Volume IV. Number 1. April 2014

We present the first number of the fourth volume of the “Mathematical Thinking” Journal. It includes some papers framed in the different sections of the Journal. The articles cover a wide range of the Mathematics topics and its applications.

Title: Créditos editoriales, Índice de artículos y Editorial del Número 1 (Vol. IV)
Author: Equipo Editorial
Teaching Experiences

Dropout in higher education is a concern in universities worldwide and has a significant impact in our country, especially in engineering and architecture degrees. There are multiple and different perspectives to analyze this phenomenon; however, there is not a unified approach to conceptualize it. Adequate ways to measure and compare the dropout dimension in different institutions or countries have not been found so far. Consequently, it is difficult to find effective procedures to improve retention rates and to minimize negative consequences -both personal and social- of the abandonment of higher education. This article is about two projects which have been promoted by the Technical University of Madrid (UPM) whose main objective is to deepen the knowledge of academic attrition and to determine palliative approaches to be applied in different contexts…

Title: El abandono académico: análisis y propuestas paliativas. Dos proyectos de la Universidad Politécnica de Madrid
Author: Ana Casaravilla
History of Mathematics

En este trabajo se presentan los problemas “de mezclas´´ contenidos en la colección medieval Propositiones ad acuendos juvenes de Alcuino de York y se analizan posibles métodos de resolución, puramente aritméticos, que pudo haber seguido el autor del texto original. Pensamos que un análisis de este tipo puede tener interesantes implicaciones didácticas a la hora de afrontar el paso de la Aritmética al Álgebra.

Title: Los curiosos problemas de mezclas de Alcuino de York
Author: Antonio M. Oller Marcén

Hoy en día, el carácter aritmético de los valores de la función zeta de Riemann en argumentos enteros y en particular en impares, continúa siendo un problema abierto dentro de la comunidad matemática. Este artículo se dedica a presentar los principales resultados alcanzados por varios matemáticos desde el siglo XVII hasta la actualidad, correspondientes al carácter aritmético que siguen los valores de la función zeta de Riemann en argumentos enteros.

Title: Aritmética de los valores de la función zeta de Riemann en argumentos enteros
Author: Anier Soria Lorente
Mathematical Stories

El siguiente relato trata de poner de manifiesto cómo tras la “ignorancia´´ matemática puede haber atrevimiento por el que se puede llegar a cualquier resultado por extraño que éste resulte, todo ello llevado en un tono narrativo ameno y divertido.

Title: Matemáticas para todos
Author: José Miguel Bel Martínez

The idea of parametric architecture has an instrumental side in the use of software oriented to the management of the information of the architectural project, in particular when complex geometries are involved. But the idea of defining form, regardless its geometry, by means of a limited number of parameters can be far reaching on account of the possibilities of generating variations by the modification of these parameters, the manipulation of form in optimization processes and the relation between the mathematical-formal structures generated and the classical concept of formal unity in a work of art.

Title: Arquitectura paramétrica discreta: exploración en el ámbito de la geometría ortogonal
Authors: Óscar del Castillo Sánchez

Fractional Calculus provides an opportunity to spread the concepts of derivative and integral to not integer orders. In this context, we may consider a generalization of Newton´s second Law in which the second derivative is replaced by other of α order (1,5<α≤2). In this research some classical systems (pendulum, projectile and spring) are discussed under this new approach.

Title: Cálculo Fraccionario y dinámica newtoniana
Authors: Antón Lombardero Ozores

In this paper the advantages of parallel computing are shown by solving the heat conduction equation in two dimensions with the forward in time central in space (FTCS) finite difference method. Two different levels of parallelization are consider and compared with traditional serial procedures. We show in this work the importance of parallel computing when dealing with large problems that are impractical or impossible to solve them with a serial computing procedure. In the first section a summary of parallel computing approach is presented. Subsequently, the forward in time central in space (FTCS) finite difference method for the heat conduction equation is outline, describing how the heat flow equation is derived in two dimensions and the particularities of the finite difference numerical technique considered. Then, a specific initial boundary value problem is solved by the FTCS finite difference method and serial and parallel pseudo codes are provided. Finally after results are discussed some conclusions are presented.

Title: Programación en paralelo GPGPU del método en diferencias finitas FTCS para la ecuación del calor
Author: Vicente Cuellar Moro, Miguel Martín Stickle y Manuel Pastor Pérez

Theory and applications of rare events, very important in recent years due to its practical importance in very different fields such as insurance, finance, engineering or environmental science. This paper presents a methodology for predicting rare events based on Bayesian networks that in turn allows to study alternative scenarios.

Title: Estimación de sucesos raros mediante Redes Bayesianas
Author: Francisco Soler Flores y José Ángel Olivas Varela
Games and Mathematical Oddities

Among triangular numbers, some are squares in disguise. We uncover them, and in so doing we come across some interesting people such as continuous fractions, Pell´s equation and aproximation of solutions.

Title: Números triangulares cuadrados (la cuadratura del triángulo)
Author: Dionisio Pérez Esteban

There exists a sequence of natural numbers, starting at zero and increases every time the integer corresponding to the order of the same element which have curious properties that are fully understood after a study of the same . The sequence also generates some interesting identities such as one that determine the powers of any integer as a function of the elements of the sequence.

Title: Una Sucesión Matemática Curiosa
Author: Marco Vinicio Vásquez Bernal
Cri­tics and Reviews

This paper presents a report of the book, that belongs to the collection “El mundo es matemático´´. Another book from this collection was commented by the author in a previous paper.

Title: Informe sobre el libro: “El enigma de Fermat. Tres siglos de desafío a la matemática´´, de Albert Violant
Author: Javier Rodrigo Hitos

“I`m a mathematician. Before I was a musician, or so I thought. Then, I began to say I was a good mathematician among musicians and a good musician among mathematicians. But now I assume myself as a mathematician, although I continue making some music. Perhaps the difference is that now I do not feel musician I enjoy it much more´´. Here the self-portrait I have extracted from Pablo when we started this conversation; for those who know him a bit this is not much, but it is a valuable tool to introduce this mathematician to reader.

Title: Pablo Amster: La Música de la Matemática
Author: Rosa María Herrera

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