AI Foundations & Maths

The language of machine learning. What AI engineering is, plus the linear algebra, calculus, probability, statistics and optimisation every model relies on.

• Introduction to AI Engineering & the ML Workflow — From idea to deployed intelligence. Learn what AI, machine learning, deep learning and generative AI are and how they relate, the types of learning (supervised, unsupervised, self-supervised, reinforcement), the end-to-end ML workflow (problem framing, data collection and labelling, splitting, baselines, training, evaluation, deployment, monitoring), features and labels, overfitting and generalisation, the AI engineer's toolkit (Python, NumPy, pandas, scikit-learn, PyTorch, cloud, vector DBs) and responsible AI — with a runnable example that splits data, builds a baseline and learns a simple rule.
• Matrices & Determinants — Matrices organise systems of numbers and linear maps. Learn matrix types (square, diagonal, identity, symmetric, triangular, orthogonal), addition and multiplication, transpose and conjugate transpose, determinants by cofactor expansion and row reduction, minors and cofactors, the inverse and adjugate, and properties like det(AB) = det A det B.
• Eigenvalues & Eigenvectors — Eigenvectors are directions a matrix only stretches. Learn the characteristic equation, computing eigenvalues and eigenvectors, algebraic and geometric multiplicity, diagonalisation A = PDP⁻¹, symmetric matrices and orthogonal eigenvectors, powers and exponentials of matrices, and engineering uses in vibration modes, stability, principal stresses and PCA.
• Partial Differentiation — Partial derivatives measure change in one variable while holding others fixed. Learn first and higher-order partials, mixed derivatives and Clairaut's theorem, the multivariable chain rule, implicit differentiation, homogeneous functions and Euler's theorem, and applications to thermodynamics and fields.
• Probability Fundamentals & Bayes — Probability quantifies uncertainty. Learn experiments, sample spaces and events, the axioms, complements, unions and intersections, conditional probability, independence, the multiplication rule, total probability, Bayes' theorem, and reliability of series and parallel systems.
• Descriptive Statistics — Summarise and visualise data before analysing it. Learn mean, median and mode, range, variance and standard deviation, percentiles, quartiles and IQR, outliers, skewness and kurtosis, histograms, box plots, scatter plots and probability plots.
• Unconstrained Optimisation — Find the best design without constraints. Learn objective functions and decision variables, local vs global optima, gradient and Hessian conditions, convexity, gradient descent and learning rates, Newton's method for optimisation, and line searches — with a Python gradient-descent example.