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The urgency of the problem specified in the article stems from the fact that within the scope of transition to Federal State Educational Standards of the third generation and to a new Unified Standard for Teachers, preparation of academically flexible teachers who will possess a certain scope of knowledge both in the subject area and in the allied sciences and well-versed in new achievements of various sciences, becomes a particularly important task. They should face professional problems and be able to independently develop and implement new active teaching methods and techniques in the educational process meeting the presentday needs of educational institutions. The purpose of the article is to study interactive forms application in the process of training of future physics teachers. Interactive teaching methods providing interaction not only between teachers and students, but also between students consist in giving opportunity to students of all-round education in the chosen field of study. The key methods of the research are theoretical analysis of pedagogical literature providing an overview of learning technologies' development and interactive teaching methods survey as applied to bachelor's students majoring in pedagogy. The core results of the research consist in describing the use of some interactive learning methods. They make it possible to organize practice-oriented educational process, assess students' knowledge quality in the subject area, as well as evaluate the level of students' basic professional competencies in accordance with the requirements of the Unified Standard for teachers.

The most important component of the professional competence of an engineer is the synthesis of project and technical competences-project-technical competence, suggesting a set of special knowledge, skills and proficiencies, personal qualities necessary for the effective specialists' performance of their professional duties, in particular, for the successful implementation of engineering projects requiring technical calculations running, capabilities to effectively operate in real life, to get oriented in production situations, to adapt to changing conditions, to work in different teams. In this connection, the problem of selecting and structuring teaching content of physical and mathematical disciplines, aimed at the formation of project-technical competence of technical university students, is becoming relevant. The paper presents an algorithm for selecting and structuring the physical and mathematical disciplines teaching content, aimed at the formation of students' project-technical competence, involving a sequence of analytical and preparatory, organizational-substantive, procedural-methodological, as well as correction-implemental stages. The article submissions are of practical value to Mathematics and Physics teachers for selecting and structuring the content of these disciplines.

Digitalization and wide introduction of advanced information technologies, based on the applied application of mathematical methods and models, affect all areas of life of the Russian Federation. The development and implementation of software (software) in the road transport area, when preparing the driver's train, is an urgent task. The article deals with the application of some of the models presented in the works (Georgiev et al. in Stud Syst Dec Control 316:89-97, 2021; Epifanov and Epifanova in Maintenance and repair of cars, 280 p, 2017; Zotov in Investigation and prevention of road accidents, 245 p, 2016) in the simulator systems of driving schools for training and training the drivers. The applied use of algorithms of mathematical models is considered, such as: graph (automatic) model, tensor model and some other models. The implementation of this approach is presented in the form of applied software of the Auto School-Driving training complex. The "Driving School" simulator is designed for motorists and includes: original application software; a hardware and software unit including a computer peripheral device and an analog-to-digital converter; ergonomic workplace of a motorist. The software allows you to teach confident taxiing skills, competent speed switching and braking skills, complex actions in non-standard situations on roads, on highways, in the city, etc., The Driving School-Driving training complex software allows you to prepare in conditions of different grip of car tires with pavement; preparation for driving in winter conditions; modeling and the possibility of combining different weather conditions. All these different modes, the application software allows you to combine when modeling the road situation in virtual space. The original software allows you to typologize cars according to different criteria: by brands; by gearbox type; by drive type; by engine type, etc. In the Applied Software, the possibility of training in of training of motorists to avoid road incidents deserves special attention.

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