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Exploring mathematics

Exploring mathematics builds on the concepts and techniques in Using mathematics (MST121) and uses the same software. It looks at questions underlying some of those techniques, such as why particular patterns occur in mathematical solutions and how you can be confident that a result is true. It introduces the role of reasoning and offers opportunities to investigate mathematical problems. Together with Using mathematics this module will give you a good foundation for higher-level mathematics, science and engineering modules. Even if you don't intend to study further, you will gain a good, university-level understanding of the nature and scope of mathematics.

You are advised to be confident with the content of Using mathematics (MST121), or equivalent from elsewhere, before commencing study of this module.

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OU qualifications are modular in structure; the credits from this undergraduate-level module could count towards a certificate of higher education, diploma of higher education, foundation degree or honours degree.

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Module code
Study level
2 8 5
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
See Am I ready?

Student Reviews

As other people have said this is another top quality open university course, where the material seems to be more...
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What you will study

Exploring mathematics offers both a way in to honours-level mathematics and deeper insights into the mathematics that supports other areas of study. It rounds off the suite of modules designed to provide a rich and enlightening introduction to mathematical ideas and techniques.

This module builds on the approach and design of our OU level 1 module Using mathematics (MST121), extending the mathematical concepts and techniques (to cover more calculus, for example), the range of applications, and use of the module software. It looks at questions underlying some of the methods from MST121, such as why particular patterns occur in mathematical solutions, and how you can be confident that a result is true. It introduces the role of reasoning in mathematics, and offers opportunities to investigate mathematical questions for yourself. By the end of the module you will have encountered many of the topics that are developed in later mathematics modules, in particular in our main OU level 2 modules Pure mathematics (M208), and Mathematical methods, models and modelling (MST210). It also provides a good mathematical basis for modules in physics and engineering.

There are four sections, with each of the first three revisiting and developing the ideas introduced in the corresponding section in MST121. An important theme that runs through the module is mathematical reasoning.

Work on numbers and sequences is extended to Fibonacci and related sequences; that on circles is extended to the study of other conic sections. There is further exploration of the properties of functions and matrices, including applications in transformation geometry. The computer is used to help with important ideas of iteration in discrete mathematics. The ideas of calculus are extended to include more sophisticated techniques of differentiation and integration and use in the approximation of functions using Taylor series.

The last section of the module introduces important mathematical ideas, such as complex numbers, number theory and groups, that are built on in later modules. It concludes with a chapter on the role of proof in mathematics.

The module also develops more general skills such as communication of mathematical ideas, which will be useful in studying later modules.

You will learn

Successful study of this module should improve your skills in:

  • communicating mathematical ideas clearly and succinctly
  • working with abstract concepts
  • thinking logically
  • constructing logical arguments
  • finding solutions to problems
  • using a computer algebra software package.

Professional recognition

This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.

Teaching and assessment

Support from your tutor

You will have a tutor who will help you with the study material, mark and comment on your written work, and whom you can ask for advice and guidance. We may also be able to offer group tutorials or day schools that you are encouraged, but not obliged, to attend. Where your tutorials are held will depend on the distribution of students taking the module. Contact our Student Registration & Enquiry Service if you want to know more about study with The Open University before you register.


The assessment details for this module can be found in the facts box above.

Please note that tutor-marked assignments (TMAs) for all undergraduate mathematics and statistics modules must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.

Each TMA typically consists of six questions, covering one block of the module. Each of the questions typically involves some calculation, algebraic manipulation, creating and/or interpreting a graph, some written work to explain your interpretations and conclusions, and may involve using the module software and providing printouts. The first TMA is to be submitted about eight weeks after the start of the module.

The examination contains two parts. The first consists of short answer questions covering the whole of the module. The second contains longer questions, one on each block, and you are required to attempt up to two of these.

Future availability

The details given here are for the module that starts in February and October 2014, when it will be available for the last time. 

The combination of the OU level 1 module Using mathematics (MST121) and this module (MS221) will be replaced by Essential mathematics 1 (MST124) and either Essential mathematics 2 (MST125) or Mathematical methods (MST224).


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

Course work includes:

4 Tutor-marked assignments (TMAs)
No residential school

Course satisfaction survey

See the satisfaction survey results for this course.


This module is the third part of the mathematics entry suite that starts with Discovering mathematics (MU123) and goes on to Using mathematics (MST121) and MS221. Your choice of which to take depends on how much mathematical knowledge you already have and on the degree you have in mind. It is not advisable to take either MST121 or MS221 in the same year as MU123, and you should not take MS221 before studying MST121.

If you have any doubt about the suitability of the module, or about choosing the most suitable mathematics entry module, please contact our Student Registration & Enquiry Service.


Start End England fee Register
04 Oct 2014 Jun 2015 £1316.00

Registration closes 18/09/14 (places subject to availability)


The deadline for financial support applications has now passed

October 2014 is the final start date for this course. For more information, see Future availability.

Ways to pay for this module

Open University Student Budget Account

The Open University Student Budget Accounts Ltd (OUSBA) offers a convenient 'pay as you go' option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that The Open University works exclusively with OUSBA and is not able to offer you credit facilities from any other provider. All credit is subject to status and proof that you can afford the repayments.

You pay the OU through OUSBA in one of the following ways:

  • Register now, pay later – OUSBA pays your module fee direct to the OU. You then repay OUSBA interest-free and in full just before your module starts. 0% APR representative. This option could give you the extra time you may need to secure the funding to repay OUSBA.
  • Pay by instalments – OUSBA calculates your annual fees and spreads them out over up to a year, enabling you to pay your fees monthly and walk away with a qualification without any further debt. APR 5.1% representative.

Read more about Open University Student Budget Accounts (OUSBA).  

Employer sponsorship

Studying with The Open University can boost your employability. OU qualifications are recognised and respected by employers for their excellence and the commitment they take to achieve one. They also value the skills that students learn and can apply in the workplace.

More than one in 10 OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the qualification you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees. 

  • Your employer just needs to complete a simple form to confirm how much they will be paying and we will invoice them.
  • You won’t need to get your employer to complete the form until after you’ve chosen your modules.  

Credit/debit card

You can pay part or all of your tuition fees upfront with a debit or credit card when you register for each module. 

We accept American Express, Maestro (UK only), Mastercard, Visa/Delta and Visa Electron. 

Gift vouchers

You can pay for part or all of your tuition fees with OU gift vouchers. Vouchers are currently available in the following denominations, £10, £20, £50 and £100. 

Mixed payments

We know that sometimes you may want to combine payment options. You may, for example wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Accounts (OUSBA).

For more information about combining payment options, speak to an adviser.

Note: Your permanent address/domicile will affect your fee status and therefore the fees you are charged and any financial support available to you. The fees and funding information provided here is based upon current details for  year 1 August 2014 to 31 July 2015.
This information was provided on 18/09/2014.

What's included

Module books, computer software on CD-ROM, audio CD, DVD (for video material), website.

You will need

Audio CD and video DVD playback facilities; scientific or graphics calculator.

You require internet access at least once a week during the module to download module resources and to keep up to date with module news. If your tutor offers online tutorials, we also recommend a headset with a microphone and earphones to talk to your tutor and other students online.

Computing requirements

You will need a computer with internet access to study this module. It includes online activities – you can access using a web browser – and some module software provided on disk.

  • If you have purchased a new desktop or laptop computer running Windows since 2008 you should have no problems completing the computer-based activities.
  • A netbook, tablet or other mobile device is not suitable for this module – check our Technical requirements section.
  • If you have an Apple Mac or Linux computer – please note that you can only use it for this module by running Windows on it using Boot Camp or a similar dual-boot system.

You can also visit the Technical requirements section for further computing information (including details of the support we provide).

If you have a disability

An integral part of study on this module is the use of specific software, which includes on-screen graphs and mathematical notation. Parts of this module are delivered online and through a CD-ROM so you will need to spend considerable amounts of time using a personal computer.  If you use specialist hardware or software to assist you in operating a computer or accessing the internet and have any concerns about accessing the types of study materials outlined you are advised to talk to our Student Registration & Enquiry Service about support which can be given to meet your needs.

Adobe Portable Document Format (PDF) versions of the printed study materials are available. However some Adobe PDF components may not be available or fully accessible using a screen reader and mathematical materials may be particularly difficult to read in this way. The study materials are also available on audio in DAISY Digital Talking Book format. Written transcripts are available for the audio-visual material. 

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. Find out more about our services for disabled students.