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Sets for Mathematics

Name: Sets for Mathematics
Brand: Cambridge University Press
SKU: 04089477
Price: 26009 HUF
Availability: InStock
Author: F William Lawvere
ISBN: 9780521010603

F William Lawvere

Language

English

Book Paperback

Libristo code: 04089477

Publishers Cambridge University Press, January 2003

Advanced undergraduate or beginning graduate students need a unified foundation for their study of g... Full description

Libristo code: 04089477

173 b

26 009 Ft

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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.