IME - Instituto de Matemática e Estatística
URI Permanente desta comunidade
Navegar
Navegando IME - Instituto de Matemática e Estatística por Título
Agora exibindo 1 - 20 de 421
Resultados por página
Opções de Ordenação
Item A matemática da música: uma possibilidade para o ensino-aprendizagem(Universidade Federal de Goiás, 2023-11-29) Oliveira, Jéfferson Neres; Santos, Ronaldo Antonio dos; http://lattes.cnpq.br/9663485072140551; Santos, Ronaldo Antonio dos; Gomes, Alacyr José; Batista, Marcos RobertoIn our society, Mathematics and Music often hold opposing positions. While the former is associated with suffering, difficulty, and, for some, even elicits repulsion, the latter is a source of enjoyment and happiness, consistently linked with feelings of pleasure and well-being. Although seemingly at odds when we consider about the sensations that each one evokes within us, music and mathematics share profound connections. In this work we study and explore these connections with the aim of gaining a deeper understanding of the history and theoretical underpinnings of music. Additionally, we propose contributions related to this subject to enhance the teaching and learning process, making it more meaningful. We believe that the most effective way to fully leverage the connections between music and mathematics is through the use of an Active Methodology. The type of methodology we chose was problematization, which presents a logical sequence that involves collecting data, raising hypotheses, discussions, experiments, reaching the synthesis and consolidation of this knowledge, and even the generalization of results. In this sense, we present proposals that involve the contents of ratios, proportions, directly and inversely proportional quantities, logarithms, operations with radicals, and trigonometric functions. We emphasize that the proposals do not aim to teach the mentioned contents from the beginning but rather to deepen these concepts, promoting more meaningful learning. The proposals we present aim to emphasize mathematics' capacity to extend into various other fields, typically aiding in the comprehension of the specific characteristics of those domains and offering tools for their systematization. This characteristic has often been overlooked in the context of mathematics teaching and learning.Item Ação de automorfismos livres de pontos fixos(Universidade Federal de Goiás, 2016-05-13) Araujo, Daniel dos Santos; Oliveira, Ricardo Nunes de; http://lattes.cnpq.br/0563210461148997; Silva, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; Silva, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; Oliveira, Ricardo Nunes de; http://lattes.cnpq.br/0563210461148997; Acciarri, Cristina; Lima, Aline de SouzaIf a Zn-graded Lie ring L admits a fixed point free automorphism of order n, then L is soluble and the derived length of L is bounded in function only on n. In this work, we study some results about the derived length of the Zn-graded Lie rings and in the particular case that n = 6, we also study properties to the nilpotency class of the lower central series of L. For this, we introduce some basic results of Lie algebras theory and Lie rings, as well preliminary concepts of modules and tensor product. Finally, we study a Lie ring associated to a group once many problems in group theory can be treated by linear methods about Lie algebras and Lie rings.Item Ajuste de curvas usando métodos numéricos(Universidade Federal de Goiás, 2018-06-28) Sousa Neto, Theófilo Machado de; Vieira, Ewerton Rocha; http://lattes.cnpq.br/9011778118531233; Vieira, Ewerton Rocha; Andrade, Kamila da Silva; Lima, Dahisy Valadão de SouzaGiven the need to discuss mathematical methods capable of adjusting curves that represent experimental data. This work presents seven methods of curves adjustment, three of these, methods that use least squares regression techniques and the other four, using interpolation techniques. Initially, it brings some definitions that present to the reader all the mathematical foundation that rules the equations. In parallel, it seeks to discuss, through examples, the area of attribution of the described methods, realizing whenever possible a comparation between the several techniques presented and their errors in the estimates. In order to demonstrate that the techniques discussed here are feasible for use in basic education, it exposes an experience of applying one of these methods in solving a basic problem of the discipline of Physics. After presenting the step-by-step method of obtaining soil resistivity, a variable that is of the utmost importance for the elaboration of projects for grounding meshes that supply energy substations, We finish this work by solving the problem with the aid of adjustment techniques curves studied, proposing the inclusion of the methods addressed in one of the steps of the procedure to obtain soil resistivity.Item A álgebra dos polinômios(Universidade Federal de Goiás, 2020-05-28) Sousa, Reginaldo Jacinto de; Dias , Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias , Ivonildes Ribeiro Martins; Martins, Ivonildes Ribeiro; Assis, Aline Mota de MesquitaIn this work, we will approach the definition of polynomial using the concept of sequence, which allows you to remove the ambiguity from the symbol x, and we will study the algebraic structure of the polynomial rings, the concept and criteria of polynomial irreducibility and factoring of a polynomial in the product of irreducible polynomials, aiming to provide mathematics teachers who work in high school, a deepening in the study of abstract algebra. Obtaining, some suggestions of applications in the classroom, for example, the study of the rationality of a given number.Item Álgebras associadas a grafos orientados em níveis e a propriedade da Koszulidade(Universidade Federal de Goiás, 2014-11-20) Vasconcelos, José Eder Salvador de; Lima, Aline de Souza; Silva, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; Rodrigues, Paulo Henrique de Azevedo; Lima, Aline de Souza; Guerreiro, Marinês; Lemos, Manoel José Machado Soares; Castonguay, DianeIn this work we study classes of algebras associated with layered directed graphs. Let be a layered directed graph. We determine the algebra Apq; generated by the edges of the graph, satisfying a set of quadratic relations R; and the dual algebra Apq!, associated with grpApqq. For each P Autpq we determine: the algebra Ap q; where is the subgraph of whose vertices are xed by ; the graded trace generating functions Tr pApq; tq and Tr pApq!; tq: We also determine the multiplicities of the irreducible representations of AutpApqq acting on Apq and Apq!: We show that for a layered directed graph , satisfying some hypotheses, AutpApqq K Autpq. Finally, we verify the property Tr pApq; tq Tr pApq!; tq 1 for all P Autpq, called koszulity property. We consider two classes of algebras, the algebra associated to the Hasse graph of the partially ordered set of faces of a star polygon, Ap q; and the algebra associated with the Hasse graph of the lattice of subespaces of a nite dimensional vector space over Fq; ApLpn; qqq:Item Um algoritmo para estimar a dimensão do segundo grupo de homologia de um grupo finitamente apresentado(Universidade Federal de Goiás, 2012-04-12) VIEIRA, Flavio Pinto; SERCONEK, Shirlei; http://lattes.cnpq.br/2718527331501182; ADORNO, Ticianne Proença Bueno; http://lattes.cnpq.br/7769491630579878The main goal of this work is to establish a primary bound for the dimension of the second homology group of a group G, with coefficients in a field k of characteristic p, H2(G;k), using the operating system GAP. It will be presented with several examples, where in some cases, will be calculated the exact dimensions and in other cases only an upper bound.Item Um algoritmo proximal com quase-distância(Universidade Federal de Goiás, 2015-02-25) Assunção Filho, Pedro Bonfim de; Bento, Glaydston de Carvalho; http://lattes.cnpq.br/1089906772427394; Bento, Glaydston de Carvalho Bento; Cruz Neto, João Xavier da; Ferreira, Orizon PereiraIn this work, based in [1, 18], we study the convergence of method of proximal point (MPP) regularized by a quasi-distance, applied to an optimization problem. The objective function considered not is necessarily convex and satisfies the property of Kurdyka- Lojasiewicz around by their generalized critical points. More specifically, we will show that any limited sequence, generated from MPP, converge the a generalized critical point.Item Algoritmo proximal inexato tipo descida para otimização suave(Universidade Federal de Goiás, 2013-05-20) Godoi, Gean Henrique; Silva, Geci José Pereira da; http://lattes.cnpq.br/9174074436425246; Silva, Geci José Pereira da; Santos, Paulo Sérgio Marques dos; Ferreira, Orizon PereiraThe proximal method is a standard regularization approach in optimization. In this work we focus on a stopping rule of this algorithm, when smoothness is present, so that Newton-like method can be used to solve the subproblems. The basis for our stopping test is a "sufficient" decrease in the objective function where we establish the convergence of the algorithm obtained.Item Algoritmos utilizados para as quatro operações elementares(Universidade Federal de Goiás, 2016-09-26) Santana, Gracielly da Silva; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Dias, Ivonildes Ribeiro Martins; Vasconcelos, José Eder Salvador deThis work is meant to study some properties of the four elementary operations on the set of natural numbers. Some relevant aspects to Decimal Numbering System will be verified as well as the expansion of a number on that system. It will also demonstrate the usage of the "Golden Beads", a very useful pedagogical resource when it comes to understanding the Decimal Numbering System and even its usage to solve one of the elementary operations. Therefore, some of the algorithms that can be used to solve each of the four operations: addition, subtraction, multiplication and division.Item Alguns problemas de soma-zero com peso(Universidade Federal de Goiás, 2015-03-02) Pereira, Nara Reges Faria de Paiva; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Rodrigues, Paulo Henrique de Azevedo; Chagas, Sheila Campos; Chaves, Ana Paula de AraújoIn this work we study some results about Davenport’s constant for finite abelian groups. We also study some weighted zero-sum problems for especific cyclic groups and for this we prove some relations between the invariants sA, gA e hA for such groups.Item Altura e equidistribuição de pontos algébricos(Universidade Federal de Goiás, 2017-06-20) Santos, Jefferson Marques; Chaves, Ana Paula de Araújo; http://lattes.cnpq.br/2332073500640724; Chaves , Ana Paula de Araújo; Lopes , José Othon Dantas; Rodrigues , Paulo Henrique de Azevedo; Oliveira, Ricardo Nunes deThe concept of roots of a polynomial is quite simple but has several applications. This concept extends more generally to the case of "small" algebraic points sequences in a curve. This dissertation aims to estimate the size of algebraic numbers by means of Weil height. In addition to showing that they are distributed evenly around the unit circle, through Bilu Equidistribution Theorem.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 Análise do discriminante em equações polinomiais de terceiro grau a partir de funções simétricas(Universidade Federal de Goiás, 2020-11-09) Costa, Debora Naiure Araujo; Gomes, Alacyr José; http://lattes.cnpq.br/5994366998164007; Silva, Geci José Pereira da; Belisário, Hugo Leonardo da Silva; Gomes, Alacyr JoséThe objective of this work is to make a study on the characteristics of the roots of polynomial equations of degrees 2 and 3, studying the discriminant written in function of invariants that depend only on the coefficients of an initial equation. We will start by remembering some important definitions and propositions about polynomials, symmetric functions of the roots and develop the resolution of the cubic by radicals using two different methods. Finally, it will be possible to analyze the discriminant through algebraic manipulations that we will do, using the content presented in the previous chapters, and then we will write the discriminant from the roots of the equations, which enable to develop a proof for the theorems that relate the roots of the equations 2º and 3º degrees with their discriminants.Item Análise semi-local do método de Gauss-Newton sob uma condição majorante(Universidade Federal de Goiás, 2014-12-18) Aguiar, Ademir Alves; Gonçalves, Max Leandro Nobre; http://lattes.cnpq.br/7841103869154032; Gonçalves, Max Leandro Nobre; Gonçalves, Douglas Soares; Melo, Jefferson Divino Gonçalves deIn this dissertation we present a semi-local convergence analysis for the Gauss-Newton method to solve a special class of systems of non-linear equations, under the hypothesis that the derivative of the non-linear operator satisfies a majorant condition. The proofs and conditions of convergence presented in this work are simplified by using a simple majorant condition. Another tool of demonstration that simplifies our study is to identify regions where the iteration of Gauss-Newton is “well-defined”. Moreover, special cases of the general theory are presented as applications.Item Uma análise sobre as novas modalidades de financiamento imobiliário(Universidade Federal de Goiás, 2020-06-16) Barra, Willian do Amaral; Lemes, Max Valério; http://lattes.cnpq.br/6512955169729670; Lemes, Max Valério; Moreira, Fernando Ricardo; Lourenço, Kélem GomesThis dissertation presents a discussion on the importance of Financial Mathematics and Financial Education in relation to practical everyday situations, such as when contracting real estate financing. In August 2019, a decision by the National Monetary Council changed the rules for contracting real estate financing, with this, new financing modalities emerged. We will perform some simulations of real estate financing comparing the current modalities, assessing the advantages and disadvantages of the credit lines offered. To support the discussions on financing, we will present some concepts and examples related to financial mathematics, such as interest rates, compound capitalization system, uniform series and amortization systems. Concepts and laws that regulate the real estate financing system will be presented in order to assist the reader in making strategic decisions.Item Uma aplicação da congruência na determinação de critérios de divisibilidade(Universidade Federal de Goiás, 2015-03-27) Silva, Luis Henrique Pereira da; Souza, Mário José de; Souza, Mário José de; Cecconello, Moiseis dos Santos; Lima, Lidiane dos Santos MonteiroThis work aims to demonstrate in a practical way the divisibility criteria 2-97 in sieve Eratostenes with cutting the right and the left, based on the method of multiplication and division Egyptian. The entire process is demonstrated using the divisibility to whole numbers, greatest common divisor, prime numbers, decomposition in prime factors and matching.Item Aplicação do mínimo múltiplo comum generalizado nas ondas de pêndulos(Universidade Federal de Goiás, 2016-03-30) Silva, Jean Carlo de Sousa e; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Rodrigues, Paulo Henrique de Azevedo; Smith, Ole Peter; Vasconcelos, Jose Eder Salvador deThe simple pendulums have oscillatory and periodic movements. Thus, if we analyze some of them with independent movements, they may again return to be in the same spot, if your periods are comensurávies. We present the basic concepts needed to understand this phenomenon. Ending with a hint of implementation.Item Aplicação do polinômio de Taylor na aproximação da função Seno(Universidade Federal de Goiás, 2014-07-03) Curi Neto, Emilio; Silva, Maxwell Lizete da; http://lattes.cnpq.br/9078818338290451; Silva, Maxwell Lizete da; Silva, Sílvia Cristina Belo e; Tonon, Durval JoséIn this work the main goal is focused on applying the theory of Taylor polynomial approximations applied on the trigonometric function defined by f : [0; 2 ] ! R, where f(x) = sin(x). To achieve this goal, eight sections were developed, in which initially a reflection on the problem and the need to obtain the values in this respect in that it is wide angle measure x is presented. Is presented and subsequently treated a problem involving the movement of a pendulum, which uses the approximation sin(x) x where x belongs to a certain range. In the sections that follow a literature review of the theories of differential and integral calculus is presented, and the related theory of Taylor approximation of functions by polynomials. Later we used these theories to analyze and determine polynomials approximating the function f(x) = sin(x) in a neighborhood of the point x = 0, and estimate the error when we applied these approaches. At this time the error occurred due to the approach used in the pendulum problem was also analyzed. Finally a hint of practice to be held in the classroom using the theories treated here as well as the study of the problem of heat transfer in a bar through the theory of Fourier activity is presented.Item Uma aplicação web como recurso didático em aritmética(Universidade Federal de Goiás, 2020-03-13) Lima, Felipe Viterbo de; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Leandro, Bianka Carneiro; Lima, Thaynara Arielly deIn this work, we aim to show the efficiency brought by a given web application that was developed with the purpose of serving as a pedagogical resource, in the mathematics teaching, specifically arithmetic. The conclusions of the present study come from the analyzes carried out and the results obtained during the period of experimentation of this application. Here will be described in detail the functionalities existing in this software, how it was disseminated and how the evaluation made by its users will also be presented. In order to have a good understanding of the mathematical context involved in this dissertation, it is worth mentioning that its target audience is composed of students and teachers who already have knowledge of the main basic concepts related to the arithmetic theory of numbers.Item Aplicações da álgebra linear nas cadeias de Markov(Universidade Federal de Goiás, 2013-04-11) Silva, Carlos Eduardo Vitória da; Mota, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539; Mota, Jesus Carlos da; Seimetz, Rui; Smith, Ole PeterThe theory of linear algebra and matrices and systems particularly are linear math topics that can be applied not only within mathematics itself, but also in various other areas of human knowledge, such as physics, chemistry, biology, all engineering, psychology, economy, transportation, administration, statistics and probability, etc... The Markov chains are used to solve certain problems in the theory of probability. Applications of Markov chains in these problems, depend directly on the theory of matrices and linear systems. In this work we use the techniques of Markov Chains to solve three problems of probability, in three distinct areas. One in genetics, other in psychology and the other in the area of mass transit in a transit system. All work is developed with the intention that a high school student can read and understand the solutions of three problems presented.