Book description
Discrete Mathematics will be of use to any undergraduate as well as post graduate courses in Computer Science and Mathematics. The syllabi of all these courses have been studied in depth and utmost care has been taken to ensure that all the essential topics in discrete structures are adequately emphasized. The book will enable the students to develop the requisite computational skills needed in software engineering.
Table of contents
 Cover
 Title page
 Contents
 About the Author
 Dedication
 List of Symbols
 Preface

Chapter 1 Sets, Relations and Functions
 1.1 Sets
 1.2 Algebra of Sets
 1.3 Representation of Relations on Finite Set
 1.4 Mappings (Functions)
 1.5 Composition of Mappings
 1.6 Countability of Sets
 1.7 Partially Ordered Sets
 1.8 Hasse Diagram
 1.9 Isomorphic (Similar) Ordered Sets
 1.10 Hashing Function
 1.11 Principle of Mathematical Induction
 Exercises
 Chapter 2 Counting

Chapter 3 Recurrence Relations
 3.1 Recurrence Relations
 3.2 Explicit Formula for a Sequence
 3.3 Solutions of Recurrence Relations
 3.4 Homogeneous Recurrence Relations with Constant Coefficients
 3.5 Particular Solution of a Difference Equation
 3.6 Recursive Functions
 3.7 Generating Functions
 3.8 Convolution of Numeric Functions
 3.9 Solution of Recurrence Relations by the Method of Generating Function
 Exercises
 Chapter 4 Logic

Chapter 5 Algebraic Structures
 5.1 Binary Operations
 5.2 Properties of Binary Operation
 5.3 Semigroups and Monoids
 5.4 Homomorphism of Semigroups
 5.5 Quotient Structures
 5.6 Equivalence Classes
 5.7 Direct Product of Semigroups
 5.8 Groups
 5.9 Subgroups
 5.10 Normal Subgroup
 5.11 Quotient Group (Factor Group)
 5.12 Homomorphism of Groups
 5.13 Cyclic Groups
 5.14 Permutation Groups
 5.15 Direct Product and Direct Sum of Groups
 5.16 Group as Direct Product of its Subgroups
 5.17 Rings
 5.18 Ring Homomorphism
 5.19 Ideals and Quotient Rings
 5.20 Polynomial Rings
 5.21 Division Algorithm for Polynomials Over a Field
 5.22 Algebraic Coding Theory
 Exercises
 Chapter 6 Lattices
 Chapter 7 Boolean Algebra

Chapter 8 Graphs
 8.1 Definitions and Basic Concepts
 8.2 Special Graphs
 8.3 Subgraphs
 8.4 Isomorphisms of Graphs
 8.5 Walks, Paths and Circuits
 8.6 Eulerian Paths and Circuits
 8.7 Hamiltonian Circuits
 8.8 Matrix Representation of Graphs
 8.9 Planar Graphs
 8.10 Colouring of Graph
 8.11 Directed Graphs
 8.12 Trees
 8.13 Isomorphism of Trees
 8.14 Representation of Algebraic Expressions by Binary Trees
 8.15 Spanning Tree of a Graph
 8.16 Shortest Path Problem
 8.17 Minimal Spanning Tree
 8.18 Cut Sets
 8.19 Tree Searching
 8.20 Transport Networks
 Exercises
 Chapter 9 Finite State Automata
 Chapter 10 Languages and Grammars
 Appendix
 Answers to Exercises
 Copyright
Product information
 Title: Discrete Mathematics
 Author(s):
 Release date: July 2010
 Publisher(s): Pearson India
 ISBN: 9788131733103
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