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3000 Years of Analysis

Mathematics in History and Culture

Birkhäuser

Authors:

  • Presents the history of analysis in its full breadth

  • Describes cultural and historical environments

  • Contains a large number of pictures and figures

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XX
  2. Prologue: 3000 Years of Analysis

    • Thomas Sonar
    Pages 1-16
  3. Continuum and Atomism in Scholasticism

    • Thomas Sonar
    Pages 109-154
  4. Newton and Leibniz – Giants and Opponents

    • Thomas Sonar
    Pages 345-421
  5. Analysis at Every Turn

    • Thomas Sonar
    Pages 629-639
  6. Back Matter

    Pages 641-706

About this book

What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals?

You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.

Keywords

  • calculus
  • continuum
  • differential and integral
  • history of mathematics
  • infinitesimal and indivisible

Reviews

“Advanced school students and well-motivated undergraduates can profitably read it, and it is a very useful general reference for the history of substantial parts of mathematics, placed in the context of contemporary social and political events. … as a readable … and refreshingly detailed account of the whole sweep of ‘infinitesimal methods’ from antiquity to the 1990s, this book is highly recommended.” (Peter Giblin, The Mathematical Gazette, Vol. 107 (570), November, 2023)

“This is a stilted but pleasantly readable English translation with some modifications of the 2016 second edition of the author's book … . The author concludes with an appreciation of the impact of analysis in modern society. … Each major figure is given a short biography, and there is a wealth of illustrations: a painting, sketch or photograph of each person discussed … . He illustrates the thought and practice of mathematicians … .”  (E. J. Barbeau, Mathematical Reviews, June, 2022)

“The work is intended to be broadly accessible and the clearly written text succeeds admirably at its purpose. The volume is profusely illustrated. … The author has pulled together a mass of information and provides copious references to an extensive bibliography for the reader who wishes to delve deeper into particular topics.” (Duncan J. Melville, zbMATH 1471.01004, 2021)


“The book is well referenced. … The diagrams and other visuals are attractive and inviting. Individual personalities or figures in the history of mathematics are discussed in greater depth and color than that in other histories of mathematics. … I very much enjoyed Sonar’s book and can see possible uses for its material in undergraduate history of mathematics courses. Anyone interested in the history of mathematics will find some unique things in this book.” (Steven Deckelman, MAA Reviews, September 19, 2021)

Authors and Affiliations

  • Institut für Analysis Computational Mathematics, Technische Universität Braunschweig, Braunschweig, Germany

    Thomas Sonar

Bibliographic Information

  • Book Title: 3000 Years of Analysis

  • Book Subtitle: Mathematics in History and Culture

  • Authors: Thomas Sonar

  • Translated by: Morton Patricia, Keith William Morton

  • DOI: https://doi.org/10.1007/978-3-030-58223-4

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-58221-0Published: 28 December 2021

  • eBook ISBN: 978-3-030-58223-4Published: 27 December 2021

  • Edition Number: 1

  • Number of Pages: XX, 706

  • Number of Illustrations: 129 b/w illustrations, 267 illustrations in colour

  • Topics: History of Mathematical Sciences

Buy it now

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access