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Fractal geometry

In recent years there has been an explosion of interest in the mathematics of fractals – sets whose geometry cannot easily be described in classical terms. There’s no simple definition but all fractals have a highly intricate structure. Many fractals contain copies of themselves at many different scales, and computer pictures have shown that such sets (which are often very beautiful) are a very good representation of shapes of natural phenomena such as clouds, mountains and ferns. This module deals with the theory of fractals and their geometry, and looks at examples to which the theory can be applied.

Qualifications

M835 is an optional module in our:

This module can also count towards M03, which is no longer available to new students.

Module

Module code
M835
Credits

Credits

  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
30
Study level
To enable you to make international comparisons, the information provided shows how OU postgraduate modules correspond to the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ).
OU Postgraduate
FHEQ 7
Study method
Distance learning
Find out more in Why the OU?
Module cost
See Module registration
Entry requirements

Find out more about entry requirements.

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What you will study

The theory of fractal geometry provides a general framework for the study of sets that had been thought to be exceptional oddities. This is an active area of research and both the theory and applications of fractal geometry are still being developed.

The module is based on the set book Fractal Geometry: Mathematical Foundations and Applications (Third edition) by K. J. Falconer (Wiley), which is in two parts.

Part I has eight chapters dealing with the general theory of fractals and their geometry.

Part II looks at examples of fractals to which the theory of Part I can be applied. These examples are drawn from a wide variety of areas of mathematics and physics.

The module begins with an introductory chapter covering the necessary background material. Next we study the material in chapters two to four of the book, which introduce appropriate definitions of dimension and methods for calculating such dimensions.

The second half of the module looks at applications including data compression, examples from number theory, dynamical systems and Julia sets.

You will learn

Successful study of this module should enhance your skills in understanding complex mathematical texts, constructing solutions to problems logically and communicating mathematical ideas clearly.

Teaching and assessment

Support from your tutor

Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:

  • Marking your assignments (TMAs) and providing detailed feedback for you to improve.
  • Guiding you to additional learning resources.
  • Providing individual guidance, whether that’s for general study skills or specific module content.
  • Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part. If you want to participate, you’ll likely need a headset with a microphone.

Assessment

The assessment details can be found in the facts box above.

You will be expected to submit your tutor-marked assignments (TMAs) online using the eTMA system, unless there are some difficulties which prevent you from doing so. In these circumstances, you must negotiate with your tutor to get their agreement to submit your assignment on paper.

Course work includes

4 Tutor-marked assignments (TMAs)
Examination
No residential school

Future availability

Fractal geometry (M835) starts every other year – in October.

This page describes the module that will start in October 2021.

We expect it to start for the last time in October 2025.

Regulations

As a student of The Open University, you should be aware of the content of the academic regulations which are available on our Student Policies and Regulations website.

    Entry requirements

    To study this module you must declare the MSc in Mathematics (or another qualification towards which the module can count) as your qualification intention.

    Normally, you should have also completed at least one of the entry modules of the MSc in Mathematics (F04), Calculus of variations and advanced calculus (M820) or Analytic number theory I (M823).

    All teaching is in English and your proficiency in the English language should be adequate for the level of study you wish to take. We strongly recommend that students have achieved an IELTS (International English Language Testing System) score of at least 7. To assess your English language skills in relation to your proposed studies you can visit the IELTS website.

    If you have any doubt about the suitability of the module, please speak to an adviser.

    Register

    Start End Fee Register
    02 Oct 2021 Jun 2022 Not yet available

    Registration closes 09/09/21 (places subject to availability)

    Register
    This module is expected to start for the last time in October 2025.

    Future availability

    Fractal geometry (M835) starts every other year – in October.

    This page describes the module that will start in October 2021.

    We expect it to start for the last time in October 2025.

    Additional costs

    Study costs

    There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

    Study weekend

    This module normally includes an optional study weekend, for which there is an additional cost. You’ll pay this charge when you book, after you’ve registered on the module. If the study weekend is face-to-face, you must also pay for your travel to and from the venue and your accommodation if you need it.

    Study materials

    What's included

    You'll have access to a module website, which includes:

    • a week-by-week study planner
    • course-specific module materials
    • audio and video content
    • relevant computer software and associated guidance
    • assessment details and submission section
    • online tutorial access
    • access to student and tutor group forums.

    You'll also be provided with course notes covering the content of the module, including explanations, exercises and solutions to aid your understanding of the concepts and associated skills and techniques that are contained in the set book. You will need to obtain your own copy of the set book, and only the set book as printed by the publisher will be permitted in the examination, and not a version you have printed yourself.

    Computing requirements

    A computing device with a browser and broadband internet access is required for this module. Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

    Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

    • A desktop or laptop computer with an up-to-date version of Windows
    • The screen must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

    To join in the spoken conversation in our online rooms we recommend a headset (headphones or earphones with an integrated microphone).

    Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students.

    Materials to buy

    Set books

    • Falconer, K.J. Fractal Geometry: Mathematical Foundations and Applications (3rd edn) Wiley £40.50 - ISBN 9781119942399

    If you have a disability

    The material contains small print and diagrams, which may cause problems if you find reading text difficult.

    If you have particular study requirements please tell us as soon as possible, as some of our support services may take several weeks to arrange. Visit our Disability support website to find more about what we offer.