Nonstandard Analysis for the Working Mathematician

Autor: Peter A. Loeb, Manfred P. H. Wolff

Jazyk:

Väzba: Brožovaná

Vydavateľ: Springer

Dostupnosť: Skladom u dodávateľa

Odosielame za 5-8 dní

110.09 €

Starting with a simple formulation accessible to all mathematicians, this second edition is designed...

Informácie o knihe

Autor

Peter A. Loeb, Manfred P. H. Wolff

Jazyk

Angličtina

Väzba

Kniha - Brožovaná

Vydalo

2016

Stránok

481

EAN

9789401776240

ISBN

9401776245

Enbook ID

15366653

Vydavateľ

Springer

Hmotnosť

7489

Rozmery

155 x 235 x 27

Kompletný popis

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.

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