Aplicações de matrizes no ensino médio e no estudo de mergulhos métricos

Abstract

Algebra is undoubtedly one of the great foundations of the teaching of Mathematics. As a rule, this matter is presented in all its formality and most of the time without the glimpse of practical applications in everyday life. In the view of the student, this type of didactic failure can generate a block in learning. One of the objectives of this master's dissertation work is to propose a sequential presentation of some of the main topics studied in algebra, both in high school and in a primary course of higher education in mathematics. At first, and in a motivational character, we will present problem situations involving matrices and linear systems. Then, we will do a theoretical review of elementary themes in higher education, such as, for example, vector spaces, metric and standard spaces. The main purpose of this dissertation, contained in Chapter 4, deals with metric dives and their motivations, a topic of great effervescence in research in the area of ​​Metric Geometry in recent years. In order to facilitate the understanding of this topic of study, the dissertation was structured in order to contemplate all the necessary requirements for this. The main result of this chapter is a theorem about isometric dives of a class of limited and separable metric spaces in Banach spaces containing isomorphic copies of the infinite space.