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This article analyzes the implementation of e-learning technologies in the study of mathematics at Tomsk Polytechnic University. It describes research findings of the suitability of the e-learning technology for first year students of an engineering university. The research involved 248 students and 38 teachers of Tomsk Polytechnic University. The authors surveyed first-year students to check whether they are ready to learn in the electronic environment. In addition, the students and teachers were surveyed on the possibility of teaching a course in mathematics in the electronic environment and on the preferred mode of learning: web-based instruction, blended learning, or full e-learning. The research identified the main difficulties when working with e-learning courses as well as the optimal form of e-learning for the study of mathematics.