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).

Cryptographic properties of Boolean functions defining elementary cellular automata

In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time.

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,

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.

A presynaptic locus for long-term potentiation of elementary synaptic transmission at mossy fiber synapses in culture.

The complex circuitry of the CA3 region and the abundance of collateral connections has made it difficult to study the mossy fiber pathway in hippocampal slices and therefore to establish the site of expression of long-term potentiation at these synapses. Using a novel cell culture system, we have produced long-term potentiation of the elementary synaptic connections on single CA3 pyramidal neurons following tetanic stimulation of individual dentate gyrus granule cells. As is the case for the hippocampal slice, this potentiation was independent of N-methyl-D-aspartate receptor activation, was simulated by application of forskolin, and its induction did not require any modulatory input. The increase in synaptic strength was accompanied by a reduction in the number of failures of transmission and by an increase in the coefficient of variation of the responses and was prevented by presynaptic injection of an inhibitor of protein kinase A. These findings show that mossy fiber long-term potentiation has a presynaptic locus and that its expression is dependent on protein kinase A.

The First Child In A Chinese Family Who Could Read Prior To Entry Into Elementary School: A Qualitative Intrinsic Case Study

ABSTRACT This study is an account of the literacy-related human environment a Chinese girl experienced as the first person in the history of her family who was able to read prior to entry into elementary school. Temporally speaking, the study spanned more than a decade from the initial, tentative research question to the formal, primary research question. Spatially speaking, it crossed three cultures: the Chinese, Korean, and American cultures. The study was inspired by the Zero Project in China, known as the "Project of Quality Education and Implementation for Children Aged Zero (fetus) to Six." The significance of the content issue in a child's literacy curriculum was explored in an interdisciplinary way. Case study served as a holistic research approach and provided the researcher with free temporal and spatial distance to pursue the indefinably multi-dimensional intricacies of a child's early literacy acquisition among generations in the family. Interpretation of the case was based on the relevant concepts within the scope of the researcher's knowledge of Chinese culture. Major findings revealed that the child's literacy acquisition was inseparably related to her parents' background as well as their awareness of and attitudes towards literacy, and that the foundation of all this was the harmony of the family. Through the lens of generational attitudes towards literacy and especially the lens of the researcher's multicultural life experiences, this study contributes to the field of curriculum studies in general and early literacy curriculum in particular by stimulating people to reconsider what to read to children, besides how to read to them. It calls attention once again to the classic curriculum question, "What knowledge is of most worth?" as well as what is the most essential spiritual food human beings need besides physical needs. This study suggests that Chinese philosophy should be included in a child's early literacy curriculum in China and calls for dialogues on the content issue of curriculum to gain a deeper understanding of human nature so that humans might co-live peacefully with all beings in the universe.

Mathematics Game e-Library for Elementary School, study case: Mexico

One of the most relevant subjects for the intellectual formation of elementary school students is Mathematics where its importance goes back to ancient civilizations and which its importance is underestimated nowadays. This phenomenon occurs in Mexico, where 63.1% of the total population of elementary school students between the third and sixth grade have insufficient/elemental level of mathematics knowledge. This has resulted in the need to use a new mechanism to complement student’s classroom learning. With the rapid growth of wireless and mobile technologies, the mobile learning has been gradually considered as a novel and effective form of learning due to it inherits all the advantages of e-learning as well as breaks the limitations of learning time and space occurring in the traditional classroom teaching. This project proposes the use of a Mathematics Game e-Library integrated by a set of games for mobile devices and a distribution/management tool. The games are developed for running on mobile devices and for cover the six competencies related with the mathematics learning approach established in Mexico. The distribution/management tool allows students to reach contents according to their needs; this is achieved through a core engine that infers, from an initial profile, the games that cover the user’s knowledge gaps.

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.