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Synopsis
This is an introduction to nonstandard analysis based on a course of lectures given several times by the author. It is suitable for use as a text at the beginning graduate or upper undergraduate level, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions; a source of new ideas, objects and proofs; and a wellspring of powerful new principles of reasoning (transfer, overflow, saturation, enlargement, hyperfinite approximation etc.).
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Présentation de l'éditeur
An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.
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Lectures on the Hyperreals
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Springer New York, 2012
ISBN 10 : 1461268419
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a. N° de réf. du vendeur 4189479
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Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics)
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Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
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Lectures on the Hyperreals
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Springer New York Okt 2012, 2012
ISBN 10 : 1461268419
ISBN 13 : 9781461268413
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual. 312 pp. Englisch. N° de réf. du vendeur 9781461268413
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Lectures on the Hyperreals
Edité par
Springer New York, Springer US Okt 2012, 2012
ISBN 10 : 1461268419
ISBN 13 : 9781461268413
Neuf
Taschenbuch
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Taschenbuch. Etat : Neu. Neuware -There are good reasons to believe that nonstandard analysis, in some ver sion or other, will be the analysis of the future. KURT GODEL This book is a compilation and development of lecture notes written for a course on nonstandard analysis that I have now taught several times. Students taking the course have typically received previous introductions to standard real analysis and abstract algebra, but few have studied formal logic. Most of the notes have been used several times in class and revised in the light of that experience. The earlier chapters could be used as the basis of a course at the upper undergraduate level, but the work as a whole, including the later applications, may be more suited to a beginning graduate course. This prefacedescribes my motivationsand objectives in writingthe book. For the most part, these remarks are addressed to the potential instructor. Mathematical understanding develops by a mysterious interplay between intuitive insight and symbolic manipulation. Nonstandard analysis requires an enhanced sensitivity to the particular symbolic form that is used to ex press our intuitions, and so the subject poses some unique and challenging pedagogical issues. The most fundamental ofthese is how to turn the trans fer principle into a working tool of mathematical practice. I have found it vi Preface unproductive to try to give a proof of this principle by introducing the formal Tarskian semantics for first-order languages and working through the proofofLos's theorem.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 312 pp. Englisch. N° de réf. du vendeur 9781461268413
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Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
Edité par
Springer New York, Springer US, 2012
ISBN 10 : 1461268419
ISBN 13 : 9781461268413
Neuf
Taschenbuch
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - There are good reasons to believe that nonstandard analysis, in some ver sion or other, will be the analysis of the future. KURT GODEL This book is a compilation and development of lecture notes written for a course on nonstandard analysis that I have now taught several times. Students taking the course have typically received previous introductions to standard real analysis and abstract algebra, but few have studied formal logic. Most of the notes have been used several times in class and revised in the light of that experience. The earlier chapters could be used as the basis of a course at the upper undergraduate level, but the work as a whole, including the later applications, may be more suited to a beginning graduate course. This prefacedescribes my motivationsand objectives in writingthe book. For the most part, these remarks are addressed to the potential instructor. Mathematical understanding develops by a mysterious interplay between intuitive insight and symbolic manipulation. Nonstandard analysis requires an enhanced sensitivity to the particular symbolic form that is used to ex press our intuitions, and so the subject poses some unique and challenging pedagogical issues. The most fundamental ofthese is how to turn the trans fer principle into a working tool of mathematical practice. I have found it vi Preface unproductive to try to give a proof of this principle by introducing the formal Tarskian semantics for first-order languages and working through the proofofLos's theorem. N° de réf. du vendeur 9781461268413
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Lectures on the Hyperreals: An Introduction to Nonstandard Analysis
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Springer-Verlag New York Inc., 2012
ISBN 10 : 1461268419
ISBN 13 : 9781461268413
Neuf
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Lectures on the Hyperreals
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Lectures on the Hyperreals
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Etat : New. Print on Demand pp. 312 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam This item is printed on demand. N° de réf. du vendeur 55082067
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Lectures on the Hyperreals
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Etat : New. PRINT ON DEMAND pp. 312. N° de réf. du vendeur 1854510470
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