Methodological orientation of heuristic strategies in cognitive understanding of mathematical analysis

Philosophical reflection of heuristic techniques and cognition methods reveals the essence of mathematical concepts, designing methods of mathematical objects and enriches ideas about the mathematical world picture. It deepens the subject of his own philosophical and methodological research in the philosophy of mathematical education. Although heuristic ideas have long been used in philosophical studies, the heuristic activity in mathematics is the process of setting a new problem and finding its solution. The article is devoted to philosophical and methodological analysis of mathematic heuristic strategies in the context of cognitive understanding of mathematic philosophy problems and reflexive analysis of problem-oriented topics of mathematical analysis. Heuristic approaches to higher mathematics differ from the methodological techniques of the algorithmic type, focused on formal logical analysis. Heuristic techniques direct thought to a meaningful analysis of mathematical problems, it stimulates intuitive thinking in solving new problems. The article draws particular attention to the problem of the mathematical knowledge substantiating when interpreting mathematical analysis as the most complex part of higher mathematics and in connection with the expansion of the field of its applications. The reflection of heuristic methods in the study of sections and directions of mathematical analysis has methodological significance. It is a search for a new approach to the formalization of cognitive research creative activities. This approach becomes a necessary component of the modern system of university mathematical education at various professionally necessary severity levels.