The foundations of mathematics / / Ian Stewart and David Tall
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| Autore: |
Stewart Ian <1945->
|
| Titolo: |
The foundations of mathematics / / Ian Stewart and David Tall
|
| Pubblicazione: | New York, New York : , : Oxford University Press, , 2015 |
| ©2015 | |
| Edizione: | Second edition. |
| Descrizione fisica: | 1 online resource (409 p.) |
| Disciplina: | 510 |
| Soggetto topico: | Mathematics |
| Logic, Symbolic and mathematical | |
| Persona (resp. second.): | TallDavid Orme |
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | Cover -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Part I The Intuitive Background -- 1 Mathematical Thinking -- 2 Number Systems -- Part II The Beginnings of Formalisation -- 3 Sets -- 4 Relations -- 5 Functions -- 6 Mathematical Logic -- 7 Mathematical Proof -- Part III The Development of Axiomatic Systems -- 8 Natural Numbers and Proof by Induction -- 9 Real Numbers -- 10 Real Numbers as a Complete Ordered Field -- 11 Complex Numbers and Beyond -- Part IV Using Axiomatic Systems -- 12 Axiomatic Systems, Structure Theorems, and Flexible Thinking -- 13 Permutations and Groups -- 14 Cardinal Numbers -- 15 Infinitesimals -- Part V Strengthening the Foundations -- 16 Axioms for Set Theory -- Appendix: How to Read Proofs: The 'Self-Explanation' Strategy -- References and Further Reading -- Index. |
| Sommario/riassunto: | The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on stude |
| Titolo autorizzato: | The foundations of mathematics |
| ISBN: | 0-19-870644-8 |
| 0-19-101647-0 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910819903003321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |