About this product

Product Identifiers

PublisherCambridge University Press

ISBN-100521010608

ISBN-139780521010603

eBay Product ID (ePID)1941009

Product Key Features

Number of Pages276 Pages

LanguageEnglish

Publication NameSets for Mathematics

SubjectSet Theory, Logic

Publication Year2003

TypeTextbook

Subject AreaMathematics

AuthorRobert Rosebrugh, F. William Lawvere

FormatTrade Paperback

Dimensions

Item Height0.7 in

Item Weight17.3 Oz

Item Length9.9 in

Item Width6.7 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2002-071478

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

Dewey Edition21

IllustratedYes

Dewey Decimal511

Table Of ContentForeword; 1. Abstract sets and mappings; 2. Sums, monomorphisms and parts; 3. Finite inverse limits; 4. Colimits, epimorphisms and the axiom of choice; 5. Mapping sets and exponentials; 6. Summary of the axioms and an example of variable sets; 7. Consequences and uses of exponentials; 8. More on power sets; 9. Introduction to variable sets; 10. Models of additional variation; Appendices; Bibliography.

SynopsisAdvanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time, 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 that express universal properties of sums, products, mapping sets, and natural number recursion., In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra. Starting with intuitive descriptions of mathematically and physically common phenomena, it leads up to a precise specification of the Category of Sets. Suitable for advanced undergraduates and beginning graduate students., Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, 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.

LC Classification NumberQA248.L28 2002