Mathematical Foundations Of Computer Science

Mathematical Foundations Of Computer Science
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Mathematical Foundations Of Computer Science

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Publisher: IK International
ISBN: 9788188237494
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Preface
This book explains some of the fundamental concepts in mathematics. It can be used by the students in computer science as an introduction to the fundamental ideas of mathematics for computer science. The topics mathematical logic, predicates, relations, functions, combinatorics, algebraic structures and graph theory have been discussed in this book. Throughout, I have made an extensive use of worked examples to develop the general ideas. Chapter 1 Deals with mathematical logic. Propositions, well formed formulas, logical equivalence, tautologies, fallacies, and duality principle were briefly discussed in this chapter. Chapter 2 This chapter provides an introduction to predicate logic. Rules of inference and different methods were briefly discussed in this chapter. Chapter 3 Deals with set theory. Properties of set containment, union of sets. Intersection of sets, complement of a set, difference of sets and their properties were discussed. This chapter presents the notions of relations and functions. It also deals with partially ordered sets, lattices and Hasse diagrams. Chapter 4 Deals with algebraic system. In this chapter we give the basic theory of graphs. Semigraphs, normal subgraphs, cosets. Permutations. Groups Homomorphism and Isomorphism were briefly discussed in this chapter. Chapter 5 Covers elementary combinatorics. Permutations, Combinations and Binomial theorem have been discussed in this chapter. Chapter 6 Deals with recurrence relations. Generating functions, and the methods of solving recurrence relations were discussed in this chapter. Chapter 7 It is devoted to graph theory. This chapter presents the terminology. Connected graphs, bipartite graphs, planarity, trees, spanning trees and binary trees were discussed. Chapter 8 Deals with applications of graph theory. Euler s, graphs and Hamiltonian graphs have been discussed. Coloring of graphs, and Chromatic polynomial have been explored in this chapter.
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Preface
The book has a wide variety of exercises at all levels and it can be used for either a one or two semester course. I am much indebted to Sri Shiv kumar Regional manager A.P., I.K. International Publishing house Pvt. Ltd. Whose suggestions helped me in writing the book. I am thankful to Sonia Mamgain. Sponsoring Editor, I.K. International publishing House Pvt. Ltd. for her encouragement, interest and cooperation during the production of the book. Finally, a sincere expression of thanks goes to Sri Krishan Makhijani, Managing Director, I.K. International Publishing house Pvt. Ltd. for his encouragement and support. Any suggestions for future improvements of this book will be gratefully accepted. G. Shanker Rao