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Nonstandard analysis for the working mathematician[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515
書名/作者:	Nonstandard analysis for the working mathematician/ edited by Peter A. Loeb, Manfred P.H. Wolff.
其他作者:	Loeb, Peter A.
出版者:	Dordrecht : : Springer Netherlands :, 2015.
面頁冊數:	xv, 481 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Nonstandard mathematical analysis.
標題:	Mathematics.
標題:	Functional Analysis.
標題:	Measure and Integration.
標題:	Operator Theory.
標題:	Game Theory, Economics, Social and Behav. Sciences.
標題:	Mathematical Logic and Foundations.
標題:	Number Theory.
ISBN:	9789401773270
ISBN:	9789401773263
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-94-017-7327-0

Nonstandard analysis for the working mathematician[electronic resource] /
Nonstandard analysis for the working mathematician[electronic resource] /edited by Peter A. Loeb, Manfred P.H. Wolff. - 2nd ed. - Dordrecht :Springer Netherlands :2015. - xv, 481 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9789401773270

Standard No.: 10.1007/978-94-017-7327-0doiSubjects--Topical Terms:

556829
Nonstandard mathematical analysis.

LC Class. No.: QA299.82

Dewey Class. No.: 515

Nonstandard analysis for the working mathematician[electronic resource] /
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