This course is a first introduction to probability for all students in engineering and the quantitative sciences. It covers basic notions of set theory, outcomes, events, sample space, probability, conditional probability, Bayes’ rule, permutations and combinations, random variables, expected value, variance, binomial, Poisson, and normal distributions, and the central limit theorem.

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# Matrix Algebra

The course introduces matrix arithmetic, inverses, matrix models in population biology, eigenvalues and eigenvectors, Markov chains, and ecological succession.

# Modeling Dynamics in Industrial Systems

Dynamical Systems often behave in a counter-intuitive fashion and are, therefore, complicated to predict, to organize and to regulate. The counter-intuitive behavior comes from nonlinear interactions between the system components.

This course provides a nutshell view on nonlinear dynamics, leading to a toolbox for understanding and simulating complex situations.

Starting from high-school level mathematics (basic calculus, probabilities etc.) this course will introduce ideas from nonlinear dynamics and illustrate, how this perspective had led to breakthroughs in identifying the organizing principles behind dynamical observations.

The basic questions we will discuss have an immediate appeal to industrial systems: Why can a single feedback loop lead to oscillations? When does a chain of processes become unstable? What are the limits for accurate predictions in nonlinear systems?

Topics include the stability analysis in systems of ordinary differential equations; conditions of oscillations; deterministic chaos; agent-based models and cellular automata; dynamic processes on networks.

In all these cases it will be shown, how the abstract theoretical concepts are linked with explicit observations and how these concepts can help understand processes in industrial systems.

# Case Study Design (Thesis)

Description TBA.

# Qualitative Research (Thesis)

Officially: **Qualitative Research: Methods and Design**

Qualitative researchers explore the structure of everyday life and the meaning that events, other persons and their actions hold for us. To do so, they take an in-depth look at a few selected cases, such as organizations, campaigns, or people. The focus of this course is on the different ways and methods of doing this and of collecting data, for example semi-structured and narrative interviews, focus groups, observation, working with documents and with visuals. Ways of purposefully selecting participants and materials will also be discussed, as well as some of the frameworks and approaches underlying these methods, for example grounded theory methodology or ethnography. The course is complemented by ‘Qualitative Research: Analysis of Text and Images’ where the focus is on methods for analysing qualitative data.

The course is held in part as a seminar and in part as a lab where students apply the methods to data from their own fields of study. During the lab sessions, students are required to participate in and report on activities involving the application and trying out of selected methods.

# Advanced Programming in Python

This course is the continuation of the first semester course unit and offers a more advanced view of the programming skills learned during the first unit. It covers advanced topics of Python programming such as object oriented programming, advanced data structures, file handling, graphics, problem solving using frameworks and simulations. It also includes creating tables using formatted output, generating HTML tables, processing CSV files, and interactive graphics with multiple modules. The students have to apply the learned knowledge for solving problem assignments under the supervision and with the help of teaching assistants.

# Data Analysis and Statistical Interface with R

We live in a world full of data and ever more decisions are taken based on a comprehensive analysis of data. This course provides an introduction to quantitative data analysis using graphical representations, numerical summary statistics, correlation and simple regression. It also introduces the fundamental concepts of statistical inference. Students learn about the different data types, how to best visualize them and how to draw conclusions from the graphical representations. The lecture will develop the different steps and ingredients of hypothesis testing by focusing on the practical aspects. Students will learn how to become an intelligent user of basic statistical techniques from a prosumers perspective in order to assess the quality of presented statistical results and to produce high quality analysis by themselves. By using illustrative examples from economics, engineering, the natural and social sciences students will gain the relevant background knowledge for their specific major as well as an interdisciplinary glimpse to other research fields. Regular exercises, homework assignments and practical sessions using the statistical software R will enhance the students’ learning experience.

# Applied Calculus II

This course introduces limits, derivatives, and their applications, followed by a brief introduction to integration.

# Programming in Python

This course offers an introduction to programming using the programming language Python. After a short overview of the program development cycle the course presents the basics of Python programming. It covers fundamental programming components and constructs as well as simple algorithms in a hands-on manner. After learning the concepts of data types, variables, operators and basic data structures, programming constructs like branching, iterations, and data structures like strings, lists, tuples, and dictionaries are presented. The course also gives an introduction into objects and methods, functions, recursive functions, simple file handling as well as simple graphics. Finally, it includes programming assignments, which can be solved during lab sessions under the supervision and with the help of teaching assistants.

# Language

Students are required to take 4 foreign language courses during the three years. Students can choose between German, French, Spanish and Chinese courses. Unless a student is an absolute beginner, Language Placement Test is mandatory to determine the appropriate level.