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Mathematical Foundations II: Linear Algebra and Statistics
Grundlagen der Mathematik II (Lineare Algebra und Statistik)
Last Updated: 2026-02-05 16:21:59
Abstract
Systems of linear equations; matrix algebra, determinants; vector spaces, norms and scalar products; linear maps, basis transformations; eigenvalues and eigenvectors.Random variables and probability, discrete and continuous distribution models; expectation, variance, central limit theorem, parameter estimation; statistical hypothesis tests; confidence intervals; regression analysis.
Objective
A sound knowledge of mathematics is an essential prerequisite for a quantitative and computer-based approach to natural sciences. In an intensive two-semester course the most important basic concepts of mathematics, namely univariate and multivariate calculus, linear algebra and statistics are taught.
Content
Systems of linear equations; matrix algebra, determinants; vector spaces, norms and scalar products; linear maps, basis transformations; eigenvalues and eigenvectors. - Least squares fitting and regression models; random variables, statistical properties of least-squares estimators; tests, confidence and prediction intervals in regression models; residual analysis. Lecture homepage: https://moodle-app2.let.ethz.ch/course/view.php?id=11841
Resources
Lecture Notes
For the part on Linear Algebra, there is a short script (in German) which summarizes the main concepts and results without examples. For a self-contained presentation, the book by Nipp and Stoffer should be used. For the part on Statistics there is a detailed script (in German) available which should be self-contained. The book by Stahel can be used for additional information.
Literature
Linear Algebra: K. Nipp/D. Stoffer: "Lineare Algebra", vdf, 5th edition, 2002. Statistics: W. Stahel, "Statistische Datenanalyse", Vieweg, 5rd edition, 2008.
General Information
- Language
- German
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 90 minutes
- Aids
- Beliebige schriftliche Unterlagen, PC mit Matlab
- Digital
- The exam takes place on devices provided by ETH Zurich.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Grundlagen der Mathematik II (Lineare Algebra und Statistik) |
|
2 h weekly |
| exercise |
Grundlagen der Mathematik II (Lineare Algebra und Statistik)
Groups are selected in myStudies.
Mo 16-17, Do 10-11 oder Do 11-12 gemäss Gruppeneinteilung.
|
|
1 h weekly |