MA8551 Syllabus ALGEBRA AND NUMBER THEORY
MA8551 Syllabus ALGEBRA AND NUMBER THEORY Regulation 2017 Anna University free download. ALGEBRA AND NUMBER THEORY Syllabus MA8551 pdf free download.
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 12 MA8551 Syllabus ALGEBRA AND NUMBER THEORY
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 12 MA8551 Syllabus ALGEBRA AND NUMBER THEORY
Rings – Polynomial rings – Irreducible polynomials over finite fields – Factorization of polynomials over finite fields.
UNIT III DIVISIBILITY THEORY AND CANONICAL DECOMPOSITIONS 12 MA8551 Syllabus ALGEBRA AND NUMBER THEORY
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 12 MA8551 Syllabus ALGEBRA AND NUMBER THEORY
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 12 MA8551 Syllabus ALGEBRA AND NUMBER THEORY
Wilson‘s theorem – Fermat‘s little theorem – Euler‘s theorem – Euler‘s Phi functions – Tau and Sigma functions.
| Subject name | ALGEBRA AND NUMBER THEORY |
| Short Name | ANT |
| Semester | 5 |
| Subject Code | MA8551 |
| Regulation | 2017 regulation |
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