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Approximation theory

Approximation theory is concerned with approximating functions of a given class, or data of a given type, using functions from another, usually more elementary, class. A simple example is the problem of approximating a function such as ex by means of polynomial functions. The efficient solution of such problems is of great importance for computing such approximations, and this module will introduce the mathematical theory behind many approximation methods in common use. This intermediate-level module is based on the set book Approximation Theory and Methods by M. J. D. Powell.

Qualifications

M832 is an optional module in our:

This module can also count towards M03, which is no longer available to new students.

Module

Module code
M832
Credits

Credits

  • 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.
30
Study level
Across the UK, there are two parallel frameworks for higher education qualifications, the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ) and the Scottish Credit and Qualifications Framework (SCQF). These define a hierarchy of levels and describe the achievement expected at each level. The information provided shows how OU postgraduate modules correspond to these frameworks.
OU Postgraduate
SCQF 11
FHEQ 7
Study method
Distance learning
Module cost
See Module registration
Entry requirements

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Module details Entry requirements Module registration Study materials

What you will study

The subject of approximation theory lies at the frontier between applied mathematics and pure mathematics. Practical problems, such as the computer calculation of special functions like ex, lead naturally to theoretical problems, such as ‘how well can we approximate by a given method?’ or ‘how fast does a given algorithm converge?’.

The module is based on Approximation Theory and Methods by M. J. D. Powell (Cambridge University Press, 1981). This book provides an excellent introduction to these theoretical problems, covering the basic theory of a wide range of approximation methods

You will learn

Successful study of this module should enhance your skills in understanding complex mathematical texts, constructing solutions to problems logically and communicating mathematical ideas clearly.

Note you must study this module if you wish to take the ‘Advances in approximation theory’ topic for your Dissertation in mathematics (M840).

Teaching and assessment

Support from your tutor

Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:

  • Marking your assignments (TMAs) and providing detailed feedback for you to improve.
  • Guiding you to additional learning resources.
  • Providing individual guidance, whether that’s for general study skills or specific module content.

The module has a dedicated and moderated forum where you can join in online discussions with your fellow students. There are also online module-wide tutorials. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part. If you want to participate, you’ll likely need a headset with a microphone.

Assessment

The assessment details can be found in the facts box.

Course work includes

4 Tutor-marked assignments (TMAs)
Examination
No residential school

Future availability

Approximation theory (M832) starts every other year – in October.

This page describes the module that will start in October 2022.

We expect it to start for the last time in October 2022.

Regulations

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

    Entry requirements

    To study this module you must declare the MSc in Mathematics (or another qualification towards which the module can count) as your qualification intention.

    Normally, you should have also completed at least one of the entry modules for the MSc in Mathematics (F04), Calculus of variations and advanced calculus (M820) or Analytic number theory I (M823).

    The subject of approximation theory lies at the frontier between applied mathematics and pure mathematics, since practical problems such as how to calculate special functions on a computer lead to theoretical problems such as ‘which approximation method is best?’. Therefore you will need some familiarity with real analysis and linear algebra, such as that developed in typical undergraduate courses, and knowing the basic properties of metric spaces would also be useful.

    All teaching is in English and your proficiency in the English language should be adequate for the level of study you wish to take. We strongly recommend that students have achieved an IELTS (International English Language Testing System) score of at least 7. To assess your English language skills in relation to your proposed studies you can visit the IELTS website.

    If you have any doubt about the suitability of the module, please speak to an adviser.

    Register

    Start End England fee Register
    01 Oct 2022 Jun 2023 £1125.00

    Registration closes 08/09/22 (places subject to availability)

    Register
    October 2022 is the final start date for this course. For more information, see Future availability.

    Future availability

    Approximation theory (M832) starts every other year – in October.

    This page describes the module that will start in October 2022.

    We expect it to start for the last time in October 2022.

    Additional costs

    Study costs

    There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

    Study weekend

    This module has an optional study weekend. You must pay £60 for tuition and refreshments. You must also pay for your travel to and from the venue, and accommodation if you need it.

    Due to the ongoing pandemic, we may replace face-to-face events with online alternatives.

    Ways to pay for this module

    We know there’s a lot to think about when choosing to study, not least how much it’s going to cost and how you can pay.

    That’s why we keep our fees as low as possible and offer a range of flexible payment and funding options, including a postgraduate loan, if you study this module as part of an eligible qualification. To find out more, see Fees and funding.

    Study materials

    What's included

    You’ll have access to a module website, which includes:

    • a week-by-week study planner
    • course-specific module materials
    • audio and video content
    • assessment details and submission section
    • online tutorial access
    • access to student and tutor group forums.

    You’ll be provided with printed materials covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques that are contained in the set book. You will need to obtain your own copy of the set book.

    You will need

    A scientific calculator.

    Computing requirements

    You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11), or macOS (10.15 or higher).

    Any additional software will be provided or is generally freely available.

    To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).

    Our module websites comply with web standards, and any modern browser is suitable for most activities.

    Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

    It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop as described above.

    Materials to buy

    Set books

    • Powell, M.J.D. Approximation Theory and Methods Cambridge University Press £57.99 - ISBN 9780521295147 This book is Print on Demand and can be ordered through any bookseller. Please allow at least 2 weeks for receipt following order.

    If you have a disability

    The material contains small print and diagrams, which may cause problems if you find reading text difficult. You will also need to be able to use a scientific calculator.

    If you have particular study requirements please tell us as soon as possible, as some of our support services may take several weeks to arrange. Visit our Disability support website to find more about what we offer.