An example of Learning based on competences: Use of Maxima in Linear Algebra for Engineers

This paper analyzes the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is defined as an indicator of the generic ompetence: Use of Technology. Additionally, we show that using CAS could help to enhance the following generic competences: Self Learning, Planning and Organization, Communication and Writing, Mathematical and Technical Writing, Information Management and Critical Thinking.

Differential algebra techniques for space applications

This project investigates the utility of differential algebra (DA) techniques applied to the problem of orbital dynamics with initial uncertainties in the orbital determination of the involved bodies. The use of DA theory allows the splitting of a common Monte Carlo simulation in two parts: the generation of a Taylor map of the final states with regard to the perturbation in the initial coordinates, and the evaluation of the map for many points. A propagator is implemented exploiting DA techniques, and tested in the field of asteroid impact risk monitoring with the potentially hazardous 2011 AG5 and 2007 VK184 as test cases. Results show that the new method is able to simulate 2.5 million trajectories with a precision good enough for the impact probability to be accurately reproduced, while running much faster than a traditional Monte Carlo approach (in 1 and 2 days, respectively).

DERIVE and Linear Algebra

This work describes an experience with a methodology for learning based on competences in Linear Algebra for engineering students. The experience has been based in autonomous team work of students. DERIVE tutorials for Linear Algebra topics are provided to the students. They have to work with the tutorials as their homework. After, worksheets with exercises have been prepared to be solved by the students organized in teams, using DERIVE function previously defined in the tutorials. The students send to the instructor the solution of the proposed exercises and they fill a survey with their impressions about the following items: ease of use of the files, usefulness of the tutorials for understanding the mathematical topics and the time spent in the experience. As a final work, we have designed an activity directed to the interested students. They have to prepare a project, related with a real problem in Science and Engineering. The students are free to choose the topic and to develop it but they have to use DERIVE in the solution. Obviously they are guided by the instructor. Some examples of activities related with Orthogonal Transformations will be presented.

A toolbox with DERIVE: calculus on several variables, Applications of Computer Algebra

A toolbox is a set of procedures taking advantage of the computing power and graphical capacities of a CAS. With these procedures the students can solve math problems, apply mathematics to engineering or simply reinforce the learning of certain mathematical concepts. From the point of view of their construction, we can consider two types of toolboxes: (i) the closed box, built by the teacher, in which the utility files are provided to the students together with the respective tutorials and several worksheets with proposed exercises and problems,

Análisis de la distribución espacial de centros eruptivos monogenéticos en las Islas Canarias según el análisis de vecino más próximo de Poisson.

El objetivo principal de este trabajo es estudiar la distribución espacial de los centros eruptivos monogenéticos según el análisis de vecino más próximo de Poisson, propuesto por Clark y Evans (1954), en las Islas Canarias. Se pretende adquirir así unos valores cuantitativos que permitan interpretar si los centros eruptivos monogenéticos se distribuyen de forma aleatoria, concentrada o dispersa en cada isla. La confrontación de estos resultados con la bibliografía ayudará a interpretarlos mediante comparación. Como objetivo secundario y parte fundamental del trabajo se presenta la necesidad y el fin de adquirir conocimientos teóricos y prácticos de análisis espacial, además de destreza en el uso de lenguajes y entornos de programación adecuados para este tipo de estudios. Otro de los objetivos es desarrollar una aplicación que haga extensible este tipo de estudios de forma sencilla y ponga a disposición, en el caso de una publicación final, de la comunidad científica y de los usuarios a nivel universitario, una herramienta eficaz de análisis cuantitativo para hallar los índices requeridos para llevar a cabo el análisis de vecino más próximo de Poisson. El área de estudio son las Islas Canarias que conforman un archipiélago de siete islas mayores (Fig. 1): Tenerife, Fuerteventura, Gran Canaria, Lanzarote, La Palma, La Gomera y El Hierro; cuatro islas menores: Lobos, La Graciosa, Montaña Clara y Alegranza; y varios roques. Queda comprendido entre los paralelos 27 º 37 ' N y 29 º 35 ' N (Punta de La Restinga, en El Hierro; Punta de los Mosegos, en la isla de la Alegranza) y entre los meridianos 13 º 20 ' W y 18 º 10 ' W (Roque del Este; Punta de Orchilla, en El Hierro) y se encuentra a distancias de entre 100 km y 500 km de la costa noroccidental africana. Queda englobado dentro de la región de la Macaronesia, conjunto de cinco archipiélagos de origen volcánico situado en el Atlántico Oriental, a saber: Azores, Madeira, Salvajes, Canarias y Cabo Verde; y está limitada por los paralelos 14 º 49 ' N y 39 º 45 ' N, y por los meridianos 13 º 20 ' W y 31 º 17 ' W, estando separados entre sus puntos norte y sur por 2 700 km y entre sus puntos este y oeste por 1 800 km de distancia (Gosálvez et al., 2010). Sobre el origen del archipiélago y su contexto geodinámico, se han propuesto varias hipótesis, e.g.: Carracedo et al. (1998), Anguita y Hernán (2000), Ancochea et al. (2006), en las que aún no queda completamente claro el origen de la Islas Canarias, ya que algunos dan un protagonismo mayor a la actividad tectónica como causante del ascenso del magma a través de la corteza y otros defienden la existencia de un punto caliente como verdadera causa del volcanismo en Canarias.

Poisson dynamic models. An application to interurban accidents in Spain

In this study we apply count data models to four integer–valued time series related to accidentality in Spanish roads applying both the frequentist and Bayesian approaches. The time series are: number of fatalities, number of fatal accidents, number of killed or seriously injured (KSI) and number of accidents with KSI. The model structure is Poisson regression with first order autoregressive errors. The purpose of the paper is first to sort out the explanatory variables by relevance and second to carry out a prediction exercise for validation.

Libro primero, de Arithmetica Algebratica, enel qual se contiene el arte Mercantiuol, con otras muchas Reglas del arte menor, y la Regla del Algebra, vulgarmente llamada Arte mayor, o Regla de la cosa ... [Texto impreso] ...]

Marca tip. en v. de port. y en v. de última h.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

An introduction to alysidal algebra (IV)

Purpose – Deontical impure systems are systems whose object set is formed by an s-impure set, whose elements are perceptuales significances (relative beings) of material and/or energetic objects (absolute beings) and whose relational set is freeways of relations, formed by sheaves of relations going in two-way directions and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty. The paper aims to discuss these issues. Design/methodology/approach – Mathematical and logical development of human society ethical and normative structure. Findings – Existence of relations with positive imperative modality (obligation) would constitute the skeleton of the system. Negative imperative modality (prohibition) would be the immunological system of protection of the system. Modality permission the muscular system, that gives the necessary flexibility. Four theorems have been formulated based on Gödel's theorem demonstrating the inconsistency or incompleteness of DISs. For each constructed systemic conception can happen to it one of the two following things: either some allowed responses are not produced or else some forbidden responses are produced. Responses prohibited by the system are defined as nonwished effects. Originality/value – This paper is a continuation of the four previous papers and is developed the theory of deontical impure systems.

An introduction to alysidal algebra (V): phenomenological components

Purpose – This paper aims to refer to a subjective approach to a type of complex system: human ecosystems, referred to as deontical impure systems (DIS) to capture a set of properties fundamental to the distinction between human and natural ecosystems. There are four main phenomenological components: directionality, intensity, connection energy and volume. The paper establishes thermodynamics of deontical systems based on the Law of Zipf and the temperature of information. Design/methodology/approach – Mathematical and logical development of human society structure. Findings – A fundamental question in this approach to DIS is the intensity or forces of a relation. Concepts are introduced as the system volume and propose a system thermodynamic theory. It hints at the possibility of adapting the fractal theory by introducing the fractal dimension of the system. Originality/value – This paper is a continuation of other previous papers and developing the theory of DIS.

Un receuil: containing painting, penmanship, algebra and pieces selected from various authors in prose and verse, with a few pieces in French with their translation / by Phebe Folger of Nantucket : manuscript, 1797-1806

Written mostly in a copperplate hand in black ink, and illustrated with watercolor drawings.

Algebra, or universal mathematics: revived 1738 with notes and additions : manuscript, [after 1738]

Instructional book in algebra with exercises.

Leibniz e o hermetismo: a sua ligação com Cudworth

O presente artigo visa demonstrar que o hermetismo foi uma corrente de pensamento presente (e influente) na modernidade seiscentista apresentando interpretações desta época em que tal tese é relevante, nomeadamente Frances Yates e Paolo Rossi. Este tema é desenvolvido a partir de um autor – Leibniz – do qual se destacam as ligações com o hermetismo, apresentando-se o seu diferendo com Ralph Cudworth, a propósito do tema das naturezas plásticas.

Moi et temps chez Leibniz: ou l’unité de la notio completa et de la vis primitiva

La fusion entre la logique et la dynamique déclenche chez G. W. Leibniz une réforme de la notion de substance qui altère profondément le rapport entre le Je et le temps. Prototype de la substantialité, miroir de Dieu et expression du Tout créé, le Je dirait beaucoup, notamment Être, Un, Même: la persistance d’un « sujet » logique, d’un « je ne sais quoi » de métaphysique et d’un « personnage » moral. Sous l’angle de la temporalité, le Je véhicule tous les temps possibles et réels, passés et futurs. Il est question donc d’une communauté poly- et pan-chronique qui propose une sorte de synchronie de la diversité temporelle dans la notion complète et dans la force primitive qui semblent ainsi s’incliner vers ou se déplier de l’Eternel.