Calculus and Probability for Actuarial Students

From the INTRODUCTION. Actuarial science is peculiarly dependent upon the Theory of Probabilities, the solution of many of its problems is best effected by resort to the Differential and Integral Calculus and in practical work the Calculus of Finite Differences is almost indispensable. Excellent text-books on these subjects are, of course, available but none of them has been written with the special requirements of the actuary in view. In beginning his training the student is, therefore, confronted by the difficulty of judicious selection and in the circumstances it has appeared to the Council of the Institute of Actuaries that a mathematical text-book sufficiently comprehensive, with the standard works on Higher Algebra, to provide the ground- work of an actuarial education would be of great value. At the request of the Council, Mr. Alfred Henry has undertaken the preparation of such a work and the resulting volume is issued in the confident expectation that it will materially lighten the toil of those who essay to qualify themselves for an actuarial career. From the AUTHOR'S PREFACE Actuarial science is essentially practical in that, whilst it is based on the processes of pure mathematics, the object of the worker must be to produce a numerical result. For this reason it is necessary for considerable prominence to be given, in the curriculum of the actuarial student, to the subject of Finite Differences, and it thus becomes convenient, in the study of those subjects not included under the heading of Algebra, to deal with this part of the syllabus first and, notwithstanding certain theoretical objections, to treat the fundamental propositions of the Differential and the Integral Calculus as being, substantially, special cases of similar propositions in Finite Differences. The subjects enumerated cover so wide a field that it has been necessary to exercise considerable compression and to include only such problems as are requisite for a proper knowledge of the subjects within the syllabus. In the chapter on probability it will be seen that the numerical or "frequency" theory of probability has been adopted. Having regard to the practical nature of the actuary's work, it is thought that strict adherence to this aspect of the subject is necessary if the student is to acquire sound views from the outset. The subject of Inverse Probability has been excluded from the examination syllabus in recent years and for this reason it is not introduced into the present work.... wholly alone....