Brief History of Analysis

With Emphasis on Philosophy, Concepts, and Numbers, Including Weierstraß' Real Numbers

Inbunden, Engelska, 2022

AvDetlef D. Spalt

1 169 kr

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This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. 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.

Produktinformation

Utgivningsdatum2022-08-03
Mått155 x 235 x 23 mm
Vikt576 g
FormatInbunden
SpråkEngelska
Antal sidor254
FörlagBirkhauser Verlag AG
ISBN9783031006494
OriginaltitelEine kurze Geschichte der Analysis

Tillhör följande kategorier

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.

“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)