Practical Foundations of Mathematics
Practical Foundations of Mathematics
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USDPractical 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.
- Covers fundamentals that underly maths and computer science
- Immensely wide-ranging
- No comparable books exist
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
Product details
May 1999Hardback
9780521631075
588 pages
236 × 157 × 35 mm
0.88kg
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.
