Practical Foundations of Mathematics [+ Errata and Reviews]

Paul Taylor0521631076, 9780521631075

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.

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Table of contents :
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Practical Foundations of Mathematics……Page 1
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Practical Foundations of Mathematics……Page 593
Errata to emph{Practical Foundations of Mathematics}……Page 632
Additional errata to {Practical Foundations of Mathematics}……Page 638
Book Review for Bulletin of the LMS……Page 640
Review by Peter Johnstone……Page 645
Paul Taylor – Foundations of Mathematics and Computation……Page 6
Cambridge University Press……Page 8