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04098nam a22004935i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-0-8176-4475-8 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20161121231029.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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100301s2006 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780817644758 |
| -- |
978-0-8176-4475-8 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/0-8176-4475-X |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA21-27 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBX |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT015000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510.9 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Steffens, Karl-Georg. |
| Relator term |
author. |
| 245 14 - TITLE STATEMENT |
|---|
| Title |
The History of Approximation Theory |
| Medium |
[electronic resource] : |
| Remainder of title |
From Euler to Bernstein / |
| Statement of responsibility, etc. |
by Karl-Georg Steffens ; edited by George A. Anastassiou. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
Boston, MA : |
| Name of producer, publisher, distributor, manufacturer |
Birkh�user Boston, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2006. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XIX, 219 p. 12 illus. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda0 |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Forerunners -- Pafnuti Lvovich Chebyshev -- The Saint Petersburg Mathematical School -- Development Outside Russia -- Constructive Function Theory: Kharkiv. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc. |
The problem of approximating a given quantity is one of the oldest challenges faced by mathematicians. Its increasing importance in contemporary mathematics has created an entirely new area known as Approximation Theory. The modern theory was initially developed along two divergent schools of thought: the Eastern or Russian group, employing almost exclusively algebraic methods, was headed by Chebyshev together with his coterie at the Saint Petersburg Mathematical School, while the Western mathematicians, adopting a more analytical approach, included Weierstrass, Hilbert, Klein, and others. This work traces the history of approximation theory from Leonhard Euler's cartographic investigations at the end of the 18th century to the early 20th century contributions of Sergei Bernstein in defining a new branch of function theory. One of the key strengths of this book is the narrative itself. The author combines a mathematical analysis of the subject with an engaging discussion of the differing philosophical underpinnings in approach as demonstrated by the various mathematicians. This exciting exposition integrates history, philosophy, and mathematics. While demonstrating excellent technical control of the underlying mathematics, the work is focused on essential results for the development of the theory. The exposition begins with a history of the forerunners of modern approximation theory, i.e., Euler, Laplace, and Fourier. The treatment then shifts to Chebyshev, his overall philosophy of mathematics, and the Saint Petersburg Mathematical School, stressing in particular the roles played by Zolotarev and the Markov brothers. A philosophical dialectic then unfolds, contrasting East vs. West, detailing the work of Weierstrass as well as that of the Goettingen school led by Hilbert and Klein. The final chapter emphasizes the important work of the Russian Jewish mathematician Sergei Bernstein, whose constructive proof of the Weierstrass theorem and extension of Chebyshev's work serve to unify East and West in their approaches to approximation theory. Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation. |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Approximation theory. |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Fourier analysis. |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Sequences (Mathematics). |
| 650 0# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
History.1 |
| 650 4# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics.2 |
| 650 4# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
History of Mathematical Sciences.2 |
| 650 4# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Approximations and Expansions.2 |
| 650 4# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Sequences, Series, Summability.2 |
| 650 4# - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Fourier Analysis.1 |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Anastassiou, George A. |
| Relator term |
editor.2 |
| 710 ## - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service)0 |
| 773 ## - HOST ITEM ENTRY |
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| Title |
Springer eBooks0 |
| 776 8# - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
97808176435394 |
| 856 0# - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
http://dx.doi.org/10.1007/0-8176-4475-X |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
