# Fiches de cours

## Probability and statistics for materials science

#### Enseignant(s) :

Moll Philip Johannes Walter

English

#### Summary

The students understand elementary concepts of statistical methods, including standard statistical tests, regression analysis and experimental design. They apply computational statistical methods to analyse larger data sets.

#### Content

• Basic statistics and probability theory. Introduce concepts of uncertainty, random variables, probability distributions and apply them to examples from materials science.
• Statistical testing of hypothesis. Formulate hypothesis and test them on data sets in the presence of statistical uncertainty. Identify in real-life problems which methods to apply.
• Assess the limitations of statistics. Develop the skill to interpret a given statistical analysis, and critically assess the validity of its conclusion.
• Computational analysis in R. Introduction into the basic aspects of the statistical programming language R. Construct hypotheses and perform associated statistical tests on large sets of data.

#### Keywords

Statistics, Probability, big data, experimental design, R

#### Learning Prerequisites

##### Important concepts to start the course

• Basic concepts of programming
• Basic calculus and matrix calculations

#### Learning Outcomes

By the end of the course, the student must be able to:
• Examine the conclusions of a given statistical analysis.
• Use the method of least squares
• Define random variables, probability distributions, the central limit theorem and the law of big numbers.
• Analyze a population according to the ANOVA method.
• Perform a Student Test.
• Implement statistical methods computationally using R-code.

#### Transversal skills

• Take account of the social and human dimensions of the engineering profession.
• Access and evaluate appropriate sources of information.

#### Teaching methods

Lectures combined with exercises to solve computational examples.

#### Expected student activities

Attendance of lectures and solving of exercises on the computer. A laptop computer will be required for this course.

written exam

#### Supervision

 Assistants Yes

#### Resources

No

##### Bibliography

Introduction to Statistics and Data Analysis, Christian Heumann and Michael Schomaker Shalabh, Springer

### Semaine de référence

LuMaMeJeVe
8-9
9-10MXG110
10-11
11-12MXG110
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand