Fall 2024

Complex Systems

Listed in: Physics and Astronomy, as PHYS-303


William A. Loinaz (Section 01)


Reductionist methods, reducing complicated systems to the simplest elements, have been powerful tools for understanding in science. But in many phenomena, more than the nature of the individual elements it is the multiplicity of elements and the rules of their interactions that determine the collective behavior. Complex systems---systems with many interacting components or degrees of freedom---are ubiquitous and include both natural systems (insect colonies, gene networks, brains, climate, fluids) and manmade systems (stock markets, cities, traffic, electric circuits, political systems). Complex systems can exhibit fascinating phenomena, including nonlinearity, self-organization and emergence, catastrophes, feedback loops, and adaptation, that are not evident from study of individual degrees of freedom. We will survey and examine complex systems and their phenomenology. We will develop tools to model, characterize, and study complex systems, including networks, information theory, agent-based models, chaos, and methods from statistical physics. With these tools we will ask: How do complex system emerge and form patterns? In which ways are they more than the sum of parts? How do they adapt? Can they be predicted and controlled? What might it mean for a system to be sick or healthy? Are there general principles that might apply to all complex systems? The focus will be on quantitative approaches and the application of mathematical and computational methods with the aim of achieving a qualitative understanding of such systems. 

Prerequisite: MATH 211 or permission of the instructor. Three 50-minute lecture meetings per week. Fall semester: Professor Loinaz.

How to handle overenrollment: null

Students who enroll in this course will likely encounter and be expected to engage in the following intellectual skills, modes of learning, and assessment: quantitative work and working in groups

Course Materials


Other years: Offered in Fall 2024