You are here: Home / Shop / Product Detail Page |

## Dolciani Mathematical Expositions No. 21: Logic as Algebra (Softcover)"This book is an introduction to modern logic, but it is quite different from other introductory books on the subject." — From the back cover ## $19.79 |

### Need More Info?

Please contact us if you've got questions about this product.## Condition

**GOOD:** Except for a bend in the front cover and some of the first pages, this book is in excellent condition. There is no writing on the pages and the binding is tight.

## Description

From the back cover: The book’s “purpose, according to the preface, is ‘…to show that logic an (and perhaps should) be viewed from an algebraic perspective. When so viewed, many of its principal notions are seen to be old friends, familiar algebraic notions that were “disguised” in logical clothing. Moreover, the connection between the principal theorems of the subject and well-known theorems in algebra becomes clearer. Even the proofs often gain in simplicity.’

“The presentation is aimed at a broad audience—mathematics amateurs, students, teachers, philosophers, linguists, computer scientists, engineers, and professional mathematicians. Whether the reader’s goal is a quick glimpse of modern logic or a more serious study of the subject, the book’s fresh approach will bring novel and illuminating insights to beginners and professionals alike. All that is required of the reader is an acquaintance with some of the basic notions encountered in a first course in modern algebra. In particular, no prior knowledge of logic is assumed. The book could serve equally well as a fireside companion and as a course text.

“Propositional logic and nomadic predicate calculus—predicate logic with a single quantifier—are the principal topics treated. The connections between logic and algebra are carefully explained. The key notions and the fundamental theorems are elucidated from both a logical and an algebraic perspective. The final section gives a unique and illuminating algebraic treatment of the theory of syllogisms—perhaps the oldest branch of logic, and a subject that is neglected in most modern logic texts.”

**BRIEF CONTENTS**

**What is logic?**

- To count or to think
- A small alphabet
- A small grammar
- A small logic
- What is truth?
- Motivation of the small language
- All mathematics

**Propositional calculus**

- Propositional symbols
- Propositional abbreviations
- Polish notation
- Language as an algebra
- Concatenation
- Theorem schemata
- Formal proofs
- Entailment
- Logical equivalence
- Conjunction
- Algebraic Identities

**Boolean Algebra**

- Equivalence classes
- Interpretations
- Consistency and Boolean algebra
- Duality and commutativity
- Properties of Boolean algebras
- Subtraction
- Examples of Boolean algebras

**Boolean universal algebra**

- Subalgebras
- Homomorphisms
- Examples of homomorphisms
- Free algebras
- Kernels and ideals
- Maximal ideals
- Homomorphism theorem
- Consequences
- Representation theorem

**Logic via algebra**

- Pre-Boolean algebras
- Substitution rule
- Boolean logics
- Algebra of the propositional calculus
- Algebra of proof and consequence

**Lattices and infinite operations**

- Lattices
- Non-distributive lattices
- Infinite operations

**Monadic predicate calculus**

- Propositional functions
- Finite functions
- Functional monadic algebras
- Functional quantifiers
- Monadic algebras
- Free monadic algebras
- Modal logics
- Monadic logics
- Syllogisms

The book ends with an Index.

## Details

- SKU:
- 1924
- Author:
- Halmos, Paul and Steven Givant
- Publisher:
- The Mathematical Association of America
- Publish Date:
- 1998 (First Printing)
- Format:
- Softcover
- Weight (pounds):
- 0.46
- Dimensions (W”xL”xH”):
- 6″x9″x0.3″
- ISBN-13:
- 9780883853276
- ISBN-10:
- 0883853272
- Series:
- Dolciani Mathematical Expositions

## Related Products

### Products related to "Dolciani Mathematical Expositions No. 21: Logic as Algebra (Softcover)"

- Views:

#### Texts and Monographs in Computer Science: A Logical Approach to Discrete Math (Hardback)

$5.99

"Logic is the glue that binds together arguments and proofs in all domains. This text aims to teach the use of this fundamental and pervasive tool and exercise it thoroughly in applications that arise in computer science and mathematics." — From the back cover

#### Handbook of Mathematics and Computational Science (Hardback)

$39.50

"The Harris and Stocker Handbook of Mathematics and Computation Science is a complete desk-top reference for working scientists, engineers, and students. It serves as a veritable math toolbox for rapid access to a wealth of mathematics information for everyday use in problem solving, homework, examinations, etc." — From the back cover

#### The Lambda Calculus: Its Syntax and Semantics, Revised Edition (Softcover)

$24.99

"Around 1930 the type free lambda calculus was introduced as a foundation for logic and mathematics. Due to the appearance of paradoxes, this aim was not fulfilled, however. Nevertheless a consistent part of the theory turned out to be quite successful as a theory of computations. It gave an imporatnt momentum to early recusion theory and more recently to computer science." — From the back cover

#### Geometric Problems on MAXIMA and MINIMA (Softcover)

$12.50

"Written by a team of established mathematicians and professors, this work draws on the authors' experience in the classroom and as Olympiad coaches." — From the back cover

#### The Volume Library (2-Volume Hardback Set)

$8.99

"

*The Volume Library*, which is revised and updated annually, was designed for interested, well-informed people—students and adults who need an authoritative reference book for their home book-shelves, and parents who want to keep abreast of the subjects their children are studying in school."—Preface#### Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality (Hardback)

$71.59

"Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century—a feat he celebrated by carving the founding equations into a stone bridge—mathematicians and engineers have been fascinated by these mathematical objects." — From the back cover

#### Numerical Solution of Stochastic Differential Equations (Hardback)

$71.49

"The book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations." — From the back cover

#### Universitext: The Calculus of Variations (Hardback)

$52.95

"This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. The mathematical background assumed of the reader is a course in multivariable calculus, and some familiarity with the elements of real analysis and ordinary differential equations." — From the back cover

#### Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus, Second Edition (Softcover)

$52.29

"Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. This second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes." — From the back cover

#### Clifford Algebras with Numeric and Symbolic Computations (Hardback)

$37.99

"This new book is an excellent resource for those mathematicians, physicists, engineers, and scientific computing researchers who currently use Clifford algebra methods in their investigations. It is also appealing to those who would like to quickly become familiar with the theory and computational practice in some of the most recent and fascinating applications of Clifford algebras." — From the back cover

#### Quantum Computer Science: An Introduction (Hardback)

$34.95

"In the 1990s it was realized that quantum physics has some spectacular applications in computer science. This book is a concise introduction to quantum computation, developing the basic elements of this new branch of computational theory without assuming any background in physics." — From the back cover

#### Performance Analysis of Local Computer Networks (Hardback)

$12.95

"This is the first book to present a unified and self-contained treatment of local networks from the perspective of performance analysis. The performance models discussed are developed in as elementary a manner as possible, often using a heuristic rather than a rigorous approach." — About the Book, Dust Jacket

#### Computer Graphics and Geometric Modeling: Mathematics (Hardback)

$12.49

"In addition to its use as a companion volume to computer graphics or geometric modeling courses, this volume would also make a good mathematics reference book, in particular for practitioners in the field of geometric modeling. Furthermore, because of its broad coverage and emphasis on explanation it could even be used as text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential and algebraic)." — From the back cover

#### Introduction to Information Theory and Data Compression (Hardback)

$9.99

"This textbook is aimed at graduate students and upper level undergraduates in mathematics, engineering, and computer science." — From the Preface

#### Numerical Methods for Scientists and Engineers, Second Edition (Softcover)

$9.49

"In this second edition, Professor Hamming (Naval Postgraduate School, Monterey, California) extensively rearranged, rewrote and enlarged the material. Moreover, this book is unique in its emphasis on the frequency approach and its use in the solution of problems." — From the back cover

#### Dynamics (Hardback + Supplemental Problems Booklet)

$4.95

"The challenge and responsibility of modern engineering practice demand a high level of creative activity which, in turn, requires the support of strong analytical capability. The subject of engineering mechanics, which includes statics and dynamics, constitutes one of the cornerstones of analytical capability, and all engineers should have a basic background in this field of study." — J. L. Meriam, Author

#### Perturbation Techniques in Mathematics, Engineering & Physics (Softcover)

$3.89

"An introduction to a variety of perturbation techniques for ordinary differential equations, this work outlines applications through specific examples. Mathematicians, engineers, and applied scientists will find its exposition entirely accessible." — From the back cover

#### Introduction to Logic and the Methodology of Deductive Sciences (Softcover)

$3.75

This book is a textbook for elementary college courses in logic and the methodology of deductive science. It is from a revised second edition of a classical work that was first published in Polish in 1936.

#### Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians (Hardback)

$279.95

From the Preface: “This book is a classical and detailed introduction to advanced analytical mechanics (AM), with special emphasis on its basic principles and equations of motion, as they apply to the most general constrained mechanical systems with a finite number of degrees of freedom..."

#### Encyclopedia of Mathematics and Its Applications 20: Finite Fields (Hardback)

$123.50

"In this book, which is the first one devoted entirely to finite fields, we have aimed at presenting both the classical and the applications-oriented aspect of the subject. Thus, in addition to what has to be considered the essential core of the theory, the reader will find results and techniques that are of importance mainly because of their use in applications." — From the Authors in the Preface