ISCAP - ATC de Matemática
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- Os algoritmos, o PASCAL e a matemáticaPublication . Duarte, Manuel Pedro de AlmeidaOs algoritmos, o PASCAL e a matemática
- Geostatistical Mapping of Outfall Plume Dispersion Data gathered with an autonomous underwater vehiclePublication . Ramos, Patricia; Monego, M.; Neves, M. V.The main purpose of this study was to examine the applicability of geostatistical modeling to obtain valuable information for assessing the environmental impact of sewage outfall discharges. The data set used was obtained in a monitoring campaign to S. Jacinto outfall, located off the Portuguese west coast near Aveiro region, using an AUV. The Matheron’s classical estimator was used the compute the experimental semivariogram which was fitted to three theoretical models: spherical, exponential and gaussian. The cross-validation procedure suggested the best semivariogram model and ordinary kriging was used to obtain the predictions of salinity at unknown locations. The generated map shows clearly the plume dispersion in the studied area, indicating that the effluent does not reach the near by beaches. Our study suggests that an optimal design for the AUV sampling trajectory from a geostatistical prediction point of view, can help to compute more precise predictions and hence to quantify more accurately dilution. Moreover, since accurate measurements of plume’s dilution are rare, these studies might be very helpful in the future for validation of dispersion models.
- Lanczos algorithm on the grassmann manifoldPublication . Lopes, Ana Paula
- The active mathematics project at ISCAPPublication . Azevedo, Jose Manuel; babo, lurdes; Lopes, Ana PaulaThis paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.
- O projecto matactiva no ISCAPPublication . Torres, Cristina; Lopes, Ana Paula; Azevedo, Jose Manuel; babo, lurdesA partir do ano 2007/2008 todos os cursos do ISCAP foram adequados ao Processo de Bolonha, o que pressupõe várias mudanças a nível dos papéis do professor e do aluno, das metodologias e da avaliação. A carga horária semanal das disciplinas da Matemática foi bastante reduzida, por isso foi necessário desenvolver novas estratégias e metodologias de apoio ao aluno. Para complementar as aulas teóricas e práticas desenvolvemos um projecto com o nome MatActiva baseado na plataforma Moodle, disponibilizada pelo PAOL (Projecto de Apoio On-Line). O Moodle permite usar a linguagem TEX para criar materiais que utilizam símbolos matemáticos. Fazendo uso desta funcionalidade, criámos um conjunto de recursos interactivos de fácil utilização. No MatActiva os estudantes têm acesso a um conjunto diversificado de materiais: apontamentos teóricos que lhes fornecem, não só os pré-requisitos necessários para as disciplinas de matemática, mas também material de acompanhamento aos respectivos programas. Para isso, criaram-se vários recursos sendo os testes de escolha múltipla os mais procurados pelos alunos. Estes testes podem ser realizados e corrigidos on-line e para cada resposta errada existe um feedback de resolução. Como o ISCAP recebe alunos ERASMUS e estes frequentam a disciplina de Matemática, foi também desenvolvido material em inglês. Os principais objectivos do nosso projecto são motivar os alunos, encoraja-los a superar as suas dificuldades de uma forma autónoma, permitindo-lhes aumentar a sua autoconfiança e gosto pela aprendizagem da Matemática, assim como fomentar a comunicação professor-aluno e aluno-aluno.
- Algoritmo de lanczos na variedade de grassmannPublication . Paula Lopes, Ana; Viamonte, Ana Júlia; Pascoal, António JoséO problema do cálculo de valores próprios, vectores próprios e subespaços invariantes está presente em áreas tão diversas como Engenharia, Física, Ciências de Computação e Matemática. Considerando a importância deste problema em tantas aplicações práticas, não é de surpreender que tenha sido e continue a ser objecto de intensa investigação, dando corpo a uma literatura muito vasta. Desenvolvemos um novo algoritmo de Lanczos na variedade de Grassmann. Este trabalho surgiu na sequência de um artigo de A. Edelman, T. A. Arias and S. T. Smith, The geometry of algorithms with orthogonality constraints, onde apresentam um novo algoritmo do gradiente conjugado na variedade de Grassmann. Desenvolveram um enquadramento geométrico o que ofereceu uma nova aproximação aos algoritmos numéricos envolvendo restrições de ortogonalidade. Ora, estando o método de Lanczos e o método dos gradientes conjugados intimamente relacionados, e sendo um dos principais problemas do método de Lanczos a perda de ortogonalidade, surgiu a ideia de tentar verificar se algum dos algoritmos de Lanczos seria uma iteração na variedade de Grassmann.
- How to teach mathematics with MOODLEPublication . Torres, Cristina; Azevedo, Jose Manuel; Lopes, Ana Paula; babo, lurdesThe aim of this article is to present a Project in the Oporto’s Institute of Accounting and Administration, which pretends to contribute for a change in the way of teaching and learning Mathematics. One of the main objectives of this project is to innovate the teaching and learning processes, exploring technologies as a pedagogical resource and to induce higher motivation to students, improve the rate of success and make available to students a set of materials adapted to their needs. This concern is justified due to the fact that students have a weak preparation, without consolidated basis. Since the year 2007/2008 the courses were adjusted to the Bologna process, which requires several changes in teacher’s and student’s roles, methodologies and assessment. The number of weekly classes has been reduced, so it was necessary to develop new strategies and methodologies to support the student. With the implementation of the Bologna Process in the Accounting degree, we felt a great need to provide other types of activities to students. To complement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio On-Line (Online Support Project). Moodle allows us to use the language TEX to create materials that use mathematical symbols. Using this functionality, we created a set of easy to use interactive resources. In MatActiva project, the students have access to a variety of different materials. We have followed a strategy that makes the project compatible with the theoretical and practical subjects/classes, complementing them. To do so, we created some resources, for instance multiple-choice tests, which are the most accessed by the students. These tests can be realized and corrected on-line and for each wrong answer there is a feedback with the resolution. We can find other types of resources: diagnostic tests, theoretical notes. There are not only the pre-requirements for subjects mathematics, but also materials to help students follow up the programs. We also developed several lessons. This activity consists of a number of pages, where each page has contents and leads to other pages, based on the student's progress. The teacher creates the choices and determines the next page that the student will see, based upon their knowledge. There is also an area of doubts, where the students can place all the mathematical doubts they have, and a teacher gives the answers or clues to help them in their work. MatActiva also offers an area where we can find some humour, curiosities, contests and games including mathematical contents to test the math skills, as well as links to pages about mathematical contents that could be useful for the study. Since ISCAP receives ERASMUS students and some of them attend mathematics, we developed some materials in English, so they can also use MatActiva. The main objectives of our project are not only to bring success in the subjects of mathematics, but also to motivate the students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence and improve their relationship with the mathematics as well as the communication between students and teachers and among students.
- Teaching and learning mathematics using moodlePublication . Lopes, Ana Paula; babo, lurdes; Azevedo, Jose ManuelThis paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.
- A new approach to numerical algorithmsPublication . Lopes, Ana Paula; Pascoal, António JoséIn this paper we developed a new Lanczos algorithm on the Grassmann manifold. This work comes in the wake of the article by A. Edelman, T. A. Arias and S. T. Smith, “The geometry of algorithms with orthogonality constraints”
- Matemática activa - moodlePublication . Torres, Cristina; Babo, Lurdes; Azevedo, Jose Manuel; Lopes, Ana PaulaEsta sessão prática tem como objectivo explorar algumas funcionalidades da plataforma Moodle, familiarizar os formandos com a sua utilização, mostrando as suas potencialidades na elaboração de recursos educativos e a sua aplicação no processo de ensino/aprendizagem, incentivando a produção de materiais de apoio ao ensino da Matemática. Desta forma, os formandos poderão acrescentar à sua disciplina on-line uma nova dimensão de interactividade e promover uma participação mais activa dos alunos Sugere-se que os formandos tragam alguns testes de avaliação ou fichas de trabalho que já tenham realizado, de preferência em formato digital, para que a sessão seja mais produtiva.