The article deals with the problems of information and communication technologies (ICT) development in teaching mathematics of engineering specialities students in the United States. In the article the nature of trends of convergence of information system in higher technical education and other tendencies in the USA are сharacterized. The main historical stages of development of the theory and methods of ICT use in teaching mathematics of engineering specialities students in the United States are defined. The study of historical sources has been allowed to emphasize six stages, at each stage it is analyzed the use of ICT for teaching mathematics, it is shown the contradictions and the main features of the use of ICT in teaching mathematics of engineering specialities students.