Digital Dice. Computational Solutions to Practical Probability Problems
Books containing interesting problems from probability theory and/or mathematical statistics are very popular among teachers and students. This kind of recreational mathematics offers supplementary material for use in classes. The formulation of problems gives an opportunity of discussing how to construct models in real life. Solutions often lead to seemingly paradoxical results. Sometimes calculations are based on theorems from quite different branches of mathematics, which makes it possible to present the beauty of mathematical thinking. Collections of such problems have been published for many years. Contemporary books containing such material include those by G. J. Székely (Akadémiai Kiadó, Budapest, 1986), P. J. Nahin (Princeton Univ. Press, 2000), H. Tijms (Cambridge Univ. Press, 2004) and also my book (J. Anděl, Wiley, New York, 2001).
In this book the author includes problems that come from some aspect of everyday real life. However, even simply formulated problems may be too hard to be solved analytically. On the other hand, numerical answers can be reached using simulations. This is the main difference between this book and the others. The author first presents a MATLAB code and the results of simulations and only then an analytic solution is given (or outlined) – if it is known. The book is divided into three parts. The first part contains the formulation of the problems with some historical remarks, the second part describes the MATLAB solutions to the problems and the third part is composed of nine appendices. In the appendices, we find some theoretical complements to presented problems. Of course, some additional references to problems presented in the book can be given. For example, an interesting motivation to the material on page 22 can be found in the book by J. Swift (The Math. Teacher, 76, 268-269,1983). I have two critical remarks. In all computations, where a random number generator is used, I strongly recommend fixing the seed at the beginning of calculations. Only in this way can everybody repeat the whole process with the same results. Unfortunately, the author does not use this approach. Secondly, the author presents remarks as a special subsection at the end of each section. I find this annoying; it would be much better to print them as footnotes. In conclusion, though, I believe that this book will find many readers and that the problems presented here will refresh introductory courses in probability theory.