DepartmentofMathematicsUkaTarsadiaUniversity

2016

IntegratedM.Sc.(Mathematics)(Semester1)

TeachingScheduleSubjectCode:060090106

SubjectName:CC2ElementaryAlgebraCourseObjectives:

To rephrase basic concept of complex numbers, functions, integers, matrix algebra andvectorspaceforconstructingbasetoillustratecomplexanalysis,linearalgebra.

UnitSubUnit

No.ofLecture(s)

TopicsReferenceChapter/AdditionalReading

TeachingMethodologytobeused

Unit1:ComplexNumbers

1

1.1 5Polarrepresentationofcomplexnumbers

TituAndreescuandDorinAndrica#2

ChalkandTalk

1.2 3 nthrootsofunityTituAndreescuandDorinAndrica#2

ChalkandTalk

1.3 7Demoivre’stheoremforrationalindincesanditsapplication

TituAndreescuandDorinAndrica#2

ChalkandTalk

Unit2:FunctionsandIntegers

2

2.1 2 Equivalencerelations Goodaire#2 ChalkandTalk

2.2 2 Functions Goodaire#3 ChalkandTalk

2.3 1 Compositionsoffunctions Goodaire#3 ChalkandTalk

2.4 1 Invertiblefunctions Goodaire#3 ChalkandTalk

2.5 2Onetoonecorrespondenceandcardinalityofaset

Goodaire#3 ChalkandTalk

2.6 2Well-orderingpropertyofpositiveintegers

Goodaire#3 ChalkandTalk

2.7 1 DivisionAlgorithm Goodaire#4 ChalkandTalk

2.8 2DivisiblityandEuclideanalgorithm

Goodaire#4 ChalkandTalk

2.9 2Congruencerelationbetweenintegers

Goodaire#4 ChalkandTalk

2.10 3Principlesofmathematicalindunction

Goodaire#5 ChalkandTalk

2.11 2Statementoffundamentaltheoremofarithmetic

Goodaire#5 ChalkandTalk

Unit3:MatrixAlgebra

33.1 2

Definitionsandtypesofmatrices

Anton#1,Lay#1audiovideo

tool3.2 1 Operationsonmatrices Anton#1,Lay#1 ChalkandTalk

Textbook:1. HowardAntonandCharisRorres–“ElementaryLinearAlgebra-Applications

version”-9thEdition,WileyIndiaEdition.Referencebooks:

1. GilbertStrang–“LinearAlgebraanditsApplications”-4thEdition,CengageLearning2. DavidC.Lay-“LinearAlgebraanditsApplications”-3rdEdition,PearsonEducation-

Asia,IndianReprint,2007.3. JKSharma-“DiscreteMathematics”-3rdEdition,MacmillanIndiaLimited,2011.4. RosenK.H.–“DiscreteMathematicsanditsApplications”,6thEdition,TataMcGrawHill,2006.5.TituAndreescuandDorinAndrica–“ComplexNumbersfromAto...Z”,Birkhauser6. Edgar G. Goodaire andMicheal M. Parmenter- “ DiscreteMatheatics with Graph

theory”-2ndEdition,PearsonEducationLtd,2002.

3.3 2 Inverseofamatrix Anton#1,Lay#1 ChalkandTalk

3.4 3Rowreductionandechelonforms

Anton#1,Lay#1 ChalkandTalk

3.5 2 RankandNullityofMatrix Anton#1,Lay#1 ChalkandTalk

3.6 2Introductiontosystemoflinearequations

Anton#1,Lay#1 ChalkandTalk

3.7 3HomogenousandNon-Homogenoussystemoflinearequations

Anton#1,Lay#1 ChalkandTalk

3.8 3Methodstosolvesystemoflinearequations

Anton#1,Lay#1 ChalkandTalk

Unit4:BasicConceptsofVectorsandVectorSpace

4

4.1 1 Introductiontovectors Anton#3,Lay#3audiovideo

tool4.2 1 Normofavector Anton#3,Lay#3 ChalkandTalk4.3 2 Vectorarithmetic, Anton#3,Lay#3 ChalkandTalk4.4 2 Dotproduct Anton#3,Lay#3 ChalkandTalk4.5 2 Projection Anton#3,Lay#3 ChalkandTalk4.6 2 CrossProduct Anton#3,Lay#3 ChalkandTalk4.7 2 LinesandPlanesin3-Space Anton#3,Lay#3 ChalkandTalk