Development of the creative component of the educational process in the teaching mathematical disciplines using analogy method

The article presents an overview of various methods for improving the quality of teaching and motivating learners. Features of the analogy method and the possibility of its application as an effective educational technology have been considered. The use of the analogy method in the educational process in the course of studying graph theory by students has been described. Cartesian graph is proposed as a method obtained with the help of analogy method for describing the graphs by the auxiliary function. The features of the Cartesian graph are studied and the basic laws are revealed, which enable to draw conclusions about the properties of a corresponding traditional graph. Two modifications of the Cartesian graph have been introduced, possessing a certain specific form of representation of the graph and thus helping to carry out more detailed investigation of it. Statements about some relationships between the characteristics of the traditional graph and the corresponding Cartesian graph with its modifications are proved. A computer program is described for modeling graphs in various forms of representation: in the form of a traditional diagram, a Cartesian graph, vertex and axial modifications of the Cartesian graph.