Detlef D. Spalt: A Brief History of Analysis

Cover: 9783031006524 | A Brief History of Analysis | Detlef D. Spalt | Taschenbuch | xxiii

Rückseite: 9783031006524 | A Brief History of Analysis | Detlef D. Spalt | Taschenbuch | xxiii

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

¿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.

Zusammenfassung

Explores the history of mathematical analysis, emphasizing accessibility, clarity, and precision throughout

Offers a unique historical perspective on famous mathematicians, their ideas, and familiar concepts

Examines how analysis was formed, how it has changed over time, and how it continues to evolve today

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2023
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Inhalt:	xxiii 254 S. 23 s/w Illustr. 254 p. 23 illus.
ISBN-13:	9783031006524
ISBN-10:	3031006526
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Spalt, Detlef D.
Hersteller:	Birkhäuser Palgrave Macmillan Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 16 mm
Von/Mit:	Detlef D. Spalt
Erscheinungsdatum:	17.08.2023
Gewicht:	0,429 kg