Verwandte Artikel zu Lectures on the Hyperreals: An Introduction to Nonstandard...
Lectures on the Hyperreals: An Introduction to Nonstandard Analysis: 188 (Graduate Texts in Mathematics) - Softcover
Inhaltsangabe
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.).
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Críticas
R. Goldblatt
Lectures on the Hyperreals
An Introduction to Nonstandard Analysis
"Suitable for a graduate course . . . could be covered in an advanced undergraduate course . . . The author’s ideas on how to achieve both intelligibility and rigor . . . will be useful reading for anyone intending to teach nonstandard analysis."―AMERICAN MATHEMATICAL SOCIETY
Reseña del editor
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.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
EUR 122,37
EUR 28,84 für den Versand von Vereinigtes Königreich nach Deutschland
Versandziele, Kosten & DauerNeu kaufen
Diesen Artikel anzeigen
EUR 60,06
Gratis für den Versand innerhalb von/der Deutschland
Versandziele, Kosten & DauerWeitere beliebte Ausgaben desselben Titels
Suchergebnisse für Lectures on the Hyperreals: An Introduction to Nonstandard...
Foto des Verkäufers
Lectures on the Hyperreals
Print-on-DemandAnbieter: moluna, Greven, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Zustand: 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. Bestandsnummer des Verkäufers 4189479
Anzahl: Mehr als 20 verfügbar
Foto des Verkäufers
Lectures on the Hyperreals
Verlag:
Springer New York, Springer US Okt 2012, 2012
ISBN 10: 1461268419
ISBN 13: 9781461268413
Neu
Taschenbuch
Anbieter: buchversandmimpf2000, Emtmannsberg, BAYE, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Taschenbuch. Zustand: 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. Bestandsnummer des Verkäufers 9781461268413
Anzahl: 2 verfügbar
Foto des Verkäufers
Lectures on the Hyperreals
Print-on-DemandAnbieter: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Taschenbuch. Zustand: 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. Bestandsnummer des Verkäufers 9781461268413
Anzahl: 2 verfügbar
Foto des Verkäufers
Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
Verlag:
Springer New York, Springer US, 2012
ISBN 10: 1461268419
ISBN 13: 9781461268413
Neu
Taschenbuch
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Taschenbuch. Zustand: 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. Bestandsnummer des Verkäufers 9781461268413
Anzahl: 1 verfügbar
Beispielbild für diese ISBN
Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics)
Anbieter: Ria Christie Collections, Uxbridge, Vereinigtes Königreich
Verkäuferbewertung 5 von 5 Sternen
Zustand: New. In. Bestandsnummer des Verkäufers ria9781461268413_new
Anzahl: Mehr als 20 verfügbar
Beispielbild für diese ISBN
Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
Anbieter: Chiron Media, Wallingford, Vereinigtes Königreich
Verkäuferbewertung 4 von 5 Sternen
PF. Zustand: New. Bestandsnummer des Verkäufers 6666-IUK-9781461268413
Anzahl: 10 verfügbar
Beispielbild für diese ISBN
Lectures on the Hyperreals: An Introduction to Nonstandard Analysis
Verlag:
Springer-Verlag New York Inc., 2012
ISBN 10: 1461268419
ISBN 13: 9781461268413
Neu
Paperback / softback
Anbieter: THE SAINT BOOKSTORE, Southport, Vereinigtes Königreich
Verkäuferbewertung 5 von 5 Sternen
Paperback / softback. Zustand: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 475. Bestandsnummer des Verkäufers C9781461268413
Anzahl: Mehr als 20 verfügbar
Beispielbild für diese ISBN
Lectures on the Hyperreals
Anbieter: Books Puddle, New York, NY, USA
Verkäuferbewertung 4 von 5 Sternen
Zustand: New. pp. 312. Bestandsnummer des Verkäufers 2654510476
Anzahl: 4 verfügbar
Beispielbild für diese ISBN
Lectures on the Hyperreals
Print-on-DemandAnbieter: Biblios, Frankfurt am main, HESSE, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Zustand: New. PRINT ON DEMAND pp. 312. Bestandsnummer des Verkäufers 1854510470
Anzahl: 4 verfügbar
Beispielbild für diese ISBN
Lectures on the Hyperreals
Print-on-DemandAnbieter: Majestic Books, Hounslow, Vereinigtes Königreich
Verkäuferbewertung 5 von 5 Sternen
Zustand: 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. Bestandsnummer des Verkäufers 55082067
Anzahl: 4 verfügbar