The history of approximation theory : from Euler to Bernstein

This book traces the history of approximation theory from Leonhard Euler's cartographic investigations at the end of the 18th century to the early 20th century work of Sergei Bernstein defining a new branch of function theory. Two different schools of thought are treated: the Russian group, employing almost exclusively algebraic methods, and Western mathematicians, who developed a more analytical approach. The author presents a mathematical analysis of the subject together with a discussion of the philosophical underpinnings demonstrated by the differences in approach. The exposition is exciting:  history, philosophy, and mathematics are integrated. While demonstrating excellent technical control of the underlying mathematics, the work is focused on the essential results in the development of the theory. The exposition begins with a history of the forerunners of modern approximation theory, i.e. Euler, Laplace, and Fourier. It then plunges into the work of Chebyshev - his overall philosophy of mathematics - and the Saint Petersburg Mathematical School, with the key focus on the roles played by Zolotarev and the Markov brothers. The Russian approach is contrasted with that of Weierstrass' as well as the Gottingen school led by Hilbert and Klein. The final chapter stresses the important work of Sergei Bernstein who, in extending the work of Chebyshev and giving a constructive proof of the Weierstrass theorem, unifies East and West in their approaches to approximation theory. Biographical data about some sixty eminent mathematicians and an excellent index round out the work. Historians as well as students interested in the history of mathematics will find this book useful. TOC:Preface * Introduction * Forerunners * Pafnutii L'vovic Cebyshev * St. Petersburg Mathematical School * Developments Outside of Russia * Constructive Function Theory * Biographies of other Contributors * Explanations * Translations of Original Documents * Bibliography

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• ISBN: 9780817643539 ; 0817643532
• Dimensions: 24 cm
• Extent: XIX, 219 S.
• Language: Englisch
• Notes: Literaturverz. S. 201 - 216

Classification and Topics

• Classification: Mathematik
• Keyword: Geschichte Anfänge-1919 ; Approximationstheorie

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Boston, Basel, Berlin
• (who): Birkhäuser
• (when): 2006
• Creator: Steffens, Karl-Georg

Further information

• Table of contents: https://d-nb.info/971959013/04
• Rights: Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
• Last update: 11.03.2025, 11:54 AM CET