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## Fundamental approach to discrete mathematics 2009 book # Fundamental approach to discrete mathematics

```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
```

price : \$12.48 16 With 22% OFF

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## Abstract Of The Book

```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
1.13 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```

First 10 Pages Of the book