Garnier / Taylor Discrete Mathematics

Proofs, Structures and Applications, Third Edition
3. Auflage 2011
ISBN: 978-1-4398-1281-5
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 843 Seiten

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.

Zielgruppe

Undergraduate students in mathematics, computer science, engineering, and the sciences.

Autoren/Hrsg.

Garnier, Rowan

Taylor, John

Fachgebiete

• Mathematik | Informatik EDV | Informatik Betriebssysteme
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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

Über Autor(innen)

Rowan Garnier was a professor of mathematics at Richmond, the American International University in London, where she served ten years as Chair of the Division of Mathematics, Science and Computer Science.
John Taylor is Head of the School of Computing, Mathematical and Information Sciences at the University of Brighton, UK. He has published widely on the applications of diagrammatic logic systems to computer science.