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Practical Foundations of Mathematics: PRAC FOUNDATIONS OF MATHEMATIC

by Paul Taylor

2021-02-03 03:17:37

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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 bet... Read more
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. Less

Book Details

ISBN9780521631075
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Paul Taylor
Author
Paul Taylor is a Senior Fellow at the Pew Research Center. He previously served as its executive vice president, where he oversaw demographic, social, and generational research. He is the author of Se...

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