The course introduces basic mathematical tools and software used in modeling and analysis of complex systems. Mathematical models are used to describe and understand the dynamics of real-world systems in essentially all applied sciences, such as physics, biology, chemistry, engineering, economics, social sciences etc. The theory of system dynamics is compact, intuitive and very powerful, and relies fundamentally on numerical integration of coupled ordinary differential equations (ODE). The course will cover concepts like integration methods, feedback, modeling artefacts, mechanistic and descriptive modeling, stochasticity, parameter optimization, Monte Carlo simulations and chaotic systems. In this hands-on course we will model and implement dynamical systems, understand the theoretical background and limitations, and practice understanding and communicating of models. The course assessment is a documented model of a case study conceived by the student.
- Teacher: Sven Hirsch (N Dozent)
- Teacher: Simone Ulzega (N Wiss. Mitarbeiter)
- Teacher: Dirk Wilhelm (T Dozent)
Repetition of basic statistical concepts; overview of statistical tests; introduction to statistical modeling (general linear models, logit/probit, multinomial, ordinal, mixed-effects, non-parametric); introduction to multivariate statistics (principal components, factor analysis, cluster analysis, multidimensional scaling) and time series; examples of design of experiments, conjoint analysis and statistical surveys; basics of stochastic processes and introduction to Bayes' statistics. The statistical concepts will be explained with practical examples that will be computed with R. The focus is on enabling students to use statistics for problem solving with hands-on exercises, and not on mathematical concepts. Special focus is given to Ph.D. research aspects. The course is taught as a mixture of lectures and „flipped classroom" including self-study, group work, presentations and peer- review. After completing the course students will be able to:
- Understand the aims, concepts and issues of statistical data analysis
- Analyse, visualize, and explore data using descriptive and inferential statistics
- Formulate and test appropriate statistical hypotheses
- Choose appropriate statistical methods and critically interpret their results
- Plan data experiments and data collection
- Work with the statistical software package R
- Understand how to apply statistical methods in research
- Teacher: Maria Anisimova (N Dozentin)
