Study programme

The compulsory courses will build strong applied mathematical and computational foundations. The compulsory courses include Research Skills, which will prepare you for the summer dissertation project. All courses are worth 10 credits, unless otherwise indicated.

Semester 1 compulsory courses have previously included:

• Numerical Linear Algebra
• Python Programming

Semester 2 compulsory courses have previously included:

• Applied Dynamical Systems 
• Numerical Partial Differential Equations with Applications

Compulsory courses running over both semesters have previously included:

• Research Skills for Computational Applied Mathematics (20 credits)

The optional courses cover a wide range of areas including, for example, data science and machine learning, high performance computing, and related disciplines such as informatics and physics. Alongside those listed below, you may take any other course from outside of this list (up to one) with approval from the Programme Director. All courses are worth 10 credits, unless otherwise indicated.

Semester 1 optional courses have previously included:

• Applied Stochastic Differential Equations
• Bayesian Theory
• Fundamentals of Optimisation
• Statistical Programming
• Stochastic Modelling
• Introductory Probability and Statistics
• Statistical Methodology
• Industrial Mathematics

Semester 2 optional courses have previously included:

• Machine Learning in Python
• Numerical Methods for Data 
• Bayesian Data Analysis
• Mathematics in Action A/B
• Numerical Ordinary Differential Equations and Applications 
• Large Scale Optimisation for Data Science
• Optimisation Methods in Finance
• Time Series
• High Performance Data Analytics 
• Nonlinear Optimization
• Uncertainty Quantification

The 60 credit individual dissertation takes the form of a supervised research project on a cutting-edge topic proposed by  Applied & Computational Mathematics staff, by collaborators across the University of Edinburgh, or by industry contacts. The project provides practical experience and skills for tackling scientific and industrial problems which require data-driven and computational approaches as well as mathematical insight. Projects offered by industrial contacts and companies  are completed in close collaboration with the organisation. 

Past project include (proposing company in brackets):

• Creating habitat maps from sparse labels (Space Intelligence)
• Accelerated (subsampled) Gauss-Newton algorithm for deep learning and inverse problems
•  Adversarial attacks and the limitations of neural networks
•  Scaling machine learning training using data reduction techniques (Viapontica AI) 
•  New insights into turbulence with convolutional neural networks
• Performance validation using reference turbines (Ventient)
• Combining delayed acceptance Markov chain Monte Carlo methods and machine learning for efficient inference
• Disease spread on a hypergraph model of Edinburgh
• Understanding ice-shelf basal channels through coupled ice-ocean modelling
• Measuring the depth of deep Gaussian processes
• Effects of ageing on accumulation of mutations in bacteria
• Scaling machine learning training using federated learning techniques (Viapontica AI) 
• Efficient Bayesian adaptation of neural network topology
• Differential equation constrained optimization and uncertainty quantification
• Optimal low-dimensional representation of large-scale dynamics in a turbulent boundary layer
• Positron emission particle tracking reconstruction
•  Investigating the feasibility of automatic ROV image analysis
• Mapping forests with spaceborne lidar (Space Intelligence)
• Choosing ML algorithms and training sets to predict specific output variables of computational mechanics (DEM) simulations