Mestrado Profissional em Matemática em Rede Nacional (IME)
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Item Utilização do software Geogebra no estudo de pontos de máximo e pontos de mínimo de funções de uma variável(Universidade Federal de Goiás, 2013-02-28) Moraes, Hugo Leonardo de; Souza., Mário José de; http://lattes.cnpq.br/4862963990848505; Souza., Mário José de; Souza, Flávio Raimundo de; Martins, Ivonildes RibeiroThis paper aims to present the main advantages of using the software geogebra in the study of problem situations involving points of maximum and minimum points of functions of one variable. The survey included a brief study on: geogebra software and some of their purposes, function of one variable, graphical representation of a function, limit, derivative, second derivative, critical points, maximum points, minimum points and applications of the study of points of maximum and minimum in problem situations everyday when using the software geogebra.Item Funções quadráticas - Estudo do gráfico das funções quadráticas(Universidade Federal de Goiás, 2013-02-28) Sousa, Fábio Antonio Leão; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Souza, Flávio Raimundo de; Martins, Ivonildes RibeiroThis paper aims to expand the knowledge about the quadratic function providing a new perspective on the behavior of its graph. Initially, presents the definition of Quadratic Function, as well as the basic concepts involving the Parable. Secondly, the Parable is characterized, describing the symmetry existing in relation to the vertical axis which contains the vertex, the intervals of growth and decrease of the function and the behavior of curve described by the graph. Finally, this study relates each coefficient of the quadratic function to the graph, giving a geometric character to the coefficients through the variation of its values.Item O estudo de determinantes sob a ótica do grupo de permutações(Universidade Federal de Goiás, 2013-02-28) Moraes, Walter José Rodrigues de; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Souza, Flávio Raimundo de; Martins, Ivonildes RibeiroThe study of determinants development through the permutations made on their lines or columns dates back to 1812, a memory presented by Cauchy to the French Academy of Sciences. The present work is, in some way, a historical rescue. Firstly, a permutation is de ned: from a superior point of view there is a bijective application and, as such, the set of permutations has a group structure; from the elementary point of view, there is an ordainment of a group's elements. The fundamental fact is, secondly, that the de nition of determinant adjusts perfectly to both conceptions, based on the parity of the permutations. Based on the de nitions, the determinants properties are presented and, therefore, it is possible to proceed with the appropriate justi cations about their validity. A rule that associates each square matrix to a real number will de ne a real function of the variable matrix, the determinant function. This is the actual way in which determinants are presented in higher levels: the determinant is the unique alternated multilinear function of the lines (columns) of a square matrix, as indicated in [10]. By this presentation there is in mind the fact that it can be served as an inspiration to posterior studies.Item Aplicações do princípio de Cavalieri ao cálculo de volumes e áreas(Universidade Federal de Goiás, 2013-02-28) Lula, Kariton Pereira; Chaves, Rogerio de Queiroz; http://lattes.cnpq.br/2029572406153004; Chaves, Rogerio de Queiroz; Souza, Flávio Raimundo de; Silva, Rosângela Maria daIn elementary mathematics teaching, it often occurs that some subjects are presented without proper justi cation or without a coherent logical construction that makes sense of those subjects and ideas in a wider context. The calculation of areas and volumes is an example of a subject in which these shortcomings are usually present. In this work, we present a model for the gradual development of the ideas involved in the calculation of volumes, in a way that is, at once, well justi ed and approachable by the average student at this stage. In order to achieve that, we make extensive use of the Cavalieri Principle, which allows not only an adequate justi cation of the expressions for the volume of cylinders, cones or spheres, but also the calculation of volumes of other shapes, such as parts of the sphere, ellipsoids and paraboloids. We conclude with an interesting application of the Cavalieri Principle to calculate the area of a parabolic segment and then give a demonstration of Archimedes' theorem.Item O ensino da matemática financeira no contexto do Instituto Federal de Educação, Ciência e Tecnologia do Triângulo Mineiro - Campus Paracatu(Universidade Federal de Goiás, 2013-02-28) Santos, Paulo Cesar Feracioli dos; Santos, Fabiano Fortunato Teixeira dos; http://lattes.cnpq.br/6866594296187427; Santos, Fabiano Fortunato Teixeira dos; Souza, Flávio Raimundo de; Cruz, José Hilário daIn this course conclusion work are presents the results of a survey conducted the IFTM - Campus Paracatu, where the students of technical courses integrated into the secondary education in the areas of informatics, electronics and trade and their responsible were invited to answer some questions in relation to nancial mathematics. Given the de ciencies presented by them are addressed themes that led to important applications in commercial and banking routines, using a language accessible to that guided the construction of mathematical procedures appropriate to each situation, and how support is suggested to use simple and scienti c calculators spreadsheet.Item Equações diofantinas lineares em duas incógnitas e suas aplicações(Universidade Federal de Goiás, 2013-03-01) Borges, Fábio Vieira de Andrade; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Rodrigues, Paulo Henrique de Azevedo; Seimetz, Rui; Oliveira, Ricardo Nunes deThe main objective of this assignment is to help students and also teachers with the resolution and understanding of problems involving the Linear Diophantine Equations with Two Incognits through the elaboration and application of didactic activities in order to contribute to the study of this kind of equations. Through the tasks it was aimed to dothe integration of Arithmetic with Algebra and Geometry by using some computational programs which worked as support to the graphical visualization of the entire solutions. In the first chapters the essence of the Elementary Theory of Numbers will be better known, since the mathematical tools which will be used to solve linear Diophantine equations will be displayed and demonstrated, some of them already known, like the greatest common divisor (g.d.c). Then the Diophantine equations and theirapplication methods for the solution of daily problems will be introduced. The Conclusion of this study highlights the importance of algebraic and geometric interpretation of Linear Diophantine Equations, and also emphasizes that the contact with problems of this area contributes to the students reasoning abilities development in a creative way. It is important to emphasize that this issue can be introduced in high school.Item Análise combinatória: uma questão de lógica e linguagens(Universidade Federal de Goiás, 2013-03-01) Alvim, Karina Guerra Cardoso; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Seimetz, Rui; Vieira, Elisabeth Cristina FariaThe objective of this work is to address the Combinatorial Analysis as a theme that can be treated in the classroom, without the utilization of mathematical formulas in problem solving. For this it will presented a method of reasoning that, basing on logic and languages, underscores the importance of: To read, interpret and analyze texts that are presented in the mother tongue; Formulate conjectures, make choices and seek strategies of count; and Make the correct translation between languages maternal and mathematics. Expected to show from this approach that the Combinatorial Analysis, besides its importance in various elds of knowledge, may also be seen by students and teachers as a challenging and stimulating content.Item Numericamente igual a π(Universidade Federal de Goiás, 2013-03-01) Marques, Túlio Guimarães; Tonon, Durval José; http://lattes.cnpq.br/3688981956532711; Tonon, Durval José; Couto, Maria Socorro Duarte da Silva; Baumann, Luis Rodrigo FernandesThis paper aims at introducing the science which is behind the most intriguing number known to history, the number . It has challenged generations of researchers who have tried to determine its value and articulate several areas of Mathematics such as Geometry, Algebra and Analysis. The quotient of ratio between the measure of the length of a circumference and the measure of its diameter are what de ne . Some historical references such as Archimedes, Euler, Leibniz and Lindemann have signi cantly contributed with the methods to precise . The rst real academic approach to this ratio was studied by the greatest mathematician of antiquity, Archimedes, when he created an instructive process for the study of the limits. With the unsolvable problem of the quadrature of the circle, ingenious geometrical constructions are born, in order to allow the drawing, with a ruler and compass, of a square having the same area as a previous given circle. The evolution of the forms employed in order to calculate have become more evident with the introduction of Analysis applied under the foundations of Calculus. At that time, the Series come to life, indispensable tools allowing the study of the behaviour of its decimal places. Along with the advances brought by them, the investigations turned towards the classi cation concerning the rationality or the irrationality of the number. In the end, we will present some contextualization and propose exercises with the aim of stimulating the search for knowledge.Item O uso do GeoGebra no ensino da geometria analítica: estudo da reta(Universidade Federal de Goiás, 2013-03-01) Marins, Leonardo de Souza; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Couto, Maria Socorro Duarte da Silva; Smith, Ole PeterThe proposed work aims to present activities of Analytic Geometry, speci cally the Study of Line, to be applied in the third grade of high school with the help of GeoGebra, which is a free Software for dynamic mathematics that combines resources of geometry, algebra and calculus, allowing students to understand the main contents. When handling the software chosen, teacher and student can identify its main characteristics and elements, and not just developing and solving formulas algebraically. Besides this, the work intends to motivate the activities to be proposed by a theoretical as well as ways of improving the teaching of this discipline and possible di culties encountered by students and teachers.Item Probabilidade - Uma proposta de ensino - O uso do teorema da multiplicação de probabilidades como um facilitador e integrador de diversas abordagens deste assunto(Universidade Federal de Goiás, 2013-03-01) Fonseca, Vanessa Jacob da; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Seimetz, Rui; Vieira, Elisabeth Cristina FariaThis work aims to establish links between the di erent possible ways to resolve some issues involving the calculation of the probability of an event occurring through the use of the Multiplication of Probability Theorem (Theorem 2) and, from it, to show that we can solve problems involving simultaneous withdrawals, originally settled by Combinatorial Analysis, replacing them by successive withdrawals without replacement, considering the range of possible clusters (Theorem 4). Highlighting some precursors and their contributions to the development of Probability Theory, such as Cardano, Pascal, Laplace and Kolmogorov, among others. Exemplify, through problem solving, application of Theorem 4 to show the simpli cation of the calculation of probabilities applied, and propose activities that encourage discussion in the classroom, in order to clarify with the teacher's intervention, concepts such as Independent Events and using the Binomial Distribution.Item A utilização da calculadora HP-12C no ensino da matemática financeira visando a qualificação profissional(Universidade Federal de Goiás, 2013-03-01) Simão, Júnio César Mendes; Santos, Fabiano Fortunato Teixeira dos; http://lattes.cnpq.br/6866594296187427; Seimetz, Rui; Lima, Aline de SouzaThis paper deals with the learning of some content from Financial Mathematics using the HP-12C calculator, to prepare citizens for both managing its own nances and for the labor market. The matter will be addressed through practical applications in a pleasant and e ective, with the intention to make students able to resolve nancial situations that present themselves in a critical way, not being carried away by misleading proposals. At the end we present some practical applications where advertisements will be analyzed.Item Frações contínuas e aplicações no ensino médio(Universidade Federal de Goiás, 2013-03-15) Nascimento, Amanda Melo do; Tonon, Durval José; http://lattes.cnpq.br/3688981956532711; Tonon, Durval José; Rodrigues, Luciana Maria Dias de Ávila; Souza, Anyelle Nogueira deContinued Fractions and applications in High School begins with the historical context, the socially constructed over 2500 years, over which originated the study and training of numerical sets in order to substantiate the importance of irrational numbers and their peculiarities . Reintroducing some basic concepts of Numerical Sequences and their converging that are important for understanding the study of approaches from the study of continuous fraction. The discussion and centered on the study of continued fractions, exploring its historical part, basic concepts and their relation to the Euclidean algorithm. It is shown the importance of both approximations of rational numbers as irrational, in order to decrease the gap between finite and infinite for the construction of all the dollars. In the final chapter I present a mini-course for high school students, public school, looking for higher courses in the exact sciences and aim to achieve greater integration with this important segment. All matters discussed in this work will be developed in the course, showing their properties and applications.Item A hipérbole e suas aplicações(Universidade Federal de Goiás, 2013-03-15) Silva, Diego Maradona Félix da; Tonon, Durval José; http://lattes.cnpq.br/3688981956532711; Tonon, Durval José; Rodrigues, Luciana Maria Dias de Ávila; Souza, Anyelle Nogueira deThe Hyperbole and its Applications begins with a brief historical background on the origins of the conic sections analysis, followed by a proposition of a new approach to the conic sections studies in High School, due to the large amount of important applications these studies have in everyday life. The rst chapter of the research presents the primary concepts necessary to a good hyperbole study understanding. After presenting this concepts the research focuses in the evidence of the hyperbole concept, its most important elements, the rotary axis and the hyperbole properties. Among these properties, the main object of this study is the re ective hyperbole property, since it can be applied to many elds of study such as Astronomy, in the Telescopes and even Navigations. Some other properties are brie y mentioned during this work and others have a more detailed approach. Finally, a largely used new coordinates system is presented - the Polar Coordinate System. The research purpose is to infer, by the use of this new system, the equations of the ellipse, parable and hyperbole.Item Transformações lineares no plano e aplicações(Universidade Federal de Goiás, 2013-03-15) Nogueira, Leonardo Bernardes; Melo, Maurílio Márcio; http://lattes.cnpq.br/9171320863927413; Melo, Maurilio Márcio; Borges, Venício Veloso; Medrado, João Carlos da RochaThis paper begins with a brief history about the development of vector spaces and linear transformations, then presents fundamental concepts for the study of Linear Algebra, with greater focus on linear operators in the R2 space. Through examples it explores a wide range of operators in R2 in order to show other applications of matrices in high school and prepares the ground for the presentation a version of Spectral Theorem for selfadjoint operators in R2, which says that for every operator self-adjoint T : E!E in finite dimensional vector space with inner product, exists an orthonormal basis fu1; : : : ;ung E formed by eigenvectors of T, and culminates with their applications on the study of conic sections, quadratic forms and equations of second degree in x and y; on the study of operators associated to quadratic forms, a version of Spectral Theorem could be called as The Main Axis Theorem albeit this nomenclature is not used in this paper. Thereby summarizing a study made by Lagrange in "Recherche d’arithmétique ", between 1773 and 1775, which he studied the property of numbers that are the sum of two squares. Thus he was led to study the effects of linear transformation with integer coefficients in a quadratic form in two variables.Item Números primos: pequenos tópicos(Universidade Federal de Goiás, 2013-03-15) Carvalho, Glauber Cristo Alves de; Melo, Maurílio Márcio; http://lattes.cnpq.br/9171320863927413; Melo, Maurílio Márcio; Medino, Ary Vasconcelos; Cruz, José Hilário daThis paper presents a brief history about the numbers. After some important definitions to understand the texts. Following, we encounter the world of prime numbers. This part is presented some important properties, findings and open problems. The study of these figures have managed to find some formulas to generate them, which are presented throughout the text. It presents some numbers especias such as Fermat primes, Mersene, Shopie German and others. Finally, we have an application that uses many properties presented.Item O uso do Geogebra no ensino da geometria analítica: estudo da circunferência(Universidade Federal de Goiás, 2013-03-15) Oliveira, Carlos André Neiva de; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Rodrigues, Paulo Henrique de Azevedo; Medino, Ary Vasconcelos; Smith, Ole PeterThis work refers to the GeoGebra application use for teaching analytic geometry. In this work it was made a guidelines approach about the PCNEM, to teach and discuss the use of the technologies in analytic geometry about computers, software and mathematics. It was made a brief history about the applications testing some tools checking if they are useful to develop circumference studies to apply in high school rst grades using that GeoGebra study.Item Introdução à análise convexa: conjuntos e funções convexas(Universidade Federal de Goiás, 2013-03-18) Amorim, Ronan Gomes de; Cruz, José Yunier Bello; http://lattes.cnpq.br/8377200040018415; Sandoval, Wilfredo Sosa; Cruz, José Yunier Bello; Pérez, Luis Román LucambioThis paper presents the main ideas concerning convex sets and functions. Our aim is to deal, didactically, with the main topics concerning convexity, as well as the consequent exploitation of the envolved mathematical concepts. In this sense, we have made a bibliographic revision approaching important theorems, lemmas, corollaries and propositions designed both to first readers and to those who want to work with applications arising from convexity. We hope that this study may constitute an important research source either for students, teachers or researchers who wish to learn more about convex sets.Item Problema de otimização envolvendo a matemática do ensino médio(Universidade Federal de Goiás, 2013-03-22) Rocha, Alan Martins; Chaves, Rogério de Queiroz; http://lattes.cnpq.br/2029572406153004; Chaves, Rogério de Queiroz; Souza, Flávio Raimundo de; Mizukoshi, Marina TuyakoApplied Mathematics is the branch of mathematics which deals with the application of mathematical knowledge to solving problems in other areas and, in the current curricula for secondary education in Brazil, it has not been as adequately explored as it could be. Optimization, for instance, is one type of mathematical applications which allows solving problems related to economy, management, engineering, transport and logistics, among others and can be introduced, at a basic level, in secondary school. With that in view, this work aims to present a few algebraic tools, accessible to the secondary school student, that allow solving some interesting elementary optimization problems. These tools include optimization of quadratic functions, discrete functions, some continuous functions, as well as some applications of the inequality between arithmetic and geometric means. The use of these methods is illustrated through several examples, chosen in a way that shows the rich variety of problems that can be solved with the seemingly basic tools presented. With this we aim at presenting these topics, accessible to secondary education, in a novel and interesting way that is attractive to students and, once assimilated, they can become powerful tools for solving several problems, whether they come from the daily experience, from mathematical olympics, or from exams.Item Utilização do software maxima no estudo de funções polinomiais do 1o grau e 2o grau(Universidade Federal de Goiás, 2013-03-22) Rodrigues, Maraíza Merylen Pereira; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Souza, Flávio Raimundo de; Mota, Jesus Carlos daThis work has as main objective to present the advantages of using the software MAXIMA in the study of polynomial function of 1nd degree and 2nd degree. The research included a brief study on: the MAXIMA software and its applications in functions, construction of graphics and resolution of situations everyday problems. Applications of functions with the MAXIMA software.Item Construções geométricas e os problemas de apolônio(Universidade Federal de Goiás, 2013-03-22) Vieira, Mariana Araújo; Cruz, José Yunier Bello; http://lattes.cnpq.br/8377200040018415; Cruz, José Yunier Bello; Seimetz, Rui; Martins, Ivonildes RibeiroThis paper aims to present the main problems of Apollonius....