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Mathematics for AI in Real-world Systems

MATH4120

Mathematical Modelling and Programming

BSc MARS — 2026–27

Welcome. Here you will find everything for MATH4120: lecture notes to read, computation lectures to watch and run, and computer labs to work through. No software to install — all interactive notebooks run directly in your browser.

Full Lecture Notes (PDF)

Getting Started Working with the material
Everything here is written in Python. Marimo runs in your browser for lectures and exploring. Jupyter is what you'll use to save work and submit assignments.
Chapter 0 Welcome week: can a computer get a simulation wrong?
A small-group taste of the programming side of MATH4120: predict what a numerical method will do, then watch it happen.
Chapter 1 What is a mathematical model?
The modelling cycle; units and dimensions; first ODEs from rate laws; difference equations.
Chapter 2 Dimensional analysis and nondimensionalisation
Characteristic scales; nondimensionalising an ODE; solution collapse.
Chapter 3 The Buckingham Π-theorem and the dimension matrix
Dimension matrices; finding Π-groups systematically; similarity and scaling laws.
Chapter 4 Ordinary differential equations
Separable equations; integrating factor; Bernoulli; second-order constant-coefficient ODEs; simple harmonic motion; damped oscillations.
Chapter 5 Single species models
Exponential and logistic growth; equilibria and stability; harvesting; bifurcation diagrams.
Chapter 6 Numerical solution of ODEs
Euler’s method; Heun’s method; error analysis; systems of ODEs; Lotka–Volterra and Van der Pol worked examples.
Chapter 7 Data-driven modelling with neural networks
When equations aren’t available; function approximation; feedforward networks; training; mechanistic vs data-driven models.
Assessment Coursework, test and exam
Coursework is 30% of the module: four handwritten exercises and two computational assignments (3⅓% each), plus a group project (10%). The mid-semester test is 20% and the exam 50%. Everything is submitted on Moodle.