Probability and random number: a first guide to randomness

"This is a book of elementary probability theory that includes a chapter on algorithmic randomness. It rigorously presents definitions and theorems in computation theory, and explains the meanings of the theorems by comparing them with mechanisms of the computer, which is very effective in the current computer age. Random number topics have not been treated by any books on probability theory, only some books on computation theory. However, the notion of random number is necessary for understanding the essential relation between probability and randomness. The field of probability has changed very much, thus this book will make and leave a big impact even to expert probabilists. Readers from applied sciences will benefit from this book because it presents a very proper foundation of the Monte Carlo method with practical solutions, keeping the technical level no higher than 1st year university calculus."--Page 4 de la couverture.

Publié à l'origine en langue japonaise, en 2014, sous le titre : Kakuritsu to ransū et traduit en anglais par l'auteur.

"This is an english translation of my japanese book Kakuritsu to ransū published by Sugakushobo Co. To that book, professor Masato Takei and Tetsuya Hattori gave me suggestions for better future publication. Indeed, they were very useful in preparing the present english version. Mr. Shin Yokohama at Sugakushobo encouraged me to translate the book. Professor Nicolas Bouleau carrefully read the translated english manuscript, and gave me valuable comments, which helped me improve it."--Préface.

Mathematics of coin tossing -- Random number -- Limit theorem -- Monte Carlo method.