Modulecode
SM-4328
ModuleTitle
IntroductiontoAlgebraandNumberTheory
Degree/Diploma
BachelorofScience(Mathematics)
TypeofModule
MajorOption
ModularCredits
4
TotalstudentWorkload
10
hours/week
Contacthours
4
hours/week
Prerequisite
SM-2203LinearAlgebraanditsApplications
Anti-requisite
None
Aims
Thismoduleaimstofamiliarisethestudentwithbasicpropertiesofnaturalnumbersandvarious
algebraicstructures.
LearningOutcomes
Onsuccessfulcompletionofthismodule,astudentwillbeexpectedtobeableto:
Lowerorder: 40% -usetheEuclidiananddivisionalgorithmsandsolvelinearcongruences
Middleorder:40% -applycertainresultsofnumbertheoryincryptography
Higherorder: 20% -understandmainalgebraicstructuresandusetheirproperties
ModuleContents
Methodofmathematicalinduction.DivisionandEuclidianalgorithm.
-Greatestcommondivisorandleastcommonmultiple.PrimesandFundamentalTheoremof
arithmetics.Congruencesandmodulararithmetics.StructureofZn.Solvinglinearcongruences.
ChineseRemainderTheorem.
-FermatLittleTheorem.Eulergeneralization.Publickeycryptography.
-Permutations.Orderandsign.Cycledecomposition.Definitionandexamplesofgroups.Semigroups.Ringsandfields.
-Basicpropertiesofgroups.Orderofanelement.Subgroups.Cyclicgroups.Generatingsets.
-Cosets.LagrangeTheorem.FermatandEulerTheorems.Homomorphisms.Normalsubgroups.
Assessment
Formative
assessment
Tutorialandfeedback.
Summative
assessment
Examination:60%
Coursework:40%
-1classtest(20%)
-1assignment(20%)