PREFACE The present volume has grown out of lectures on the mathe- atics of life insurance given at the University of Wisconsin for a imber of years, and is intended primarily as a first course for .ose young men and women who wish to become trained actua- ;s; or as a final course for other students who, for one reason or lother, desire an elementary knowledge of the fundamental athematical principles underlying a vast and growing business our modern world. In this book, with the exception of the few remarks in the troductory chapter, a knowledge of elementary algebra and its )plication to the theory of annuities-certain is assumed. The elementary theory of probability is developed in chapter II ith sufficient fullness to make its application to the theory of mtingent functions clear. A considerable symbolism has grown up in connection with ituarial theory and practice. The attempt is here made to keep lis symbolism as simple as possible while retaining its classic irm. The tables herein included are for illustrative purposes only. lany of the commutation symbols, as well as the Fackler valua- on symbols, were recomputed with the aid of a five-place table of igarithms and are not, therefore, accurate enough where large ims of money are involved. Glover's tables entitled Tables of .pplied Mathematics in Finance, Insurance, Statistics, is particu- irly valuable, not only for the actuary, but for all who have to eal with financial operations or with the application of statistics 3 science in general. While this volume presupposes only a knowledge of elementary lathematics, it is perhaps hardly necessary to remark that the lathematical equipment of the actuary should include a knowl- dge of the calculus. Some examples of the use of this subject vi PREFACE have been added in the Conclusion. Others will be found in advanced treatises on actuarial science or on statistics. These treatises were freely consulted in the preparation of the lectures out of which- this volume has grown. The author desires to express his gratitude to Dean Charles S. Slichter for his aid in seeing the book through the press. L. WAYLAND DOWLING. UNIVERSITY OP WISCONSIN, July, 1925.