Модели-полиады и их применение в обучении математике

Considered systems of models, called models-polyads. Components of the model-polyads are various models of a prototype object, describing the same its properties, and the exchange of information between the components of the modelpolyads occurring without distorting the information. The examples of modelspolyads, in particular, shows that in the form of models-polyads are the algebra of geometric vectors, algebra of complex numbers, etc. There are highlights the benefits of studying the objects in the form of models-polyads, and especially in the case of training, when the objects under study are presented in a models-polyads.Рассматриваются системы моделей, называемые моделями-полиадами. Компонентами модели-полиады (в частности, модели-диады, модели-триады) являются различные модели некоторого объекта- прототипа, описывающие одни и те же его особенности, причем обмен информацией между компонентами модели-полиады, происходящий без искажения этой информации. Приведены примеры моделей-полиад, в частности, показано, что в виде моделей-полиад представлены векторная алгебра, алгебра комплексных чисел и др. Выделены преимущества изучения объектов, представленных в виде моделей-полиад, и особенности обучения в случае, когда изучаемые объекты представлены в виде моделей-полиад

Algebraic Approach to Modeling the Management Systems of the Sixth Technological Mode

The aim of this research is to highlight the issues of building the models of control for automotion of the control process and, in particular, by using the artificial intelligence. The urgency of the problem is due to the passage of the economy from the fifth technological mode to the sixth one [1-5]. This passage is accompanied by the use of very complex automatic control systems, which are not limited only by automation of the executed algorithms. Management automation requires formalization of this process, construction and use of various management models. The latter requires the formalization and use of various management models that reflect various aspects of the management system. For simultaneous application of several fundamentally different models, an algebraic approach to modeling is proposed, which consists in distinguishing the following three components: 1) system of the basic models; 2) systems of standard transformations and standard combinations of models; 3) approximation mechanism intended to an approximate representation of the required model as the result of typical transformations and typical combinations of the basic models. The process plan is considered as the main activity model, we consider the strategy as the mechanism for creating the plan. Two ways of describing a strategy are proposed: a hierarchical model and an algebraic representation of a strategy. The study is a theoretical one. The methodological basis is the system analysis (A.A. Bogdanov) and the theory of modeling by Yu.B. Melnikov, in particular, the theory of adequacy, the theory of strategies, etc. Keywords: management model, algebraic approach to modeling, strategy of activity, purpose of activit