This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstraß, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today.
A Brief History of Analysis
will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.
Reviews / Votes
"This book is about basic concepts in mathematics, mainly in the field of the definition of number and its relation to analysis. It provides historical facts and discusses their connections with the transformations in what we call today analysis. The style of the book is, I would say, almost journalistic . . The author makes extensive use of italics, framed boxes, inverted commas, exclamation marks and other stylistic devices to attract the attention of the reader . ." (Pelegrí Viader, Mathematical Reviews, February, 2024)
Edition
Language
Place of publication
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
23 s/w Abbildungen
XXIII, 254 p. 23 illus.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 21 mm
Weight
ISBN-13
978-3-031-00649-4 (9783031006494)
DOI
10.1007/978-3-031-00650-0
Schweitzer Classification
¿Detlef D. Spalt verfasste neben einigen Fachaufsätzen mehrere Bücher und gab einen Tagungsband heraus. Er hielt Gastvorlesungen in Salzburg, Marburg, Frankfurt/M und Siegen. Seit seiner Promotion in Mathematik untersucht er die Geschichte seines Faches, indem er insbesondere das Zustandekommen der heutigen mathematischen Grundbegriffe aufzeigt, vorwiegend im Bereich Analysis. Das hier edierte Manuskript stellt seinen bedeutendsten (und glücklichsten) Quellenfund dar.
The Invention of the Mathematical Formula.- Numbers, Distances, Points, but No Crooked Lines.- Lines and Variables.- Individual: An Old Term, or What Does the Continuum Consist of?.- Are There Infinite Numbers? - An Unresolved Argument Between Leibniz and Johann Bernoulli.- Johann Bernoulli's Rules of Differential.- What Does "Equal" Mean?.- Euler Absolutizes Formal Arithmetic.- Accents in Algebraic Analysis, According to Euler.- Bolzano: The Republican Revolutionary of Analysis.- Cauchy: The Bourgeois Revolutionary as a Restorer.- The Interregnum: Analysis on Swampy Ground.- Weierstrass: The Last Attempt at a Substantial Analysis.- The Detachment of Analysis from Reality, and the Introduction of Actual Infinity into the Fundamentals of Mathematics.- Analysis With or Without Paradoxes.
