Steffens K.-G. The History of Approximation Theory: From Euler to Bernstein

Boston: Birkhäuser, 2005. — 219 p. — ISBN: 978-0817643539.Exciting exposition integrates history, philosophy, and mathematics.Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development.Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation.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.Forerunners.
Pafnuti Lvovich Chebyshev.
The Saint Petersburg Mathematical School.
Development Outside Russia.
Constructive Function Theory: Kharkiv.
Biographies.
Explanations.