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Practical Foundations of Mathematics

Practical Foundations of Mathematics

$199.00 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: May 1999
  • availability: Available
  • format: Hardback
  • isbn: 9780521631075

$ 199.00 (P)
Hardback

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  • Practical Foundations of Mathematics explains the basis of mathematical reasoning both in pure mathematics itself (algebra and topology in particular) and in computer science. In addition to the formal logic, this volume examines the relationship between computer languages and "plain English" mathematical proofs. The book introduces the reader to discrete mathematics, reasoning, and categorical logic. It offers a new approach to term algebras, induction and recursion and proves in detail the equivalence of types and categories. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries across universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.

    • Covers fundamentals that underly maths and computer science
    • Immensely wide-ranging
    • No comparable books exist
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    Reviews & endorsements

    "Taylor paints rhapsodically on a broad, richly detailed canvas replete with examples and exercises. He invites readers to dip in at any point and structures his book accordingly. He embroiders his text with a running commentary that often fascinates...this book covers important ground in an original style." Choice

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    Product details

    • Date Published: May 1999
    • format: Hardback
    • isbn: 9780521631075
    • length: 588 pages
    • dimensions: 238 x 150 x 43 mm
    • weight: 1.02kg
    • availability: Available
  • Table of Contents

    1. First order reasoning
    2. Types and induction
    3. Posets and lattices
    4. Cartesian closed categories
    5. Limits and colimits
    6. Structural recursion
    7. Adjunctions
    8. Algebra with dependent types
    9. The quantifiers.

  • Author

    Paul Taylor, Queen Mary University of London

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