Problems of the study process of mathematics at the modern university, aim of which is to prepare educated and competent specialists, so that they are eligible to the changes in our society that are caused by the globalization of economics and information, are mentioned in this article. Goals of the universities are becoming broader and more varied: they provide not only competent specialists, that have acquainted narrow range of knowledge in some specialty, but also create equal opportunities for extensive range of residents to get education, to gain new knowledge in high quality research and to promote the development of the national economy. Goals of mathematics are firstly determined by the fact that students must be prepared to use in practice the acquired subject in real life. The quality of the learnable competences depends not only on the amount of gained knowledge in mathematics, but mainly on the acquisition level of problem-solving abilities. It is important to update two main principles of study in the organization of the study process: implementation of the interdisciplinary approach and student’s self-directed studies. While transferring to the self-directed studies, changes in the scholastic content, diversity of the applicable methods and in the system of evaluation must be made in the study process of universities. The role of a pedagogue must be appraised. Every teacher must create the new didactic system in educating specialists in a very deliberative manner, students’ motivation and independent work must be promoted with varied methods to raise the level of competence in the future specialists.