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*.

The Internet Archive Link

The table of contents for (LML edition) is as follows:

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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Excellent books. Please keep up your extraordinary work. Expect more books.

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