ISCAP - ATC de Matemática
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- 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.
- Os algoritmos, o PASCAL e a matemáticaPublication . Duarte, Manuel Pedro de AlmeidaOs algoritmos, o PASCAL e a matemática
- Assessment experiences in a math coursePublication . Soares, Filomena Baptista; Nunes, Paula; Lopes, Ana PaulaThe role of a teacher, as knowledge promoter and learning facilitator, is frequently opposed to the simultaneously inherent “validation” tasks, as far as grading and assessing are concerned, fundamentally from the students’ point of view, but, sometimes, even from our own. The generalised Math “trauma” is a difficult start-up invisible barrier that we must overcome every single semester, by implementing different strategies, developing new materials, motivating with digital and technological resources (using students’ digital skills), among many other tactics and schemes. But, in the end, the numerical grade – the knowledge and skills construction validation – must appear posted in the “system”. As Math lecturers in a Higher Education Institution, for more than twenty years, these problems are a daily challenge we face, and the issues we intend to analyse here, emerge as a consequence of a certain "emptiness" we feel regarding the assessment we have to carry out, in the sense that we still don’t have an answer to the following question: “Is it legitimate to "close your eyes" to the basic errors (some severe) when assessing learning outcomes in advanced subjects?” We teach at "end of the line", as far as General Mathematics is concerned, since our students are, essentially, from Management and Accounting Bachelor degrees. This paper will be structured in four distinct parts, starting with the Specific and General Outcomes and skills in the Math course in question, giving also a global vision of all its syllabus components and the teaching Methodologies implemented. Subsequently, we will refer to the coherence between teaching methods and the course learning objectives as well as their connection to the syllabus items. Finally, we will go through a section of small questions and answers, with their respective detailed analysis, in order to provide an objective reading material, trying to promote a fruitful and open discussion on the subject
- Asymmetric wealth effect between US stock markets and US housing market and european stock markets: evidences from TAR and MTARPublication . Coelho, Pedro; Gomes, Luís; Ramos, PatríciaEvidence of the asymmetric wealth effect has important implications for investors and continues to merit research attention, not least because much of the evidence based on linear models has been refuted. Indeed, stock and house prices are influenced by economic activity and react nonlinearly to positive/negative shocks. This problem justifies our research. The objective of this study is to examine evidence of cointegrations between the US housing and stock markets and between the US and European stock markets, given the international relevance of these exchanges. Using data from 1989:Q1 to 2020:Q2, the Threshold Autoregression model as well as the Momentum Threshold Autoregression model were calculated by combining the US Freddie, DJIA, and SPX indices and the European STOXX and FTSE indices. The results suggest a long-term equilibrium relationship with asymmetric adjustments between the housing market and the US stock markets, as well as between the DJIA, SPX, and FTSE indices. Moreover, the wealth effect is stronger when stock prices outperform house prices above an estimated threshold. This empirical evidence is useful to portfolio managers in their search for non-perfectly related markets that allow investment diversification and control risk exposure across different assets.
- Behind video lectures in a MOOCPublication . Soares, Filomena Baptista; Lopes, Ana Paula; Vieira, IsabelThe year 2012 was the “boom year” in MOOC and all its outstanding growth until now, made us move forward in designing the first MOOC in our Institution (and the third in our country, Portugal). Most MOOC are video lectured based and the learning analytic process to these ones is just taking its first steps. Designing a video-lecture seems, at a first glance, very easy: one can just record a live lesson or lecture and turn it, directly, into a video-lecture (even here one may experience some “sound” and “camera” problems); but developing some engaging, appealing video-lecture, that motivates students to embrace knowledge and that really contributes to the teaching/learning process, it is not an easy task. Therefore questions like: “What kind of information can induce knowledge construction, in a video-lecture?”, “How can a professor interact in a video-lecture when he is not really there?”, “What are the video-lectures attributes that contribute the most to viewer’s engagement?”, “What seems to be the maximum “time-resistance” of a viewer?”, and many others, raised in our minds when designing video-lectures to a Mathematics MOOC from the scratch. We believe this technological resource can be a powerful tool to enhance students' learning process. Students that were born in digital/image era, respond and react slightly different to outside stimulus, than their teachers/professors ever did or do. In this article we will describe just how we have tried to overcome some of the difficulties and challenges we tackled when producing our own video-math-lectures and in what way, we feel, videos can contribute to the teaching and learning process at higher education level.
- Birth rate in PortugalPublication . Guerra, Maria; Pessoa, Ana; Rodrigues, Ana; Mesquita, Maria; Babo, Lurdes; Vieira, Isabel; Lopes, Isabel Cristina; Torres, CristinaThis paper presents a study on the birth rate in Portugal. The quantitative data analysis of 308 municipalities concludes that the variables “live births of mothers residing in Portugal with Portuguese and foreign nationality”, “fertility rate of the various age groups”, “live births of mothers residing in Portugal according to their level of education” and “births by gender” are strongly correlated, presenting common factors that significantly influence the birth rate.
- Blendeed learning & MOOCPublication . Soares, Filomena Baptista; Lopes, Ana PaulaThe word MOOC (Massive Open Online Courses) has its origins in an experience carried out by George Siemens and Stephen Downes in 2008 based on the theory of connectivism and social constructivism. This worldwide phenomenon appeared as an evolution of the Open Educational Resources (OER) movement. They are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums which have been taking the attention of many higher education institutions around the world. The purpose of this paper is to give us an overview of how MOOCs and Blended Learning can be used with as an educational strategy in a Mathematics Course of “non Mathematic” degree programs. The pedagogical strategy embraced in this venture, was to combine the potentialities of some, already available, “good” OER, with a blended working scheme established side by side with the course development, regarding fundamental issues considered as prerequisites to it. We will explain the specific contents involved, as well as the general and specific objectives and outcomes, the evaluation procedures established for the course support and development, finishing with a summary of the complete results. We did not want to discover the “wheel”, it is from common knowledge for decades, but to present alternative ways to make a good use of it.
- Comparing the performance of geostatistical models with additional information from covariates for sewage plume characterizationPublication . Monego, Maurici; Ribeiro, Paulo Justiniano; Ramos, PatriciaIn this work, kriging with covariates is used to model and map the spatial distribution of salinity measurements gathered by an autonomous underwater vehicle in a sea outfall monitoring campaign aiming to distinguish the effluent plume from the receiving waters and characterize its spatial variability in the vicinity of the discharge. Four different geostatistical linear models for salinity were assumed, where the distance to diffuser, the west-east positioning, and the south-north positioning were used as covariates. Sample variograms were fitted by the Mat`ern models using weighted least squares and maximum likelihood estimation methods as a way to detect eventual discrepancies. Typically, the maximum likelihood method estimated very low ranges which have limited the kriging process. So, at least for these data sets, weighted least squares showed to be the most appropriate estimation method for variogram fitting. The kriged maps show clearly the spatial variation of salinity, and it is possible to identify the effluent plume in the area studied. The results obtained show some guidelines for sewage monitoring if a geostatistical analysis of the data is in mind. It is important to treat properly the existence of anomalous values and to adopt a sampling strategy that includes transects parallel and perpendicular to the effluent dispersion.
- Cutting path as a rural postman problemPublication . Rodrigues, Ana Maria; Soeiro Ferreira, JoséThe Rural Postman Problem (RPP) is a particular Arc Routing Problem (ARP) which consists of determining a minimum cost circuit on a graph so that a given subset of required edges is traversed. The RPP is an NP-hard problem with significant real-life applications. This paper introduces an original approach based on Memetic Algorithms - the MARP algorithm - to solve the RPP and, also deals with an interesting Industrial Application, which focuses on the path optimization for component cutting operations. Memetic Algorithms are a class of Metaheuristics which may be seen as a population strategy that involves cooperation and competition processes between population elements and integrates “social knowledge”, using a local search procedure. The MARP algorithm is tested with different groups of instances and the results are compared with those gathered from other publications. MARP is also used in the context of various real-life applications.
- Data analysis and learning analytics for measure effects of gamification in a math online projectPublication . Lopes, Ana Paula; babo, lurdes; Azevedo, Jose Manuel; Torres, CristinaNowadays the use of the information and communication technologies (ICT) is more and more common in the learning and teaching process. Modern forms of education have risen and these require the implementation of new learning paradigms: situated cognition, student-centred learning, distributed cognition, constructivism, and communities of practice, among others. However there is an important problem that concerns educators, the lack of student motivation and engagement in education, especially in the e-learning environment (Online Education, Online Courses), where the motivation and the active role of students are definitely the key. Therefore, the interest of researchers in the subject of gamification, which main pillars are motivation, progressiveness and instant feedback, has increased. Furthermore, influence of gamification, depending on utilized components (challenge, curiosity, competion, recognition, etc) may have different effects on students. Thus, there is a need of deeper understanding of dependencies between engagement and implemented gamification elements. The goal of such analysis could be personalization of an e-learning system based on a model that enables management of gamification process individually for every student. The purpose of this paper is to investigate how gamification affects a Mathematics Online Course that is using this model as a pedagogical strategy. It relates such strategy with active learning practices and discusses its effectiveness, investigating how gamification can motivate students to participate more deeply and even to change their self-concept as learners. Moreover, the learning analytics and data analysis shows that implementation of the gamification components contributes to the engagement of students in an e-learning environment, having a positive impact on the final grade.