Mathematics Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (038798464X)

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Author: Robert Goldblatt
Publisher: Springer
Publish Date: 1998
ISBN: 038798464X
Pages: 312

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.). 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, emphasizing the role of the transfer principle as a working tool of mathematical practice. 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, Ramsey's Theorem, nonstandard constructions of p-adic numbers and power series, and nonstandard proofs of the Stone representation theorem for Boolean algebras and the Hahn-Banach theorem. Features of the text include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set- theoretic approach to enlargements than the usual one based on superstructures.

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	Science/Engineering An Introduction to Nonstandard Real Analysis, Volume 118 Albert E. Hurd, Peter A. Loeb “An Introduction to Nonstandard Real Analysis, Volume 118" Academic Press \| 1985-09-28 \| ISBN: 0123624401 \| 232 pages \| PDF \| 9,35 MB The aim of this book is to make Robinson's discovery, and some of the s ...
	Science/Engineering Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics) Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics)Springer \| ISBN: 038798464X \| 1998-10-01 \| PDF \| 312 pages \| 16 Mb This is an introduction to nonstandard analysis based on a course of lectu ...
	Lectures on the Hyperreals - An Introduction to Nonstandard Analysis (GTM 188) (Repost) Robert Goldblatt: "Lectures on the Hyperreals - An Introduction to Nonstandard Analysis"Springer \| English \| Oct 1 1998 \| ISBN: 038798464X \| 309 pages \| PDF \| 17 MbSpringer Graduate Texts in Mathematics #188.This is an introduction to nonst ...
	Technical Fourier Analysis: An Introduction (Princeton Lectures in Analysis, Volume 1) ISBN: 069111384X Publisher: Princeton University Press Author: Elias M. Stein, Rami ShakarchiDescription:This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analys ...
	Technical An Introduction to Nonstandard Real Analysis, Volume 118 (Pure and Applied Mathematics) ISBN: 0123624401 Publisher: Academic Press Author: Albert E. Hurd, Peter A. LoebDescription:The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with a background in undergraduate ...
	Lectures on the Hyperreals - An Introduction to Nonstandard Analysis Lectures on the Hyperreals - An Introduction to Nonstandard AnalysisLectures on the Hyperreals - An Introduction to Nonstandard AnalysisLectures on the Hyperreals - An Introduction to Nonstandard AnalysisSpringer \| English \| Oct 1 1 ...

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	Science/Engineering An Introduction to Nonstandard Real Analysis, Volume 118 Albert E. Hurd, Peter A. Loeb “An Introduction to Nonstandard Real Analysis, Volume 118" Academic Press \| 1985-09-28 \| ISBN: 0123624401 \| 232 pages \| PDF \| 9,35 MB The aim of this book is to make Robinson's discovery, and some of the s ...
	Science/Engineering Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics) Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics)Springer \| ISBN: 038798464X \| 1998-10-01 \| PDF \| 312 pages \| 16 Mb This is an introduction to nonstandard analysis based on a course of lectu ...
	Lectures on the Hyperreals - An Introduction to Nonstandard Analysis (GTM 188) (Repost) Robert Goldblatt: "Lectures on the Hyperreals - An Introduction to Nonstandard Analysis"Springer \| English \| Oct 1 1998 \| ISBN: 038798464X \| 309 pages \| PDF \| 17 MbSpringer Graduate Texts in Mathematics #188.This is an introduction to nonst ...
	Technical Fourier Analysis: An Introduction (Princeton Lectures in Analysis, Volume 1) ISBN: 069111384X Publisher: Princeton University Press Author: Elias M. Stein, Rami ShakarchiDescription:This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analys ...
	Technical An Introduction to Nonstandard Real Analysis, Volume 118 (Pure and Applied Mathematics) ISBN: 0123624401 Publisher: Academic Press Author: Albert E. Hurd, Peter A. LoebDescription:The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with a background in undergraduate ...
	Lectures on the Hyperreals - An Introduction to Nonstandard Analysis Lectures on the Hyperreals - An Introduction to Nonstandard AnalysisLectures on the Hyperreals - An Introduction to Nonstandard AnalysisLectures on the Hyperreals - An Introduction to Nonstandard AnalysisSpringer \| English \| Oct 1 1 ...

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