anna univ syllabus

MA8551 ALGEBRA AND NUMBER THEORY ANNA UNIVERSITY SYLLABUS REGULATION 2017

MA8551 ALGEBRA AND NUMBER THEORY L T P C 4 0 0 4

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
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
Rings – Polynomial rings – Irreducible polynomials over finite fields – Factorization of polynomials over finite fields.

UNIT III DIVISIBILITY THEORY AND CANONICAL DECOMPOSITIONS 12
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
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
Wilson’s theorem – Fermat’s little theorem – Euler’s theorem – Euler’s Phi functions – Tau and Sigma functions.
TOTAL: 60 PERIODS

OUTCOMES:
Upon successful completion of the course, students should be able to:
 Apply the basic notions of groups, rings, fields which will then be used to solve related problems.
 Explain the fundamental concepts of advanced algebra and their role in modern
mathematics and applied contexts.
 Demonstrate accurate and efficient use of advanced algebraic techniques.
 Demonstrate their mastery by solving non – trivial problems related to the concepts, and by proving simple theorems about the, statements proven by the text.
 Apply integrated approach to number theory and abstract algebra, and provide a firm basis for further reading and study in the subject.

TEXTBOOKS:
1. Grimaldi, R.P and Ramana, B.V., “Discrete and Combinatorial Mathematics”, Pearson Education, 5th Edition, New Delhi, 2007.
2. Koshy, T., “Elementary Number Theory with Applications”, Elsevier Publications, New Delhi, 2002.

REFERENCES:
1. Lidl, R. and Pitz, G, “Applied Abstract Algebra”, Springer Verlag, New Delhi, 2nd Edition, 2006.
2. Niven, I., Zuckerman.H.S., and Montgomery, H.L., “An Introduction to Theory of Numbers”, John Wiley and Sons , Singapore, 2004.
3. San Ling and Chaoping Xing, “Coding Theory – A first Course”, Cambridge Publications, Cambridge, 2004.

MA8551 ALGEBRA AND NUMBER THEORY R2017 ANNA UNIVERSITY QUESTION PAPER APRIL/MAY 2024 – CLICK HERE

MA8551 ALGEBRA AND NUMBER THEORY R2017 ANNA UNIVERSITY QUESTION PAPER NOVEMBER/DECEMBER 2024 – CLICK HERE