Fundamental Approach to Discrete Mathematics

About the Book: The book `Fundamental Approach to Discrete Mathematics` is a required part of pursuing a computer science degree at most universities. It provides in-depth knowledge to the subject for beginners and stimulates further interest in the topic. The salient features of this book include:...

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Bibliographic Details
Main Authors Acharjya, D.P, Sreekumar
Format eBook
LanguageEnglish
Published Daryaganj New Age International Ltd 2009
Edition2
Subjects
History
Toronto (Ont.)
Online AccessGet full text
ISBN9788122426076
8122426077

Cover

Table of Contents:
  • 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
  • 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
  • 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