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The Aplusix system has been designed for helping students to learn algebra. Its capacity to tell the students whether their calculations are correct or not, to provide families of exercises of a chosen level, and to give scores after tests allows this system to be used in the regular functioning of the class. Its capacity to record the students' actions and to replay the students' work is a valuable feature for the researcher in mathematics education. In this paper, we describe four experiments conducted in four different countries with different goals: remediation piloted by researchers in Italy; remediation integrated in the regular functioning of classes in Brazil, collaborative learning in India, and learning and use during the entire school year in France. (Contains 4 tables and 5 figures.)

In this paper, we explore the problem of establishing a network among the stocks of a market at high frequency level and give an application to program trading. Our work uses high frequency data from the National Stock Exchange, India, for the year 2014. To begin, we analyse the spectrum of the correlation matrix to establish the presence of linear relations amongst the stock returns. A comparison of correlations with pairwise mutual information shows the further existence of non-linear relations which are not captured by correlation. We also see that the non-linear relations are more pronounced at the high frequency level in comparison to the daily returns used in earlier work. We provide two applications of this approach. First, we construct minimal spanning trees for the stock network based on mutual information and study their topology. The year 2014 saw the conduct of general elections in India and the data allows us to explore their impact on aspects of the network, such as the scale-free property and sectorial clusters. Second, having established the presence of non-linear relations, we would like to be able to exploit them. Previous authors have suggested that peripheral stocks in the network would make good proxies for the Markowitz portfolio but with a much smaller number of stocks. We show that peripheral stocks selected using mutual information perform significantly better than ones selected using correlation. [ABSTRACT FROM AUTHOR]

The Aplusix system has been designed for helping students to learn algebra. Its capacity to tell the students whether their calculations are correct or not, to provide families of exercises of a chosen level, and to give scores after tests allows this system to be used in the regular functioning of the class. Its capacity to record the students' actions and to replay the students' work is a valuable feature for the researcher in mathematics education. In this paper, we describe four experiments conducted in four different countries with different goals: remediation piloted by researchers in Italy; remediation integrated in the regular functioning of classes in Brazil, collaborative learning in India, and learning and use during the entire school year in France. [ABSTRACT FROM AUTHOR]