The article defines the necessity of teaching elements of discrete mathematics to a future computer science teacher when studying professional disciplines under the computer science educational program. The elements of discrete mathematics are an integral part of the professional training of a future computer science teacher and form the basic part of the mathematical basis of computer science. Attention is drawn to the use of the most common elements of discrete mathematics, in particular, elements of mathematical logic and graph theory. And also the ways of solving logical problems with the help of the truth table and in the MS Excel table processor are considered. In addition, the directions of application of graph theory applications in computer science are outlined. The results of the study showed that the integrated teaching of discrete mathematics elements in the content of professional disciplines of the educational program contributes to improving the quality of education. In the future, the results of the study will be used to develop and meet the needs of future computer science teachers.