## MA8551 ANT Syllabus

Anna University Regulation 2017 CSC MA8551 ANT Syllabus for all 5 units are provided below. Download link for CSC 5th Sem MA8551 ALGEBRA AND NUMBER THEORY Engineering Syllabus is listed down for students to make perfect utilization and score maximum marks with our study materials.

### Anna University Regulation 2017 CSC Engineering (CSC) 5th Sem MA8551 ALGEBRA AND NUMBER THEORY Engineering Syllabus

MA8551 ALGEBRA AND NUMBER THEORY
OBJECTIVES:
 To introduce the basic notions of groups, rings, fields which will then be used to solve related problems.
 To introduce and apply the concepts of rings, finite fields and polynomials.
 To understand the basic concepts in number theory
 To examine the key questions in the Theory of Numbers.
 To give an integrated approach to number theory and abstract algebra, and provide a firm basis for further reading and study in the subject.
UNIT I GROUPS AND RINGS
Groups : Definition – Properties – Homomorphism – Isomorphism – Cyclic groups – Cosets – Lagrange’s theorem. Rings: Definition – Sub rings – Integral domain – Field – Integer modulo n – Ring homomorphism.

UNIT II FINITE FIELDS AND POLYNOMIALS
Rings – Polynomial rings – Irreducible polynomials over finite fields – Factorization of polynomials over finite fields.

UNIT III DIVISIBILITY THEORY AND CANONICAL DECOMPOSITIONS
Division algorithm – Base – b representations – Number patterns – Prime and composite numbers – GCD – Euclidean algorithm – Fundamental theorem of arithmetic – LCM

UNIT IV DIOPHANTINE EQUATIONS AND CONGRUENCES
Linear Diophantine equations – Congruence‘s – Linear Congruence‘s – Applications: Divisibility tests – Modular exponentiation-Chinese remainder theorem – 2 x 2 linear systems.

UNIT V CLASSICAL THEOREMS AND MULTIPLICATIVE FUNCTIONS
Wilson‘s theorem – Fermat‘s little theorem – Euler‘s theorem – Euler‘s Phi functions – Tau and Sigma functions.

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MA8551 ANT Syllabus

Anna University 5th Sem CSC ANT Syllabus