392245 Applied Modelling (S) (WiSe 2017/2018)

The course aims at providing students with some basic knowledge and skills to build models of their own. This includes a certain 'literacy' of models as well as the ability to express real-world problems in a formal way, such that solutions can be obtained via mathematical algorithms. In other words: This is a course about looking at problems from the right angle, such that established mathematical tools can help us in finding solutions.

In more detail, the course will introduce the following topics:

• Vector Spaces (applications e.g. in physics, psychology, engineering and machine learning)
• Graph Theory (applications e.g. in object-oriented programming, network analysis and the semantic web)
• Formal Languages (applications e.g. in compiler building and bioinformatics)
• (Convex) Optimization (applications e.g. in machine learning, robotics and economy)
• Dynamical Systems (applications e.g. in engineering and physics)
• Probability Theory & Bayesian Reasoning (applications e.g. in machine learning and robotics)
• Self-Learning Systems/Neural networks (applications e.g. in pattern recognition and language processing)
• Ethics of mathematical models

From this range, students can select one or multiple topics for their own model.

In all topics, examples and applications will guide the seminar to make the topics as intuitive as possible. Note that the breadth of the topic and the limited scope of the seminar make it impossible to go too deep into any topic. Instead, the seminar will provide pointers for further reading or other courses here in Bielefeld to get a more in-depth picture of the topics introduced.

Formally, this is a 3 CP course as part of the 'Ergänzungsmodul Informatik' 39-Inf-EGMI. However, the course is open to members of all faculties. The course will be entirely in English.

Requirements for participation, required level

Prior knowledge is not strictly required. However, mathematical models are the topic of this seminar. Therefore, it is recommended to have some prior exposition to university grade math.

Bibliography

The following literature list covers many of the topics in the seminar, but in greater detail. Note that it is not required to read these books for the seminar.

• Neil Gershenfeld (1999): The Nature of Mathematical Modeling, Cambridge University Press
• Zbigniew Michalewicz, David Fogel (2000): How to Solve It: Modern Heuristics, Springer
• Stephen Boyd, Lieven Vandenberghe (2009): Convex Optimization, Cambridge University Press
• David Barber (2010): Bayesian Reasoning and Machine Learning, Cambridge University Press
• Christopher Bishop (2006): Pattern Recognition and Machine Learning, Springer
• Cathy O'Neil (2016): Weapons of Math destruction: How Big Data Increases Inequality and Threatens Democracy, Crown Publishing Group