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Accessibility statement
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:
We’re using a new examination verification process for this module. We may ask you to attend a 15-minute post-exam video discussion, where you’ll present a photo ID and discuss your answers to a small number of questions with a tutor or member of the module team. The discussion isn’t graded; it’s only to verify that you completed the exam yourself.
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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