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Deterministic and stochastic dynamics

Deterministic and stochastic dynamics is designed to be studied as your first applied mathematics module 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. The module will use the Maxima computer algebra system to illustrate how computers are used to explore properties of dynamical systems. To study this module, you should have a good prior knowledge of the subject area, including differential equations, and some knowledge of mechanics, as provided by the appropriate OU level 2 study.

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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
To enable you to make international comparisons, the information provided shows how OU levels correspond to the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ).
OU FHEQ
3 6
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
See Entry requirements

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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 will also introduce a framework for discussing random processes, such as random walks.

Book 2: Deterministic dynamics

The second book will develop 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 will consider the use of maps to model dynamical processes. ‘Chaos’ will be defined and explored using the strange attractor. The book will introduce the notions of Lyapunov exponents, fractal dimensions of attractors, and their connection via the ‘Lyapunov dimension’ formula.

Book 3: Stochastic processes and diffusion

Finally, the third book will investigate the random walk as the archetypical random dynamical process, and explain its connection to the diffusion equation. Fourier methods (both series and transforms) will be treated by illustrating their role in treatment of the diffusion equation and probability theory. The module will conclude with a look at some further applications of random dynamical systems, including the models used for option pricing in mathematical finance.

The module will use 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 will be possible to complete the module without very 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.

Read the full content list here.

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

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.
  • Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. 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 for this module can be found in the facts box above.

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

Future availability

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

This page describes the module that will start in October 2020.

We expect it to start for the last time in October 2023.

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.

    Course work includes:

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


    Entry requirements

    There is no formal pre-requisite study, but you must have the required mathematical skills.

    You can check you’re ready for MS327 and see the topics it covers here.

    Talk to an advisor if you’re not sure you’re ready.

    Preparatory work

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

    The key topics to revise include:

    • differential equations
    • mechanics.

    Mathematical methods, models and modelling (MST210) or Mathematical methods (MST224) is ideal preparation.

    Register

    Start End Fee
    - - -

    No current presentation - see Future availability

    This module is expected to start for the last time in October 2023.

    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 are in receipt of 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

    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 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 Open University Student Budget Accounts (OUSBA).  

    Employer sponsorship

    Studying with The Open University 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.

    More than one in ten OU students are sponsored by their employer, and 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 Open University Student Budget Account (OUSBA).


    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 fees and funding information provided here is valid for modules starting before 31 July 2021. Fees normally increase annually in line with inflation and the University's strategic approach to fees. 

    This information was provided on 29/11/2020.

    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

    A computing device with a browser and broadband internet access is required for this module. Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

    Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

    A desktop or laptop computer with an up-to-date version of Windows, macOS or Linux.

    The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

    To join in the spoken conversation in our online rooms we recommend a headset (headphones or earphones with an integrated microphone).

    Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students.

    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 Disability support website.