Syllabus

Course overview

How do the complex movement patterns we observe from bird flocks, insect swarms, and fish schools emerge from the interactions of many individuals? Complex systems, or complexity science, examines how interactions between many individuals can lead to complex emergent patterns, and can help us understand patterns in systems ranging from cells, to societies, to climate change. This course covers a broad range of introductory topics in complex systems, exploring how the tools and ideas of complex systems can help us understand the world around us. As part of this course, students will also gain a friendly introduction to programming in an applied context.

Topics in this course include agent based models, network theory, measures of complexity, chaos, game theory, computational social science methods, and modeling complex adaptive systems and emergence, with applications to climate change, evolution, the COVID-19 pandemic, the brain and consciousness, political polarization, collective intelligence, social media, and others.

You will need a laptop for this course, if necessary you can borrow one through ITS (you can use this link).

Course structure

The class will consist of a mix of lectures, group discussions, demonstrations/interactive exercises, and computer exercises. Most lectures and interactive exercises, as well as some discussions, will occur during the lecture portion, and most computational exercises and discussions will occur during the lab section although there will likely be some variation in course modality.

Course components

You will work weekly on homework sets which will contain a mix of qualitative, quantitative, and computational questions. There will be three quizzes, the first two will take place at the discussion session time and the last one will be during finals week. You will also work collectively on a project. The final grade will be composed of 45% from homework sets, 35% from quizzes, and 20% from the project.

Concepts & Methods

Emergent behavior/phenomena
Feedback loops
Networks
Basic ideas of equilibria, stability, and bifurcations
Chaos and fractals
Collective behavior and collective intelligence
Game & decision theory
Pattern formation
Evolution and adaptation
Introductory programming

Application Areas

Climate change
Consciousness and the brain as a complex system
Evolution
Financial markets and the 2008 recession
Infectious disease spread and COVID-19
Political polarization and social media
Structural racism, neighborhood segregation
Swarming, flocking behavior in animals
Traffic flow