Después de Einstein: una arquitectura para una teoría

En 1905, aparecen en la revista "Annalen der physik" tres artículos que revolucionarán las ciencias físicas y pondrán en jaque los asentados conceptos newtonianos de Espacio y Tiempo. La formulación de la Teoría de la Relatividad por Albert Einstein pone en crisis el valor absoluto de estos conceptos, y permite proponer nuevas reflexiones a propósito de su concepción dentro del campo de la física. Esta revolución ¿podría extrapolarse al campo de la arquitectura, donde Espacio y Tiempo tienen un papel protagonista? Hay que entender la complejidad del hecho arquitectónico y las innumerables variables que participan de su definición. Se estudia en esta Tesis Doctoral un aspecto muy concreto: cómo un paradigma (la Teoría de la Relatividad) puede intervenir y modificar, o no, la Arquitectura. Se plantea para ello ir al origen; desentrañar el momento de interacción entre la Teoría de la Relatividad y la Teoría de la Arquitectura, que permita determinar si aquella influyó sobre ésta en los escritos teóricos de las vanguardias aplicados a la Arquitectura. “Después de Einstein. Una arquitectura para una teoría” buscará los puntos de conexión de la Teoría de la Relatividad con la teoría arquitectónica de las vanguardias de principio del siglo XX, su influencia, la contaminación entre una y otra, con posibles resultados arquitectónicos a partir de esta interacción, capaz de definir nuevos argumentos formales para un nuevo lenguaje enArquitectura. Annalen der physik Después de Einstein. Una arquitectura para una teoría Para ello la Tesis se estructura en cuatro capítulos. El primero expone el ámbito geográfico y cronológico donde se desarrolla la Teoría de la Relatividad con la repercusión teórica que tiene para el arte, en función de una nueva definición de espacio vinculado al tiempo, como evento que se desarrolla en un ámbito cuatridimensional; la indeterminación de las medidas de espacio y de las medidas de tiempo, y la importancia de entender la materia como energía. El segundo capítulo estudia los movimientos de vanguardia coetáneos a la eclosión de la Relatividad, enmarcados en su ámbito geográfico más próximo. El cubismo se muestra como movimiento que participa ocasionalmente de las matemáticas y la geometría, bajo el influjo del científico Henri Poincaré y las geometrías no euclidianas. El futurismo indaga en los avances de la ciencia desde una cierta lejanía, cierta falta de rigor o profundidad científica para extraer las leyes de su nuevo idealismo plástico constructivo, definiendo e interpretando su Universo a partir de los avances de la ciencia, en respuesta a la crisis del espacio y del tiempo newtonianos. El lenguaje científico se encuentra presente en conceptos como "simultaneidad" (Boccioni), "expansión esférica de la luz en el espacio" (Severini y Carrá), "cuatridimensionalidad", "espacio-tiempo", "aire-luz-fuerza", "materia y energía" que paralelamente conforman el cuerpo operacional de la teoría de Einstein. Si bien no es posible atribuir a la Teoría de la Relatividad un papel protagonista como referente para el pensamiento artístico, en 1936, con la aparición del manifiesto Dimensionista, se atribuyen explícitamente a las teorías de Einstein las nuevas ideas de espacio-tiempo del espíritu europeo seguido por cubistas y futuristas. El tercer capítulo describe cómo la Teoría de la Relatividad llegó a ser fuente de inspiración para la Teoría de la Arquitectura. Estructurado en tres subcapítulos, se estudia el autor principal que aportó para la Arquitectura conceptos e ideas extrapoladas de la Teoría de la Relatividad después de su estudio e interpretación (Van Doesburg), dónde se produjeron las influencias y puntos de contacto (Lissitzky, Eggeling, Moholy-Nagy) y cómo fueron difundidas a través de la arquitectura (Einsteinturm de Mendelsohn) y de las revistas especializadas. El cuarto capítulo extrae las conclusiones del estudio realizado en esta Tesis, que bien pudiera resumir MoholyNagy en su texto "Vision inmotion" (1946) al comentar: "Ya que el "espacio-tiempo" puede ser un término engañoso, tiene que hacerse especialmente hincapié en que los problemas de espacio-tiempo en el arte no están necesariamente basados en la Teoría de la Relatividad de Einstein. Esto no tiene intención de descartar la relevancia de su teoría para las artes. Pero los artistas y los laicos rara vez tienen el conocimiento matemático para visualizar en fórmulas científicas las analogías con su propio trabajo. La terminología de Einstein del "espacio-tiempo" y la "relatividad" ha sido absorbida por nuestro lenguaje diario." ABSTRACT. "AFTER EINSTEIN:ANARCHITECTUREFORATHEORY." In 1905, three articles were published in the journal "Annalen der Physik ". They revolutionized physical sciences and threw into crisis the newtonian concepts of Space and Time. The formulation of the Theory of Relativity by Albert Einstein put a strain on the absolute value of these concepts, and proposed new reflections about them in the field of Physics. Could this revolution be extrapolated to the field of Architecture, where Space and Time have a main role? It is necessary to understand the complexity of architecture and the countless variables involved in its definition. For this reason, in this PhD. Thesis, we study a specific aspect: how a paradigm (Theory of Relativity) can intervene and modify -or not- Architecture. It is proposed to go back to the origin; to unravel the moment in which the interaction between the Theory of Relativity and the Theory of Architecture takes place, to determine whether the Theory of Relativity influenced on the theoretical avant-garde writings applied to Architecture. "After Einstein.An architecture for a theory " will search the connection points between the Theory of Relativity and architectural avant-garde theory of the early twentieth century, the influence and contamination between them, giving rise to new architectures that define new formal arguments for a new architectural language. Annalen der Physik This thesis is divided into four chapters. The first one describes the geographical and chronological scope in which the Theory of Relativity is developed showing its theoretical implications in the field of art, according to a new definition of Space linked to Time, as an event that takes place in a fourdimensional space; the indetermination of the measurement of space and time, and the importance of understanding "matter" as "energy". The second chapter examines the avant-garde movements contemporary to the theory of relativity. Cubism is shown as an artist movement that occasionally participates in mathematics and geometry, under the influence of Henri Poincaré and non-Euclidean geometries. Futurism explores the advances of science at a certain distance, with lack of scientific rigor to extract the laws of their new plastic constructive idealism. Scientific language is present in concepts like "simultaneity" (Boccioni), "expanding light in space" (Severini and Carra), "four-dimensional space", "space-time", "light-air-force," "matter and energy" similar to the operational concepts of Einstein´s theory. While it is not possible to attribute a leading role to the Theory of Relativity, as a benchmark for artistic laws, in 1936, with the publication of the Dimensionist manifest, the new ideas of space-time followed by cubist and futurist were attributed to the Einstein's theory. The third chapter describes how the Theory of Relativity became an inspiration for the architectural theory. Structured into three subsections, we study the main author who studied the theory of relativity and ,as a consequence, contributed with some concepts and ideas to the theory of architecture (Van Doesburg), where influences and contact points took place (Lissitzky, Eggeling, Moholy-Nagy) and how were disseminated throughArchitecture (Einsteinturm, by Mendelsohn) and journals. The fourth chapter draws the conclusions of this PhD. Thesis, which could be well summarized by Moholy Nagy in his text "Vision in Motion" (1946): vi Since "space-time" can be a misleading term, it especially has to be emphasized that the space-time problems in the arts are not necessarily based upon Einstein´s Theory of Relativity. This is not meant to discount the relevance of his theory to the arts. But artists and laymen seldom have the mathematical knowledge to visualize in scientific formulae the analogies to their own work. Einstein's terminology of "space-time" and "relativity" has been absorbed by our daily language.

Método para el análisis independiente de problemas

habilidades de comprensión y resolución de problemas. Tanto es así que se puede afirmar con rotundidad que no existe el método perfecto para cada una de las etapas de desarrollo y tampoco existe el modelo de ciclo de vida perfecto: cada nuevo problema que se plantea es diferente a los anteriores en algún aspecto y esto hace que técnicas que funcionaron en proyectos anteriores fracasen en los proyectos nuevos. Por ello actualmente se realiza un planteamiento integrador que pretende utilizar en cada caso las técnicas, métodos y herramientas más acordes con las características del problema planteado al ingeniero. Bajo este punto de vista se plantean nuevos problemas. En primer lugar está la selección de enfoques de desarrollo. Si no existe el mejor enfoque, ¿cómo se hace para elegir el más adecuado de entre el conjunto de los existentes? Un segundo problema estriba en la relación entre las etapas de análisis y diseño. En este sentido existen dos grandes riesgos. Por un lado, se puede hacer un análisis del problema demasiado superficial, con lo que se produce una excesiva distancia entre el análisis y el diseño que muchas veces imposibilita el paso de uno a otro. Por otro lado, se puede optar por un análisis en términos del diseño que provoca que no cumpla su objetivo de centrarse en el problema, sino que se convierte en una primera versión de la solución, lo que se conoce como diseño preliminar. Como consecuencia de lo anterior surge el dilema del análisis, que puede plantearse como sigue: para cada problema planteado hay que elegir las técnicas más adecuadas, lo que requiere que se conozcan las características del problema. Para ello, a su vez, se debe analizar el problema, eligiendo una técnica antes de conocerlo. Si la técnica utiliza términos de diseño entonces se ha precondicionado el paradigma de solución y es posible que no sea el más adecuado para resolver el problema. En último lugar están las barreras pragmáticas que frenan la expansión del uso de métodos con base formal, dificultando su aplicación en la práctica cotidiana. Teniendo en cuenta todos los problemas planteados, se requieren métodos de análisis del problema que cumplan una serie de objetivos, el primero de los cuales es la necesidad de una base formal, con el fin de evitar la ambigüedad y permitir verificar la corrección de los modelos generados. Un segundo objetivo es la independencia de diseño: se deben utilizar términos que no tengan reflejo directo en el diseño, para que permitan centrarse en las características del problema. Además los métodos deben permitir analizar problemas de cualquier tipo: algorítmicos, de soporte a la decisión o basados en el conocimiento, entre otros. En siguiente lugar están los objetivos relacionados con aspectos pragmáticos. Por un lado deben incorporar una notación textual formal pero no matemática, de forma que se facilite su validación y comprensión por personas sin conocimientos matemáticos profundos pero al mismo tiempo sea lo suficientemente rigurosa para facilitar su verificación. Por otro lado, se requiere una notación gráfica complementaria para representar los modelos, de forma que puedan ser comprendidos y validados cómodamente por parte de los clientes y usuarios. Esta tesis doctoral presenta SETCM, un método de análisis que cumple estos objetivos. Para ello se han definido todos los elementos que forman los modelos de análisis usando una terminología independiente de paradigmas de diseño y se han formalizado dichas definiciones usando los elementos fundamentales de la teoría de conjuntos: elementos, conjuntos y relaciones entre conjuntos. Por otro lado se ha definido un lenguaje formal para representar los elementos de los modelos de análisis – evitando en lo posible el uso de notaciones matemáticas – complementado con una notación gráfica que permite representar de forma visual las partes más relevantes de los modelos. El método propuesto ha sido sometido a una intensa fase de experimentación, durante la que fue aplicado a 13 casos de estudio, todos ellos proyectos reales que han concluido en productos transferidos a entidades públicas o privadas. Durante la experimentación se ha evaluado la adecuación de SETCM para el análisis de problemas de distinto tamaño y en sistemas cuyo diseño final usaba paradigmas diferentes e incluso paradigmas mixtos. También se ha evaluado su uso por analistas con distinto nivel de experiencia – noveles, intermedios o expertos – analizando en todos los casos la curva de aprendizaje, con el fin de averiguar si es fácil de aprender su uso, independientemente de si se conoce o no alguna otra técnica de análisis. Por otro lado se ha estudiado la capacidad de ampliación de modelos generados con SETCM, para comprobar si permite abordar proyectos realizados en varias fases, en los que el análisis de una fase consista en ampliar el análisis de la fase anterior. En resumidas cuentas, se ha tratado de evaluar la capacidad de integración de SETCM en una organización como la técnica de análisis preferida para el desarrollo de software. Los resultados obtenidos tras esta experimentación han sido muy positivos, habiéndose alcanzado un alto grado de cumplimiento de todos los objetivos planteados al definir el método.---ABSTRACT---Software development is an inherently complex activity, which requires specific abilities of problem comprehension and solving. It is so difficult that it can even be said that there is no perfect method for each of the development stages and that there is no perfect life cycle model: each new problem is different to the precedent ones in some respect and the techniques that worked in other problems can fail in the new ones. Given that situation, the current trend is to integrate different methods, tools and techniques, using the best suited for each situation. This trend, however, raises some new problems. The first one is the selection of development approaches. If there is no a manifestly single best approach, how does one go about choosing an approach from the array of available options? The second problem has to do with the relationship between the analysis and design phases. This relation can lead to two major risks. On one hand, the analysis could be too shallow and far away from the design, making it very difficult to perform the transition between them. On the other hand, the analysis could be expressed using design terminology, thus becoming more a kind of preliminary design than a model of the problem to be solved. In third place there is the analysis dilemma, which can be expressed as follows. The developer has to choose the most adequate techniques for each problem, and to make this decision it is necessary to know the most relevant properties of the problem. This implies that the developer has to analyse the problem, choosing an analysis method before really knowing the problem. If the chosen technique uses design terminology then the solution paradigm has been preconditioned and it is possible that, once the problem is well known, that paradigm wouldn’t be the chosen one. The last problem consists of some pragmatic barriers that limit the applicability of formal based methods, making it difficult to use them in current practice. In order to solve these problems there is a need for analysis methods that fulfil several goals. The first one is the need of a formal base, which prevents ambiguity and allows the verification of the analysis models. The second goal is design-independence: the analysis should use a terminology different from the design, to facilitate a real comprehension of the problem under study. In third place the analysis method should allow the developer to study different kinds of problems: algorithmic, decision-support, knowledge based, etc. Next there are two goals related to pragmatic aspects. Firstly, the methods should have a non mathematical but formal textual notation. This notation will allow people without deep mathematical knowledge to understand and validate the resulting models, without losing the needed rigour for verification. Secondly, the methods should have a complementary graphical notation to make more natural the understanding and validation of the relevant parts of the analysis. This Thesis proposes such a method, called SETCM. The elements conforming the analysis models have been defined using a terminology that is independent from design paradigms. Those terms have been then formalised using the main concepts of the set theory: elements, sets and correspondences between sets. In addition, a formal language has been created, which avoids the use of mathematical notations. Finally, a graphical notation has been defined, which can visually represent the most relevant elements of the models. The proposed method has been thoroughly tested during the experimentation phase. It has been used to perform the analysis of 13 actual projects, all of them resulting in transferred products. This experimentation allowed evaluating the adequacy of SETCM for the analysis of problems of varying size, whose final design used different paradigms and even mixed ones. The use of the method by people with different levels of expertise was also evaluated, along with the corresponding learning curve, in order to assess if the method is easy to learn, independently of previous knowledge on other analysis techniques. In addition, the expandability of the analysis models was evaluated, assessing if the technique was adequate for projects organised in incremental steps, in which the analysis of one step grows from the precedent models. The final goal was to assess if SETCM can be used inside an organisation as the preferred analysis method for software development. The obtained results have been very positive, as SETCM has obtained a high degree of fulfilment of the goals stated for the method.

Multidisciplinary Learning, Another way of Teaching Maths in Engineering

Multidisciplinary training is widely appreciated in industry and business, and nevertheless usually is not addressed in the early stages of most undergraduate programs. We outline here a multidisciplinary course for undergraduates studying engineering in which mathematics would be the common language, the transverse tool. The goal is motivating students to learn more mathematics and as a result, improve the quality of engineering education. The course would be structured around projects in four branches in engineering: mechanical, electrical, civil and bio-tech. The projects would be chosen among a wide variety of topics in engineering practice selected with the guidance of professional engineers. In these projects mathematics should interact with at least two other basic areas of knowledge in engineering: chemistry, computers science, economics, design or physics.

A new way of teaching different subjects in a foreign language in the Building Engineering Degree at the Universidad Politécnica.

The European Union has been promoting linguistic diversity for many years as one of its main educational goals. This is an element that facilitates student mobility and student exchanges between different universities and countries and enriches the education of young undergraduates. In particular, a higher degree of competence in the English language is becoming essential for engineers, architects and researchers in general, as English has become the lingua franca that opens up horizons to internationalisation and the transfer of knowledge in today’s world. Many experts point to the Integrated Approach to Contents and Foreign Languages System as being an option that has certain benefits over the traditional method of teaching a second language that is exclusively based on specific subjects. This system advocates teaching the different subjects in the syllabus in a language other than one’s mother tongue, without prioritising knowledge of the language over the subject. This was the idea that in the 2009/10 academic year gave rise to the Second Language Integration Programme (SLI Programme) at the Escuela Arquitectura Técnica in the Universidad Politécnica Madrid (EUATM-UPM), just at the beginning of the tuition of the new Building Engineering Degree, which had been adapted to the European Higher Education Area (EHEA) model. This programme is an interdisciplinary initiative for the set of subjects taught during the semester and is coordinated through the Assistant Director Office for Educational Innovation. The SLI Programme has a dual goal; to familiarise students with the specific English terminology of the subject being taught, and at the same time improve their communication skills in English. A total of thirty lecturers are taking part in the teaching of eleven first year subjects and twelve in the second year, with around 120 students who have voluntarily enrolled in a special group in each semester. During the 2010/2011 academic year the degree of acceptance and the results of the SLI Programme have been monitored. Tools have been designed to aid interdisciplinary coordination and to analyse satisfaction, such as coordination records and surveys. The results currently available refer to the first and second year and are divided into specific aspects of the different subjects involved and into general aspects of the ongoing experience.

The introduction of teaching innovations into the traditional teaching of construction and building materials

The traditional teaching methods used for training civil engineers are currently being called into question as a result of the new knowledge and skills now required by the labor market. In addition, the European Higher Education Area is requesting that students be given a greater say in their learning. In the subject called Construction and Building Materials at the Civil Engineering School of the Universidad Politécnica de Madrid, a path was set three academic years ago to lead to an improvement in traditional teaching by introducing active methodologies. The innovations are based on cooperative learning, new technologies, and continuous assessment. The writers’ proposal is to offer their experience as a contribution to the debate on how students can be encouraged to acquire the skills currently demanded from a civil engineer, though not overlooking solid, top-quality training. From the outcomes obtained, it can be concluded that using new teaching techniques to supplement a traditional approach provides more opportunities for students to learn while boosting their motivation. In our case, the introduction of these changes has resulted in an increased pass rate of 29% on average, when such a figure is considered in the light of the mean value of passes during the last decade.

Student Reciprocal Peer Teaching as a Method for Active Learning: An Experience in an Electrotechnical Laboratory

Active learning is one of the most efficient mechanisms for learning, according to the psychology of learning. When students act as teachers for other students, the communication is more fluent and knowledge is transferred easier than in a traditional classroom. This teaching method is referred to in the literature as reciprocal peer teaching. In this study, the method is applied to laboratory sessions of a higher education institution course, and the students who act as teachers are referred to as ‘‘laboratory monitors.’’ A particular way to select the monitors and its impact in the final marks is proposed. A total of 181 students participated in the experiment, experiences with laboratory monitors are discussed, and methods for motivating and training laboratory monitors and regular students are proposed. The types of laboratory sessions that can be led by classmates are discussed. This work is related to the changes in teaching methods in the Spanish higher education system, prompted by the Bologna Process for the construction of the European Higher Education Area

A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes.

Traditional education vs modern education. What is the impact of teaching techniques' evolution on students learning process?

The main objective of this article is to focus on the analysis of teaching techniques, ranging from the use of the blackboard and chalk in old traditional classes, using slides and overhead projectors in the eighties and use of presentation software in the nineties, to the video, electronic board and network resources nowadays. Furthermore, all the aforementioned, is viewed under the different mentalities in which the teacher conditions the student using the new teaching technique, improving soft skills but maybe leading either to encouragement or disinterest, and including the lack of educational knowledge consolidation at scientific, technology and specific levels. In the same way, we study the process of adaptation required for teachers, the differences in the processes of information transfer and education towards the student, and even the existence of teachers who are not any longer appealed by their work due which has become much simpler due to new technologies and the greater ease in the development of classes due to the criteria described on the new Grade Programs adopted by the European Higher Education Area. Moreover, it is also intended to understand the evolution of students’ profiles, from the eighties to present time, in order to understand certain attitudes, behaviours, accomplishments and acknowledgements acquired over the semesters within the degree Programs. As an Educational Innovation Group, another key question also arises. What will be the learning techniques in the future?. How these evolving matters will affect both positively and negatively on the mentality, attitude, behaviour, learning, achievement of goals and satisfaction levels of all elements involved in universities’ education? Clearly, this evolution from chalk to the electronic board, the three-dimensional view of our works and their sequence, greatly facilitates the understanding and adaptation later on to the business world, but does not answer to the unknowns regarding the knowledge and the full development of achievement’s indicators in basic skills of a degree. This is the underlying question which steers the roots of the presented research.

Jerónimo Sánchez Carranza y la Escuela Española de Esgrima

El deporte de la esgrima no siempre ha sido considerado como actualmente se conoce, ni tampoco el empleo de las armas ha sido el mismo en las diferentes épocas de la historia. Si nos centramos en la española, podemos decir que se hablaba de una forma particular de hacer esgrima, la cual era muy apreciada por el resto de los países europeos. También lo era la que se hacía en Italia. Como cualquier actividad que se desarrolla a lo largo del tiempo debe generarse desde unos comienzos. Estos comienzos siempre están en relación a alguna causa. Para centrarnos en nuestro estudio, los comienzos del manejo de la espada, de una manera lógica y razonada, se une en la persona y en la vida de Jerónimo Sánchez Carranza porque hasta que él no se decide a estudiar en profundidad la ciencia de las armas, no se ve con claridad si todo lo que se hacía con ellas era correcto o no y si todo lo que la inmensa mayoría hacía cuando tenía que utilizarlas estaba revestido de cierta coherencia y fundamento, es decir, tenía su verdad que se pudiera demostrar. Carranza estudia la esgrima que se empleaba en su época y en las anteriores y se da cuenta que tiene que dar una nueva visión de la forma de usar las armas, diferente a lo que la gran mayoría entendía hasta entonces. A Carranza se le ha considerado por muchos autores como el inventor de la esgrima española, hecho que se puede leer con bastante facilidad si se hojea algún tratado que hable de la esgrima española, sin embargo también se habla de Luis Pacheco de Narváez asignándole el mismo calificativo, aunn- ;o es posteriora Carranza. or tanto nuestro estudio se ha centrado en la vida de Jerónimo Sánchez Carranza y en ueva forma de emplear las armas por lo que hace que la tesis sea una tesis biográfica de dicho personaje, donde se ha resaltado mucho más el aspecto del manejo de las armas, de la Destreza. Partimos de las siguientes hipótesis: Carranza es el que sienta los principios técnicos dando forma y coherencia a la escuela de esgrima española gracias a sus aportaciones en los distintos aspectos metodológicos, técnicos y tácticos. La escuela de esgrima española tiene una estructura interna, responde a unas características determinadas y sirve de base a la esgrima que posteriormente se practica. Para que el estudio se pudiera llevar a cabo tuvimos que diseñar un esquema donde se pudieran recoger todos los aspectos que estuvieran relacionados con nuestro autor, de ahí surge el porqué de cada uno de los capítulos que hemos confeccionado. Dicho esquema responde a la visión actual de diferentes facetas de lo que hoy se estudia en diversas ciencias y que cuando Carranza vivía aún no se conocían. Para recoger información sobre su persona y su obra tuvimos en cuenta los distintos lugares donde se podía localizar la documentación necesaria, sobre todo Bibliotecas y Archivos, para ir confeccionando el método de trabajo que consistió en la recopilación de fuentes de todo tipo referidas al tema, pasando luego a la interpretación de las mismas. Esto nos dio una visión de conjunto que hizo que nos adentráramos en aquellos aspectos que más tarde tendríamos que analizar con mucho más detenimiento. En la tesis se puede observar dos partes bien diferenciadas que son las relacionadas; por un lado, a su vida y su tratado y, por otro, al contenido de sus teorías que son realmente las que se deben analizar necesariamente bajo unos conocimientos específicos de la actividad de la esgrima. En cuanto a su vida, se han destacado y estudiado los hechos más importantes de los que hay que resaltar, sobre todo, el que fuera considerado como el inventor de la destreza y de la manera tan particular de concebir dicho arte, diferente a lo que hasta ahora se venía haciendo y que dio paso a lo que se entendió por esgrima científica, quedando plasmada de tal manera que dio pie a la creación de una doctrina y una nueva forma de entender la esgrima la cual generó una línea de actuación que fue continuada por numerosos seguidores. Para todo ello tuvo mucho que ver el que Carranza fuera militar, la cultura y los estudios que poseía, así como la situación en la que se encontraba España además de la gente con quien se relacionaba, que por lo general, era gente culta y de clase social alta. Se ha estudiado también dentro del mismo apartado de su vida unos hechos que se le imputan y que en nuestra opinión son erróneos. Hemos considerado como más relevantes el que Carranza no fue quien riñó con Quevedo como se afirma en algunas de las obras que hemos tratado, sino que fue Pacheco quien tuvo dicha riña, ya que más bien Quevedo se mostraba partidario de las enseñanzas de Carranza, estando en contra de Pacheco. Tampoco fue quien inventó el florete como se dice en algunas ocasiones, ya que el florete aparece posteriormente como un arma de estudio de la técnica de la esgrima. Con respecto al apartado de su obra, se debe decir que tan solo escribió un único tratado que se publicó en 1582, aunque estaba acabado desde el año 1569. En el apartado de su escuela se debe destacar los fundamentos en los que basó sus postulados para que la destreza alcanzara el mismo nivel de las demás artes liberales y que lo hizo a través del estudio de la propia destreza. A lo largo del estudio que hemos realizado se puede apreciar cómo se está generando un arte que hasta ahora no había sido estudiado, viéndose los problemas que ello suponía, desde la organización de la materia a tratar, hasta cómo se debía enseñar, pasando a veces a tener que denominar conceptos de nueva aparición o renombrar y modificar antiguos que estaban anclados en puntos de partida equivocados, siendo éstos los que mayor trabajo le supuso. Diferencia bien dos aspectos básicos que debían existir en cualquier arte y más concretamente en la destreza que son: la teoría y la práctica, ambas deben estar en base a la razón ya que sería una de las formas por la que la destreza perduraría en el tiempo, junto con que esta razón estuviera apoyada en otras ciencias y con los principios de ellas. Carranza fue de la opinión de que el diestro debía conocer mediante el estudio, los elementos fundamentales con los que había que trabajar la destreza, estos elementos son el cuerpo del diestro y las armas, porque ambos van a intervenir en cualquier gesto o acción que se vaya a realizar. Del cuerpo estudió cada una de las partes que más importancia tiene cada vez que el diestro interviene y lo hace sobre todo en base a la medicina, relacionándolo con las matemáticas para poder sacar el máximo provecho, aconsejando que por el conocimiento del propio cuerpo, como el del contrario, se podrá emplear en determinadas situaciones, que si no se supiera de ello, no se sacaría el mismo resultado. De las armas lo que más resaltó fue, por un lado, que la espada debía ser el único arma que el diestro debía utilizar y, por otro, el hecho de que la espada la graduara para poder demostrar que no se hacia todo igual con las distintas partes de la misma porque no todo el arma tenía las mismas propiedades cuando se actuaba con ella. Una de las recomendaciones que dio fue que con la parte más próxima a la empuñadura se debía practicar la defensa por tener más fuerza con esta parte que con la punta y lo demostró con principios matemáticos. Se puede ver con la lectura de la tesis cómo Carranza aporta una nueva forma de trabajo en la que le da mucha importancia a la aplicación de los conocimientos, que previamente se han adquirido y para ello, es importante conocer bien los puntos fuertes y débiles del adversario. La adquisición de la práctica se debe realizar a través de la repetición para crear el hábito necesario que haga que el gesto salga fluido en cada uno de los movimientos que el diestro ejecute. Todo esto no sería posible si quien lo enseña no conoce cada uno de los elementos que intervienen en la destreza, por tanto, a la figura del maestro le da un lugar de una gran relevancia, ya que va a ser él quien tenga que guiar a los alumnos que enseñe. Lo primero que debe hacer los maestros es procurar saber lo máximo de la materia que va a enseñar, por lo que el maestro debe saber casi todo sobre la teoría y la práctica de la destreza, pero además esta teoría y práctica debe ser la correcta. Carranza persigue con su estudio, establecer los principios de la destreza, por lo menos, los más importantes, aunque fueran elementales, para que posteriormente se siguiera trabajando sobre ellos y poder conseguir que la destreza tenga cuerpo y forma de arte liberal, pudiéndose estudiar como cualquier otra, así de esta manera se haría un bien público, ya que los jóvenes se instruirían eficazmente en el uso de las armas, aunque el verdadero fin se encuentra en la conservación de la vida como manda la Fe Católica, siendo la destreza uno de los medios más eficaces para conseguirlo. Hemos dedicado un apartado de técnica y de táctica donde se refleja todo lo relacionado con las posiciones y movimientos que debe realizar el diestro para llegar a conseguir su objetivo, que es herir sin ser herido. Se han analizado las distintas tretas y el porqué de cada una desde el punto de vista del gesto y del movimiento. Si lo que se hace en destreza se relaciona con el adversario, nos adentramos en el terreno de la táctica donde se han estudiado como más importantes los conceptos del tiempo y la distancia, así como las energías que debe conservar el diestro para poder llevar a cabo un combate y del mismo salir victorioso sin llegar al agotamiento. Concluimos diciendo que de todo el estudio que se ha realizado, se ha podido comprobar que Carranza fue quien dotó a la destreza de unos principios técnicos, tácticos y metodológicos, por su forma de concebir este nuevo arte, así como que por la manera en que estableció sus teorías hizo que la destreza que se practicaba en España disfrutara de una estructura interna coherente que perduró a través de los años. SUMMARY The sport of fencing has not always been the respected sport that we know it to be today ñor has the use of weapons been the same throughout history. If we concéntrate on Spainish weapons, we can say that one particular type of sword ¡s spoken about. this sword being very respected by outher European countries, it was also the one that was respected and used in Italy. As with any activity that develops in time, it must evlove from some simple beginnings. Such basics beginnings are always in relation to a cause. To concéntrate on our study, the beginnings are, the use of the sword in a reasoned and logical manner, brought together in the life and times of Jerónimo Sánchez Carranza because until he decided to study in depth the science of weapons, we cannot see with calrity if their use was correct or not and if the vast majority , when they had to use them, used any foundation or coherence, that ¡s to say if any exactness of logical use could be demonstrated. Carranza studied the sword used in his time and those that had gone before, bearing in mind that he had a new visión of the form of use of weapons, different to what the vast majority had until then understood. Carranza has been considered by many historians as the inventor of the Spanish sword, a fact which can be seen with relative ease if one flicks through any work which deals with the Spanish sword, however, they also speak of Luis Pacheco de Narváez affording him the same title, even though he followed Carranza. In ar H our study has been centred on the life of Jerónimo Sánchez Carranza and his ne-" use of weapons. In effect this thesis is a biographical thesis of the said wherein the aspect of the use of weapons stands out more than their mastery. Given the following hypothesis: It was Carranza who evolved the first techniques giving form and coherence to the .Spanish School of Fencing, thanks to his contributions to the different aspects of method, íechnique and tactic. The Spanish School of Fencing had an ¡nternal structure anaswerable to pre-detremined characteristics and served as a base for the fencing that was to, in later days, be practised. For this study to come to a head, we had to design a plan wherein we could collate all of the aspects we could, related to our inventor. From there springs the reason for each of the chapters that we have put together. The said plan responding to the actual visión of different facets that are studied today in different sciences, that were not known in Carranza's lifetime. To collect information on his person and his works we bore in mind the different places in which we could lócate the necessary documentation, above all in libraries and archives. Developing the work-method that consisted in extracing from every source, every thing relative to the theme, re-writing later our interpretation of the same. This brought us closer and made us focus of those aspects that much later we would have to analize in greater detail. In the thesis one can observe two defferent parts that are related; on the one hand his life and works and on the other his theories, which are those that should be really analised and as such, necessarily analised within the confines of a specific knowledge of fencing. In that his life has been isolated and studied the most important facts that stand out above all, is that he was considered to be the inventor of swordmanship and the particular manner of interpreting the said art, different to its interpretaion uptil then. It gave a footing to what they understood as scientific fencing, giving shape and form to the creation of a doctrine and a new form of fencing which developed a line of action that was continued by numerious followers. For all that, much had to do with the facts that Carranza was a military man, the culture, the level of studies he had and the situation in which he found himself. What's more the people with whom he mixed were, in general, cultured and of high social standing. We have also seen in the same article on his life some dubious facts which in our opinión are erróneos. We have considered the most relevent to be that it wasnt Carranza who was in dispute with Quevedo as is stated in some of the works with which we have dealt but rather it was with Pacheco he had such disputes. What's more Quevedo demonstrated his partiality to the teachings of Carranza, going against Pacheco ñor was it him who invented The Florete, a famous Spanish sword, as was said on some ocassions, eventhough the florete appeared later as a weapon in the study of fencing technique. With respect to the article on his works, we must say that there was only one article which was published in 1582, even though it was finished in 1569. In the article on his life one must distinguish between the foundations on which he based his teachings in which swordmanship reached the same levéis as other libral art forms and what he did through the study of the self same mastery. Throughout the study which we have done, one can appreciate how he was developing an art which uptill then had not been studied, seeing for himself the problems he had fortold, from the organisation of materials at hand to how it should be taught, at times having to domínate comparative concepts again or clarify and modify ones which were anchored in erróneos points of a fencing match, feeling these to be the main forseeable jobs-at-hand. Differenciating between two basic concepts which must exist in whatever arte form and more concretly in the skill that is; the theory and practice , both being fundamental to the reason why the skill endured through time, together with this reason he was supported by other sciences and the beginnings of such. Carranza was of the opinión that the swordsman must acquired by way of study, the fundemental elements with which he had to work, these elements being the body of the swordsman and the weapons, because both were going to intervene in whatever movement or action that was going to be taken. The body studied, each of the parts having more importance each time the skill intervened and above all what it did based on medicne relating it to matemathics to exact the máximum advantage, one could employ in certain circumstances, that if they were not employed, the same advantages would not result. On weapons, what resulted best was, on the one hand, the sword should be the only weapon that the swordsman should use and on the other hand, the sword should be graded to show that one cannot do the same with the different parts of the same because not all of the weapon had the same properties when used. One of the recomendations he made was that the part nearest to the hand-guard should be used for defence because one could use more forcé with it than the point and he demonstrated this with mathematical principies. One can see on reading this thesis how Carranza brought forth a new work form, in which he put much importance on the application of experience that had previously been acquired and because of it, it was important to know well the strenghts and weaknesses of an adversery. The acquisition of technique should be realised through repetition to form the habit necessary for movement to flow freely each time the swordsman executed a movement. None of this would be possible if whoever was teaching did not know each one of the elements that intervened, affording the fencing master a great reverence, in that it was he who had to guide the students he was to teach. The first thing that the master had to do was to make sure he had the maximun knowledge over which he was going to teach, to that end, the master had to know almost everything about the theory and practice of the skill of fencing but what's more that such theory and practice had to be the correct one. Carranza persued his studies, establishing the principies of technique, at least, the most important ones even though they were elementary, so that later they could continué working on them and it could be seen that the technique had a shape and form of any other art form, allowing it to be studied like any other form, as such it had a good following, even young people could be instructed in the correct use of weapons, however the real end could be found in the conservaron of life as ordered by the Catholic Church, feeling that skill with the sword was one of the most effective methods for assuring it. We have dedicated an article to technique and tactics wherein is reflected everything related to positions and movement that the swordsman must do to achieve his objective, that is, wound without being wounded. We have analised the different tricks and the reasons from every point of view of movement and action. If what is done by technique is related with the adversery we enter in the territory of tactics wherein we have studied, most importantly, the concepts of time and distance just as, the energy the swordsman muse conserve to bring to a head a bout and arrive victorious without being exhausted. We conclude by saying that everything that has been realised by this study, has shown that it was Carranza who gave to the skill, the first basic techniques, tactics and methodology, by his conception of this new art form, just as the manner in which he established his theories, made possible the tecnhiques practiced in Spain would enjoy an intemal coherent structure, which would endure throughout the years.

Learning and Assessing Competencies: New challenges for Mathematics in Engineering Degrees in Spain.

The introduction of new degrees adapted to the European Area of Higher Education (EAHE) has involved a radically different approach to the curriculum. The new programs are structured around competencies that should be acquired. Considering the competencies, teachers must define and develop learning objectives, design teaching methods and establish appropriate evaluation systems. While most Spanish universities have incorporated methodological innovations and evaluation systems different from traditional exams, there is enough confusion about how to teach and assess competencies and learning outcomes, as traditionally the teaching and assessment have focused on knowledge. In this paper we analyze the state-of-the-art in the mathematical courses of the new engineering degrees in some Spanish universities.

Teaching automatic control in non-specialist engineering schools

Automatic Control Teaching in the new degree syllabus has reduced both, its contents and its implementation course, with regard to traditional engineering careers. On the other hand, where the qualification is not considered as automatic control specialist, it is required an adapted methodology to provide the minimum contents that the student needs to assimilate, even in the case that students do not perceive these contents as the most important in their future career. In this paper we present the contents of a small automatic course taught Naval Architecture and Marine Engineering Degrees at the School of Naval Engineering of the Polytechnic University of Madrid. We have included the contents covered using the proposed methodology which is based on practical work after lectures. Firstly, the students performed exercises by hand. Secondly, they solve the exercises using informatics support tools, and finally, they validate their previous results and their knowledge in the laboratory platforms.

Teaching and evaluating mechanical vibrations with Matlab®

The study of the response of mechanical systems to external excitations, even in the simplest cases, involves solving second-order ordinary differential equations or systems thereof. Finding the natural frequencies of a system and understanding the effect of variations of the excitation frequencies on the response of the system are essential when designing mechanisms [1] and structures [2]. However, faced with the mathematical complexity of the problem, students tend to focus on the mathematical resolution rather than on the interpretation of the results. To overcome this difficulty, once the general theoretical problem and its solution through the state space [3] have been presented, Matlab®[4] and Simulink®[5] are used to simulate specific situations. Without them, the discussion of the effect of slight variations in input variables on the outcome of the model becomes burdensome due to the excessive calculation time required. Conversely, with the help of those simulation tools, students can easily reach practical conclusions and their evaluation can be based on their interpretation of results and not on their mathematical skills

An Analysis Of The Recommended Knowledge For The Software Project Management Discipline

According to the PMBOK (Project Management Body of Knowledge), project management is “the application of knowledge, skills, tools, and techniques to project activities to meet the project requirements” [1]. Project Management has proven to be one of the most important disciplines at the moment of determining the success of any project [2][3][4]. Given that many of the activities covered by this discipline can be said that are “horizontal” for any kind of domain, the importance of acknowledge the concepts and practices becomes even more obvious. The specific case of the projects that fall in the domain of Software Engineering are not the exception about the great influence of Project Management for their success. The critical role that this discipline plays in the industry has come to numbers. A report by McKinsey & Co [4] shows that the establishment of programs for the teaching of critical skills of project management can improve the performance of the project in time and costs. As an example of the above, the reports exposes: “One defense organization used these programs to train several waves of project managers and leaders who together administered a portfolio of more than 1,000 capital projects ranging in Project management size from $100,000 to $500 million. Managers who successfully completed the training were able to cut costs on most projects by between 20 and 35 percent. Over time, the organization expects savings of about 15 percent of its entire baseline spending”. In a white paper by the PMI (Project Management Institute) about the value of project management [5], it is stated that: “Leading organizations across sectors and geographic borders have been steadily embracing project management as a way to control spending and improve project results”. According to the research made by the PMI for the paper, after the economical crisis “Executives discovered that adhering to project management methods and strategies reduced risks, cut costs and improved success rates—all vital to surviving the economic crisis”. In every elite company, a proper execution of the project management discipline has become a must. Several members of the software industry have putted effort into achieving ways of assuring high quality results from projects; many standards, best practices, methodologies and other resources have been produced by experts from different fields of expertise. In the industry and the academic community, there is a continuous research on how to teach better software engineering together with project management [4][6]. For the general practices of Project Management the PMI produced a guide of the required knowledge that any project manager should have in their toolbox to lead any kind of project, this guide is called the PMBOK. On the side of best practices 10 and required knowledge for the Software Engineering discipline, the IEEE (Institute of Electrical and Electronics Engineers) developed the SWEBOK (Software Engineering Body of Knowledge) in collaboration with software industry experts and academic researchers, introducing into the guide many of the needed knowledge for a 5-year expertise software engineer [7]. The SWEBOK also covers management from the perspective of a software project. This thesis is developed to provide guidance to practitioners and members of the academic community about project management applied to software engineering. The way used in this thesis to get useful information for practitioners is to take an industry-approved guide for software engineering professionals such as the SWEBOK, and compare the content to what is found in the PMBOK. After comparing the contents of the SWEBOK and the PMBOK, what is found missing in the SWEBOK is used to give recommendations on how to enrich project management skills for a software engineering professional. Recommendations for members of the academic community on the other hand, are given taking into account the GSwE2009 (Graduated Software Engineering 2009) standard [8]. GSwE2009 is often used as a main reference for software engineering master programs [9]. The standard is mostly based on the content of the SWEBOK, plus some contents that are considered to reinforce the education of software engineering. Given the similarities between the SWEBOK and the GSwE2009, the results of comparing SWEBOK and PMBOK are also considered valid to enrich what the GSwE2009 proposes. So in the end the recommendations for practitioners end up being also useful for the academic community and their strategies to teach project management in the context of software engineering.

Design and implementation of a mathematical videogame

This paper presents videogames as a very useful tool in high studies with respect to mathematical matters. It describes the implementation of a videogame developed by its authors which makes it possible for students to reinforce mathematical concepts in a motivating environment. With this work we intend to contribute to the process of engaging a bigger number of university teaching professionals and researchers in the use of serious games and the study of their theoretical frameworks, design, development and application of scientific education. With this idea the authors of the present paper have created and developed the videogame “The Math Castle” which consists in a series of tests through which various aspects of Mathematics are dealt with, especially in the areas of Discrete Mathematics, which due to its nature can be particularly well adapted to this kind of activity, Analysis or Geometry. In this paper there lies a complete description of the game developed and the results obtained with it.

Teaching Planning of Forestry Engineering in Spain : origins and evolution

This paper addresses the historical evolution of, from its inception, to the present day, within the changing context of EHEA and linked to professional competences. The research methodology, although it is mainly a historical document review, expert opinions on university educational planning of university education of forestry engineering in Spain are also included. The results show the evolution of centralized planning, based on technical knowledge transmission to an approach based on competences (technical, contextual and behavioral) focusing on learning for improving employability.