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.