Licenciatura em Matemática (Sede)

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

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APP - Artigo Publicado em Periódico
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TCC - Trabalho de Conclusão de Curso

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Análise de correlação entre a produção primária bruta do sensor MODIS e balanço hídrico do SWAT para bacia hidrográfica do Riacho do Pontal, Pernambuco
(2021-07-19) Brito, Pedro Vinícius da Silva; Silva, Antonio Samuel Alves da; http://lattes.cnpq.br/0249875496935177; http://lattes.cnpq.br/2946714997867399
The correlation between gross primary production and the water balance of the Riacho do Pontal watershed, located in the state of Pernambuco, Brazil, was evaluated. For this, the components of precipitation (PRECIP), water production (WYLD), soil water storage (SW), surface runoff (SURQ), potential evapotranspiration (PET) and actual evapotranspiration (ET) of the water balance were used simulated by the SWAT model and the MOD17A2H remote sensing product of Gross Primary Productivity (GPP) from the MODIS (MODerate Resolution Imaging Spectroradiometer) sensor. The data obtained by the MODIS sensor and the SWAT model were analyzed and then correlated using Spearman correlation coefficient. The results show that the minimum GPP with runoff had the lowest correlation value of the entire analysis (of 0.13), a negative correlation with the potential evapotranspiration (of -0.63) and positive with the other components of the balance water, ranging from 0.22 with precipitation to 0.38 with actual evapotranspiration. With the average GPP, there was a negative correlation for potential evapoternspiration (from -0.74), and with the other components of the water balance, there was a positive correlation, ranging from 0.36 with runoff to 0.6 with real evapotranspiration. At maximum GPP, there was again a negative correlation with potential evapotranspiration (from -0.76), and a positive correlation with all other components of the water balance, ranging from 0.28 with runoff to 0.46 with actual evapotranspiration and water production. The existence of a correlation between the gross primary production and the water balance was observed, even if it is low, as occurred between the minimum GPP and the runoff. The correlation between GPP and real and potential evapotranspiration was greater than the correlation between GPP and the other components of the water balance, with the exception of the maximum GPP with water production, which had the same value as the maximum GPP with the real evapotranspiration. Thus, monitoring evapotranspiration in semiarid regions is of great importance for predicting gross primary production. And according to the predictions of the Intergovernmental Panel on Climate Change (IPCC), which predicts the increase of extreme events in semiarid regions, it is possible to say that if climate change scenarios come to occur, there is a strong trend in production primary gross, in semiarid regions, decrease.
Uma análise de um livro didático de matemática à luz do Conhecimento Tecnológico Pedagógico do Conteúdo (TPACK)
(2019-12-20) Santos, Matheus Henrique Silva de Lima; Costa, Wagner Rodrigues; http://lattes.cnpq.br/7087770599703498; http://lattes.cnpq.br/7593592713599499
In the last years, several teaching materials have been developed to improve mathematics teaching. Among these resources, materials such as books, handouts and class notes have been badly seen in the student’s eyes, because they carry a more refined mathematical language. In this context, the emergence of Information and Communication Technologies (ICT) for teaching is increasingly present in the school environment, however are they all well applied and on time? Do these technologies really help as they promise? What about the teacher, are they prepared to use this kind of tool? Based on these questions, this article presents concepts present in the Technological Pedagogical Content Knowledge (TPACK), studied by Koehler and Mishra by adding the technology to Shulman's studies on Pedagogical Content Knowledge (PCK). Also used in the research were the foundations described in the Common National Curriculum Base (CNCB) about the skills that students should have about geometry in basic education. After an in-depth analysis of these two theoretical foundations, an analysis was performed in a textbook of the 9th grade of Elementary School, in order to seek the guidance present in it for the use of technologies in the classroom. In the end, direct references to CNCB and the use of technologies such as Geogebra, websites to assist studies, links to videos with educational content and suggestions on dynamic activities that enhance student’s learning in the classroom, as well as contributing to the maintenance and the improvement of the methodologies of the teachers of the basic education.
Bingo Pitagórico: um recurso didático para o estudo do teorema de Pitágoras com estudantes surdos
(2024-03-07) Oliveira, Izadora Matilde de; Espíndola, Elisângela Bastos de Melo; Marques, Rafael Emil Korossy; http://lattes.cnpq.br/7531969835893918; http://lattes.cnpq.br/0367382856462792; http://lattes.cnpq.br/6855272795384830
This research aims to analyze the use of the "Pythagorean Bingo" as a didactic resource to promote the understanding of deaf students of the 1st year of High School about the Pythagorean theorem. For this, we took as theoretical support research on the teaching of mathematics to the deaf. The research was carried out with 12 deaf participants, students of a public school in Recife-PE. Data production occurred in three stages. In the first, we made a diagnosis about the students' difficulties in Mathematics and especially about the Pythagorean theorem. In the second, we aim to explain how to calculate the measurement of one of the sides of the right triangle in order to prepare students for the use of the game. In the third stage, we applied a questionnaire for the students to give their opinion on the activities that were carried out in the previous stages. The results indicate that the students had a good development in the understanding of the Pythagorean theorem with the realization of the game. This reveals clues about the need for more research on games and other didactic resources for teaching Mathematics to deaf people in the final years of Elementary School and/or High School.
Um breve estudo sobre a curvatura média e o teorema de Aleksandrov
(2022-06-08) Lira, Yasmin Alves Sobrinho; Gomes, Renato Teixeira; http://lattes.cnpq.br/0570606157057337; http://lattes.cnpq.br/4862014205090674
When looking for the eigenvalues of the differential of the normal Gauss map dN, naturally arise in its characteristic polynomial two functions that are invariant by change of base of this operator: the determinant of the matrix of the normal Gauss map, called Gaussian curvature and the trace of this application. As this linear map is self-adjoint,there is an orthonormal basis in which its matrix is written diagonally in terms of the principal curvatures, and its determinant and trace are given by det(dN) = (−k1)(−k2) and its dash by tr(dN) = −(k1+k2). The negative half of the H = k1 + k2/2 is the so-called mean curvature, which was introduced by French mathematician Sophie Germain when studying a problem related to membrane vibrations. At this time, a problem proposed by Lagrange, which later received the name of Plateau’s problem, a Belgian physicist who carried out several experiments and in-depth studies on soap films around 1850, was, roughly speaking, to determine a surface that has the smallest area among those which have the edge given by a prescribed Jordan curve. It can be shown that such a surface has zero mean curvature at its regular points. Such surfaces are called minimal and are named after Lagrange. In this work we will make a brief study on mean curvature and minimal surfaces,demonstrating some results and presenting some examples of such surfaces. Furthermore, we will demonstrate Aleksandrov’s theorem which under certain assumptions says that the only compact surface with constant mean curvature in R3 is the sphere. For this, we will demonstrate this result with a different “machinery” the one used by Aleksandrov. We will follow R. Reilly’s approach in his article “Mean Curvature, the Laplacian and Soap Bubbles” which makes use of more basic knowledge of differential and integral calculus and surface theory for its demonstration.
Um breve estudo sobre a geometria diferencial de superfícies em R3
(2021-07-23) Santos, Túlio José de Souza; Gomes, Renato Teixeira; http://lattes.cnpq.br/0570606157057337; http://lattes.cnpq.br/5181696493328012
The purpose of this work is to make a brief study on the differential geometry of surfaces in R3, with the objective of demonstrating the Gauss-Bonnet theorem in its local and global version. This relevant result relates the geometry and topology of surfaces in R3 and has very interesting consequences. Through it, it is possible to give an answer to an ancient problem of determining whether Euclid’s fifth postulate is an axiom or a theorem. In fact, what is obtained is that there is no harm in denying the fifth postulate, that is, to suppose that there may be more than one or no parallel line to a line r passing through a point p outside of r. What is found are "brave new worlds"that have different geometries from the Euclidean one.
Um breve estudo sobre o transporte paralelo, geodésicas e a aplicação exponencial
(2023-09-15) Costa, Matheus Rabelo Viana da; Gomes, Renato Teixeira; http://lattes.cnpq.br/0570606157057337; http://lattes.cnpq.br/3078665075835586
Geodesics are curves on a regular surface that have the property of locally minimizing length, that is, if two points are close together, the curve that has the shortest length connecting these two points is a geodesic. They are roughly the "straight lines"of the surface, as they have a constant velocity vector norm, and are zero acceleration curves. We can arrive at these curves through the solution of a variational problem, or following the "path of Geometry"in which we define geodesics as a curve whose field of tangent vectors is parallel. The study of these curves on a surface leads us to the knowledge of several important geometric properties, in addition to the development of new machinery, such as special coordinate systems, for example, which facilitate the study of surfaces and help in the calculation of their important geometric structures. In this work we will make a brief study about parallel transport, Geodesics and the exponential map and its properties. We will study the notion of a covariant derivative, and how we parallel transport vectors along curves. With this idea of parallelism, we will define geodesics as a curve that has a field of parallel tangent vectors, we will study some properties of these curves and the geodesic curvature of curves on surfaces. Finally, we will study the exponential map, the normal coordinate system and the geodesic polar coordinate system and we will use this one to, among other things, show that geodesics have the property of locally minimizing the length.
Cálculo de área dos triângulos e quadriláteros: um estudo sobre as fórmulas de Heron e Brahmagupta
(2023-12-18) Santos, Ricardo Araújo dos; Souza, Cícero Monteiro de; http://lattes.cnpq.br/7540654793551489; http://lattes.cnpq.br/7957290918342325
The present work aims to make a historical analysis of the calculation of areas of triangles and quadrilaterals. Initially, a brief history of mathematics was necessary, more specifically of Geometry in ancient civilizations such as: Mesopotamia, Egypt, India and Greece from Thales of Miletus (c. 624 – 546 B.C.) and Pythagoras (c. 585 – 500 B.C.). In Greece, the areas of plane figures were systematized and recorded in the 13 books of Euclid's Elements. In the 1st century, the mathematician Heron of Alexandria (c.10 – 70 A.D.) came up with a formula to calculate the area of any triangle, requiring only knowledge of its perimeter. In the 7th century, using as a basis the knowledge left by Heron, Brahmagupta (598 – 668) created a formula to determine the area of any quadrilateral when its sides were known. Later, with the advancement of trigonometry, it was found that Brahmagupta's formula was valid only for cyclic or inscribable quadrilaterals.
Cálculo Diferencial e Integral: Uma abordagem prática mediante o uso do Software Geogebra
(2019-12-20) Santos, Elizabeth Bispo dos; Silva, Tarciana Maria Santos da; http://lattes.cnpq.br/1650180237175460; http://lattes.cnpq.br/9799662711705928
This monograph has as its theme the use of Geogebra in the teaching of differential and integral calculus. To this end, we made a historical overview showing how the calculation has developed over the years as well as a manual on how to work the concepts of Derivative and Integral through Geogebra Software, making the approach of these contents more playful and current. In higher education, the teaching of differential and integral calculus is characterized as an abstract process, as it is new concepts for students. The difficulty of these disciplines is apparent from their abstraction and the need for graphical and algebraic representations which students find arduous. In view of this, a workbook for the use of Geogebra Software was developed in this work, with the objective of assisting teachers and academics in the contents of these subjects. The work addresses the main concepts of derivatives and integrals and then their graphical representations through Geogebra. Geogebra Software has great potential in helping classroom practices, as it provides new pedagogical approaches to teachers, positively influencing the posture and pedagogical practices of each teacher.
A compacidade em alguns universos topológicos
(2021-07-13) Lima, Alexandre César Bispo; Carvalho, Gilson Mamede de; http://lattes.cnpq.br/0044877127514130; http://lattes.cnpq.br/4592972030162451
This work aims to study and establish relationships between compact sets and topology, emphasizing the compactness of the unitary closed ball in different contexts. For this, initially we dealt with topological spaces in Chapter 1, we developed basic concepts and tools that will be useful until we get to the central theme of compactness. Then, in Chapter 2, we focus the study on the more particular environment of metric spaces, where we develop the concepts and results in order to end the chapter with a compactness characterization of the unitary closed ball of space. Finally, in Chapter 3, we study how weak and weak* topologies, drawing as a final result the famous Banach- Alaoglu-Bourbaki Theorem, which tells us that the unitary closed ball in the topological dual of a space of Banach is weak* compact.
Os conceitos de fração parte-todo, quociente e operador: a necessária diferenciação desses subconstrutos na prática docente
(2019-08-12) Brito Junior, Jairo Jose Ribeiro Toscano de; Rodrigues, Cleide Oliveira; http://lattes.cnpq.br/2951731416008876; http://lattes.cnpq.br/1567270124477805
Os conhecimentos matemáticos de feirantes da cidade de Jaboatão dos Guararapes - PE
(2023-05-03) Nascimento, Dayvid de Oliveira; Alves, Maria do Socorro Valois; http://lattes.cnpq.br/1019759205900756; http://lattes.cnpq.br/9504031141445096
Construções de fractais com o GeoGebra e dimensão fractal
(2021-12-21) Souto, Rafael Almeida; Tanaka, Thiago Yukio; Didier, Maria Ângela Caldas; http://lattes.cnpq.br/9721552594807972; http://lattes.cnpq.br/3394446426392577; http://lattes.cnpq.br/5859671240920200
In this work, we will present the elements and concepts related to Fractal Geometry such as its definition, classification into types, properties, and some measurable characteristics such as area, perimeter, and dimension measurements. At first, we will focus on the characterization of the most classic fractals of the theory, such as the Sierpinski triangle, the Koch curve, the Cantor set, among others. We will show how to build these objects using the mathematical tool of geometric transformations and their matrix translations and the implementation of these concepts through GeoGebra dynamic geometry software, which allows us to build the vast majority of fractals that will be mentioned during the work. Finally, we will also present a study on the concept of fractal dimension, whose applications are vast in various areas such as Economics, Medicine, Biology, among others. More precisely, we will present two methods of obtaining a fractal dimension, the first using the Hausdorff-Besicovitch method and a second way using the box-counting method. We believe that this monograph can be used as the first guiding material for studies and research in the field of Fractal Geometry, mainly due to the richness of details, especially for those who are unaware or know little about the theory. In addition, by bringing construction methods with GeoGebra, we believe that the material also serves as a guide to guide the use of theory in the classroom for students of the Licentiate Degree in Mathematics, future teachers. Finally, for those who already have a basic knowledge of fractals, the dimension study serves as a basis for guiding the application of this object.
As contribuições do GeoGebra na prática docente para o desenvolvimento de tarefas exploratórias de função afim
(2022-06-07) Nascimento, Tatiane Gervásio do; Rodrigues, Cleide Oliveira; http://lattes.cnpq.br/2951731416008876
Cremona, Jonquières e o Dual Complementar de Newton
(2021-02-25) Bonfim, Silvio Cavalcanti; Silva, Bárbara Costa da; http://lattes.cnpq.br/9423717597968308; http://lattes.cnpq.br/0303286905054643
The present work deals with the relationship between Newton’s dual complement and birational maps, which it originated in the works of B. Costa, A. Simis and A. Dória. Initially, it presented the necessary concepts of commutative algebra and algebraic geometry through algebraic optics. In sequence, it addressed Newton’s main, dual complementary theme and its properties, assuming that the sets of monomials satisfy the canonical constraint. And then, it discussed the relationship between birationality and Newton’s complementary dual, analyzing that the dual complements and preserves the elements of the Cremona group and the Jonquières maps subgroup.
Da propagação do calor à construção de desenhos: uma aplicação das séries de Fourier com Python
(2024) Domingos, Cleianderson Paz; Freitas, Lorena Brizza Soares; http://lattes.cnpq.br/2302580820419163; http://lattes.cnpq.br/8909785797719318
This work aims to present an application of Fourier series in generating figures. To do so, we first study the problem of heat conduction in a finite rod, as well as the equation that models it and its solution, both proposed by Joseph Fourier in the early 19th century. Initially, a historical note is presented, exhibiting some facts that lead to the motivation for studying heat propagation. Then, we derive the Heat Equation from two physical laws and study how Fourier series emerge in an attempt to solve this equation. Subsequently, through convergence theorems, we study necessary conditions for a function to be represented by its Fourier series. Finally, we explore an application of Fourier series in figure generation using epicycles and develop a Python algorithm to visualize this application.
Dados estatísticos da pandemia do COVID-19: possíveis utilizações para o letramento estatístico
(2021-05-27) Silva, Diego Felipe Lourenço da; Oliveira, Wanderson Aleksander da Silva; http://lattes.cnpq.br/2008221101871542; http://lattes.cnpq.br/0553453285776196
The COVID-19 pandemic has led to many unforeseen situations, among which we can highlight those related to the advancement of information and communication technologies, such as, for example, the increase in the use of electronic commerce and the implementation of teaching models inspired by the hybrid education, but many difficult and bad situations for the population, highlighting the Brazilian, reality in question. Still in this perspective, there is a massive amount of information disseminated at all times about the pandemic, including in the form of statistical data. However, it is of paramount importance that these data are understood by the population, and then concerns about Statistical Literacy (LE) in schools emerge assist in the formation of citizens. Thus, this research aims to identify activities that can be developed with the statistical data of the pandemic of the new coronavirus, aiming at Statistical Literacy for students of Basic Education, based on the discussions of Gal (2002). Therefore, it was necessary to frame the research as qualitative and as a case study to analyze the data of the pandemic in Brazil, additionally, research was carried out on the official websites of the Ministry of Health to extract the data necessary for analysis. As a result, it was possible to identify mathematical subjects, more specifically in elementary school, final years 9th year, which can be incorporated together with statistical data, enabling the development of activities in order to provide Statistical Literacy. Therefore, the research brings the visibility of the importance of the LE for the formation of the citizen, with activities that can be applied in the 9th year and can improve the statistical understanding of the students, resulting in beneficial social impacts for society.
Do binômio de Newton ao polinômio de Leibniz, demonstrações e aplicações
(2021-07-29) Oliveira, Marcílio Souza Rodrigues de; Oliveira, Wanderson Aleksander da Silva; http://lattes.cnpq.br/2008221101871542; http://lattes.cnpq.br/9049854828595642
The purpose of this work is to present Newton’s Binomial (1643-1727) focusing on its generalization given by Leibniz’s Polynomial (1646-1716) and its utilities for calculating probabilities, establishing connections with real or non-real contexts. The idea of enabling applications of Newton’s Binomial and Leibniz’s Polynomial through practical examples such as coin toss, probability of defeat and their use in genetics, aimed to show the applicability and usability of these tools in events of any nature. In addition, we detail, in the algebraic and combinatorial scope, the demonstrations of all the properties and theorems existing in the work, with the aim of the reader to satisfactorily reach an understanding of the concepts presented. Finally, it is worth noting that in the body of the work the reader will be introduced to the history of the concepts that will be worked on and of the mathematicians present.
Domínios com Fatoração Única em Ideais
(2019-01-10) Soares, Matheus Nunes; Guedes, Gabriel Araújo; http://lattes.cnpq.br/6087142765405339; http://lattes.cnpq.br/3706962639781669
The following work is a study on integral domains that are not UFD, but are Dedekind Domains, in other words, the elements of the domain do not have unique factoration but your ideals have it. The principal objective is proof that the quadratic ring Z[√-5] is Dedekind domains but not UFD.
Elaboração de tarefas de sequências de padrões por professores dos anos iniciais em um processo formativo remoto
(2023-05-10) Santos, Débora Beatriz Batista dos; Almeida, Jadilson Ramos de; http://lattes.cnpq.br/5828404099372063; http://lattes.cnpq.br/3802386317184840
The objective of this work was to present a study about the formation process of algebraic thinking of teachers in the early years of elementary school, according to the Objectification Theory, when they elaborate tasks of sequences and patterns in a remote formative process. The continuing education, carried out by the search group Al-Jabr with support from FACEPE (Publication APQ 16/2021), involved the participation of teachers and coordinators of elementary schools in the state of Pernambuco, debated how to work specific tasks in classrooms aimed at students' ability to think algebraically. The continuing education was based on the Objectification Theory (OT). The OT is a cultural-historical theory focused at non-individualistic teaching and learning. We focused on the analysis of the 6th meeting of a small group of teachers who created two tasks about sequences and patterns in a remote joint labor. In this sense, we had specific objectives to analyze how teachers elaborate task commands and if there is the presence of the three vectors of algebraic thinking. Among the results obtained, we identified that the teachers were able to create the tasks and discuss their analysis of the presence of vectors. The teachers were also able to determine the type of generalization of each elaborated task. We conclude that adequate continuing education for teachers transforms their attitudes as educators and we can observe that the remote joint labor was a process that aimed to make teachers reflective and critical in the elaboration process.
Ensino e aprendizagem dos polígonos regulares: uma abordagem lúdica sobre os movimentos de simetria no ensino fundamental
(2022-10-19) Amorim, Welisson de Almeida; Silva, Thiago Dias Oliveira; http://lattes.cnpq.br/7439995985621562; http://lattes.cnpq.br/3297151195837218
The teaching of geometry in elementary school is linked to the visualization of the geometric object and essential mathematical notions. When possible, one should co-relate physical objects with the theory in order to establish a better understanding for the students. Thus, this work uses this argument for its construction and addresses an intimate relationship with the use of physical objects and theory. This work focuses on presenting the teaching and learning process of regular polygons about their symmetry movements. Given in a systematic way, this process is given through the relationship with the theory of dihedral groups and the use of playful materials that permeate children’s daily lives. In particular, such materials are related to the character “Patrick Estrela" from the children’s series “SpongeBob” and a children’s board game called “Gometric board”. Regular polygons but also their characteristics. Speaking of which, a very important characteristic of regular polygons is their invariant form when rotation and reflection movements are applied. Hence, this work uses this property and the physical/playful objects already mentioned to establish a better assimilation in the teaching and learning about regular polygons When formulated, such relationships will be applied in a 6th grade elementary school class, explaining at the end all the results of the intervention.