Las foliaciones no dicríticas de segundo tipo fueron caracterizadas por Mattei - Salem [Ma-Sa] en término de su multiplicidad y de su unión de separatrices. En este trabajo de tesis, damos otra caracterización a las foliaciones no dicríticas de segundo tipo con el polígono de Newton de la foliación y el de su unión de separatrices. De otro lado, Loray [Lo] enuncia una caracterización para un tipo de foliaciones con singularidades cuspidales que tienen la misma resolución que su unión de separatrices, sin embargo Fernández, Mozo y Neciosup [F-Mo-N] encuentran una impresición en la caracterización debido a que la condición es necesaria pero no suficiente. Lo que hacemos en este trabajo es caracterizar a dicha familia de foliaciones cuando son de segundo tipo y damos condiciones necesarias y suficientes cuando son de tipo curva generalizada en términos de su orden pesado. Fi...

In this workshop we will share a proposal for teaching quadratic functions whose correspondence rules contain parameters in their mathematical expression and certain conditions that their range must fulfill. We will use GeoGebra as a support tool for the validation of the parameter values obtained in the algebraic process. This workshop has two purposes, the first is to propose problems with context in which the solutions involve real numbers, and the second is to present to teachers the potential of GeoGebra to validate algebraic processes. Likewise, we are interested in generating a space to discuss the advantages and disadvantages offered by GeoGebra tools in the verification of results obtained algebraically and to reflect on its incorporation in our classes. As for the didactic analysis, aspects of the Theory of Semiotic Representation Registers are taken. In relation to the methodo...

Mathematical optimization is a recurring theme in professional careers such as mathematics, engineering, and economics. Using the notion of didactic suitability of the EOS theoretical framework, the main objective of this research is to assess the didactic suitability of an instructional process on the optimization of real functions of two variables in Economics students. In this qualitative research, the reference meanings of the partial derivatives involved in optimization problems are identified, indicators of didactic suitability are adapted in their six facets, and the instructional process implemented by the teacher is analyzed by comparing it with the suitability indicators. The conclusion is that the observed teaching process largely complies with the proposed indicators, particularly in the epistemic and cognitive facets, which makes it a suitable process, considering some aspec...