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1
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GUILHERME FERNANDES CARIAS BARBOSA
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Applications of Linear Algebra in Image Compression.
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Leader : HUMBERTO CESAR FERNANDES LEMOS
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MEMBRES DE LA BANQUE :
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RICARDO RIBEIRO DE ÁVILA
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HUMBERTO CESAR FERNANDES LEMOS
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MAURICIO REIS E SILVA JUNIOR
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Data: 21 janv. 2021
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Afficher le Résumé
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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, Human 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.
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2
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AMANDA ALVES DE OLIVEIRA
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Statistical Properties of a Multiplicative Process in a Discrete Sample Space
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Leader : TELLES TIMOTEO DA SILVA
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MEMBRES DE LA BANQUE :
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HELVECIO GEOVANI FARGNOLI FILHO
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HUMBERTO CESAR FERNANDES LEMOS
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TELLES TIMOTEO DA SILVA
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Data: 28 janv. 2021
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Afficher le Résumé
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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.
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3
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RENATA MOURA
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Reed Solomon Codes.
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Leader : MARIANA GARABINI CORNELISSEN HOYOS
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MEMBRES DE LA BANQUE :
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EDNEY AUGUSTO JESUS DE OLIVEIRA
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MARIANA GARABINI CORNELISSEN HOYOS
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PEDRO BENEDINI RIUL
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Data: 24 mars 2021
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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.
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4
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SIDICLEI JOSÉ PEREIRA DOS SANTOS
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Virtual Reality and Augmented Reality: A case studyProcesses in Teaching Processes in Mathematics
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Leader : ALEXANDRE CELESTINO LEITE ALMEIDA
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MEMBRES DE LA BANQUE :
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ALEXANDRE CELESTINO LEITE ALMEIDA
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BEN DEIVIDE DE OLIVEIRA BATISTA
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JOÃO BATISTA QUEIROZ ZULIANI
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Data: 11 juin 2021
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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.
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5
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THIAGO PATROCINIO RODRIGUES
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Generalized Happy Numbers
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Leader : MARCELO OLIVEIRA VELOSO
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MEMBRES DE LA BANQUE :
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MARCELO OLIVEIRA VELOSO
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JOSE ELOY OTTONI
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GILCELIA REGIANE DE SOUZA
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ROGÉRIO CASAGRANDE
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Data: 28 juil. 2021
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Afficher le Résumé
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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
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6
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OTÁVIO SOARES DE MACEDO
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Ordinary Differential Equations: Modeling Applied to Health Area
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Leader : GILCELIA REGIANE DE SOUZA
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MEMBRES DE LA BANQUE :
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GILCELIA REGIANE DE SOUZA
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ALEXANDRE CELESTINO LEITE ALMEIDA
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MEHRAN SABETI
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Data: 22 oct. 2021
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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.
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7
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JOSE GERALDO DOS SANTOS BARBOSA
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An active methodology for teaching mathematics in higher education using choreographies of teaching: online modality
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Leader : BEN DEIVIDE DE OLIVEIRA BATISTA
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MEMBRES DE LA BANQUE :
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BEN DEIVIDE DE OLIVEIRA BATISTA
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EDUARDO SARQUIS SOARES
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QUERTE TERESINHA CONZI MEHLECKE
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MARCO ANTONIO AMARAL
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Data: 16 déc. 2021
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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.
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8
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FLAVIA CRISTINE MIRANDA MILAGRES
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LEARNING DEVELOPED COLLECTIVELY FACING THE CHALLENGE OF IMPROVING A VIRTUAL SCALE
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Leader : EDUARDO SARQUIS SOARES
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MEMBRES DE LA BANQUE :
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ANDRE AUGUSTO DEODATO
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EDUARDO SARQUIS SOARES
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MARIANA GARABINI CORNELISSEN HOYOS
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Data: 17 déc. 2021
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Algebra is an essential part of teaching mathematics at both the elementary and secondary levels. However, there is a certain difficulty, both in teaching and in learning. Thus it becomes a challenge, considering that teaching this content requires the adoption of methodologies that contribute to the effective construction of knowledge. From this perspective, a research workgroup, formed by professors and researchers, aims to study and experiment with methodologies for teaching science and mathematics in order to improve their work. And, 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 learning, inherent 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 that, given the need to find the best way to teach equations, analysis and the search for a solution were necessary, which contributed to the expansion of knowledge, the improvement of methodology and the improvement in the balance. The work with the scales has not yet ended, considering 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 sense, studies should still be continued, since the question of the insertion of negative numbers is still an unanswered question, requiring discussions between the research group. Therefore, the 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 classroom, which will generate further developments.
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9
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MARINA MARIA MOREIRA
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Differential geometry of curves in euclidean spaces and R-equivalence
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Leader : PEDRO BENEDINI RIUL
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MEMBRES DE LA BANQUE :
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PEDRO BENEDINI RIUL
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AMANDA GONCALVES SARAIVA OTTONI
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RAFAELLA DE SOUZA MARTINS
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Data: 20 déc. 2021
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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.
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