МЕТОДОЛОГІЧНІ ЗНАННЯ КОНКРЕТНОНАУКОВОГО РІВНЯ З НАВЧАЛЬНОЇ ДИСЦИПЛІНИ «КОМПЛЕКСНИЙ АНАЛІЗ» МАЙБУТНЬОГО ВЧИТЕЛЯ МАТЕМАТИКИ

The article deals with the problem of isolating methodological knowledge of future mathematics teacher. The paper considers methodological knowledge of concrete scientific level of the complex analysis. This knowledge is about the subject, method, fundamental concepts, basic facts of complex analysis, the fundamental relationship between the facts, and development of the history. Methods of research: theoretical analysis, synthesis, analogy, comparison, comparative-historical, systematic approach. The subject of complex analysis is a function of a complex variable, the main method is the method of limits. In addition, the complex analysis widely used the method of coordinates, methods of vector algebra, linear algebra methods, and the method of analogies. It was found out the main ties between a complex analysis and educational disciplines of mathematical cycle: mathematical analysis, linear algebra, analytic geometry, algebra and number theory, differential geometry, mathematics methods of teaching. It was found out that the majority of fundamental concepts and basic facts of complex analysis introduced similar concepts to relevant facts of mathematical analysis. There were given the examples of applying a complex analysis for solution of applied problems from various fields of science. It was carried out a brief comparative analysis of the various programs of study complex analysis in Ukraine and Poland. It was concluded that the familiarization of the future teacher of mathematics with methodological knowledge of concretely scientific level of complex analysis shows the ways of discovering new facts, equips of methods of obtaining new knowledge. In future research it is planned to find out the ways of creating a system of methodological knowledge of complex analysis. Prospects of further studies in this direction are to find out the ways of formation of system of methodological knowledge and skills for complex analysis of future mathematics teacher.