## MA8551 Algebra and Number Theory Syllabus Notes Question Paper Question Banks with answers Anna University

#### Anna University Algebra and Number Theory Syllabus Notes Question Bank Question Papers Regulation 2017

#### MA8551 Algebra and Number Theory Syllabus Regulation 2017

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 Algebra and Number Theory Regulation 2017 notes

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MA8551 Algebra and Number Theory Notes Syllabus

MA8551 Algebra and Number Theory Notes

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