Hiroshi Sugita - Böcker

This volume is the Proceedings of the international conference on Probability and Number Theory held at Kanazawa, Japan, in June 2005, and includes several survey articles on probabilistic number theory, and research papers on various recent topics around the border area between probability theory and number theory. This volume is useful for all researchers and graduate students who are interested in probability theory and number theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

Although the Monte Carlo method is used in so many fields, its mathematical foundation has been weak until now because of the fundamental problem that a computer cannot generate random numbers. This book presents a strong mathematical formulation of the Monte Carlo method which is based on the theory of random number by Kolmogorov and others and that of pseudorandom number by Blum and others. As a result, we see that the Monte Carlo method may not need random numbers and pseudorandom numbers may suffice. In particular, for the Monte Carlo integration, there exist pseudorandom numbers which serve as complete substitutes for random numbers.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

Though there has been much discussion on the academic aspects of Japanese education abroad (e.g., high scores on international tests, lesson study), there has been little information on the non-academic aspects of Japanese schooling. This non-academic aspect is called Tokkatsu (tokubetsu katsudo).Unlike math and reading, Tokkatsu is not confined to a certain period, but extends throughout the school day and even after-school activities — such as school excursions. It includes classroom activities such as classroom discussions, morning and afternoon meetings that take place daily, cleaning and serving lunch, school events such as sports day, school excursions, student councils, and club activities. Such activities occur every single day, throughout one's school years, from elementary school (actually, even kindergarten) to high school. They are, however, bound together by the common goals of the Tokkatsu framework.This book is the foremost attempt to address a gap in English literature on Tokkatsu.

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.