Conceptual Mathematics: A First Introduction to Categories
Autor F. William Lawvere, Stephen H. Schanuelen Limba Engleză Paperback – 29 iul 2009
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Specificații
ISBN-13: 9780521719162
ISBN-10: 052171916X
Pagini: 404
Ilustrații: 575 b/w illus. 12 tables 213 exercises
Dimensiuni: 171 x 244 x 25 mm
Greutate: 0.82 kg
Ediția:Revised
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:Cambridge, United Kingdom
ISBN-10: 052171916X
Pagini: 404
Ilustrații: 575 b/w illus. 12 tables 213 exercises
Dimensiuni: 171 x 244 x 25 mm
Greutate: 0.82 kg
Ediția:Revised
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:Cambridge, United Kingdom
Cuprins
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.
Recenzii
'This text, written by two experts in Category Theory and tried out carefully in courses at SUNY Buffalo, provides a simple and effective first course on conceptual mathematics.' American Mathematical Monthly
'… every mathematician should know the basic ideas and techniques explained in this book …' Monatshefte für Mathematik
'Conceptual Mathematics provides an excellent introductory account to categories for those who are starting from scratch. It treats material which will appear simple and familiar to many philosophers, but in an unfamiliar way.' Studies in History and Philosophy of Modern Physics
'Category Theory slices across the artificial boundaries dividing algebra, arithmetic, calculus, geometry, logic, topology. If you have students you wish to introduce to the subject, I suggest this delightfully elementary book . Lawvere is one of the greatest visionaries of mathematics in the last half of the twentieth century. He characteristically digs down beneath the foundations of a concept in order to simplify its understanding. Schanuel has published research in diverse areas of Algebra, Topology, and Number Theory and is known as a great teacher. I have recommended this book to motivated high school students. I certainly suggest it for undergraduates. I even suggest it for the mathematician who needs a refresher on modern concepts.' National Association of Mathematicians Newsletter
'Conceptual Mathematics is the first book to serve both as a skeleton key to mathematics for the general reader or beginning student and as an introduction to categories for computer scientists, logicians, physicists, linguists, etc … The fundamental ideas are illuminated in an engaging way.' L'Enseignment Mathématique
'… every mathematician should know the basic ideas and techniques explained in this book …' Monatshefte für Mathematik
'Conceptual Mathematics provides an excellent introductory account to categories for those who are starting from scratch. It treats material which will appear simple and familiar to many philosophers, but in an unfamiliar way.' Studies in History and Philosophy of Modern Physics
'Category Theory slices across the artificial boundaries dividing algebra, arithmetic, calculus, geometry, logic, topology. If you have students you wish to introduce to the subject, I suggest this delightfully elementary book . Lawvere is one of the greatest visionaries of mathematics in the last half of the twentieth century. He characteristically digs down beneath the foundations of a concept in order to simplify its understanding. Schanuel has published research in diverse areas of Algebra, Topology, and Number Theory and is known as a great teacher. I have recommended this book to motivated high school students. I certainly suggest it for undergraduates. I even suggest it for the mathematician who needs a refresher on modern concepts.' National Association of Mathematicians Newsletter
'Conceptual Mathematics is the first book to serve both as a skeleton key to mathematics for the general reader or beginning student and as an introduction to categories for computer scientists, logicians, physicists, linguists, etc … The fundamental ideas are illuminated in an engaging way.' L'Enseignment Mathématique
Notă biografică
Descriere
This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.