Lectures on constructive mathematical analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
1984
|
| Schriftenreihe: | Translations of mathematical monographs
60 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | V, 346 S. Ill. |
| ISBN: | 0821845136 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | TRANSLATIONS OF MATHEMATICAL MONOGRAPHS
VOLUME 6 0
Lectures on
Constructive
Mathematical Analysis
by B A KUSHNER
American Mathematical Society • Providence • Rhode Island
Table of Contents
Preface v
Introduction 1
CHAPTER 1 Normal Algorithms and Enumerable Sets 29
1 Normal algorithms 29
2 Some undecidable algorithmic problems of the theory of
algorithms 62
3 Decidable and enumerable sets 66
CHAPTER 2 Constructive Real Numbers 79
1 Natural numbers, integers, and rational numbers 79
2 Constructive real numbers (CRNs) Basic definitions 87
3 Equality and order relations on the set of CRNs 90
4 Arithmetic operations on CRNs 105
5 Rational numbers in the constructive continuum 113
CHAPTER 3 Constructive Convergence Effective Uncountability of
the Constructive Continuum 117
1 Basic definitions First theorems on limits 117
2 Completeness of the constructive continuum Nested segments
theorem 121
3 Example of a monotonic, bounded, nonconvergent sequence of
rational numbers 129
4 Effective uncountability of the constructive continuum 134
CHAPTER 4 The Impossibility of Certain Algorithms Connected
With Constructive Real Numbers 139
1 Some algorithmic problems connected with the equality and order
relations on the constructive continuum Applications to algebra 139
2 The impossibility of some algorithms connected with convergence 148
3 Constructive real numbers and systematic expansions 153
iv TABLE OF CONTENTS
CHAPTER 5 Constructive Functions
1 Basic definitions Some examples
2 Properties of continuity Uniformly continuous functions
3 The structure of constructive functions
4 Mean value theorems for constructive functions
CHAPTER 6 Differentiation of Constructive Functions
1 Basic definitions
2 Mean value theorems of differential calculus
3 The impossibility of certain algorithms with differentiation
CHAPTER 7 Riemann Integration of Constructive Functions
1 Basic definitions Theorems on boundedness of integrable
functions
2 Some criteria of integrability Integrability of uniformly
continuous functions Integrability of the absolute value and
product of integrable functions
3 The integral as a function of the upper limit The Newton-Leibn
theorem Theorem on substitution of variables
CHAPTER 8 Singular Coverings and Some of Their Applications
1 Basic definitions Existence of singular coverings
2 Examples of constructive functions with unusual properties
3 Impossibility of certain algorithms connected with integration
CHAPTER 9 Constructive Metric Spaces
1 Constructive metric spaces Basic definitions and some examples
Completion of constructive metric spaces
2 Consistent sets Algorithmic operators Continuity theorem (firs
formulation)
3 Theorem on the choice of an enumerable covering Strong form
the continuity theorem Some counterexamples
Bibliography
Index of Names
Subject Index
Index of Notation
|
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| author_facet | Kušner, Boris Abramovič 1941- |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000352508 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:12:47Z |
| institution | BVB |
| isbn | 0821845136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000219169 |
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| physical | V, 346 S. Ill. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Kušner, Boris Abramovič 1941- Verfasser (DE-588)172202531 aut Lekcii po konstruktivnomu matematičeskomu analizu Lectures on constructive mathematical analysis by B. A. Kushner Providence, R.I. American Mathematical Society 1984 V, 346 S. Ill. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 60 Konstruktive Mathematik (DE-588)4165105-4 gnd rswk-swf Konstruktive Analysis (DE-588)4473957-6 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Konstruktive Analysis (DE-588)4473957-6 s DE-604 Konstruktive Mathematik (DE-588)4165105-4 s Analysis (DE-588)4001865-9 s Translations of mathematical monographs 60 (DE-604)BV000002394 60 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000219169&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kušner, Boris Abramovič 1941- Lectures on constructive mathematical analysis Translations of mathematical monographs Konstruktive Mathematik (DE-588)4165105-4 gnd Konstruktive Analysis (DE-588)4473957-6 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4165105-4 (DE-588)4473957-6 (DE-588)4001865-9 |
| title | Lectures on constructive mathematical analysis |
| title_alt | Lekcii po konstruktivnomu matematičeskomu analizu |
| title_auth | Lectures on constructive mathematical analysis |
| title_exact_search | Lectures on constructive mathematical analysis |
| title_full | Lectures on constructive mathematical analysis by B. A. Kushner |
| title_fullStr | Lectures on constructive mathematical analysis by B. A. Kushner |
| title_full_unstemmed | Lectures on constructive mathematical analysis by B. A. Kushner |
| title_short | Lectures on constructive mathematical analysis |
| title_sort | lectures on constructive mathematical analysis |
| topic | Konstruktive Mathematik (DE-588)4165105-4 gnd Konstruktive Analysis (DE-588)4473957-6 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Konstruktive Mathematik Konstruktive Analysis Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000219169&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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