DSpace Communidade:http://www.repositorio.ufc.br/handle/riufc/47462019-10-20T09:38:29Z2019-10-20T09:38:29ZPolinômios com raízes no círculo unitárioSales, Christiano de Almeidahttp://www.repositorio.ufc.br/handle/riufc/452152019-09-04T12:00:20Z2017-01-01T00:00:00ZTítulo: Polinômios com raízes no círculo unitário
Autor(es): Sales, Christiano de Almeida
Abstract: The objective of this work is to characterize the polynomials in Q [x] that have roots in the unitary circle. From this characterization we will estimate how many are these roots. To this end, we will establish a correspondence between the family of palindromic polynomials P (x) of degree 2m and their respective Chebyshev transforms. This will allow us to relate the number of roots of P (x) in the unit circle to the actual roots of the Chebyshev transform of P (x) in the range [-2,2]. Finally, with the aid of the Descartes Signal Rule, we will estimate the amount of roots of the Chebyshev transform in that interval. This work was guided by the title article: "Roots in unity circle" by author KEITH CONRAD.2017-01-01T00:00:00ZSobre várias demonstrações do pequeno teorema de Fermat e as inter-relações entre as áreas da matemática.Oliveira, Francisco Erilson Freire dehttp://www.repositorio.ufc.br/handle/riufc/442312019-08-27T11:13:33Z2019-01-01T00:00:00ZTítulo: Sobre várias demonstrações do pequeno teorema de Fermat e as inter-relações entre as áreas da matemática.
Autor(es): Oliveira, Francisco Erilson Freire de
Abstract: The purpose of this dissertation is to present different demonstrations for one of the most important theorems in Number Theory, namely Fermat's Little Theorem. Our interest in this claim is to show the interrelationships between the most diverse areas of mathematics. Our work, in a sense, is also a bibliographical research. Initially, we make a brief survey about the history of Pierre de Fermat, listing some of his various contributions to mathematics, especially to the theory of numbers. We continue in the second chapter, presenting the best known demonstrations for Fermat's Little Theorem. In the third chapter, we begin the alternative demonstrations, first presenting one by Combinatorial Analysis, consequently using introductory ideas of Graph Theory and concluding with a demonstration that uses the Taylor Series as its main content. In the next chapter, we bring up a demonstration using the ideas of Dynamic Systems and then develop a demonstration via Group Theory. Finally, we present our considerations about the work developed, emphasizing Pierre de Fermat's contributions to Mathematics, the interrelationships between the most diverse areas of this Science and the importance of using mathematical demonstrations for students of Basic Education.2019-01-01T00:00:00ZO lúdico no ensino da matemática: o nim, o tangram e os pentaminós como ferramentas de aprendizagem.Ferreira, Antonio Erivan Bezerrahttp://www.repositorio.ufc.br/handle/riufc/432292019-07-18T16:37:39Z2019-01-01T00:00:00ZTítulo: O lúdico no ensino da matemática: o nim, o tangram e os pentaminós como ferramentas de aprendizagem.
Autor(es): Ferreira, Antonio Erivan Bezerra
Abstract: The main objective of this work is to present play activities as a resource to improve the learning of Mathematics, seeking to establish the relationship between the game, teaching and learning new mathematical knowledge. We try to highlight the pedagogical role of games when exploring and applying mathematical concepts through the elaboration of strategies; and to show that by using games in Mathematics teaching, we can improve learning, stimulate concentration, make the learner more involved, thus making it possible to develop skills in the individual as well as make him an ally in the acquisition of mathematical knowledge. We also show that, when using games in Mathematics teaching, the student becomes motivated, favoring the interrelation and causing the learner to take the lead in the learning process. Finally, we try to show the mathematical strategy that leads to the victory of the game Nim in two versions, one using the Algorithm of the division and another using the system of binary numbering.2019-01-01T00:00:00ZRepresentação de inteiros por formas quadráticas binárias.Bezerra, Thedy Barbosahttp://www.repositorio.ufc.br/handle/riufc/432062019-08-16T14:21:00Z2019-01-01T00:00:00ZTítulo: Representação de inteiros por formas quadráticas binárias.
Autor(es): Bezerra, Thedy Barbosa
Abstract: This work consists in presenting answers to the following questions: be the quadratic form ax2 + bxy + cy2, discriminant Δ = b2-4ac, in two variables x and y, with a, b, c integers given, not all 0; for which integers n are integers x and y such that n = ax2 + bxy + cy2? What is the characterization of positive integers that can be written as the sum of two squares? What are the primes p> 3 that can be represented by the form 2x2 + 3y2 or by the form x2 + 6y2? In this dissertation, we study the mathematical theories that allow the resolution of the questions discussed above. In this sense, we present a good part of the prerequisites essential to the appreciation of the central results that we have discussed. Then, we discuss the representation of integers by binary quadratic forms, establishing a useful criterion, from which we can determine if an integer n is or not representable by some quadratic form, given its discriminant.
Finally, we present answers to the last two questions and we weave our considerations regarding the work produced, pointing to what goes beyond the theory developed here and recognizing the relevance of the interrelations between different areas of Mathematics.2019-01-01T00:00:00Z