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Conceptual Mathematics A First Introduction to Categories

ISBN-10: 052171916X
ISBN-13: 9780521719162
Edition: 2nd 2008
List price: $69.99 Buy it from $50.46
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Description: In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students  More...

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Book details

List price: $69.99
Edition: 2nd
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 7/30/2009
Binding: Paperback
Pages: 404
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.452
Language: English

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

Foreword
Note to the reader
Preview
The Category of Sets
Sets, maps, composition
The Algebra of Composition
Isomorphisms
Categories of Structured Sets
Examples of categories
Elementary Universal Mapping Properties
Universal mapping properties
Higher Universal Mapping Properties
Map objects
The contravariant parts functor
The components functor; Appendix
Geometry of figures and algebra of functions; Appendix
Adjoint functors; Appendix
The emergence of category theory within mathematics
Appendix
Annotated bibliography

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