A Compreensão da idéia do número racional e suas operações na EJA: uma forma de inclusão em sala de aula

The awareness of the difficulty which pupils, in general have in understanding the concept and operations with Rational numbers, it made to develop this study which searches to collaborate for such understanding. Our intuition was to do with that the pupils of the Education of Young and Adults, with difficulty in understanding the Rational numbers, feel included in the learning-teaching process of mathematics. It deals with a classroom research in a qualitative approach with analysis of the activities resolved for a group of pupils in classroom of a municipal school of Natal. For us elaborate such activities we accomplished the survey difficulties and obstacles that the pupils experience, when inserted in the learning-teaching process of the Rational numbers. The results indicate that the sequence of activities applied in classroom collaborated so that the pupils to overcome some impediments in the learning of this numbers

Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text