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Introduction to Complex Systems (2025/2026: Semester 1)
Cursusdoel
Er is geen informatie over het cursusdoel bekend.
Vakinhoudelijk
Schedule. Wednesday 17.15-19.00.
In recent years there has been a growing interest in the science of complex systems. A complex systems is loosely defined as one whose collective dynamical behavior cannot be readily deduced by a reductive study of its individual components. For example, it is difficult to predict where traffic jams will occur by studying the behavior of individual drivers, or to understand turbulence in water by studying the behavior of water molecules.
Important questions are how coherent collective behavior emerges in (seemingly) random systems, how complex systems undergo change, what makes certain behavior more or less stable. In this course we will study mechanisms for emergence, including synchronization and pattern formation, and mechanisms for transitions between system regimes, with an emphasis on analytical and computational methods. We will ask, what are the mathematical foundations of complexity science? What aspects of complex systems can we model successfully with mathematics, and where do we fall short?
Topics. Emergence, synchronization, entropy, large deviations, resilience of complex systems, critical transitions. Applications in biology, climate science, economics, sociology, innovation science.
Prerequisites. Familiarity with elementary concepts from linear algebra (eigenvalues), dynamical systems and probability. Programming in mathematical software (Matlab, Mathematica).
Format. Lectures will alternate between introductions to concepts and theory of complex systems and guest lectures by researchers from other disciplines. Each student will submit two research reports involving computer simulations. There will be a final exam.
Learning goals with assessment weighting. After completion of the course, the student is able to:
In recent years there has been a growing interest in the science of complex systems. A complex systems is loosely defined as one whose collective dynamical behavior cannot be readily deduced by a reductive study of its individual components. For example, it is difficult to predict where traffic jams will occur by studying the behavior of individual drivers, or to understand turbulence in water by studying the behavior of water molecules.
Important questions are how coherent collective behavior emerges in (seemingly) random systems, how complex systems undergo change, what makes certain behavior more or less stable. In this course we will study mechanisms for emergence, including synchronization and pattern formation, and mechanisms for transitions between system regimes, with an emphasis on analytical and computational methods. We will ask, what are the mathematical foundations of complexity science? What aspects of complex systems can we model successfully with mathematics, and where do we fall short?
Topics. Emergence, synchronization, entropy, large deviations, resilience of complex systems, critical transitions. Applications in biology, climate science, economics, sociology, innovation science.
Prerequisites. Familiarity with elementary concepts from linear algebra (eigenvalues), dynamical systems and probability. Programming in mathematical software (Matlab, Mathematica).
Format. Lectures will alternate between introductions to concepts and theory of complex systems and guest lectures by researchers from other disciplines. Each student will submit two research reports involving computer simulations. There will be a final exam.
Learning goals with assessment weighting. After completion of the course, the student is able to:
- read and demonstrate (in class discussions) understanding of multidisciplinary literature (20%)
- understand and be able to apply mathematical analysis and methods to carry out and write two project reports involving computer simulation (50%)
- demonstrate understanding of theoretical concepts on final exam (30%)
| in class discussion 20% |
project reports 50% | final exam 30% | |
| is able to read and demonstrate (in class discussions) understanding of multidisciplinary literature | x | ||
| understands and is able to apply mathematical analysis and methods to carry out and write two project reports involving computer simulation | x | ||
| is able to demonstrate understanding of theoretical concepts (emergence, synchronization, entropy, large deviations, resilience of complex systems, critical transitions) on final exam | x |
Werkvormen
Hoorcollege
Toetsing
Eindresultaat
Verplicht | Weging 100% | ECTS 7,5
Ingangseisen en voorkennis
Ingangseisen
Je moet een geldige toelatingsbeschikking hebben
Voorkennis
Er is geen informatie over benodigde voorkennis bekend.
Voertalen
- Engels
Cursusmomenten
Tentamens
Er is geen tentamenrooster beschikbaar voor deze cursus
Verplicht materiaal
Er is geen informatie over de verplichte literatuur bekend
Aanbevolen materiaal
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BOEKMay, R.M., Stability and Complexity in Model Ecosystems, Princeton University Press, 1973.
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BOEKScheffer, M., Critical Transition in Nature and Society, Princeton University Press, 2009.
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BOEKNowak, M., Supercooperators, Free Press, 2012.
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SOFTWAREUA10190 Matlab 2013a
Coördinator
| dr. C. Spitoni | C.Spitoni@uu.nl |
Docenten
Inschrijving
Deze cursus is open voor bijvakkers. Controleer wel of er aanvullende ingangseisen gelden.
Inschrijving
Van maandag 2 juni 2025 tot en met vrijdag 20 juni 2025
Na-inschrijving
Van maandag 18 augustus 2025 tot en met zondag 14 september 2025
Inschrijving niet geopend
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