Conceptual Mathematics
A First Introduction to Categories
2nd Edition
 Authors:
 F. William Lawvere, State University of New York, Buffalo
 Stephen H. Schanuel, State University of New York, Buffalo
 Date Published: August 2009
 availability: Available
 format: Paperback
 isbn: 9780521719162
Paperback

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.
Read more Authors are world class authorities on the subject
 Only text at this elementary level  requires only highschool algebra
 Applications in pure and applied mathematics, computer science, physics, linguistics, logic and philosophy
Reviews & endorsements
'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
See more reviews'… 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
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×Product details
 Edition: 2nd Edition
 Date Published: August 2009
 format: Paperback
 isbn: 9780521719162
 length: 404 pages
 dimensions: 244 x 171 x 25 mm
 weight: 0.78kg
 contains: 575 b/w illus. 12 tables 213 exercises
 availability: Available
Table of Contents
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.Instructors have used or reviewed this title for the following courses
 Finite Mathematics
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