La enseñanza y aprendizaje del análisis matemático haciendo uso de CAS (computer algebra system).

Se presentan dos investigaciones sobre la enseñanza y el aprendizaje de la integral definida y la integral impropia. Se destacan los aspectos relacionados con el uso de los CAS (Computer Algebra System) Derive y Maple. Se hace incapié en el papel que ha jugado cada uno de ellos en la investigación.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Some experiments with high order compact methods using a computer algebra software - Part I

We consider a procedure for obtaining a compact fourth order method to the steady 2D Navier-Stokes equations in the streamfunction formulation using the computer algebra system Maple. The resulting code is short and from it we obtain the Fortran program for the method. To test the procedure we have solved many cavity-type problems which include one with an analytical solution and the results are compared with results obtained by second order central differences to moderate Reynolds numbers. (c) 2005 Elsevier B.V. All rights reserved.

Some experiments with high order compact methods using a computer algebra software - Part II (non-uniform grid)

We generalize a procedure proposed by Mancera and Hunt [P.F.A. Mancera, R. Hunt, Some experiments with high order compact methods using a computer algebra software-Part 1, Appl. Math. Comput., in press, doi: 10.1016/j.amc.2005.05.015] for obtaining a compact fourth-order method to the steady 2D Navier-Stokes equations in the streamfunction formulation-vorticity using the computer algebra system Maple, which includes conformal mappings and non-uniform grids. To analyse the procedure we have solved a constricted stepped channel problem, where a fine grid is placed near the re-entrant corner by transformation of the independent variables. (c) 2006 Elsevier B.V. All rights reserved.

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

Computer algebra for x-ray spectral reconstruction between 6 and 25 MV

A previously presented algorithm for the reconstruction of bremsstrahlung spectra from transmission data has been implemented into MATHEMATICA. Spectra vectorial algebra has been used to solve the matrix system A * F = T. The new implementation has been tested by reconstructing photon spectra from transmission data acquired in narrow beam conditions, for nominal energies of 6, 15, and 25 MV. The results were in excellent agreement with the original calculations. Our implementation has the advantage to be based on a well-tested mathematical kernel. Furthermore it offers a comfortable user interface.

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Inductive Theorem Proving and Computer Algebra in the Mathweb Software Bus

Reasoning systems have reached a high degree of maturity in the last decade. However, even the most successful systems are usually not general purpose problem solvers but are typically specialised on problems in a certain domain. The MathWeb SOftware Bus (Mathweb-SB) is a system for combining reasoning specialists via a common osftware bus. We described the integration of the lambda-clam systems, a reasoning specialist for proofs by induction, into the MathWeb-SB. Due to this integration, lambda-clam now offers its theorem proving expertise to other systems in the MathWeb-SB. On the other hand, lambda-clam can use the services of any reasoning specialist already integrated. We focus on the latter and describe first experimnents on proving theorems by induction using the computational power of the MAPLE system within lambda-clam.

The Learning Affect Monitor (LAM) - A computer-based system integrating quantitative and qualitative assessment of affective states in daily life.

The Learning Affect Monitor (LAM) is a new computer-based assessment system integrating basic dimensional evaluation and discrete description of affective states in daily life, based on an autonomous adapting system. Subjects evaluate their affective states according to a tridimensional space (valence and activation circumplex as well as global intensity) and then qualify it using up to 30 adjective descriptors chosen from a list. The system gradually adapts to the user, enabling the affect descriptors it presents to be increasingly relevant. An initial study with 51 subjects, using a 1 week time-sampling with 8 to 10 randomized signals per day, produced n = 2,813 records with good reliability measures (e.g., response rate of 88.8%, mean split-half reliability of .86), user acceptance, and usability. Multilevel analyses show circadian and hebdomadal patterns, and significant individual and situational variance components of the basic dimension evaluations. Validity analyses indicate sound assignment of qualitative affect descriptors in the bidimensional semantic space according to the circumplex model of basic affect dimensions. The LAM assessment module can be implemented on different platforms (palm, desk, mobile phone) and provides very rapid and meaningful data collection, preserving complex and interindividually comparable information in the domain of emotion and well-being.

Computer-aided system for morphometric mandibular index computation (Using dental panoramic radiographs)

Objective: We propose and validate a computer aided system to measure three different mandibular indexes: cortical width, panoramic mandibular index and, mandibular alveolar bone resorption index. Study Design: Repeatability and reproducibility of the measurements are analyzed and compared to the manual estimation of the same indexes. Results: The proposed computerized system exhibits superior repeatability and reproducibility rates compared to standard manual methods. Moreover, the time required to perform the measurements using the proposed method is negligible compared to perform the measurements manually. Conclusions: We have proposed a very user friendly computerized method to measure three different morphometric mandibular indexes. From the results we can conclude that the system provides a practical manner to perform these measurements. It does not require an expert examiner and does not take more than 16 seconds per analysis. Thus, it may be suitable to diagnose osteoporosis using dental panoramic radiographs.

Computer-aided system for morphometric mandibular index computation (Using dental panoramic radiographs)

Objective: We propose and validate a computer aided system to measure three different mandibular indexes: cortical width, panoramic mandibular index and, mandibular alveolar bone resorption index. Study Design: Repeatability and reproducibility of the measurements are analyzed and compared to the manual estimation of the same indexes. Results: The proposed computerized system exhibits superior repeatability and reproducibility rates compared to standard manual methods. Moreover, the time required to perform the measurements using the proposed method is negligible compared to perform the measurements manually. Conclusions: We have proposed a very user friendly computerized method to measure three different morphometric mandibular indexes. From the results we can conclude that the system provides a practical manner to perform these measurements. It does not require an expert examiner and does not take more than 16 seconds per analysis. Thus, it may be suitable to diagnose osteoporosis using dental panoramic radiographs

Validation of a computer-assisted system on classifying lower third molars

Objectives: The present study evaluates the reliability of the Radio Memory® software (Radio Memory; Belo Horizonte,Brasil.) on classifying lower third molars, analyzing intra- and interexaminer agreement of the results. Study Design: An observational, descriptive study of 280 lower third molars was made. The corresponding orthopantomographs were analyzed by two examiners using the Radio Memory® software. The exam was repeated 30 days after the first observation by each examiner. Both intra- and interexaminer agreement were determined using the SPSS v 12.0 software package for Windows (SPSS; Chicago, USA). Results: Intra- and interexaminer agreement was shown for both the Pell & Gregory and the Winter classifications, p<0.01, with 99% significant correlation between variables in all the cases. Conclusions: The use of Radio Memory® software for the classification of lower third molars is shown to be a valid alternative to the conventional method (direct evaluation on the orthopantomograph), for both clinical and investigational applications.

Implementation of hospital-wide computer information system :a case study of this change process

This case study examines the impact of a computer information system as it was being implemented in one Ontario hospital. The attitudes of a cross section of the hospital staff acted as a barometer to measure their perceptions of the implementation process. With The Mississauga Hospital in the early stages of an extensive computer implementation project, the opportunity existed to identify staff attitudes about the computer system, overall knowledge and compare the findings with the literature. The goal of the study was to develop a greater base about the affective domain in the relationship between people and the computer system. Eight exploratory questions shaped the focus of the investigation. Data were collected from three sources: a survey questionnaire, focused interviews, and internal hospital documents. Both quantitative and qualitative data were analyzed. Instrumentation in the study consisted of a survey distributed at two points in time to randomly selected hospital employees who represented all staff levels.Other sources of data included hospital documents, and twenty-five focused interviews with staff who replied to both surveys. Leavitt's socio-technical system, with its four subsystems: task, structure, technology, and people was used to classify staff responses to the research questions. The study findings revealed that the majority of respondents felt positive about using the computer as part of their jobs. No apparent correlations were found between sex, age, or staff group and feelings about using the computer. Differences in attitudes, and attitude changes were found in potential relationship to the element of time. Another difference was found in staff group and perception of being involved in the decision making process. These findings and other evidence about the role of change agents in this change process help to emphasize that planning change is one thing, managing the transition is another.

An introduction to ordinary differential equations by computer algebra-systems

We report on an elementary course in ordinary differential equations (odes) for students in engineering sciences. The course is also intended to become a self-study package for odes and is is based on several interactive computer lessons using REDUCE and MATHEMATICA . The aim of the course is not to do Computer Algebra (CA) by example or to use it for doing classroom examples. The aim ist to teach and to learn mathematics by using CA-systems.