Conceptual Mathematics

ISBN-13: 9780521719162 / Angielski / Miękka / 2009 / 404 str.

F. William Lawvere; Stephen H. Schanuel

Opis

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.

Recenzje

'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

Spis treści

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.

O autorze

Schanuel, Stephen H.Stephen H. Schanuel is a Professor of Mathematics at the State University of New York at Buffalo. He has previously held positions at Johns Hopkins University, Institute for Advanced Study and Cornell University, as well as lecturing at institutions in Denmark, Switzerland, Germany, Italy, Colombia, Canada, Ireland, and Australia. Best known for Schanuel's Lemma in homological algebra (and related work with Bass on the beginning of algebraic K-theory), and for Schanuel's Conjecture on algebraic independence and the exponential function, his research thus wanders from algebra to number theory to analysis to geometry and topology.