This is an introductory theory course on network science for complex systems, designed as a core course for IDDD students affiliated with the Center for Complex Systems and Dynamics. The course begins with the essential concepts of graph theory needed to understand and characterize the network topology of complex systems. We explore various metrics for analyzing network structures and study canonical network topologies such as random graphs, configuration models, and Albert–Barabási power-law networks.

This course introduces students from diverse engineering and science backgrounds to complex systems and dynamics, focusing on how group-level behavior emerges from interactions between individual agents. It covers topics such as flocking (Vicsek model), pedestrian and traffic dynamics (social force models), data-driven methods (SINDy, POD, DMD), and network models (Erdős–Rényi, Watts–Strogatz, Barabási–Albert), etc. The course combines theory with hands-on computational assignments where students simulate emergent behavior. It also includes a mini-project and a term project, where students apply these concepts to complex, discipline-specific problems.

This course builds clear and effective scientific communication skills through writing, speaking, and critical reading. It covers different styles—expository, descriptive, persuasive, and narrative—and teaches how to adapt ideas for various audiences. The course emphasizes structuring arguments to be clear, logical, and compelling, while avoiding common pitfalls like the “curse of knowledge.” Students read a popular science book and engage in activities, writing, presentations, and outreach to reinforce these skills.

This is a core undergraduate course for mechanical engineering students, introducing them to the fundamental concepts of fluid mechanics. Students explore fluids as a continuum, learn the governing equations of fluid dynamics, and examine simple scenarios to develop a deeper understanding of fluid flows and fluid–structure interactions.

In the regular CFD course offered by our department, I taught approximately 30% of the syllabus, focusing on data-driven methods in fluid mechanics. We started with model order reduction using the Singular Value Decomposition (SVD) method, progressed to Dynamic Mode Decomposition (DMD) with physics-informed constraints, and concluded with sparse regression techniques for identifying reduced-order governing equations.

In this course, students are first introduced to complex systems through canonical examples, exploring key principles such as emergence, heterogeneity, uncertainty, and network topology. The focus then shifts to data-science techniques, where we study methods for identifying communities within complex systems, uncovering equations that govern both stochastic and deterministic dynamics, and developing reduced-order representations of these dynamics.