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, providing students with a broader and deeper understanding of several core areas of pure mathematics.
Read full overview

The MSc Pure Mathematics offers a modern research-oriented taught course, providing students with a broader and deeper understanding of several core areas of pure mathematics that are of strong current interest and with a solid foundation for a career in research in pure mathematics.  The programme covers a wide range of topics in algebra, analysis and number theory.

Key facts

  • The course is informed by the research interests of the members of the research groups, Algebra and 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 60 full-time academic staff.
  • In the latest independent research assessment the Research Excellence Framework (REF), the school ranked eighth in the UK in terms of research power across the three subject areas within the School of Mathematical Sciences (pure mathematics, applied mathematics, statistics and operational research).
  • For more information please visit the school's website.

International Student Satisfaction Awards 2014

Second place ranking

The University of Nottingham has been ranked amongst the top universities in the UK for international student experience.

Nottingham enters the league table at number two in the International Student Satisfaction Awards 2014 and is one of only five UK universities to receive a rating of ‘outstanding’. The rankings are compiled by StudyPortals, an independent study choice platform covering more than 1400 universities in 40 European countries.


Course details

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

Part 1 - 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.

The paired modules are:

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

Please find below a full list of course modules:

Group 1

Students must take a 120 credits from the group 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


  • Advanced Group Theory (20 credits)
  • Advanced Linear Analysis (20 credits)
  • Algebraic Geometry (20 credits)
  • Algebraic Number Theory (20 credits)
  • Combinatorial Group Theory (20 credits)  
  • Complex Analysis (20 credits)
  • Foundations of Advanced Analysis (20 credits)
  • Further Topics in Analysis (20 credits)
  • Further Topics in Rings and Modules (20 credits)
  • Higher Number Theory (20 credits)

Part 2 - dissertation

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 


Students 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 

Further Topics in Rings and Modules


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 G14FAA 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 


Advanced Linear Analysis 



Advanced Group Theory

Advanced Linear Analysis

Algebraic Geometry

Combinatorial Group Theory

Complex Analysis

Elliptic Curves

Foundations of Advanced Analysis

Further Topics in Analysis

Further Topics in Rings and Modules

Galois Theory

Higher Number Theory

Pure Mathematics Dissertation

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 have announced new postgraduate loans of up to £10,000 for students studying a taught or research masters course commencing in September 2016/17.

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.

International and EU students

The University of Nottingham offers a range of masters scholarships for international and EU students from a wide variety of countries and areas of study.

Applicants must receive an offer of study before applying for our scholarships. Please note the closing dates of any scholarships you are interested in and make sure you submit your masters course application in good time so that you have the opportunity to apply for them.

The International Office also provides information and advice for international and EU students on financing your degree, living costs, external sources of funding and working during your studies.

Find out more on our scholarships, fees and finance webpages for international applicants.



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 2015, 96% of postgraduates in 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 £28,320 with the highest being £35,000.*

*Known destinations of full-time home postgraduates 2014/15. Salaries are calculated based on 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.

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

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Dr Nikolaos Diamantis
School of Mathematical Sciences
The University of Nottingham
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