University of Edinburgh

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.

Operational Research is the science of using mathematical techniques to tackle real-life decision problems ranging from scheduling flights and routing mobile phone calls, over optimising power systems and logistic networks, to managing investments and minimising risks.  

Operational research is an important skill which is in high demand, and you will enjoy this MSc if you like solving practical quantitative problems and seeing the solutions implemented. By studying operational research you will develop a valuable combination of mathematical, modelling, analytical, computing, interpersonal and communication skills. You will also undertake a dissertation, applying skills developed earlier in the programme to real operational research problems. Projects are either proposed by research staff in the School, or can often take the form of a consultancy exercise for a sponsoring organisation.  

Within the MSc in Operational Research we offer three specialisations in Computational Optimization, Data Science, or Risk. Once admitted to the MSc in Operational Research, students have the option to add a specialisation in Computational Optimization, Data Science or Risk.

Our society revolves around variation, uncertainty and risk. In an increasingly data-driven world, statistics and operational research both play a key role in making sense of data within a rigorous mathematical framework. Thus, they continue to be increasingly important sciences of relevance in all areas of modern businesses, government, and academic research.  

This programme will help you develop professionally in the theory and practice of both statistics and operational research. You will also undertake a dissertation in the form of a supervised research project on a cutting-edge topic proposed by research staff in the School, by collaborators across the University of Edinburgh, or by industry contacts.   

You will be able to identify appropriate statistical or operational techniques, which can be applied to practical problems, and will acquire extensive skills in modelling using appropriate software packages for statistics and simulation. This MSc is accredited by the Royal Statistical Society.  

In this digital and data-rich era the demand for statistics graduates from industry, the public sector and academia is high. The recent growth of data science has increased the awareness of the importance of statistics, with the analysis of data and interpretation of the results firmly embedded within this newly recognised field.  

This programme is designed to train the next generation of statisticians with a focus on the newly recognised field of data science. The syllabus combines rigorous statistical theory with wider hands-on practical experience of applying statistical models to data. In particular the programme includes classical and Bayesian ideologies, computational statistics, regression, and data analysis of a range of models and applications. You will also have the opportunity to undertake an industry-based consultancy-style dissertation project. This MSc is accredited by the Royal Statistical Society. 

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. 

The Hodge Institute is the home of algebra, geometry, number theory and topology research groups in the School of Mathematics.

Our interests include:

• non-commutative ring theory
• non-commutative algebraic geometry
• the geometry of algebraic numbers
• Lie-theoretic representation theory
• quantum algebra
• category theory

While we offer a large community of researchers under one roof, we believe in encouraging you to gain as broad a perspective as possible. The best way to do this is to involve yourself in the international dialogue on your research area, through attending conferences and symposia, and visiting your peers in centres of research worldwide.

Throughout your studies, you’ll be given opportunities to travel to events and institutions that will allow you to gain this perspective and open up new areas of investigation.

Find out more about our PhD programme in Algebra.

The Centre for Doctoral Training (CDT) in Algebra, Geometry and Mathematical Physics 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.

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.

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.

The Hodge Institute is the home of algebra, geometry, number theory and topology research groups in the School of Mathematics.

Our interests include:

• algebraic geometry
• derived categories
• algebraic and geometric topology
• twistor theory
• category theory
• integrable systems

While we can offer a large community of researchers under one roof, we believe in encouraging you to gain as broad a perspective as possible. The best way to do this is to involve yourself in the international dialogue on your research area, through attending conferences and symposia, and visiting your peers in centres of research worldwide.

Throughout your studies, you’ll be given opportunities to travel to events and institutions that will allow you to gain this perspective, and open up new areas of investigation.

Find out more about our PhD programme in Geometry and Topology.

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.

The work in the Operational Research and Optimization research group is in three main areas: the mathematical and computing aspects of optimization, combinatorial optimization, and energy systems.

The core technology in optimization is the solution of large sparse linear and quadratic problems, and we provide world-class expertise in the two main solution methods for these: the simplex method and the interior point method. In combinatorial optimization, we provide expertise for modelling real-world problems using integer linear programming formulations and for deriving efficient exact and heuristic algorithms to solve them.

Specialist expertise in energy includes optimization of system planning and optimization, security of supply risk analysis, and decision support for public policy. We also have interests in PDE-constrained optimization, global optimization, decomposition methods, parallel computing, industrial applications of optimization and stochastic optimization.

Find out more about our PhD programme in Optimization and Operational Research.

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.

Our society revolves around variation, uncertainty and risk. By gaining a greater understanding of these variables through the study of statistics, we’re able to create systems and techniques that benefit areas as diverse as science, law and finance.

Our Statistics research group explores a wide range of statistical theory and practice, often applying its findings in collaboration with researchers in related fields, such as informatics, geosciences, medicine and biomathematics. The group leads the interdisciplinary Centre for Statistics that spans across the whole breadth of the university, providing opportunities for collaborations with researchers in many different applied fields.

The School of Mathematics is a vibrant community with researchers in many different, but related, fields – including Data Science.

Our research is balanced between classical and Bayesian statistics. Particular areas of interest include, but not limited to, high-dimensional data, computationally intensive techniques, wavelets, nonparametric regression, extreme value theory, sampling and hidden process models.

Find out more about our PhD programme in Statistics.