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Accessibility statement
Qualification dates
StartEnd
03 Oct 2026Jun 2027
Complex analysis is a rich subject of foundational importance in mathematics and science. This module develops the theory of functions of a complex variable, emphasising their geometric properties and indicating some applications. Studying this module will consolidate many of the mathematical ideas and methods you learned in earlier modules and set you in good stead for tackling further fields of study in mathematics, engineering and physics.
There is no real number whose square is –1, but mathematicians long ago invented a system of numbers, called complex numbers, in which the square root of –1 does exist. These complex numbers can be considered points in a plane, in which the arithmetic of complex numbers can be pictured. When the ideas of calculus are applied to functions of a complex variable, a powerful and elegant theory emerges, known as complex analysis.
The module shows how complex analysis can be used to:
The module consists of thirteen units split between four books:
Book A: Complex numbers and functions
Book B: Integration of complex functions
Book C: Geometric methods in complex analysis
Book D: Applications of complex analysis
The texts include many worked examples, problems, and exercises (all with complete solutions), as well as a module handbook with reference material, the main results, and an index.
The full content list is on the Open mathematics and statistics website.
There is no formal pre-requisite study, but you must have the required mathematical skills.
You can check you’re ready for M337 and see the topics it covers here.
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:
One of the following is ideal preparation: Pure mathematics (M208), Mathematical methods, models and modelling (MST210), Mathematical methods (MST224).
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:
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 a remotely invigilated (proctored) 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.
You’ll have access to a module website, which includes:
We also provide physical:
The OU strives to make all aspects of study accessible to everyone, and this Accessibility Statement outlines what studying M337 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.
Complex analysis (M337) starts once a year – in October.
It will next start in October 2026.
We expect it to start for the last time in October 2031.
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