AUTHOR'S PREFACE
IT has been my experience in dealing with the subjects of the syllabus for Part I of the Examinations of the Institute of Actuaries that it is essential to interest the student in the subject and then, when his interest has been aroused, to supply him with numerous examples illustrative of the principles that have been expounded. This is of particular importance when treating of Finite Differences and Probability, which are almost invariably new to the student. In pursuance of the first of these aims, I have had no compunction when occasion has arisen in wandering from the strict confines of the examination syllabus. For example, a little information on modern symbolic notation, or a paragraph on osculatory interwhile not essential to the immediate needs of the Part I student, may however prove of interest to him and, it is hoped, may stimulate him to further researches. Again, in accordance with my belief for the necessity for examples, I have included in the text many varied types of question and have set numerous examples for solution. The student should find considerable scope for his industry and ingenuity in working the examples set after each chapter and at the end of the book.
I have been fortunate in the assistance rendered me by my friends. In the first place, my sincerest thanks are due to Mr D. C. Fraser and Mr G. Green, who read through the book in manuscript and who were always willing to confer with me at any time and on any subject connected with the book. Then again, my colleagues on the panel of Tutors, Mr C. D. Rich and Mr C. W. Sanger, have renme much help at various stages of the work, for which I am very grateful. Finally I am deeply indebted to Mr S. H. Alison and Mr G. J. Lidstone for their expert advice. Mr Alison's suggestions on the chapters dealing with Limits and the elements of the Calculus were particularly valuable. Mr Lidstone not only read the whole of the proofs, but put at my disposal his unique knowledge of actuarial mathematics. It would not be too much to say that certain of the chapters on Finite Differences would have presented a commeagre appearance had it not been for the inspiration afforded by the published writings and the helpful suggestions of Mr Fraser and Mr Lidstone.
H. F.
December, 1930
PREFACE TO THE SECOND EDITION
IN this edition no material alterations have been made either in the text or in the examples. Effect has been given to a number of minor amendments, principally in the examples and in the answers thereto, and in a few instances an improvement has been made in the text in order to render the meaning clearer and to remove any possible ambiguity.
My thanks are due to the many correspondents who have written to me on matters connected with the book. In particular I should like to express my gratitude to Professor L. S. Vaidyanathan who forwarded to me from Bombay an exhaustive list of queries which afforded valuable assistance in the preparation of this edition.
May, 1932