MA8551 – Algebra and Number Theory – Regulation 2017 Syllabus

MA8551 – NOTES & QP

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SEMESTER QP CLICK HERE

MA8551 – SYLLABUS

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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