Письма в редакцию UDC 510.2,519.2 Educational Trajectories for Students in Mathematical Specialties L. A. Kashirskaya Division of Student Life Faculty of Physico-Mathematical and Natural Sciences Peoples’ Friendship University of Russia Miklukho-Maklaya str., 6, Moscow, 117198, Russia The paper discusses the role of mathematics in the development of scientific research, the possibility of crafting an individualized educational trajectory for students in the higher education as a mean of creating of the mathematical competence. <...> Key words and phrases: fundamental mathematics, educational trajectories, mathematical competence. <...> Science plays a distinct role in modern civilization. <...> Technological progress, responsible for a new standard of quality of life in developed nations, is grounded in applications of scientific breakthroughs. <...> The role of mathematics in modern science and acquisition of knowledge is continually growing. <...> The results are obvious: from the very first session, students in mathematical analysis and other mathematical disciplines lag behind on a massive scale. <...> In addition, a student of mathematics in a higher educational institution should know that without a mathematical description of a whole range of natural phenomena, it is impossible to reach their deeper understanding. <...> The development of physics, linguistics, and other sciences also suggests a widespread application of the mathematical technique, which has played an essential role in the exploration of space and development of computers, which found applications in a great variety of human activities. <...> Educational reform that started in the XX century has determined evolutionary paths for different educational systems. <...> Today, students can choose an individualized educational trajectory as a mean of creation their mathematical competencies. <...> Educational trajectory is a path of progress for each student in a complicated educational space. <...> The philosophical and anthropological foundations of the “individual educational trajectories” school of thought are the representation “of the person receiving education as a singular source of the semantic field of his progress. <...> The singularity and general characteristics of the source of the semantic field are the appearance to yourself and others of the vision of one’s own progress” [1]. <...> Modern-day understanding of mathematics requires examining the history of mathematics, its subject matter, and its relationship with other sciences. <...> At the International Mathematical Congress in Paris in 1900, in the section on teaching and methodology of mathematics, a 38-year-old prominent German mathematician David Hilbert held a presentation <...>