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edition: 2 Authors: D. P. Acharjya, Sreekumar. serie: ISBN : 9788122428636 publisher: New Age International (P) Ltd., Publishers publish year: 2009 pages: 407 language: English ebook format : PDF (It will be converted to PDF, EPUB OR AZW3 if requested by the user) file size: 12 MB

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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

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