History of Science and Engineering Annotation << Back Mathematical Simulation: Stages and Periods of Formation and Development Chepkasov A.I. Staselovich S.V. The history of mathematical simulation, its place in mathematics, the chronology of its development. Lighted the value and relevance of mathematical simulation for use in modern computing tasks. Keywords: mathematical simulation; mathematic; model; period. Relevance of the topic is the fact that the mathematical simulation is an important component of scientific and technological progress. The object of this research is modeling as a specific approach to the study processes of objects of different nature, the underlying cognition and subject of research – mathematical simulation as a methodology of constructing, research and analysis of mathematical models of various physical or technical objects or processes. The purpose of this research is studying, analysis and synthesis of different sources about appearance of assumptions chronology, periods and stages of formation and development of the methodology of mathematical simulation. Subject of this research involves the conceptual apparatus and knowledge in mathematics and modeling theory. The methodology of this research is a comprehensive integrative methodology caused by the modern scientific concept, considering the principle of interdisciplinarity as the most important principle of scientific cognition. The study used comparative approach and method of systemic analysis of the results of research. Structure of the article: 1. Basic concepts and categories of mathematical simulation. History of their origin. 2. Preconditions and chronology of the development of mathematical simulation. 3. Value and relevance of mathematical simulation. Conclusions: - was made an analysis of the basic concepts and categories of mathematical simulation: such as model, mathematics, mathematical model, mathematical modeling, their definitions and history of arise; - prerequisites for occurrence and development of mathematical simulation was the appearance and development of mathematics and very fast computers in the in the periods of time of the development of mathematics and its types; - relevance of mathematical simulation is so high that we can study its methodology, as a «third method» of scientific cognition. Contacts: E-mail: chapa-2010@yandex.ru Pp. 03-16.