The goal of this undergraduate thesis is to study some introdutory concepts and results of the PI-algebras theory. In particular, as main results, we describe the polinomial identities of the Grassmann algebra and 2 x 2 ...

One of the main goals of this project is to study the index of vector fields in compact surfaces and present the Poincar´e-Hopf Theorem, remarking that such a result connects topological elements to geometric objects.

In this work we will study some concepts of algebraic topology such as fundamental group and simplicial complexes, then we will present a proof of the closed surface classification theorem.

In this work, we study the concepts of degree and local degree for maps between manifolds. Furthermore, we define the Poincaré-Hopf index and study some relevant proprieties of this index such as the famous Poincaré-Hopf ...

In this work, basic definitions and results on Algebras with Polynomial Identities are introduced, some classic results of the theory that involve them are stated and demonstrated, such as the Amitsur-Levitzki Theorem, ...

Desde o surgimento da definição de superfícies parametrizadas, foi questionado sobre suas propriedades que independem da parametrização. Propriedades essas que caracterizam objetivamente a geometria dessa família facilitando ...

In the international education field, it is relevant to predict the students' performance for future courses and/or disciplines. In that matter, Rajalaxmi et al. (2019), Abledu (2012) and Gadhavi, Patel (2017) works show ...

In this monography, we study polynomial functions, starting with a brief historical research about how the general solutions of the first to third degree polynomial equations were constructed, then we proceed to analyze ...

The paper "Conformal geometry, Euler numbers, and global invertibility in higher dimensions”, by Frederico Xavier, crosses different areas of Mathematics in order to obtain its main result. Among them we have Differential ...

In this work, we present a study on the theory of differential geometry of surfaces with a language of moving references. At first, we will introduce some groups of matrices and their actions in Euclidean space. Once this ...