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.
| Course facts | |
|---|---|
| About this course: | |
| Course code | M337 |
| Credits | 30 |
| OU Level | 3 |
| SCQF level | 10 |
| FHEQ level | 6 |
| Course work includes: | |
| 4 Tutor-marked assignments (TMAs) | |
| Examination | |
| No residential school | |
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 thought of as 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 functionsThe texts have many worked examples, problems and exercises (all with full solutions), and there is a module handbook that includes reference material, the main results and an index.
You can find the full content list on the Open mathematics and statistics website.
Successful study of this module should enhance your skills in understanding complex mathematical texts, working with abstract concepts, constructing solutions to problems logically and communicating mathematical ideas clearly.
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.
Talk to an advisor if you're not sure you're ready.
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 have access to a module website, which includes:
You'll be provided with printed books covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. You'll also receive a printed module handbook.
A scientific calculator would be useful but is not essential.
You'll get help and support from an assigned tutor throughout your module.
They'll help by:
Online tutorials run throughout the module. Where possible, we'll make recordings available. While they're not compulsory, we strongly encourage you to participate.
The assessment details for this module can be found in the facts box.
The OU strives to make all aspects of study accessible to everyone. The Accessibility Statement below outlines what studying this module involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.
Printed materials are provided for the core module text. All of this module's study materials are also online; this includes PDFs of any printed materials, plus some items which are only provided online. Online-only materials include audio/video clips (with transcripts/subtitles). Online materials also include links to external resources, online forums and online tutorial rooms.
This module has online tutorials. Although not compulsory, tutorials will help you consolidate your learning.
You will not be required to work with other students on this module. However, there is opportunity to discuss with others on the lively module forums, which are closely monitored by an experienced academic. We encourage forum discussions as they can greatly benefit your learning process.
Mathematical and scientific symbols and expressions are used throughout the module and you will be required to use such notation within assessment.
The study materials contain a considerable number of figures. Interpreting these figures, and reproducing similar figures, is an important part of the study of this module, and is assessed. Figure descriptions are provided for most figures.
In this module you will be working with specialist reading material which includes mathematical notation. This is delivered both online and in printed form, and also via bespoke software.
This module has tutor-marked assignments (TMAs) that you may submit via the online TMA service or by post and a remote exam.
You will receive feedback from your tutor on your submitted Tutor-Marked Assignments (TMAs). This will help you to reflect on your TMA performance. You should refer to it to help you prepare for your next assignment.
All University modules are structured according to a set timetable and you will need time-management skills to keep your studies on track. You will be supported in developing these skills.
This module uses specialist mathematical symbols that are not covered by standard accessibility tools, and it may not be fully accessible as a result. These mathematical symbols can be created using software packages such as Microsoft Word or LaTeX, or they can be drawn by hand.
Complex analysis (M337) starts once a year – in October.
This page describes the module that will start in October 2025.
We expect it to start for the last time in October 2031.
This course is expected to start for the last time in October 2031.
This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.