DSpace Coleção:
http://www.repositorio.ufc.br/handle/riufc/4747
Sun, 08 Dec 2019 01:50:04 GMT2019-12-08T01:50:04ZIntroduzindo os conceitos de limite, derivada e integral no ensino médio.
http://www.repositorio.ufc.br/handle/riufc/48028
Título: Introduzindo os conceitos de limite, derivada e integral no ensino médio.
Autor(es): Guimarães, Maria Elisa de Castro
Abstract: This paper aims to study how to introduce the concepts of limit, derivative and integral in high school. From this perspective, this research aims to present a contribution on how to introduce each of these fundamental concepts of Calculus in this phase of schooling. Given what is recommended by the Common National Curricular Base - High School Stage for the teaching of Mathematics, the study of Calculus in High School proves to be a convenient tool for the formation of young people. To achieve this goal, we state the definition of each of these concepts, as studied in the Differential and Integral Calculus courses. Then, we present suggestions of approaches, contained in dissertations of the Professional Master in National Network Mathematics - PROFMAT, of how to introduce basic notions of these concepts in High School. Subsequently, we present contributions to the introduction of each concept in this segment. The contributions presented were based on approaches that only require knowledge that are already familiar to high school students and that seek to reach every student at this school level, except for the contribution of how to introduce the concept of integral. Because it is a slightly more sophisticated approach, it turned to students with a recognized degree of experience and maturity with mathematical argumentation. Finally, we deepen the discussion of area calculation by showing that it is not possible to calculate the area of every subset of the plane, given our intuitive notion of the area of a region.Tue, 01 Jan 2019 00:00:00 GMThttp://www.repositorio.ufc.br/handle/riufc/480282019-01-01T00:00:00ZOlimpíada cearense de matemática (OCM): laboratório de oportunidades, experiências e de desenvolvimento da matemática no estado do Ceará.
http://www.repositorio.ufc.br/handle/riufc/46959
Título: Olimpíada cearense de matemática (OCM): laboratório de oportunidades, experiências e de desenvolvimento da matemática no estado do Ceará.
Autor(es): Gomes, Keyson Gondim
Abstract: The Mathematical Olympics had their origins, according to some historians, because they are related to the "disputes" played by mathematicians in Italy during the Renaissance. Later, in the late nineteenth century, these competitions had a
similar structure to the present day. From 1894, Hungarian mathematicians organized
mathematical competitions called “Eötvös”, and today known as “Olympics
Mathematics ”. This paper aims to show the Mathematical Olympics as
source of dissemination and stimulation for the teaching and learning of mathematics in Ceará.
Where we will make a brief history of the Olympics in the world and in Brazil, emphasizing the
OCM - Cearense Mathematical Olympiad. We will also introduce the Mathematics Column
of Jornal O Povo and the Numeratizar project that played a key role in preparing
and incentive of Cearenses for several national and international Olympics, besides the
entrance exams, and its important contribution to the evolution of the level of mathematics in Ceará.
We will also talk about women's participation in the Olympics and narrate the experiences of former Olympic students who are currently math teachers. Highlighting how the CMO has
been, over the years, the gateway to a wide universe of competitions
mathematics around the world, as well as a laboratory for opportunities, experiences and
development of mathematics in the state of Ceará.Tue, 01 Jan 2019 00:00:00 GMThttp://www.repositorio.ufc.br/handle/riufc/469592019-01-01T00:00:00ZPolinômios com raízes no círculo unitário
http://www.repositorio.ufc.br/handle/riufc/45215
Título: 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.Sun, 01 Jan 2017 00:00:00 GMThttp://www.repositorio.ufc.br/handle/riufc/452152017-01-01T00:00:00ZSobre várias demonstrações do pequeno teorema de Fermat e as inter-relações entre as áreas da matemática.
http://www.repositorio.ufc.br/handle/riufc/44231
Título: 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.Tue, 01 Jan 2019 00:00:00 GMThttp://www.repositorio.ufc.br/handle/riufc/442312019-01-01T00:00:00Z