Localització òptima i planificació docent per a una acadèmia de matemàtiques a Barcelona

Abstract

The motivation for this work comes from looking for the best place to locate a Mathematics Academy for university students in Barcelona. Each of the degrees in every faculty has a mark scale which is based on certain parameters. The following parameters are taken from the net: - The number of academies which offer courses for the degree. - The number of mathematics subjects of the degree. - Average number of students enrolled for each subject. - Average number of students who fail each subject. It would be necessary to carry out many surveys of the students to obtain the following pa- rameters: - Average number of times the students need to do the subject to pass. - Average number of students who go to academies. - Degree of knowledge of the existence of other academies. - Degree of need for an mathematics academy. To avoid carrying out such an extensive number of studies, Bayesian Statistics are used to estimate the parameters properly. Bayesian methods make it possible to incorporate scientific hypothesis in the analysis(by means of prior distribution). Statistical inference about a quantity of interest is described as the modification of the uncertainty about its value in the light of evidence, and Bayes’ theorem precisely specifies how this modification should be made. Using the degree’s mark scheme and the distance between the center’s location and each place in Barcelona, a grade or mark is assigned to each location. It is done by several mathematical models which use geographical and cartesian coordinates. In models in cartesian coordinates Newton’s method is used to determine a suitable location for the academy. The work includes a didactic programming of a subject from the degree which gets the most marks. It shows how the academy will help the students to understand the subject and to become great at studying maths.