3000 years of analysis : mathematics in history and culture / Thomas Sonar; Patricia Morton; Keith William Morton.

Format:

Book

Author/Creator:

Sonar, Th. (Thomas), author.

Contributor:

Morton, K. W., translator.

Morton, Patricia, translator.

Language:

English

Subjects (All):

Mathematical analysis--History.

Mathematical analysis.

Physical Description:

1 online resource (XX, 706 p. 396 illus., 267 illus. in color.)

Edition:

1st ed. 2021.

Place of Publication:

Cham, Switzerland : Birkhäuser, [2021]

Summary:

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. From the reviews of the German edition: Three wishes granted at once: the book “3000 Jahre Analysis” is anything but a dry mixture of mathematical facts and formulae. Instead, it is a skillful blend of textbook, nonfiction, and history book rolled into one, which has been very vibrantly written. The author Thomas Sonar has managed to present the history of Analysis vividly, thrillingly, and full of intriguing details. Florian Modler, Spektrum der Wissenschaft The book [...] is simply wonderful. Everybody [...] picks up this book with a certain expectation, of course, and they won’t be disappointed! ... It is truly fun browsing the book. Peter Littelmann, Mitteilungen der DMV.

Contents:

Prologue: 3000 Years of Analysis

The Continuum in Greek-Hellenistic Antiquity

How Knowledge Migrates – From Orientto Occident

Continuum and Atomismin Scholasticism

Indivisibles and Infinitesimals in the Renaissance

At the Turn from the 16th to the 17thCentury

Newton and Leibniz-Giants and Opponents

Absolutism ,Enlightenment, Departure to New Shores

On the Way to Conceptual Rigourin the 19th Century

At theTurn to the 20th Century: Set Theory and the Search for the True Continuum

Coming to full circle: Infinitesimals in Nonstandard Analysis.

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

3-030-58223-X