The Rise and Development of the Theory of Series up to the Early 1820s (Sources and Studies in the History of Mathematics and Physical Sciences) - Hardcover

Ferraro, Giovanni

Hardcover

ISBN 10: 0387734678 ISBN 13: 9780387734675

Publisher: Springer, 2007

Synopsis

The manuscript gives a coherent and detailed account of the theory of series in the eighteenth and early nineteenth centuries. It provides in one place an account of many results that are generally to be found - if at all - scattered throughout the historical and textbook literature. It presents the subject from the viewpoint of the mathematicians of the period, and is careful to distinguish earlier conceptions from ones that prevail today.

About this title

From the Back Cover:

The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Most of the results derived from this time were derived using methods which would be found unacceptable today, and as a result, when one looks back to the theory of series prior to Cauchy without reconstructing internal motivations and the conceptual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a magician or diviner rather than the penetrating and complex work of great mathematicians.

 

This monograph not only describes the entire complex of 17th and 18th century procedures and results concerning series, but it also reconstructs the implicit and explicit principles upon which they are based, draws attention to the underlying philosophy, highlights competing approaches, and investigates the mathematical context where the theory originated. The aim here is to improve the understanding of the framework of 17th and 18th century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some sense, to a unified theory that has come down to us today.

 

Giovanni Ferraro is Professor of Mathematics and History of Mathematics at University of Molise.

Review:

From the reviews:

"Giovanni Ferraro’s book must be regarded as an important contribution to the history of mathematical analysis ... . In summary, this book is thoroughly researched; it is written with a high degree of accuracy, and the broad range of fascinating material is, in general, very well organized. Therefore ... every college and university library should have a copy. In fact, extracts from the book could be used to inject historical perspectives into courses on analysis, and it will certainly appeal to historians in general." (Peter Ruane, MathDL, April, 2008)

"The work is thoroughly referenced and should prove valuable to mathematical history researchers ... . Summing Up: Recommended. Researchers/faculty and professionals." (C. Bauer, CHOICE, Vol. 46 (01), September, 2008)

"The author begins his detailed account with the arrival of the calculus with Newton and Leibniz, and their own treatments of series. ... The range of series and functions treated is impressive ... . The story stops with a brief notice of the start of the critical phase, especially concerning the convergence (or not) of infinite series, which was put forward by Cauchy and his followers ... . The book is a valuable contribution, possibly the single most substantial source on the topic." (I. Grattan-Guinness, Mathematical Reviews, Issue 2008 k)

About this edition

• Publisher: Springer
• Publication date: 2007
• ISBN 10: 0387734678
• ISBN 13: 9780387734675
• Binding: Hardcover
• Number of pages: 408