Pure Mathematics MMath (Honours) 2022 entry

The MMath (Hons) in Pure Mathematics will teach you to understand complex patterns and structures, and develop the tools with which to analyse them. Whether these patterns relate to physical or biological phenomena or the structure of mathematics itself, the primary aim is to describe, categorise, and understand the processes involved.

Students of Pure Mathematics will acquire the analytical techniques, clear logical thinking and deductive reasoning necessary to explore and understand mathematical problems. In addition, there are many connections between pure mathematics and computer science, and you will be able to learn about these, if you wish. 

The MMath allows you to combine undergraduate and postgraduate study into a single five-year programme, graduating with a Masters degree. Students can also take Mathematics as a standard four-year BSc or MA degree.


The MMath in Pure Mathematics is accredited by the Institute of Mathematics and its Applications.

How to apply Register your interest

Key information

UCAS code


Course type

Master in Mathematics (Integrated Masters degree)

Course duration

Five years full time

  • Start date: 5 September 2022
  • End date: 30 June 2027

Entry requirements

These grades are the overall standards required to consider you for entry. Find out more about Standard and Minimum entry requirements using academic entry explained and see which entry requirements you need to look at using the entry requirements indicator.

    • Standard entry grades: AAAAB, including A in Mathematics
    • Minimum entry grades: AABB, including A in Mathematics
    • Standard entry grades: A*A*A, including A* in Mathematics
    • Minimum entry grades: A*AB, including A* in Mathematics
    • Standard entry grades: 38 (HL 6,6,6), including HL6 in Mathematics
    • Minimum entry grades: 36 (HL 6,5,5), including HL6 in Mathematics

We accept a wide range of qualifications for entry on to our programmes, please see our entry requirements for more information.

Direct entry to second year

Well-qualified school leavers are able to apply for direct entry to second year of this course. There is also the option to switch to direct entry on arrival at St Andrews, in consultation with your Adviser of Studies. 

International applicants

If English is not your first language, you will need to provide an English language test score to evidence your English language ability. Find out more about English language requirements.

How to apply

Do I need to have studied this subject before?

Yes, applicants are expected to have studied Mathematics at SQA Higher, GCE A-Level, or equivalent. 

General entry requirements

All applicants must have attained the following qualifications, or equivalent, in addition to the specific entry requirements for individual programmes.

  • SQA National 5 (B) in English and one SQA National 5 (B) from the following:

    • Biology
    • Chemistry
    • Computing science
    • Geography
    • Lifeskills Mathematics (A grade)
    • Mathematics
    • Physics
    • Psychology.
  • GCSE (5) in English language or English literature, and one GCSE (5) from the following:

    • Biology
    • Chemistry
    • Computing Science
    • Geography
    • Mathematics
    • Physics
    • Psychology.

Other qualifications

More information on how to apply via other entry routes or accreditation of prior learning and experience can be found on the University’s entry requirements web page.

Applying for a mathematics or statistics degree

Mathematics and Statistics at St Andrews is very popular, and the University is unable to make an offer to every applicant who meets or exceeds the entry requirements. The University seeks to recruit students who are enthusiastic about mathematics and possess the demonstrated potential to be successful. 

Entry requirements are the same for all single Honours degrees in mathematics and statistics, and the chance of receiving an offer does not depend on the degree or entry point applied for. 

Decisions are primarily based on mathematical ability and potential, as demonstrated by school qualifications and position in class or year. The School of Mathematics and Statistics does not use results from MAT or STEP. 

Applicants should, therefore, include as much detail about their mathematics results as possible on their application if available

  • Highers: band attained as well as the grade, and ideally the percentage attained for Higher Mathematics. 
  • A-Levels: grades obtained in each of the mathematics modules taken to date, if any. 
  • For guidance on other entry qualifications, please see entry requirements.

If possible, applicants should include their rank within their year and any awards they have won at school. Applicants should ask their referees to also include this information in their reference.

Applicants should also include any extra-curricular mathematical and scientific accomplishments. This can include, for example, competition results (for example, Maths Challenge and Olympiads) or previous university-level experience (for example, from summer programmes).  

Course information

The MMath (Hons) in Pure Mathematics is a five-year Integrated Masters course run by the School of Mathematics and Statistics. The course offers advanced study of Pure Mathematics at postgraduate level during your final year, allowing you to graduate with a Masters degree.

In the first two years, you will develop and reinforce your basic mathematical skills and refresh familiar material (for example, complex numbers, matrices, vectors, differential equations) in preparation for more specialist study at Honours level.

Alongside Mathematics, in the first year of your studies you will be required to study up to two additional subjects. In the second year, students only take Mathematics modules. Find out more about how academic years are organised.

At Honours and Masters level, students may select modules from a range of options on advanced and specialist specific topics. Specialist subject areas may include:

  • fractal geometry
  • Galois theory
  • group theory
  • measure and ergodic theory.

Final-year students must also undertake an advanced project on a topic chosen in consultation with teaching staff at the School of Mathematics and Statistics.

Well-qualified school leavers are able to apply for direct entry to second year of this course.

Students on this programme may apply to change to the BSc at any point during their sub-honours years or third year of study. 

The University of St Andrews operates on a flexible modular degree system by which degrees are obtained through the accumulation of credits. More information on the structure of the modules system can be found on the flexible degree structure web page.


In the first year of your degree, you will take the required modules in Mathematics alongside modules in at least one other subject. 

Find out more about the modular Scottish degree system.

Students will take between one and three first-year modules in mathematics. There is one core compulsory module, 'Mathematics', that can be studied in either semester.

  • Mathematics: introduces the ideas and techniques required for further study of mathematics or applications to other sciences.

First-year students can, in addition, take one or both of the optional modules in Pure and Applied Mathematics as well the module 'Statistics in Practice':

Mathematics and Statistics sub-honours (1000 and 2000 level) modules 2020-21 (PDF)

Students will take the following compulsory modules in their second year:

  • Abstract Algebra: explores the key concepts of modern abstract algebra: groups, rings and fields.
  • Analysis: introduces key concepts of real analysis: limit, continuity and differentiation.
  • Combinatorics and Probability: introduces counting techniques for finite structures and the behaviour of random variables.
  • Linear Mathematics: introduces the theory of vector spaces, linear independence, linear transformations and diagonalisation.
  • Mathematical Modelling: investigates the translation of physical problems into mathematics.
  • Multivariate Calculus: extends the techniques of calculus in a single variable to the setting of real functions of several variables.
  • Statistical Inference: introduces techniques for drawing inferences about population characteristics from observed data.
  • Vector Calculus: introduces the theory of scalar and vector fields and associated techniques for the modelling of problems arising in the physical world.

Mathematics and Statistics sub-honours (1000 and 2000 level) modules 2020-21 (PDF)

In the final three years, you choose from a wide variety of advanced options. Here is a sample of Honours modules which have been offered in previous years:

  • Graph Theory
  • Fractal Geometry
  • Number Theory
  • Topology.

As an MMath student, you will also be able to take Masters-level modules. In the past, these have included:

  • Advanced Combinatorics
  • Galois Theory
  • Hyperbolic Geometry
  • Measure and Probability Theory
  • Topics in Groups.

In your third, fourth and fifth years, you will choose from a range of 3000-level, 4000-level and 5000-level modules. Here are the modules offered in previous years:

In your final year, you also undertake an advanced project on a topic chosen in consultation with the teaching staff at the School of Mathematics and Statistics. You will be required to investigate the topic in some depth, submit a report and give a presentation.

The compulsory modules listed here must be taken in order to graduate in this subject. However, most students at St Andrews take additional modules, either in their primary subject or from other subjects they are interested in. For Honours level, students choose from a range of Honours modules, some of which are listed above. A full list of all modules appropriate to the programme for the current academic year can be found in the programme requirements.


Teaching format

In first year, teaching for each module centres on a daily lecture (100 to 300 students) and a weekly small group tutorial (8 to 12 students) where students undertake exercises and discuss each week’s topics. In addition, computer labs (25 to 60 students) are held once a week for each module to assist with both computing and problem solving skills.

In second year, each module typically comprises five lectures (100 to 300 students), one tutorial (8 to 12 students), and one examples class (25 to 60 students) per fortnight. Half of the modules also feature computer lab sessions (25 to 60 students).

You will develop increasing independence and initiative as you progress through your degree programme so that by third, fourth and fifth year the average teaching load drops to around ten hours of lectures and four tutorials per week, supplemented by private study. 

When not attending lectures, tutorials and computer labs, you will be expected to continue learning independently through self-study. Typically, this will involve:

  • working on individual and group projects
  • undertaking research in the library
  • preparing coursework assignments and presentations
  • preparing for examinations.

You will be taught by an experienced teaching team with expertise and knowledge of Mathematics. Postgraduate research students who have undertaken teacher training may also contribute to the teaching of tutorials, examples classes and computing classes under the supervision of the module leader.

Find contact information for all Mathematics staff on the School of Mathematics and Statistics website.

In addition to your studies in the School of Mathematics and Statistics, optional academic support is available through practical study skills courses and workshops hosted within the University.

The University’s student services team can help students with additional needs resulting from disabilities, long term medical conditions or learning disabilities. More information can be found on the students with disabilities web page.


Progress is monitored through tutorial assignments, and sub-honours modules are assessed by a balanced combination of coursework and written exams. At Honours level, modules may be assessed by written examination alone or a combination of written examination and coursework.

Examinations are held at the end of each semester during a dedicated exam diet with revision time provided beforehand.

The School aims to provide feedback on every assessment within three weeks to help you improve on future assessments.

Undergraduates at the University of St Andrews must achieve at least 7.0 on the St Andrews 20-point grade scale to pass a module. To gain access to Honours-level modules, students must achieve the relevant requisites as specified in the policy on entry to Honours and in the relevant programme requirements. Please note that some Schools offer qualified entry to Honours, and this will be clearly specified in the programme requirements. To find out the classification equivalent of points, please see the common reporting scale.

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Tuition fees for entry

Home-funded £1820
RUK (England, Wales, Northern Ireland) and Republic of Ireland £9250
Islands (Channel Islands, Isle of Man) £9250
EU and overseas £26350

For overseas students, tuition fees will be fixed at this level for the duration of your programme.

More information on tuition fees can be found on the undergraduate fees and funding page.

Accommodation fees

Find out about accommodation fees for University accommodation.

Funding and scholarships

The University of St Andrews offers a number of scholarships and support packages to undergraduate students each year.

Your future


Demand for mathematically trained graduates vastly outstrips the supply, and hence career prospects are excellent in a variety of fields.

Recruiters seek numerate graduates who are literate, think logically, write and present well, and can work with relevant technology – St Andrews degrees develop all of these skills.

A mathematics degree is recognised as a substantial achievement in a demanding discipline.

Around 30% of St Andrews graduates continue on to postgraduate study, either in mathematics or related disciplines such as computer science, finance, or physics.

The majority of the remaining graduates gain employment in areas including: 

  • technology firms or computer consultancies
  • financial services organisations (for example, Goldman Sachs, KPMG, and PwC) 
  • industry
  • insurance companies
  • merchant banks
  • the civil service
  • teaching.

The Careers Centre offers one-to-one advice to all students as well as a programme of events to assist students to build their employability skills.

Study abroad

Mathematics students may apply to participate in the University-wide St Andrews Abroad programme. For information about study abroad options, please see the study abroad site.

Student life

The University of St Andrews offers an array of events and opportunities which result in a truly unique student experience. Students participate in a range of traditions, notably, the red academic gown and the academic family, where older students adopt first-year students as ‘children’ and help guide them in a system of mentoring. These traditions, and the choice of over 150 sports clubs and student societies to choose from, ensure a community feel amongst students from first year onwards.

Students of Mathematics may be interested in joining the Mathematical Society (SUMS), a society dedicated to bringing people together who are interested in maths. They hold regular socials and informative talks from guest speakers.

The School of Mathematics and Statistics is currently located across two sites – the Mathematical Institute on the North Haugh and the Scott Lang Building at the Observatory. Most of the mathematics staff and research students can be found at the Mathematical Institute. 

The town of St Andrews itself has lots to offer. As University buildings are located throughout the town, walking around you encounter ancient and modern buildings, parks and beaches, providing a rich, beautiful backdrop to learning. Find out more about the town of St Andrews.

Find out more about student life at the University of St Andrews.


School of Mathematics and Statistics
University of St Andrews
Mathematical Institute
North Haugh
St Andrews
KY16 9SS

Phone: +44 (0)1334 46 3744
Email: maths@st-andrews.ac.uk

School of Mathematics and Statistics website


Admission to the University of St Andrews is governed by our admissions policy.

Information about all programmes from previous years of entry can be found in the archive.

Curriculum development

As a research intensive institution, the University ensures that its teaching references the research interests of its staff, which may change from time to time. As a result, programmes are regularly reviewed with the aim of enhancing students' learning experience. Our approach to course revision is described online.

Tuition fees

The University will clarify compulsory fees and charges it requires any student to pay at the time of offer. The offer will also clarify conditions for any variation of fees. The University’s approach to fee setting is described online.

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