Mestrado Profissional em Matemática em Rede Nacional (IME)
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Navegando Mestrado Profissional em Matemática em Rede Nacional (IME) por Por Orientador "Gomes, Alacyr José"
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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 O uso do princípio de indução matemática no ensino básico(Universidade Federal de Goiás, 2023-08-29) Goiaz Junior, Gethsemani Saraiva de; Gomes, Alacyr José; http://lattes.cnpq.br/5994366998164007; Gomes, Alacyr José; Santos, Ronaldo Antônio dos; Vasconcelos, José Eder Salvador deThe principle of finite induction is a useful and rigorous tool for mathematical proofs whose conjectures are related to the set of natural numbers. However, the use of this principle for verifications in basic education is still greatly underutilized. In this work, we intend not only to demonstrate the importance of using this strong principle but also to provide study material and support for students and teachers, based on the National Common Curricular Base (BNCC). We present various demonstrations for elementary and secondary education, covering several proposed content in these stages of education. We suggest propositions for further exploration, which can be used as pathways for high school education. We also believe that this work can spark interest and expand the use of the principle of finite induction in the teaching of mathematics and other curriculum components.Item Funções: propriedades algébricas, geométricas e suas relações(Universidade Federal de Goiás, 2021-12-21) Lima, Mylena Pasquêwitti; Gomes, Alacyr José; http://lattes.cnpq.br/5994366998164007; Gomes, Alacyr José; Souza, Flávio Raimundo de; Smith, Ole PeterThe contents of functions is considered one of the most important within Mathematics, as it is present from its simplest aspects to the most complex mathematical modeling. In this sense, during the course of the work, we discuss in detail various types of functions, covering several of their properties and characteristics, however, here we do emphasize that the purpose of this work is not to exhaust all existing classes, properties and characteristics of functions, only covering those convenient to us. Moreover, through the functions studied, we improve our understanding of the relationship between numerical, algebraic and geometric representations. The work is characterized as a bibliographic research, being based on important authors within this area of study. For the development of the work, in addition to the bibliographic research, we also rely on the software GeoGebra as well as on the TikZ programming language, the latter being employed to sketch all the graphs presented, considering that none of them were found ready. Thus, all graphics presented were created by the author.Item Estudo sobre triângulos no ensino fundamental usando o software GeoGebra(Universidade Federal de Goiás, 2021-11-30) Oliveira, Matheus Timóteo de; Gomes, Alacyr José; http://lattes.cnpq.br/5994366998164007; Santos, Ronaldo Antônio dos; Costa, Eudes Antônio da; Gomes, Alacyr JoséThe work focuses on the study of triangles in elementary school, since the student has difficulties in understanding and interpreting flat figures and creating a relationship with problems. Hence, we searched for tools capable of awakening the student’s attention to geometry. We decided to use the software GeoGebra which is capable of reproducing the information described in a prob-lem on computer screens and similar, enabling more interactive lessons. Primarily an explanation of the content of plane geometry will be done, specifically about trian-gles, exploring concepts, properties and applications in the resolution of exercises. Next, we will make use of GeoGebra tools in order to address a meaningful way to build geometric knowledge, such as when you need to move a figure from one side to the other and make comparisons, then return to the same place, or even checking the sum of the internal angles of a triangle when mov-ing one of its vertices and noting the change in the values of each angle, but with a sum always equal to 180o. This work seeks to contribute to the evolution in the use of Information and Communication Technologies (ICTs) in education, making classes enjoyable for students who will have the oppor-tunity to experience innovative classes with technological attributes that facilitate learning