Cauchy's Cours d'analyse: An Annotated Translation

by Robert E. Bradley, C. Edward Sandifer

Overview

In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d’analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d’analyse.

For this translation, the authors have also added commentary, notes, references, and an index.

Product Details

ISBN-13:	9781441905482
Publisher:	Springer New York
Publication date:	08/18/2009
Series:	Sources and Studies in the History of Mathematics and Physical Sciences
Edition description:	2009
Pages:	412
Product dimensions:	6.20(w) x 9.20(h) x 1.20(d)

Table of Contents

On real functions..- On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases..- On symmetric functions and alternating functions. The use of these functions for the solution of equations of the first degree in any number of unknowns. On homogeneous functions..- Determination of integer functions, when a certain number of particular values are known. Applications..- Determination of continuous functions of a single variable that satisfy certain conditions..- On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series..- On imaginary expressions and their moduli..- On imaginary functions and variables..- On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series..- On real or imaginary roots of algebraic equationsfor which the left-hand side is a rational and integer function of one variable. The solution of equations of this kind by algebra or trigonometry..- Decomposition of rational fractions..- On recurrent series..

Editorial Reviews

From the book reviews:

“The annotations show that the translators had not only the expert historian in mind, but also a general mathematical reader. Apparently, beginning students of mathematics are also intended as possible readers. … This is not only useful for a reader with a better command of English than of French, but also for anybody who intends to write a professional historical paper in English in which he has to quote from Cauchy’s book. This book is useful and well done.” (Hans Niels Jahnke, Historia Mathematica, Vol. 39, 2012)

“The majority of mathematical activity now takes place in English … so this translation is especially welcome. … It is a mathematical delight to read through this book. … Cauchy carefully built the subject up from the most elementary ideas in algebra and arithmetic. … Readers of this review should encourage their libraries to get this book, and anyone interested in the history of mathematical analysis will want to own a copy.” (Judith V. Grabiner, BSHM Bulletin, Vol. 26, 2011)

“Bradley (Adelphi Univ.) and Sandifer (Western Connecticut State Univ.) have written an annotated, indexed translation of Cauchy’s classic textbook from 1821. The work’s most interested readers will probably be students and researchers of the history and philosophy of mathematics education, and education in general. … it will be valuable for specialized historical collections. Summing Up: Essential. … academic history of mathematics education and history of science collections, lower-division undergraduates and above.” (M. Bona, Choice, Vol. 47 (6), February, 2010)

“It covers real functions, continuity, simultaneous linear equations, interpolation by polynomials, special functional equations, convergent and divergent series, complex numbers, functions and series, the fundamental theorem of algebra, the numerical solution of equations and infinite products, among other things. The translators provide a preface, about 200 (mostly brief) footnotes and a bibliography of 64 items. … The footnotes and bibliography give, or lead to, useful information on historical questions.” (M. E. Muldoon, Mathematical Reviews, Issue 2010 h)

"The book under review comes equipped with a well-written Translator’s Preface, full of interesting and relevant historical data, placing Cauchy’s work in the present connection in the proper historical context. … Cauchy’s Cours d’analyse, An Annotated Translation is a major contribution to mathematical historical scholarship, and it is most welcome indeed to have occasion to examine the infancy of a part of modern analysis, to recognize familiar things in archaic and even arcane phrasings … and, through it all, to witness a grandmaster in action." (Michael Berg, The Mathematical Association of America, November, 2009)

From the Publisher