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Deterministic and stochastic dynamics

This module is an accessible introduction to the study of applied mathematics at OU level 3. It introduces core topics in applied mathematics at this level and is structured around three books: Fundamental concepts of dynamics, Deterministic dynamics and Stochastic processes and diffusion. As well as using traditional pen-and-paper mathematics, the module uses the Maxima computer algebra system to illustrate and explore the properties of dynamical systems.

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

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Module

Module code

MS327

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 module levels correspond to these frameworks.
Level of Study
OU SCQF FHEQ
3 10 6

Study method

Distance Learning

Module cost

See Module registration

Entry requirements

See Entry requirements

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Module details Entry requirements Module registration Study materials

What you will study

This module is presented as three books.

Book 1: Fundamental concepts of dynamics
The first book considers ordinary differential equations, Newton’s second law, conservation of energy, and the concepts of fixed point, limit cycles and constants of motion. It also introduces a framework for discussing random processes, such as random walks.

Book 2: Deterministic dynamics
The second book develops some more advanced concepts. In the case of conservative systems, it introduces the calculus of variations and develops Lagrangian dynamics from Hamilton’s principle. In the case of dissipative systems, it uses the concepts of maps to model dynamical processes. ‘Chaos’ is defined and explored using the strange attractor. The book introduces the notions of Lyapunov exponents, fractal dimensions of attractors, and their connection via the ‘Lyapunov dimension’ formula.

Book 3: Stochastic processes and diffusion
The third book investigates the random walk as the archetypical random dynamical process, and explain its connection to the diffusion equation. Fourier methods (both series and transforms) are used in the treatment of the diffusion equation and probability theory. The module concludes with a look at some further applications of random dynamical systems, including models used for option pricing in mathematical finance.

The module uses the Maxima computer algebra system to illustrate how computers are used to explore properties of dynamical systems. You will be required to use Maxima in some of the assignments, but it is possible to complete the module without an extensive use of this package. However, there will be plenty of optional exercises which illustrate the power of computers for exploring the properties of dynamical systems.

You can find the full content list on the .

Vocational relevance

Understanding how to analyse dynamical processes is a central competence for using mathematics in science, engineering, and economics. Mastering the material in this module will give you powerful tools used by practising applied mathematicians.

Teaching and assessment

Support from your tutor

You’ll get help and support from an assigned tutor throughout your module.

They’ll help by:

  • marking your assignments and offering detailed feedback to help you improve
  • providing individual guidance, whether that’s for general study skills or specific module content
  • guiding you to additional learning resources
  • facilitating online discussions between your fellow students in the dedicated module and tutor group forums.

Online tutorials run throughout the module. Where possible, we’ll make recordings available. While they’re not compulsory, we strongly encourage you to participate.

Assessment

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

Future availability

Deterministic and stochastic dynamics (MS327) starts once a year – in October.

This page describes the module that will start in October 2025.

We expect it to start for the last time in October 2027.

Regulations

As a student of 快猫视频, you should be aware of the content of the academic regulations which are available on our website.

Course work includes:

4 Tutor-marked assignments (TMAs)
Examination


Entry requirements

You must have passed one of the following:

You can .

Preparatory work

You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz and follow the advice in the quiz.

The key topics to revise include:

  • differential equations
  • mechanics.

Register

Start End England fee Register
04 Oct 2025 Jun 2026 拢1946.00

Registration closes 11/09/25 (places subject to availability)
This module is expected to start for the last time in October 2027.

Additional Costs

Study costs

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

If your income is not more than £25,000 or you receive a qualifying benefit, you might be eligible for help with some of these costs after your module has started.

Ways to pay for this module

Open University Student Budget Account

快猫视频 Student Budget Accounts Ltd (OUSBA) offers a convenient &/courses/modules/ms327/39;pay as you go&/courses/modules/ms327/39; option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that 快猫视频 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 monthly fee and number of instalments based on the cost of the module you are studying. APR 5.1% representative.

Joint loan applications

If you feel you would be unable to obtain an OUSBA loan on your own due to credit history or affordability issues, OUSBA offers the option to apply for a joint loan application with a third party. For example, your husband, wife, partner, parent, sibling or friend. In such cases, OUSBA will be required to carry out additional affordability checks separately and/or collectively for both joint applicants who will be jointly and severally liable for loan repayments.

As additional affordability checks are required when processing joint loan applications, unfortunately, an instant decision cannot be given. On average the processing time for a joint loan application is five working days from receipt of the required documentation.

Read more about .

Employer sponsorship

Studying with 快猫视频 can boost your employability. OU courses are recognised and respected by employers for their excellence and the commitment they take to complete. They also value the skills that students learn and can apply in the workplace.

Over 30,000 employers have used the OU to develop staff so far. If the module 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 module.  

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, Mastercard, Visa and Visa Electron. 

Mixed payments

We know that sometimes you may want to combine payment options. For example, you may wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an .


Please 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 fee information provided here is valid for modules starting before 31 July 2026. Fees typically increase annually. For further information about the University&/courses/modules/ms327/39;s fee policy, visit our .

This information was provided on 04/04/2025.

Can you study an Access module for free?

Depending on eligibility and availability of places, you could apply to study your Access module for free.

To qualify, you must:

  1. be resident in England
  2. have a household income of not more than £25,000 (or be in receipt of a qualifying benefit)
  3. have not completed one year or more on any full-time undergraduate programme at FHEQ level 4 or above or successfully completed 30 credits or more of OU study within the last 10 years

How to apply to study an Access module for free

Once you&/courses/modules/ms327/39;ve started the registration process, either online or over the phone, we&/courses/modules/ms327/39;ll contact you about your payment options. This will include instructions on how you can apply to study for free if you are eligible and funded places are still available.

If you&/courses/modules/ms327/39;re unsure if you meet the criteria to study for free, you can check with one of our friendly advisers on +44 (0)300 303 0069, or you can request a call back.

Not eligible to study for free?

Don&/courses/modules/ms327/39;t worry! We offer a choice of flexible ways to help spread the cost of your Access module. The most popular options include:

  • monthly payments through OUSBA
  • part-time tuition fee loan (you&/courses/modules/ms327/39;ll need to be registered on a qualification for this option)

To explore all the options available to you, visit Fees and Funding.

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
  • Maxima algebra software and associated guidance
  • assessment details, instructions and guidance
  • online tutorial access
  • access to student and tutor group forums.

You’ll be provided with printed books covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. You’ll also receive a printed module handbook.

You will need

A scientific calculator.

Computing requirements

  • Primary device – A desktop or laptop computer. It’s possible to access some materials on a mobile phone, tablet or Chromebook; however, they will not be suitable as your primary device.
  • Peripheral device – Headphones/earphones with a built-in microphone for online tutorials.
  • Our OU Study app operates on supported versions of Android and iOS.
  • Operating systems – Windows 11 or latest supported macOS. Microsoft will no longer support Windows 10 as of 14 October 2025.
  • Internet access – Broadband or mobile connection.
  • Browser – Google Chrome and Microsoft Edge are recommended. Mozilla Firefox and Safari may be suitable.

If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying MS327 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

To find out more about what kind of support and adjustments might be available, contact us or visit our .