3000 Years of Analysis: Mathematics in History and Culture

ISBN-13: 9783030582210 / Angielski / Twarda / 2020 / 706 str.

Thomas Sonar; Morton Patricia; Keith William Morton

Recenzje

"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)

Spis treści

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.

Blurb

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