Nonstandard analysis for the working mathematician:
Gespeichert in:
Format: | Elektronisch E-Book |
---|---|
Sprache: | English |
Veröffentlicht: |
Dordrecht [u.a.]
Springer
2015
|
Ausgabe: | 2. ed. |
Schlagworte: | |
Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
Beschreibung: | 1 Online-Ressource (XV, 481 S.) |
ISBN: | 9789401773270 |
DOI: | 10.1007/978-94-017-7327-0 |
Internformat
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Datensatz im Suchindex
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adam_text | NONSTANDARD ANALYSIS FOR THE WORKING MATHEMATICIAN
/
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
NONSTANDARD ANALYSIS FOR THE WORKING MATHEMATICIAN
/
: 2015
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
any_adam_object | 1 |
building | Verbundindex |
bvnumber | BV042788205 |
callnumber-first | Q - Science |
callnumber-label | QA299 |
callnumber-raw | QA299.82 |
callnumber-search | QA299.82 |
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dewey-ones | 515 - Analysis |
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dewey-sort | 3515 |
dewey-tens | 510 - Mathematics |
discipline | Informatik Mathematik |
doi_str_mv | 10.1007/978-94-017-7327-0 |
edition | 2. ed. |
format | Electronic eBook |
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genre | Aufsatzsammlung - Nonstandard-Analysis |
genre_facet | Aufsatzsammlung - Nonstandard-Analysis |
id | DE-604.BV042788205 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T07:09:39Z |
institution | BVB |
isbn | 9789401773270 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028218083 |
oclc_num | 920965163 |
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physical | 1 Online-Ressource (XV, 481 S.) |
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publishDate | 2015 |
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publisher | Springer |
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spelling | Nonstandard analysis for the working mathematician Peter A. Loeb ..., ed. 2. ed. Dordrecht [u.a.] Springer 2015 1 Online-Ressource (XV, 481 S.) txt rdacontent c rdamedia cr rdacarrier Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Number theory Functional Analysis Measure and Integration Operator Theory Game Theory, Economics, Social and Behav. Sciences Mathematical Logic and Foundations Number Theory Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf Aufsatzsammlung - Nonstandard-Analysis Nonstandard-Analysis (DE-588)4137021-1 s DE-604 Loeb, Peter A. Sonstige oth Erscheint auch als Druckausgabe 978-94-017-7326-3 https://doi.org/10.1007/978-94-017-7327-0 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028218083&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028218083&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
spellingShingle | Nonstandard analysis for the working mathematician Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Number theory Functional Analysis Measure and Integration Operator Theory Game Theory, Economics, Social and Behav. Sciences Mathematical Logic and Foundations Number Theory Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd |
subject_GND | (DE-588)4137021-1 |
title | Nonstandard analysis for the working mathematician |
title_auth | Nonstandard analysis for the working mathematician |
title_exact_search | Nonstandard analysis for the working mathematician |
title_full | Nonstandard analysis for the working mathematician Peter A. Loeb ..., ed. |
title_fullStr | Nonstandard analysis for the working mathematician Peter A. Loeb ..., ed. |
title_full_unstemmed | Nonstandard analysis for the working mathematician Peter A. Loeb ..., ed. |
title_short | Nonstandard analysis for the working mathematician |
title_sort | nonstandard analysis for the working mathematician |
topic | Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Number theory Functional Analysis Measure and Integration Operator Theory Game Theory, Economics, Social and Behav. Sciences Mathematical Logic and Foundations Number Theory Mathematik Nonstandard-Analysis (DE-588)4137021-1 gnd |
topic_facet | Mathematics Functional analysis Operator theory Logic, Symbolic and mathematical Number theory Functional Analysis Measure and Integration Operator Theory Game Theory, Economics, Social and Behav. Sciences Mathematical Logic and Foundations Number Theory Mathematik Nonstandard-Analysis Aufsatzsammlung - Nonstandard-Analysis |
url | https://doi.org/10.1007/978-94-017-7327-0 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028218083&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028218083&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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