10021 Basic Algebra I (2)
LearningOutcomesforBasicAlgebraI,MATH-10021
Knowledge
Thestudentsshould learnoperationsonintegers,fractions,decimalsandpercents,propertiesofrealnumbers. Shouldbefamiliarwiththefirstdegreeequationsandstartproblem-solvingwithformulas.Shouldlearnhowtosolveequationsandinequalitiesinonevariable,linearequations.
Comprehension
Shouldunderstandthenotionoftherateofchangeandslope, shouldbeabletodrawgraphsintheCartesianplane.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletosolvefirstdegreeequationsandstartproblem-solvingwithformulas
Synthesis
Shouldstartdevelopingabstractthinking.
Evaluation
ShouldworkconsistentlytocompleteprogressandcomprehensiveassessmentsinALEKS
ClassActivities
Tosolveproblemsinclassanddiscussmathematicalideas.
OutofclassActivities
ToworkregularlytosolveproblemsandaddtopicstotheALEKSpie.
10022 Basic Algebra II (2)
LearningOutcomesforBasicAlgebraII,MATH-10022
Knowledge
Thestudentsshould learnthenotionsof functions,systemsoflinearequations,exponents,polynomialoperations, shouldgetacquaintedwithscientificnotation.
Comprehension
Shouldunderstand factoringpolynomials,solvingquadraticsbyfactoring,radicalsandrationalexponents.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletofactorpolynomials, andtosolvequadraticsbyfactoring, solveproblemsrelatedtoradicalsandrationalexponents.
Synthesis
Should continuedevelopingabstractthinking.
Evaluation
ShouldworkconsistentlytocompleteprogressandcomprehensiveassessmentsinALEKS
ClassActivities
Tosolveproblemsinclassanddiscussmathematicalideas.
OutofclassActivities
ToworkregularlytosolveproblemsandaddtopicstotheALEKSpie.
10023 Basic Algebra III (2)
LearningOutcomesforBasicAlgebraIII,MATH-10023
Knowledge
Thestudentsshouldlearnthenotionsof zerosoffunctions,rationalexpressionsandequations,problem-solvingwithrationalexpressions,intermediatefactoringtechniques.
Comprehension
Should beabletounderstandnotionsrelatedtoQuadratics:functions,graphs,equations,inequalities,"quadratictype"equations.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Should beabletoanalyzethegraphs,equations,inequalitiesrelatedtoquadratics.
Synthesis
Shouldcontinuedevelopingabstractthinking.
Evaluation
ShouldworkconsistentlytocompleteprogressandcomprehensiveassessmentsinALEKS
ClassActivities
Tosolveproblemsinclassanddiscussmathematicalideas.
OutofclassActivities
ToworkregularlytosolveproblemsandaddtopicstotheALEKSpie.
10024 Basic Algebra IV (2)
LearningOutcomesforBasicAlgebraIV,MATH-10024
Knowledge
Thestudentsshould learntheadvancedfactoringtechniques,rationalfunctions,radicalequations,absolutevalueequationsandinequalities,exponentialandlogarithmicfunctions.
Comprehension
Should beabletosolveproblems withExponentialandlogarithmicfunctions.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Should beableto analyzethegraphsof andtheinformationrelatedtotheexponentialandlogarithmicfunctions.
Synthesis
Shouldcontinuedevelopingabstractthinking.
Evaluation
ShouldworkconsistentlytocompleteprogressandcomprehensiveassessmentsinALEKS
ClassActivities
Tosolveproblemsinclassanddiscussmathematicalideas.
OutofclassActivities
ToworkregularlytosolveproblemsandaddtopicstotheALEKSpie.
10041 Elementary Probability and Statistics (3)
LearningOutcomesforElementaryProbabilityandStatistics,MATH-10041
Knowledge
Thestudentsshould learnthenotionsofdescriptivestatistics,probabilityconcepts,binomialandnormaldistributions,aswellasthenotionsofconditionalprobabilityand countingtechniques.
Comprehension
Shouldunderstandthenotionsofsampling,estimation,andhypothesistesting.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeableto analyzethepaireddata,linearmodelsandcorrelation.
Synthesis
Should continuedevelopingabstractthinking.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
11008ExplorationsinModernMathematics(3)
LearningOutcomesforExplorationsinModernMathematics,MATH-11008
Knowledge
Thestudentshoulddiscovermathematicalideasthataffecteverydaylifebycomparingvariousvotingmethodsinmathematicsofsocialchoiceanddemonstratinganunderstandingofmathematicalconceptsappearinginnatureandmanagementscience.
Comprehension
Shouldunderstandthenotionsofgrowthandsymmetry.Shouldgetacquaintedwiththemathematicsofsocialchoiceandstatistics.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletoanalyzetheodds,thechancesandprobabilitiesofevents.
Synthesis
Shouldcontinuedevelopingabstractthinking.
Evaluation
Shouldcompletehomeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
Learning Outcomes for Modeling Algebra (4), Math 11009
KnowledgeAnalyzeagivensetofreal-worlddiscretedatanumericallyandgraphicallyanddeterminewhichoftheelementaryfunctionswouldbeanappropriatemathematicalmodel.
Withtheaidofaspreadsheet,graphingcalculator,orsimilartechnology,studentscanconstructamodelthatcapturesessentialfeaturesofasituationdescribedby discretedata.
Studentcanuseafunctionmodeltoanalyzeandinterpretasituationdescribedverballyorwithdata.
Compareandcontrastcharacteristics(numeric,graphical,symbolic)offunctionsstudiedinthecourse: linear,quadratic,exponential,logarithmic,polynomial.
Masteralgebraictechniquesandmanipulationsnecessaryforproblemsolvingandmodelinginthiscourse.
Insight / Discernwhethermental,paperandpencil,algebraic,ortechnology-basedtechniquesareappropriateastheyformulate,validate,andanalyzeproblems.
Exhibitatendencytoapplymathematicalmodelingtohelpthemanswerquestionsthatariseintheirdailyliveseitheratworkorathome.
Describetheroleandusefulnessofmathematicalmodelinginthedecisionmakingprocessofsocialandlifescientists,businesspersonnelandgovernmentagencies.
Correctlyinterpretagivenmathematicalresult(i.e.asolutiontoamathproblem).
Developapersonalframeworkofproblem-solvingtechniques
Engagement / Considerandexplaintheroleofmathematicsinunderstandingbusinessandsocialproblems
Analyzetherelevanceofmathematicalmodelingtotheirfieldofstudyandgiveatleastoneconcreteexample.
Improvetheirconfidenceinandattitudetowardmathbecauseofthesense-makingemphasisinthecourse.
Participateactivelyinclassdiscussions.
Responsibility
Developskillsasateamplayerand decisionmakinginagroupsetting.
Developconfidenceandcompetenceincommunicatingmathematicalknowledgetopeers.
Demonstratecompetent,ethical,andresponsibleuseofinformationinacademicwork.
Evaluategroupdynamicswithintheir group
Learntoprioritizeandmanagetimeastheybalancethevarietyofassignmentsinthecourse.
11010 Algebra for Calculus (3)Algebra for Calculus Learning Outcomes
Knowledge / Representfunctionsverbally,numerically,graphicallyandalgebraically,includinglinear,quadratic,polynomial,rational,root/radical/power,piecewise-defined,exponential,andlogarithmic,functions.Performoperationsonfunctionsandtransformationsonthegraphsoffunctions.
Analyzethealgebraicstructureandgraphofafunction,includingthoselistedabovetodetermineintercepts,domain,range,intervalsonwhichthefunctionisincreasing,decreasingorconstant,thevertexofaquadraticfunction,asymptotes,whetherthefunctionisone-to-one,whetherthegraphhassymmetry(even/odd),etc.,andgiventhegraphofafunctiontodeterminepossiblealgebraicdefinition.
Findinversesoffunctionslistedaboveandunderstandtherelationshipofthegraphofafunctiontothatofitsinverse.
Solveavarietyofequationsandinequalities,includingpolynomial,rational,exponential,andlogarithmic,includingthosearisinginapplicationproblems.
Identifyandexpresstheconics(quadraticequationsintwovariables)instandardrectangularform,graphtheconics,andsolveappliedproblemsinvolvingconics.
Insight / Usefunctions,includingthoselistedabove,tomodelavarietyofreal-worldproblemsolvingapplications.
Understandthedifferencebetweenanalgebraicequationofone,twoormorevariablesandafunction,andtherelationshipamongthesolutionsofanequationinonevariable,thezerosofthecorrespondingfunction,andthecoordinatesofthex-interceptsofthegraphofthatfunction.
Representsequencesverbally,numerically,graphicallyandalgebraically,includingboththegeneraltermandrecursively.
Engagement / Considerandexplaintheroleofmathematicsinunderstandingbusinessandsocialproblems
Improvetheirconfidenceinandattitudetowardmathbecauseofthesense-makingemphasisinthecourse.
Participateactivelyinclassdiscussions.
Responsibility / Developskillsasateamplayeranddecisionmakinginagroupsetting.
Developconfidenceandcompetenceincommunicatingmathematicalknowledgetopeers.
LearningOutcomesforIntuitiveCalculus,MATH-11012
Knowledge
Thestudentsshouldbeabletocomputethederivativeandtheintegralsofsomeelementaryfunctions.
Comprehension
Shouldunderstandthemeaningsofthederivative,theindefiniteanddefiniteintegralsofafunction.
Application
Tofindtherateofchangeofafunction,tominimizeandmaximizeafunction,tofindtheareaofaregionboundedbycertaingivencurves.
Analysis
Shouldunderstandsomebasicproofsinthetopicsofderivativesandintegrals.
Synthesis
N/A.
Evaluation
Shouldbeabletoapplytheknowledgeofdifferentiationandintegrationtosolvesomeapplicationproblems.
ClassActivities
Tosolveproblemsinclass.
OutofclassActivities
Todothehomework.
Math 11022 - Trigonometry Learning Outcomes
Knowledge / Expressanglesinbothdegreeandradianmeasure.Solverightandobliquetrianglesindegreesandradiansforbothspecialandnon-specialangles.
Representtrigonometricandinversetrigonometricfunctionsverbally,numerically,graphicallyandalgebraically;definethesixtrigonometricfunctionsintermsofrighttrianglesandtheunitcircle.
Performtransformationsoftrigonometricandinversetrigonometricfunctions – translations,reflectionsandstretchingandshrinking(amplitude,periodandphaseshift).
Analyzethealgebraicstructureandgraphoftrigonometricandinversetrigonometricfunctionstodetermineintercepts,domain,range,intervalsonwhichthefunctionisincreasing,decreasingorconstant,asymptotes,whetherthefunctionisone-to-one,whetherthegraphhassymmetry(even/odd),etc.,andgiventhegraphofafunctiontodeterminepossiblealgebraicdefinitions.
Solveavarietyoftrigonometricandinversetrigonometricequations,includingthoserequiringtheuseofthefundamentaltrigonometricidentitiesindegreesandradiansforbothspecialandnon-specialangles.Solveapplicationproblemsthatinvolvesuchequations.
Identifyandexpresstheconics(quadraticequationsintwovariables)instandardrectangularform,graphtheconics,andsolveappliedproblemsinvolvingconics.
Representvectorsgraphicallyinbothrectangularandpolarcoordinates.
Performbasicvectoroperationsbothgraphicallyandalgebraically – addition,subtractionandscalarmultiplication.
Insight / Usetrigonometricfunctionstomodelavarietyofreal-worldproblemsolvingapplications.
Understandthedifferencebetweenatrigonometricfunctionandaninversetrigonometricfunction.Understandtherelationshipamongthesolutionsofatrigonometricequationinonevariable,thezerosofthecorrespondingfunction,andthecoordinatesofthex-interceptsofthegraphofthatfunction.
Verifytrigonometricidentitiesbyalgebraicallymanipulatingtrigonometricexpressionsusingfundamentaltrigonometricidentities.
Solveapplicationproblemsthatinvolverightandobliquetriangles.
Understandtheconceptualandnotationaldifferencebetweenavectorandapointintheplane.
Solveapplicationproblemsusingvectors.
Engagement / Considerandexplaintheroleoftrigonometryinunderstandingscienceandsocialproblems
Improvetheirconfidenceinandattitudetowardtrigonometrybecauseofthecourse.
Participateactivelyinclassdiscussions.
Responsibility / Developconfidenceandcompetenceincommunicatingmathematicalknowledgetopeers.
Developconceptualunderstandingandfluencywithtrigonometricfunctions,techniques,andmanipulationsnecessaryforsuccessinCalculus.
LearningOutcomesforMath12001
LearningOutcomesforMATH-12001
Knowledge
Thestudentsshoulddemonstratearigorousunderstandingofelementaryfunctions,includingpolynomial,exponential,logarithmic,andperiodictypes.Solveproblemsinalgebraandtrigonometryandbeabletoapplymathematicaltechniquesassociatedwithmulti-stepproblems.
Comprehension
Shouldbeabletounderstand thenotionsoftrigonometryrelatedtofourtrigonometricfunctions,andtheirinverses,aswellasasthenotionsfromalgebraforcalculus.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletosolvetrigonometricinequalities, simplifytrigonometric expressions,analyzethedataof “mixed” (trigonometricandalgebraic)origin.
Synthesis
Should bereadyfortakingCalculuscourses.
Evaluation
Shouldcompletehomeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
12002AnalyticGeometryandCalculusI(5)MATH12002
LearningOutcomesforAnalyticGeometryCalculusI,MATH-12002
Knowledge
Thestudentsshouldbeabletounderstandtheconceptsoflimits,continuity,
derivatives,ratesofchange,linearapproximationanddifferentials,
definiteandindefiniteintegrals,inversefunctions.Theyshouldto
formulatetheMeanValueTheorem
andtheFundamentalTheoremofCalculus.
Comprehension
Shouldbeabletocomputethederivativesandintegralsusingbasic
differentiation
andintegrationformulas.
Application
Themainandmostimportantapplicationis tosolvemanydifferent
problemsrelatedtothesubject.
Analysis
Shouldbeabletorelatethederivativesandshapesofgraphs.
Shouldusethisinformationforthecurvesketching.
Synthesis
Should getusetocombinetheirskillsfromelementarymathematical
coursestosolvetheproblemsinCalculus.
Evaluation
Shouldbeabletofindthederivativeandindefiniteintegral
ofaconstant,powerfunction,trigonometricfunctionslike
sineandcosine,logarithmicand
exponentialfunctions.Shouldbeabletoevaluateareasbetweencurves.
ClassActivities
TosolveproblemsandproveTheoremsinclass.
OutofclassActivities
Tosubmiteveryweekhomeassignments.
12003AnalyticGeometryandCalculusII(5)MATH12003
LearningOutcomesforAnalyticGeometryCalculusII,MATH-12003
Knowledge
Thestudentsshouldbeabletodeveloptheirdeeperunderstandingof theconceptstheylearnedinCalcI:limits,continuity,
derivatives,ratesofchange,linearapproximationanddifferentials,
definiteandindefiniteintegrals,inversefunctions. Theyshouldalso
studythetechniquesandapplicationsofintegration;trigonometric,logarithmicandexponentialfunctions;polarcoordinates;vectors;parametricequations;sequencesandseries.
Comprehension
Shouldbeabletodecidewhetherthegivenseriesisdivergentorconvergent.Shouldunderstandthenotionsoftangentvectors,equationsoflinesandplanes.
Application
Themainandmostimportantapplicationistosolvemanydifferent
problemsrelatedtothesubject.
Analysis
Shouldbeabletousetheanalytictechniquestoattackgeometricproblems.
Synthesis
Should getusedtocombinetheirskillsfromelementarymathematical
coursestosolvethemoreadvancedproblemsinCalculus.
Evaluation
Shouldbeabletodecomposethefunctionintopowerseries.
ClassActivities
TosolveproblemsandproveTheoremsinclass.
OutofclassActivities
Tosubmiteveryweekhomeassignments.
12011 Calculus with Precalculus I (3)
LearningOutcomesforCalculuswithPrecalculusI,MATH-12011
Knowledge
Thestudentsshould reviewalgebraandtrigonometry:equationsoflines,functionsandgraphs,exponents,squaringandcubingofbinomials.Thenshouldunderstandthenotionsrelatedtoexponents,factoring,functions,graphs,tangentlines,limits,continuity,derivativesandrelatedrates.
Comprehension
Shouldunderstandthenotionsofimplicitdifferentiation,higher
orderderivatives,applicationstoratesofchangeinscienceandbusiness.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Maximumandminimumvalues,criticalnumbers,ExtremeValueTheorem,MeanValue
Theorem.
Synthesis
Should continuedevelopingabstractthinking.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
12012 Calculus with Precalculus II (3)
LearningOutcomesforCalculuswithPrecalculusII,MATH-12012
Knowledge
Developmentofintegralcalculusandcontinuedstudyofdifferentialcalculus.Includescurvesketchingoptimizationfundamentaltheoremofcalculusareasbetweencurves,exponentialandlogarithmicfunctions.
Comprehension
Shouldunderstandthenotionsofareasanddistances,Riemannsums,thedefiniteintegral,anti-derivatives,FundamentalTheoremofCalculus,indefiniteintegrals,integrationbysubstitution.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletoanalyzethenetchange,areasbetweencurves,averagevalueofafunction.[
Synthesis
Should continuedevelopingabstractthinking.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
12021 Calculus for Life Sciences (4)
LearningOutcomesforCalculusforLifeSciences,MATH-12021
Knowledge
Shouldunderstandthedifferentialandintegralcalculususingexamplesandproblemsinlifesciences.
Comprehension
ShouldunderstandthenotionsofLimits,Derivatives,andContinuousTimePhenomena,aswellasFirstOrderDifferentialEquationsandtheIntegral, andTheSolutionofAutonomous(Separable)Equations.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
ShouldbeabletouseanalyticskillstoDiffusionacrossamembraneproblemsandamodelforneuronfiring:Fitzhugh-NagumoEquations.
Synthesis
Should beabletoapplytheabstractthinkingtothereallifeproblems.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
12022ProbabilityandStatisticsforLifeSciences(3)MATH12022
LearningOutcomesforStatisticsfortheLifeSciences,
Knowledge
Studentswilllearnelementaryappliedstatisticalmethodswithemphasisonsolvingproblemsdealingwiththebiomedicalfield. Principaltopicsincludeestimationandhypothesistestingforpopulationmeans,differencesbetweentwomeans,proportions,andvariances. Linearregressionandcorrelationwillbestudied,andestimation/testsofhypothesesconcerningregressionparameterswillbecovered. Hypothesesdealingwithseveralpopulationmeanswillbeconsidered,andsingle-factoranalysisofvariance(ANOVA)willbecovered. Thelearningobjectiveistheacquisitionofproblem-solvingskillsratherthantheory.
Comprehension
Studentswillberequiredtounderstandbasicconceptsfromelementaryprobabilitytheoryandinferentialstatisticsonlytotheextentthatisrequiredtosolvepracticalproblemsinbiostatistics.
Application
Students will demonstrate understanding of the basic theory by testing hypotheses and calculating confidence intervals for a variety of population parameters. They will solve real-world problems both by hand and using statistical analysis software. They will learn the basic paradigm of scientific inquiry as it applies to biological and medical research by actually framing and solving real-world problems in these fields.
Analysis
Analyticalskillsinthiscoursefocusontheplanningforthecollectionofandanalyzingof biomedicaldata. Emphasisisplacedonidentifyingassumptionsthatvalidatetheanalyticaltools,andbeingawardofpossiblerisksassociatedwiththeseassumptions.
Synthesis
Studentstakingthiscoursewillhavehadatleastonepriorcourseincalculus. Methodsofcalculuswillbeusedinthestudyofdiscreteandcontinuousrandomvariablesandindeterminingleast-squaresestimatesofregressionparameters. Additionally,studentswillbeexposedtomethodsofscientificinquirythatintegratestatisticswithbiologyandmedicalscience.
Evaluation
Studentsareevaluatedbasedontheirperformanceon3or4in-classexaminationsandacomprehensivefinalexamination. Atthediscretionoftheinstructor,studentsmayalsobeevaluatedbasedonout-of-classprojectsinvolvingcomputeranalysisofdata.
ClassActivities
Duetolargeclasssizes,in-classworkwillbeprimarilylectureandquestion/answersessions.
OutofclassActivities
Outofclassactivitiesfocusonhomework(numericalproblem-solving)andcomputer-baseddataanalysisprojects. Theseactivitiesareaimedathelpingstudentstobecomefamiliarwithstatisticalanalysissoftwareaswellashelpingthemgainskillatsolvingroutineproblemsbyhand.
14001 Basic Mathematical Concepts I (4)
LearningOutcomesforBasicMathConceptsI(MATH14001)
Knowledge
Studentsshouldbeabletodefinethenumbersystemscontainedwithinthesetofrealnumbers.Theywillalsobeabletodefinethevarioussymbolsusedinlogicandwithdifferentnumberbases.
Comprehension
Studentsshouldbeabletounderstandtheconceptsnecessarytoadd,subtract,multiplyanddividewithinthesetsofnumbers. Theywillalsobeabletounderstandthepropertieswithinthesetsofnumberstoappreciatethesophisticationanddevelopmentoftherealnumbers.
Application
Studentswillapplytheirunderstandingofthefourbasicoperationstosolveproblems.Theywillalsousetruthtablestodeterminewhetherlogicalargumentsarevalidorinvalid.Theywillapplytheirunderstandingofthenumberpropertiestosolveproblemsefficiently.
Analysis
StudentswilluseVenndiagramstodeterminethevalidityofDeMorgan'slaws.Theywillappraisetheircurrentunderstandingofthesubsetsoftherealnumbersystemandidentifypriormisconceptions. Theywilllistentoeachother’sexplanationsandtrytomakesenseofthem.
Synthesis
StudentswillintegrateskillsthatweredevelopedinBasicAlgebracoursestosolvewordproblems.Theywillalsousetheseproblemsolvingskillstodevelopappropriatestrategiesforfindingsolutionstomoreinvolvedproblems.
Evaluation
Studentswillfindalgebraicsolutionstoproblemsandevaluatevarioussolutionmethodstofindanefficientapproach.Studentswillalsousetruthtablestodeterminewhenstatementsarelogicallyequivalent.
ClassActivities
Studentswillworkincooperativegroupstodiscussthevalidityofstatementsandothertopicssothataconcensusofclassunderstandingcanbedetermined.Theywilldiscusstopicsbeginningwithconcreteobjectsthenmovetoapictorialandthenanabstractdiscussionoftopics.Ateachleveltheywillendeavortomakesenseoftheconcept.
OutofClassActivities
Studentswillhavehomeworkassignmentsthatallowthemtoshowtheirunderstandingoftheconceptsdiscussedinclassandinthebook.Theseassignmentswillbecollectedperiodicallyandtheinstructorwillrandomlycheckproblems todetermineifsufficientunderstandingis demonstrated.
14002 Basic Mathematical Concepts II (4)
LearningOutcomesforBasicMathConceptsII(MATH14002)
Knowledge
Studentsshouldbeabletodefinegeometrictermssuchaspolygon,polyhedron,perimeter,area,surfacearea,andvolume.Studentswillalsodefinetermsusedinstatisticssuchasmean,median,mode,variance,andstandarddeviation.Theywilltabulateprobabilityofsimpleexperiments.
Comprehension
Studentsshouldbeabletounderstandtheconceptsnecessarytofindperimeterandareaofpolygons,aswellsassurfaceareaandvolumeforpolyhedral.Studentswillalsounderstandthethreetypesof “average” instatistics(mean,median,andmode).Theywillexplaincharacteristicsofquadrilateralsusingalgebraictermssuchasslopeanddistance.
Application
Studentswillapplytheirunderstandingofperimeterandareaofpolygonstofindappropriateperimetersandareasforpolygons.Theywillapplytheirunderstandingofsurfaceareaandvolumetofindappropriatesurfaceareasandvolumesforsolids.Theywillapplytheirunderstandingofformulastosolveproblemsefficiently.Givensetsofdata,studentswillfindthemean,median,mode,variance,andstandarddeviationforthedata.Studentswilldeterminetheprobabilityofsimpleandcomplexprobabilityexperiments.
Analysis
Studentswilluseintuitivemethodstodeterminethevalidityofformulasforperimeterandareaofpolygonsaswellassurfaceareaandvolumeofpolyhedral.Theywillappraisetheircurrentunderstandingofgeometryandidentifypriormisconceptions.Studentswilldiscusstheirmethodsforfindingmean,median,andmodeforasetofdata.Theywilllistentoeachother’sexplanationsandtrytomakesenseofthem.
Synthesis
StudentswillintegrateskillsthatweredevelopedinBasicAlgebracoursestosolvewordproblems.Theywillalsousetheseproblemsolvingskillstodevelopappropriatestrategiesforfindingsolutionstomoreinvolvedproblems. Students willuseconstructiontechniqueswithcompassandstraightedge,algebraicreasoningwithslopesanddistances,andgeometricreasoningtosynthesizecharacteristicsofgeometricshapes.
Evaluation
Studentswillfindalgebraicsolutionstogeometryproblemsandevaluatevarioussolutionmethodstofindanefficientapproach.Studentswillalsouseboxandwhiskerplotsandothergraphicaldisplaysofdatatodetermineefficientwaysofprojectingusefulinformationfromasetofdata.
ClassActivities
Studentswillworkincooperativegroupstodiscussthevalidityofstatementsandothertopicssothataconsensusofclassunderstandingcanbedetermined.Theywilldiscusstopicsbeginningwithconcreteobjectsthenmovetoapictorialandthenanabstractdiscussionoftopics.Ateachleveltheywillendeavortomakesenseoftheconcept.
OutofClassActivities
Studentswillhavehomeworkassignmentsthatallowthemtoshowtheirunderstandingoftheconceptsdiscussedinclassandinthebook.Theseassignmentswillbecollectedperiodicallyandtheinstructorwillrandomlycheckproblemstodetermineifsufficientunderstandingisdemonstrated.
LearningOutcomesforFieldexperienceinmathematicsInstruction,MATH-19099
Knowledge
Thedeeperunderstandingofthetopicsthatyoututor.
Comprehension
Shouldgetanexperienceinprovidingexplanationsofmathematicalconcepts.
Application
Themainandmostimportantapplicationisto helpsolvingandsolvingof manydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
N/A
Evaluation
Should(inadvance)complete homeworksthataregoingtobeusedinclass.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Toprepare homeworkassignments.
20095 Special Topics in Mathematics (1-5)
LearningOutcomesfor specialtopicsinmathematics,MATH-20095
Knowledge
Understandingofthetopicoftheclass.
Comprehension
Shouldunderstandthematerialofthespecialtopic.
Application
Themainandmostimportantapplicationisto helpsolvingandsolvingof manydifferentproblemsrelatedtothetopic.
Analysis
N/A
Synthesis
N/A
Evaluation
Shouldcomplete homeworks.
ClassActivities
Tosolveproblems anddiscusstheorems.
OutofclassActivities
Toprepare homeworkassignments.
21001 Linear Algebra with Applications (3)
LearningOutcomesforLinearAlgebrawithApplications,MATH-21001
Knowledge
Thestudentsshouldbeabletodefinecharacteristicpolynomialofasquarematrix,andanilpotentmatrix.
Comprehension
Shouldbeabletofindthecharacteristicpolynomialbycomputingadeterminant,andcomputethepowerofasquarematrix.
Application
Atypicalapplicationistodeterminewhetherasquarematrixofsmallsizeisnilpotent.
Analysis
Shouldbeabletodeterminewhethera2x2,3x3,4x4,anda5x5matrixisnilpotent. Shouldknowthat,basedonthecharacteristicpolynomialofthematrix,whatisthehighestpowerofthematrixtocomputertoconclude.
Synthesis
ShouldgetusetocombinetheirskillsfromLinearAlgebratosolveamoreadvancedproblem.
Evaluation
Shouldbeabletofindthecharacteristicpolynomialforanyspecificsquarematrixofsmallsize,andforsomemoregeneralmatricesofspecialtype.
ClassActivities
Tosolveproblemsinclass.
OutofclassActivities
Tosubmiteveryweekhomeassignments. Honorstudentsarealsorequiredtoreadmaterialonminimalpolynomialofmatricesaswell,andprovesomegeneralresults.
22005AnalyticGeometryandCalculusIII(3)
LearningOutcomesforAnalyticGeometryCalculusIII,MATH-22005
Knowledge
Thestudentsshouldbeabletounderstandtheconceptsof
vectors,geometryofspace,partialderivatives,multipleintegrals,and
vectorcalculus.
TheyshouldtoformulatetheFundamentalTheoremforlineintegrals,
theGreen'sTheorem,theStokes'TheoremandtheDivergenceTheorem.
Comprehension
Shouldbeabletocomputethearclengthandcurvature,findequationsof
tangentplanes
andlinearapproximation,multipleintegrals,curlanddivergenceofa
vectorfield.
Application
Themainandmostimportantapplicationis tosolvemanydifferent
problemsrelatedtothesubject.
Analysis
Shouldbeabletousepolar,cylindricalandsphericalcoordinates.
ShouldknowhowtousetheVectorCalculustomodelthemotioninspace.
Synthesis
Should getusetocombinetheirskillsfromCalculusIandCalculusIIto
solvetheproblemsinCalculusIII.
Evaluation
Shouldbeabletofindthe directionalderivativesandthegradientvector,
linearintegrals,doubleandtripleintegrals,areasofparametricsurfaces.
ClassActivities
TosolveproblemsandproveTheoremsinclass.
OutofclassActivities
Tosubmiteveryweekhomeassignments.
23022 Discrete Structures for Computer Science (3)
LearningOutcomesforDiscreteStructuresforComputerScience,MATH-23022
Knowledge
Thestudentsshouldlearndiscretestructuresforcomputerscientistswithafocuson:mathematicalreasoning,combinatorialanalysis,discretestructures,algorithmicthinking,applicationsandmodeling.
Comprehension
Shouldunderstandthe notionsoflogic,sets,functions,relations,algorithms,prooftechniques,counting,graphs,trees,Booleanalgebra,grammarsandlanguages.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Should combinethe“discreteandanalytic” thinking.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
LearningOutcomesforBasicProbabilityandStatistics,MATH-30011
Knowledge
ThestudentsshouldlearntheAnalysisandrepresentationofdata.Controlledexperimentsandobservations.Measurementerrors.
Comprehension
Shouldunderstandthenotionsofcorrelationandregression,sampling, theprobabilitymodelsandtestsofmodels,andnference.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Should combine “probabilisticandanalytic” thinking.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
30055 Mathematical Theory of Interest (3)
LearningOutcomesforMathematicaltheoryofInterest,MATH-30055
Knowledge
Thestudentsshouldlearnacalculus-basedintroductiontothemathematicsoffinance,limitedtodeterministicanalysisofinterestratesannuitiesbondsandimmunization.
Comprehension
Shouldemphasizethemathematicaltheoryofthesubjectmatter.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Should combine “probabilisticandanalytic” thinkingto mathematicsoffinance.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
31011 Discrete Mathematics (3)
Learning Outcomes for Discrete Mathematics, MATH 31011
Knowledge
Thestudentsshouldbeabletorecognizeseveralclassicalformsof
syllogisms,andapplytheseastheoremprovingtechniquesthroughout
thecourse. Theyshouldalsobeableidentifyusefularithmetic
identitiesthatmayariseindiversesituationssuchascounting
arguments,settheory,orproblemsinvolvingprobability.
Comprehension
The students should be able to comprehend valid arguments, recognize
invalid ones, and to provide counter-examples to the latter.
Application
The students should be able to formulate and apply their theorem
proving skills to such mathematical situations as those that arise
in number theory, counting, probability, set theory and other similar
situations.
Analysis
The students should be expected to handle simple arithmetic identities
and solve recurrence relations. They should also experiment with testing
different solutions, relying on mathematical induction as a tool to
identify correct answers.
Synthesis
Thestudentsshouldbeabletotranslaterealworldproblems
intoprecisemathematicalterms. Forexample,theyshould
beabletoformulateformalmathematicalpropositionsinvolving
quantifiersoutofproblemsstatedineverydayterms,andthey
shouldbeabletoisolatehypothesesfromtheconclusion.
Evaluation
The students should be tested regularly by quizzes and in-class
tests, in order to assess their progress throughout the course.
Class Activities
The students are expected to participate in class by actively
constructing examples and engaging with the instructor during
any process of inquiry.
Out of class Activities
The students should be challenged with homework assignments,
at least two per week, to test their problem solving skills.
31045 Formal Logic (3)
LearningOutcomesforformallogic,MATH-31045
Knowledge
ToUnderstand thefirstorderpredicatecalculuswithidentityandfunctionsymbols.
Comprehension
Shouldunderstandthe languageofthefunctionsymbols.
Application
Themainandmostimportantapplicationisto helpsolvingandsolvingof manydifferentproblemsrelatedtothetopic.
Analysis
N/A
Synthesis
N/A
Evaluation
Shouldcomplete homeworks.
ClassActivities
Tosolveproblems anddiscusstheorems.
OutofclassActivities
Toprepare homeworkassignments.
32044IntroductiontoOrdinaryDifferentialEquations(3)
LearningOutcomes
MATH32044IntroductiontoOrdinaryDifferentialEquations
preparedbyChuckGartland
March31,2012
KNOWLEDGE
Classificationofordinarydifferentialequations(ODEs):order,linearvsnonlinear,homogeneousvsnon-homogeneous.
WronskiantestforlinearindependenceofsolutionsoflinearODEs.
COMPREHENSION
Abilitytoclassify1st-orderODEsbytype:exact,separable,linear.
UnderstandthestructureofthegeneralsolutionofalinearODE:integrationconstants,particularintegrals/solutions.
Understandthevariousdynamicalbehaviorsofaforcedspring-mass-dampersystem:simpleharmonicmotion,dampedoscillations,beating,resonance.
APPLICATION
Solve1st-orderODEsbyseveralmethods:directintegration,exact,integratingfactors,separable,linear.
Solve2nd-order,linear,constant-coefficient,homogenousODEsusingcharacteristicpolynomialsandroots,reductionoforder.
Findparticularintegralsof2nd-orderlinearconstant-coefficientnon-homogeneousODEsbytwomethods:undeterminedcoefficients,variationofparameters.
Solve2-by-2linear,constant-coeffiecent,homogeneousODEcoupledsystemsusingmatrixeigenvaluesandeigenvectors.
ANALYSIS
Analyzethequalitativebehaviorofsolutionsof1st-orderODEsusingdirectionfieldsandisoclines.
AnalyzethenatureofsingularpointsusingthemethodofFrobeniusexpansions.
SYNTHESIS
Develop/formulatemathematicalmodelsofsimpleevolutionprocessesintermsof1st-orderODEs:populationgrowth,radioactivedecay,mixing,Newton’sLawofCooling.
Develop/formulateamathematicalmodelofaforcedspring-mass-dampersystemasa2nd-orderlinearconstant-coefficientnon-homogeneousODE.
EVALUATION
Interpretthesolutionsofthespring-mass-dampersystemmodelindifferentparameterregimes(e.g.,over-dampedvsunder-damped).
CLASSACTIVITIES
Lectures:development,exposition,examples,andillustrations.
Hourlyexams.
OUTOFCLASSACTIVITIES
Writtenhomework.
32051 Mathematical Methods in the Physical Sciences I (4)
LearningOutcomes
MATH32051MathematicalMethodsforthePhysicalSciencesI
KNOWLEDGE
ComplexexponentialfunctionandEuler’sformula.
Hyperbolictrigonometricfunctions.
Lineardependenceandindependenceofvectors.
Orthogonalmatrices.
Partialderivatives,totaldifferentials,andmultivariableTaylorexpansions.
Definitionofdoubleandtripleintegrals.
Jacobianmatricesanddeterminants.
COMPREHENSION
Connectionbetweenlineartransformationsandmatrices.
Stuctureofsolutionsetsoflinearalgebraicsystemsofequations.
Understandingtheconnectionbetweenmultipleintegralsandphysicalproperties,suchascenterofmassandmomentofinertia.
APPLICATION
Performbasicalgebraandmanipulationswithcomplexnumbersandfunctions.
Basicmanipulationswithmatrices,vectors,anddeterminants.
Solvelinearsystemsbyeliminationwithaugmentedmatrices.
EvaluateiteratedintegralsinCartesian,polar,cylindrical,andsphericalcoordinates.
ANALYSIS
ManipulationswithEuler’sformula,suchasderivingformulasforcomplextrigonometricfunctions.
Performchangeoforderofintegrationinmultipleintegrals.
Performgeneralchangeofvariablesinmultipleintegrals.
SYNTHESIS
Formulateappropriatechainrulesforvariouscompositefunctions.
EVALUATION
Beabletoidentifymatricesassociatedwithrotations,reflections,orbothcombined.
Beabletojudgewhentousecomplex-variabletechniquestosimplifycalculations(e.g.,trigonometricseries).
CLASSACTIVITIES
Lectures:development,exposition,examples,andillustrations.
HourlyexamsoneachChapter.
OUTOFCLASSACTIVITIES
Weeklywrittenhomeworkcollection.
.
32052 Mathematical Methods in the Physical Sciences II (4)
LearningOutcomesforMathematicalMethodsinthePhysicalSciencesII,MATH-32052
Knowledge
Thestudentsshoulddeveloptheadditionalmathematicsbackgroundforupper-divisioncoursesinthephysicalsciences.
Comprehension
Shouldunderstandthenotionsofvectoranalysis,Fourierseriesandtransformsordinarydifferentialequationsandpartialdifferentialequations.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeableto applyFourieranalysistosolveordinaryandpartialdifferentialequations.
Synthesis
N/A
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
34001 Fundamental Concepts of Algebra (3)
LearningOutcomesforFUNDCONCEPTSOFALGEBRAMATH-34001
Knowledge
Thestudentsshouldbeabletosolvealgebraproblemsrelatedtodivisibility,
equations,polynomials,complexnumbers.
Comprehension
Shouldbeabletosolvequadraticequationsandpolynomialequationsoflargerdegrees,applyinduction,findgreatestcommondivisorsofpolynomials, usecongruencesfordivisibilitycriteria.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletosolvealgebraproblemsonnumbersandpolynomials.
Synthesis
Shoulddevelopabstractthinkingnecessaryforunderstandingalgebraicconcepts.
Evaluation
Shouldcomplete10homework,pass2midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit10homeworkassignments.
34002 Fundamental Concepts of Geometry (3)
LearningOutcomesforFUNDCONCEPTSOFGEOMETRYMATH-34002
Knowledge
TounderstandtheoriginanddevelopmentofthegeometryofEuclidwithmodernrefinements,topics,approaches.Togetacquaintedwithothergeometries.
Comprehension
Shouldbeabletosolvequadraticequationsandpolynomialequationsoflargerdegrees,applyinduction,findgreatestcommondivisorsofpolynomials, usecongruencesfordivisibilitycriteria.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Shoulddevelop geometryskills to givesimpleandmoreconceptual solutionstotheproblemsfromschoolgeometry.
Evaluation
Shouldcomplete homeworks,passmidtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
40011 Introduction to Probability Theory and Applications (3)
LearningOutcomesfor Introductiontoprobabilitytheoryandapplications,MATH-40011
Knowledge
Permutationsandcombinations,discreteandcontinuousdistributions,andrandomvariables.
Comprehension
Conditionalprobabilities,Baye'sformula,mathematicalexpectation,lawoflargenumbers,normalapproximations,basiclimittheorems.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Shoulddevelop combinatorial andanalyticskills to solveproblemsinprobability.
Evaluation
Shouldcomplete homeworks,passmidtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
40012 Introduction to Statistical Concepts (3)
LearningOutcomesfor Introductiontostatisticalconcepts,MATH-40012
Knowledge
Shouldlearnthesamplespaces,continuousdistributions,samplingdistributions,pointandintervalestimation.
Comprehension
Tounderstandthehypothesistesting,typesoferror,levelandpoweroftests,sequentialandnonparametricmethods.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Shoulddevelop combinatorial andanalyticskills to solveproblemsinstatistics.
Evaluation
Shouldcomplete homeworks,passmidtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
40022 Linear Models and Statistical Analysis (3)
LearningOutcomesforLinearModelsandStatisticalAnalysis,MATH-40022
Knowledge
ShouldlearntheRegressionmodel,multivariatenormaldistribution,pointandintervalestimates.
Comprehension
To learnGauss-MarkovTheorem,correlationandregression,testsofhypotheses,applications.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Shoulddevelop combinatorial andanalyticskills to solveproblemsinstatisticalanalysisandprobability.
Evaluation
Shouldcomplete homeworks,passmidtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
40031 Basic Nonparametric Statistics (3)
LearningOutcomesforBasicNonparametricStatistics,MATH-40031
Knowledge
ShouldlearnRanktestsfordifferentkindsofhypothesis,largesampletheory.
Comprehension
To learntestsofKolmogorov-Smirnovtype.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Shoulddevelop combinatorial andanalyticskills to solveproblemsinstatistics.
Evaluation
Shouldcomplete homeworks,passmidtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
40041 Statistical Methods for Experiments (3)
LearningOutcomesforStatisticalMethodsforExperiments,MATH-40041
Knowledge
ShouldlearnComparisonoftwogroups,t-andF-statistics;ANOVA,one-wayandmultiwaylayouts,randomizationblocking.
Comprehension
To learnLinearregression,correlationandanalysisofcovariance(ANCOVA).Repeatedmeasuresanalysisofvariance
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Todevelop numerical andanalyticskills to solveproblemsinstatistics.
Evaluation
Shouldcomplete homeworks,passmidtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
40042 Sampling Theory (3)
LearningOutcomesforSamplingTheory,MATH-40042
Knowledge
Shouldlearnthemethodologyforthedesignandanalysisofsamplingandsurveyingstudies.
Comprehension
Tolearnsimplerandom,stratified,cluster,PPSandtwo-stagesamplingtechniques.Linear,ratioandregressionestimators.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Todevelop numerical andanalyticskills to solveproblemsinsamplingtheory.
Evaluation
Shouldcomplete homeworks,passmidtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
40051 Topics in Probability Theory and Stochastic Processes (3)
LearningOutcomesforTopicsinprobabilityandstochasticprocesses,MATH-40051
Knowledge
Shouldlearnaboutconditionalexpectations,Markovchains,Markovprocesses.
Comprehension
TolearnBrownianmotionandMartingalesandtheirapplicationstostochasticcalculus.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
Todevelopanalyticskills to solveproblemsinprobability.
Evaluation
Shouldcomplete homeworks,passmidtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
40055 Actuarial Mathematics I (4)
LearningOutcomesforActuarialMathematics,MATH-40055
Knowledge
Shouldlearntopicsfromsurvivalmodels,stochasticanalysisofannuitiesandlifeinsuranceandcasualtymodels.
Application
Students will solve the problems from the subject.
Analysis
Studentswillapplymethodsofprobabilitytheoryanddifferentialequationstostochasticanalysisofannuitiesandlifeinsuranceandcasualtymodels.
Synthesis
Theheavydependenceoftheoflifecontingencytheoryonprobabilitytheoryandordinarydifferentialequationsprovidesthestudentswithopportunitiestointegratethesetoolsintotheformulationofpracticalmodelsthatarisenaturallyinthestudyofrisk. KeymethodsofODEandprobabilitywillbereviewedasnecessaryandappropriate.
Evaluation
Studentsareevaluatedbasedonhomeworkassignmentsandmidtermandfinalexaminations. Bothhomeworkandexaminationswillincludethenumericsolutionofappliedproblemsaswellasthederivationoftheoreticalresults.
ClassActivities
Studentsarerequiredtopresentboththeoreticalderivationsofimportanttheoremsandnumericalsolutionsofpracticalproblemsinclass. Theirpresentationsarecritiquedbothformathematicalcorrectnessandforclarityofpresentation.
OutofclassActivities
Outofclassactivitiesincludethesolutionofnumericalappliedproblemsandproofoftheoreticalresults.
40056 Actuarial Mathematics II (4)
LearningOutcomesforActuarialMathII,MATH40056
Knowledge
Studentswilldevelopbackgroundinbenefitpremiums,andbenefitreservesforavarietyoflifeinsuranceproducts. Theywillalsolearnthebasicconceptsofmultipledecrementtheoryandmultiplelifefunctions,andwillbeintroducedtocertainnon-homogeneousMarkovprocessesthatariseintheinsurancecontext.
Comprehension
Studentswillbeabletocalculatepremiumsandreservesforavarietyofinsuranceproducts,andwillbeabletoderivestandardformulasforthesequantities. Studentswillacquirealevelofknowledgethatenablesthemtoprovebasictheoremsregardingreservesandpremiumsforindividualsandfortypicalentitiesassociatedwithjointlifeandlastsurvivorstatuses.
Application
Students will demonstrate knowledge of the underlying theory by calculating reserves and premiums for both continuous-time and curtate future life models.
Analysis
Studentswillapplymethodsofprobabilitytheoryanddifferentialequationstomodelpremiumsandreservesforindividuallivesandmorecomplexentities. Theywillalsolearnconventionalmethodsofincorporatingcostsandprofitintopremiumcalculations.
Synthesis
Theheavydependenceoftheoflifecontingencytheoryonprobabilitytheoryandordinarydifferentialequationsprovidesthestudentswithopportunitiestointegratethesetoolsintotheformulationofpracticalmodelsthatarisenaturallyinthestudyofrisk. KeymethodsofODEandprobabilitywillbereviewedasnecessaryandappropriate.
Evaluation
Studentsareevaluatedbasedonhomeworkassignmentsandmidtermandfinalexaminations. Bothhomeworkandexaminationswillincludethenumericsolutionofappliedproblemsaswellasthederivationoftheoreticalresults.
ClassActivities
Studentsarerequiredtopresentboththeoreticalderivationsofimportanttheoremsandnumericalsolutionsofpracticalproblemsinclass. Theirpresentationsarecritiquedbothformathematicalcorrectnessandforclarityofpresentation.
OutofclassActivities
Outofclassactivitiesincludethesolutionofnumericalappliedproblemsandproofoftheoreticalresults.
40091 Seminar in Actuarial Mathematics (2)
LearningOutcomesforActuarialMathSeminar,MATH40091
Knowledge
Theactuarialmathseminarcentersonthedevelopmentandapplicationofbasicprinciplesoffinancialengineering. Studentswilllearntheprinciplesofvariousoptionpricingmethods,includingthebinomialandBlack-Scholesmodels. Theywilllearntheunderlyingmathematicsthatsupportsthesemodels. ThisincludesanelementarycomprehensionofBrownianmotion,Itoprocesses(semimartingales)andstochasticcalculus.
Comprehension
ThestudentswilllearnboththeunderlyingtheoryofBlack-Scholesoptionpricingandbeabletoapplystochasticmodelstoactuallycalculatearbitrage-freepricesofavarietyofcallandputoptions.
Application
Students will demonstrate understanding of the basic theory by calculating prices of options based on stocks, currency exchange rates, futures, and interest rates. They will study sensitivity of option prices to the various parameters involved in such calculations, including dividend rate, interest rate, underlying asset price, and volatility.
Analysis
Studentswillgainanalyticalskillsbyderivingbasicmodelsforoptionprices. Theseincludebothdiscrete-time(binomial)andcontinuous-time(semi-martingale)models.
Synthesis
Studentswilllearnhowpuremathematics(discreteandcontinuous-timestochasticprocesses,stochasticdifferentialequations,deterministicpartialdifferentialequations,etc.)arisenaturallyinthestudyofoptionpricing. ThroughthestudyofItocalculusandtheFeinman-KacTheorem,theywillgainanappreciationofthepowerofabstractmathematicstomodelreal-worldphenomena.
Evaluation
Studentsareevaluatedbasedonhomeworkassignmentsandmidtermandfinalexaminations. Bothhomeworkandexaminationswillincludethenumericsolutionofappliedproblemsaswellasthederivationoftheoreticalresults.
ClassActivities
Studentsarerequiredtopresentboththeoreticalderivationsofimportanttheoremsandnumericalsolutionsofpracticalproblemsinclass. Theirpresentationsarecritiquedbothformathematicalcorrectnessandforclarityofpresentation.
OutofclassActivities
Outofclassactivitiesincludethesolutionofnumericalappliedproblemsandproofoftheoreticalresults.
40093 Variable Title Workshop in Mathematics (1-6)
LearningOutcomesforVariableTitleWorkshopinMathematics,MATH-40093
Knowledge
Thestudentsshould learnthematerialoftheworkshop.
Comprehension
To understandthematerialdeeperthroughthestudentspresentationprojects.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
N/A
Evaluation
Shouldmakeapresentationonacertainsubject.
ClassActivities
Tosolveproblems anddiscusstheorems.
OutofclassActivities
Topreparethepresentation.
41001 Introduction to Modern Algebra I (3)
LearningOutcomesforModernAlgebraI,MATH-41001
Knowledge
Thestudentsshould learntheBasicpropertiesofgroups,subgroups,factorgroups.
Comprehension
ShouldunderstandtheBasicpropertiesofrings,integraldomains,andhomomorphisms.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletounderstandthematerialona higherlevelofmathematical educationtoprepare
Themselves(ifnecessary)tothegraduateschool.
Synthesis
Should extensivelyexercisetheabstractthinking.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
41002 Introduction to Modern Algebra II (3)
LearningOutcomesforModernAlgebraII,MATH-41002
Knowledge
Thestudentsshould continuelearningthematerialofMATH41001throughemphasizingpropertiesofrings,theirideals,polynomialringextensions,fields.
Comprehension
Shouldunderstandthefinitedegreeextensions,rootsofpolynomials,constructability.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletounderstandthematerialona higherlevelofmathematical educationtoprepare
themselves(ifnecessary)tothegraduateschool.
Synthesis
Should extensivelyexercisetheabstractthinking.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
41012 Finite Mathematics (3)
LearningOutcomesforFiniteMathematics,MATH-41012
Knowledge
Thestudentsshould continuelearningthematerialofDiscreteMathematics throughemphasizingof
Combinatorialtechniques.
Comprehension
Shouldunderstandgraphapplicationsinalgorithms,finitealgebra,numbertheoryandprobability.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
Shouldbeabletounderstandthematerialona higherlevelofmathematical education.
Synthesis
Should extensivelyexercisethecombinatorialandabstractthinking.
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
41021TheoryofMatrices(3)
LearningOutcomesforTheoryofMatrices,MATH-41021
Knowledge
Thestudentsshouldbeabletoknowthesimilaritytransformationtheoriesonthematrices,andinparticulartheJordancanonicalforms.
Comprehension
Shouldbeabletounderstandthesimplestformthatamatrixcanbesimilarto,andbeabletodeterminetheJordancanonicalformofagivenmatrix.
Application
Someapplicationsonsolvinglinearfirstorderordinarydifferentialequations.
Analysis
Beabletoproveorunderstandtheproofsofsomeclassicaltheoriesofmatrices.
Synthesis
ShouldhaveabetterandmorecomprehensiveunderstandingofwhatstudiedinLinearAlgebra.
Evaluation
Shouldbeabletousetheoriestofindimportantinformationofagivenmatrix.
ClassActivities
TosolveproblemsandproveTheoremsinclass.
OutofclassActivities
Todohomework.
LearningOutcomesforMetalogic,MATH-41045
Knowledge
Thestudentsshouldconsidervariousmetatheorems,includingsoundnessandcompletenessofpropositionalandpredicatecalculus.
Comprehension
Shouldbeabletounderstandtheundecidabilityofpredicatecalculusandincompletenessofthetheoryofarithmetic
Application
N/A.
Analysis
N/A
Synthesis
N/A
Evaluation
N/A
ClassActivities
TosolveproblemsandproveTheoremsinclass.
OutofclassActivities
Todohomework.
42001IntroductiontoAnalysisI(3)
LearningOutcomesforINTRODUCTIONTOANALYSISI,MATH42001
Knowledge
Studentshouldunderstandtheconceptofrealnumbers,limit,convergence,andcompletenessoftherealnumbers,Cauchysequences,continuity,differentiationandRiemannintegrationoffunctionsontherealline.
Comprehension
Studentsshouldunderstandthedefinitions,statementsandproofsofmainfactsaboutsequencesandtheirlimitsaswellasrealvaluedfunctionstheircontinuity,differentiationandintegration.
Application
ThegeneraltheorycoveredinthiscourseisusefulandprovidethebaseforstudyofallfurtheradvancedMATHclasses.Itisalsorequiredineconomics,engineering,finance,naturalandsocialsciences.
Analysis
Studentsshouldunderstandtheconnectionsbetweensequencesofrealnumbers,limits,derivatives,andintegrals.Shouldbeablesolvetheoreticalproblemsrelatedtotheabovenotions.
Synthesis
Studentsshouldbeabletousetheirknowledgeoftheabovetopicstoprovideprovesofbasicclassicalfactsinanalysisbeabletoconstructexampleorcounterexamplestoquestionsaboutsequencesorrealnumbersaswellascontinuity/differentiability/integrabilityofrealvaluedfunctions
Evaluation
Studentsshouldbeabletodetermineappropriatetechniquesandknowledgenecessarytosolvemathematicalorappliedproblemsinvolvingbasicknowledgeofsequencesandfunctionsofrealvariables.
ClassActivities
Lecture/discussionofappropriatetopicsinAnalysis;weeklyhomeworks,includingtheoreticalproblemswhichcanbeworkedoutindividuallyoringroups;andexams.
OutofclassActivities
Readingandstudyingthetext;dailyhomeworkproblemsfromthetext/lecturenotes;writingassignmentsonconceptscoveredinclass.
42002IntroductiontoAnalysisII(3)
LearningOutcomesforINTRODUCTIONTOANALYSISII,MATH42002
Knowledge
StudentsmustknowtopicsstudiedinIntroductiontoAnalysisI,MATH42001. Inadditionstudentshouldunderstandtheconceptsinfiniteseries,convergenceanduniformconvergenceorrealvaluedfunctionsandseriesoffunctions,furtherstudyofIntegrationandDifferentiationtheoryaswellaslearnbasicconceptsofmetricspaces.
Comprehension
Studentsshouldunderstandthedefinitions,statementsandproofsofmainfactsaboutinfiniteseries,convergenceanuniformconvergenceofsequencesofrealvaluedfunctions;GeneralizedRiemanIntegration.
Application
ThegeneraltheorycoveredinthiscourseisusefulandprovidethebaseforstudyofallfurtheradvancedMATHclasses.Itisalsorequiredineconomics,engineering,finance,naturalandsocialsciences.
Analysis
Studentsshouldunderstandtheconnectionsbetweensequencesofrealvaluedfunctions,convergence,derivatives,andintegrals.Shouldbeablesolvetheoreticalproblemsrelatedtotheabovenotions.
Synthesis
Studentsshouldbeabletousetheirknowledgeoftheabovetopicstoprovideprovesofbasicclassicalfactsinanalysisbeabletoconstructexampleorcounterexamplestoquestionsaboutinfiniteseriesandsequencesofrealvaluedfunctions.
Evaluation
Studentsshouldbeabletodetermineappropriatetechniquesandknowledgenecessarytosolvemathematicalorappliedproblemsinvolvingbasicknowledgeofinfiniteseries,sequencesofrealvaluedfunctions,generalizedRiemannintegration.
ClassActivities
Lecture/discussionofappropriatetopicsinAnalysis;weeklyhomeworks,includingtheoreticalproblemswhichcanbeworkedoutindividuallyoringroups;andexams.
OutofclassActivities
Readingandstudyingthetext;dailyhomeworkproblemsfromthetext/lecturenotes;writingassignmentsonconceptscoveredinclass.
42011 Mathematical Optimization (3)
LearningOutcomesforMathematicalOptimization,MATH-42011
Knowledge
Thestudentsshould learn bothanalyticandnumericaltechniquesforlocationofextremepointsoffunctionsandcalculusofvariations.
Comprehension
Shouldunderstand andsolvebothconstrainedandunconstrainedproblems
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
N/A
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.
ClassActivities
Tosolveproblemsinclassanddiscusstheorems.
OutofclassActivities
Tosubmit homeworkassignments.
42021 Graph Theory and Combinatorics (3)
LearningOutcomesforGraphTheoryandCombinatorics,MATH-42021
Knowledge
Thestudentsshould learnfundamentalsandapplicationsofcombinatorialmathematics.
Comprehension
Shouldunderstand thetopicsincludetraversability,colorability,networks,inclusionandexclusion,matchinganddesigns.
Application
Themainandmostimportantapplicationistosolvemanydifferentproblemsrelatedtothesubject.
Analysis
N/A
Synthesis
N/A
Evaluation
Shouldcomplete homeworks,pass midtermtestsandafinalexam.