Introduction to Complexity Science

Course Aim

The overarching learning outcome is the ability to approach a new complex system and possess the ability to devise steps towards understanding its structure, dynamics, agency, and function. The specific learning objectives follow from this.

Course Description

Complex systems are ubiquitous and play key roles in physical nature, biological life, and social dynamics. We will address the following questions: What is systems thinking, and how can it help us recognize commonalities across disciplines and domains of application? How can complex systems be understood and modeled, including their structure, dynamics, agency, and function? What are the key tools in a complexity scientist’s toolbox? Addressing these questions, we will use a cross-disciplinary approach suitable for students with backgrounds in physics, chemistry, biology, neuroscience, social sciences, mathematics, and computer science.

Course Contents

1. Systems thinking
Structure: discern a system’s elements, boundary, structure, interactions, and feedbacks; understand the main types of model structures; recognize networks of different types; become familiar with a wide range of indicators of network structure; understand boundary conditions.
2. Main types of model structures
3. Network types
4. Indicators of network structure
5. Boundary conditions
Dynamics: understand the main types of model dynamics; understand the basics of couple first-order ordinary differential equations; be able to conduct a linear stability analysis; under different types of attractors; understand bifurcations; become familiar with the basics of stochastic processes; understand maximum-entropy approaches.
6. Main types of model dynamics
7. Dynamical systems
8. Linear stability analysis
9. Attractors
10. Bifurcations
11. Stochastic processes and maximum entropy
Agency: be familiar with the basics of agent-based modeling; recognize mechanisms of adaptation through evolution and learning; understand bounded rationality and how to model it.
12. Agent-based modeling
13. Evolution
14. Learning
15. Bounded rationality
Function: understand models of coordination and cooperation; be aware of emergent phenomena and self-organized criticality; be familiar with the basics of socio-economic modeling; understand plural rationality and how to model it.
16. Coordination and cooperation
17. Emergence and self-organized criticality
18. Socio-economic modeling
19. Plural rationality
20. Systems thinking revisited


Quizzes 33%; Paper presentation 33%; Programming project 33%

Prerequisites or Prior Knowledge

Basics of calculus, linear algebra, and programming.