Practical Foundations of Mathematics

This book is about the basis of mathematical reasoning both in pure mathematics itself and in computing.

Paul Taylor (Author)

9780521631075, Cambridge University Press

Hardback, published 13 May 1999

588 pages
23.6 x 15.7 x 3.5 cm, 0.88 kg

Review of the hardback: 'This is a fascinating and rewarding book … each chapter has several pages of subtle, provocative and imaginative exercises. In summary, it is a magnificent compilation of ideas and techniques: it is a mine of (well-organised) information suitable for the graduate student and experienced researcher alike.' Roy Dyckhoff, Bulletin of the London Mathematical Society

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.

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.

Subject Areas: Mathematical foundations [PBC]