Sets for Mathematics

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Hardcover | 10 April 2003

At a Glance

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276 Pages

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25.4 x 17.78 x 1.75

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Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape.

Industry Reviews

"...the categorical approach to mathematics has never been presented with greater conviction than it has in this book. The authors show that the use of categories in analyzing the set concept is not only natural, but inevitable." Mathematical Reviews "To learn set theory this way means not having to relearn it later... Recommended." Choice

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Set Theory Mathematical Logic

Other Editions and Formats

Paperback

Published: 16th June 2003

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Foreword
Abstract sets and mappings
Sums, monomorphisms and parts
Finite inverse limits
Colimits, epimorphisms and the axiom of choice
Mapping sets and exponentials
Summary of the axioms and an example of variable sets
Consequences and uses of exponentials
More on power sets
Introduction to variable sets
Models of additional variation
Appendices
Bibliography
Table of Contents provided by Publisher. All Rights Reserved.

Sets for Mathematics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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