Computational applied mathematics
This module develops the computer programming skills you need to find numerical solutions to mathematical problems. You’ll learn various numerical methods to solve problems encountered in applied mathematics, data science, engineering and the physical, biological and social sciences. Using the Python programming language, you’ll develop your understanding of programming structures, controls and data types and how to use libraries.
What you will study
Applying numerical methods to mathematical problems is an important skill for applied mathematicians. This module introduces mathematical methods commonly used in computer programming and uses Python to demonstrate these.
The module comprises ten units:
Unit 1: Getting started
You’ll start with an introduction to Python – solving equations of one variable using various iterative methods such as simple iteration, bisection methods and the Newton–Raphson method. 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 starts with solving linear equations by LU decomposition and then discusses ill-conditioning and applications in finding eigenvalues and least-squares regression analysis.
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 mainly covers the simplex method and includes graphical formulations, 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 optimization
This unit starts with minimising functions of one variable before moving on to multivariate problems – including 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 method. Initial value problems are solved using Euler and Runge–Kutta methods; 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.
Units 10: Case studies
The final unit contains a series of case studies that consolidate ideas presented in the previous units and provide background to the end-of-module assignment.
You can find the full content list on the .
Entry requirements
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.
What's included
You’ll have access to a module website, which includes:
- a week-by-week study planner
- course-specific module materials, including activities completed using the module software
- assessment details, instructions and guidance
- online tutorial access
- access to student and tutor group forums.
We provide printed books covering the module content, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. We also provide a printed module handbook.
You will need
A scientific calculator.
Computing requirements
You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Ventura or higher.
Any additional software will be provided or is generally freely available.
To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).
Our module websites comply with web standards, and any modern browser is suitable for most activities.
Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.
It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.