This article describes the results of Mathematical Olympiads of students of a physical and mathematical boarding school for gifted children in the Turkestan region on the basis of the curriculum of the discipline "solving Olympic problems" for students of the Department of Mathematics of the M. Auezov South Kazakhstan University through advanced training courses developed within the framework of a doctoral dissertation to determine the effectiveness of the education system introduced to students of a boarding school for gifted children in the Turkestan region. The quality of education and organization, the level of implementation of curricula, the professional competence of teaching staff and their activity in ensuring the desired results in education, the individual achievements of students, as well as the parameters of school achievements in ensuring the quality of education in general, are determined.

Experimental studies on the Olympiad in Mathematics conducted in the period from 2020 to 2023 are presented. A survey was organized and conducted among teachers and students of general education schools, universities in the Turkestan region. It also shows that the experimental group of students was 13.95% higher than the quality result of the Olympic Training Program in mathematics and the results of the control group, the mastery of the basic school program in mathematics was 16.25% higher, and it was possible to see the superiority of 76% of the participants in quality performance in theory and methods of solving Olympic problems.

The article presents the theoretical content of the future study, developed within the framework of the doctoral dissertation. Scientific research work has been carried out that corresponds to the stage of setting the problem, which consists in developing the concept of research, determining the directions and specific tasks of the study. At the same time, Zh.Kapparov showed the results of the annual research and the links between teachers and students of the specialized physical and mathematical boarding school No. 5.