ABSTRACT

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book discusses the fundamental works by S. N. Bernshtein, R. von Mises, and A. N. Kolmogorov which are the basis of modern probability theory. It presents the basis of probability theory – a mathematical discipline studying the principle of random events. The book examines P. L. Chebyshev's results connected with the Law of Large Numbers, Markov chains, and Lyapounov's central limit theorem. It shows that the outstanding scientists analyzing hazard games foresaw a fundamental philosophical role of the science of studying random events. The philosophical basis for the use of probability theory lies in the fact that "mass" phenomena generate new principles. The development of the natural sciences, especially physics, confirms the extreme usefulness of probability theory for the purposes of mathematical modelling.