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Postgraduate Certificate in Mathematics

This flexible course will be of interest to mathematically inclined scientists and engineers as well as to mathematicians. It offers a wide choice of modules enabling you to tailor your studies to your particular area of interest, and is applicable to work in industry, business and commerce – as well as providing a firm foundation for additional study at masters and doctorate level.

Key features of the course

  • Develops your problem-solving and decision-making capabilities.
  • A wide choice of modules enables you to tailor the course to your needs.
  • Helps you stand out in a crowded jobs market.

This certificate is the first stage of a study programme that progresses to a postgraduate diploma and finally a masters degree. You can step off at any point, or study the whole programme.


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 – 1 year
Read more about how long it takes
Study method
Distance learning
Find out more in Why the OU?
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 60 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 No current presentation
Analytic number theory I (M823)

This entry-level pure mathematics module introduces several concepts from number theory, and culminates in a proof of Dirichlet's theorem on prime numbers in arithmetic progressions.

See full description

30 No current presentation

0–601 credits from:

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

Advanced mathematical methods using the algebraic computing language Maple. Perturbation expansions, accelerated convergence, Padé approximations, asymptotic expansions, eigenvalue problems, Green’s functions.

See full description

30 No current presentation
Analytic number theory II (M829) 2

Sequel to M823, based on the second half of Apostol’s Introduction to Analytic Number Theory. Includes a proof of the prime number theorem.

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30 No current presentation
Approximation theory (M832)

This module, based on M.J.D. Powell’s ‘Approximation Theory and Methods’, will develop your understanding of the mathematics behind many methods of approximating functions and data.

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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.

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30 No current presentation
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.

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30 No current presentation
Galois theory (M838) NEW

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.

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30 No current presentation
Or, subject to the rules about excluded combinations, the discontinued modules M431, M822, M824, M826, M827, M830 and M841
1Only under exceptional circumstances may you study 60 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 20 credits from OU modules that have not been counted in any other OU qualification that has previously been awarded to you.

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 17 March 2020.

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 successful completion of the required modules you can be awarded a Postgraduate Certificate in Mathematics entitling you to use the letters PG Cert Maths (Open) after your name.

You may continue your studies and add a further 60 credits to your certificate to gain a Postgraduate Diploma in Mathematics (E23), or a further 120 credits to obtain the 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. 

Entry requirements

You should normally have a minimum of a 2:2 honours degree in mathematics or a 2:1 honours degree in a subject with a high mathematical content. Whatever your background, you should assess your suitability for our certificate by completing our diagnostic quiz.

If you’re new to postgraduate study in mathematics, start with a single module; 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 study this qualification in two years at the rate of one module per year. The minimum time to complete is one year. There is no maximum time limit for completing this qualification but we cannot guarantee that the same selection of modules will continue to be available. Not every module is presented each year.

Career relevance

Mathematics is at the heart of advances in science, engineering and technology, as well as being an indispensable problem-solving and decision-making tool in many other areas of life. It is no surprise therefore that 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 on 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.