The article is devoted to the problems in the training of professional production personnel. In particular, this applies to boatmasters. The discipline "Mathematical Fundamentals of Navigation" is directly related to the accuracy of the ship's observation (determining the location of its position) and the accuracy of its wiring along the laid course. It is not an easy task to determine what should be taught in this course, how exactly it should be taught, how the content of the course should depend on the navigation equipment used, etc. In addition, the theoretical basis for the course is the standard course of higher mathematics for technical universities, without which it is impossible to understand applied mathematical courses. There is some contradiction between the theoretical and applied parts of special mathematical courses that have applied significance, in terms of differences in the categorical apparatus, the levels of abstraction of the mathematical apparatus, psychology and technology of applying knowledge and skills. Similar problems exist in other applied mathematics courses, theoretical branches of mathematics, such as set theory, whose applications relate to other abstract branches of mathematics. For the first time this problem was considered in the work [3], namely in IL the application to the course "Mathematical foundations of navigation". In addition to this work, within the framework of the course of discrete mathematics taught by the author at his university, the issue of synthesizing methods for theoretical and applied aspects of set theory, graph theory, and mathematical logic was considered. The effectiveness of the synthesized methods was checked by statistical methods and was confirmed by them. The question of justifying the need to develop synthetic methods and the choice of certain methods for specific disciplines remained open. This publication is dedicated to these issues.

Keywords: genetic, humanitarian, formal-logical, activity-based approaches in teaching, cognitive psychology, synthesis of teaching methods.