The basic objectives of higher technical education consist of providing college and university graduates with a system of essential knowledge, abilities, and skills, and also of developing their capacity and readiness to put their knowledge to work in professional activity. In studies that have to do with the modernization of higher technical education, there are two directions that are applicable to these objectives: (1) The fundamentalization of education which consists of searching for ways to improve the quality of the fundamental training of the future engineer, the quality of his basic, system-forming stock of knowledge; and (2) The competence approach in the instruction which focused on the engineer's ability to put the knowledge that he has acquired to use in practical activity. It appears that in engineering an increasingly important role is going to be assigned to innovative technologies that impose high demands not only on the specialized training of an engineer but also on his fundamental training, which is why it is essential that the training simultaneously ensure a high quality of fundamental knowledge and the graduate's readiness to engage in professional activity. However, many college and university instructors believe that the competence approach is applicable only in the specialized training of an engineer, but that fundamental education, which has firmly established traditions, does not need competences to be involved. This article, using the teaching of mathematics, summarizes some studies of the interconnection between the fundamentalization of education and the competence approach in instruction.