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 appearance 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.