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.
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 explains its connection to the diffusion equation. Fourier methods (both series and transforms) are used to treat 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 can explore the properties of dynamical systems. Although you will be required to use Maxima in some of the assignments, it is possible to complete the module without extensive use of this package. There will be plenty of optional exercises that illustrate the power of computers for exploring the properties of dynamical systems.
The full content list is on the Open mathematics and statistics website.
Entry requirements
You must have passed one of the following:
Mathematical methods (MST224)
Mathematical methods, models and modelling (MST210)
Mathematical methods and models (MST209)
You can check you’re ready for MS327 and see the topics it covers here.
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.
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 forums.
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Assessment
Course work includes:
4 Tutor-marked assignments (TMAs)
Examination
For this module, we may use an assessment verification process to meet the requirements of relevant accrediting, professional, statutory or regulatory bodies. As part of this process, you may be asked to attend a short post-assessment video discussion, lasting around 15 minutes. During the discussion, you’ll need to show a photo ID and talk through your answers to a small number of questions with a tutor or a member of the module team. The discussion is not graded and is only used to confirm that you completed the assessment yourself.
We regularly review the assessments in our modules, so we may update the examination method used for this module to an in-person exam or an online invigilated exam. When we are making such a change, we will make it clear on this page. If we need to make a change after you have registered, we will notify you as soon as possible. If you have additional requirements, we will support you to complete your assessments.
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 forums.
Additionally, the website includes:
Maxima algebra software and associated guidance.
We also provide physical:
module books
module handbook.
You will need
a scientific calculator.
Computing requirements
Primary device – A desktop or laptop computer with at least 8 GB of RAM and a quad-core processor (2.4 GHz minimum speed). It’s possible to access some materials on a mobile phone, tablet or Chromebook; however, they will not be suitable as your primary device or for taking your online exam.
Peripheral devices – Headphones/earphones with a built-in microphone for online tutorials, plus an external webcam and a microphone.
Operating systems – Windows 11 or the latest supported macOS.
Internet access – A broadband or mobile connection with at least 3 Mbps upload and download speed.
Browser – Google Chrome and Microsoft Edge are recommended. Mozilla Firefox and Safari may be suitable. You may need to use Google Chrome specifically for some activities.
Our OU Study app operates on supported versions of Android and iOS.
Software – Any additional software will be provided or is generally freely available.
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.
Future availability
Deterministic and stochastic dynamics (MS327) starts once a year – in October.
It will next start in October 2027.
We expect it to start for the last time in October 2031.