Disertación/Tesis
2024
Disertaciones
1
  • ANA CLÁUDIA HOTT PAIVA RICARDO
  • Fractals for polynomials teaching: a practical approach

  • Líder : MAURICIO REIS E SILVA JUNIOR
  • MIEMBROS DE LA BANCA :
  • MAURICIO REIS E SILVA JUNIOR
  • JOSE ELOY OTTONI
  • ROGÉRIO CASAGRANDE
  • Data: 27-feb-2024


  • Resumen Espectáculo
  • This work aims to present an introduction about fractals in high school level, with focus on practical approach of mathematical concepts, specially those relates to polinomial operations, exploring iterative process, general formulae and algorithms and incentive to the use of tables. This initiative aims to provide a visual and recursive perspective for the understanding of patterns, based on the self-similarity property of fractals. Adapted to the requirements of the BNCC, this practical approach is an example of an innovative pedagogical strategy in mathematical learning.

2023
Disertaciones
1
  • Lucas Oliveira de Carvalho
  • THE TEACHING OF EQUATIONS USING A VIRTUAL SCALE THAT INCLUDES THE REPRESENTATION OF NEGATIVE NUMBERS

  • Líder : EDUARDO SARQUIS SOARES
  • MIEMBROS DE LA BANCA :
  • EDUARDO SARQUIS SOARES
  • GILCELIA REGIANE DE SOUZA
  • PAULO HENRIQUE DIAS MENEZES
  • Data: 07-jul-2023


  • Resumen Espectáculo
  • The present work aims to analyze the applicability in the classroom of a virtual torque scale, created to interactively represent a 1st degree equation. We will base our analysis on the theory of meaningful learning, understanding the acquisition of knowledge as a constructive/individual process and, at the same time, resulting from broad social interactions. It is therefore necessary to adopt a theoretical approach that dialogues with Piagetian constructivism and humanism inspired by Paulo Freire. For the fieldwork, 120 students from four 9th grade classes at João Gonçalves Neto state school were involved. The virtual torque balance, while allowing the manipulation of weights of positive and negative values, aims to contribute to the teaching of the formal method of solving equations, which consists of carrying out compensatory operations on both sides of the equation. Despite the interest generated by the use of the equilibrium model and its possibilities, and even taking into account the commitment to learning of the students involved in the study, the analysis of the reasoning developed and the results in the evaluations suggests that the students expressed a marked gap in the domain skills that, supposedly, should have been  onsolidated in previous stages. In this sense, difficulties in the basic operations of addition and subtraction with
    decimal numbers were observed. Even acknowledging such difficulties, our work shows signs of encouraging results obtained by using the tool analyzed here.

2
  • Cérvulo Augusto Ferreira de Almeida
  • Fractional Calculus: the differences between the derivatives of Riemann-Liouville and Caputo

  • Líder : AMANDA GONCALVES SARAIVA OTTONI
  • MIEMBROS DE LA BANCA :
  • AMANDA GONCALVES SARAIVA OTTONI
  • ANA PAULA DA SILVA COTA QUEIROZ
  • HUMBERTO CESAR FERNANDES LEMOS
  • Data: 15-sep-2023


  • Resumen Espectáculo
  • This work presents a brief introduction to Fractional Calculus. Just as prior knowledge about elementary functions is essential to Differential and Integral Calculus, the study of arbitrary order calculus is largely supported by some of the so-called special functions, namely: the Gamma function, the Beta function and the Mittag-Leffler function. Given the importance of these three functions, they will be presented in this work. In the sequence, two of the most known approaches of Integral and Fractional Derivative extend the concepts of derivative and integral from integer order to arbitrary orders. Finally, the differences between the Riemann-Liouville and Caputo derivatives for some functions will be explained. In addition to the theoretical part, the work also brings a proposal for an activity aimed at Basic Education, presenting some concepts used in Fractional Calculus.

3
  • Nathalia Cássia Leal de Deus
  • The algebra of ternary numbers

  • Líder : JOSE ELOY OTTONI
  • MIEMBROS DE LA BANCA :
  • ANA PAULA DA SILVA COTA QUEIROZ
  • JOSE ELOY OTTONI
  • MARCELO OLIVEIRA VELOSO
  • MARIANA GARABINI CORNELISSEN HOYOS
  • Data: 15-sep-2023


  • Resumen Espectáculo
  • This work aims to present the algebra of ternary numbers. First, some elementary algebraic structures such as groups, subgroups, rings, ideals and fields will be recalled. Next, we will present the complex numbers with their basic properties, and we will verify their algebraic structure. After a brief study on the complex numbers, we will present the ternary numbers, where we use the analogy with the set of complex numbers to facilitate the reading and presentation of the theme. For a
    deeper understanding of the set of ternary numbers, we are going to study the algebraic structure of this set, the cubic modulus function, the relationship with the so-called hyperbolic functions of the third order, and we are going to analyze the properties of a curious third order polynomial that helps much to characterize this set. At the end, a section is presented that has the application of some algebraic structures presented and the matrix representation of complex numbers for students
    of the third year of high school in public schools, in addition to a brief conclusion about the work.

2022
Disertaciones
1
  • CARLOS EUGENIO LOURENÇO CAMPOLINO
  • Mathematics in the construction of an electric model aircraft for educational purposes

  • Líder : RICARDO DE CARVALHO FALCAO
  • MIEMBROS DE LA BANCA :
  • ROBSON LUIZ SANTOS
  • JOSE ELOY OTTONI
  • RICARDO DE CARVALHO FALCAO
  • Data: 18-feb-2022


  • Resumen Espectáculo
  • As an elementary and high school math teacher, I taught in a private school for $19$ years and in a state public school, where I am now a full-time teacher. In addition, I currently also teach in higher education. During this time, I implemented the model airplane pedagogical project several times, a group work of a few students, where they built a small styrofoam glider without remote control with common styrofoam. During these years, it was possible to observe that students aroused interest in making a more complex and interesting project. In this work, we intend to present a pedagogical guide in which students will build an electric model airplane as simply as possible, but with greater complexity, inside the classroom, with explanations about the step by step to be developed. Students, in general, are interested in understanding the entire process from construction to flight. Let's take advantage of this interest to introduce some geometry concepts, which appear naturally in the construction process. Our focus will be on the construction and description of the wing, which, in this case, is a ruled surface. We will therefore take advantage of the device developed to build the wing to build other ruled surfaces and describe them. We will also use other materials such as bamboo, wire, wood and tape to show these surfaces to students clearly.


     

    Ícone "Verificada pela comunidade"
     
     
     
     
     
2
  • Fábio Nogueira da Silva Costa
  • Linear Programming - Basic Concepts

  • Líder : GILCELIA REGIANE DE SOUZA
  • MIEMBROS DE LA BANCA :
  • EVELISE ROMAN CORBALAN GOIS FREIRE
  • AMANDA GONCALVES SARAIVA OTTONI
  • GILCELIA REGIANE DE SOUZA
  • MARCELO OLIVEIRA VELOSO
  • Data: 07-mar-2022


  • Resumen Espectáculo
  • Linear Programming (PL) is an optimization tool that helps decision making by ensuring efficient resource management. It involves problems that present linear characteristics and a single objective function, which can be used for both maximization and minimization. The present work presents some ways to solve optimization problems based on Linear Programming, emphasizing basic concepts for consolidation and understanding of the method. It is important to understand when the problem has an optimal solution, it is at one of the vertices of a convex polygon formed by the constraints. In addition, Linear Programming is a great resource to show high school students that mathematics is in everything and answer those famous questions "why should I study this?", "where will I apply these concepts in my life?" faced by teachers. Some contents necessary in the development of PL are seen in High School, so the teacher can present a certain theme showing that the same applies in PL, that is, in the search for maximizing profits or minimizing losses. And that alone is a great motivation for studying the topic.

3
  • JULIANE NASSARALLA ALMEIDA
  • leem package: Laboratory of teaching to statistics and mathematics

  • Líder : BEN DEIVIDE DE OLIVEIRA BATISTA
  • MIEMBROS DE LA BANCA :
  • ALEXANDRE CELESTINO LEITE ALMEIDA
  • BEN DEIVIDE DE OLIVEIRA BATISTA
  • HENRIQUE JOSE DE PAULA
  • Data: 10-mar-2022


  • Resumen Espectáculo
  • With the increasing advancement of remote teaching or distance learning (online), this work aimed to develop the leem package, in the R environment, as an auxiliary tool for the teaching of mathematics and statistics for elementary and higher education. With the implementation of a graphical interface, the user is able to use leem without the need to program in R.

2021
Disertaciones
1
  • GUILHERME FERNANDES CARIAS BARBOSA
  • Applications of Linear Algebra in Image Compression.

  • Líder : HUMBERTO CESAR FERNANDES LEMOS
  • MIEMBROS DE LA BANCA :
  • RICARDO RIBEIRO DE ÁVILA
  • HUMBERTO CESAR FERNANDES LEMOS
  • MAURICIO REIS E SILVA JUNIOR
  • Data: 21-ene-2021


  • Resumen Espectáculo
  • This work aims to illustrate some basic ideas of Linear Algebra applied to the
    lossy image compression process. As an example, we describe a process that mainly uses
    the discrete cosine transform (DCT). In addition, Hu man encoding is used and the steps
    for compression in JPEG format are described. We will deal with lossy compression, as
    our emphasis is on the basic principles of compression and Linear Algebra topics used in
    the process, remembering that our interest is not to improve storage or preserve image
    quality.

2
  • AMANDA ALVES DE OLIVEIRA
  • Statistical Properties of a Multiplicative Process in a Discrete Sample Space

  • Líder : TELLES TIMOTEO DA SILVA
  • MIEMBROS DE LA BANCA :
  • HELVECIO GEOVANI FARGNOLI FILHO
  • HUMBERTO CESAR FERNANDES LEMOS
  • TELLES TIMOTEO DA SILVA
  • Data: 28-ene-2021


  • Resumen Espectáculo
  • The objective of this work is to present some results necessary to understand the asymptotic behavior of random multiplicative processes. These processes have been relatively less studied, because there are no limit theorems governing their distribution, in comparison with the additive processes that are subject, under certain conditions, to the Central Limit Theorem. We will focus the study on the binomial multiplicative processes and, more generally, on the multinomial multiplicative processes. A proposal for an activity to be carried out in the classroom will be discussed. This activity aims to make students realize the extreme behavior that multiplicative processes can have.

3
  • RENATA MOURA
  • Reed Solomon Codes.

  • Líder : MARIANA GARABINI CORNELISSEN HOYOS
  • MIEMBROS DE LA BANCA :
  • EDNEY AUGUSTO JESUS DE OLIVEIRA
  • MARIANA GARABINI CORNELISSEN HOYOS
  • PEDRO BENEDINI RIUL
  • Data: 24-mar-2021


  • Resumen Espectáculo
  • This work presents the original version of the Reed-Solomon Codes published in 1960 by mathematicians and engineers Irving Stoy Reed and Gustave Solomon. These codes constitute a class of cyclic error correcting codes and are widely used in digital communication systems technologies. In particular, we present in this work the Quick Response Codes, QR Codes, which use the Reed-Solomon codes for the detection and correction of errors.

4
  • SIDICLEI JOSÉ PEREIRA DOS SANTOS
  • Virtual Reality and Augmented Reality: A case studyProcesses in Teaching Processes in Mathematics

  • Líder : ALEXANDRE CELESTINO LEITE ALMEIDA
  • MIEMBROS DE LA BANCA :
  • ALEXANDRE CELESTINO LEITE ALMEIDA
  • BEN DEIVIDE DE OLIVEIRA BATISTA
  • JOÃO BATISTA QUEIROZ ZULIANI
  • Data: 11-jun-2021


  • Resumen Espectáculo
  • Poor performance in mathematics education has been a growing problem in recent years in Brazil. On the other hand, there is an increasing number of students using smartphones and tablets. In view of this reality, it is essential to search for solutions that make teaching more attractive to this technological generation. Given this perspective, Virtual Reality and Augmented Reality makes it an important tool in order to attract students’ attention to a playful and attractive interaction. This work presents examples of application of Virtual Reality and Augmented Reality, in order to demonstrate that the use of these technologies can be effective for complementing learning and attractiveness for the teaching of mathematics and consequently contributing to the development of education. Teaching activities are presented that use different technologies of virtual and augmented reality to present solutions to practical problems by various types of media, including videos, to be shown through interactive documents.

5
  • THIAGO PATROCINIO RODRIGUES
  • Generalized Happy Numbers

  • Líder : MARCELO OLIVEIRA VELOSO
  • MIEMBROS DE LA BANCA :
  • MARCELO OLIVEIRA VELOSO
  • JOSE ELOY OTTONI
  • GILCELIA REGIANE DE SOUZA
  • ROGÉRIO CASAGRANDE
  • Data: 28-jul-2021


  • Resumen Espectáculo
  • This work presents a brief study of happy numbers and their generalizations, on any positional system. In particular, some results about the 3-happy numbers and its fixed points on bases less than six. In addition, it proposes the use of electronic spreadsheets, as a didactic strategy,  to introduce the subject for elementary school studen

6
  • OTÁVIO SOARES DE MACEDO
  • Ordinary Differential Equations: Modeling Applied to Health Area

  • Líder : GILCELIA REGIANE DE SOUZA
  • MIEMBROS DE LA BANCA :
  • GILCELIA REGIANE DE SOUZA
  • ALEXANDRE CELESTINO LEITE ALMEIDA
  • MEHRAN SABETI
  • Data: 22-oct-2021


  • Resumen Espectáculo
  • The current study presents Differential Equations applied health and public health and proposes a didactic sequence involving a computer laboratory. This sequence aims to help high school (HS) mathematics teachers, allowing them to use the differential equations through the usage of techniques of recapturing and improving students’ knowledge about exponential and logarithmic functions and offering students autonomously learning. After studying Gompertz Equation and its parameters for tumors in humans, we used the data from a previous study on tumor growth in laboratory rats, which made it possible to estimate the parameter for the growth speed of the tumor in rodents. This parameter was obtained using the software SciDaVis, then was performed the sketch of the curve in the software GeoGebra. Similarly, we have researched the SIR (Susceptible-Infected-Removed) model. To exemplify the SIR model, we researched epidemiological data from the city of Belo Horizonte regarding the new coronavirus epidemic, which made it possible to calculate the Reproduction Number R0 through the resources available in the software LibreOffice. Later, analyzing the SIR model in GeoGebra, thus displaying the three curves S(t), I(t), and R(t), which represent the functions of susceptible, infected, and removed, respectively.
    The proposed activities were designed to escape the traditionalism of regular classes through a differentiated and interdisciplinary way aiming to promote the learning process via interesting and appealing themes for the students. We have developed two didactic sequences to enhance the pedagogical practice of the teacher in this research, aiming to help professionals when teaching exponential and logarithmic functions in primary school. The activities are supported by BNCC for High School parameters and its proposed competencies and skills. The pedagogical effects arising from applying these sequences in the classroom will not be analyzed in this paper but may be the subject of future research.

7
  • JOSE GERALDO DOS SANTOS BARBOSA
  • An active methodology for teaching mathematics in higher education using choreographies of teaching: online modality

  • Líder : BEN DEIVIDE DE OLIVEIRA BATISTA
  • MIEMBROS DE LA BANCA :
  • BEN DEIVIDE DE OLIVEIRA BATISTA
  • EDUARDO SARQUIS SOARES
  • QUERTE TERESINHA CONZI MEHLECKE
  • MARCO ANTONIO AMARAL
  • Data: 16-dic-2021


  • Resumen Espectáculo
  • With the changes in teaching/learning throughout the pandemic, several processes in Brazilian education were accelerated and aggravated. With remote teaching, the conventional form of class, both the teaching process and the learning format had to be updated. Thus, the present work presents an alternative form for a new classroom format for the subject of Mathematics in higher education, in the online modality. For this, the resources of choreographies of teaching were used, providing the professor with several technological tools, so that these can be implemented in their universities, within the possibilities of implementation. At the end, a case study was approached, showing signs of how active methodologies can add to the relationship between the student and the teacher, in the learning process.

8
  • FLAVIA CRISTINE MIRANDA MILAGRES
  • LEARNING DEVELOPED COLLECTIVELY FACING THE CHALLENGE OF IMPROVING A VIRTUAL SCALE 

  • Líder : EDUARDO SARQUIS SOARES
  • MIEMBROS DE LA BANCA :
  • ANDRE AUGUSTO DEODATO
  • EDUARDO SARQUIS SOARES
  • MARIANA GARABINI CORNELISSEN HOYOS
  • Data: 17-dic-2021


  • Resumen Espectáculo
  • Algebra is an essential part of teaching mathematics at both the elementary and secondary levelsHoweverthere is a certain difficultyboth in teaching and in learningThus it becomes a challengeconsidering that teaching this content requires the adoption of methodologies that contribute to the effective construction of knowledgeFrom this perspective, a research workgroup, formed by professors and researchersaims to study and experiment with methodologies for teaching science and mathematics in order to improve their workAnd, as the objective of this research, it is proposed to describe and analyze part of the group's learning in the exploration of the possibilities of the virtual scale. The Theory of Learning will be used to better describe the actions of the group of researchers and the learning process experienced by the group itself. The concept of expansive learninginherent to the version of the Theory of Learning adopted here will assist in the analysis of the achievements of this group in this planning process until then assumed by the members. The results showed thatgiven the need to find the best way to teach equationsanalysis and the search for a solution were necessarywhich contributed to the expansion of knowledgethe improvement of methodology and the improvement in the balance. The work with the scales has not yet endedconsidering that the Covid-19 pandemic required the interruption of face-to-face classes (and thus experimentation with students in the classroom), as well as only virtual meetings by the research group. In this sensestudies should still be continuedsince the question of the insertion of negative numbers is still an unanswered questionrequiring discussions between the research groupThereforethe group will still meet with the objective of discovering how to deal with negative numbers and equations from the virtual scale. In addition, it remains to be seen that all this formulated experience is applied in the classroomwhich will generate further developments. 

9
  • MARINA MARIA MOREIRA
  • Differential geometry of curves in euclidean spaces and R-equivalence

  • Líder : PEDRO BENEDINI RIUL
  • MIEMBROS DE LA BANCA :
  • PEDRO BENEDINI RIUL
  • AMANDA GONCALVES SARAIVA OTTONI
  • RAFAELLA DE SOUZA MARTINS
  • Data: 20-dic-2021


  • Resumen Espectáculo
  • This paper presents a study of regular curves in Euclidean spaces in two contexts. First, it is done through the classical differential geometry and then from the point of view of the contact theory. The contact of curves with reference objects, these being straight lines and circles for plane curves and planes and spheres for space curves, is measured through the singularities of the height and distance-squared functions. Moreover, we investigate the $\mathcal{R}$-equivalence of one-variable real functions, relating it to contact theory.

2020
Disertaciones
1
  • BRUNA PAULA CAMPOS
  • The Use of Short Videos in Teaching
    Mathematics

  • Líder : ALEXANDRE CELESTINO LEITE ALMEIDA
  • MIEMBROS DE LA BANCA :
  • ALEXANDRE CELESTINO LEITE ALMEIDA
  • GILCELIA REGIANE DE SOUZA
  • LUCIANA BORGES GOECKING
  • Data: 23-ene-2020


  • Resumen Espectáculo
  • In agreement with history of the technological evolution, informational technologies are developed and employed in society’s daily life in order to help with tasks such as small financial applications, domestic control, obesity control and monitoring, disease treatments,etc. It is not different on education. Many computer programs and applications can be used. However, there is still a great discussion about technology usage (hardware and software)in formal education of teenagers and young people in classrooms, focusing on a big unknown question: what is its contribution to learning? Does it hinder? How far? In this line, the present work attempt to measure, through the exhibition of long and short videos to 120 students distributed among 4 classes (pilot project), how efficient the proposed teaching methodology can be

2
  • ADONAIA APOLINARIO
  • The Fascinating World of Palindromes.

  • Líder : MARCELO OLIVEIRA VELOSO
  • MIEMBROS DE LA BANCA :
  • GILCELIA REGIANE DE SOUZA
  • MARCELO OLIVEIRA VELOSO
  • ROGÉRIO CASAGRANDE
  • Data: 20-feb-2020


  • Resumen Espectáculo
  • A positive integer is called a palindrome if its decimal representation
    remains the same if we reverse the order of their digits. For example, 1977791 and 1111
    are palindromes. In this work, we explore some of the properties of palindromes, in
    any positional basis b greater than 1. In particular, we display a formula for the number
    of palndromes with n digits. We also studied the palindromic polynomials and some of
    its properties. At the end of the text, we present a proposal to address the subject
    in the classroom

3
  • TERESA CRISTINA FIRMO GUARANI
  • Counting Problems: The Burnside and Pólya Theorems

  • Líder : AMANDA GONCALVES SARAIVA OTTONI
  • MIEMBROS DE LA BANCA :
  • AMANDA GONCALVES SARAIVA OTTONI
  • RICARDO DE CARVALHO FALCAO
  • ROGÉRIO CASAGRANDE
  • Data: 21-feb-2020


  • Resumen Espectáculo
  • This paper aims to present the Burnside’s Theorem and Polya’s Theorem, which focuses on determining the number of orbits of the action of a symmetry group in all the colorations of a figure. The Theorems demonstrate how to solve counting problems utilizing the concepts of group actions, coloring, orbit, stabilizer, cycle index, weights and standard inventory. An activity has been developed with high school students in order to apply the theme in secondary school.

4
  • RENATA GONÇALVES DE ALMEIDA
  • Use of Groups in Geometric Transformations.

  • Líder : MAURICIO REIS E SILVA JUNIOR
  • MIEMBROS DE LA BANCA :
  • AMANDA GONCALVES SARAIVA OTTONI
  • GILCELIA REGIANE DE SOUZA
  • MAURICIO REIS E SILVA JUNIOR
  • ROGÉRIO CASAGRANDE
  • Data: 21-feb-2020


  • Resumen Espectáculo
  • This work aims to present an introduction to group theory. In order to achieve this objective, the basic elements of the product group structure and a relationship between a group theory with some geometric transformations were approached, highlighting reflections and rotations. In addition, it is a proposal to address this issue in the curriculum structure of elementary education.

5
  • TALISON GOMES MOREIRA
  • A study on third-order trigonometric and hyperbolic functions.

  • Líder : JOSE ELOY OTTONI
  • MIEMBROS DE LA BANCA :
  • GERALDO CESAR GONÇALVES FERREIRA
  • AMANDA GONCALVES SARAIVA OTTONI
  • JOSE ELOY OTTONI
  • RICARDO DE CARVALHO FALCAO
  • Data: 17-dic-2020


  • Resumen Espectáculo
  • This work aims to present the generalised trigonometric and hyperbolic functions, more specifically the third order trigonometric and hyperbolic functions,
    as well as the relationship between them, their graphs, their derivatives and some mention of their history and applications. First, the ordinary circular trigonometric
    functions will be defined, with their respective graphs, their relationship with the geometry of the circle, the most important trigonometric identities, arcs addition formulas,
    derivatives, integrals of these functions and their inverses will be demonstrated. Next, through the geometry of the equilateral hyperbola, the classic hyperbolic functions, as well as their parameterization in relation to the exponential function and applications.
    Their graphs, fundamental identities, arc addition formulas, their derivatives, integrals and inverse functions will also be shown. Subsequently, third-order hyperbolic functions will be defined as a special case of generalised hyperbolic. The focus will be on the study of this special case, and its graphs will be drawn,
    and the calculus of its derivatives and fundamental relations. Finally, the trigonometric functions of third order and a relationship between third-order trigonometric and hyperbolic will be defined. Through this relationship between them
    and the properties of the hyperbolic ones, already studied, the derivatives, the sum of arcs formulas, some identities and graphs of the trigonometrics will be shown. At the end, there will be a section with an application of circular and hyperbolic trigonometric functions of second order for high school students and a brief conclusion about future
    perspectives that this work may entail.

6
  • ADAILTON JOSÉ DA SILVA
  • Kontsevich's theorem and polynomial interchanges

  • Líder : AMANDA GONCALVES SARAIVA OTTONI
  • MIEMBROS DE LA BANCA :
  • AMANDA GONCALVES SARAIVA OTTONI
  • ANA PAULA DA SILVA COTA QUEIROZ
  • JOSE ELOY OTTONI
  • PEDRO BENEDINI RIUL
  • Data: 21-dic-2020


  • Resumen Espectáculo
  • After receiving a subway ticket from his colleague Maxim Kontsevich with some scribbles, Étienne Gys could hardly believe that he wanted to share with him a new theorem about relative position of polynomials. This work aims to present Kontsevich's Theorem, the result of which are some restrictions for the relative position of graphs of four real polynomials.

2019
Disertaciones
1
  • JACIARA CRISTINA DA ROCHA SILVA RODRIGUES
  • -

  • Líder : ALEXANDRE CELESTINO LEITE ALMEIDA
  • MIEMBROS DE LA BANCA :
  • ALEXANDRE CELESTINO LEITE ALMEIDA
  • FABRÍCIO GOECKING AVELAR
  • JOSE ELOY OTTONI
  • Data: 08-jul-2019


  • Resumen Espectáculo
  • This work has for objective to present structural properties of a simple graph obtained bymeans of its adjacency matrix. It will show that, through the adjacency matrix, it is possibleto determine several structural characteristics of a graph, some simple, such as number ofvertices, number of edges, number of triangles in the graph, and more complex ones suchas, for example, determine the diameter and radius of the graph, check whether or not thegraph is bipartite, and determine whether the graph is connected or disconnected. It willalso approach the spectrum of the adjacency matrix, establishing the properties of the graphsdetermined through them.

2
  • LUIZ FERNANDO PINHEIRO RAMOS
  • -

  • Líder : HUMBERTO CESAR FERNANDES LEMOS
  • MIEMBROS DE LA BANCA :
  • BEN DEIVIDE DE OLIVEIRA BATISTA
  • GILCIONE NONATO COSTA
  • HUMBERTO CESAR FERNANDES LEMOS
  • MAURICIO REIS E SILVA JUNIOR
  • Data: 08-jul-2019


  • Resumen Espectáculo
  • This study proposes to construct a method to calculate soccer probabilitiesand compare the results with the UFMG Mathematics Department model. In the pre-sented methodology, we assume that the number of goals scored by the teams in a matchare independent and follow a Poisson distribution, where the average reflects the attackfactor or defense factor. Applied in 250 games of Series A of the 2018 Brazilian Cham-pionship, the methodology studied presented results consistent with the UFMG model.It was possible to predict with good accuracy the champion and obtained satisfactoryresults for the qualifiers for the Copa Libertadores of America, as well as for the relegatedteams. The DeFinetti measurement average was 0.568 and approximately 57 % of theresults are below 2/3. The proposed methodology was implemented in the software R.

3
  • JONILSON DOS SANTOS OLIVEIRA
  • -

  • Líder : MARCELO OLIVEIRA VELOSO
  • MIEMBROS DE LA BANCA :
  • MARCELO OLIVEIRA VELOSO
  • JOSE ELOY OTTONI
  • GILCELIA REGIANE DE SOUZA
  • ROGÉRIO CASAGRANDE
  • Data: 19-ago-2019


  • Resumen Espectáculo
  • In this study, we approach the metallic numbers and its related themes. Itwill be explored the link with the second degree equations, Fibonacci sequences, geometricinterpretations and other correlations. The main result, Theorem 6.1, shows that it is notpossible to obtain the bronze number as the ratio between any diagonal and the side of aregular polygon. We introduce the concept of metalic area and we display a formula for itscalculation as an application in elementary and high school. The language used is intendedto be accessible to elementary and high school teachers.

4
  • EDSON PEREIRA ARRUDA FILHO
  • -

  • Líder : JOSE ELOY OTTONI
  • MIEMBROS DE LA BANCA :
  • JOSE ELOY OTTONI
  • MARCELO OLIVEIRA VELOSO
  • AMANDA GONCALVES SARAIVA OTTONI
  • ROGÉRIO CASAGRANDE
  • Data: 19-ago-2019


  • Resumen Espectáculo
  • The present work aims to present, to the high school students, some appli-cations of matrices; especially of the circulant matrices and their importance from thecomputational point of view. Despite their seeming simplicity, circulant matrices linktogether very different subjects in the scenery of mathematics. In this work, we alsohave the opportunity to merge the circulant matrices with geometry using Geogebra. Wepass a brief idea about the complex numbers, in order to calculate the eigenvalues of anycirculant matrix. We will also talk about the generalized hyperbolic functions, and provesome of its properties employing circulant matrices.

5
  • WILLSANDER DE JESUS
  • -

  • Líder : GILCELIA REGIANE DE SOUZA
  • MIEMBROS DE LA BANCA :
  • GILCELIA REGIANE DE SOUZA
  • HELVECIO GEOVANI FARGNOLI FILHO
  • TELLES TIMOTEO DA SILVA
  • Data: 18-dic-2019


  • Resumen Espectáculo
  • Musical chords are elements of music that form the basis of all musical arrange-ments and compositions. In an orchestra, for example, some instruments (such as flute, soloviolin, trumpet) play phrases composed of a sequence of musical notes, while others (piano,stringed instrument set) play simultaneous notes that combine, thus forming the base for themusic. The role of this base is to fill the spaces of time and make a connection with the soloinstruments or the vocal. The objective of this work is to convert these musical elementsinto mathematical elements, so that we can see them from another perspective and, throughcomputational tools, study the formation, the identification and classification of these chords.Based on this objective, an algorithm was developed for this purpose. In summary, this algo-rithm (i) calculates the chord Fourier transform to identify yours frequency components; (ii)applies the tempered scale equation to establish the relationship between these frequenciesand (iii) classify the chord based on the concepts of the musical theory.

6
  • CLARICE AUGUSTA REZENDE DE OLIVEIRA
  • -

  • Líder : RICARDO DE CARVALHO FALCAO
  • MIEMBROS DE LA BANCA :
  • AMANDA GONCALVES SARAIVA OTTONI
  • ANTONIO MARCOS FERREIRA DA SILVA
  • RICARDO DE CARVALHO FALCAO
  • Data: 18-dic-2019


  • Resumen Espectáculo
  • Music and mathematics are intertwined and the purpose of this article is toshow a way of composing using Fibonacci numbers and arithmetic congruence in order touse music as a complementary mathematics teaching tool for high school students. TheFibonacci sequence is a subject that is not often addressed in textbooks, but is present incompetitions, college entrance exams, and Olympic math questions. The Fibonacci sequence,the relationship between music and mathematics, the use of Fibonacci numbers by famouscomposers, the formation of generalized Fibonacci sequences through F(mod m), and thegeneration of residue cycles of F(mod m) to create melodies and to be able to use music asa playful mathematical teaching tool.

7
  • JOSE EDUARDO BARBOSA DE OLIVEIRA
  • -

  • Líder : RICARDO DE CARVALHO FALCAO
  • MIEMBROS DE LA BANCA :
  • RICARDO DE CARVALHO FALCAO
  • JOSE ELOY OTTONI
  • HELVECIO GEOVANI FARGNOLI FILHO
  • Data: 18-dic-2019


  • Resumen Espectáculo
  • This work aims to present an overview of the probability theory passing throughthe normal or Gaussian distribution followed by the Central Limit Theorem and its appli-cations until presenting the L ́evy Distribution and finally the L ́evy Flights. The work alsoproposes an activity aimed at high school that consists of a game where students will buildtwo models of walks (Browniana and L ́evy) in which one follows a normal distribution whileanother follows the distribution of L ́evy.

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