401-0622-00L Mathematical Foundations II: Linear Algebra and Statistics
|Semester||Spring Semester 2016|
|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.