Angel F. Tenorio

El articulo versa sobre una metodologia docente y evaluativa diferente de las tradicionales clases magistrales y examenes finales. Los autores han implementado una dinamica de trabajo cooperativo en grupos que confluye en el desarrollo de un juego de rol. El diseno docente de la asignatura Historia de las Relaciones Internacionales (RRII), del Grado en Ciencias Politicas, busca alcanzar los objetivos cognitivos marcados en el plan de estudios y desarrollar las competencias adscritas a la materia. El juego de rol y su preparacion ha permitido que el alumnado conozca los fundamentos de la Historia de las RRII, desarrollando las competencias de expresion escrita y busqueda de informacion autonoma, pudiendo el profesorado realizar una evaluacion continua del alumnado, evitando examenes finales memoristicos. La asignatura de Historia de las RRII pertenece al modulo “Areas de desarrollo profesional”, cuyo caracter especializado permite que el alumnado adquiera competencias directamente relacionadas con los ambitos laborales en los que los politologos suelen desempenar su profesion. Entre los objetivos ligados a la materia, se incluyen entender las relaciones internacionales desde una perspectiva historica (en sus vertientes politicas, sociales y economicas) y prestar especial atencion a los procesos de integracion politica y economica acaecidos en las dos ultimas centurias ligadas al conocimiento de la evolucion historica de las organizaciones internacionales. Las relaciones internacionales de esos siglos dirimian sus diferencias en conflictos belicos, por lo que la asignatura quiere mostrar al alumnado alternativas a la guerra en un claro fomento de la cultura de la paz.

aftenorio@upo.esAbstractThis paper shows an overview about the concept and the philosophy ofWebQuest. Besides, most of WebQuest are studied between those whichcan be found in Internet dealing with Statistics and Probability in Spanish.To do it, these are analyzed in-depth by indicating the aspects which arefavorable and those which can be improved.Keywords: WebQuest, Statistics, Probability, High School level.AMS Subject classiflcations: 62B99, 60-01 90B30,62F15,62F30,62J99

The main goal of this paper is to compute a minimal matrix representation for each non-isomorphic nilpotent Lie algebra of dimension less than $6$. Indeed, for each of these algebras, we search the natural number $n\in\mathsf{N}\setminus\{1\}$ such that the linear algebra $\mathfrak{g}_n$, formed by all the $n \times n$ complex strictly upper-triangular matrices, contains a representation of this algebra. Besides, we show an algorithmic procedure which computes such a minimal representation by using the Lie algebras $\mathfrak{g}_n$. In this way, a classification of such algebras according to the dimension of their minimal matrix representations is obtained. In this way, we improve some results by Burde related to the value of the minimal dimension of the matrix representations for nilpotent Lie algebras.

El presente artículo muestra cómo evaluar al alumnado en la asignatura Métodos Matemáticos para la Ingeniería de la Universidad Pablo de Olavide, mediante una evaluación continua de tipo portafolio en la que el alumnado irá realizando una serie de actividades por tema que serán las que se emplearán para su evaluación final y que realizarán bajo la supervisión del profesorado haciendo uso de las tutorías. En vista del tipo de actividades evaluativas empleadas, se hará necesario disponer de mecanismos de control que aseguren tanto autoría como comprensión de trabajos. Los contenidos de esta asignatura son eminentemente prácticos y basados en la resolución de problemas, con la ayuda de un paquete de cálculo simbólico. El uso de este tipo de recursos conlleva un cambio en los criterios de evaluación y en la metodología evaluativa con respecto a una metodología clásica con su evaluación centrada en realizar problemas "a mano".

In this paper, we show a new algorithmic method for classifying filiform Lie algebras. It is based on considering the maximal dimension of abelian ideals and studying the relation between them and some known invariants of filiform Lie algebras which allows us to obtain the laws of these algebras. To explain the algorithm, some specific examples of its application are also shown.

This paper shows how to associate the Lie algebra gn (n ∈ N), of n×n strictly upper-triangular matrices, with a specific 2-dimensional triangular configuration. The properties of those configu-rations are analyzed here by using Graph Theory and, finally, applied to obtain some results about Representation Theory for nilpotent Lie algebras.

Resumen Durante los últimos cursos académicos, son varias las sesiones realizadas en el Aula Abierta de Mayores de la Universidad Pablo de Olavide que estaban dedicadas a tratar algunos contenidos matemáticos con una perspectiva atractiva y útil para el alumnado (cuya edad supera los 55 años). A este respecto, se buscaron temáticas que estuviesen presentes y relacionadas con la vida cotidiana. Más concretamente, se trataron temas como arte, naturaleza y matemáticas, juegos de azar, encuestas o algunos divertimentos matemáticos. Tanto la metodología como la temática de cada sesión permitieron que tanto alumnado como profesorado hayan quedado plenamente satisfechos al finalizar estas experiencias. Abstract In the last academic years, Senior Citizens' Open Lecture Room of Pablo de Olavide University has held several sessions about mathematical topics from an attractive, useful perspective for the students (whose age is greater than 55). Regarding this, the topics considered were re...

Given a finite-dimensional Leibniz algebra with certain basis, we show how to associate such a Lie algebra with a combinatorial structure of dimension 2. In some particular cases, this structure can be reduced to a digraph or a pseudodigraph. In this paper, we study some theoretical properties about this association and we determine the type of Leibniz algebra associated with each of these structures having no more than 3 vertices.

This paper shows a new computational method to obtain filiform Lie algebras, which is based on the relation between some known invariants of these algebras and the maximal dimension of their abelian ideals. Using this relation, the law of each of these algebras can be completely determined and characterized by means of the triple consisting of its dimension and the invariants z 1 and z 2 . As examples of application, we have included a table showing all valid triples determining filiform Lie algebras for dimension 13.

The main goal of this paper is to compute the maximal abelian dimension of each solvable non-decomposable Lie algebra of dimension less than 7. To do it, we apply an algorithmic method which goes ruling out non-valid maximal abelian dimensions until obtaining its exact value. Based on Mubarakzyanov and Turkowsky's classical classifications of solvable Lie algebras (see [13] and [19]) and the classification of 6-dimensional nilpo-tent Lie algebras by Goze and Khakimdjanov [7], we have explicitly computed the maximal abelian dimension for the algebras given in those classifications.

Abelian subalgebras play an important role in the study of Lie algebras and their properties and structures. In this paper, the historical evolution of this concept is shown, analyzing the current status for the research on this topic. So, the main results obtained from previous years are indicated and commented here. Additionally, a list of some related open problems is also given.

In this paper some results on the structure of finite-dimensional Lie algebras are obtained by means of the concept of maximal abelian dimension. More concretely, a sucient condition is given for the solvability in finite-dimensional Lie algebras by using maximal abelian dimensions. Besides, a necessary condition for the nilpotency is also stated for such Lie algebras. Finally, the maximal abelian

ABSTRACT This paper studies the law of the Lie algebras hn associated with a particular type of Lie groups: the Lie groups Hn formed by all the n × n upper-triangular matrices without zeros in their main diagonal. Indeed, these laws are obtained by means of a computational algorithm which we have constructed and particularly implemented by using the symbolic computation package MAPLE. Besides, the complexity of this algorithm is studied by considering the number of computations carried out with this implementation.