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Accessibility statement
This module introduces important numerical methods used to solve mathematical problems encountered in applied mathematics, data science, engineering and the physical, biological and social sciences. You will study the theory behind the methods and develop computer programming skills by using the Python programming language to implement them. You will also learn how to use modern library implementations of these methods.
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.
There are no formal entry requirements to study this module.
However, you’ll need appropriate knowledge of mathematics. You’d normally prepare by having passed:
or their equivalent.
Are you ready for MST374?
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:
The OU strives to make all aspects of study accessible to everyone, and this Accessibility Statement outlines what studying MST374 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.
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.
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