Robert Goldblatt: Lectures on the Hyperreals

Cover: 9781461268413 | Lectures on the Hyperreals | An Introduction to Nonstandard Analysis

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Sprache: Englisch

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Beschreibung

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.).

Zusammenfassung

Inhaltsverzeichnis

I Foundations.- 1 What Are the Hyperreals?.- 2 Large Sets.- 3 Ultrapower Construction of the Hyperreals.- 4 The Transfer Principle.- 5 Hyperreals Great and Small.- II Basic Analysis.- 6 Convergence of Sequences and Series.- 7 Continuous Functions.- 8 Differentiation.- 9 The Riemann Integral.- 10 Topology of the Reals.- III Internal and External Entities.- 11 Internal and External Sets.- 12 Internal Functions and Hyperfinite Sets.- IV Nonstandard Frameworks.- 13 Universes and Frameworks.- 14 The Existence of Nonstandard Entities.- 15 Permanence, Comprehensiveness, Saturation.- V Applications.- 16 Loeb Measure.- 17 Ramsey Theory.- 18 Completion by Enlargement.- 19 Hyperfinite Approximation.- 20 Books on Nonstandard Analysis.

Details

Erscheinungsjahr:	2012
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 293 S.
ISBN-13:	9781461268413
ISBN-10:	1461268419
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Goldblatt, Robert
Hersteller:	Springer Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 17 mm
Von/Mit:	Robert Goldblatt
Erscheinungsdatum:	03.10.2012
Gewicht:	0,476 kg