Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.
Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.
This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.
This undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.
Authoritative account of the development of Boole's ideas in logic and probability theory ranges from The Mathematical Analysis of Logic to the end of his career. The Laws of Thought formed the most systematic statement of Boole's theories; this volume contains incomplete studies intended for a follow-up volume. 1952 edition.
An introduction to logic from the perspective of algebra.
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic. Part One addresses monadic algebras, with articles on general theory, representation, and freedom. Part Two explores polyadic algebras, progressing from general theory and terms to equality. Part Three offers three items on polyadic Boolean algebras, including a survey of predicates, terms, operations, and equality. The book concludes with an additional bibliography and index.
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Mathematics Ones and Zeros Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets Ones and Zeros explains, in lay terms, Boolean algebra, the suprisingly simple system of mathematical logic used in digital computer circuitry. Anecdotal in style and often funny, Ones and Zeros follows the development of this logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. Readers will learn about the interesting history of the development of symbolic logic in particular, and the often misunderstood process of mathematical invention and scientific discovery, in general. Ones and Zeros also features practical exercises with answers, real-world examples of digital circuit design, and a reading list. This fascinating look at the crucial technology of the twentieth century will be enjoyed by anyone who has a general interest in science, technology, and mathematics. Ones and Zeros will be of particular interest to software engineers who want to gain a comprehensive understanding of computer hardware. Outstanding features include: A history of mathematical logic An explanation of the logic of digital circuits Hands-on exercises and examples About the IEEE Press Understanding Science & Technology Series The IEEE Press Understanding Science & Technology Series treats important topics in science and technology in a simple and easy to understand manner. Designed expressly for the nonspecialist engineer, scientist, or technician, as well as the technologically curious, each volume stresses practical information over mathematical theorems and complicated derivations.
Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.
Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.
This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.
George Boole, for whom Boolean logic is named, developed the idea of expressing any idea as a mathematical or logical statement. Today, Boolean logic is foundational to computer programs and computer hardware, but it is also important in our everyday thinking. This guide includes an overview of logic gates and a review of differences between computer logic and human logic. The author’s clever use of a famous movie line—“Lions and tigers and bears!”—truly helps make a potentially difficult topic easy to grasp for readers of all ages. Photographs, illustrations, and sidebars round out the educational experience.
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.
Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. In particular, it is a major element in theoretical computer science and has undergone a huge revival with the explosion of interest in computers and computer science. This book provides students with a clear and accessible introduction to this important subject. The concept of model underlies the whole book, giving the text a theoretical coherence whilst still covering a wide area of logic.
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.
Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.