Core01: Mathematical Modelling
Mathematical modelling is the process of formulating real-world situations or processes in mathematical terms. In this course we will consider some recipes and techniques that are common to formulating and analysing many models. Students will gain hands-on experience of making, solving and interpreting models.
Core02: Scientific Computing
Matlab is a programming environment designed specifically for numerical mathematical modelling. Scientific Computing will involve a crash course in the essentials of programming in Matlab, followed by its application to fundamental numerical topics including linear algebra, differential equations and optimization. These applications will involve exploring inbuilt solvers, toolboxes, external software and test data. The course is run in parallel with Mathematical Modelling, and some of programming task will make links with this course. The last part of the course will explore issues around developing code in teams for industry, and will include a final group programming task.
Core03: Modelling Analysis and Computation of continuous real-world problems
Prof Please, Prof Cartis, Dr Ricardo Ruiz Baier
Modelling, Analysis and Computation of Continuous Real-World Problems will introduce a number of key methods for studying continuum models. Each week we start from real-world problems and show how to derive the corresponding mathematical model. We then use these models as vehicles to demonstrate the relevant analytical and computational methods. At the end of each week, the students will have the complete set of tools needed to set up, analyse and solve a class of mathematical models
Core04: Modelling Analysis and Computation of discrete real-world problems
Dr Thompson, Prof Tanner, Dr Bick
Modelling, Analysis and Computation of Discrete Real-World Problems will introduce key methods for generating and analysing discrete models. Examples will be drawn from industrial problems such as radio channel assignment, asset pricing, large-scale computing, image compression and facility location, and from biology.
Specialist01: Maths for Energy
Dr Vassilios Dallas
Maths for Energy will examine four major energy topics: oil extraction, photovoltaic devices, boiler dynamics and energy storage. For each topic, we will discuss the high level issues and then focus on specific problems where the use of mathematics provides useful insight. Examples will include water intrusion in porous media, solar cell device behaviour, multiphase flow, and battery electrochemistry. Mathematical techniques that will be employed include: WKB, homogenisation and singular perturbations.
Specialist02: Continuum Models in Industry
Dr Ian Griffiths
This course introduces students to advanced theoretical methods for building, simplifying and analysing mathematical models based on differential equations. Practical industrial problems will be use to motivate each of the models and techniques. Many industrial processes involve free boundary problems, where the shape of the region in which the equations are posed must be determined as part of the solution. These will be motivated and studied using real-world examples including welding and electropainting. Perturbation methods are key to analysing and simplifying such problems. In examples such as engine bearings, coating flows and optical fibre drawing, the geometry is thin and geometrical reduction is possible using lubrication theory. On the other hand, problems such as filtration and bubbles in liquid glass involve thin obstacles or inclusions which can be analysed using slender body theory. The study of thin elastic objects such as beams, rods and plates will be motivated by industrial processes involving rope, hair, cables and disk drives. Finally, models involving nonlinear waves and friction will be motivated by problems including river flow and high-speed trains in tunnels.
Specialist03: Contemporary Numerical Techniques
Prof Cartis, Dr Haji-Ali, Dr Ruiz Baier, Prof Tanner
The course will examine four major numerical topics: optimisation, partial differential equations, linear algebra and Monte Carlo simulation. For each topic, industrial problems will be used to motivate concepts including, for example, demand forecasting for supermarkets, processing and displaying data on curved surfaces, the “Netflix” challenge, uncertainty quantification and the solution of large-scale fluid problems. Numerical techniques that will be used include descent methods, optimisation of expensive functions, stochastic differential equations, high dimension PDEs, matrix completion, approximation, factorisation, stochastic estimation, numerical linear algebra, finite differences, and interpolation schemes.
Specialist04: Mathematical Analytics
This course addresses short- and long-term challenges arising in customer-facing industries and will exploit data available from shopping baskets, twitter, mobile telecoms and energy demands. The course will start with probability, covers graphs and their application to social networks, looks at dynamically evolving networks, clustering and classification, hypothesis testing and forecasting.