MSc in Pure Mathematics


Program Description

The MSc provides you with in-depth knowledge of algebra, number theory, group theory and analysis. Your interest in mathematical theorems will be fuelled by studying optional modules in topics ranging from Elliptic Curves to Linear Analysis.

You'll learn from mathematicians with research interests ranging from algebraic geometry to applied analysis. This is reflected in the wide range of previous dissertation projects. They have included a broad spectrum of subjects, including:

  • Homotopic topology
  • The sieve of Eratosthenes
  • Reduced models for ferromagnetic materials.

Teaching is influenced by the research work of the Algebra and Analysis and the Number Theory and Geometry groups. Some of the topics studied by group members include:

  • Analytic number theory
  • Arithmetic, algebraic and anabelian geometry
  • Categorical representation theory
  • Data and image analysis

The master's course provides flexibility for a range of careers whether your interests lie in pure or applied maths. Many of our graduates go on to study a PhD. Others use it more widely for jobs in industry, teaching, government and finance.


Why choose this course?

  • One-to-one supervision by faculty staff during dissertation project
  • No programming assumed yet some staff are programming experts who contribute to Sage and other PC algebra systems
  • Flexibility to focus by specialising in one of the strands of algebra, analysis or number theory and geometry
  • Top 10 UK ranking research power and quality. Many 4* level papers in pure maths featured in the REF submission (Research Excellence Framework 2014)
  • Optional modules allow you to tailor the degree to suit your interests.
  • Acclaimed lecturers regularly contribute to articles in mathematical journals including Compositio Mathematica, Crelle's Journal.

Course content

You will study six modules across the year, split between three modules per semester, plus a dissertation. Students must take 120 credits worth of optional modules and a dissertation worth 60 credits.

Central to the course are pairs of modules each consisting of autumn and a spring module. In 2019/20, students selected modules from at least one of the following pairs, plus additional optional modules to suit their specific interests.

  • Advanced Group Theory and Combinational Group Theory
  • Higher Number Theory and Algebraic Number Theory

By completing one of these topic combinations, you will gain advanced knowledge and expertise in one of the key areas of group theory or number theory.


Core modules

  • Pure Mathematics Dissertation

Choose one combination from the following:

  • Advanced Group Theory
  • Combinatorial Group Theory


  • Higher Number Theory
  • Algebraic Number Theory

Remaining optional modules to be chosen from:

  • Advanced Group Theory
  • Advanced Linear Analysis
  • Algebraic Number Theory
  • Combinatorial Group Theory
  • Elliptic Curves
  • Foundations of Advanced Analysis
  • Further topics in Rings and Modules
  • Higher Number Theory

Learning and assessment

How you will learn

  • Lectures
  • Problem classes
  • Tutorials

How you will be assessed

  • Examinations
  • Coursework
  • Dissertation

You will be awarded the Master of Science Degree provided you have successfully completed the taught stage by achieving a weighted average mark of at least 50%, with no more than 40 credits below 50% and no more than 20 credits below 40%.

You must achieve a mark of at least 50% in the dissertation.

Candidates for the master's degree who fail to reach the required standard for the award may be awarded a Postgraduate Diploma or a Postgraduate Certificate under certain circumstances.

Contact time and study hours

The number of formal contact hours and class sizes varies depending on the optional modules you are studying. As a guide, in the Autumn and Spring semesters, you will typically spend around 12 hours per week between Monday and Friday in classes.

You will work on your research project between June and September, usually based at the University.

Teaching is provided by academic staff within the School of Mathematical Sciences. The majority of modules are typically delivered by Professors, Associate and Assistant Professors. Additional support in small group and practical classes may include PhD students and post-doctoral researchers.

Programming skills are not required for the course, however, several staff members are experts in computational aspects, including Sage to which some regularly contribute.

The majority of your lecturers and tutors will be based within the mathematics building. This means if you need to get in touch with them during office hours, they can be contacted easily as they are close by.

Entry requirements

All candidates are considered on an individual basis and we accept a broad range of qualifications. The entrance requirements below apply to 2021 entry.

Home/ UK students

Undergraduate degree 2:1 in mathematics, or a closely related subject with substantial pure mathematics content.

EU/ International students

Undergraduate degree 2:1 (or international equivalent) in mathematics, or a closely related subject with substantial pure mathematics content
International and EU equivalents We accept a wide range of qualifications from all over the world.
IELTS 6.0 (no less than 5.5 in any element)
English language requirements As well as IELTS (listed above), we also accept other English language qualifications. This includes TOEFL iBT, Pearson PTE, GCSE, IB and O level English.

English language support

If you need support to meet the required level, you may be able to attend a presessional course. Our Centre for English Language Education is accredited by the British Council for the teaching of English in the UK.

For presessional English courses, you must take IELTS for UKVI to meet visa regulations.

If you successfully complete your presessional course to the required level, you can then progress to your degree course. This means that you won't need to retake IELTS or equivalent.

Alternative qualifications

We recognise that applicants have a variety of experiences and follow different pathways to postgraduate study.

We treat all applicants with alternative qualifications on an individual basis. We may also consider relevant work experience.

If you are unsure whether your qualifications or work experience are relevant, contact us.

laptop, computer, browser

Where you will learn

University Park Campus

University Park Campus covers 300 acres, with green spaces, wildlife, period buildings and modern facilities. It is one of the UK's most beautiful and sustainable campuses, winning a national Green Flag award every year since 2003.

Most schools and departments are based here. You will have access to libraries, shops, cafes, the Students’ Union, sports village and a health centre.

You can walk or cycle around campus. Free hopper buses connect you to our other campuses. Nottingham city centre is 15 minutes away by public bus or tram.

Dedicated MSc study room

There is a dedicated workroom for masters students, based within the School of Mathematical Sciences.  It is equipped with desktop computers, this provides a quiet study space.


Careers advice

We offer individual careers support for all postgraduate students.

Expert staff can help you research career options and job vacancies, build your CV or résumé, develop your interview skills and meet employers.

More than 1,500 employers advertise graduate jobs and internships through our online vacancy service. We host regular careers fairs, including specialist fairs for different sectors.

Job prospects

Graduate destinations

Graduates go on to pursue a variety of careers. Some enter roles that have a direct relationship with pure mathematics including cryptography and statistical programming. Others choose to pursue a PhD in mathematics directly related to pure mathematics or even in applied mathematics.

Graduate destinations include:

  • Government Communications Headquarters
  • Phastar

Career progression

97.5% of postgraduates from the School of Mathematical Sciences secured graduate-level employment or further study within 15 months of graduation. The average annual salary for these graduates was £28,131.*

* HESA Graduate Outcomes in 2020. The Graduate Outcomes % is derived using The Guardian University Guide methodology. The average annual salary is based on graduates working full-time within the UK.

Last updated Oct 2020

About the School

The Faculty of Science undertakes world-class research spanning wide-ranging topics including quantum physics, plant genomics, human imaging, sustainable chemistry, neuroscience, mathematical modellin ... Read More

The Faculty of Science undertakes world-class research spanning wide-ranging topics including quantum physics, plant genomics, human imaging, sustainable chemistry, neuroscience, mathematical modelling and beyond. We work closely with industry on the training of the next generation of scientists and collaborate worldwide to ensure our research has a major societal impact. The Faculty of Science comprises seven schools and has strong links with the School of Life Sciences and School of Veterinary Medicine and Science. Schools from within the faculty also collaborate with those from the University's other faculties to form various research centres and research institutes. Read less
Nottingham , Sutton Bonington , Nottingham + 2 More Less