A conference on Nonstandard Methods and Applications in Mathematics (NS2002) was held in Pisa, Italy from June 12-16, 2002. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. In addition to the important philosophical achievement of providing a sound mathematical basis for using infinitesimals in analysis, the methodology is now well established as a tool for both research and teaching, and has become a fruitful field of investigation in its own right. This book is a collection of peer-reviewed papers solicited from some of the participants of this conference with the aim of providing something more timely than a textbook, but less ephemeral than a conventional proceedings. It contains both survey papers and research articles with special consideration for one, "Nonstandard analysis at pre-university level: naive magnitude analysis" in which the author discusses his experience teaching calculus through an infinitesimal approach.
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About the Author
Nigel J. Cutland is a professor of Pure Mathematics at the University of Hull where he researches logic and foundations of mathematics, stochastic analysis, and nonstandard analysis and its applications. Mauro Di Nasso is a professor at the Universita di Pisa where he researches model theory and nonstandard analysis. David A. Ross is a professor at the University of Hawaii, Honolulu where he researches nonstandard analysis and probability theory.
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Inside This Book
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First Sentence:
Introduction. Since the original work [39, 40] by Abraham Robinson, many different presentations to the methods of nonstandard analysis have been proposed over the last forty years. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
American Mathematical Society, Approximation Theorem, Power Set, New York, Mathematics Edited, Ross Lecture Notes, Bounded Idealization, Axiom of Standardization, Standard Size Choice, Standard Size Collection, Academic Press, Cambridge University Press, Los's Theorem, Peter Loeb, Bounded Enlarging, Kluwer Acad, Mathematica Japonica, Studia Logica, Well-Ordering Principle, Abraham Robinson, Fundamenta Mathematicae, Mathematics Subject Classification, Normal Form Theorem New!
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Introduction. Since the original work [39, 40] by Abraham Robinson, many different presentations to the methods of nonstandard analysis have been proposed over the last forty years. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
American Mathematical Society, Approximation Theorem, Power Set, New York, Mathematics Edited, Ross Lecture Notes, Bounded Idealization, Axiom of Standardization, Standard Size Choice, Standard Size Collection, Academic Press, Cambridge University Press, Los's Theorem, Peter Loeb, Bounded Enlarging, Kluwer Acad, Mathematica Japonica, Studia Logica, Well-Ordering Principle, Abraham Robinson, Fundamenta Mathematicae, Mathematics Subject Classification, Normal Form Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 16
books:
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cites this book:
- Descriptive Set Theory and Forcing: How to prove theorems about Borel sets the hard way (Lecture Notes in Logic) by Arnold Miller in Back Matter
- Model Theory, Third Edition (Studies in Logic and the Foundations of Mathematics) by C.C. Chang in Back Matter
- The Core Model Iterability Problem (Lecture Notes in Logic) by John Steel in Back Matter
- Pure Mathematics 3 & 4 (Advanced Modular Mathematics) (v. 3 & 4) by Graham Smithers on page 121
- Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman, Lecture Notes in Logic 15 by Wilfried Sieg in Back Matter
See all 16 books this book cites
- Nonstandard Methods and Applications in Mathematics (Lecture Notes in Logic) by Nigel J. Cutland on 11 pages
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