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Discrete Mathematics: Proofs, Structures and Applications

By: Garnier, Rowan.
Contributor(s): Taylor, John.
Material type: materialTypeLabelBookPublisher: Boca Raton CRC Press 2010Edition: 3rd ed.Description: xxi, 821p.ISBN: 9781439812808.Subject(s): Discrete MathematicsDDC classification: 511.1
Contents:
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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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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