MAT482TopicsinMathematics:MathModels

"Ifpeopledonotbelievethatmathematicsissimple,itisonlybecausetheydonotrealizehowcomplicatedlifeis."--JohnvonNeumannCourseSynopsisThiscourseisdesignedtoprovideupperlevelundergraduatesandbeginninggraduatestudentswithanunderstandingofhowmathematicalmodelingisthelinkbetweenmathematicsandtherestoftheworld.Natureishighlycomplexandmathematicalmodelingcanhelptounlockthesecretstoproblemsinengineering,physics,astronomy,biology,medicine,chemistry,economics,andthesocialsciencesamongotherfields.Modelingisawayofstructuringquestionsabouttheworldsothatmathematicaltechniquesmayprovideinsight.Itisasmuchanartasascience.Thiscoursewillcoverabroadspectrumofmodelingapproachesincludingoptimization,dynamicalsystems,andstochasticprocesses.Sometopicscoveredincludesensitivityanalysis,modelrobustness,multi-variableoptimization,linearprogramming,operationsresearch,compartmentmodels,neuronalmodels,bifurcationtheory,renewaltheory,Markovchains,queuingtheory,diffusion,andsomestochasticmodelsinbiology.Regularcomputerlabsessionswillbeusedtoteachvisualizationandsimulationofthemathematicalmodelsstudied.Asubstantialcomponentofthecoursegradewillbeamodelingprojectwithastudent-selectedtopic.Evaluationoftheprojectwillbebasedonaresearchreportandapresentation.Regularwrittenhomeworkandtwomidtermexamswillalsobepartofthecoursegrade.InstructorDr.AdamR.StinchcombeOffice:TBDE-mail:TBDOfficeHours:TBDorbyappointmentCourseLocationTBDCourseWebsiteURLTBD.Thewebsitewillbeusedtopostannouncements,aswellastoassignandcollecthomeworkandlabreports.

PrerequisitesInordertobesuccessfulinthiscourse,itwillbenecessarytohaveasolidfoundationinordinarydifferentialequations(MAT244)andlinearalgebra(MAT223,MAT224).AcourseinprobabilityorsomeexperiencewithMatlaborPythonwouldbehelpful.ProjectStudentsshouldworkinteamsoftwoorthree,preferably,althoughyoucandiscusswithmethepossibilityofindividualprojectsorlargergroups.Fortheproject,youwillgivea15minutein-classpresentationduringthelasttwoweeksofthecourseandsubmitaresearchreport.Attendanceatthepresentationsofothergroupswillformpartofyourgrade.Startthinkingearlyabouttopicsthatinterestyouandlocateresearchmaterialsonthattopic.Bepreparedtosubmitaprojectoutlineinmid-March.Fortheproject,youcandevelopanovelmathematicalmodelrelatedtoyourtopic,orprovideextensionsornewapplicationsforanexistingmathematicalmodel.Itwillnotbesufficienttostudyanexistingmodelandpresentalreadyreportedresultsforthemodel;theremustbeanovelcomponenttoyourproject.Projectpresentationswilltakeplaceinclassonthelastthreelecturedates.Thefinalprojectreportisdueat5:00pmonthelastdayofclasses.ExamsTherewillbetwoin-classmidtermexams(datesTBD).Pleasecontactmeassoonaspossibleifyouhaveanunavoidableconflictwiththesedates.Thiscoursedoesnothaveafinalexam.ComputerLabsTherewillberegularcomputerlabs,onlyonFridays.WewillmakeconsiderableuseofMatlab.HomeworkTherewillbeapproximatelythreewrittenhomeworkassignmentsandsevenlabreports.PleasesubmitaPDFonthecoursewebsiteontheduedatebefore11:59pm.Latehomeworkwillnotbeacceptedunlesspermissionisgivenaheadoftime.GradingSchemeCoursegradeswillbedeterminedfromthefollowingcomponents:

• writtenhomeworkandlabreports 30%• twomidtermexams 2x15%• projectreportandpresentation 40%

TextbookRequired:"MathematicalModeling"byMarkM.Meerschaert(4thed.)ISBN:0123869129Optional:"ModelingandSimulationinMedicineandtheLifeSciences"byFrankC.HoppensteadtandCharlesPeskin(2nded.)ISBN:978-0387215716TestingAccommodationsIfyouthinkyouneedanaccommodationforadisability,pleaseletmeknowassoonaspossible.Pleaseprovideappropriatedocumentationtomeatleasttwoweekspriortotheneedforatestaccommodation.