifferentialequations;boundarylayerequationsandthemethodofmatchedasymptoticexpansions;WKBmethod.

ClassHour: 11.00am



MT3812 Nonlinear Partial Differential Equations



Pre(Co)requisite: MT3504

Description: Theaimofthismoduleistogiveaninsightintotheroleofnonlinearpartialdifferentialequationsoftheevolutiontypeinmodernappliedmathematics.Afteranintroductiontomethodsforlinearequations,themodulewilldealwithtechniquesfortheanalysisofapplicationsinsuchareasascompressiblefluidflowandtheformationofshockwaves,travellingwaves,spreadofthinfilms,solitons,trafficflowandotherareasofthephysicalandbiologicalsciences.

ClassHour: 11.00am



MT3813 Fractal Geometry




Description: Theaimofthismoduleistointroducethemathematicsusedtodescribeandanalysefractalsandtoshowhowthetheorymaybeappliedtoexamplesdrawnfromacrossmathematicsandscience.Themodulediscussesthephilosophyandscopeoffractalgeometry;andmayincludetopicssuchasdimension,representationoffractalsbyiteratedfunctionsystems,fractalsinotherareasofmathematicssuchasdynamicalsystemsandnumbertheory,JuliasetsandtheMandelbrotset.




MT3814 Graph Theory




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



MT3815 Functional Analysis


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Description: Thisobjectofthismoduleistofamiliarisestudentswiththebasicnotionsoffunctionalanalysis,thatisanalysisonnormedspacesandHilbertspace.Themodulewillcovernormedspaces,convergenceandcompleteness,operators,HilbertspacesandmayincludetopicssuchasspectraltheoryandtheHahn-Banachtheorem.




MT3816 Finite Mathematics




Description: Theaimofthismoduleistointroducestudentstosometopicsinthemathematicsofcombinatorialstructures.Thistheoryhaswideapplications,bothinclassicalmathematicsandintheoreticalcomputerscience.Topicstobecoveredmayinclude:codingtheory,finitegeometries,Latinsquares,designs.




MT3817 Rings and Fields




Description: Historically,ringshaveappearedasgeneralisationsofnumbersystems(integers,inparticular)withtheintentionofgainingdeeperinsightintonumbersystemsthemselves.Thiswillbereflectedinthismodule,wherestudentswillstudyfamiliarconcepts,suchasfactorisation,primeness,divisibilityetc.,inanew,moregeneral,settingofcommutativerings.Inaddition,themodulemayincludetopicsfrom:ringsofquotients,finitefieldsandextensionsoffields.

ClassHour: 11.00am



MT3818 Topics in Geometry




Description: Theaimof thismodule is to introducestudents to thefieldofGeometryand inparticular tousetheknowledgetheyhavegainedofModernAlgebrainothermodulestoelucidateboththeareasofEuclideanandnon-Euclideangeometry.TheaxiomaticapproachtogeometryoriginallyintroducedbytheAncientGreekswasmodifiedinthe19thCenturyfollowingthediscoveryofnon-Euclideangeometries.Ageometrycanberegardedasbeingdeterminedbyitsgroupofallowabletransformationsandinthismodulewewillemphasisethisapproach.Topicstobecoveredmayinclude:EuclideangeometryandtheEuclideangroupinR2andR3,Projectivegeometry,Ellipticgeometry,Hyperbolicgeometry,anintroductiontothetopologyofsurfaces.

ClassHour: 11.00am



MT3819 Number Theory


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Description: Theaimof thismodule is to introducestudents tosometopics inelementarynumber theory,rangingfromproblemsfirstconsideredinancienttimestoworkstimulatedbyrecentadvancesincomputers.Topicstobecoveredmayinclude:primenumbers,cryptography,continuedfractions,Pell’sequation,theGaussianintegersandwritingnumbersassumsofsquares.

ClassHour: 10.00am



MT3820 Linear Algebra




Description: Thismoduleextendsthetheoryofvectorspacesandlinearmappings. Thesyllabusincludesbases,thedimensiontheorem,eigenvaluesandeigenvectors,theCayley-Hamiltontheorem,minimumpolynomials,sumsanddirectsumsofsubspaces,theprimarydecompositiontheorem,diagonalisation,similarity,variouscanonicalforms.

ClassHour: 11.00am



MT3821 Modules and Categories




Description: Thebasicideaofacategoryandthefundamentalnotionsoffunctionandnaturaltransformationareintroducedwithparticularreferencetotheabeliancategoryofmodules.Universalconstructionsareusedthroughout.Thesyllabusincludesmorphisms,exactsequences,quotientmodules,isomorphismtheorems,freemodules,productsandcoproducts,kernelsandcokernels,binormalcategories,groupsofmorphisms,additivecategories,abeliancategories,equivalentcategories,adjointfunctors.

ClassHour: 10.00am



MT3822 Metric and Topological Spaces




Description: Thismoduleextendsideasofconvergenceandcontinuitytotheverygeneralsettingsofmetricspacesandtopologicalspaces.Topicstobecoveredmayincludecompletemetricspacesandthecontractionmappingtheorem,compactnessinmetricspaces,topologicalspacesaxiomatizedviaopensets,compactnessandconnectednessintopologicalspaces.Manyexamplesandapplicationswillbegiven.

ClassHour: 11.00am



MT3823 Semigroups



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Description: Semigrouptheoryisoneoftheneweralgebraicdisciplines,andisrelatedtoanumberoffieldsofmathematicssuchasgroups,theoreticalcomputerscienceanduniversalalgebra.Inthefirstpartofthemodulethestudentswilllearnfundamentalconceptsofsemigrouptheory,includingthoseofsubsemigroups,homomorphisms,congruences,aswellasGreen’sstructuretheory.Inthesecondpartofthemodulethistheorywillbeappliedtostudyvariouskindsofsemigroupssuchas:simplesemigroups, inversesemigroups, regularsemigroups,etc.SemigrouptheoryisoneoftheactiveresearchareasintheSchool,andthechoiceoftopicswillreflectthis.




MT3824 Topics in Groups




Description: ThismodulecontinuesthestudyofgroupsbeguninMT3603.Themainaimofthismoduleisforstudentstogetadeeperunderstandingoftheinternalstructureofgroups,andofdifferentwaysthegroupsmayappear.Themodulemayincludetopicsfrom:thetheoryofpermutationgroups,representationsofgroupsbymatrices,solubleandnilpotentgroups,grouppresentationsandcomputationalgrouptheory.GrouptheoryisoneoftheactiveresearchareasintheSchool,andthechoiceoftopicswillreflectthis.

ClassHour: 10.00am



MT3825 Topics in Modern Analysis




Description: Thismodule introduces someof thepowerful techniques and ideas ofmodernmathematicalanalysisthatareimportantbothinanalysisinitsownrightandinitsmanyapplicationsinmathematicsandscience.Topicstobecoveredmayinclude:measuretheory,theergodictheorem,martingaletheory,Fuchsiangroups.AnalysisisoneoftheactiveresearchareasintheSchool,andthechoiceoftopicswillreflectthis.

ClassHour: 11.00am



MT3827 Forecasting




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.




MT3828 Classification



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Description: Theaimofthismoduleistointroducestudentstothebasicideasofclusteranalysisandgraphicalproceduresforsummarisinganddisplayingrelationshipsinmultivariatedatasets.ItwillillustratetheseproceduresbyuseoftheCLUSTANcomputerpackage.Thesyllabusincludes:typesofdata;dissimilaritymeasures;partitioningalgorithms;hierarchicalclassifications;principalcoordinatesanalysis;non-metricmultidimensionalscaling;stagesinanumericalclassification;theCLUSTANpackage.

ClassHour: 11.00am



MT3830 Population Genetics




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.




MT3831 Bayesian Inference




Description: Thismoduleisintendedtoofferare-examinationofstandardstatisticalproblemsfromaBayesianviewpointandanintroductiontoareas,suchassequentialestimationandsequentialhypothesistesting,towhichtheBayesiandecisiontheoreticapproachisideallysuited.Thesyllabusincludes:Bayestheorem(discreteandcontinuouscases);inferencebasedonthenormaldistribution;statisticaldecisiontheory;BayesactionsandBayesrules;SequentialProbabilityRatioTest(SPRT).

ClassHour: 10.00am



MT3832 Mathematical Programming




Description: Theaimofthismoduleistointroducestudentstotheformulationandsolutionofvariouslinearprogrammingproblems.Thesubjectmatterwillbeillustratedbyapplyingthemethodsofsolutiontorealexamples.Thesyllabusincludes:formulationoflinearproblems;solutiongraphicallyandbysimplexalgorithm;sensitivityanalysis;duality;transportationandtransshipment;theassignmentproblem;non-linearprogramming;integerprogramming.




MT3833 Utilities, Decisions and InventoriesCredits: 15.0 Semester: 2



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Description: Thismoduleisintendedtoprovideanintroductiontotheformulationandsolutionofproblemsofdecision-takingandproblemsinthemanagementofinventorysystemsforasingleitem,tomotivatetheneedforutilityfunctions,andtoexplainhowtheyareassessedandemployed.Thesyllabusincludes:decisiontheory;maximumandBayesianapproaches;Bayestheorem;Bellman’soptimalityprinciple;utilitytheory;utilityfunctions;inventorytheory.




MT3834 Ecological Modelling Credits: 15.0 Semester: 2



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



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


Assessment: ProjectReport=25%,2HourExamination=75%

MT3838 Robust Statistical MethodsCredits: 15.0 Semester: 2



Description: Classicalandmodernrobustmethodsfordataanalysisaredescribed.PermutationtestsandintervalsandMonteCarlotests,whichspanbothclassicalmethodsandmodern,computer-intensivemethods,arecovered,asaresomemorerecentcomputer-intensivemethods,notablythebootstrap.Illustrationsaregivenoftheapplicationofmodernmethodstostandardstatisticalproblems;theemphasisforclassicalmethodsisonorderstatisticsandrankingmethods.

ClassHour: 11.00am



MT3850 Lattice Theory



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Mathematics & Statistics - 3000 & 4000 Level modules



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.



MT3999 Project in Mathematics/Statistics

Credits: 15.0 Semester: WholeYear

Description: Thestudentwillchooseaprojectfromalistpublishedannuallyalthoughatopicoutwiththelistmaybeapproved.Studentswillberequiredtoreportregularlytotheirsupervisorandareportofnomorethan5,000wordsmustbesubmittedbytheendofthesecondsemester.


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




Description: ThismoduleaimstoenablestudentstouseMapleasatoolintheirothermodulesandtoturnnaturallytosuchapackagewhensolvingmathematicalproblems.Themoduleaimstoillustratethefollowingpoints:asymboliccomputationpackageallowsonetoconductmathematicalexperiments;asymboliccomputationpackageallowsonetocollectdataaboutaproblembeingstudied.Thisissimilartothewayotherscientistswork.Itiseasiertotryseveraldifferentapproachestoaproblemandseewhichworks.Themachineisstupid.Intelligencecomesfromtheuser.Theuserthinks,theuserinterprets,thecomputercalculates.StudentswillundertakeamoresubstantialprojectthanthatrequiredforMT3611.

ClassHour: 9.00am

Teaching: Twolectures,onetutorial


MT4612 Advanced Computing in Mathematics



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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



MT4701 Advanced Statistical Inference



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



MT4702 Advanced Generalized Linear Models and Data Analysis



Co-requisite: MT3501

Description: Thismoduleaimstodemonstratethepowerandeleganceofunifyingalargenumberofsimplestatisticalmodelswithintheframeworkofthegeneralizedlinearmodel.Itwilltrainstudentsintheinterpretation,analysisandreportingofdata,whenasingleresponsemeasurementisinterpretedintermsofoneoranumberofothervariables.AswellasstudyingthematerialcoveredinMT3702,studentswillundertakeasubstantialpieceofprojectwork.

ClassHour: 11.00am

Teaching: 2lectures,1tutorial,practicalclassesandprojectrelatedtutorials.


MT4704 Advanced Sampling Theory




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Description: ThismodulecomprisesMT3704butwithamoreadvancedprojectwhichwillrequiresomeorallofthefollowing:supplementaryreading,aliteraturereview,acritiqueofasurvey,questionnaireandsurveydesign,surveyimplementation,anddataanalysis.TheprimarygoaloftheadvancedprojectwillbetohavestudentsinvestigateingreaterdepthoneormorespecifictopicsencounteredinMT3704.




MT4705 Advanced Multivariate Analysis



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



MT4803 Advanced Interpolation and Approximation




Description: ThismodulecoversthematerialofMT3803,withtheadditionoftopics,coveredbydirectedreadingand/oradditionallectures,requiringamuchmorematureunderstandingofanalysis.

ClassHour: 10.00am


Assessment: Two-and-a-halfHourExamination=100%

MT4804 Advanced - The Sun



Description: ThismoduleconsistsofMT3804withtheadditionofdirectedreadingonmoreadvancedaspectsofthesubjectandarequirementforstudentstocarryoutadetailedanalyticalinvestigationofaparticularsystemoradetailedliteraturesurveyofaspecificarea.Thesyllabusincludes:observationsoftheSunanditsmagneticphenomena;theequationsofmagnetohydrodynamics,theirpropertiesandapplicationtosolarmagnetism;convectionanddiffusionofmagneticfield;magneticequilibria,force-freefields,magneticfluxtubes;MHDwaves;wavesinmagneticfluxtubes,intensetubes,sunspots,coronalloops;coronalheating;prominences;Solarwind;helioseismology.

ClassHour: 11.00am



MT4805 Advanced Electromagnetism




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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.




MT4806 Advanced Numerical Solution of Partial Differential Equations




Description: ThismoduleconsistsofMT3806withtheadditionthatstudentswillberequiredtogainexpertiseinaprogramminglanguageandundertakecomputationalprojects.Thesyllabusincludes:convergenceandstabilityoffinite-differenceapproximationstoinitialvalueproblemsinoneandtwospacedimensions;theinvestigationofdispersionanddissipationintheapproximationofconservativelaws.




MT4807 Advanced Classical Mechanics




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



MT4808 Advanced Dynamical Systems




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Description: ThismoduleconsistsofMT3808withtheadditionofdirectedreadingonmoreadvancedortechnicalaspectsofthesubjectandarequirementforstudentstocarryoutadetailedanalyticandnumericalinvestigationofaparticularsystem.Thesyllabusincludes:discreteandcontinuousdynamicalsystems;perioddoubling,intermittency,bifurcationsandchaosinmappingsanddifferentialsystems;homoclinicandheteroclinicpointsandorbitsandtheirroleinthedevelopmentofchaos;theSmalehorseshoemappingandsymbolicdynamics;thebifurcationsofcodimensiononeandtheuseofcentremanifoldtheory;Melnikov’smethod;Strangeattractors,dimensionandLyapunovexponents;HamiltoniandynamicsandtheKolmogorov-Arnold-Mosertheorem.

ClassHour: 10.00am



MT4809 Advanced Fluid Dynamics




Description: ThismoduleconsistsofMT3809withtheadditionofdirectedreadingonmoreadvancedaspectsofthesubject.Bytheendofthemodulestudentsareexpectedtounderstandthevariousphysicalpropertiesoffluids;theworkingsofPitottubesandVenturimeters;theconceptsofFroudeandReynoldsnumber;gasbubblesoscillations;howtosolveLaplace’sequationforvariousvelocitypotentialproblems;theconceptofastreamfunction;Navier-Stokesequationsandtheirsolutioninsimplesituations;applicationofcomplexvariabletheorytofluidflowsanditsuseinpredictingliftanddragroundrotatingbodies;aerofoiltheory;waterwavetheory;comprehensiblefluidtheories;Machnumberandshocklines;Prandtl-Meyrexpansions;Rankine-Huguneotrelationships.




MT4811 Advanced Asymptotic Analysis and Perturbation Theory



Prerequisites: MT3503,MT3504

Description: ThismoduleconsistsofMT3811withtheadditionofdirectedreadingonmoreadvancedtopicsinbothAsymptoticAnalysisandPerturbationTheory.Theadvancedtopicsmayinclude,forexample,themethodofsteepestdescents,advancedboundarylayermethodsandtheLangertransformationfortwoturningpointproblemsinWKBtheory.Studentswillbeaskedtocompletemoredemandingtutorialsheetsandcarryoutdetailedcalculationsusingthesemoreadvancedtechniques. Thesyllabuswill includethatforMT3811plusadvancedasymptoticandperturbationmethods.Forexample,additionalmethodscouldbechosenfrom(i)themethodofsteepestdescents,(ii)advancedboundarylayermethodsand(iii)Langertransformationsforturningpointproblems.

ClassHour: 11.00am



MT4812 Advanced Partial Differential Equations




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Description: Theaimofthismoduleistogiveaninsightintotheroleofnonlinearpartialdifferentialequationsoftheevolutiontypeinmodernappliedmathematics.Afteranintroductiontomethodsforlinearequations,themodulewilldealwithtechniquesfortheanalysisofapplicationsinsuchareasascompressiblefluidflowandtheformationofshockwaves,travellingwaves,spreadofthinfilms,solitons,trafficflowandotherareasofthephysicalandbiologicalsciences.TheparticularfocusofthismodulewillbeadescriptionoftheinversescatteringmethodforthesolutionoftheKorteweg-deVriesequation.

ClassHour: 11.00am



MT4813 Advanced Fractal Geometry



Prerequisites: MT2001orMT2101

Description: ThismoduleconsistsofMT3813withtheadditionoftutorialsanddirectedreadingonextensionsofthesubjectandmoresophisticatedmathematicalanalysis.Theaimofthismoduleistointroducethemathematicsusedtodescribeandanalysefractalsandtoshowhowthetheorymaybeappliedtoexamplesdrawnfromacrossmathematicsandscience.Themodulediscussesthephilosophyandscopeoffractalgeometry;andcoversconceptssuchasdimension,representationoffractalsbyiteratedfunctionsystems,fractalsinotherareasofmathematicssuchasdynamicalsystemsandnumbertheory,JuliasetsandtheMandelbrotset.




MT4814 Advanced Graph Theory




Description: ThismoduleincludesandextendsthecontentsofMT3814.Additionaltopicstobecoveredmayinclude:applicationsofgraphstogroupsandotheralgebraicstructures,automorphismgroups,furtheralgorithms,complexityofalgorithms.

ClassHour: 10.00am



MT4815 Advanced Functional Analysis




Description: ThismoduleconsistsofMT3815withadditionaladvancedmaterialleadingtoaproject.Themodulewillfamiliarisestudentswiththebasicnotionsoffunctionalanalysis,thatisanalysisonnormedspacesandHilbertspace.Themodulewillcovernormedspaces,convergenceandcompleteness,operators,HilbertspacesandtopicssuchasspectraltheoryandtheHahn-Banachtheorem.




MT4816 Advanced Finite Mathematics




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Description: ThismoduleincludesandextendsthecontentsofMT3816.Additionaltopicstobecoveredmayinclude:Booleanalgebras,furthercombinatorialstructures.




MT4817 Advanced Rings and Fields




Description: ThismoduleconsistsofMT3817togetherwithadditionaladvancedmaterial,whichisdesignedtogivestudentsadeeperunderstandingofthestructureofringsandfieldsandtheirapplications.Itmayincludetopicsfromradicaltheory,semisimplicity,Galoistheoryandprimaryidealsanddecompositions.

ClassHour: 11.00am



MT4818 Advanced Topics in Geometry




Description: ThismoduleincludesandextendsthecontentsofMT3818.Additionaltopicstobecoveredmayinclude:crystallographicandfriezegroupsandtheirclassification,anintroductiontoalgebraictopology.

ClassHour: 11.00am


Assessment: Two-and-a-halfhourexamination=100%

MT4819 Advanced Number Theory




Description: ThismoduleincludesandextendsthecontentsofMT3819.Additionaltopicstobecoveredmayinclude:quadraticreciprocity,quadraticforms,arithmeticfunctions,furtherDiophantineequations.

ClassHour: 10.00am


Assessment: Two-and-a-halfhourexamination=100%

MT4820 Advanced Linear Algebra




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Description: ThismoduleconsistsofMT3820withtheadditionofmoreadvancedmaterial.Thesyllabusincludesbases, thedimensiontheorem,eigenvaluesandeigenvectors, theCaley-Hamiltontheorem,minimumpolynomials,sumsanddirectsumsofsubspaces,theprimarydecompositiontheorem,diagonalisation,similarity,variouscanonicalforms.

ClassHour: 11.00am



MT4821 Advanced Modules and Categories




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



MT4822 Advanced Metric and Topological Spaces




Description: ThismoduleconsistsofMT3822withadditionaladvancedmaterialleadingtoaproject.Thismoduleextendsideasofconvergenceandcontinuitytoverygeneralsettings.Topicsincludemetricspaces,completenessandthecontractionmappingtheorem,compactness,topologicalspacesaxiomatizedviaopensets,compactnessandconnectedness.

ClassHour: 11.00am



MT4823 Advanced Semigroups




Description: ThismodulewillconsistofMT3823,togetherwithadditionaladvancedmaterial,designedtotakestudentstothefrontiersofcurrentresearchinsemigrouptheory.Itmaycontaintopicsfrom:semigrouppresentations,decidabilityproblems,finitenessconditions,amalgamation,matrixsemigroupsandsemigroupvarieties.




MT4824 Advanced Topics in GroupsCredits: 20.0 Semester: 2



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Description: ThismodulewillconsistofMT3824togetherwithadditionaladvancedmaterial,inwhichtheresultsfromthebasicpartofthemodulewillbeusedtoobtaindeeperinformationaboutfinitegroupsofsmallorders,simplegroups,solubilityproblemsforfinitelypresentedgroupsandBurnsidetypeproblems.Thisadditionalpartofthemodulewillbedesignedsoastogivestudentsatasteofthecurrentresearchingrouptheory.

ClassHour: 10.00am



MT4825 Advanced Topics in Modern AnalysisCredits: 20.0 Semester: 2



Description: ThismoduleconsistsofMT3825withadditionaladvancedmaterialleadingtoaproject.Thismoduleintroducessomeofthepowerfultechniquesandideasofmodernmathematicalanalysisthatareimportantbothinanalysisinitsownrightandinitsmanyapplicationsinmathematicsandscience.Themodulewillincludetopicssuchas:measuretheory,theergodictheorem,martingaletheory,Fuchsiangroups.Analysisisoneoftheactiveresearchareasattheschool,andthechoiceoftopicswillreflectthis.

ClassHour: 11.00am



MT4828 Advanced ClassificationCredits: 20.0 Semester: 2



Description: ThismoduleconsistsofMT3828with theadditionofdirected readingonmoreadvancedortechnicalaspectsofthesubjectandarequirementforstudentstoapplythemethodologyinadetailedexaminationofdata.Thesyllabusincludes:typesofdataandclassifications;constructionofdissimilaritymeasures;partitioningalgorithms;hierarchicalclassifications;principalco-ordinatesanalysis;non-metricmultidimensionalscaling;stagesinnumericalclassification;analysisofdatausingtheCLUSTANpackage.

ClassHour: 11.00am



MT4831 Advanced Bayesian InferenceCredits: 20.0 Semester: 2



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



MT4832 Advanced Mathematical ProgrammingCredits: 20.0 Semester: 2



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Description: ThismoduleconsistsofMT3832withtheadditionofdirectedreadingonmoreadvancedaspectsofthesubjectandarequirementforstudentstocarryoutaproject.Thesyllabusincludes:formulationoflinearprogrammingproblems;solutiongraphicallyandbyuseofthesimplexalgorithm;sensitivityanalysis;thedualproblemanditsrelationtotheprimalproblem;thetransportationproblemanditssolutionusingtheNorthWestCornermethodandVogel’srule;theassignmentproblemanditssolution;transshipment;nonlinearprogramming;integerprogramming.



MT4834 Advanced Ecological Modelling




Description: Thismodule consistsofMT3834with the additionof an advancedproject, in the formof aliteraturerevieworaprojectonsomeaspectofmodelling.

ClassHour: 10.00am


Assessment: Essay=10%,AdvancedProjectReport=25%,2HourExamination=65%

MT4835 Advanced Wildlife Population Assessment




Description: ThismoduleconsistsofMT3835withtheadditionofanadvancedproject,whichmightcoveranyaspectofthemodule.

ClassHour: 11.00am


Assessment: AdvancedProjectReport=45%,2HourExamination=55%

MT4838 Advanced Robust Statistical Methods




Description: ThismoduleconsistsofMT3838withtheadditionofanadvancedproject,whichmightcoveranyaspectofthemodule.

ClassHour: 11.00am


Assessment: ContinuousAssessment=20%,AdvancedProject=25%,2HourExamination=55%

MT4850 Advanced Lattice Theory



Prerequisites: MT2002

Page 13.30


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.


Assessment: TwoHourExamination=100%

MT4998 Advanced Project in Mathematics/Statistics


Prerequisite: EntrytotheMScidegreeinMathematicsandTheoreticalPhysics


Description: Theprojectwillbechosenfromanapprovedlistoftopicsandthecreditratingwillreflectthecontentanddepthofaninvestigationinvolved.


MT4999 Advanced Project in Mathematics/Statistics



Description: Thisisamoresubstantialprojectwhich,forM.Sci.studentswillreplacetheexistingHonoursproject.Theprojectwillbechosenfromanapprovedlistoftopics.Thestudentmayberequiredtoreviewcurrentliteratureandinvestigateatopicinsomedepth.
