Discrete Mathematics Proofs, Structures and Applications, 3rd Edition Third Edition By Rowan Garnier, John Taylor

Discrete Mathematics Proofs, Structures and Applications, 3rd Edition Third Edition

                                                      ════ ⋆★⋆ ═══

 Writer                 ✤      Rowan Garnier, John Taylor

Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow progression from the basic mathematical ideas to the more sophisticated concepts examined later in the book. This edition preserves the philosophy of its predecessors while updating and revising some of the content.

New to the Third Edition
In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors.

Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the ever-evolving discipline of computer science.

TABLE OF CONTENT 

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