Department of Mathematics 2016 - UTUutu.ac.in/DMathematics/download/Sem-1/TS/TS_060090106.pdf ·...
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Department of Mathematics Uka Tarsadia University 2016 Integrated M.Sc. (Mathematics)(Semester 1) Teaching Schedule Subject Code: 060090106 Subject Name: CC2 Elementary Algebra Course Objectives: To rephrase basic concept of complex numbers, functions, integers, matrix algebra and vector space for constructing base to illustrate complex analysis, linear algebra. Unit Sub Unit No. of Lectur e(s) Topics Reference Chapter/ Additional Reading Teaching Methodology to be used Unit 1: Complex Numbers 1 1.1 5 Polar representation of complex numbers Titu Andreescu and Dorin Andrica # 2 Chalk and Talk 1.2 3 nth roots of unity Titu Andreescu and Dorin Andrica # 2 Chalk and Talk 1.3 7 De moivre’s theorem for rational indinces and its application Titu Andreescu and Dorin Andrica # 2 Chalk and Talk Unit 2: Functions and Integers 2 2.1 2 Equivalence relations Goodaire # 2 Chalk and Talk 2.2 2 Functions Goodaire # 3 Chalk and Talk 2.3 1 Compositions of functions Goodaire # 3 Chalk and Talk 2.4 1 Invertible functions Goodaire # 3 Chalk and Talk 2.5 2 One to one correspondence and cardinality of a set Goodaire # 3 Chalk and Talk 2.6 2 Well-ordering property of positive integers Goodaire # 3 Chalk and Talk 2.7 1 Division Algorithm Goodaire # 4 Chalk and Talk 2.8 2 Divisiblity and Euclidean algorithm Goodaire # 4 Chalk and Talk 2.9 2 Congruence relation between integers Goodaire # 4 Chalk and Talk 2.10 3 Principles of mathematical indunction Goodaire # 5 Chalk and Talk 2.11 2 Statement of fundamental theorem of arithmetic Goodaire # 5 Chalk and Talk Unit 3: Matrix Algebra 3 3.1 2 Definitions and types of matrices Anton# 1, Lay#1 audio video tool 3.2 1 Operations on matrices Anton# 1, Lay#1 Chalk and Talk
Transcript of Department of Mathematics 2016 - UTUutu.ac.in/DMathematics/download/Sem-1/TS/TS_060090106.pdf ·...
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
