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出版者:Cambridge University Press

作者:Paul Taylor

出品人:

页数:588

译者:

出版时间:1999-05-13

价格:USD 120.00

装帧:Hardcover

isbn号码:9780521631075

丛书系列:Cambridge Studies in Advanced Mathematics

图书标签:

数学
计算机
编程语言理论
work
onshelf
mathematics
IT

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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.