# 401-0622-00L Mathematical Foundations II: Linear Algebra and Statistics

Semester | Spring Semester 2016 |

Lecturers | M. Dettling |

Periodicity | yearly recurring course |

Language of instruction | German |

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 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. Statistics: W. Stahel, "Statistische Datenanalyse", Vieweg, 3rd edition. |