maths phd edinburgh

A unique approach in doctoral training linking mathematicians with scientists and engineers

THE PROGRAMME

MAC-MIGS is a prestigious EPSRC-funded PhD programme in Mathematical Modelling, Analysis and Computation,  run jointly by Edinburgh and Heriot-Watt universities, as part of the Maxwell Institute Graduate School, that offers fully-funded scholarships.

MAC-MIGS offers its PhD students an intensive 4-year training and research programme that equips them with the skills needed to tackle challenges in the formulation, analysis and implementation of state-of-the-art mathematical and computational models and methods. 

RECENT AND Upcoming Events

Mac-migs-amsterdam/utrecht workshop on scientific computation, statistics and pdes, mac-migs deep dive on stochastic partial differential equations (12th/13th march), mac-migs deep dive on quantum machine learning (5th/6th june), latest news from the programme, industrial sandpits: 21st and 28th october 2022, 5 november 15:00-16:30 - this is what we do event 1, mac-migs student andrés miniguano-trujillo wins the first place prize at the 13th aimms-mopta optimization modelling competition .

At the end of the programme you will be on your way to becoming a leader of your field – in business , as an entrepreneur or as a future academic – but along the way you will be able have a laugh with your fellow students and explore some of the stimulating cultural, social and recreational opportunities provided by Edinburgh and Scotland.

OUR INDUSTRY PARTNERS

As a MAC-MIGS student, you will have many opportunities to work with our Industrial Partners .  These range from afternoon events such as our Sandpits, where you will find out how mathematics can be used to tackle real-world problems, through semester-long group projects working directly with our Partners, to full PhDs co-funded by industry.  These collaborations provide excellent training and engagement opportunities, whatever your future career path.

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Edinburgh Hodge Institute

Welcome to the Hodge Institute

BW version with names . Atiyah Portrait Gallery .

We are the algebra, geometry, number theory and topology research groups in the School of Mathematics at the University of Edinburgh. Together we have around 20 permanent faculty, and a large number of PhD students and post-docs. We run several weekly seminars, together with many working groups and the SMSTC graduate training programme. Edinburgh has a rich mathematical history, which has been turned into a mathematical map of Edinburgh by Sophie Powell-Hall.

In general, our work traverses algebraic geometry, algebraic number theory, algebraic topology, category theory, noncommutative algebra, representation theory. Specific research interests include:

• Algebraic Geometry related to neighbouring fields: Combinatorics, Commutative Algebra, Gauge Theory, Mathematical Physics, Homotopy theory, Symplectic Geometry
• Birational Geometry, Positivity properties of divisors
• Category Theory and its Applications
• Derived Categories and Moduli Spaces
• Derived Algebraic Geometry
• Homological Commutative Algebra
• Knots, Links and Braids
• Noncommutative Algebraic Geometry
• Noncommutative Ring Theory
• Representation Theory related to: Combinatorics, Lie theory, Mathematical Physics
• Topology of Manifolds
• Toric and tropical geometry

Agata Smoktunowicz has won a European Mathematical Society Prize, the Whitehead Prize of the London Mathematical Society, the Whittaker Prize of the Edinburgh Mathematical Society and the Wacław Sierpiński Prize of the Polish Academy of Sciences, and also gave an invited lecture at the 2006 International Congress of Mathematicians. She was awarded an ERC advanced investigator grant in 2013. Iain Gordon was awarded the LMS Berwick Prize in 2005, was an EPSRC Leadership Fellow 2008-2013, and was an invited speaker at the 2010 International Congress of Mathematicians. Jon Pridham held an EPSRC 5-year Fellowship, ending in 2016. In 2013, Arend Bayer won an ERC starting grant. In 2015, David Jordan won an ERC starting grant and Arend Bayer won the Cambridge University Adams Prize. In 2016, Arend Bayer was awarded the Whitehead Prize of the London Mathematical Society and the Whittaker Prize of the Edinburgh Mathematical Society. Nick Sheridan and Ben Davison both hold Royal Society University Research Fellowships, and Ben Davison also holds an ERC starting grant. In 2018, Arend Bayer won an ERC consolidator grant. In 2019, the London Mathematical Society awarded a Whitehead Prize to Nick Sheridan and a Berwick Prize to Clark Barwick. In 2020, Milena Hering was awarded an LMS Emmy Noether Felowship and Nick Sheridan was awarded a Leverhulme Prize. Ben Davison was awarded the Whitehead Prize of the London Mathematical Scoiety in 2020 and the Whittaker Prize of the Edinburgh Mathematical Society in 2021.

In 2018, a group at the Hodge Institute, together with researchers in Glasgow and Sheffield, was awarded the EPSRC programme grant Enhancing Representation Theory, Noncommutative Algebra and Geometry.

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.

• Schools & departments

School of Mathematics PhD Studentships

The School of Mathematics is able to provide PhD scholarships for up to 20 new students per academic year.

These PhD studentships will pay a stipend at the equivalent rate to that offered by UKRI (in the 2021/22 academic year this will be £15609pa) plus either Home or overseas tuition fees.

Eligible applicants will automatically be considered for this scholarship, this does not require a separate scholarship application.

Deadline Date:  31 January 2021

Further information

School of Mathematics

Contact: [email protected]

This article was published on 2024-05-29

• Schools & departments

Support during your MSc

Computational applied mathematics, financial mathematics, operational research.

• School of Mathematics
• Studying Here

Postgraduate Taught Programmes

Through our MSc programmes you will develop a wide range of applicable mathematical, statistical, computing and personal skills, leading to exciting careers or further study.

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 for 2025 entry are now open, and more details can be found on the  Martingale Foundation website .

If you have any queries about postgraduate taught study in the School of Mathematics please get in touch with us at [email protected] .

• 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.

(Revised 15 April 2024 to remove the ‘Only apply to one Mathematics programme’ section from the introduction)

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 (2024/25)

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 65 with at least 54 in each component. We do not accept PTE Academic Online.*

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.

(*Revised 24 May 2024 to change PTE Academic requirement from total 62 with at least 54 in each component, and to clarify that we do not accept PTE Academic online.)

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?
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Degrees in Mathematics

9 degrees in mathematics.

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

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More information

Search the degree finder.