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List of publications on a keyword: «algebra»

  • Realizatsiia fundamental'noi napravlennosti normal'nykh form bulevykh funktsii pri obuchenii matematike kursantov voennogo vuza

    Book Chapter
    Pedagogy and Psychology as the Sciences of Forming the Potential of Modern Society
    Authors:
    Nikolai V. Sadovnikov, Elena V. Shipanova, Galiia A. Sultanova
    Work direction:
    Глава I. Педагогические аспекты обучения и воспитания
    Abstract:
    The relationship between the fundamentality and professional orientation of cadets of military university of simplification logical functions is shown, which consist in finding dead-end, and then minimal forms of it. A convenient minimization method to simplify the search for gluing terms is the use of Veitch diagrams. The question of dual functions and the completeness and closeness of the system of logical functions is discussed.
    Keywords:
    minimal form of logical functions, disjunctive normal form (DNF), conjunctive normal form (CNF) of boolean functions, implicant, simple implicant, dead-end form of boolean functions, Veitch diagram, duality principle, functionally complete system, Zhegalkin algebra, closed class of functions
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  • Analysis of Applied Problems in Modern Textbooks of Algebra and Geometry from Positions of the FSES BGE Requirements

    Research Article
    Development of education No 4 (6)
    Author:
    Aleksandr V. Bychkov
    Work direction:
    Education system in Russia
    Abstract:
    The article discusses the concept of «mathematical literacy», which is important from positions of the PISA international studies requirements. There are three types of activity (formulation of the situation mathematically, application of mathematics, interpretation of the result), the possession of which is checked in the PISA study. The article presents the subject results formulated in the FSES of BGE, on the study of which the subject area «Mathematics» is aimed, reflecting the need for the formation of selected components of mathematical literacy in students. The article presents the results of the analysis of tasks presented in the most common textbooks on algebra and geometry of the main school. The purpose of the analysis was to identify the presence of practice-oriented tasks in textbooks that meet the requirements of the FSES of BGE and the requirements of diagnostic tools used in international PISA studies. During the study the following methods were used: comparison, analysis, theoretical. The study was based on the most frequently used in school practice textbooks of the following authors: L.S. Atanasyan, V.F. Butuzov, S.B. Kadomtsev, E.G. Poznyak, I.I. Yudina, L.S. Atanasyan, V.F. Butuzov, etc. Result: the article presents the results of the analysis of the problem material presented in the most common textbooks on algebra and geometry of the general school. On the basis of the analysis of three author's lines on the study of geometry in the general school, common problems are identified. An example of a practical problem, confirming the conclusions, formulated during the analysis is given. The authorcomes to the conclusion that there is still lack of practice-oriented tasks in modern textbooks on algebra, helping to motivate students to conscious assimilation of mathematical facts and statements, providing the formation of the ability to model on the basis of a real, life situation.
    Keywords:
    international PISA studies, FSES of BGE, disadvantages of national tasks, formulating situation mathematically, application of mathematics, interpretation, algebra, geometry
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  • Razdel matematiki "Osnovy algebry logiki" v zadachakh EGE po informatike i IKT

    Book Chapter
    Education and science: current trends
    Author:
    Iuliia V. Zhulidova
    Work direction:
    Парадигмы современного образования
    Abstract:
    Professions in the field of information technology today are almost the most popular. Therefore, school graduates, who have decided to enroll in these areas of training, choose Computer Science Exam as one of the USE exams. But the statistics on the performance of certain tasks by schoolchildren on specific topics is still low.
    Keywords:
    fundamentals of logic algebra, USE in computer science and ICT, task execution statistics, recommendations when preparing schoolchildren
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  • The inclusion of additional topics to the program of linear algebra course for economists and managers

    Research Article
    Development of education No 1 (3)
    Author:
    Sergej Y. Shashkin
    Work direction:
    Theoretical and applied research in education
    Abstract:
    The paper generalizes the concept of “solving a system of linear algebraic equations in order to formulate a unified approach to the analysis of incompatible, indefinite and unstable systems”. Examples of unstable systems of linear algebraic equations are considered, which solutions depend on small changes in the numerical coefficients in the equations. The reasons for the instability of linear systems and the regularization algorithm for finding the solution of any system of linear algebraic equations are discussed. As the author notes, the Tikhonov regulatory algorithm is the most popular and practically convenient for solving unstable SLAES.
    Keywords:
    pseudo solution of a system of linear algebraic equations, condition number, Tikhonov algorithm
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