Volume XI. Number 1. April 2021

After a complicated and different 2020, Science seems to be the solution to the big problems again. We are all hopeful that the vaccine against Covid 19 will allow us to reverse a situation that has been really hard both from the human and economic point of view. Our Journal has received papers of great interest that we would like to share with all the public interested in mathematics.

Title: Créditos editoriales, Índice de artículos y Editorial del Número 1 (Vol. XI)
Author: Equipo Editorial
Investigation This paper presents a linear regression method that minimizes the residual error for a set of points xi, yi with i = 1, 2, …, N, this error being understood as the minimum distance of the point to the regression line. Moreover, this method is compared with the traditional one-sided linear regression methods of X on Y and Y on X.
Title: Regresión lineal ortogonal
Author: José Manuel Recio López

In this contribution, a fragile watermarking scheme based on orthogonal Krawtchouk moments is proposed. The proposed algorithm inserts the generated watermark into the first eight coefficients of the Krawtchouk moments, computed from the covered image, with the purpose of guaranteeing the integrity and authenticity of the emitting source.
Title: Una marca de agua frágil en el dominio de los momentos ortogonales de Krawtchouk
Authors: Alicia María Centurión Fajardo, Nancy Céspedes Trujillo y Eduardo Moreno Roque
Teaching Experiences In this paper, we present an experience with Secondary School students to whom we pose a problem composed of several subproblems that require mathematical modeling and we expose an evaluation proposal for this type of activities in order to take into account all the aspects involved in this process. The teacher guides in the resolution and explains the tools offered by GeoGebra (International Geogebra Institute, 2020). Finally, the guide for individual and group evaluation is proposed, including two instruments: rubric and target.
Title: Modelización matemática con Geogebra: colocación de circunferencias y esferas
Authors: Ricardo José García Bonaviña, Almudena Lloréns Payá, Carmen Romero-García y Ana María Zarco García

The purpose of this article is to describe a Mathematics Problem Solving workshop with concrete material and to report the opinions of the participating teachers. Students from the Pre-University of the Universidad del Bío-Bío participated in the workshops. A descriptive analysis of the data collected on the implementation of the workshops was carried out by means of semi-structured interviews with the teachers who conducted the workshops.
Title: Taller de Resolución de Problemas de Matemática con material concreto: opinión de profesores
Authors: Héctor Bastías Montaner y Ángelo Fierro Fierro

Having noticed the lack of training in statistical tools in some mathematics degrees, as well as the growing importance of R programming software, it has been necessary to teach a course on Data Analysis with R. This course has been developed within the “Compumates” initiative of the Faculty of Mathematical Sciences, Complutense University of Madrid. Mathematics, Complutense University of Madrid, and consisted of different sessions, starting from the installation of the software and use of basic commands, to its application in analysis and prediction techniques. For this purpose, the students have been provided with a learning manual. This work shows the results of the experience in the student’s learning and their evaluation of it.
Title: Enseñanza del Software Estadístico R a alumnos de matemáticas
Authors: Elena Castilla y Pedro J. Chocano
History of Mathematics There is a whole constellation of proteins present in the human body that express our genetic material and determine how our cells function. A mutation in one of our genes can produce a change in one of these proteins that causes a certain disease. In addition, viruses can enter cells using proteins, such as the S protein of coronaviruses that forms spicules to attach to our cells. But, at the same time, vaccines can be designed by making proteins that geometrically fit our antibodies, activating our immune system. We understand a change when we understand what has remained unchanged after it. The various geometries consider properties that do not vary – they are invariant – when a certain group of transformations or symmetries act. The concept of a group of symmetries has applications, not only aesthetically, but as something constitutive of physical space and biology. Symmetry groups influence artistic compositions in fine art, music or poetry, but they also govern the behavior of the elementary particles of physics, of neuronal connections, of the configuration of our genetic material and the function of our proteins, so we are geometry.
Title: Geometría eres tú
Author: María Jesús Vázquez-Gallo
Games and Mathematical Oddities This article analyzes a particular case of de Bruijn’s successions that will be used to create a mentalism game involving four spectators. The effect consists of finding out the means of transport thought of by each of the participants from a total of sixteen land, air and sea vehicles. As a starting point for the creation of the game, the concept of a de Bruijn sequence is first defined, which is exemplified by a sequence of order n using the symbols 0 and 1 as alphabet and an explanation of how to construct this type of sequence using the so-called de Bruijn graphs.
Title: Adivinación cobriza
Author: Aurelio Sánchez Estévez
Mathematical Tales This article shows one of the stories submitted to the contest of stories with mathematical content organized by the GIE (Grupo de Innovación Educativa) Pensamiento Matemático of the UPM (Universidad Politécnica de Madrid), for students of ESO, Bachillerato and university students. In this case it is a story made by a high school student.
Title: Soñar. . . ¿te da alas?
Author: Alba González Martín
Critics and Reviews This article presents a computer game, intended to run in the browser, that teaches the properties of functions in an interactive way. At startup, the program randomly selects a function from a list of 28, and the user must guess which one it is by asking True/False questions, similar to the traditional “Who’s Who?” game. In addition, the answers to the questions are converted into a binary code based on ones and zeros that the player must convert to decimal in order to receive his or her score based on a ranking.
Title: Video Juego Who’s That Function
Author: Equipo Editorial
Interviews Mariano Soler Dorda is University Professor at the School of Civil Engineering of the Polytechnic University of Madrid and has been teaching Mathematics for more than 35 years. He has just received the award for the best teacher of the past academic year 2010-2011. He is a person committed to the teaching of Mathematics and with great experience in this subject. We have talked to him about the teaching of Mathematics at the University. Aurelio Sánchez Estévez is Deputy Director General of Kumon Instituto de Educación de España and a member of the Red de Divulgación Matemática (DiMa). In addition to his professional activity at Kumon, he gives numerous workshops and conferences for families and students of all educational levels in Spain and abroad, as well as teacher training courses.
Title: Aurelio Sánchez: el método KUMON
Author: Equipo Editorial
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