A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

Perceptions of Usability and Usefulness in Digital Libraries

This paper provides an overview of a case study research that investigated the use of Digital Library (DL) resources in two undergraduate classes and explored faculty and students’ perceptions of educational digital libraries. This study found that students and faculty use academic DLs primarily for textual resources, but turn to the open Web for visual and multimedia resources. The study participants did not perceive academic libraries as a useful source of digital images and used search engines when searching for visual resources. The limited use of digital library resources for teaching and learning is associated with perceptions of usefulness and ease of use, especially if considered in a broader information landscape, in conjunction with other library information systems, and in the context of Web resources. The limited use of digital libraries is related to the following perceptions: 1) Library systems are not viewed as user-friendly, which in turn discourages potential users from trying DLs provided by academic libraries; 2) Academic libraries are perceived as places of primarily textual resources; perceptions of usefulness, especially in regard to relevance of content, coverage, and currency, seem to have a negative effect on user intention to use DLs, especially when searching for visual materials.

Synchronous collaboration of virtual and remote laboratories

Virtual and remote laboratories(VRLs) are e-learning resources which enhance the accessibility of experimental setups providing a distance teaching framework which meets the student's hands-on learning needs. In addition, online collaborative communication represents a practical and a constructivist method to transmit the knowledge and experience from the teacher to students, overcoming physical distance and isolation. Thus, the integration of learning environments in the form of VRLs inside collaborative learning spaces is strongly desired. Considering these facts, the authors of this document present an original approach which enables user to share practical experiences while they work collaboratively through the Internet. This practical experimentation is based on VRLs, which have been integrated inside a synchronous collaborative e-learning framework. This article describes the main features of this system and its successful application for science and engineering subjects.

Awareness of L1 and L2 word-formation mechanisms for the development of a more autonomous L2 learner

Unlike traditional approaches, new communicative trends disregard the role of word-formation mechanisms. They tend to focus on syntax and/or vocabulary without analyzing the mechanisms involved in the creation of lexical items. In this paper, based on the analysis of the use of prefixes by L2 learners in oral and written productions, as provided by the SULEC, we emphasize the advantages that word-formation awareness and knowledge may have for the learners in terms of production, creativity, understanding, autonomy, and proficiency. Through the teaching of word-formation learners may more easily decipher, decode and/or encode messages, create words they have never seen before, etc.

Innovation in the teaching of sustainable development in Europe: the case of ISLE Erasmus Network

Sustainable Development (SD) is one of the most widely used terms during the last years. It is a multidisciplinary concept, which applies mostly to life sciences but is not limited to them. Even though the short survey conducted by the authors revealed that there are only a few cases of Higher Educational Institutes (HEIs) around Europe that provide programs dedicated to SD, it is obvious that there is a constant raise in the need for implementing courses related to SD in existing programs. This paper discusses the case study of I.S.L.E., an Erasmus Academic Network, which aims to use the existing knowledge and tools in the context of teaching sustainable development topics in Universities and HEIs around Europe as a basis, and elaborate further by introducing an innovative approach towards the improvement of teaching SD in HEIs, based on the current needs as they are identified by the actions of the Network.

Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

Accurate integration of forced and damped oscillators

The new methods accurately integrate forced and damped oscillators. A family of analytical functions is introduced known as T-functions which are dependent on three parameters. The solution is expressed as a series of T-functions calculating their coefficients by means of recurrences which involve the perturbation function. In the T-functions series method the perturbation parameter is the factor in the local truncation error. Furthermore, this method is zero-stable and convergent. An application of this method is exposed to resolve a physic IVP, modeled by means of forced and damped oscillators. The good behavior and precision of the methods, is evidenced by contrasting the results with other-reputed algorithms implemented in MAPLE.

An Hebrew grammar, collected chiefly from those of Mr. Israel Lyons, teacher of Hebrew in the University of Cambridge; and the Rev. Richard Grey, D.D. rector of Hinton, in Northamptonshire: To which is subjoined a praxis, taken from the sacred classics, and containing a specimen of the whole Hebrew language: with a sketch of the Hebrew poetry

as retrieved by Bishop Hare ...

Student lecture notes on the Theory & Practice of Physic, and patient case histories, of Lyman Spalding, 1795-1799 (inclusive)

Contains notes taken by Harvard student Lyman Spalding from lectures delivered by Hersey Professor of the Theory and Practice of Physic Benjamin Waterhouse (1754-1846) in 1795. The notes cover the history of medicine, theories of contemporary physicians like Herman Boerhaave, William Cullen, and John Brown, and topics like fetal growth, digestion, and circulation. The volume also contains six pages of patient case notes from Spalding’s medical practice in Walpole, New Hampshire, in 1799, which detail the patients’ symptoms and course of treatment he pursued. In the case of a young man who complained of pain in his breast following a wrestling match, Spalding bled him and prescribed a cathartic of soap and aloes. Spalding also operated on a man who cut off part of his ankle with an ax.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

Brazilian Portuguese idiom list, selected on the basis of range and frequency of occurrence;

"Issued under the auspices of the Committee on Foreign Language Teaching of the American Council on Education in conjunction with the Institute for Brazilian Studies in Vanderbilt University."

The training of teachers and methods of instruction : selected papers /

Selected from "three small volumes of essays and addresses on educational topics" published by the author during the last twenty years. "Two papers, one on Universities and the other on History in the school, have not before been published in book-form."

...The principles and practice of early and infant school-education, with an appendix of infant-school hymns and songs with appropriate melodies.

Music : p. 285-310.