## Marc Auer: Catalogue data in Spring Semester 2021 |

Name | Prof. Dr. Marc Auer (Professor FHO - HTW Hochschule für Technik und Wirtschaft Chur (bis 2019)) |

Address | FHGR Fachhochschule Graubünden Pulvermühlestrasse 57 7004 Chur SWITZERLAND |

Telephone | +41 81 286 24 75 |

Fax | +41 81 286 24 00 |

marc.auer@math.ethz.ch | |

Department | Mathematics |

Relationship | Lecturer |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-0622-00L | Mathematical Foundations II: Linear Algebra and Statistics | 3 credits | 2V + 1U | M. Auer | |

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 homepage: https://moodle-app2.let.ethz.ch/course/view.php?id=11841 | ||||

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. |