|MATH 300 - Principles of Complex Systems|
Peter Sheridan Dodds
Many of the problems we face in the modern world revolve around comprehending, controlling, and designing multi-scale, interconnected systems. Networked systems, for example, facilitate the diffusion and creation of ideas, the physical transportation of people and goods, and the distribution and redistribution of energy. Complex systems such as the human body and ecological systems are typically highly balanced, flexible, and robust, but are also susceptible to systemic collapse. These complex problems almost always have economic, social, and technological aspects.
So what do we know about complex systems? The basic aim of this introductory interdisciplinary course is to present a suite of theories and ideas that have evolved over the last couple of decades in the pursuit of understanding complex systems. The central focus will be on understanding small-scale mechanisms that give rise to observed systemic phenomena. Students will be encouraged to see how different areas connect to each other and, just as importantly, where analogies break down.
Familiarity with the following would be good but not completely necessary: standard calculus, differential equations, difference equations, linear algebra, statistical physics, and statistical methods.
Computing: Proficiency in coding (C, Matlab, perl, python) will be beneficial (and indeed necessary) for certain projects but is not required.
Agent-based simulation / cellular automata, Multi-scale modeling, Network/graph science, Statistical modeling
Environmental Systems, Biological Systems:, Between organisms (e.g., ecological, sociological, evolution), Transportation Systems
|Frequency: Once a year|
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