Applied Math Lab

Syllabus (Program Overview)

Program

This site is organized around six course modules spanning low-dimensional dynamics, collective behaviour, randomness, pattern formation, networks, and discrete models.

The sidebar navigation is the ground-truth order for the material, and this page follows the same structure.

Module 1: Low-Dimensional Dynamics

Build the first simulation workflow with low-dimensional ODEs. You move from modelling principles and one-dimensional systems to epidemics, planar phase portraits, oscillators, excitable systems, and the Lorenz attractor.

Module 2: Synchronization and Collective Behaviour

Study synchronization and collective motion. You connect flows on the circle, Kuramoto synchronization, the Millennium Bridge, Vicsek-style alignment, Couzin rules, and social-force models.

Module 3: Modelling with Randomness

Use random walks, diffusion, heavy-tailed distributions, and financial returns to understand how stochastic models turn data into interpretable mathematical structure.

Module 4: Space and Pattern Formation

Discretize reaction-diffusion systems in one and two spatial dimensions. You study Turing instability, finite-difference Laplacians, boundary conditions, Gierer-Meinhardt dynamics, and Gray-Scott patterns.

Module 5: Complex Networks

Represent systems as graphs with networkx. You measure connectivity and centrality, generate standard graph models, and simulate SIS and SIR spreading on synthetic and real networks.

Module 6: Explorables and Discrete Models

Switch from continuous fields to fully discrete local rules and student explorables. You implement cellular automata, study Game of Life behaviour, and use traffic as the main agent-based case study.