Data Science and Artificial Intelligence

Graph theory and system dynamics

Integrated course, 2.50 ECTS

 

Course content

Area 1: Graph theory
- Basic terms of graphs
- Incidence matrix, degree matrix, adjacency matrix, distance matrix, Laplace matrix
- Relationship of graphs
- Planar and bipartite graphs
- Euler and Hamiltonian graphs
- Basics of directed graphs
Area 2: System dynamics
- Overview of modeling and simulation
- Systems science basics
- Effect graphs, effect matrices and pulse models
- Eigenvalue problem, matrix norms, singular values and diagonalization
- Markov chains
- Cybernetic and control engineering basics
- Linear and non-linear differential equations
- Taylor series and linearization
- Initial value problems and numerical integration
- Equilibria and stabilities of differential equations
- Basics of event-oriented simulation

Learning outcomes

Students have a profound understanding of graph theory and its applications. They know the basics of systems science, control engineering and cybernetics and have a basic understanding of mathematical modeling and simulation. They can model dynamic systems using ordinary differential equations and solve them numerically.

Recommended or required reading and other learning resources / tools

Recommended journals and selected articles:
- Arens, T., et al. (2017). Ergänzungen und Vertiefungen zu Arens et al., Mathematik. Springer Spektrum, 2. Auflage.
- Arens, T., Hettlich, F. (2018). Mathematik. Springer Spektrum, 4. Auflage.
- Bishop, C. M. (2011). Pattern Recognition and Machine Learning, Springer, 1. Auflage.
- Bossel, H. (2004). Systeme, Dynamik, Simulation: Modellbildung, Analyse und Simulation komplexer Systeme. BoD - Books on Demand, 1. Auflage.
- Bossel, H. (2004). Systemzoo 2: Klima, Ökosysteme und Ressourcen. BoD - Books on Demand, 1. Auflage.
- Bossel, H. (2004). Systemzoo 3: Wirtschaft, Gesellschaft und Entwicklung. BoD - Books on Demand, 1. Auflage.
- Bossel, H. (2007). Systemzoo 1: Elementarsysteme, Technik und Physik. BoD - Books on Demand, 2. Auflage.
- Bronstein, I. N., Mühlig, H. (2016). Taschenbuch der Mathematik. Europa-Lehrmittel, 10. Auflage.
- Büsing, C. (2010). Graphen- und Netzwerkoptimierung. Spektrum Akademischer Verlag, 1. Auflage.
- Ertel, W., Löhmann, E. (2018). Angewandte Kryptographie, Hanser, 5. Auflage.
- Lutz, H., Wendt, W. (2014). Taschenbuch der Regelungstechnik: mit MATLAB und Simulink. Europa-Lehrmittel, 10. Auflage.
- Murphy, K. P. (2012). Machine Learning: A Probabilistic Perspective (Adaptive computation and machine learning). MIT Press.
- Sayama, H. (2015). Introduction to the Modeling and Analysis of Complex Systems. Open SUNY Textbooks, 1. Auflage (print edition).
- Scheinerman, E. R. (2013). Invitation to Dynamical Systems (Dover Books on Mathematics). Dover Publications, 1. Auflage (reprint).
- Shannon, C. E. (1963). Mathematical Theory of Communication. Combined Academic Publ., 1. Ausgabe.
- Thuselt, F., Gennrich, F. P. (2014). Praktische Mathematik mit MATLAB, Scilab und Octave: für Ingenieure und Naturwissenschaftler. Springer Spektrum, 1. Auflage.
- Tittmann, P. (2019). Graphentheorie: Eine anwendungsorientierte Einführung. Carl Hanser Verlag Gmbh & Co. KG, 3. Auflage.
- Vande Wouwer, A., et al (2017). Simulation of ODE/PDE Models with MATLAB, OCTAVE and SCILAB: Scientific and Engineering Applications. Springer, 1. Auflage (softcover reprint).
- Weitz, E. (2018). Konkrete Mathematik (nicht nur) für Informatiker: Mit vielen Grafiken und Algorithmen in Python. Springer Spektrum: 1. Auflage.
Recommended journals and selected articles:
All relevant journals and articles will be given in the class.
Typical software for this module:
Python/Spyder/PyCharm, Matlab/Octave/Scilab, Vensim, OpenModelica, Simul8 etc.

Mode of delivery

1,25 ECTS Lecture, 1,25 ECTS Exercise

Prerequisites and co-requisites

none

Assessment methods and criteria

Lecture: final exam, Exercise: examination character