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.
Author(s): Paul Taylor
Series: Cambridge Studies in Advanced Mathematics, Vol. 59
Publisher: Cambridge University Press
Year: 1999
Language: English
Commentary: created from html files, with very badly formatted formulas, many of them being unreadable [cover added w.r.t. the other pdf version]
Pages: 648
Tags: Математика;Прочие разделы математики;
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Errata to \emph{Practical Foundations of Mathematics}......Page 633
Additional errata to {Practical Foundations of Mathematics}......Page 639
Book Review for Bulletin of the LMS......Page 641
Review by Peter Johnstone......Page 646
Paul Taylor - Foundations of Mathematics and Computation......Page 7
Cambridge University Press......Page 9
