Nonstandard analysis for the working mathematician [electronic resource] / Peter A. Loeb and Manfred P.H. Wolff, editors.
2015
QA299.82
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Details
Title
Nonstandard analysis for the working mathematician [electronic resource] / Peter A. Loeb and Manfred P.H. Wolff, editors.
Edition
Second edition.
ISBN
9789401773270 electronic book
9401773270 electronic book
9789401773263
9401773270 electronic book
9789401773263
Published
Dordrecht : Springer, 2015.
Copyright
©2015
Language
English
Description
1 online resource.
Item Number
10.1007/978-94-017-7327-0 doi
Call Number
QA299.82
Dewey Decimal Classification
515
Summary
Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a 'secret weapon' by those who know the technique. This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler's internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems. All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (viewed August 31, 2015).
Added Author
Loeb, Peter A., editor.
Wolff, Manfred P.H., editor.
Wolff, Manfred P.H., editor.
Available in Other Form
Print version: 9789401773263
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Table of Contents
Simple Nonstandard Analysis and Applications
An Introduction to General Nonstandard Analysis
Topology and Measure Theory
Banach Spaces and Linear Operators
General and End Compactifications
Measure theory and integration
Stochastic Analysis
New Understanding of Stochastic Independence
Nonstandard Analysis in Mathematical Economics
Density Problems and Freiman's Inverse Problem
Hypernatural numbers as ultrafilters.
An Introduction to General Nonstandard Analysis
Topology and Measure Theory
Banach Spaces and Linear Operators
General and End Compactifications
Measure theory and integration
Stochastic Analysis
New Understanding of Stochastic Independence
Nonstandard Analysis in Mathematical Economics
Density Problems and Freiman's Inverse Problem
Hypernatural numbers as ultrafilters.