Tuesday, August 24, 2021

MA6351- TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATION-PDF DOWNLOADED

DINESH KUMAR M August 24, 2021 0 Comments

ANNA UNIVERSITY 2013 REGULATION

II st YEAR III rd SEMESTER

MA6351

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATION

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Friday, August 20, 2021

BE-CSE AND BE-IT ALGEBRA AND NUMBER THEORY SYLLABUS

DINESH KUMAR M August 20, 2021 0 Comments

ANNA UNIVERSITY, CHENNAI
AFFILIATED INSTITUTIONS

MA8551

ALGEBRA AND NUMBER THEORY

B.E-CSE AND B.E -IT

REGULATION-2017

III-YEAR ,V-SEMESTER

COURSE OBJECTIVE:

   * To introduce the basic notions of groups, rings, fields which will then be used to solve
   * 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 an related problems.

COURSE OUTCOME
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.

UNIT-I GROUPS AND RINGS (12)

Groups : Definition - Properties - Homomorphism - Isomorphism - Cyclic groups - Co sets - 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 DECOMPOSITION(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 CONGRUENCE'S (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.

TEXTBOOKS:

* Grimaldi, R.P and Ramana, B.V., "Discrete and Combinatorial Mathematics", Pearson Education, $5^th$ Edition, New Delhi, 2007
* Koshy, T., ―Elementary Number Theory with Applications‖, Elsevier Publications, New Delhi, 2002.

REFERENCES :

* Lidl, R. and Pitz, G, "Applied Abstract Algebra", Springer Verlag, New Delhi, $2^nd$ Edition, 2006.
* Niven, I., Zuckerman.H.S., and Montgomery, H.L., ―An Introduction to Theory of Numbers‖, John Wiley and Sons , Singapore, 2004.
* San Ling and Chaoping Xing, ―Coding Theory – A first Course‖, Cambridge Publications, Cambridge, 2004.