Mathematics and Its Applications

By: B. Plotkin

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Hardcover | 31 January 1994

At a Glance

Hardcover
460 Pages

Dimensions(cm)
25.4 x 17.15 x 3.18

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Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Computing & I.T.Databases Algebra Computer Science Artificial Intelligence Probability & Statistics Groups & Group Theory

Preface
Introduction	p. 1
General View on Objectives and Contents of the Book	p. 3
Universal Algebra	p. 27
Sets, Algebras, Models	p. 29
Fundamental Structures	p. 47
Categories	p. 65
The Category of Sets. Topoi. Fuzzy Sets	p. 85
Varieties of Algebras. Axiomatizable Classes	p. 115
Category Algebra and Algebraic Theories	p. 129
Algebraic Logic	p. 153
Boolean Algebras and Propositional Calculus	p. 155
Halmos Algebras and Predicate Calculus	p. 173
Specialized Halmos Algebras	p. 201
Connections with Model Theory	p. 229
The Categorial Approach to Algebraic Logic	p. 247
Databases - Algebraic Aspects	p. 275
Algebraic Model of a Database	p. 277
Equivalence and Reorganization of Databases	p. 305
Symmetries of Relations and Galois Theory of Databases	p. 329
Constructions in Database Theory	p. 365
Discussion and Conclusion	p. 389
Bibliography	p. 423
Index	p. 434
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematics and Its Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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