Today the development of information technology is closely related to the creation and application of machine learning and data analysis methods. In this regard, the need for training specialists in this area is growing. Very often, the study of machine learning methods is combined with the study of a certain programming language and the tools of its specialized library. This approach is undoubtedly justified, because it provides the possibility of accelerated application of the knowledge gained in practice. At the same time, it should be noted that with this approach, it is rather not machine learning methods that are studied, but a certain set of methodological techniques for using the tools of the specialized library. The presented work is devoted to the experience of creating an adaptive educational course on the mathematical foundations of machine learning. This course is aimed at undergraduate and graduate students of mathematical specialties. It is divided into core and variable parts. The obligatory core part is built around the PAC learning model and the binary classification problem. Within the variable part, issues of the weak learning model and the boosting methods are considered. Also a methodology of changing the variable part of the course is discussed.