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Charles Jordan, "Calculus of Finite Differences, 2 Ed. "

INTRODUCTION

There is more than mere coincidence in the fact that the recent rapid growth in the theory and application of mathematical statistics has been accompanied by a revival in interest in the Calculus of Finite Differences. The reason for this phenomena is clear: the student of mathematical statistics must now

regard the finite calculus as just as important a tool and prerequisite as the infinitesimal calculus.

To my mind, the progress that has been made to date in the development of the finite calculus has been marked and stimulated by the appearence of four outstanding texts.

The first of these was the treatise by George Boole that appeared in 1860. I do not me& by this to underestimate the valuable contributions of earlier writers on this subject or to overlook the elaborate work of Lacroix.’ I merely wish to state that Boole was the first to present’ this subject in a form best

suited to the needs of student and teacher.

The second milestone was the remarkable work of Narlund that appeared in 1924. This book presented the first rigorous treatment of the subject, and was written from the point of view of the mathematician rather .than the statistician. It was most oportune. ’ Steffensen’s Interpolation, the third of the four texts to which ‘I have referred, presents an excellent treatment of one section of the Calculus of Finite Differences, namely interpolation and summation formulae, and merits the commendation of both mathematicians and statisticians.

I do not hesitate to predict that the fourth of the texts that 1 Volume 3 of Trait6 du Calcul Diffdrentiel et du Calcul Int&pl,entitled Trait6 des diffbences et des shies. S. F, Lacroix, 1819.

I have in mind, Professor Jordan’s Calculus of Finite Differences, is destined to remain the classic treatment of this subject- especially for statisticians - for many years to come. Although an inspection of the table of contents reveals a coverage so extensive that the work of more than 600 pages might lead one at first to regard this book as an encyclopedia on the subject, yet a reading of any chapter of the text will impress the reader as a friendly lecture revealing an ununsual appreciation of both rigor and the computing technique so important to the statistician.

The author has made a most thorough study of the literature that has appeared during the last two centuries on the calculus of finite differences and has not hesitated in resurrecting for- ’ gotten journal contributions and giving them the emphasis that his long experience indicates they deserve in this day of mathematical statistics.

In a word, Professor Jordan’s work is a most readable and detailed record of lectures on the Calculus of Finite Differences which will certainly appeal tremendously to the statistician and which could have been written only by one possessing a deep appreciation of mathematical statistics.

Harry C. Carver.

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