skip to content
Nonstandard Analysis for the Working Mathematician Preview this item
ClosePreview this item
Checking...

Nonstandard Analysis for the Working Mathematician

Author: Peter A Loeb; Manfred Wolff
Publisher: Dordrecht : Springer Netherlands : Imprint : Springer, 2000.
Series: Mathematics and Its Applications ;, 510.
Edition/Format:   eBook : Bibliographic data : EnglishView all editions and formats
Database:WorldCat
Summary:
This book is addressed to mathematicians working in analysis and its applications. The aim is to provide an understandable introduction to the basic theory of non-standard analysis and to illuminate some of its most striking applications. Problems are posed in all chapters. <br/> The opening chapter of the book presents a simplified form of the general theory that is suitable for the results of calculus and  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Bibliographic data, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Peter A Loeb; Manfred Wolff
ISBN: 9789401141680 9401141681 9780792363415 0792363418
OCLC Number: 840310142
Description: 1 online resource (328 pages).
Contents: I An Introduction to Nonstandard Analysis by Peter A. Loeb --
1 A Simple Introduction to Nonstandard Analysis --
2 An Introduction to General Nonstandard Analysis --
3 Topology and Measure Theory --
II Functional Analysis by Manfred P.H. Wolff --
4 Functional Analysis --
III Measure and Probability Theory and Applications by Horst Osswald and Yeneng Sun --
5 Measure Theory and Integration --
6 Probability Theory --
7 Conventional Operations on Nonstandard Constructions --
IV Economics and Nonstandard Analysis by Yeneng Sun --
8 Nonstandard Analysis in Mathematical Economics.
Series Title: Mathematics and Its Applications ;, 510.
Responsibility: edited by Peter A. Loeb, Manfred Wolff.

Abstract:

This book is addressed to mathematicians working in analysis and its applications. The aim is to provide an understandable introduction to the basic theory of non-standard analysis and to illuminate some of its most striking applications. Problems are posed in all chapters. <br/> The opening chapter of the book presents a simplified form of the general theory that is suitable for the results of calculus and basic real analysis. The presentation is intended to facilitate the acquisition of basic skills in the subject, so that a reader who begins with no background in mathematical logic should find it relatively easy to continue. The book then proceeds with the full theory. <br/> Following Part I, each chapter takes up a different field for applications, beginning with a gentle introduction that even non-experts can read with profit. The remainder of each chapter is then addressed to experts, showing how to use non-standard analysis in the search for solutions of open problems and how to obtain rich new structures that produce deep insights into the field under consideration. The particular applications discussed here are in functional analysis including operator theory, probability theory including stochastic processes, and economics including game theory and financial mathematics. In working through this book the reader should gain many new and helpful insights into the enterprise of mathematics. <br/> Audience: This work will be of interest to specialists whose work involves real functions, probability theory, stochastic processes, logic and foundations. Much of the book, in particular the introductory Part I, can be used in a graduate course.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/840310142> # Nonstandard Analysis for the Working Mathematician
    a schema:Book, schema:CreativeWork ;
    library:oclcnum "840310142" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/ne> ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/350547483#Place/dordrecht> ; # Dordrecht
    rdfs:comment "Unknown 'gen' value: bdt" ;
    schema:about <http://id.worldcat.org/fast/895600> ; # Distribution (Probability theory)
    schema:about <http://id.worldcat.org/fast/1002068> ; # Logic, Symbolic and mathematical
    schema:about <http://id.worldcat.org/fast/1012163> ; # Mathematics
    schema:about <http://dewey.info/class/515.8/e23/> ;
    schema:bookFormat schema:EBook ;
    schema:contributor <http://experiment.worldcat.org/entity/work/data/350547483#Person/wolff_manfred> ; # Manfred Wolff
    schema:creator <http://viaf.org/viaf/64067471> ; # Peter A. Loeb
    schema:datePublished "2000" ;
    schema:description "This book is addressed to mathematicians working in analysis and its applications. The aim is to provide an understandable introduction to the basic theory of non-standard analysis and to illuminate some of its most striking applications. Problems are posed in all chapters.
The opening chapter of the book presents a simplified form of the general theory that is suitable for the results of calculus and basic real analysis. The presentation is intended to facilitate the acquisition of basic skills in the subject, so that a reader who begins with no background in mathematical logic should find it relatively easy to continue. The book then proceeds with the full theory.
Following Part I, each chapter takes up a different field for applications, beginning with a gentle introduction that even non-experts can read with profit. The remainder of each chapter is then addressed to experts, showing how to use non-standard analysis in the search for solutions of open problems and how to obtain rich new structures that produce deep insights into the field under consideration. The particular applications discussed here are in functional analysis including operator theory, probability theory including stochastic processes, and economics including game theory and financial mathematics. In working through this book the reader should gain many new and helpful insights into the enterprise of mathematics.
Audience: This work will be of interest to specialists whose work involves real functions, probability theory, stochastic processes, logic and foundations. Much of the book, in particular the introductory Part I, can be used in a graduate course.
"@en ;
    schema:description "I An Introduction to Nonstandard Analysis by Peter A. Loeb -- 1 A Simple Introduction to Nonstandard Analysis -- 2 An Introduction to General Nonstandard Analysis -- 3 Topology and Measure Theory -- II Functional Analysis by Manfred P.H. Wolff -- 4 Functional Analysis -- III Measure and Probability Theory and Applications by Horst Osswald and Yeneng Sun -- 5 Measure Theory and Integration -- 6 Probability Theory -- 7 Conventional Operations on Nonstandard Constructions -- IV Economics and Nonstandard Analysis by Yeneng Sun -- 8 Nonstandard Analysis in Mathematical Economics."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/350547483> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/350547483#Series/mathematics_and_its_applications> ; # Mathematics and Its Applications ; ;
    schema:isSimilarTo <http://worldcat.org/entity/work/data/350547483#CreativeWork/> ;
    schema:name "Nonstandard Analysis for the Working Mathematician"@en ;
    schema:productID "840310142" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/840310142#PublicationEvent/dordrecht_springer_netherlands_imprint_springer_2000> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/350547483#Agent/springer> ; # Springer
    schema:publisher <http://experiment.worldcat.org/entity/work/data/350547483#Agent/springer_netherlands> ; # Springer Netherlands
    schema:publisher <http://experiment.worldcat.org/entity/work/data/350547483#Agent/imprint> ; # Imprint
    schema:url <http://dx.doi.org/10.1007/978-94-011-4168-0> ;
    schema:url <http://public.eblib.com/choice/publicfullrecord.aspx?p=3106361> ;
    schema:workExample <http://dx.doi.org/10.1007/978-94-011-4168-0> ;
    schema:workExample <http://worldcat.org/isbn/9780792363415> ;
    schema:workExample <http://worldcat.org/isbn/9789401141680> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/840310142> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/350547483#Agent/springer_netherlands> # Springer Netherlands
    a bgn:Agent ;
    schema:name "Springer Netherlands" ;
    .

<http://experiment.worldcat.org/entity/work/data/350547483#Person/wolff_manfred> # Manfred Wolff
    a schema:Person ;
    schema:familyName "Wolff" ;
    schema:givenName "Manfred" ;
    schema:name "Manfred Wolff" ;
    .

<http://experiment.worldcat.org/entity/work/data/350547483#Series/mathematics_and_its_applications> # Mathematics and Its Applications ; ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/840310142> ; # Nonstandard Analysis for the Working Mathematician
    schema:name "Mathematics and Its Applications ; ;" ;
    schema:name "Mathematics and Its Applications ;" ;
    .

<http://id.worldcat.org/fast/1002068> # Logic, Symbolic and mathematical
    a schema:Intangible ;
    schema:name "Logic, Symbolic and mathematical"@en ;
    .

<http://id.worldcat.org/fast/1012163> # Mathematics
    a schema:Intangible ;
    schema:name "Mathematics"@en ;
    .

<http://id.worldcat.org/fast/895600> # Distribution (Probability theory)
    a schema:Intangible ;
    schema:name "Distribution (Probability theory)"@en ;
    .

<http://viaf.org/viaf/64067471> # Peter A. Loeb
    a schema:Person ;
    schema:familyName "Loeb" ;
    schema:givenName "Peter A." ;
    schema:name "Peter A. Loeb" ;
    .

<http://worldcat.org/entity/work/data/350547483#CreativeWork/>
    a schema:CreativeWork ;
    schema:description "Printed edition:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/840310142> ; # Nonstandard Analysis for the Working Mathematician
    .

<http://worldcat.org/isbn/9780792363415>
    a schema:ProductModel ;
    schema:isbn "0792363418" ;
    schema:isbn "9780792363415" ;
    .

<http://worldcat.org/isbn/9789401141680>
    a schema:ProductModel ;
    schema:isbn "9401141681" ;
    schema:isbn "9789401141680" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.