Удосконалення математичної компетентності студентів інформаційно-технологічних спеціальностей засобами НДР з теорії наближення
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Дата
2020
Назва журналу
Номер ISSN
Назва тому
Видавець
СумДПУ імені А. С. Макаренка
Анотація
У роботі показано переваги науково-дослідної роботи студентів (НДРС) з теорії наближення як методу вдосконалення дослідницької складової математичної компетентності студентів інформаційно-технологічних спеціальностей. Запропоновано один зі шляхів досягнення цієї мети – підготовка та проведення наукового дослідження, яке стосується питань наближення класів періодичних функцій тригонометричними поліномами. Цілеспрямоване формування дослідницького стилю мислення в процесі НДРС із теорії наближення сприяє формуванню в майбутнього фахівця здатності використовувати свої математичні знання для розв’язання різноманітних практичних і теоретичних задач, які зустрічаються в професійній діяльності.
The research work of students in mathematics is considered as part of the educational process aimed at formation in students of the research component of mathematical competence, which is based on the organization of current scientific research in the priority fields of modern mathematics. For a number of tasks of obtaining, modeling or registering data and processing them, it is important to create a unified methodological approach based on common mathematical principles. Spectral-analytical methods are highly efficient and can be selected as the nucleus of such a single approach, with their main advantage being the combination of digital calculations with analytical transformations and conclusions in order to improve the accuracy and speed of computer calculations. The advantages of the research work of students on the theory of approximation as a method of improving the research component of mathematical competence of students of information and technological specialties are shown in the work. One of the ways to achieve this goal is to prepare and conduct a scientific study concerning approximation in classes of periodic functions by the trigonometric polynomials generated by linear methods of summation of Fourier series in a uniform metric. A prerequisite for conducting research on the theory of approximation of periodic functions and the theory of the Fourier series is presence in students of deep professional knowledge of elementary mathematics and mathematical analysis, creative abilities, as well as basic knowledge of other fundamental disciplines. To do this, it is necessary to achieve in advance a level of fundamental, and, in particular, mathematical knowledge that would allow the student to use them freely while performing scientific research. Research work of students on the approximation of periodic functions by trigonometric polynomials generated by linear methods of summation of Fourier series forms the skills of scientific work, including qualitative study of literature and information search, analysis of recent studies in the chosen direction, formulation of the problem, self-study own generalizations and conclusions. Purposeful formation of a research style of thinking in the process of research on the theory of approximation contributes to the formation of a future specialist’s ability to use their mathematical knowledge to solve various practical and theoretical problems encountered in professional activity.
The research work of students in mathematics is considered as part of the educational process aimed at formation in students of the research component of mathematical competence, which is based on the organization of current scientific research in the priority fields of modern mathematics. For a number of tasks of obtaining, modeling or registering data and processing them, it is important to create a unified methodological approach based on common mathematical principles. Spectral-analytical methods are highly efficient and can be selected as the nucleus of such a single approach, with their main advantage being the combination of digital calculations with analytical transformations and conclusions in order to improve the accuracy and speed of computer calculations. The advantages of the research work of students on the theory of approximation as a method of improving the research component of mathematical competence of students of information and technological specialties are shown in the work. One of the ways to achieve this goal is to prepare and conduct a scientific study concerning approximation in classes of periodic functions by the trigonometric polynomials generated by linear methods of summation of Fourier series in a uniform metric. A prerequisite for conducting research on the theory of approximation of periodic functions and the theory of the Fourier series is presence in students of deep professional knowledge of elementary mathematics and mathematical analysis, creative abilities, as well as basic knowledge of other fundamental disciplines. To do this, it is necessary to achieve in advance a level of fundamental, and, in particular, mathematical knowledge that would allow the student to use them freely while performing scientific research. Research work of students on the approximation of periodic functions by trigonometric polynomials generated by linear methods of summation of Fourier series forms the skills of scientific work, including qualitative study of literature and information search, analysis of recent studies in the chosen direction, formulation of the problem, self-study own generalizations and conclusions. Purposeful formation of a research style of thinking in the process of research on the theory of approximation contributes to the formation of a future specialist’s ability to use their mathematical knowledge to solve various practical and theoretical problems encountered in professional activity.
Опис
Ключові слова
науково-дослідна робота студентів, математична компетентність, інформаційно-технологічна спеціальність, теорія наближення, students research, mathematical competence, information technology specialty, approximation theory
Бібліографічний опис
Ровенська, О. Удосконалення математичної компетентності студентів інформаційно-технологічних спеціальностей засобами НДР з теорії наближення [Текст] / О. Ровенська, В. Астахов // Педагогічні науки: теорія, історія, інноваційні технології : науковий журнал / МОН України, Сумський держ. пед. ун-т ім. А. С. Макаренка ; [редкол.: А. А. Сбруєва, О. А. Біда, Ю. А. Бондаренко та ін.]. – Суми : СумДПУ ім. А. С. Макаренка, 2020. – № 1 (95). – С. 289–299. – DOI: 10.24139/2312-5993/2020.01/289-299.