語系:
繁體中文
English
說明(常見問題)
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Nonstandard analysis for the working...
~
Loeb, Peter A.
Nonstandard analysis for the working mathematician
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/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. -
電子資源:
http://dx.doi.org/10.1007/978-94-017-7327-0
ISBN:
9789401773270
Nonstandard analysis for the working mathematician
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:
904380
Nonstandard mathematical analysis.
LC Class. No.: QA299.82
Dewey Class. No.: 515
Nonstandard analysis for the working mathematician
LDR
:02873nam a2200325 a 4500
001
837290
003
DE-He213
005
20160310104449.0
006
m d
007
cr nn 008maaau
008
160421s2015 ne s 0 eng d
020
$a
9789401773270
$q
(electronic bk.)
020
$a
9789401773263
$q
(paper)
024
7
$a
10.1007/978-94-017-7327-0
$2
doi
035
$a
978-94-017-7327-0
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA299.82
072
7
$a
PBKF
$2
bicssc
072
7
$a
MAT037000
$2
bisacsh
082
0 4
$a
515
$2
23
090
$a
QA299.82
$b
.N814 2015
245
0 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.
260
$a
Dordrecht :
$c
2015.
$b
Springer Netherlands :
$b
Imprint: Springer,
300
$a
xv, 481 p. :
$b
ill., digital ;
$c
24 cm.
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
Nonstandard mathematical analysis.
$3
904380
650
1 4
$a
Mathematics.
$3
527692
650
2 4
$a
Functional Analysis.
$3
672166
650
2 4
$a
Measure and Integration.
$3
672015
650
2 4
$a
Operator Theory.
$3
672127
650
2 4
$a
Game Theory, Economics, Social and Behav. Sciences.
$3
669497
650
2 4
$a
Mathematical Logic and Foundations.
$3
669393
650
2 4
$a
Number Theory.
$3
672023
700
1
$a
Loeb, Peter A.
$3
907586
700
1
$a
Wolff, Manfred P. H.
$3
1068012
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer eBooks
856
4 0
$u
http://dx.doi.org/10.1007/978-94-017-7327-0
950
$a
Mathematics and Statistics (Springer-11649)
筆 0 讀者評論
多媒體
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼[密碼必須為2種組合(英文和數字)及長度為10碼以上]
登入