Items related to Lectures on the Hyperreals: An Introduction to Nonstandard...
Lectures on the Hyperreals: An Introduction to Nonstandard Analysis: 188 (Graduate Texts in Mathematics, 188) - Softcover
Synopsis
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.
"synopsis" may belong to another edition of this title.
Review
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
"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date2012
- ISBN 10 1461268419
- ISBN 13 9781461268413
- BindingPaperback
- LanguageEnglish
- Number of pages307
Other Popular Editions of the Same Title
Search results for Lectures on the Hyperreals: An Introduction to Nonstandard...
Seller Image
Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
Seller: GreatBookPrices, Columbia, MD, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # 19199719-n
Quantity: Over 20 available
Stock Image
Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics)
Seller: California Books, Miami, FL, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # I-9781461268413
Quantity: Over 20 available
Stock Image
Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
Seller: Chiron Media, Wallingford, United Kingdom
Seller rating 5 out of 5 stars
PF. Condition: New. Seller Inventory # 6666-IUK-9781461268413
Quantity: 10 available
Stock Image
Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics)
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. In. Seller Inventory # ria9781461268413_new
Quantity: Over 20 available
Seller Image
Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
Seller: GreatBookPricesUK, Woodford Green, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # 19199719-n
Quantity: Over 20 available
Seller Image
Lectures on the Hyperreals
Published by
Springer New York Okt 2012, 2012
ISBN 10: 1461268419
ISBN 13: 9781461268413
New
Taschenbuch
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: 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. Seller Inventory # 9781461268413
Quantity: 2 available
Stock Image
Lectures on the Hyperreals: An Introduction to Nonstandard Analysis
Published by
Springer-Verlag New York Inc., 2012
ISBN 10: 1461268419
ISBN 13: 9781461268413
New
Paperback / softback
Seller: THE SAINT BOOKSTORE, Southport, United Kingdom
Seller rating 5 out of 5 stars
Paperback / softback. Condition: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 475. Seller Inventory # C9781461268413
Quantity: Over 20 available
Seller Image
Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
Published by
Springer New York, Springer US, 2012
ISBN 10: 1461268419
ISBN 13: 9781461268413
New
Taschenbuch
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: 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. Seller Inventory # 9781461268413
Quantity: 1 available
Seller Image
Lectures on the Hyperreals
Print on DemandSeller: moluna, Greven, Germany
Seller rating 5 out of 5 stars
Condition: 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. Seller Inventory # 4189479
Quantity: Over 20 available
Seller Image
Lectures on the Hyperreals : An Introduction to Nonstandard Analysis
Seller: GreatBookPricesUK, Woodford Green, United Kingdom
Seller rating 5 out of 5 stars
Condition: As New. Unread book in perfect condition. Seller Inventory # 19199719
Quantity: Over 20 available