The article deals with the problem of integrated teaching of discrete mathematics elements to the content of the main specialized disciplines in the preparation of future computer science teachers. The ways of solving some problems in the preparation of future computer science teachers on the elements of discrete mathematics and the need for its training are described. The analysis of scientific research of domestic and foreign scientists involved in the issues of teaching computer science in discrete mathematics is carried out. As a result of the research, the necessity of teaching computer science teachers the elements of discrete mathematics is scientifically substantiated. When considering the content of professional disciplines, the necessity of teaching elements of discrete mathematics is revealed, the rationale for including topics in the content of teaching by sections is given. The list of topics that can be considered in the content of specialized disciplines of discrete mathematics elements is described schematically. These topics are presented as an example of the content of specific disciplines and recommendations are given that it is necessary to specifically study the above, develop and present a teaching methodology