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Abstract: The article deals with the methods and means of formation of professional and creative competence in teaching mathematics the students of higher school of core subjects of natural science specialties. It presents a conceptual model of adaptive methodological system of formation of a competence (AMSFC). The proposed methodology aims to create AMSFC and ensure the following educational technologies: creation of basic training options; automatic generation of the base or the other variants of new individual options and their automated or automatic adaptation and optimization; training on individual options; control of the degree of formation of a competence, and its results may be adjusted to form the current or new individual options for the next stage of training, etc. The authors have developed a teaching method that allows students to develop integrative thinking, and build their professional and creative competence. The proposed method is implemented by means of a standard and a new set of methods and means of education and the developed complex of mathematical and integrative specialized tasks (CMIT). In this article the focus is on a new set of techniques, which is a feature of the method of using a set of CMIT and adaptive methods, resulting in effective development of creativity, integrity and, eventually, productive and creative professional competence of future specialists.