# Discrete Mathematics: Proofs, Structures and Applications

##### By: Garnier, Rowan.

##### Contributor(s): Taylor, John.

Material type: BookPublisher: Boca Raton CRC Press 2010Edition: 3rd ed.Description: xxi, 821p.ISBN: 9781439812808.Subject(s): Discrete MathematicsDDC classification: 511.1Item type | Current location | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|

General Book | Nava Nalanda Central Library General Section | GEN | 511.1 GA-D (Browse shelf) | Available | 129039 | |

General Book | Nava Nalanda Central Library General Section | GEN | 511.1 GA-D (Browse shelf) | Available | 129040 | |

General Book | Nava Nalanda Central Library General Section | GEN | 511.1 GA-D (Browse shelf) | Available | 129041 |

Table of Contents

Logic

Propositions and Truth Values

Logical Connectives and Truth Tables

Tautologies and Contradictions

Logical Equivalence and Logical Implication

The Algebra of Propositions

Arguments

Formal Proof of the Validity of Arguments

Predicate Logic

Arguments in Predicate Logic

Mathematical Proof

The Nature of Proof

Axioms and Axiom Systems

Methods of Proof

Mathematical Induction

Sets

Sets and Membership

Subsets

Operations on Sets

Counting Techniques

The Algebra of Sets

Families of Sets

The Cartesian Product

Types and Typed Set Theory

Relations

Relations and Their Representations

Properties of Relations

Intersections and Unions of Relations

Equivalence Relations and Partitions

Order Relations

Hasse Diagrams

Application: Relational Databases

Functions

Definitions and Examples

Composite Functions

Injections and Surjections

Bijections and Inverse Functions

More on Cardinality

Databases: Functional Dependence and Normal Forms

Matrix Algebra

Introduction

Some Special Matrices

Operations on Matrices

Elementary Matrices

The Inverse of a Matrix

Systems of Linear Equations

Introduction

Matrix Inverse Method

Gauss–Jordan Elimination

Gaussian Elimination

Algebraic Structures

Binary Operations and Their Properties

Algebraic Structures

More about Groups

Some Families of Groups

Substructures

Morphisms

Group Codes

Introduction to Number Theory

Divisibility

Prime Numbers

Linear Congruences

Groups in Modular Arithmetic

Public Key Cryptography

Boolean Algebra

Introduction

Properties of Boolean Algebras

Boolean Functions

Switching Circuits

Logic Networks

Minimization of Boolean Expressions

Graph Theory

Definitions and Examples

Paths and Cycles

Isomorphism of Graphs

Trees

Planar Graphs

Directed Graphs

Applications of Graph Theory

Introduction

Rooted Trees

Sorting

Searching Strategies

Weighted Graphs

The Shortest Path and Traveling Salesman Problems

Networks and Flows

References and Further Reading

Hints and Solutions to Selected Exercises

Index

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