Calculations on whiteboard

Postgraduate Diploma in Mathematics

This diploma comprises four 30-credit modules from a wide choice. Topics include analytic number theory, calculus of variations and nonlinear ordinary differential equations. Extend your understanding of areas of mathematics applicable to science, engineering and technology. It’s also the first two stages of our postgraduate mathematics programme. After this diploma, you can achieve the MSc in Mathematics by taking a further two 30-credit modules.

Key features of the course

  • Extends your understanding of key areas of mathematics, including analytic number theory, advanced calculus and differential equations
  • A wide choice of modules enables you to tailor the course to your needs
  • The opportunity to top up to our MSc in Mathematics in just one more year


Course code


  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
How long it takes
Minimum - 2 years
Read more about how long it takes
Study method
Distance learning
Course cost
See Fees and funding
Entry requirements

Find out more about entry requirements.

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Course details


To gain this qualification, you need 120 credits as follows:

30–60 credits from:
Entry-level modules Credits Next start
Calculus of variations and advanced calculus (M820)

M820 Calculus of Variations and Advanced Calculus covers functionals, Gâteaux differential, Euler–Lagrange equation, First-integral, Noether’s Theorem, Second variation/Jacobi equation and Sturm–Liouville systems.

See full description

30 07 Oct 2023
Analytic number theory I (M823)

This entry-level pure mathematics module introduces several concepts from number theory, including congruences, arithmetical functions and their averages, distributions of primes, quadratic reciprocity and Dirichlet’s theorem.

See full description

30 07 Oct 2023

60–1201 credits from:

Intermediate-level modules Credits Next start
Advanced mathematical methods (M833)

This module uses the Maple computing language to teach: perturbation expansions, accelerated convergence, Padé approximations, asymptotic expansions, eigenvalue problems, and Green’s functions.

See full description

30 07 Oct 2023
Analytic number theory II (M829) 2

This module covers the second half of Apostol’s Introduction to Analytic Number Theory and proof of the prime number theorem.

See full description

30 No current presentation
Coding theory (M836)

This module examines error-detecting and error-correcting codes built on algebraic structures, with associated encoding/decoding procedures and applicability, concluding with elements of cryptography.

See full description

30 07 Oct 2023
Fractal geometry (M835)

This module deals with the geometry of fractals, sets that are often very beautiful and contain copies of themselves at many different scales.

See full description

30 07 Oct 2023
Galois theory (M838)

This postgraduate mathematics module explores the relationship between groups and fields as described by Galois in the 19th century.

See full description

30 No current presentation
Nonlinear ordinary differential equations (M821)

The theory of nonlinear ordinary differential equations is introduced with emphasis on geometrical aspects, approximation schemes and the determination of stability and periodicity of solutions.

See full description

30 No current presentation
Or, subject to the rules about excluded combinations, the discontinued modules M431, M822, M824, M826, M827, M828, M830, M832, M841, M860, M861, MZX861, PMT600 and PMT601.
1Only under exceptional circumstances may you study 120 credits at intermediate level, i.e. without first studying an entry-level module.
2If you choose Analytic number theory II (M829), you must take Analytic number theory I (M823) first.

You should note that the University’s unique study rule applies to this qualification. This means that you must include at least 40 credits from OU modules that have not been counted in any other OU qualification that has previously been awarded to you.

Learning outcomes, teaching and assessment

The learning outcomes of this qualification are described in four areas:

  • Knowledge and understanding
  • Cognitive skills
  • Practical and professional skills
  • Key skills
Read more detailed information about the learning outcomes.

Credit transfer

For this qualification, we do not allow you to count credit for study you have already done elsewhere.

On completion

On successfully completing this course, we’ll award you our Postgraduate Diploma in Mathematics. You’ll be entitled to use the letters PG Dip Maths (Open) after your name.

You can progress from this Postgraduate Diploma in Mathematics to our MSc in Mathematics (F04).


As a student of The Open University, you should be aware of the content of the qualification-specific regulations below and the academic regulations that are available on our Student Policies and Regulations website. 

We regularly review our curriculum; therefore, the qualification described on this page – including its availability, its structure, and available modules – may change over time. If we make changes to this qualification, we’ll update this page as soon as possible. Once you’ve registered or are studying this qualification, where practicable, we’ll inform you in good time of any upcoming changes. If you’d like to know more about the circumstances in which the University might make changes to the curriculum, see our Academic Regulations or contact us. This description was last updated on 15 March 2022.

Entry requirements

You should normally have a minimum of either:

  • a 2:2 honours degree in mathematics or
  • a 2:1 honours degree in a subject with a high mathematical content.

If you don’t have such a qualification, your application will still be considered, but you may be asked to complete an entry test. Non-graduates will not normally be admitted.

Whatever your background, you should assess your suitability by completing our diagnostic quiz.

If you’re new to postgraduate study in mathematics, start with a single module: either the applied mathematics module Calculus of variations and advanced calculus (M820) or the pure mathematics module Analytic number theory I (M823).

How long it takes

  • Most students complete this qualification in four years, at the rate of one module per year.
  • The minimum time you may complete this qualification in is two years.
  • There’s no time limit for completing this qualification, but we can’t guarantee the same selection of modules will continue to be available.
  • Some modules start only once every two years.

Career relevance

Mathematics postgraduates can be found throughout industry, business and commerce, in the public and private sectors. Employers value the intellectual rigour and reasoning skills that mathematics students can acquire, their familiarity with numerical and symbolic thinking and the analytic approach to problem-solving which is their hallmark.

There are a variety of reasons for studying mathematics at postgraduate level. You may want a postgraduate qualification in order to distinguish yourself from an increasingly large graduate population. You may find that your undergraduate mathematical knowledge is becoming insufficient for your career requirements, especially if you are hoping to specialise in one of the more mathematical areas, which are becoming more sought after by employers. Or you may want to move to a PhD in Mathematics. The extent of opportunities is vast and mathematics postgraduates are equipped with skills and knowledge required for jobs in fields such as finance, education, engineering, science and business, as well as mathematics and mathematical science research.

Careers and Employability Services have more information on how OU study can improve your employability.