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    A new approach to numerical algorithms
    (Maltepe Üniversitesi, 2009) Lopes, Ana Paula; Jose Pascoal, Antonio
    The problem of computing eigenvalues, eigenvectors and invariant subspaces is always present in areas as diverse as Engineering, Physics, Computer Science and Mathematics. Considering the importance of these problems in many practical applications, it is not surprising that has been and continues to be the subject of intense research. 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, where they presented a new conjugate gradient algorithm on the Grassmann and Stiefel manifolds. These manifolds which are based on orthogonality constraints, yields penetrating insight into many numerical algorithms of linear algebra. They have developed an approach to numerical algorithms involving orthogonality constraints. As the Lanczos method and the method of conjugate gradients are closely related, and one of the main problems of the Lanczos method is the loss of orthogonality, arose the idea of checking whether it would be possible to get a Lanczos algorithm on the Grassmann manifold.
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    Using moodle as a tool for learning and developing math skills
    (Maltepe Üniversitesi, Lisansüstü Eğitim Enstitüsü, 2009) Lopes, Ana Paula; Babo, Lurdes; Azevedo, Jose; Torres, Cristina
    MatActiva is a Mathematics project based on the platform Moodle, which is being developed in the Institute of Accounting and Administration of Porto - ISCAP. The main objective of this project is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and making students keen on Mathematics. The adequacy of the courses to the Bologna process has created new challenges, such as the management of hours per class, and also the methods and types of activities proposed. MatActiva provides a variety of materials, which include theoretical notes, multiple choice tests that can be done online and automatically provide quantitative results and the feedback for each question when the student misses, forum of doubts moderated by the teachers that are responsible for the project, challenges, etc. As ISCAP receives many students through the ERASMUS program, the MatActiva also includes a range of materials in English. This project wishes to be a real advantage in teaching/learning of mathematics at higher education level.