algebra

Courname:AdvancedAlgebra

CourNo.:SMG1151301Credits:5

CourDescription

A

itablefor

courwewillstudy

Determinant,Matrix,houtthecour,we

wilsthe

antecedentcourofothersubquentlectivecours.

CourLearningOutcomes

Thestudentlearningoutcomesarewhatstudentwouldbeabletoknowandtodo

ilsare:

nthepropertiesofdeterminantandmatrix,thestructureofsolution.

tandVectorspace,Euclideanspace.

eandmanipulatesimpleversionsoftheforms.

implemathematicalmodelstocalculatetheresultofchangesinthe

advancedalgebra.

standardmodelstointerpretandanalyrealproblemsinadvanced

algebra.

RelationshiptoOtherCours

Pre-requisites:Highschoolmath

TextbookandReadingLists

Thetextbookforthiscouris:

WangEfang,ShiShengming(2003),“AdvancedAlgebra”,

EducationPress.

Suggestedreadinglists:

LiuZhongkui(2010),“AdvancedAlgebra”,EducationPress.

QianJilin(2010),“Advancedalgebraantithesis”,lUniversity

forNationalitiesPress

CourAsssment

ItemTitleDueDateValue

1HomeworkEveryweek10%

2QuestionsinclassRandomlylectedweeks10%

3TestinclassWeek1010%

4FinalexamExamperiod70%

CourSchedule

Week

TopicText

Week4

Determinant:

Thedefinitionandpropertiesofdeterminant,

Norderdeterminant,Cramer’sRule

Chapter1

Week5NationalDay

Week6-7

MatrixⅠ:

Thedefinitionandpropertiesofmatrix

Matrixcalculations,Invermatrix

Chapter2

Week8-9

MatrixⅡ:

Rankofmatrix,Symmetricmatrix,Quadraticform,

Positivedefinitematrix

Chapter3

Week10-12

Vectorspace:

Linearcorrelation,Subspace,Spatialisomorphism

Basisanddimensionofvectorspace

Chapter5

Week13-14

Systemoflinearequations:

Elementarytransformation,Thestructureofsolution,

Eigenvaluesandeigenvector

Chapter6

Week15-16

Lineartransforms:

Thecalculationoflineartransform,Invariantsubspace,

Eigenvaluesandeigenvector

Chapter7

Week17

Euclideanspace:

Metricmatrix,Orthogonalbasis,Orthogonalmatrix,

Orthogonaltransformation

Chapter8

Week18Review

19Finalexam