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Conceptual Mathematics : A First Introduction to Categories by Stephen H. Schanuel and F. William Lawvere (2009, Trade Paperback)
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-10052171916X
ISBN-139780521719162
eBay Product ID (ePID)16038299308
Product Key Features
Number of Pages404 Pages
Publication NameConceptual Mathematics : a First Introduction to Categories
LanguageEnglish
SubjectGroup Theory, Logic
Publication Year2009
TypeTextbook
Subject AreaMathematics
AuthorStephen H. Schanuel, F. William Lawvere
FormatTrade Paperback
Dimensions
Item Height1 in
Item Weight27.6 Oz
Item Length9.6 in
Item Width6.7 in
Additional Product Features
Edition Number2
Intended AudienceCollege Audience
LCCN2007-043671
Dewey Edition22
ReviewsConceptual 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. LEnseignment Mathimatique, every mathematician should know the basic ideas and techniques explained in this book Monatshefte für Mathematik, 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, '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, 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, '… every mathematician should know the basic ideas and techniques explained in this book …' Monatshefte fr Mathematik, '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, "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, '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, "This outstanding book on category theory is in a class by itself. It should be consulted at various stages of one's mastery of this fundamental body of knowledge." George Hacken, reviews.com, '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 Mathèmatique, 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, '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 Mathmatique, '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 Math_matique, '... every mathematician should know the basic ideas and techniques explained in this book ...' Monatshefte f8r Mathematik
IllustratedYes
Dewey Decimal512/.62
Table Of ContentForeword; 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.
SynopsisConceptual Mathematics introduces the concept of category to beginning students and practising mathematical scientists based on a leisurely introduction to the important categories of directed graphs and discrete dynamical systems. The expanded second edition approaches more advanced topics via historical sketches and a concise introduction to adjoint functors., 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., In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics, Second Edition, introduces the concept of 'category' for the learning, development, and use of mathematics, to both beginning students and general readers, and to practicing mathematical scientists. 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.
LC Classification NumberQA169.L355 2008
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