## Little Mathematics Library – The Monte Carlo Method We now come to The Monte Carlo Method by I. M. Sobol in the Little Mathematics Library series. The book has a random number table as one of the appendices, which is sort of out dated, when we have access to computers so easily. In the Preface the author says:

Everybody had at some moment used the words “probability”
and “random variable”. The intuitive idea of the probability (considered as frequency) corresponds more or less to the true meaning of this concept. But as a rule the intuitive idea of the random variable differs quite considerably from the mathematical definition. Thus, the notion of the probability is assumed known in Sec. 2, and only the more complicated notion of the random variable is clarified. This section cannot replace a course in the probability
theory: the presentation is simplified and proofs are omitted.
But it still presents certain concept of the random variables sufficient for understanding of Monte Carlo techniques.

The basic aim of this book is to prompt the specialists in various branches of knowledge to the fact that there are problems in their fields that can be solved by the Monte Carlo method.

The book was translated from the Russian by V. I. Kisin and was first published by Mir in 1975. This book was also published as Popular Lectures in Mathematics by University of Chicago in 1974, and this edition was translated by by Robert Messer, John Stone, and
Peter Fortini.

Preface 7
Introduction 9
Sec. 1. General 9
Chapter I. Simulation of Random Variables 14
Sec. 2. Random Variables. 14
Sec. 3. Generation of Random Variables by Electronic Computers 25
Sec. 4. Transformations of Random Variables 30
Chapter II. Examples of Application of the Monte Carlo Method 39
Sec. 5. Simulation of a Mass Servicing System 39
Sec. 6. Computation or Quality and Reliability of Complex Devices 44
Sec. 7. Computation of Neutron Transmission Through a Plate 51
Sec. 8. Calculation of a Definite Integral 58
Appendix 64
Sec. 9. Proofs of Selected Statements 64
Sec. 10. On Pseudo-Random Numbers  70
Random Number Table 74
Bibliography 77

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### 5 Responses to Little Mathematics Library – The Monte Carlo Method

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