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Boolean Algebra and Its Applications
This is by far one of the best math books in the Dover catalogue. While the prose is admittedly dry, the clarity of the exposition is flawless. The author begins his discussion with a chapter on set theory and wisely takes an intuitive appraoch rather than a theoretical one. This makes the second chapter, which gives an axiomatic account of the fundamentals of Boolean algebra, much easier to digest. Once you master the first two chapters, the rest of the books is smooth sailing. From here the author gives detailed, yet succinct, accounts of the applicatons of Boolean algebra to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. Although the book is aimed primarily at math, computer science, and electrical engineering majors, it accessible to anyone who is comfortable with college level mathematics. It is especially helpful to the philosophy student who wishes to learn about symbolic logic and its applications to the foundations of computer science.

Boolean Algebra
Though written with dry prose, this book is very much worth studying toanyone with an interest in the subject.

Targeted toward math and computerscience undergraduates and to a certain extent electrical engineeringtypes, the book progresses like a math course. It gives the greatestemphasis to the key topics (like the title) and builds on the most basicsub-topics. In Boolean Algebra, that sub-topic is Set Theory. Thereforethis book requires a level of thinking beyond the ordinary, but once youunderstand Set Theory, the rest is easy. And to make it easier on thereader, the lessons on Set Theory are totally intuitive, assuming thereader has at least taken algebra.

dry
This book fell to the floor where it was pounced upon and chewed by my nieces 3 pounddog who `forthwith' lost 10 pounds of the nectar of life. We shall be suing Dover for her wrongful death by dehydration. BooleanAlgebra is a fine subject but this book ... the most turgid bit of writingsince `OG the trog-dude' first scratched a mark on a cave wall. ... Read more

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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 logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. ONES AND ZEROS will be enjoyed by anyone who has a general interest in science and technology. ... Read more

Customer Reviews (6)

The very best book I have read on Boolean
I'm a Computer Engineering student and have read many books on the subject.Until I read this book, I was constantly struggling with complex Boolean equations. Fortunately, this book has helped me master the subject -with a lot of hard work. I highly recommend this book for any student in the Computer Engineering field.

Excellent Introduction
This is an extremely clear introduction to Boolean Algebra.It is very well written and edited.Plenty of exercises will answers to cement the concepts in your brain.

The book covers number systems, logic gates, and some elementary set theory.They are all covered well.There is no coverage of flip-flops which I would have liked to have seen.

I should note this is not an electronics book.There are no real circuits but there are plenty of logic diagrams.Read this book to understand the concepts then go on to an electronic book if you actually wanted to build any of this stuff.

Great books for boolean algebra
Incredible book for understanding boolean algebra. What I like about the book is the simple and clear language that the author uses and a lot of very helpful examples throughout the book to help understand the concept.

Excellent book
This is an rxcellent book for anyone interested in digital circuits and boolean algebra. It is very easy to understand, but does go into enough detail for the advanced to learn from it also. We can all improve our skills after reading this book. Also the price is right!

THE book on ones and zeros
If you are looking for a complete understanding of boolean algebra, this book will definitely statisfy your needs. It provides several interestingexamples with each chapter to keep your mind working. Great way to startout learning about boolean logic. ... Read more

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"The author writes very well ... provid[ing] a solid foundational (graduate-level) text for mathematicians, engineers, and logicians ... the author does a good job of drawing examples from the field of logic designed to illustrate useful applications of theory."--Randal E. Bryant, Carnegie Mellon UniversityA systematic treatment of Boolean reasoning, this concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished research results. The book begins with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras, based on Huntington's postulate. It defines operators for elimination, division, and expansion, providing a systematic basis for subsequent discussions of syllogistic reasoning, the solution of Boolean equations, and functional deduction. Two concluding chapters deal with applications; one applies Boolean reasoning to diagnostic problems, and the other discusses the design of multiple-output logic-circuits. 1990 edition. 18 figures. 19 tables.
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Customer Reviews (2)

goes deeper than most CS courses
Boolean algebra is the bedrock of computing. So if you want to deepen your understanding of computing, Brown presents this exposition. Beware. It is a lot more abstruse than the way Boolean logic is often taught in computer science courses. It shows a depth and elegance far removed from those treatments. There is a beauty here in the Boolean expressions that is sadly not appreciated by enough programmers.

Along the way, Brown explains Karnaugh maps to good detail. He also ties this into programs that optimise Boolean expressions according to various criteria. So yes, there are actual code examples, just in case you think this is all too airy fairy.

from Rome
I'd like to point out the following URL containing a complete review of the book
http://www.philosophy.unimelb.edu.au/ajl/2005/2005_6.pdf ... Read more

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This book is an informal, although systematic presentation of lectures given by the authors on Boolean algebras, intended for advanced undergraduates and beginning graduate students. In a bold and refreshing style, this book treats Boolean algebras, develops some intriguing ideas, and provides rare insights. Exercises are generously sprinkled throughout the text for course study.

This book can be considered a sequel to Paul Halmos's Lectures on Boolean Algebras, with the following changes: (1) the material in every section has been explained in more detail, and is now more accessible to undergraduates; (2) there are three times as many exercises, and the authors have now prepared a solutions manual; (3) a more careful explanation of the relationship between Boolean rings and Boolean algebras has been added; (4) thirteen chapters have been added, including chapters on topology and on continuous functions, a chapter on the extension theorem for homomorphisms, a new chapter on congruences and quotient algebras, a chapter on the lattice of ideals, and a chapter on duality theory for products.

Customer Reviews (2)

Superb introduction. (Contains one flaw.)
As always, Halmos is an excellent expositor. The brief first chapter has been known to scare away physicists and other intelligent people who don't happen to know ring theory, but fortunately the first chapter can be skipped. The book is at the right level to be used by mathematics graduate students learning Boolean algebras and Stone spaces for the first time.

Some people draw a sharp distinction between the concepts of "Boolean space" (a totally disconnected compact Hausdorff space) and "Stone space", the difference being that a Stone space is the Stone space _of_ a Boolean algebra. A Boolean algebra's Stone space is the space of all of its 2-valued homomorphisms with the topology of pointwise convergence of nets of such homomorphisms. That every Boolean space is the Stone space of some Boolean algebra (namely, the Boolean algebra of all of its clopen subsets) is one of the important facts of "Stone's duality". Halmos never mentions the phrase "Stone space", but he proves the basic facts about "Stone's duality": that the category of Boolean algebras and Boolean homomorphisms is the opposite of the category of Boolean spaces and continuous functions.

The flaw is in Lecture 21. Much of that section is founded upon an error -- that a Boolean algebra may have various non-isomorphic completions, of which one is "minimal". A careful mathematician can reconstruct that lecture and get much that is of value, but some may be unfortunately misled.

One other thing irritates me: Halmos uses the word "non-atomic" rather than the much better term "atomless". The problem with "non-atomic" is that it may be mistaken for "not atomic", and that is a quite different thing.

This book is now out of print. I'd like to see Dover reprint it.

ONE OF THE BEST
A very good book, going through the stuff in a very nice kind. Giving you intuitive insights, easy proofs, and written with a large sense of humor. ... Read more

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Customer Reviews (1)

Still useful for initial study or review of Boolean algebra
Although this book was printed nearly thirty years ago, the content still provides value; in fact it is roughly the first two chapters of the book that I last used for a college course in digital logic for computer scientists. Boolean algebra is the fundamental mathematics used to represent the action of basic computer circuits such as the adder/subtractor and the flip-flop. The representation of numbers in binary and arithmetic as performed in binary are also covered. There are many diagrams of switches and logic gates to emphasize how the devices are implemented.
This book remains a solid introduction to Boolean algebra as it is applied to basic computer circuitry, it can be used for initial study or as a refresher.
... Read more

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A uniquely designed quide to the basic elements of Boolean algebra programed for self-instruction and fashioned for application to the field of computer logic design. Featuring a linear programed format, it provides every element required to assume complete mastery of the subject, using as illustrative bases, switching circuits, logical equations, and word problems to amplify basic discussions.

This manual provides an ideal method for the introduction or broadening of any individual to the mathematic techniques employed in computer technology. The mathematical discussions throughout are applied to the key factor of the field - computer circuitry - the formal and informal methods which allow the selection of the simplest of two circuits, as well as the further simplifying of existing computer circuits. ... Read more

Customer Reviews (1)

A great way to learn how Boolean algebra is applied to circuits
This book should really have the title, "Boolean Algebra as applied to Switching and Digital Circuits." There is little in the way of the abstract theory of Boolean algebra, the emphasis is on the practical uses in describing and manipulating circuits. On that level, the book is excellent. It steps you through the basics, one step at a time and with complete explanations of the problem and the solution. After completion, you will have learned how Boolean algebra describes the digital operations behind computing, the rules of manipulation and how to create and simplify basic digital devices. ... Read more

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This Handbook treats those parts of the theory of Boolean algebras of most interest to pure mathematicians: the set-theoretical abstract theory and applications and relationships to measure theory, topology, and logic. It is divided into two parts (published in three volumes). Part I (volume 1) is a comprehensive, self-contained introduction to the set-theoretical aspects of the theory of Boolean Algebras. It includes, in addition to a systematic introduction of basic algebra and topological ideas, recent developments such as the Balcar-Franek and Shelah-Shapirovskii results on free subalgebras. Part II (volumes 2 and 3) contains articles on special topics describing - mostly with full proofs - the most recent results in special areas such as automorphism groups, Ketonen's theorem, recursive Boolean algebras, and measure algebras. ... Read more

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The treatment here of Boolean algebra, deeper than in most elementary texts, can serve as a supplement or an introduction to graduate-level study. The explanations of switching and logic circuits refer to combinatorial circuits. The theory in both of these areas is illustrated and amplified by many problems with detailed solutions, giving students a secure grounding. Supplementary problems provide a complete review of the material. ... Read more

Customer Reviews (3)

A definite career builder for me
This is one of the elements of the Schaum's set that helped make my career. When I was first starting out as a college instructor, I was a math major but had little experience in computer science. In order to quickly flesh out my skills so that I could teach discrete mathematics, I checked this book out of the library and started working the problems. Although my background in abstract algebra helped in my understanding of the theory, my real goal was to learn the applications to digital circuits.
This goal was satisfied, in a short time, I was able to cover digital circuits in the discrete class and a short time later, was able to teach a class in digital logic for computer science majors.

Good book on boolean algebra and logic for more advanced students
This book is devoted to two separate and related topics: the theory of Boolean algebra and logic and also the synthesis and simplification of switching and logic circuits. This is a good book for students taking a course on digital logic that has more of a computer science or mathematics perspective rather than an electrical engineering viewpoint. There is no mention of gates or digital circuit building blocks of any kind in this outline.The treatment of switching and logic circuits is limited to the combinational circuits - those circuits whose outputs depend only on the present inputs.
Chapter 1 goes over the basics of boolean logic and the notation used in this outline. Chapter 2 discusses sets and their operations and extends boolean logic to sets of objects. Chapter 3 discusses Boolean algebra, which is a set B together with two binary operations, a singular operation, the two specific elements 0 and 1, and a set of axioms.Thus, in this chapter we are led more into the realm of mathematics than circuits with a good number of proofs as exercises. Chapter 4 abruptly changes course and discusses switching and logic circuits. Here, previous discussions of Boolean logic lead to the practical tasks of minimization and the finding of all prime implicants of a set. The final chapter changes course once again and discusses some advanced topics in Boolean algebra such as lattices, rings, and m-completeness.
Although no specific previous knowledge is really explicitly required to understand this material, I would say that working through the material I found that experience with mathematical proofs, set theory, and oddly enough, abstract algebra were all very advantageous in understanding this outline. It is one of the better written Schaum's outline in that the theory is very well explained. I would recommend it for the more mathematically inclined who are interested in digital logic.

digital designers can find useful problems
For those of you inclined to the theoretical aspects of computing, this book may be good revision. The first half of the book deals with set theory and then with Boolean algebra. The Boolean concepts should be easy to follow, and likewise with the problems presented to you here.

What is more challenging is the second half, dealing with switching circuits. You can see techniques that map from a logic circuit to its Boolean representation. And then the vital idea of a Karnaugh map, in order to simplify that representation. Digital circuit designers live for this stuff! Many problems to chew on. See how well you really understand the material.

You might look with askance on the publication date of 1970. 1970?! Moore had barely formulated his law a few years earlier. And Medium Scale Integration was the order of the day, perhaps, with the first microprocessor still under design. But the maths in this book still holds true now. In fact, it is even more relevant today. Because the circuits are orders of magnitude larger, so finding efficient means of circuit minimisation are more urgent. For that, you need a solid theoretical basis. And this book can test that understanding. ... Read more

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Topics include set theory, sentential calculus,fundamental ideas of Boolean algebras, lattices, rings and Booleanalgebras, the structure of a Boolean algebra, and Boolean algebra incommunication systems. ... Read more

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Computer algebra systems are gaining more and more importance in all areas of science and engineering. This textbook gives a thorough introduction to the subject, which is the basis of the mathematical engine in computer algebra systems. It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. However its comprehensiveness and authority will mean it will be an essential reference also for professionals in the area. Special features include: detailed study of algorithmics including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; a wide variety of applications (including in chemistry, coding theory, cryptography, and the design of calendars and musical scales). Some of this material has never appeared before in book form. Finally, a great deal of historical information and illustration is included. ... Read more

Customer Reviews (5)

Very nice
This is a very nicely written text, comprehensive in what it aims to cover.The illustrations are plentiful and very helpful.The material is mostly self-contained and presented in a novel way (Fermat, Euler, Hilbert each have their own groups of sections!).

This is the best treatment I've seen for lattice basis reduction (a topic treated in many other texts) as well as for polynomial factoring over fields (Cantor Zassenhaus) and other topics.I've read parts of this book that were irrelevant for my research simply because the book is a joy to read.Highly recommended to anyone with an interest and some degree of mathematical maturity.

The only drawback is that my edition has a number of typos, some serious (however the authors do provide an online corrigenda).

State-of-the-art in CAS
I am a C programmer and this book was fundamental to introduce myself in the field of computer algebra systems (CAS). It's very well structured and at the state-of-the-art in that discipline. The only remarks is about the strong presence of author's mother-tongue influences in some English phrases.

Good overview
A good and complete review, a very good bibliography. Wonderfull graphics. A subtle sense of humor.

Mod. Computer Algebra
A lucidly written book.Has well balanced background and problems.However, it needs to have more tricky problems that really makes one think deeper though there are some. The book proves a very good assest to the Library.

MCA - very adequate book on computer algebra topics
Covering a lot of topics on "Computer Algebra" this book is a fine workout. Many mathematical proofs are provided and most subjects are explained and outlined very accurately. Only sometimes things can not aseasily be seen as the author clames. The homepage of Mr. von zur Gathenprovides a postscript file with corrections and additions and even more onecontaining solutions to many of the given exercises. ... Read more

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Logic forms the basis of mathematics and is a fundamental part of any mathematics course. This book provides students with a clear and accessible introduction to this important subject, using the concept of model as the main focus and covering a wide area of logic. The chapters of the book cover propositional calculus, boolean algebras, predicate calculus and completelness theorems with answeres to all of the exercises and the end of the volume. This is an ideal introduction to mathematics and logic for the advanced undergraduate student. ... Read more

Customer Reviews (1)

If you read just one book on logic and/or boolean algebra...
make it this one.

Despite the subject matter, the author comes across as enthusiastic, humorous, and incredibly intelligent.

Don't let this book's date fool you!"Logic and Boolean Algebra" is one of the most effective learning tools I have ever used.Whether it be an 8th grade science project or a stopper to balance a wobbly dining room table, "Logic and Boolean Algebra" is a steal at under $2! ... Read more

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This monograph is a follow up to the author's classic text Boolean-Valued Models and Independence Proofs in Set Theory, providing an exposition of some of the most important results in set theory obtained in the 20th century-the independence of the continuum hypothesis and the axiom of choice.Aimed at research students and academics in mathematics, mathematical logic, philosophy, and computer science, the text has been extensively updated with expanded introductory material, new chapters and a new appendix on category theory, and includes recent developments in the field.Numerous exercises, along with the enlarged and entirely updated background material, make this an ideal text for students in logic and set theory. ... Read more