Currently, modern educational technologies are actively used in the educational environment. However, the main method of training remains the traditional method. Therefore, we described and investigated the innovative technology of the flipped classroom in the study of mathematics and compared its effectiveness with traditional learning. As the subject of the research, strategies for using this technology for teaching second-year students mathematics are presented. The subject of study determined the purpose of the study, which is to describe implementation technology of the flipped classroom, focused on the study of the theory of functions of a complex variable. A pedagogical experiment was held at TPU, during which students who studied using the technology of the flipped classroom before a lecture on a specific topic made a summary of this lecture, the material of which was placed in the LMS MOODLE as a PDF file. Students were proposed to take notes of the lecture (if necessary, make notes about what was not clear, so that they could discuss it in class). At the same time, they should have left space in the notebook for proving theorems or for solving examples that demonstrate the use of theoretical material. A pedagogical experiment demonstrated that the use of technology of the flipped classroom improved student achievement. This technology allowed us to present the theoretical material in full. The flipped classroom technology allows you to spend as much time studying a topic as you need to understand it.