Applying numerical methods to solve complex mathematical problems is an essential skill for applied mathematicians, data scientists and others. This module introduces the techniques needed to solve a variety of important problem types and applies these methods using the Python programming language. We introduce all the necessary elements of the Python language within the module.
The module comprises ten units:
Unit 1: Getting started
You’ll start with solving equations of one variable using various iterative methods, such as the bisection method, simple iteration, and the Newton–Raphson method. The Python programming language is introduced and used to implement these methods. You’ll also learn about the convergence of simple iterative schemes.
Unit 2: Interpolation
This unit introduces practical root-finding, Lagrange interpolation, least-squares curve fitting and splines.
Unit 3: Systems of linear equations
Unit 3 begins with solving systems of linear equations by LU decomposition and then discusses ill-conditioning and applications in finding eigenvalues and least-squares curve fitting.
Unit 4: Data analysis
In this unit, you’ll learn methods for analysing big data, including singular value decomposition (SVD), principal component analysis (PCA), independent component analysis (ICA), and multidimensional scaling and k-means.
Unit 5: Linear programming
This unit primarily covers the simplex method for solving linear programming problems, including the two-phase simplex method, duality, and sensitivity analysis.
Unit 6: Systems of nonlinear equations
In this unit, you’ll learn the Newton–Raphson method for multivariate problems and quasi-Newton methods, such as Broyden’s method. The unit also further discusses the convergence of simple iterative schemes.
Unit 7: Nonlinear optimisation
This unit starts with minimising functions of one variable before moving on to multivariate problems, including both unconstrained minimisation and constrained minimisation with equality and inequality constraints.
Unit 8: Differential equations
This covers numerical differentiation and integration using Newton–Cotes formulae, such as the trapezium and Simpson methods. Initial value problems are solved using Euler and Runge–Kutta methods, and boundary value and eigenvalue problems are solved using shooting methods.
Unit 9: Random processes
This unit introduces the basic theory of random variables, including random walks and Markov chains. The unit discusses Monte Carlo integration and finishes with the numerical solution to stochastic differential equations.
Unit 10: Case studies
The final unit contains a series of case studies that consolidate ideas presented in the previous units and provide background for the end-of-module assignment.
The full content list is on the Open mathematics and statistics website.
This module has been awarded a quality mark by the Royal Statistical Society, providing reassurance that the teaching, learning and assessment within this module is of high quality and meets the needs of students and employers.
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Course work includes:
You’ll have access to a module website, which includes:
Additionally, the website includes:
We also provide physical:
You can study this module on its own or use the credits you gain towards an Open University qualification.
MST374 is an option module in our:
Computational applied mathematics (MST374) starts once a year – in October.
It will next start in October 2026.
We expect it to start for the last time in October 2030.
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.
| Start | End | Register by | England fee |
|---|
| No current presentation |
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.
There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.
If your personal income is £25,000 or less, or you’re on certain benefits, you could qualify for a grant and OU top-up funding to cover 100% of your course fees. Apply online at the same time as you register on your module.
For more information on how to apply, visit our Part-Time Fee Grants for students in Scotland page.
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:
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).
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.
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.
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.
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).
We know that sometimes you may want to combine payment options. For example, you may get support from your employer to pay part of your tuition fee and pay the remainder by credit or debit card.
For more information about combining payment options, contact an adviser.
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's fee policy, visit our Fee Rules.
