maths phd edinburgh

A world-class PhD training programme which equips students with the skills and confidence to lead their discipline .

TRAINING FOR LEADERSHIP

Skills in analysis and data-driven, computational modelling

Collaborative projects focus

Responsible research and innovation

Entrepreneurship training

About the mac-migs programme.

MAC-MIGS students have a world of opportunity for developing and applying mathematics in collaboration with scientists and engineers, interacting with over 30 industrial and governmental partners, and visiting international collaborators around the world.  MAC-MIGS is not just PhD instruction, it is world-class PhD training that equips students with the skills and confidence to lead their discipline.

We accept applications from students interested in a wide variety of areas of mathematics, including mathematical modelling, applied and pure ordinary and partial differential equations, calculus of variations, numerical analysis, pure and applied statistics, machine learning, inverse problems, fluid dynamics, stochastic analysis, and any interdisciplinary topic involving these branches of mathematics and their interplay with other fields such as biology, chemistry, engineering and physics.

WHAT TO EXPECT FROM THE PROGRAMME

MAC-MIGS is a joint PhD programme of the University of Edinburgh and Heriot-Watt University, leading to the award of a joint degree from both universities. During your first year as a student, you are based at the new Bayes Centre in central Edinburgh, where you take courses and carry out group and individual projects, often involving industrial or government partners. Towards the end of the year, you are matched with a PhD project proposed by MAC-MIGS supervisors.

There are opportunities for interdisciplinary internships and periods of time spent in industry or with one of the overseas academic partners in our global network, including Brown University; Duke University; Ecole des Ponts; Norwegian University of Science & Technology; University of Potsdam; University of Turin; Technology University of Berlin; Vienna University of Technology; Utrecht University and the Technical University of Denmark. 

As a MAC-MIGS student, you study topics such as mathematical modelling, computational mathematics, analysis of ordinary, partial and stochastic differential equations, optimal transport theory, statistical methods and applied probability, optimisation, calculus of variations, high performance computing, data analytics (e.g. machine learning), and uncertainty quantification.

MAC-MIGS staff are well aware of the need to address state of the art challenges in data-driven mathematical modelling; our colleagues in the Bayes Centre , EPCC and the Alan Turing Institute will assist us in giving you access to advanced skills to future-proof your education and prepare you for leadership in this rapidly evolving field.

Students in the programme are trained to work on interdisciplinary projects – analysing equations, identifying relevant model structures and testing computational methods in a real-world setting. Our training is outward facing and involves participation of researchers from the sciences and engineeering, as well as industry partners. The training also includes topics in support of research and future employment, presentation skills, entrepreneurship, and responsible innovation.

A PHD WITH INTEGRATED STUDY IN MATHEMATICAL MODELLING, ANALYSIS AND COMPUTATION

The PhD programme will provide a broad training that cuts across disciplinary boundaries to include mathematical analysis – pure, applied, numerical and stochastic – data-science and statistical techniques and the domain-specific advanced knowledge necessary for cutting-edge applications.

Students on this integrated degree will join the broader Maxwell Institute Graduate School in its Bayes Centre. They will benefit from dedicated academic training in subjects that include mathematical analysis, computational mathematics, multi-scale modelling, model reduction, Bayesian inference, uncertainty quantification, inverse problems and data assimilation, and machine learning; extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships; outstanding early-career training, with a strong focus on entrepreneurship; a dynamic and forward-looking community of mathematicians, scientists and engineers, sharing strong values of collaboration, respect, and social and scientific responsibility.

The students trained on this programme will have expertise in a broad array of mathematical modelling techniques and of their application in multidisciplinary contexts as well as experience of industrial collaboration. 

Their skills will be highly valuable for all sectors of business and government as is reflected by our wide network of industry and agency partners covering manufacturing, energy, finance, healthcare, digital technologies, and environmental protection. Immediate benefits to these sectors will be realised through the projects carried out by the students in collaboration with these partners; long-term benefits will be achieved throughout the students’ careers, as they take up leadership positions and influence the future of their sectors.

Industrial and agency partners will provide internships, development programmes and research projects, and help maximise the impact of the students’ work. Our collaborations with academic partners representing leading institutions in Europe and in the US, will provide further opportunities for collaborations and research visits. 

The students will integrate into a vibrant research environment, closely interacting with many academics drawn from the faculties of both Edinburgh and Heriot-Watt Universities.

MAC-MIGS PROGRAMME STUDIES

All students are based in the Bayes Centre during their first year. Students take around 180 credits of study, divided as follows:

• A 15 credit module on Computational Methods for Data-Driven Modelling
• A 15 credit module on Mathematical Modelling and Applied Analysis
• 60-70 units of additional approved coursework (typically at Master’s level) from the Scottish Mathematical Sciences Training Centre, or the two universities, to be agreed with the Cohort Director
• A 15 credit Group Project
• A 15 credit Group Project on an industry or government-relevant theme
• A 60 credit Extended Individual Project

In addition, during the first year, students engage in a Modelling Camp, an Industrial Sandpit, training in and Presentation Skills. Near the end of their first year, all students participate in the 3-day Residential Camp, held at Millport on the Isle of Cumbrae or at The Burn, a large country house in the Scottish Highlands where they gain practice in presentation, hear science lectures and talks on responsible research and innovation, and learn about state of the art industrial challenges.

Years Two-Four

In the second year, students are based in the same building as their supervisor, at one of the campuses of Edinburgh and Heriot-Watt Universities. The work is focussed on the student’s agreed research project, which is typically supervised by a team including staff from both Edinburgh and Heriot-Watt Universities. Students are expected to take around 20 credits of academic coursework in each year. They are also required to participate in MAC-MIGS Skills and Citizenship courses which provide training in responsible research and innovation, equality, diversity and inclusion, project and time management, and other important topics. They also obtain specific instruction in Entrepreneurship.

Students return frequently to the Bayes Centre throughout their studies, for cohort activites, for seminars, for research group meetings and study groups, and to attend workshops at ICMS.

Taster Projects

First-year students work on two taster projects of their choice – one each term – in groups of three or four students. This is a way to get a flavour of the different research areas and to challenge themselves with more advanced material. 

Projects in 2021/22

• Machine Learning for new Numerical Methods in Viscoelastic Fluid Dynamics
• Optimal Infrastructure Planning for Large Scale  CO 2 removal from the Atmosphere
• What is a Quantum Annealer?
• Baysian Inference of the Double-Glazing Model (IBM Research)
• Comparison between DEM and NSDEM (EDEM)
• Understanding the Public Health Waiting Times Landscape in Scotland: Finding Key Drivers and Forecasting Demand (Public Health Scotland)
• Performance Validation using Reference Turbines (Ventient Energy)
• Model Selection by Simulation (Moody’s Analytics)
• Reconciling Robustness and Interpretability in Machine Learning (Moody’s Analytics)

Projects in 2020/21

• Reinforcement Learning via Relaxed Stochastic Control Approach
• Rare event Simulation
• Quantifying Uncertainty in Chaotic Systems using Multi-Level Monte Carlo Methods
• Computational Optimal Transport and Modern Methods of Optimisation
• Deep Learning in Computational Imaging
• Classification of Self-Assembled Structures using Machine Learning 
• Defining Good Neighbours: Modelling Root Traits for Beneficial Plant-Plant Interactions
• Validating Hidden Markov Models as Tools to Identify Seabird Foraging Areas
• Constructing Land Valuation Models to Find Profitable Investments
• Fluid Damping Model for Wave Energy Conversion

Projects in 2019/20

• Modelling Opinion Dynamics
• Control Variates for Path Tracing
• Dispersion in Random Flows: Homogenisation and beyond
• Modelling and Simulation of Multiscale Stochastic Systems in Living Cells
• Deep Learning in Imaging Inverse Problems and Application to Medicine
• Efficient Approximation of Pricing Functions
• Machine Learning for the Prediction of Battery Life
• Stochastic Plant Roots Growth in Granular Media

Home » Programme

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Graduate School

Over 140 academics and excellent facilities provide a superb environment for phd study in all areas of the mathematical sciences, a rich environment and lively seminar programme.

Our graduate school includes an EPSRC-funded Centre for Doctoral Training (CDT), and  covers all areas of mathematics, operational research and statistics. There are numerous meetings, workshops and conferences held through the year, both at the two universities and, often jointly, at the Edinburgh-based International Centre for Mathematical Sciences .

What's On Offer

Our different types of phd programme:, analysis and probability.

Our theme conducts a wide variety of research in modern analysis and probability.  Areas that are well represented at the theme include harmonic analysis, analysis and numerics for stochastic differential equations, dispersive, elliptic, and parabolic partial differential equations (PDEs), geometric measure theory, stochastic PDEs, general relatively, machine learning, limit theorems for stochastic processes, random graphs and processes on them, stochastic networks, interacting-particle system, calculus of variations and spectral theory.

DATA AND Decisions

The Data and Decisions research theme undertakes research at the forefront of modern mathematical, statistical and computational problems related to core elements of Data Science: optimization, operational research, statistics & uncertainty quantification, as well as their applications in imaging, environmental and medical statistics, epidemiology, actuarial science and financial mathematics.

TECHNOLOGY ENHANCED MATHEMATICAL SCIENCES EDUCATION

You will join a team of researchers investigating the teaching and learning of Mathematics in Higher Education.  The team has expertise in the use of technology for teaching and assessing mathematics and developing strategies for lecturers’ development. We welcome proposals on the transition from school to university mathematics and on the teaching, learning and  assessment of Mathematics at the university level, preferably through the use of  technology 

GlaMS is a joint PhD training centre between the University of Glasgow, the University of Edinburgh and Heriot-Watt University. Offering innovative training within a broadly interpreted remit of algebraic structures which includes geometry and mathematical physics. 

Applied and computational mathematics

Our theme works on core research topics in modern applied and computational mathematics.  We offer PhD training in the broad area of applied and computational mathematics including mathematical and computational modelling, numerical analysis, mathematical biology, fluid dynamics, machine learning, industrial mathematics, applied stochastic analysis etc. Our PhD projects are generally offered through the MAC-MIGS 2024 PhD Collaborative Training Centre.

Mac-Migs 2024 Programme

The Mathematical Modelling, Analysis and Computation ( MAC-MIGS ) PhD programme is a collaborative training programme, focused on the formulation, analysis and implementation of state-of-the-art mathematical and computational models.  

Maxwell Institute Training Programme

Our core training programme, offered to all PhD students in any of the research themes of  the Maxwell Institute Graduate School, covering topics  such as  Analysis & Probability, Optimisation, Operational Research, Statistics & Actuarial Mathematics, Structure & Symmetry and more. 

Our application procedure

We actively promote equality, diversity and inclusion and welcome applications from all qualified applicants.

Check you meet the programme entry requirements. 

• If you are applying for a University of Edinburgh programme, please check this website .
• If you are applying for a Heriot-Watt University programme, please check this website . Applications are reviewed continuously until June 15th, but early applications (preferably before the end of March) have the best chance of success. 
• If you are applying to the MAC-MIGS CDT, please check this website . 
• If you are applying to GlaMS, please check this website .

Research Interests – this section is not for MAC-MIGS applicants

Identify your research interest and determine in which theme you wish to carry out your work. 

You should contact staff members prior to making an application in order to identify possible projects and supervisors. This is especially the case for international applicants who may not have the opportunity to attend an interview. However, it isn’t essential for you to have secured a supervisor before making your application. 

You can use the search function in the “Possible PhD Supervisors” section below or the search function in the People section to identify possible supervisors and research areas/ topics. When using the search function to identify potential supervisors, please filter by status and select “staff”.

English Language

You must demonstrate a level of English language competency that will enable you to succeed in your studies, regardless of your nationality or country of residence.

Language requirements vary between programmes so check the relevant website.

Required Documents

• All degree certificates and transcripts – if you do not yet have a transcript, please subit an interim transcript. If you do not yet have a degree certificate, please request a letter from your University stating you have satisfactorily completed your studies or are expected to.
• 2 Academic references  to be provided directly by your referees.
• English Language Certificate  (where applicable).

Where you are asked for a research proposal, you may ignore that request as mathematics does not require one. 

Submit your application 

You should submit your application via the relevant application portal-

• University of Edinburgh   – please note if you wish to apply to the University of Edinburgh, you must select the appropriate PhD programme (i.e. Algebra, Statistics, etc) when submitting your online application by 22nd January 2024.
• Heriot-Watt University – please note if you wish to apply to Heriot-Watt University, you must follow the steps to create an account before you can submit your application.
• MAC-MIGS CDT programme  

Possible PhD supervisors

This part is NOT FOR MAC-MIGS applicants.  Please use the search function below to identify potential supervisors based on your current research interests.  If you do not have fully-formed views on these, you can use the search function to identify possibilities. We would encourage you to contact supervisors directly so that you can get an idea of the types of project that may be on offer. When seeking to identify potential supervisors, you should select “Filter by status” and choose “Staff”. 

Moreover, each research theme , includes various research groups.  A list of research groups can be found below. Some of research groups have additional information about supervisors and projects on dedicated webpages.

Research groups at the University of Edinburgh

• Applied and Computational Mathematics
• Edinburgh Mathematical Physics Group
• Hodge Institute
• Optimization and Operational Research

Research groups at Heriot-Watt University

• Actuarial & Financial Mathematics
• Algebra, Geometry & Topology
• Analysis and PDEs
• Applied Mathematics
• Computational Mathematics
• Mathematical Biology & Ecology
• Mathematical Physics
• Probability & Statistics

A description of the PhD projects offered by the HW research groups can be found here . 

If you are applying for the MAC-MIGS CDT Programme we expect you to keep an open mind about research topics and supervisors. Matching between students and supervisors will usually be done in the middle of the first year – see the MAC-MIGS CDT  web site  for more details.

What we offer:

Admission to the Maxwell Institute Graduate School often includes a scholarship covering fees and living expenses, but we also consider self-funded applicants. The funding period for PhD projects varies between 36 and 48 months, depending on the previous experience of the candidate. The MAC-MIGS doctoral training scholarships are all for 48 months.

The Bayes Centre in the Edinburgh city centre offers a modern space where all MIGS 1st year PhD students will be located.

A complete range of high quality training is on offer to all of our students to take advantage of - both academic and beyond.

More than 150 fellow PhD students between Heriot-Watt University and the University of Edinburgh.

A vibrant research environment including many seminar series and further activities

For a PhD in Analysis and Probability, Data and Decisions, TEMSE

Please use the search function to find academics working in the area of research that interests you. You should then contact them via email to discuss possible research topics. 

You are encouraged to apply by 22nd January 2023 for full consideration. Later applications will be considered until all positions are filled. If you are shortlisted for a PhD programme, you will be invited for interview. These will be held online.

MAC-MIGS CDT and Applied and Computational Mathematics

Please go to the MAC-MIGS programme website for further information about the application process. 

GlaMS Programme PhDs​

Please see the GlaMS  website for further detail and information about the application procedure.

MAC-MIGS CDT and MIGSAA CDT

These two CDTs are no longer hiring. For information about the activities of the MAC-MIGS CDT  see here .

The MAC-MIGS CDT has been replaced by its follow-up programme, the  MAC-MIGS 2024 PhD Programme . the latter is both active and hiring!

To learn more about our MIGSAA programme you can view related information at the archive site .

how to apply

For further information about how to apply to the Maxwell Institute Graduate School, visit our PhD Admissions page. 

Any further questions?

To learn more about our PhD studies or view key contact information on our programmes, visit our FAQs page.

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Welcome to GlaMS PhD training Centre, a joint PhD training centre between the University of Glasgow , the University of Edinburgh and Heriot-Watt University .

Our 60+ supervisors cover the full range of Algebra Structures, across Algebra, Mathematical Physics, and Geometry & Topology, and we train within the remit of algebraic methods, interpreted broadly.  We offer innovative training , including courses and working seminars in the first year, group projects, and 3-month placements.  For more information, please consult About , and our FAQs .

We have now completed four intakes of students. We very strongly encourage applications from across the mathematical sciences, and across traditional boundaries.  For more details, see our Apply page.

EMS PhD Thesis Prize

Starting in 2019, the society periodically awards an EMS PhD Thesis Prize for the best PhD thesis in pure mathematics, applied mathematics, mathematical physics or statistics.

The EMS PhD Thesis Prize for 2021 was awarded to Dr Leonardo Tolomeo of the Mathematisches Institut der Universität Bonn (PhD, University of Edinburgh) for his outstanding thesis ‘Stochastic dispersive PDEs with additive space-time white noise’.

The EMS PhD Thesis Prize will next be awarded in 2023.

Previous winners

• 2019: Dr Soheyla Feyzbakhsh

Whittaker Prize

Periodically, the Society awards the Sir Edmund Whittaker Memorial Prize to an outstanding early-career mathematician having a specified connection with Scotland.

The Sir Edmund Whittaker Memorial Prize for 2021 has been awarded to Dr Ben Davison of the University of Edinburgh in recognition of his outstanding research achievements in the fields of enumerative counting invariants in algebraic geometry and non-commutative algebra.

• 2019: Dr Michela Ottobre
• 2016: Dr Arend Bayer
• 2013: Dr Stuart White
• 2009: Prof. Agata Smoktunowicz

EMS Impact Prize

Introduced in 2021, the EMS Impact Prize recognises the contribution of individuals, teams or partnerships whose work in pure mathematics, applied mathematics, mathematical physics or statistics has had outstanding, demonstrable impact or influence in fields beyond the mathematical sciences.

2022 winners: Prof. Chris Dent, Dr Amy Wilson (The University of Edinburgh) and Dr Stan Zachary (Heriot-Watt University)

The prize was awarded for the recipients’ collaboration supporting National Grid with methodology for assessment of the risk of electricity supply shortfalls in Great Britain and recommending capacity to mitigate this risk; and for wider contributions to development of collaboration between the energy sector and the mathematical sciences community.

About the winners

Chris Dent is Professor of Industrial Mathematics and the University of Edinburgh, and a Fellow at the Alan Turing Institute. He has worked since 2007 on energy systems analysis, with wider interests in decision support in infrastructure, public policy and climate resilience. In 2023-24 he will spend half his time on a knowledge exchange project sponsored by the International Centre for Mathematical Sciences to work with the Global Power System Transformation consortium

Amy Wilson is lecturer in Industrial Mathematics at the University of Edinburgh, with a background in applied statistics for problems in industry and government. She has worked on a range of applications including the work with National Grid on assessing the risk of electricity supply shortfalls, emulation of large-scale energy planning models, decision-making under uncertainty, and statistics and the law.

Stan Zachary is an Honorary Fellow of the School of Mathematical and Computer Sciences at Heriot-Watt University, having been a faculty member in the School from 1979-2015. He is a mathematician and statistician with a particular interest in the management of complex energy systems, particularly in the presence of uncertainty.

2021: Prof. Marian Scott OBE (University of Glasgow) and Prof. Andrew Cairns (Heriot-Watt University)

Marian Scott is Professor of environmental Statistics at the University of Glasgow. She is an applied statistician with broad research interests. Her current projects span archaeology and radiocarbon dating, measuring animal welfare and quality of life and more widely, the environment, whether that be air pollution and health, or water quality in lakes and rivers.

Andrew Cairns is Professor of actuarial mathematics at Heriot-Watt University. His work on the development of models for mortality and longevity has produced quantitative tools now adopted as the industry standard in the pensions and life insurance industry.

For EMS PhD Thesis Prize rules click  here .

For Whittaker Prize rules click here .

For EMS Impact Prize rules click here .

Edinburgh Research Archive

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Mathematics thesis and dissertation collection

By Issue Date Authors Titles Subjects Publication Type Sponsor Supervisors

Search within this Collection:

This collection contains a selection of the latest doctoral theses completed at the School of Mathematics. Please note this is not a comprehensive record.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

Recent Submissions

Investigating computer aided assessment of mathematical proof by varying the format of students' answers and the structure of assessment design by stack , estimation and application of bayesian hawkes process models , novel statistical learning approaches for open banking-type data , statistical and machine learning approaches to genomic medicine , using markov chain monte carlo in vector generalized linear mixed models: with an application to integral projection models in ecology , symmetries of riemann surfaces and magnetic monopoles , kan extensions in probability theory , regression analysis for extreme value responses and covariates , categorical torelli theorems for fano threefolds , laplacians for structure recovery on directed and higher-order graphs , efficient interior point algorithms for large scale convex optimization problems , solving sampling and optimization problems via tamed langevin mcmc algorithms in the presence of super-linearities , algebraic combinatorial structures for singular stochastic dynamics , stochastic modelling and inference of ocean transport , convergence problems for singular stochastic dynamics , classification of supersymmetric black holes in ads₅ , bps cohomology for 2-calabi—yau categories , quantitative finance informed machine learning , efficient model fitting approaches for estimating abundance and demographic rates for marked and unmarked populations , path-based splitting methods for sdes and machine learning for battery lifetime prognostics .

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Research Programmes

• Prospective Students
• Postgraduate Study

The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes.

Select a course below to visit the University’s Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines.

Research Areas and Potential Supervisors

Determining whether your interests and ambitions align with our research and expertise is a vital part of the application and admissions process. When we receive your formal application, we will consider the information you provide on your research interests carefully, alongside other factors such as your academic suitability and potential, how you compare to other applicants in the field, and whether we have a suitable academic supervisor with the capacity to take on new students.

We are committed to widening participation in mathematical research at Cambridge. We welcome and encourage applications from people from groups underrepresented in postgraduate study.

Before making an application to study with us we recommend you:

• Investigate our areas of research and consider how they fit with your interests and ambitions.

A list of broad research areas is provided below, together with links to further information. Your interests may span more than one area. On your application form you will be asked to indicate at least one broad area of interest. This is to help us direct your application to the most suitable group of people to review it.

• Identify 2 or 3 appropriate supervisor(s) with whom you might work.

The information linked below will take you to lists of supervisors working in each broad research area, with an indication of their availability. You are encouraged to make informal contact with potential supervisors prior to making an application. Initial contact should be made by email. In your email we recommend you provide a concise explanation of your areas of interest, how your research interests align with the supervisor(s) research, and that you highlight any relevant work you have done in this area. We recommend that you attach an up-to-date CV. The purpose of this contact is to enquire on supervisor capacity and willingness to supervise, and to see if there is a good fit between your interests and theirs.

If you haven’t had a response to an informal enquiry, you are still welcome to apply and list the individual concerned on your application form, although you may also wish to consider other options.

• Give some thought to your intended research and why you want to study with us.

On your application form you will be asked to submit a short research summary, details of your research experience and your reasons for applying to undertake a PhD/MPhil with us. Whilst you are not expected to submit a detailed research proposal at any stage of the process, we do want to know that you have considered the areas of research that you wish to pursue.

Research areas

Click on a research area to find out more about available supervisors and their research:

Please note that a  large majority of the successful applicants for PhD studentships with  the High Energy Physics, and General Relativity & Cosmology (GR) groups   will have taken Part III of the Mathematical Tripos.

Funding Opportunities

Each Department works hard to secure funding for as many offer holders as possible, either from within its own funds, in collaboration with funding partners, or via the University Postgraduate Funding Competition. However, funding is not guaranteed via these routes, and you should investigate funding opportunities early in the process to be sure that you can meet advertised deadlines.

All application deadlines are 23:59pm (midnight) UK time on the stated date. So that your application can be given full consideration please apply by the following deadlines:

Note for PhD applicants:

We will accept applications for an October start up until the general University deadline in May, but your chances of obtaining funding are significantly reduced. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Only in exceptional circumstances will we consider admission to a later start date in the academic year (i.e., January or April). If you intend to apply for a later start date please contact us at [email protected] so we can advise you on the feasibility of your plan.

Note for MPhil applicants:

We will accept applications until the general University deadline in February, but you will not be considered for funding. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Most interviews are expected to take place in the second half of January.

The purpose of the interview is to try to ascertain the extent of the applicant's relevant knowledge and experience, and to gauge whether their interests and abilities align with the research of the potential supervisor and/or research group. It will most likely consist of a discussion of your background and motivations for applying to the course, as well as some questions on relevant topics.

Not all applicants will be selected for interview.

If you are selected for interview, you will be contacted by email at the address you provided on your application. The email should confirm:

• the location of the interview (it may be in-person or on-line dependent upon interviewer availability, your distance from Cambridge, as well as individual preferences),
• the interview format and whether you should prepare anything specific in advance,
• the approximate duration of the interview,
• who you will be meeting.

Prior to interview you may declare a disability, serious health problem or caring responsibility which may require reasonable adjustments for the interview to be made.

Due to interviewer availability and the tight admissions timetable, we can usually only rearrange the time and date of your interview under exceptional circumstances.

Decision timeline

Both DAMTP and DPMMS make most of their PhD/MPhil admissions decisions for October entry in January and early February, and you should not expect to receive a decision on your application before mid-February (even if you apply much earlier). We expect to have made decisions on all applications by mid-July. The Department makes every effort to take decisions on applications at the earliest opportunity. In some cases, however, it may take some time for a decision to be made. Applications may need to be viewed by several potential supervisors before a final decision can be reached.

To consider your application formally we must receive a complete application form, together with all supporting documents, by the deadline.

Communication of outcomes

You will be notified of the formal outcome of your application via the Applicant Portal.

Following an interview, you can normally expect to receive notification of the outcome within a week or two.

If you are successful, the University’s Postgraduate Admissions Office will issue a formal offer of admission which will outline all your conditions. As processing times can vary, we may also contact you informally to notify you of our decision.

We do not provide formal feedback to applicants who are unsuccessful at either the application or interview stage.

Take a look at our frequently asked questions for PhD applicants.

Forthcoming Seminars

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Funding Opportunities

The School of Mathematics offers several fully funded PhD studentships each year. Students receiving School funding are awarded a stipend equivalent to UKRI stipend rates for a period of 4 years plus fees.  Applications must be received by Monday 22 January 2024 in order to be considered for School and ESPSRC funding opportunities. Late applications may also be considered if there are still places.  There is no need to submit a separate application for these. 

Martingale Foundation Scholarships

We are delighted to announce that we are one of the Martingale Foundation's newest university partners. The Martingale Foundation helps provide access to postgraduate mathematics study for UK students facing financial barriers by offering fully-funded MSc and PhD programmes. 

Applications are made via the  Martingale Foundation website  and the application deadline is Wednesday 25 October 2023.

These awards are available to all applicants and provide full support (fees and stipend). The stipend is set by UKRI on an annual basis (stipend payment levels for 2023-24 are £18,622).  Applications must be received by Monday 22 January 2024 in order to be considered for School and ESPSRC funding opportunities. Late applications may also be considered if there are still places.  There is no need to submit a separate application for these. 

Edinburgh Doctoral College Scholarships 

In 2024-25, the School will offer a fully funded Edinburgh Doctoral College Scholarship. This scholarship provides tuition fees and a stipend for 4 years. The award is open to UK and overseas applicants applying to start their first year of study in 2024-25.

Applicants must be of outstanding academic merit and research potential. Candidates must have, or expect to obtain, a UK first class or 2.1 honours degree at undergraduate level or the international equivalent. 

Successful applicants will undertake a package of training and development which will help you to develop the necessary skills required to meet your career choices and offer you a breath of development opportunities in areas suuch as teaching, public engagement, entrepreneurship, data science and research. 

The application deadline for this opportunity is the end of Monday 19 February 2024.

The EDCS application must be made via the Scholarships portal on MyEd. Once you have made an application for the programme of study, you will receive an email with MyEd login details.

In order to gain access to the scholarship application system, applicants must have applied for admission to the University of Edinburgh.  Please note that, following the submission of an application for admission, it can take up to 10 working days for all system checks to be completed and for access to be granted.

The online scholarship application form is located in EUCLID and can be accessed via MyEd our web based information portal at  https://www.myed.ed.ac.uk

When logging in to MyEd, you will need your University User Name and password.  If you require assistance, please go to  http://www.ed.ac.uk/student-systems/support-guidance

If you are considering applying for this scholarship, we would strongly suggest that you submit your EUCLID admission application for the programme of study at least 10 working days before the application deadline to ensure you have enough time to apply for the scholarship via the Scholarship application portal.

China Scholarship Council/University of Edinburgh Scholarships

There will be one scholarship available for PhD study to candidates who are citizens and permanent residents of the People's Republic of China at the time of applying for entry for the academic year 2024-25. Candidates should not be working outside China at the time of application and successful candidates must agree to return to China upon completion of their degree. Candidates studying outside China are eligible to apply but not those who have already commenced a PhD programme prior to the 2024-25 academic year. 

The application deadline for this opportunity will be announced shortly.  

To be considered for this scholarship applicants should complete the below China Scholarship Council/University of Edinburgh Scholarship application form with should be submitted to [email protected]  by the deadline .  

There will be an internal selection process and successful candidates will be notified via email.  Candidates nominated by the University to be considered for a scholarship should satisfy the selection criteria set out by CSC by completing the CSC Application form and CSC Employer Reference form which can be found on their website . You must ensure you select the correct scholarship scheme -  Institutional & Personal Channel , as there are several schemes. Please note that applicants for this scholarship must be able to prove that they meet the University's English language requirements at the time of application. 

The scholarship is awarded on the basis of academic merit and candidates must have obtained, or be predicted to obtain, the equivalent of a first-class honours degree from a Chinese University. 

Other Studentships

• https://www.ed.ac.uk/student-funding/postgraduate

• Schools & departments

BSc Mathematics

UCAS code: G100

Duration: 4 years

Delivery: Full-time

School: Mathematics

College: Science and Engineering

Introducing BSc Mathematics

Mathematics at university encourages you to think in an entirely different way.

You will develop a rigorous mindset and be introduced to new mathematical concepts not explored at school level.

By the end of your programme, you will specialise in an area of your particular mathematical interest.

This new way of approaching and analysing complex problems is a particularly valuable skill, applicable to many exciting career paths. This makes mathematics graduates extremely employable.

Optional courses

In Years 1 and 2, you will study your mathematics courses as well as optional courses in other subjects. These may be in related areas such as physics or informatics, or from the wide and varied range offered across the University, such as philosophy or languages.

From Year 3 onwards, you will study only your degree subject.

Flexibility between BSc and MMath

You can change between the BSc and MMath programmes up until the beginning of Year 4, subject to strong academic performance.

Second year entry

This degree programme offers the option to start your studies in Year 2 and study an accelerated degree programme. This option shortens the length of your degree by a year, meaning the BSc degree takes three years instead of four.

On this route, you will focus on mathematics from the beginning, rather than studying a broader range of subjects in Years 1 and 2.

For information about the programme structure, please see the details listed under 'What you will study' (Year 2).

Entry requirements for this accelerated programme can be found under the Second Year Entry drop-down section.

Only apply to one Mathematics programme

We usually consider a maximum of two applications to programmes in the College of Science and Engineering as this helps ensure we make offers to as many students as possible.

However, if you are applying for a Mathematics programme, due to high demand, we can only accept one application for a programme in this subject area. You can use your second application for any other Science and Engineering programme.

What you will study

This is a four-year programme.

In your first two years, you will study mathematics alongside your choice of outside subjects. At this stage, the mathematics courses are mostly compulsory. This allows you to develop as a well-rounded mathematician and widens your options for specialisation later on.

From Year 3 onwards, you will study mathematics only.

Year 3 is when you can begin to specialise in an area of mathematics, while still taking some core compulsory courses. This gives you free choice of courses for Year 4 when you can specialise in your particular area of interest.

Please note: the courses below may be subject to change.

You will take a number of compulsory courses. These have previously included:

• Introduction to Linear Algebra
• Calculus and its Applications
• Proofs and Problem Solving

These are common to all our mathematics programmes and will take up half of your timetable. They build on your knowledge of pure mathematics and introduce you to the more rigorous ways of mathematical thinking required at university level.

The rest of your timetable will mostly be made up of subjects other than mathematics.

We also offer optional mathematics courses, for example:

Introduction to Data Science, where you will learn to collect and explore data, before using models and predictions to make rigorous conclusions.

Fundamentals of Algebra and Calculus, an online, introductory course that provides extra preparation in key topics from advanced high school level mathematics and supports your transition to university.

In Year 2, you will spend between half and two-thirds of your time on mathematics.

You will study a number of compulsory courses that will extend your knowledge of calculus, probability and analysis and introduce you to the abstract ideas of group theory. They also cover topics in statistics and applied mathematics. Compulsory courses have previously included:

• Fundamentals of Pure Mathematics
• Several Variable Calculus and Differential Equations
• Computing and Numerics
• Probability

Optional and outside courses

The rest of your time will be made up of a combination of optional mathematics courses or subjects other than mathematics. Your outside courses can follow on from your choices in Year 1, or explore other subject areas.

Facets of Mathematics is an optional Year 2 mathematics course. In this course, you will explore the wide range of applications of mathematics, and develop skills in teamwork and presenting mathematics. This course is assessed by coursework only.

For students taking the accelerated programme, you will study compulsory Year 2 mathematics courses as well as specially designed courses that cover the compulsory material from Year 1, for example:

• Accelerated Algebra and Calculus
• Accelerated Proofs and Problem Solving

As a result, you will study mostly mathematics from the start, rather than having a breadth of subjects available to you. Most students have space for just one outside course from another subject.

The accelerated programme is more challenging than our broad programmes as you will be learning Years 1 and 2 content alongside one another. As a result, it has different entry requirements which can be seen in the Second Year Entry section below.

From this year onwards, you will focus on the main subjects of your programme.

You will study a number of compulsory mathematics courses. These have previously included:

• Honours Algebra
• Honours Analysis
• Honours Complex Variables
• Honours Differential Equations

These courses provide an excellent grounding in advanced mathematics and prepare you for the options available later on.

Each honours course contains a skills component. This enables you to develop valuable employability skills such as:

• programming
• presentation skills

The rest of your time will be spent studying other courses from the School of Mathematics. This is when you will begin to specialise and narrow your mathematical focus.

Previous optional courses have included:

• Financial Mathematics
• Introduction to Number Theory
• Statistical Computing

In Year 4, you will complete at least one of the following:

• a research project
• our Mathematical Education course
• our Statistical Case Studies course

Research project

Completing the project allows you to research a topic in-depth. You can do this as a group or individually.

Mathematical Education course

If you choose this option, you will learn about the theories of learning and teaching mathematics. Then you will put your knowledge into practice; taking short placements at local primary schools or organising revision sessions for local Advanced Higher students.

Statistical Case Studies course

This course allows you to undertake consultancy-style projects as part of a team. Projects will focus on data analysis problems using complex, real-world data.

You will also choose from a wide range of mathematics courses to create a programme that suits your particular interests and career aspirations.

Our course selection is influenced by our School's varied research interests. We offer a large selection of courses in:

• pure mathematics
• applied mathematics
• operational research
• financial mathematics
• mathematical biology
• mathematical education

To find out more about the School of Mathematics' broad ranging research interests, take a look at our Researchers on Record video series.

Researchers on Record | School of Mathematics (YouTube video)

Previous course options have included:

• General Topology
• Numerical Ordinary Differential Equations and Applications
• Stochastic Modelling
• Entrepreneurship in the Mathematical Sciences

Programme structure

Find out more about the compulsory and optional courses in this degree programme.

To give you an idea of what you will study on this programme, we publish the latest available information. However, please note this may not be for your year of entry, but for a different academic year.

Programme structure (2023/24)

Where you will study

Our facilities.

The School of Mathematics is based in the James Clerk Maxwell Building at the King's Buildings campus. Your mathematics teaching will take place at the King's Buildings campus throughout your degree.

Note: your outside subjects in Years 1 and 2 may be taught on other campuses, so you may need to travel between campuses for classes.

Take a virtual tour of our School

You can take a closer look at the School of Mathematics and explore our facilities and campus on the University's Virtual Visit site.

Virtual visit – School of Mathematics

Study abroad

You will have opportunities to study abroad through exchange programmes. Students have recently completed placements in:

• British Columbia

Exchanges are typically taken in Year 3, before returning to Edinburgh to complete Year 4. They are available to students on both the broad programme and the accelerated programme (second year entry).

What are my options for going abroad?

Learning and assessment

How will i learn.

Mathematics is taught through a mixture of lectures and workshops.

You will have about 15 hours of teaching each week. However, this varies depending on your year of study and your chosen outside subjects.

In Year 1, lectures are usually interactive; lecturers use online voting systems and encourage small-group discussions to improve your understanding of core material.

These lectures are linked to your subject reading, so you will be familiar with the content before you attend.

Lectures in later years follow a more 'traditional' lecturing style but occasionally include the voting system.

Lectures are supported by small-group workshops. These sessions give you the opportunity to apply the concepts you have learned in lectures, and to develop your understanding. You will work with five to six other students, with a tutor on hand to support you and answer questions.

You will have access to broad-ranging support from within the School of Mathematics, including:

• drop-in Year 1 mathematics support
• option to take part in our peer-assisted learning scheme, MathPALS
• Mathematics Student Services team

How will I be assessed?

Mathematics courses are mostly assessed through exams.

In your first and second year, these exams are primarily 'open book' exams, where you can use your textbook and notes. This allows you to concentrate on understanding and using the ideas and concepts involved, rather than memorising procedures.

In later years, there is a mixture of open and closed-book exams, depending on the course.

Most mathematics courses have regular assessments throughout the year, both written and online, so you can get feedback on your progress. These typically count for a small part of your course grade.

Later in the degree, there are some courses available which are entirely assessed by coursework, usually in the form of reports, posters, projects or presentations.

Career opportunities

As a mathematics graduate, you will have a wide range of careers open to you.

You will develop skills that are highly sought-after by employers:

• logical and analytic abilities
• data analysis
• practical problem-solving

Our graduates

Many recent graduates have been employed by large firms in the financial sector. Others have gone into fields including:

• software engineering
• the civil service

Further study is also a popular option. You can progress from this programme into masters or PhD level study in mathematics, or apply your mathematical training to postgraduate study in another subject.

We regularly invite alumni back to share their experiences and showcase the range of careers available to you.

Enhance your CV

Within the School of Mathematics, you will have many opportunities to develop your skills and enhance your CV. For example:

• Share your love of mathematics by working with the wider community as a member of our Outreach Team.
• Join our team of Student Ambassadors and enthuse prospective students.
• Become a MathPALS leader and support Year 1 students.
• Apply for a project scholarship and work with a lecturer during the summer.

Employability support

You will also be able to access the School’s weekly employability events including:

• presentations from industry employers
• alumni careers showcases
• useful workshops to help you prepare for applying to internships, jobs and further study

Entry requirements

Standard entry requirement.

The standard entry requirement is:

• SQA Highers: AAAAA (achievement by end of S5 preferred). BBB must be achieved in one year of S4-S6.
• A Levels: A*AA - A*AB in one set of exams.
• IB : 38 points with 766 at HL - 34 points with 765 at HL.

Minimum entry requirement

The minimum entry requirement for widening access applicants is:

• SQA Highers: AABB by end of S6. BBB must be achieved in one year of S4-S6.
• A Levels: A*AB.
• IB : 32 points with 765 at HL.

More information for widening access applicants

Required subjects

The grades used to meet our entry requirements must include:

• SQA : Highers: Mathematics at A. Higher Applications of Mathematics is not accepted in place of Higher Mathematics. Advanced Higher Mathematics is recommended. Your Mathematics qualifications must have been achieved no more than two academic years prior to entry. National 5s: English at C.
• A Levels: Mathematics at A*. Your Mathematics qualifications must have been achieved no more than two academic years prior to entry. GCSEs: English at C or 4.
• IB : HL: Mathematics (Analysis and approaches only) at 7. Your Mathematics qualifications must have been achieved no more than two academic years prior to entry. SL: English at 5.

Find out more about entry requirements

International applicants

We welcome applications from students studying a wide range of international qualifications.

Entry requirements by country

Mature applicants

We welcome applications from mature students and accept a range of qualifications.

Mature applicant qualifications

For direct entry to second year the standard requirements must be exceeded, including the following:

• SQA Advanced Highers: AAA to include Mathematics. Your Mathematics qualifications must have been achieved no more than two academic years prior to entry. One further science subject is recommended.
• A Levels: A*AA in one set of exams to include Mathematics at A* and Further Mathematics at A. Your Mathematics qualifications must have been achieved no more than two academic years prior to entry.

IB : 38 points with 766 at HL to include Mathematics (Analysis and approaches only) at 7. Your Mathematics qualifications must have been achieved no more than two academic years prior to entry*.

(Revised 02/04/2024 to remove recommendation for Further Mathematics.)

Other entry pathways

Entry to many degrees in Science & Engineering is possible via other qualifications (eg HNC/D, Access, SWAP).

• Science & Engineering applications

English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency at a level that will enable you to succeed in your studies.

SQA , GCSE and IB

For SQA , GCSE and IB students, unless a higher level is specified in the stated entry requirements, a pass is required in English at the following grades or higher:

• SQA National 5 at C
• GCSE at C or 4
• Level 2 Certificate at C
• IB Standard Level at 5 (English ab initio is not accepted for entry)

English language tests

We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 5.5 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced ( CAE ) / C2 Proficiency ( CPE ): total 176 with at least 162 in each component.
• Trinity ISE : ISE II with distinctions in all four components.
• PTE Academic: total 62 with at least 54 in each component.

We also accept a wider range of international qualifications and tests.

Unless you are a national of a majority English speaking country, your English language qualification must be no more than three and a half years old from the start of the month in which the degree you are applying to study begins. If you are using an IELTS , PTE Academic, TOEFL or Trinity ISE test, it must be no more than two years old on the first of the month in which the degree begins, regardless of your nationality.

We normally make offers to the highest qualified applicants. If competition for places is high this may mean that offers will only be made to applicants who are predicted, or who have achieved, above the single set of grades or the upper grade level in a range. Any conditional offer made may require you to achieve grades above the upper grade level. Therefore, achieving the top of our standard entry requirements does not guarantee a place on the relevant degree.

Please apply for only one degree in the School of Mathematics as we are only able to consider one application to this subject area. You will have the opportunity to switch between programmes in later years provided the required courses have been passed.

Discover Uni data

This information is part of a government initiative to enhance the material that higher education institutions provide about their degree programmes.

It is one of many sources of information which will enable you to make an informed decision on what and where to study.

Please note that some programmes do not have Discover Uni data available.

Fees, costs and funding

Tuition fees.

Tuition fees for BSc Mathematics

Additional costs

You should expect to buy the necessary textbooks for some components of your programme.

For more information on how much it will cost to study with us and the financial support available see our fees and funding information.

Fees and funding

• Have a query about undergraduate study?
• Send an enquiry

Degrees in Mathematics

9 degrees in mathematics.

• Applied Mathematics (MMath) G121
• Applied Mathematics (BSc) G120
• Mathematics (MMath) G101
• Mathematics (BSc) G100
• Mathematics (MA) G102
• Mathematics and Business (BSc) GN11
• Mathematics and Music (BSc) GW13
• Mathematics and Physics (BSc) GF13
• Mathematics and Statistics (BSc) GG13

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• How to apply
• Why choose Mathematics

More information

Search the degree finder.