Conceptual Mathematics

Name: Conceptual Mathematics
Brand: CAMBRIDGE UNIVERSITY PRESS
SKU: 401168
Price: 79.71 EUR
Availability: InStock

F. WILLIAM LAWVERE

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79,71 €

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ISBN

9780521719162

Mladinska knjiga ID

401168

Leto izida

2009

Datum izida

30.08.2009

Status dobavljivosti

Na zalogi pri dobavitelju

Jezik

ANG

Založnik

CAMBRIDGE UNIVERSITY PRESS

Avtor

F. WILLIAM LAWVERE

Opis

A First Introduction to CategoriesThis truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.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; Part I. The Category of Sets: 1. Sets, maps, composition; Part II. The Algebra of Composition: 2. Isomorphisms; Part III. Categories of Structured Sets: 3. Examples of categories; Part IV. Elementary Universal Mapping Properties: 4. Universal mapping properties; Part V. Higher Universal Mapping Properties: 5. Map objects; 6. The contravariant parts functor; 7. The components functor; Appendix 1. Geometry of figures and algebra of functions; Appendix 2. Adjoint functors; Appendix 3. The emergence of category theory within mathematics; Appendix 4. Annotated bibliography.