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Nonstandard Analysis for the Working Mathematician
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor Corporativo: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Dordrecht :
Springer Netherlands : Imprint: Springer,
2015.
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| Edición: | 2nd ed. 2015. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-94-017-7327-0 | ||
| 003 | DE-He213 | ||
| 005 | 20220117223322.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 150826s2015 ne | s |||| 0|eng d | ||
| 020 | |a 9789401773270 |9 978-94-017-7327-0 | ||
| 024 | 7 | |a 10.1007/978-94-017-7327-0 |2 doi | |
| 050 | 4 | |a QA319-329.9 | |
| 072 | 7 | |a PBKF |2 bicssc | |
| 072 | 7 | |a MAT037000 |2 bisacsh | |
| 072 | 7 | |a PBKF |2 thema | |
| 082 | 0 | 4 | |a 515.7 |2 23 |
| 245 | 1 | 0 | |a Nonstandard Analysis for the Working Mathematician |h [electronic resource] / |c edited by Peter A. Loeb, Manfred P. H. Wolff. |
| 250 | |a 2nd ed. 2015. | ||
| 264 | 1 | |a Dordrecht : |b Springer Netherlands : |b Imprint: Springer, |c 2015. | |
| 300 | |a XV, 481 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Measure theory. | |
| 650 | 0 | |a Operator theory. | |
| 650 | 0 | |a Game theory. | |
| 650 | 0 | |a Mathematical logic. | |
| 650 | 0 | |a Number theory. | |
| 650 | 1 | 4 | |a Functional Analysis. |
| 650 | 2 | 4 | |a Measure and Integration. |
| 650 | 2 | 4 | |a Operator Theory. |
| 650 | 2 | 4 | |a Game Theory. |
| 650 | 2 | 4 | |a Mathematical Logic and Foundations. |
| 650 | 2 | 4 | |a Number Theory. |
| 700 | 1 | |a Loeb, Peter A. |e editor. |4 edt |4 http://id.loc.gov/vocabulary/relators/edt | |
| 700 | 1 | |a Wolff, Manfred P. H. |e editor. |4 edt |4 http://id.loc.gov/vocabulary/relators/edt | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9789401773263 |
| 776 | 0 | 8 | |i Printed edition: |z 9789401773287 |
| 776 | 0 | 8 | |i Printed edition: |z 9789401776240 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-94-017-7327-0 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||