The Computational Applied Mathematics MSc programme trains a new generation of applied mathematicians with strong expertise in computational and data-driven methods.

Mathematical models and computational methods are at the heart of the technological and scientific advances that are shaping our world. This MSc provides students with the strong foundations needed to contribute to these advances and become science and technology leaders. It equips them with vital skills in mathematical and statistical modelling, numerical methods, data science, machine learning and high-performance computing.

Students will also undertake a dissertation in 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.

This course is supported by XTX Markets.

This Masters is taught at the UK’s longest-established academic centres studying artificial intelligence, which remains one of the best in the world. 

Many of the courses are taught by internationally-known researchers spanning a wide range of areas in artificial intelligence that draw on research in related fields such as:

• neuroscience 

• cognitive science 

• linguistics 

• mathematics 

This programme aims to give you the fundamental knowledge and practical skills needed to design, build, and apply AI systems in your chosen area of specialisation. 

This course is supported by XTX Markets and Google DeepMind.

The Centre for Doctoral Training (CDT) in Algebra, Geometry and Quantum Fields aims to train graduate students to research excellence in diverse disciplines, such as:

• pure mathematics
• mathematical and theoretical physics, including:
  • algebra
  • geometry
  • topology
  • quantum field theory
  • gauge theory
  • gravity

You will navigate the many vibrant interfaces among these disciplines, learning to communicate ideas fluently across different areas of mathematics and physics, and harnessing the power of interfaces to advance research.

You will incorporate advanced computing methods in your research and will have the opportunity to work with some of our 30+ partners in the international academic community, industry, and the third sector.

You will train together in cohorts, combining multiple disciplines and backgrounds. You will be supported to work on short group projects and to participate in a variety of activities to enhance your mathematical/scientific breadth and communication skills.

This course is supported by XTX Markets.

Our analysis research group is one of the UK’s top centres for research in the field, especially in linear and nonlinear PDEs and harmonic analysis.

Your passion for mathematical analysis will be rewarded by contact with, and supervision by, world-leading academic staff, a rich seminar and working group programme and ultimately a qualification that boasts an internationally respected pedigree.

We have a unique focus on the interplay of classical Euclidean harmonic analysis with the modern theory of PDEs. We study harmonic analytic ideas in number theory, geometric measure theory, combinatorics, and discrete geometry and geometrically invariant inequalities; and we investigate applications of harmonic analysis to elliptic and parabolic PDEs with rough coefficients and/or on rough domains.

We also study:

• nonlinear hyperbolic, dispersive and kinetic equations and systems arising in the classical field theories of mathematical physics, mathematical biology and, in connection with black holes, mathematical general relativity
• free-boundary problems, optimal mass transportation and Monge-Ampère equations in nonlinear elasticity and other continuum theories
• well-posedness for supercritical initial value problems with noisy initial data

Find out more about our PhD programme in Analysis.

This course is supported by XTX Markets.

The Applied and Computational Mathematics research group combines expertise in dynamics, classical and statistical mechanics and advanced scientific computing techniques, to develop techniques for applications such as molecular dynamics, geophysical and astrophysical fluid dynamics and optoelectronics.

If you have a passion for applied mathematics, our facilities, people and environment will help you develop your research ideas to their full potential.

Our research interests are varied and include:

• astrophysical fluid dynamics
• multiscale modelling and analysis
• molecular dynamics
• mathematical meteorology
• Hamiltonian dynamics
• nonlinear waves in fluids and solids
• optoelectronics
• signal processing
• mathematical biology
• exponential asymptotics
• homogenisation theory

Find out more about our PhD programme in Applied and Computational Mathematics.

This course is supported by XTX Markets.

We are a multidisciplinary research group with close connections with the School’s Algebra and Geometry & Topology groups.

You’ll benefit from being not only in one of the largest mathematics research groups in the UK but also part of the Edinburgh Mathematical Physics Group – a joint research collective formed in 1999 with Heriot- Watt University and now part of the Maxwell Institute.

Our group pursues wide-ranging interests spanning a number of disciplines. A central goal is to understand the principles behind quantum gravity, through the study of black holes, cosmologies and spacetime singularities, and via the use of holography and the interplay with quantum gauge field theory through the gauge/gravity correspondence.

Particularly fruitful areas of research are the geometry of higher-dimensional black holes and their near-horizon geometries in the context of higher-dimensional generalisations of general relativity.

Find out more about our PhD programme in Mathematical Physics.

This course is supported by XTX Markets.

Our research group operates in what is perhaps the most widely applied area of mathematics. The financial sector, in particular, is a major focus of our research, and graduates with the right research experience can make their way into highly rewarding roles in industry.

As part of our small, specialised group, you’ll enjoy a research environment that features a balance between theory and practice, access to one of the most powerful computing facilities in the UK and strong links with relevant industries.

Our research focuses on the following themes:

• stochastic differential equations and stochastic partial differential equations (PDEs) and their applications in nonlinear filtering and stochastic control
• applications of stochastic analysis of PDEs, stochastic PDEs and stochastic differential equations (accelerated numerical methods in particular)

We’re also involved in the applications of probability theory, mainly to mathematical finance, particularly stochastic volatility models, equivalent martingale measures and incomplete markets. Other applications include engineering, signal procession and biological sciences.

Find out more about our PhD programme in Probability & Stochastic Analysis.

This course is supported by XTX Markets.

At the Artificial Intelligence and its Applications Institute (AIAI), we enable computer systems to reproduce and complement human abilities, work with people, and support collaboration between humans.

We conduct world-leading research in the foundations of Artificial Intelligence, for example, in:

• knowledge representation and reasoning
• emergence of meaning
• theory and ontology change
• creativity
• computer-based proof

We also research its applications to intelligent systems, for example:

• autonomous and multi-agent systems
• social computation
• scientific collaboration platforms
• web semantics and linked data

Our research methods focus on the development of models of knowledge, reasoning, and interaction that can be used to understand and automate aspects of human and machine intelligence, but are also understandable and usable to the designers and users of AI systems in order to address broader issues such as fairness, accountability, transparency and safety.

To achieve this, we combine theoretical research into AI models, architectures and algorithms with a strong element of applied research.

Find out more here.

This course is supported by XTX Markets.

The Institute for Adaptive and Neural Computation (ANC) is a world-leading institute dedicated to the theoretical and empirical study of adaptive processes in both artificial and biological systems. We are one of the UK’s largest and most prestigious academic teams in these fields.

We foster world-class interdisciplinary and collaborative research bringing together a range of disciplines.

Our research falls into three areas:

• machine learning
• computational neuroscience
• computational biology

In machine learning, we develop probabilistic methods that find patterns and structure in data, and apply them to scientific and technological problems. Applications include areas as diverse as astronomy, health sciences and computing.

In computational neuroscience and neuroinformatics, we study how the brain processes information, and analyse and interpret data from neuroscientific experiments.

The focus in the computational biology area is to develop computational strategies to store, analyse and model a variety of biological data (from protein measurements to insect behavioural data).

Find out more here.

This course is supported by XTX Markets.

The Laboratory for Foundations of Computer Science (LFCS) continues to lead the way in the development of mathematical models, algorithms, theories and tools that probe the possibilities of computation and communication.

Our students benefit from being part of one of the largest and strongest groups of theoretical computer scientists in the world.

Our research is aimed at establishing deep understanding of computation in its many forms. Using advanced mathematical principles, we create theories and software tools allowing fundamental capabilities of computation to be explored, as well as designing languages that can be used to construct safe and effective programs.

Areas of interest within LFCS include: algorithms and complexity, cryptography, databases, logic, programming languages and semantics, performance modelling, quantum computing, security and privacy, software modelling and testing, and verification.

Find out more here.

This course is supported by XTX Markets.

This course is offered in collaboration with the EPSRC Centre for Doctoral Training in Fusion Power. Find out more here.

This course is supported by the UK Atomic Energy Authority.