Discrete Mathematical Structures, Sem-III (MGU), Kerala CS & IT By Jayasree T. G.

Discrete Mathematical Structures, Sem-III (MGU), Kerala CS & IT By Jayasree T. G.
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Discrete Mathematical Structures, Sem-III (MGU), Kerala CS & IT By Jayasree T. G.

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Publisher: Laxmi Publications
ISBN: 9789381159569
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PREFACE
Continuous Mathematics and Discrete Mathematics are the two main branches of the subject Mathematical Science. Discrete Mathematics is an essential tool in the study of Computer Science. The objective of this book is to introduce some discrete structures to undergraduate courses of Computer Science in an easy and simple way. The topics which are very relevant with respect to university syllabus are fully covered by this book and will support in self study. Each chapter of this book covers a module as per the latest syllabus prescribed by Mahatma Gandhi University for the third semester of B.Tech. Courses in Computer Science. Almost all problems are worked out and additional problems are incorporated from latest Mahatma Gandhi University Question papers to increase the flavor of the book. All efforts have been made to keep the book free from errors. Although suggestions for improvement will be highly appreciated and gratefully acknowledged. The author wishes you all, for good luck and brilliant success in life.
AUTHOR
vii
SYLLABUS M.G.U., KERALA EN010301 B ENGINEERING MATHEMATICS II
Credits 4
B. Tech. Semester III, CS IT TEACHING SCHEME 2 hours lecture and 2 hours tutorial per week OBJECTIVES To know the importance of learning theories and strategies in Mathematics and graphs. MODULE 1 Mathematical Logic 12 hours Basic concept of statement, logical connectives, Tautology and logical equivalence Laws of algebra of propositions equivalence formulas Tautological implications proof not expected for the above laws, formulas and implications . Theory of inference for statements Predicate calculus quantifiers valid formulas and equivalences free and bound variables inference theory of predicate calculus. MODULE 2 Number Theory and Functions 12 hours Fundamental concepts Divisibility Prime numbers relatively prime numbers fundamental theorem of arithmetic g.c.d. Euclidean algorithm properties of g.c.d. no proof l.c.m. Modular Arithmetic congruence properties congruence class modulo n Fermat s theorem Euler s Totient functions Euler s theorem Discrete logarithm. Function types of functions composite functions inverse of a function pigeon hole principles. MODULE 3 Relations 10 hours Relations binary relation types of relations equivalence relation partition equivalence classes partial ordering relation Hasse diagram poset. MODULE 4 Lattice 14 hours Lattice as a poset some properties of lattice no proof Algebraic system general properties lattice as algebraic system sublattices complete lattice Bounded Lattice complemented