Practical foundations of mathematics

Author(s)

• Taylor, Paul

Bibliographic Information

Practical foundations of mathematics

Paul Taylor

（Cambridge studies in advanced mathematics, 59）

Cambridge University Press, 1999

• : hardback

Note

"Transferred to digital printing 2003"--T.p. verso of 2003 printing

Includes bibliographical references (p. [530]-552) and index

Description and Table of Contents

Description

Practical Foundations collects the methods of construction of the objects of twentieth-century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic Zermelo-Fraenkel logic, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between 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.

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.

by "Nielsen BookData"

Details

• NCID: BA40980043
• ISBN:
  • 0521631076
• LCCN: 98039472
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge ; New York
• Pages/Volumes: xi, 572 p.
• Size: 24 cm
• Classification:
  • LCC : QA39.2
  • DC21 : 510
• Subject Headings:
  • LCSH : Mathematics
• Parent Bibliography ID:
  • BA00109761