Fundamental approach to discrete mathematics

Cover
Preface to the Second Edition
Preface to the First Edition
Contents
List of Symbols
Chapter 1. Mathematical Logic
	1.0 Introduction
	1.1 Statement (Proposition)
	1.2 Logical Connectives
	1.3 Conditional
	1.4 Bi-Conditional
	1.5 Converse
	1.6 Inverse
	1.7 Contra Positive
	1.8 Exclusive OR
	1.9 NAND
	1.10 NOR
	1.11 Tautology
	1.12 Contradiction
	1.13 Satisfiable
	1.14 Duality Law
	1.15 Algebra of Propositions
	1.16 Mathematical Induction
	Solved Examples
	Exercises
Chapter 2. Set Theory
	2.0 Introduction
	2.1 Sets
	2.2 Types of Sets
	2.3 Cardinality of a Set
	2.4 Subset and Superset
	2.5 Comparability of Sets
	2.6 Power Set
	2.7 Operations on Sets
	2.8 Disjoint Sets
	2.9 Application of Set Theory
	2.10 Product of Sets
	2.11 Fundamental Products
	Solved Examples
	Exercises
Chapter 3. Binary Relation
	3.0 Introduction
	3.1 Binary Relation
	3.2 Inverse Relation
	3.3 Graph of Relation
	3.4 Kinds of Relation
	3.5 Arrow Diagram
	3.6 Void Relation
	3.7 Identity Relation
	3.8 Universal Relation
	3.9 Relation Matrix (Matrix of the Relation)
	3.10 Composition of Relations
	3.11 Types of Relations
	3.12 Types of Relations and Relation Matrix
	3.13 Equivalence Relation
	3.14 Partial Order Relation
	3.15 Total Order Relation
	3.16 Closures of Relations
	3.17 Equivalence Classes
	3.18 Partitions
	Solved Examples
	Exercises
Chapter 4. Function
	4.0 Introduction
	4.1 Function
	4.2 Equality of Functions
	4.3 Types of Function
	4.4 Graph of Function
	4.5 Composition of Functions
	4.6 Inverse Function
	4.7 Some Important Functions
	4.8 Hash Function
	Solved Examples
	Exercises
Chapter 5. Generating Function and Recurrence Relation
	5.0 Introduction
	5.1 Generating Functions
	5.2 Partitions of Integers
	5.3 Recurrence Relations
	5.4 Models of Recurrence Relation
	5.5 Linear Recurrence Relation With Constant Coefficients
	5.6 Different Methods of Solution
	5.7 Homogeneous Solutions
	5.8 Particular Solution
	5.9 Total Solution
	5.10 Solution by Generating Function
	5.11 Analysis of the Algorithms
	Solved Examples
	Exercises
Chapter 6. Combinatorics
	6.0 Introduction
	6.1 Fundamental Principle of Counting
	6.2 Factorial Notation
	6.3 Permutation
	6.4 Combination
	6.5 The Binomial Theorem
	6.6 Binomial Theorem for Rational Index
	6.7 The Catalan Numbers
	6.8 Ramsey Number
Chapter 7. Group Theory
	7.0 Introduction
	7.1 Binary Operation On a Set
	7.2 Algebraic Structure
	7.3 Group
	7.4 Subgroup
	7.5 Cyclic Group
	7.6 Cosets
	7.7 Homomorphism
	Solved Examples
	Exercises
Chapter 8. Codes and Group Codes
	8.0 Introduction
	8.1 Terminologies
	8.2 Error Correction
	8.3 Group Codes
	8.4 Weight of Code Word
	8.5 Distance Between the Code Words
	8.6 Error Correction for Block Code
	8.7 Cosets
	Solved Examples
	Exercises
Chapter 9. Ring Theory
	9.0 Introduction
	9.1 Ring
	9.2 Special Types of Ring
	9.3 Ring Without Zero Divisor
	9.4 Integral Domain
	9.5 Division Ring
	9.6 Field
	9.7 The Pigeonhole Principle
	9.8 Characteristics of a Ring
	9.9 Sub Ring
	9.10 Homomorphism
	9.11 Kernal of Homomorphism of Ring
	9.12 Isomorphism
	Solved Examples
	Exercises
Chapter 10 Boolean Algebra
	10.1 Introduction
	10.1 Gates
	10.2 More Logic Gates
	10.3 Combinatorial Circuit
	10.4 Boolean Expression
	10.5 Equivalent Combinatorial Cricuits
	10.6 Boolean Algebra
	10.7 Dual of a Statement
	10.8 Boolean Function
	10.9 Various Normal Forms
	Solved Examples
	Exercises
Chapter 11. Introduction of Lattices
	11.0 Introduction
	11.1 Lattices
	11.2 Hasse Diagram
	11.3 Principle of Duality
	11.4 Distributive Lattice
	11.5 Bounded Lattice
	11.6 Complemented Lattice
	11.7 Some Special Lattices
	Solved Examples
	Exercises
Chapter 12. Graph Theory
	21.0 Introduction
	12.1 Graph
	12.2 Kinds of Graph
	12.3 Digraph
	12.4 Weighted Graph
	12.5 Degree of a Vertex
	12.6 Path
	12.7 Complete Graph
	12.8 Regular Graph
	12.9 Cycle
	12.10 Pendant Vertex
	12.11 Acyclic Graph
	12.12 Matrix Representation of Graphs
	12.13 Connected Graph
	12.14 Graph Isomorphism
	12.15 Bipartite Graph
	12.16 Subgraph
	12.17 Walks
	12.18 Operations on Graphs
	12.19 Fusion of Graphs
	Solved Examples
	Exercises
Chapter 13. Tree
	13.0 Introduction
	13.1 Tree
	13.2 Fundamental Terminologies
	13.3 Binary Tree
	13.4 Bridge
	13.5 Distance and Eccentricity
	13.6 Central Point and Centre
	13.7 Spanning Tree
	13.8 Searching Algorithms
	13.9 Shortest Path Algorithms
	13.10 Cut Vertices
	13.11 Euler Graph
	13.12 Hamiltoniah Path
	13.13 Closure of a Graph
	13.14 Travelling Salesman Problem
	Solved Examples
	Exercises
Chapter 14 Fuzzy Set Theory
	14.0 Introduction
	14.1 Fuzzy Versus Crisp
	14.2 Fuzzy Sets
	14.3 Basic Definitions
	14.4 Basic Operations on Fuzzy Sets
	14.5 Properties of Fuzzy Sets
	14.6 Interval Valued Fuzzy Set
	14.7 Operations on l-v Fuzzy Sets
	14.8 Fuzzy Relations
	14.9 Operations on Fuzzy Relations
	14.10 Fuzzy Logic
	Solved Examples
	Exercises
References
Index