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Record Nr. |
UNINA9910460462103321 |
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Autore |
Stewart Ian <1945-> |
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Titolo |
The foundations of mathematics / / Ian Stewart and David Tall |
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Pubbl/distr/stampa |
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New York, New York : , : Oxford University Press, , 2015 |
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©2015 |
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ISBN |
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0-19-870644-8 |
0-19-101647-0 |
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Edizione |
[Second edition.] |
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Descrizione fisica |
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1 online resource (409 p.) |
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Disciplina |
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Soggetti |
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Mathematics |
Logic, Symbolic and mathematical |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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""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"" |
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Sommario/riassunto |
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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, |
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