Pure Mathematics MSc


Fact file

MSc Pure Mathematics
1 year full-time
Entry requirements
2:1 (upper second class honours degree or international equivalent) in mathematics, or a closely related subject, with substantial pure mathematics content.
Other requirements
6.0 (no less than 5.5 in any element)

If these grades are not met, English preparatory courses are available
Start date
University Park Campus
Tuition fees
You can find fee information on our fees table.


This course offers a modern research-oriented taught course covering a wide range of topics in algebra, analysis and number theory. It provides students with a broader and deeper understanding of several core areas of pure mathematics that are of strong current interest. On completion, it offers a solid foundation for a career in research in pure mathematics.
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Key facts

  • The course is informed by the research interests of the members of the research groups Algebra, Analysis, and Number Theory and Geometry.
  • The School of Mathematical Sciences is one of the largest and strongest mathematics departments in the UK, with over 70 full-time academic staff.
  • The Research Excellence Framework (REF) 2014 results place the School in the top 10 nationally within Mathematical Sciences for 'research power' and 'research quality'; with 32% of its research recognised as world-leading and a further 56% as internationally excellent.
  • The research environment was classified as 75% world-leading in vitality and sustainability, with the remaining 25% internationally excellent, reflecting the outstanding setting the School provides for its academic staff as well as its postdoctoral and postgraduate researchers.
  • Ranked 8th in the UK for three subject areas within the School, namely pure mathematics, applied mathematics, statistics and operational research.
  • The School scored 94% for Student Satisfaction in the 2017 National Student Survey.

For more information, please visit the School's website.

Academic English preparation and support

If you require additional support to take your language skills to the required level, you may be able to attend a presessional course at the Centre for English Language Education, which is accredited by the British Council for the teaching of English in the UK. Students who successfully complete the presessional course to the required level can progress to postgraduate study without retaking IELTS or equivalent. You could be eligible for a joint offer, which means you will only need to apply for your visa once.


Course details

The course comprises 180 credits, split across 120 credits of taught modules and a 60-credit research project. 

Taught modules

This consists of taught modules of which students must take up to 120 credits worth. Central to the course are three pairs of modules each consisting of an autumn and a spring module. Students must choose at least one such pair of modules. Each pair provides a substantial foundation in analysis, algebra (in particular group theory) and number theory, respectively.

Group 1

Students must take a 120 credits from the group listed under 'Modules' below. This must include both modules from at least one of the following pairs:

  • Foundations of Advanced Analysis and Further Topics in Analysis
  • Advanced Group Theory and Combinational Group Theory
  • Higher Number Theory and Algebraic Number Theory


During the summer period, you will conduct an independent research project under the supervision of academic staff, which is worth 60 credits.

Course Structure

The MSc Pure Mathematics is offered on a full-time basis over one year and is designed for students with a degree in Mathematics with a substantial component in pure mathematics. 

Students should have a strong interest in pure mathematics and specifically they should have a good background in at least two to three of the following subject areas: algebra, number theory, group theory or analysis.

Modules are mainly delivered through lectures and example and/or problem classes for smaller groups. You will typically be assessed by a combination of examination, coursework and a class test. 

Prerequisite Information

Specific prerequisites and recommended books, where appropriate, are listed below for all the taught modules on the course. 

Semester 1

Foundations of Advanced Analysis

You should have a good background in real analysis.

  • Sutherland; Metric and Topological Spaces 

Advanced Group Theory

Basic knowledge in algebra and group theory.

  • J B Fraleigh; A First Course in Abstract Algebra
  • W Ledermann & A J Weir; Introduction to group theory (2nd edition, Longman Mathematical Series) 

Algebraic Geometry

Good math background in algebra and commutative ring theory.

  • W. Fulton; Algebraic Curves 
  • M Atiyah, R Macdonald; Introduction to Commutative Algebra 

Complex Analysis

A good first mathematical course in complex analysis and solid background in real analysis as covered in J W Brown; Complex variables and applications.

  • L V Ahlfors; Complex analysis: an introduction to the theory of analytic functions of one complex variable 

Higher Number Theory

A solid maths back ground in basic number theory (factorisation, Diophantine equations, classical theorems, multiplicative arithmetic functions, perfect numbers and Mersenne numbers).

  • K Rosen; Elementary number theory and its applications
  • K Ireland, M Rosen; A Classical Introduction to Modern Number Theory 
  • F Gouvêa; p-adic numbers: an introduction

Semester 2

Further Topics in Analysis

A solid background in metric and topological spaces covering completeness etc. as covered in Foundations of Advanced Analysis and a solid knowledge of linear algebra.

  • Bollobás, Béla; Linear analysis: an introductory course 

Algebraic Number Theory

A solid background in advanced number theory, algebra, rings and modules and Galois theory.

  • S Lang; Algebraic Number Theory 

Combinatorial Group Theory

A solid background in group theory.

  • D L Johnson; Presentations of Groups


The modules we offer are inspired by the research interests of our staff and as a result may change for reasons of, for example, research developments or legislation changes. This list is an example of typical modules we offer, not a definitive list.



UK/EU Students 

Tuition Fees

Information on current course tuition fees can be found on the University finance pages.

Postgraduate loans

The government offers loans of up to £10,280 for students studying a taught or research masters course commencing in September 2017.

These loans will be a contribution towards the costs associated with completing a postgraduate masters course and can be used towards tuition fees or living costs as you decide. The loan is non means tested and will be paid directly to you, the student, rather than the University.

If you are a home student or have UK residential status you will be eligible for a government loan and in some cases EU students may also be eligible.

Full information can be found at the postgraduate loan page on the student services website. 

Graduate School

The Graduate School website at The University of Nottingham provides more information on internal and external sources of postgraduate funding.

International Students

Tuition Fees

Information on current course tuition fees can be found on the University finance pages.

School Scholarships for UoN UK alumni

For 2018-19 entry, 10% Alumni scholarships may be offered to former University of Nottingham graduates who have studied at the UK campus.

Government loans for masters courses

The Government offers postgraduate student loans of up to £10,609 for students studying a taught or research masters course. Applicants must ordinarily live in England or the EU. Student loans are also available for students from Wales, Northern Ireland and Scotland.

International and EU students

Masters scholarships are available for international and EU students from a wide variety of countries and areas of study. You must already have an offer to study at Nottingham to apply. Please note closing dates to ensure your course application is submitted in good time.

Information and advice on funding your degree, living costs and working while you study is available on our website, as well as country-specific resources.



Graduates of our mathematics MScs have gone into:

  • Industry
  • Business
  • Commerce
  • Statistics (environment, forensic, government, medical)
  • Medical research
  • The pharmaceutical industry
  • Biometrics
  • PhD study  

Average starting salary and career progression

In 2016, 89% of postgraduates from the School of Mathematical Sciences who were available for employment had secured work or further study within six months of graduation. The average starting salary was £25,933, with the highest being £35,000.*

*Known destinations of full-time home postgraduates 2015/16. Salaries are calculated based on the median of those in full-time paid employment within the UK.

Career prospects and employability

The University of Nottingham is consistently named as one of the most targeted universities by Britain’s leading graduate employers** and 
can offer you a head-start when it comes to your career. 

Those who take up a postgraduate research opportunity with us will not only receive support in terms of close contact with supervisors and 
specific training related to your area of research, you will also benefit from dedicated careers advice from our Careers and Employability Service

Our Careers and Employability Service offers a range of services including advice sessions, employer events, recruitment fairs and skills 
workshops – and once you have graduated, you will have access to the service for life.

** The Graduate Market 2013-2016, High Fliers Research.

Explore it - Virtual Nottingham

This online prospectus has been drafted in advance of the academic year to which it applies. Every effort has been made to ensure that the information is accurate at the time of publishing, but changes (for example to course content) are likely to occur given the interval between publishing and commencement of the course. It is therefore very important to check this website for any updates before you apply for the course where there has been an interval between you reading this website and applying.

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Dr Nikolaos Diamantis
School of Mathematical Sciences
The University of Nottingham
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