Boolean Algebra

This volume concentrates on the structure of Boolean algebras and rings as developed through simpler algebraic systems. The algebra of logic and set theory appears as applications or illustrations thr

This introduction to Boolean algebra begins with an intuitive approach to set theory and an axiomatic account of the fundamentals of Boolean algebra, proceeding to concise accounts of applications to

Written for students and researchers in the fields of behavioral sciences, history and logic, this textbook on comparative methods with Boolean algebra explains how these mathematical theories are use

This elementary treatment by a distinguished mathematician begins with the algebra of classes and proceeds to discussions of several different axiomatizations and Boolean algebra in the setting of the

This book explains, in lay terms, the surprisingly simple system of mathematical logic used in digital computer circuitry. Anecdotal in its style and often funny, it follows the development of this lo

This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise

This unique monograph building bridges among a number of different areas of mathematics such as algebra, topology, and category theory. The author uses various tools to develop new applications of cla

This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the car

Volume I was corrected and revised in September 2017.This book begins the task of defining, explaining, arguing for, and, in the end, providing a rationale for information processing. Volume I is conc

This collection of papers presents a series of in-depth examinations of a variety of advanced topics related to Boolean functions and expressions. The chapters are written by some of the most prominent experts in their respective fields and cover topics ranging from algebra and propositional logic to learning theory, cryptography, computational complexity, electrical engineering, and reliability theory. Beyond the diversity of the questions raised and investigated in different chapters, a remarkable feature of the collection is the common thread created by the fundamental language, concepts, models, and tools provided by Boolean theory. Many readers will be surprised to discover the countless links between seemingly remote topics discussed in various chapters of the book. This text will help them draw on such connections to further their understanding of their own scientific discipline and to explore new avenues for research.

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The second volume continues the course of study started in Volume 1, but may be used independently by those already possessing an elementary knowledge of the subject. A summary of basic group theory is followed by accounts of group homomorphisms, rings, fields and integral domains. The related concepts of an invariant subgroup and an ideal in a ring are brought in and the reader introduced to vector spaces and Boolean algebra. The theorems behind the abstract work and the reasons for their importance are discussed in greater detail than is usual at this level. The book is intended both for those who, educated in traditional mathematics, wish to know something about modern algebra and also for those already familiar with the elements of the subject who wish to study further. Fresh ideas and structures are introduced gradually and in a simpler manner, with concrete examples and much more informal discussion. There are many graded exercises, including some worked examples. This book is th

An illustrated journey through the past, present, and future of artificial intelligence, from popular science author Cliff Pickover.From medieval robots and Boolean algebra to facial recognition, arti

This book has been designed for a first course on digital design for engineering and computer science students. It offers an extensive introduction on fundamental theories, from Boolean algebra and bi

This book has been designed for a first course on digital design for engineering and computer science students. It offers an extensive introduction on fundamental theories, from Boolean algebra and bi

This book is a comprehensive guide to qualitative comparative analysis (QCA) using R. Using Boolean algebra to implement principles of comparison used by scholars engaged in the qualitative study of

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to our kitchen gadgets and home appliances. How did a system

Now with new introductory material, Charles Ragin’s The Comparative Method proposes a synthetic new strategy, based on an application of Boolean algebra that, by combining the strengths of both qualit

Beginning with the fundamentals such as logic families, number systems, Boolean algebra and logic gates, and combinational circuits, the book proceeds on to cover the applied aspects like sequential l

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to our kitchen gadgets and home appliances. How did a system

Introduction to Mathematical Logic Resolution Principle, Second Edition, in nine chapters, discusses Boolean algebra theory, propositional calculus and predicated calculus theory, resolution principl

In Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are 'close' to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.

Self-taught mathematician and father of Boolean algebra, George Boole (1815–1864) published A Treatise on the Calculus of Finite Differences in 1860 as a sequel to his Treatise on Differential Equations (1859). Both books became instant classics that were used as textbooks for many years and eventually became the basis for our contemporary digital computer systems. The book discusses direct theories of finite differences and integration, linear equations, variations of a constant, and equations of partial and mixed differences. Boole also includes exercises for daring students to ponder, and also supplies answers. Long a proponent of positioning logic firmly in the camp of mathematics rather than philosophy, Boole was instrumental in developing a notational system that allowed logical statements to be symbolically represented by algebraic equations. One of history's most insightful mathematicians, Boole is compelling reading for today's student of logic and Boolean thinking.

Self-taught mathematician and father of Boolean algebra, George Boole (1815–1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a system one can use to understand the human mind. In the first 12 chapters, he sets down the rules necessary to represent logic in this unique way. Then he analyses a variety of arguments and propositions of various writers from Aristotle to Spinoza. One of history's most insightful mathematicians, Boole is compelling reading for today's student of intellectual history and the science of the mind.

A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students a

Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous sys

Written by the founder of symbolic logic (and Boolean algebra), this classic treatise on the calculus of finite differences offers a thorough discussion of the basic principles of the subject, coverin

Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theor

In Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are 'close' to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.

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 illu

Over the last 45 years, Boolean theorem has been generalized and extended in several different directions and its applications have reached into almost every area of modern mathematics; but since it lies on the frontiers of algebra, geometry, general topology and functional analysis, the corpus of mathematics which has arisen in this way is seldom seen as a whole. In order to give a unified treatment of this rather diverse body of material, Dr Johnstone begins by developing the theory of locales (a lattice-theoretic approach to 'general topology without points' which has achieved some notable results in the past ten years but which has not previously been treated in book form). This development culminates in the proof of Stone's Representation Theorem.