Explore mathematical representations and models in this 53-minute lecture by Professor Jared Tanner of Oxford University. Delve into topics such as Fourier series, localisation, coherence, match filtering, and random matrix theory. Learn about dictionary learning and singular value decomposition, with practical examples provided. Gain insights from a renowned expert in applied mathematics and information theory, whose research focuses on extracting models from high-dimensional data. Discover how these techniques enable more efficient information acquisition and handling of missing data, with applications in compressed sensing and matrix completion.