http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/4331 Sat, 27 Sep 2025 13:46:51 GMT 2025-09-27T13:46:51Z http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8465 Título: Funções elementares e teoria dos números Autor: SILVA, Eldaline Rocha da Primeiro orientador: CLEMENTE, Rodrigo Genuino Abstract: In this Dissertation we will carry out a study on some arithmetic functions. We will see theorems, properties, demonstrations and some important results. In addition, we will use combinatorial analysis techniques to clarify relationships between them, which is extremely important, as it disfigures the idea that mathematics is disconnected and segmented. We seek to offer a combinatorial approach to elementary number theory. The justification for this view is that we can present combinatorial analysis and number theory as sister disciplines. They share a certain intersection of common knowledge and each genuinely enriches the other. Thus, when studying number theory from a combinatorial perspective, students and teachers benefit from the consequent simplicity of the proofs of many theorems, being spared repetition and gaining new insights. Instituição: Universidade Federal Rural de Pernambuco Tipo do documento: Dissertação Fri, 29 Mar 2019 00:00:00 GMT http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8465 2019-03-29T00:00:00Z http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8464 Título: O menor limite inferior de vértices de grau 2 para um grafo minimal 2-aresta-conexo Autor: DULTRA JÚNIOR, José Ivan Primeiro orientador: GOMES JUNIOR, Antonio José Ferreira Abstract: Studying graph theory is undoubtedly an experience that shows us the importance of this subject due to its applicability in several branches of Mathematics as well as its notorious appearance in everyday situations. In this sense, our work aims at first to base the reader on the initial concepts of graphs such as their elements (vertices and edges), valence of each vertex, types of walk, isomorphism and operations with graphs. From this, we present the concept of connectedness so that the reader can recognize a connected or disconnected graph, the definitions of trees and forests as well as their properties. Familiar with these concepts, we then insert the concept of minimal 2 − edge − connected graphs. Using the rigor of mathematics, we test by induction the equation that brings us to the lowest lower bound of vertices of degree 2 in a minimal 2 − edge − connected graph. At this point, we are faced with an inconsistency. We found a case where the minimality of the graph was not observed but, however, the effectiveness of the equation was not compromised. After that, for the modeling of graphs, we use programs and software such as geogebra, google maps and Lucidchart, the latter specific for the assembly of network systems. We also cite the use of concrete materials such as the Geoplane that consists of a platform with pins and alloys, completely manipulable that were used in the application of a playful activity with 32 students of high school / technical in logistics which helped us in the didactic question, enabling a greater interaction between the people involved in the construction process. The proposal to involve them in this activity of obtaining a viable connection system applicable in their logistics projects generated interesting results and questions that aroused their desire to delve deeper into the theme. Instituição: Universidade Federal Rural de Pernambuco Tipo do documento: Dissertação Thu, 25 Apr 2019 00:00:00 GMT http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8464 2019-04-25T00:00:00Z http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8463 Título: Fractais : uma ferramenta no ensino médio Autor: ALVES, Delba Costa da Silva Primeiro orientador: NASCIMENTO, Ross Alves do Abstract: This work presents a proposal of analysis of the fractal geometry associated to the concepts of progressions and representation of the notion of function, specifically in the application of knowledge obtained in learning in the classroom. The proposal was constructed from a sequence of three activities, which was applied in a second year high school class of a state public school. We seek to investigate whether students working in activities based on fractal geometry, specifically the Sierpinski Triangle, seek to investigate patterns and mathematical writing based on arithmetic and geometric progression knowledge and on the concept of functions. Instituição: Universidade Federal Rural de Pernambuco Tipo do documento: Dissertação Thu, 16 May 2019 00:00:00 GMT http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8463 2019-05-16T00:00:00Z http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8462 Título: Aritmética na OBMEP : Uma análise de questões da primeira fase do nível 3 Autor: CUNHA, Thiago Andrade Lins Primeiro orientador: BARBOZA, Eudes Mendes Abstract: This work has as main objective to analyze questions of the OBMEP with an emphasis on arithmetic, to serve of support the elaboration of a material that can be used for possible and future formations given to the teachers of the High School, so that this also serves for students who intend to participate in the Brazilian Mathematical Olympiad. By reading this complete material and making some coherent adaptations, the teacher can take advantage of this selection of issues analyzed in a group assessment with problem solving in the classroom. For this, all questions of arithmetic were filtered and solved present in the Brazilian Mathematics Olympiad of the Public Schools-OBMEP from 2005 to 2018 with the purpose of facilitating the work of those who are researching a study material on arithmetic. Instituição: Universidade Federal Rural de Pernambuco Tipo do documento: Dissertação Thu, 27 Jun 2019 00:00:00 GMT http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/8462 2019-06-27T00:00:00Z