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Practical Foundations of Mathematics
Buch von Paul Taylor
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
1. First order reasoning; 2. Types and induction; 3. Posets and lattices; 4. Cartesian closed categories; 5. Limits and colimits; 6. Structural recursion; 7. Adjunctions; 8. Algebra with dependent types; 9. The quantifiers.
Details
Erscheinungsjahr: 2003
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
ISBN-13: 9780521631075
ISBN-10: 0521631076
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Taylor, Paul
Redaktion: Bollobas, Bela
Hersteller: Cambridge University Press
Maße: 235 x 157 x 39 mm
Von/Mit: Paul Taylor
Erscheinungsdatum: 27.11.2003
Gewicht: 1,096 kg
Artikel-ID: 102563529
Inhaltsverzeichnis
1. First order reasoning; 2. Types and induction; 3. Posets and lattices; 4. Cartesian closed categories; 5. Limits and colimits; 6. Structural recursion; 7. Adjunctions; 8. Algebra with dependent types; 9. The quantifiers.
Details
Erscheinungsjahr: 2003
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
ISBN-13: 9780521631075
ISBN-10: 0521631076
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Taylor, Paul
Redaktion: Bollobas, Bela
Hersteller: Cambridge University Press
Maße: 235 x 157 x 39 mm
Von/Mit: Paul Taylor
Erscheinungsdatum: 27.11.2003
Gewicht: 1,096 kg
Artikel-ID: 102563529
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