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Conceptual Mathematics
A First Introduction to Categories

2nd Edition

$65.99 (X)

  • Date Published: August 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521719162

$ 65.99 (X)

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About the Authors
  • 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.

    • Authors are world class authorities on the subject
    • Only text at this elementary level - requires only high-school algebra
    • Applications in pure and applied mathematics, computer science, physics, linguistics, logic and philosophy
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    Reviews & endorsements

    "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,

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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

    Note to the reader
    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
  • Authors

    F. William Lawvere, State University of New York, Buffalo
    F. William Lawvere is a Professor Emeritus of Mathematics at the State University of New York. He has previously held positions at Reed College, the University of Chicago and the City University of New York, as well as visiting Professorships at other institutions worldwide. At the 1970 International Congress of Mathematicians in Nice, Prof. Lawvere delivered an invited lecture in which he introduced an algebraic version of topos theory which united several previously 'unrelated' areas in geometry and in set theory; over a dozen books, several dozen international meetings, and hundreds of research papers have since appeared, continuing to develop the consequences of that unification.

    Stephen H. Schanuel, State University of New York, Buffalo
    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.

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