Pure Mathematics MMath (Hons)
2017 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 some of these fascinating areas of research.

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 degree.

Applications for 2017 entry for this course have now closed, see which courses are available for the upcoming academic year.

UCAS code


Course type

Master in Mathematics (Integrated Masters degree)

Course duration

Five years full time

Entry requirements

SQA Highers

AAAB, including A in Mathematics and an A or B grade in one of the following:

  • Biology
  • Chemistry
  • Computing Science or equivalent
  • Geography
  • Geology
  • Physics
  • Psychology.
GCE A-Levels AAA, including A in Mathematics.
IB points 36, including HL6 in Mathematics.

Well-qualified school leavers may be able to apply for admission directly into the second year of this course, and others may be interested in the Fast Track degree route. Find out more about direct entry to second year and Fast Track for Mathematics.

For degrees combining more than one subject, the subject with the higher entry requirements determines the grades you need. You will also need to meet any further subject specific entrance requirements as outlined on their pages.

Find out more about international entry requirements.

Applications for 2017 entry for this course have now closed, see which courses are available for the upcoming academic year.

Do I need to have studied this subject before?

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

Faculty entry requirements

You must also meet the Faculty of Science minimum qualifications. These vary depending on which qualifications you hold.

Other qualifications

Passes in other examinations at equivalent levels and subjects may be accepted by the Dean of the Faculty.

Find out more about Faculty of Science entry requirements.

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 (e.g. complex numbers, matrices, vectors, differential equations) in preparation for more specialist study at Honours level.

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

  • group theory
  • fractal geometry
  • measure and ergodic theory
  • Galois 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 may be able to apply for admission directly into the second year of this course, and others may be interested in the Fast Track degree route. Find out more about direct entry to second year and Fast Track for Mathematics

Students can also take Mathematics as a standard four-year BSc degree.

Find out more about studying Mathematics at St Andrews.


In the first two years of your degree (known as sub-honours) 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 one first-year compulsory Mathematics module.

  • Mathematics: introduces ideas, methods and techniques required for applying mathematics in the physical sciences or for further study in mathematics.

Students who do not possess at least a B at Advanced Higher or A-Level Mathematics will need to take Introductory Mathematics in their first semester before taking the compulsory Mathematics module. 

  • Introductory Mathematicsdesigned for students who do not meet the entry requirements for the Mathematics module above. Provides a secure base in elementary calculus.

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

  • Linear Mathematics: builds on existing knowledge of matrices and systems of linear equations.
  • Analysis: introduces key concepts of real analysis: limit, continuity and differentiation.
  • Multivariate Calculus: extends basic calculus in a single variable to the setting of real functions of several variables.
  • Combinatorics and Probability: covers combinatorics and finite sets and also the study of probability.
  • Abstract Algebra: explores the key concepts of modern abstract algebra: groups, rings and fields.
  • Vector Calculus: examines the fundamental techniques that are used throughout the mathematical modelling of problems arising in the physical world such as grad, div and curl.
  • Mathematical Modelling: investigates the translation of physical problems into mathematics.
  • Statistical Inference: introduces mathematical models of randomness.

If you decide to take Pure Mathematics in your final three years, you choose from a wide variety of advanced options, including modules in complex analysis, combinatorics, symbolic computation, functional analysis and sampling theory.

Here is a sample of Honours modules which have been offered in previous years:

  • Group Theory
  • Fractal Geometry
  • Measure and Ergodic Theory.

In fifth year, you will be able to take Masters-level modules. In the past, these have included:

  • Advanced Combinatorics
  • Semigroups
  • Galois Theory
  • Advanced Data Analysis
  • Graph Theory. 

In your final year, students also undertake an advanced project in Pure Mathematics on a topic chosen from an approved list. You will be required to investigate the topic in some depth, submit a report and give a presentation.

The modules listed here are the compulsory modules that students must take 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. A full list of all modules currently available can be found in the module catalogue.


Teaching format

In first year, teaching for each module centres on a daily lecture (100 to 150 students) and a weekly small group tutorial (5 to 10 students) where students undertake exercises and discuss each week’s topics. In addition, computer labs are held once a week for each module to assist with both IT and problem solving skills.

In second year, each module typically comprises five lectures (100 to 250 students), one tutorial (8 to 12 students), one computer lab (25 to 60 students), and one examples class per fortnight.

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. 


Progress is monitored through tutorial assignments and almost all of the modules are assessed by a balanced combination of coursework and written exams.

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

Coursework takes the form of essays, along with other kinds of assessed work including oral presentations and group projects. The School provides feedback on every assessment, with a view to improving your performance in future.


Tuition fees for 2017 entry

Scotland and EU £1,820
Rest of the UK £9,250
Overseas £20,570

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 in 2017.

Funding and scholarships

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

Find out more about undergraduate scholarships.

Your future


The demand for mathematically-able graduates often exceeds the supply, so the career prospects for graduates in Mathematics from St Andrews are excellent. Clear logical thinking, deductive reasoning, confidence in data handling, and IT skills are attributes that are highly prized by employers.

Around one third of Mathematics graduates go on to pursue postgraduate qualifications either in the UK or abroad, and develop research careers. Others gain employment in a variety of sectors including:

  • merchant banking
  • insurance
  • teaching
  • civil service
  • financial service organisations
  • computer consultancies.

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

The University is delighted to offer undergraduates a number of exciting opportunities to apply to spend a semester or year abroad as part of a St Andrews degree programme. St Andrews is partnered with large and small institutions, ancient and young, across the globe. What unites all of our programmes is the quality of the academic provision, ensuring that participation in a St Andrews Study abroad programme opens the door to a new and valuable academic experience at another world-class institution. Study Abroad for credit is permitted on existing University-approved programmes only.

Student life

From the outset, 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 ensures a community feel amongst students from first year onwards.

Students of Mathematics may be interested in joining the Mathematics 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 split between 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 the campus is located around town, walking around you encounter ancient and modern buildings and areas of greenery and seaside which provide a rich, beautiful backdrop to learning. If you want a change of scenery, St Andrews' position near surrounding towns and cities such as Anstruther, Dundee and Edinburgh make it ideal for getting to know more about Scotland. 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 3774
Email: maths@st-andrews.ac.uk 

Mathematics and Statistics website