Passive knowledge of English.

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With regard to the AA reference system of the Bachelor programme in mathematics, this teaching unit allows students to master: · as a priority, the following LOs: x.x, ....;
· in a secondary way the following LO: x.x, .....
With regard to the AA reference system of the Bachelor programme in physics, this teaching unit allows students to master: · as a priority, the following LOs: A1.2, A1.5, A2.3, A3.4; · in a secondary way the following LOs: A5.3, A6.5, A4.4.
¿ analyze a potentially large data set via descriptive tools using specialized software; |

*The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.*

· Structuring of statistical data and nature of the variables (discrete / continuous quantitative, nominal / ordinal quality).

· Numeric tools to summarize data by nature: frequency tables, position indices (mode, median, mean), dispersion indices (range, interquartile range, standard deviation, variance, coefficient of variation), percentiles, correlation coefficient.

· Graphical tools to summarize data: histogram, empirical distribution function, bar graph, box-plot, time graph, X-Y graph (simple or matrix), Q-Q-plot.

· Random experimentation and basic notions of probability theory: the definition of a probability and its elementary properties and the calculation of probability on events.

· Random variables (univariate) and their properties (moments, distribution ...). Introduction of the most frequently used distributions in the analysis of data encountered in applications seen in the course: uniform law, binomial, Fish and normal.

· Simple algorithms for generating random numbers according to these introduced probability laws.

· Principle of random sampling and estimation.

· Intuitive concept of sampling distribution and confidence interval.

· Application to mean (and variance) in normal distribution.

· Notions of error and measurement uncertainty.

· Quantification and expression of uncertainty on a simple or repeated measurement (including uncertainty widened by confidence interval).

· Calculation of composite uncertainties in the case of sums, products and nonlinear transformations of independent or correlated measurements. Applications to laboratory measurements in various fields (physics, biology, ...).

· Adjustment of a linear or polynomial model (simple linear regression) by least squares method.

· Initiation to a statistical programming language (for example, R). Approach through management projects and data analysis and simulations.

· lectures that will present the subject on the basis of examples,

· exercises sessions to systematically put into practice the different notions seen in the course on well-targeted cases and using specialized software,

· projects that will give the student the opportunity to integrate the different tools in fields of application of mathematics and physics.

The pedagogical approach will favor the active learning of students and will try to respect the pedagogical orientations proposed by the Faculty of Sciences.

· During the exam session: computer-based written exam.

**SC**