As olimpíadas de matemática e uma introdução ao estudo de equações funcionais

Abstract

The Mathematics Olympiads are international competitions that seek to stimulate interest in the subject, in addition to testing the participants’ skills with regard to complex problems. When analyzing the questions proposed in these competitions, the frequent presence of functional equations is observed, which consist of equations involving unknown functions. Therefore, the general objective of this research is to discuss the use of functional equations in Mathematics Olympiads. As a methodology, a qualitative bibliographical research was chosen, so that initially a bibliographical review was carried out on the concepts in depth in the study, then it brought to light a brief report by the researcher about the workshops that were given to some teachers and students with the aim of precisely to discuss the mathematics olympiads and how they can contribute to both the knowledge of teachers and students. In this research, we propose the development of a series of lectures focused on the Mathematics Olympics, together with a didactic sequence on Functional Equations, to be applied in study groups focused on Olympic competitions. This sequence was prepared in accordance with the guidelines established for the creation of an Educational Product, with the aim of providing a structured and effective approach to learning and preparing students for the challenges of the Mathematics Olympiads. The lecture cycle was an extension action promoted by IME/UFG and PROFMAT for the popularization and dissemination of Mathematics.