Course Description: Computational Methods for Complex Systems at Georgia Tech is a modeling and simulation class exploring common themes arising in diverse domains of science and engineering. The class introduces broadly-applicable computational and analytical methods via four modules that cover topics in physics, biology, engineering, applied math and computer science. The modules are:

1. Networks: graph representations, network structure, measures and metrics: connectivity, clustering, centrality, modularity, hierarchy; network models in biology, models of growth and self-organization, percolation, phase transitions, spreading processes, network dynamics.

2. Entropy and Information: thermodynamic entropy, information entropy, entropy of card shuffling, entropy of black holes, algorithmic information, burning information and Maxwellian demons, reversible computation, data compression, information geometry.

3. Biology and Computation: random walks and emergent properties, run & tumble bacterium, Lévy flight, kinetic proofreading in cells, fruitfly behavior map, molecular motors, discrete-event simulation; entropy, aging and DNA; active matter, flocking, synchronization.

4. Dynamical Systems: logistic map; chaos, Lyapunov and entropy increase, fractal dimensions, invariant measures, crackling noise, periodic doubling routes to chaos, renormalization group and the onset of chaos, Jupiter and the KAM theorem.

Students will investigate each of these modules via a series of exercises and carry out a final project in a topic of their choice.

Instructor: Nabil Imam. Email: nimam6@gatech.edu.

Textbook:

• Statistical Mechanics: Entropy, Order Parameters, and Complexity, JP Sethna, Oxford University Press, 2021.

Pre-requisites: familiarity with undergraduate probability and calculus; familiarity with a programming language (e.g. Python).

Grading: four assignments 20% each (one for each module), final project 20%