№ 09 (September)

For the professional education of specialists who are able to carry out scientific and research activities, an important task is to adapt the programs of higher professional education to the modern condition of science. Methods of mathematical modeling are often used in studies of many technological processes and natural phenomena. One of the varieties of physical processes is the flow of liquid or gaseous media. At the same time, there are often flows of inhomogeneous media in applied research, and there is no methodology for modeling the dynamics of inhomogeneous "complex" media in the classical course "Fluid and gas mechanics". For specialists in mathematical modeling, it is necessary to know the methods of mathematical modeling of the inhomogeneous media dynamics in addition to the classical methods of hydrodynamics. The purpose of this work is to develop a methodology for teaching the section of hydrodynamics related to the flows of inhomogeneous media. The section of the course "Hydrodynamics" is designed from the standpoint of the development of mathematical models and methods for their analytical solution. Students of the specialty "Applied Mathematics" are shown the main approaches to the development of mathematical models of "complex" flows, as well as the exact solutions of systems of equations are shown using simple examples. As part of the inclusion of inhomogeneous media dynamics elements in the course of "hydrodynamics", various concepts of developing models of inhomogeneous media dynamics are demonstrated. The models are presented in the form of systems of partial differential equations, including the equations of conservation of mass, momentum and energy. Taking into account the specifics of the specialty "Applied Mathematics", this work considers the use of methods of both the theory of partial differential equations and the theory of ordinary differential equations. For specialists in applied mathematics, it is important to understand the basic methodologies for modeling flows of inhomogeneous media. The techniques differ in approaches, which is important for modeling various types of inhomogeneous media, depending on the composition of the inhomogeneous medium and different volumetric contents of the components in the total volume of the mixture. The paper presents various types of mathematical models on the example of flows that allow simple analytical solutions. The material presented in the work can be useful in compiling the course "Hydrodynamics" for the specialty "Applied Mathematics", which would include elements of the theory of inhomogeneous media dynamics. Such a section could give a general idea of the mathematical models of multiphase and multicomponent media, and the understanding of methods for simplifying models and integrating systems of differential equations is also important.

A modern highly qualified engineer must have an up-to-date set of digital competences that are essential for a successful professional career in the digital era. One of the characteristic features of digitization is the integration of sciences, which is especially evident in the use of digital technologies. In this regard, it is necessary to develop the digital competences of students, using the didactic potential of intersubject integration carried out in the process of information and mathematical training of engineers. The purpose of the work is to study the implementation of information and mathematical training of students from technical universities under the conditions of the globalization of Industry 4.0. The article analyzes the contextual competence-oriented and CDIO approaches in organizing the educational process at a technical university. The novelty of this research: the scientific and methodological apparatus for enhancing the student's activity in solving practice-oriented problems of interdisciplinary content has been expanded by including the optimizing tasks of "contextual" content in the learning process. The authors consider the activity of solving the optimizing tasks of "contextual" content as one of the conditions for the development of digital skills for a student of a technical university. The conducted theoretical analysis of research works on the topic made it possible to highlight the didactic opportunities of the optimizing tasks of "contextual" content and to highlight the digital technologies used to solve them. The article provides a methodology for the development of digital competences of future engineers worked out by the authors through a system of optimization tasks of "contextual" content. This study initiates possible prospects for further research on the development of digital competences for future engineers. The variant of the typology of the optimizing tasks of "contextual" content presented by the authors should be recommended to a wide range of teaching staff of information and mathematical departments of technical universities for using in scientific, methodological and practical work.

This study deals with the problem that almost every adult person has complex professional or interpersonal situations when psychological assistance is needed, which gives rise to the need for the training of highly qualified psychologists of service activities, capable of effective self-realization after completing their studies at the university. The results of the study presented in this article confirmed the authors' assumption that university graduates in psychological specialties have a low and medium level of psychological readiness for professional self-realization but the graduate has a general idea of himself/herself as a professional capable of effective self-realization in the chosen profession. The development and implementation of the "Program for the Development of the Psychological Readiness of Students for Professional Self-Realization in the Conditions of Higher Education" creates an opportunity to form the psychological readiness of the future psychologist of service activity for professional self-realization purposefully, stage-by-stage. The purpose of the article is to draw attention to the problem of psychological readiness of students – future psychologists for professional self-realization and its possible formation within the educational system of the university at the final stage of training. The leading methods of studying the problem of psychological readiness of students – future psychologists for professional self-realization are the study of psychological and pedagogical literature, empirical methods of psychodiagnostics, the development and implementation of a program for the development of psychological readiness of students for professional self-realization in the conditions of university education, a pedagogical experiment. The theoretical significance of the article consists in disclosing an approach to the concept of "professional self-realization" in science and substantiating the need to form the psychological readiness of students – future psychologists for professional self-realization in the conditions of university education. The practical significance of the article lies in the analysis of the results of testing the "Program for the development of psychological readiness of students for professional self-realization in the conditions of university education." This program presents the target, resource and phenomenological components, it includes two content blocks (informational and practical), which makes it possible to repeat this experimental experience based on the material of other studies.

The study of history is a necessary condition for the education of a patriotic and moral person. History accompanies us throughout our lives. As children, we listen to fascinating myths, and later we encounter history wherever we are. History is a set of sciences that study the past of human society. Thus, in order to form a correct idea of historical events, it is necessary to cultivate a historical awareness among the population. This issue should be approached systematically, cultivating the historical awareness at different stages of a person's life. In particular, this process is important in adolescence – the period of self-awareness development, determining one's place in society, active self-tests, expanding the sphere of socialization, reflection. The purpose of the study was to examine the concept of "historical awareness" and define the components of this phenomenon, as well as to work out and test a program for the formation of historical awareness in students of grades 5-6. Historical awareness is considered as a source of social experience, a sense of self-consciousness in it, contributing to the understanding of the unity of oneself and society, based on the memory of the past of a person, society and humanity. Historical awareness is represented as the sum of four components: historical memory, historical feeling, experience and knowledge. It is suggested that the process of cultivating historical awareness will be effective with a comprehensive pedagogical impact on all the listed components, thereby forming the so-called "historical combo", which will contribute to the education of a patriotic person. The authors present the results of a questionnaire for students aimed at studying historical knowledge, emotional attitude to history, awareness of the traditions of their family and the country. The article describes the main elements of the program for the formation of students' historical knowledge. The program includes five sections: "Primitive society. The resettlement of the Eastern Slavs", "The Rule of the Rurik dynasty", "The Rule of the Romanovs", "The Formation of the Union of Soviet Socialist Republics", "Modern Russia". After the program implementation, students of grades 5-6 have shown positive changes in the process of forming historical awareness and its components (historical knowledge, memory, experience, feeling).

The period of study at the university is one of the most significant stages of professional socialization, since at this time the knowledge and skills necessary for successful professional activity are acquired, value attitudes and adaptive abilities necessary for successful solution of professional tasks in a dynamically changing world are formed. The process of professional socialization of foreign students studying at regional Russian universities has a pronounced specificity, which is insufficiently studied in modern pedagogical science. The article presents the normative knowledge about the organization of the process of foreign students’ professional socialization in a regional university. The purpose of the study is to substantiate the model of activity of teachers of a regional university and other persons organizing the process of professional socialization of foreign students. The leading approach to the study of the problem is the theory of the dialogue of cultures, which allows us to consider the professional socialization of foreign students from the standpoint of their inclusion in the context of professional culture. The main results of the study include the allocation of meaningful characteristics, typical problems and a means of professional socialization for each stage of foreign students’ professional socialization. The scientific novelty of the research consists in the development of a normative model of foreign students’ professional socialization in a regional university, which represents the unity of three stages – adaptation, individualization and integration. The theoretical significance of the study is that its results concretize scientific ideas about the professional socialization of students, taking into account the specifics of professional training in a foreign cultural environment at the regional level. The practical significance of the research results reflected in the article lies in the possibility of using them to improve the effectiveness of the process of professional training of foreign students at the regional level.

Pre-professional pedagogical training (PPT) of schoolchildren is one of the target functions of general education and professional organizations. This is an important stage of continuing professional education, which exerts a profound influence on the improvement of the teachers’ training quality and the education of modern young people in general. During this period, students acquire the most important professional and personal qualities, the experience of active participation in solving socio-pedagogical problems and creative activities. Pre-professional pedagogical training of schoolchildren contributes to the conscious choice of a profession in the field of education, professional and personal self-determination of students. At the same time, there are some problems caused by the insufficient validity and development of conceptual provisions, in particular, the ideas and principles of the PPT of schoolchildren, which interferes with the successful organization of career guidance work in educational organizations, complicates the activities of teachers and schoolchildren at the stage of pre-professional pedagogical education. The purpose of the article is to substantiate and characterize the principles of pre-professional pedagogical training, to offer options and ways of their implementation in the activities of teachers and schoolchildren. The leading approaches that form the basis of the theoretical justification and practical implementation of the PPT of students are the following: systemic, reflexive activity-oriented, and subject-oriented ones. When considering the principles, a binary approach is used, which represents the PPT as a process of interaction between two subjects: teachers and students. The article substantiates three groups of goals of pre-professional pedagogical training of schoolchildren, due to the challenges of society, the demands of the education system, the needs and characteristics of modern children; the main ideas of training students are identified: pedagogization of the social environment, individualization of the educational process, integration and convergence. Two groups of principles implemented in the process of pre-professional pedagogical training are defined and briefly characterized: the principles of organizing the activities of teachers and schoolchildren. The proposed principles can be used in the development of scientific, methodological, and educational support for PPT at the regional, municipal levels in an educational organization. It is useful for teachers and schoolchildren to consider these principles when working out the content, forms, methods, and technologies of PPT, ensuring continuity of support and self-development of students.

The numerical assessment of a person's willpower always remains an urgent scientific problem. This situation is typical not only for psychology. The problem is relevant for historical, social, and political sciences, as well as in the practice of managing economic systems. The purpose of the study is to modify the information and mathematical method for the quantitative assessment of a person's volitional characteristics based on his biographical data. For this purpose, three interrelated concepts are used: the power of an independent volitional quality, the power of expression of will and willpower. The method proposed by the authors is used to assess the volitional properties of a number of outstanding Russian figures. These examples allow us to better understand not only the method presented in the work, but they also have an independent historical and psychological significance.