Abstract
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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