Licenciatura em Matemática (Sede)

URI permanente desta comunidadehttps://arandu.ufrpe.br/handle/123456789/24

Siglas das Coleções:

APP - Artigo Publicado em Periódico
TAE - Trabalho Apresentado em Evento
TCC - Trabalho de Conclusão de Curso

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Espaços métricos: continuidade, completude e compacidade
(2021-02-19) Oliveira, Alessandra Arcanjo Lisboa de; Araújo, Yane Lísley Ramos; Carvalho, Gilson Mamede de; http://lattes.cnpq.br/0044877127514130; http://lattes.cnpq.br/6642941380570085; http://lattes.cnpq.br/2572639684291501
This work has as main objective to study continuity, completeness and compactness in the theory of metric spaces. A metric space is a non-empty set in which the notion of distance between its elements is well defined. The present study is interesting because the results presented here generalize some of the results observed in the theory of continuity and compactness in Euclidean spaces, Rn, with n [greater than or equal to] 1. Furthermore, these results are valid in more abstract spaces such as some sequence or function spaces, whose notion of distance escapes from intuition and entails intriguing facts, such as the fact that closed balls are not necessarily compact.
Um estudo sobre completude e compacidade em espaços métricos
(2019-12-18) Silva, Hugo Henryque Coelho e; Araújo, Yane Lísley Ramos; http://lattes.cnpq.br/6642941380570085; http://lattes.cnpq.br/1324983852661350
In this work we will present a study about the theory of complete and compact metric spaces. Initially, we will cover some basic concepts related to the theory of metric spaces, continuity and sequences in metric spaces. Next, we will list a motivation for the study of the theory of complete metric spaces, some of their properties and valid results in these spaces, such as Baire’s theorem and Banach’s fixed point theorem as well as some of its applications. Finally, we will present a study about the theory of compact metric spaces, addressing its general properties and some important results of the mathematical analysis that are valid in these spaces, as we can mention Riesz theorem and Ascoli-Arzelá theorem.
Existência e unicidade de solução para problemas envolvendo o operador Laplaciano
(2019-12-17) Nunes, Thays Ingrid dos Santos; Araújo, Yane Lísley Ramos; http://lattes.cnpq.br/6642941380570085; http://lattes.cnpq.br/3740642465035306
In this work we approach some basic concepts related to the theory of partial differential equations guaranteeing the existence of solution for problems involving the Laplacian operator. Initially, we use the method of variable separation and Fourier Analysis tools to ensure the existence of classical solutions to Dirichlet problems in the rectangle and unit disk involving the Laplace equation, as well as a maximum principle to ensure the uniqueness of the solution. Then, we use results from Functional Analysis and Sobolev spaces to ensure under certain conditions that there is only one weak solution to the Dirichlet problem involving the Poisson equation.
Mulheres na Matemática: contribuições, conquistas e desafios ao longo da história
(2023-05-05) Santos, Hellen Priscila de Souza; Araújo, Yane Lísley Ramos; Kulesza, Maité; http://lattes.cnpq.br/4001440813037430; http://lattes.cnpq.br/6642941380570085; http://lattes.cnpq.br/0109502986579094
In this research, motivated by the analysis of gender inequality, we conducted a bibliographical study to understand the historical and social context of education for women and men. We provided subsidies so that the community could understand the gender inequality still present in mathematics and its consequences. We portrayed female personalities who were pioneers in the field and overcame obstacles, paving the way for others. We presented important awards received by female mathematicians, highlighting the little recognition they received when compared to that received by men. We demonstrated achievements that were made through collective mobilization and struggle and observed that we still have many challenges to face and overcome. With this research, the objective provoking a reflection on the need for recognition and appreciation of women mathematicians, as well as offer examples of initiatives aimed at overcoming the difficulties they face within a predominantly male universe.