This course provides an introduction to (a) building models of complex systems (physical, biological, social and engineered) and (b) the study of networks, including topologies and dynamics of real world networks.
The course will cover the basic construction and analysis of models including identifying what is to be modeled, constructing a mathematical representation, analysis tools and implementing and simulating the model in a computer program. Particular attention will be paid to choosing the right level of detail for the model, testing its robustness, and discussing which questions a given model can or cannot answer.
The study of networks will introduce the use of network topologies and the characterization of networks describing complex systems, including such concepts as small worlds, degree distribution, diameter, clustering coefficient, modules, and motifs. Different types of network topologies and network behaviors that model aspects of real complex systems will be described including: modular, sparse, random, scale-free, influence, transport, transformation, and structure.