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Item Open Access On existence of a solution of a class of second order differential equations(Faculty of engineering and natural sciences, 2019) Zhosybayeva B.The paper was devoted to the study of issues on the existence and compactness of a resolvent, as well as estimates of the distribution function of singular numbers (s-numbers) of a differential operator of mixed type in a noncompact domain. We used the embedding theorems for Sobolev-type weighted spaces, the method of a priori estimates, the uniform localization method. In this paper, besides the above methods, an approach is proposed that allows one to find two-sided estimates of singular numbers (approximation numbers, s-numbers) of differential operators containing a sign-changing parameter. As a result of the study, the following results were obtained for a class of mixed-type differential operators defined in a noncompact domain: a theorem on the existence of a bounded inverse operator was proved: a theorem on the compactness (discreteness of the spectrum) of the resolvent of a mixed-type operator was proved; a conditions to the two-sided estimate for the distribution function of singular numbers (s-numbers) of the resolvent of a mixed-type differential operator given in an unbounded domain are obtained.Item Open Access The role of repetition in learning math(2020 International Young Scholars Workshop, 2020) Yessenbolkyzy A.; Yessirkepova A.Abstract. Mathematics is one of the most important aspects of school education. School mathematics is a meaningful, fascinating and accessible field of activity, giving the student rich food for the mind, connecting him with universal human culture, forming the most important personality traits.In learning mathematics, practice makes perfect. In the process of teaching math, the repetition of the studied material is given an important place. Properly organized repetition is one of the factors contributing to the intellectual development of each student, their achievement of deep and lasting knowledge. The need to repeat the previously studied material is caused by the very structure of the curriculum of mathematics. For example, students go through the curriculum topic: “Quadrangles” in 8th grade, but use it in grades 10-11 when studying the topics: “Surface of bodies of revolution”, “Surface area”, “Volume of bodies”, etc.To teach mathematics without repeating the material previously passed on every lesson every day, this means transmitting, retelling to students a certain amount of different laws, theorems, formulas, etc., completely not caring about how firmly and consciously this material was mastered by our pets; it means not giving children deep and lasting knowledge. Researches showed us that repetition is the main instrument of the study. Results of the analysis revealed that students exposed to repetition with variation approach had significantly higher achievement, conceptual understanding and improved retention.