Probability and statistics for materials science
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.
Assessment methods
written exam
Supervision
| Assistants | Yes |
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
Introduction to Statistics and Data Analysis, Christian Heumann and Michael Schomaker Shalabh, Springer
Ressources en bibliothèque
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Probability and statistics for materials science
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks