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    Grobner-Shirshov bases theory for Zinbiel stperalgebras
    (Faculty of Engineering and Natural Sciences, 2023) Meiirbek K.
    This thesis is a collection of 6 chapters .The Grébner-Shirshov basis is an impor- tant mathematical apparatus in algebra and commutative algebra, which is used to study and analyze polynomials and their ideals. The Grdébner-Shirshov basis has a number of important properties that make it a powerful tool for solving various algebraic problems, such as searching for ideals, solving systems of equa- tions and determining the basic invariants of polynomials. In this paper we will construct a Grobner-Shirshov basis for Zinbiel algebras. Algebra with the identity (ab) c = a(bc) + a(cb) is called the Zinbiel algebra. In the process of construct- ing the Grebner-Shirshov basis, two compositions are found and the composition lemma is proved. The method of mathematical induction is used to prove the lemma.
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    Sn-MODULE STRUCTURES OF FREE ANTI-COMMUTATIVE ALGEBRA
    (Faculty of Engineering and Natural Science, 2024) Abdibek Y,
    An algebra with identity ab = −ba is called anti-commutative algebra. In this work we study Sn-module structures of free anti-commutative algebra of degree n.
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    UNIFIED METHOD OF SOLUTION OF WORD PROBLEMS
    (типография "SDU University", 2015) Базарбаева Л.Е.
    Методическая разработка «Унифицированный метод решения текстовых задач» предназначена для бакалавров по специальностям 58060100 — «Математика» и 58010900 — «Математика» и содержит такие темы как: «От слов к алгебре», «Задачи о деньгах», «Задачи инвестирования», «Задачи на движение», «Задачи о химических растворах“.
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    Fujita hypothesis and birational models in algebraic geometry
    (Faculty of Engineering and Natural Sciences, 2019) Kunanbaev A.
    The aim of mv research is to study Fujita hypotheses. which states that if is a smooth projektive varvety of dimension n then: (i) Assume that XV. is.a minimal (i.c.. Ay is nef) varvety of general type.(ie., Ky is big == NY > 9). Then the linear system |nvAx| is free for m > n+ 2; (ii) Let A be an ample invertible sheaf on X. Then the linear system |mJvy + (n +1) Al is free. and JnKy + (n+ 2) Al is verv ample on Y, For surfaces Fujita hypotheses was proved by Igor Reider. In my work I generalize result for X not be a sinooth projektive varyety but F-rational. So if Fujita hypotheses is true for a smooth projektive varyety then it is true for more general case F-rational. I use methods of commutative algebra and definition of tight closure.
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    Problems of implementing STEM education in mathematics (grades 10–11, Algebra and the Fundamentals of Analysis)
    (SDU University, 2025) Aralbay N.
    This dissertation work examines the theoretical and practical issues of implementing the STEM education system in the subject “Algebra and Analysis Beginnings” for grades 10–11. STEM approaches not only increase students’ interest in the subject, but also allow them to connect their mathematical knowledge with reallife situations. During the study, three STEM projects based on methods such as PBL (project-based learning), the 5E model, and engineering design were developed and a practical experiment was conducted. The experimental results showed that STEM methods increase students’ scientific thinking, independent decision-making ability, and motivation to conduct research. In addition, the difficulties encountered during the study, such as the level of teacher training, resource constraints, and integration into the curriculum, were analyzed, and methodological recommendations were made. The work provides a scientific and practical basis for the effective use of STEM education in secondary school mathematics.