Module page
Fondamenti della ProbabilitÃ
| academic year: | 2013/2014 |
| instructor: | Mario Barra |
| degree course: | Mathematics (magistrale), II year |
| type of training activity: | caratterizzante |
| credits: | 6 (48 class hours) |
| scientific sector: | MAT/04 Matematiche complementari |
| teaching language: | italiano |
| period: | I sem (30/09/2013 - 17/01/2014) |
Lecture meeting time and location
Presence: highly recommended
Module subject: Epistemological, pedagogical and didactical aspects of the teaching of probability calculus. Connections between the probability calculus and other fields of the mathematics and sciences. "Generalized arithmetical triangles". Hyper-tetrahedrons and hyper-cubes and their sections in order to determine in more ways the distributions of the sums of uniforms aleatory numbers identically distributed in the discreet one and the continuous space, box-spline, Cox-De Boor's algorithm. The problem of the "division of a stake". 500 years of deepenings on the methods of evaluation of the probability. Bayesian statistics. Approximation of a density, mixtures of distributions. Use of the Beta distributions, excengebility, stable distributions. The " reversal of the Law of Large the Numbers". Convergence in distribution. Characterizing properties the Normal distribution. Theorem of the central limit through the characterizing properties the normal distribution. Introduction of the probability in the school, comparison with the ministerial programs. Didactic experimentations and aspects connected us with the dealt arguments. Montecarlo's Methods: " the game of the growth".
Suggested reading:
Castelnuovo E, Barra M., 2000 (1976). Matematica nella realtà, Boringhieri, Torino.
They will come distributed some lecture notes and bibliographical indications of some articles.
Type of course: standard
Knowledge and understanding: successful students will be able to deal with arguments concerning the teaching of the Probability Calculus, having caught up a good familiarity with fundamental aspects, as the connection between the various fields of the mathematics, between the various dimensions of the space and between discreet and the continuous space and will be able to use a dynamic geometry software.
Skills and attributes: successful students will be able to prepare lessons to teach Probability Calculus holding present some solutions to several didactic problems and taking advantage themselves also of dynamic geometry software.
Personal study: the percentage of personal study required by this course is the 65% of the total.