A new horizon for online teaching and learning

The Polytechnic Institute of Oporto (IPP), which has a solid history of online education and innovation through the use of technology, has been particularly interested and focused on Massive Open Online Courses (MOOC) developments. The aim of this paper is to present the whole process from initial discussions to completion of the “Mathematics Without Limits” MOOC Project that exists in IPP and also to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays. In 2013, IPP developed its own platform, which gave us the opportunity to explore new educational techniques as a pedagogical resource as well as to enhance students’ motivation, through a set of interactive materials at their disposal, totally adapted to their needs. Students lack of motivation is mainly justified by their weak Math preparation, poor consolidated basis on the subject and different backgrounds of the students. To tackle this issue and based on our Math online courses teaching experience, we decided to create short duration MOOC, expecting to aid retention of students and also to reverse the path of students giving up on Math by giving them a friendly way of managing their own learning commitment. We also think that this MOOC will be a good approach to level out some math skills among freshmen.

A new horizon for online teaching and learning

The Polytechnic Institute of Oporto (IPP), which has a solid history of online education and innovation through the use of technology, has been particularly interested and focused on Massive Open Online Courses (MOOC) developments. The aim of this paper is to present the whole process from initial discussions to completion of the “Mathematics Without Limits” MOOC Project that exists in IPP and also to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays. In 2013, IPP developed its own platform, which gave us the opportunity to explore new educational techniques as a pedagogical resource as well as to enhance students’ motivation, through a set of interactive materials at their disposal, totally adapted to their needs. Students lack of motivation is mainly justified by their weak Math preparation, poor consolidated basis on the subject and different backgrounds of the students. To tackle this issue and based on our Math online courses teaching experience, we decided to create short duration MOOC, expecting to aid retention of students and also to reverse the path of students giving up on Math by giving them a friendly way of managing their own learning commitment. We also think that this MOOC will be a good approach to level out some math skills among freshmen.

A New horizon for online teaching and learning

The Polytechnic Institute of Oporto (IPP), which has a solid history of online education and innovation through the use of technology, has been particularly interested and focused on Massive Open Online Courses (MOOC) developments. The aim of this paper is to present the whole process from initial discussions to completion of the “Mathematics Without Limits” MOOC Project that exists in IPP and also to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays. In 2013, IPP developed its own platform, which gave us the opportunity to explore new educational techniques as a pedagogical resource as well as to enhance students’ motivation, through a set of interactive materials at their disposal, totally adapted to their needs. Students lack of motivation is mainly justified by their weak Math preparation, poor consolidated basis on the subject and different backgrounds of the students. To tackle this issue and based on our Math online courses teaching experience, we decided to create short duration MOOC, expecting to aid retention of students and also to reverse the path of students giving up on Math by giving them a friendly way of managing their own learning commitment. We also think that this MOOC will be a good approach to level out some math skills among freshmen.

Dynamic programming for a Markov-switching jump–diffusion

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

Modelos de previsão de produção para centrais mini-hídricas

O constante crescimento dos produtores em regime especial aliado à descentralização dos pontos injetores na rede, tem permitido uma redução da importação de energia mas também tem acarretado maiores problemas para a gestão da rede. Estes problemas estão relacionados com o facto da produção estar dependente das condições climatéricas, como é o caso dos produtores eólicos, hídricos e solares. A previsão da energia produzida em função da previsão das condições climatéricas tem sido alvo de atenção por parte da comunidade empresarial do setor, pelo facto de existir modelos razoáveis para a previsão das condições climatéricas a curto prazo, e até a longo prazo. Este trabalho trata, em concreto, do problema da previsão de produção em centrais mini-hídricas, apresentando duas propostas para essa previsão. Em ambas as propostas efetua-se inicialmente a previsão do caudal que chega à central, sendo esta depois convertida em potência que é injetada na rede. Para a previsão do caudal utilizaram-se dois métodos estatísticos: o método Holt-Winters e os modelos ARMAX. Os dois modelos de previsão propostos consideram um horizonte temporal de uma semana, com discretização horária, para uma central no norte de Portugal, designadamente a central de Penide. O trabalho também contempla um pequeno estudo da bibliografia existente tanto para a previsão da produção como de afluências de centrais hidroelétricas. Aborda, ainda, conceitos relacionados com as mini-hídricas e apresenta uma caraterização do parque de centrais mini-hídricas em Portugal.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Measures in Sectorization Problems

Sectorization means dividing a whole into parts (sectors), a procedure that occurs in many contexts and applications, usually to achieve some goal or to facilitate an activity. The objective may be a better organization or simplification of a large problem into smaller sub-problems. Examples of applications are political districting and sales territory division. When designing/comparing sectors some characteristics such as contiguity, equilibrium and compactness are usually considered. This paper presents and describes new generic measures and proposes a new measure, desirability, connected with the idea of preference.

Spectral and homogenization problems

Dissertation for the Degree of Doctor of Philosophy in Mathematics

Health problems awareness during travel among faculty members of a large university in Latin America: preliminary report

Health safety during trips is based on previous counseling, vaccination and prevention of infections, previous diseases or specific problems related to the destination. Our aim was to assess two aspects, incidence of health problems related to travel and the traveler's awareness of health safety. To this end we phone-interviewed faculty members of a large public University, randomly selected from humanities, engineering and health schools. Out of 520 attempts, we were able to contact 67 (12.9%) and 46 (68.6%) agreed to participate in the study. There was a large male proportion (37/44, 84.1%), mature adults mostly in their forties and fifties (32/44, 72.7%), all of them with higher education, as you would expect of faculty members. Most described themselves as being sedentary or as taking occasional exercise, with only 15.9% (7/44) taking regular exercise. Preexisting diseases were reported by 15 travelers. Most trips lasted usually one week or less. Duration of the travel was related to the destination, with (12h) or longer trips being taken by 68.2% (30/44) of travelers, and the others taking shorter (3h) domestic trips. Most travelling was made by air (41/44) and only 31.8% (14/44) of the trips were motivated by leisure. Field research trips were not reported. Specific health counseling previous to travel was reported only by two (4.5%). Twenty seven of them (61.4%) reported updated immunization, but 11/30 reported unchecked immunizations. 30% (9/30) reported travel without any health insurance coverage. As a whole group, 6 (13.6%) travelers reported at least one health problem attributed to the trip. All of them were males travelling abroad. Five presented respiratory infections, such as influenza and common cold, one neurological, one orthopedic, one social and one hypertension. There were no gender differences regarding age groups, destination, type of transport, previous health counseling, leisure travel motivation or pre-existing diseases. Interestingly, the two cases of previous health counseling were made by domestic travelers. Our data clearly shows that despite a significant number of travel related health problems, these highly educated faculty members, had a low awareness of those risks, and a significant number of travels are made without prior counseling or health insurance. A counseling program conducted by a tourism and health professional must be implemented for faculty members in order to increase the awareness of travel related health problems.

Heuristics and policies for online pickup and delivery problems

Master Thesis