401-0622-00L Mathematical Foundations II: Linear Algebra and Statistics
| Semester | Spring Semester 2019 |
| Lecturers | M. Dettling |
| Periodicity | yearly recurring course |
| Language of instruction | German |
Courses
| Number | Title | Hours | Lecturers | |||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 401-0622-00 V | Grundlagen der Mathematik II (Lineare Algebra und Statistik) | 2 hrs |
| M. Dettling | ||||||||||||||||||||||||
| 401-0622-00 U | Grundlagen der Mathematik II (Lineare Algebra und Statistik) Mo 15-16 oder Mo 16-17 (und umgekehrt für die Übungen 401-0272-00 U) gemäss Gruppeneinteilung (für Studiengang Interdisziplinäre Naturwissenschaften. Do 10-11 oder Do 11-12 oder Do 12-13 (entsprechend gekoppelt mit den Übungen 401-0272-00 U) gemäss Gruppeneinteilung für Studiengänge Chemie bzw. Chemieingenieurwissenschaften. | 1 hrs |
| M. Dettling |
Catalogue data
| 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. |
| Learning 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 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. |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| In examination block for | Bachelor's Degree Programme in Chemical Engineering 2006; Version 27.03.2018 (Examination Block) Bachelor's Degree Programme in Chemical Engineering 2018; Version 26.09.2022 (Examination Block) Bachelor's Degree Programme in Chemistry 2005; Version 27.03.2018 (Examination Block) Bachelor's Degree Programme in Chemistry 2018; Version 26.09.2022 (Examination Block) Bachelor's Degree Programme in Interdisciplinary Sciences 2010; Version 27.03.2018 (Examination Block) Bachelor's Degree Programme in Interdisciplinary Sciences 2018; Version 12.07.2022 (Examination Block) |
| ECTS credits | 3 credits |
| Examiners | M. Dettling |
| Type | session examination |
| Language of examination | German |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | written 90 minutes |
| Written aids | Beliebige schriftliche Hilfsmittel, jedoch kein Taschenrechner. |
| If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block. This information can be updated until the beginning of the semester; information on the examination timetable is binding. | |
Learning materials
| Main link | Vorlesungshomepage |
| Only public learning materials are listed. | |
Groups
| No information on groups available. |
Restrictions
| There are no additional restrictions for the registration. |
