Fractal geometry
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| 4 Tutor-marked assignments (TMAs) | |
| Examination | No residential school |
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Summary
There has recently 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 course deals with the theory of fractals and their geometry, and looks at examples to which the theory can be applied.
Course content
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 course is based on the set book Fractal Geometry: Mathematical Foundations and Applications (second 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 course 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 course looks at applications including data compression, examples from number theory, dynamical systems and Julia sets.
Entry
You must be registered for the MSc in Mathematics, or for another qualification towards which the course can count. You should have at least second-class honours in a mathematics degree, or in another degree with a high mathematical content, such as engineering or theoretical physics. In exceptional circumstances applicants without that qualification will be considered, although non-graduates will not normally be admitted to the MSc programme. You should have taken a first course in real analysis. An adequate preparation would be our undergraduate-level course Pure mathematics (M208) (or the discontinued courses M201, M203 or M231). You must also have experience of studying higher-level mathematics courses, preferably including an advanced course in analysis such as Complex analysis (M337) (or the discontinued course M332). The course includes an introduction to some necessary background material, most of which would be covered by courses in metric spaces and measure theory. If you have any doubt about the suitability of the course, please contact our Student Registration & Enquiry Service.
Qualifications
M835 is an optional course in our
- Postgraduate Certificate in Mathematics (C90)
- Postgraduate Diploma in Mathematics (E23)
- MSc in Mathematics (F04)
Some postgraduate qualifications allow study to be chosen from other subject areas. We advise you to refer to the relevant qualification descriptions for information on the circumstances in which this course can count towards these qualifications because from time to time the structure and requirements may change.
If you have a disability or additional requirement
The material contains small print and diagrams, which may cause problems if you find reading text difficult.
If you are a new student, or new to courses using a computer or the internet, you will need to inform us of your particular needs as soon as possible, as some of our support services may take several weeks to arrange. Details of how to do this and our range of support services are described in our booklet Meeting Your Needs which you can download or request from our Student Registration & Enquiry Service.
You can also find information about accessible course materials, financial support and the Disabled Students' Allowance, equipment and other services, on our Services for disabled students website. It also includes our contact details for advice and support both before you register and while you are studying.
Course materials
What's included
Course notes, other printed materials, CD-ROM and computer notes (for optional use).
You will need
We recommend that you have access to the internet at least once a week during the course and would like to point out that vital material, such as your assignments, may be delivered online.
Computing requirements
This course includes online computer activities – you can access these using a web browser that can play Flash and Shockwave. Some of your course software will be provided on disk.
You will need internet access and a computer. If you have purchased a new Windows computer since 2002 it should meet your course computing requirements. Check our Technical Requirements section if your computer is older than this or is otherwise unusual. Please note that you cannot use an Apple Mac or Linux computer unless it is running windows Boot Camp or similar.
Materials to buy
Set books
- Falconer, K J Fractal Geometry: Mathematical Foundations and Applications, Wiley £34.95 - ISBN 9780470848623
Teaching and assessment
Support from your tutor
You will have a tutor who will help you with the course material and mark and comment on your written work, and whom you can ask for advice and guidance. Contact our Student Registration & Enquiry Service if you want to know more about study with The Open University before you register.
Assessment
The assessment details for this course can be found in the facts box above.
TMAs on MSc in Mathematics courses can be submitted electronically using a special maths eTMA processor which is used in place of the main eTMA system. We strongly recommend you submit the TMAs electronically, but there will be the facility to submit TMAs on paper.
Assessment is an essential part of the teaching, so you are expected to complete it all. But if you unavoidably miss or do badly in an assignment, some courses allow you a ‘substitution score’, calculated as a weighted average of all your scores for the course. In M835 this rule can apply to one assignment only. You will be given more detailed information when you begin the course.
Students also studied
Students who studied this course also studied at some time:
Future availability
The details given here are for the course that starts in February 2011. We expect it to be available once more, in February 2012.
How to register
Unfortunately, we are unable to accept online registrations for this course in the usual way. Instead, you may apply electronically using the MSc Mathematics application system.
About this page
A postgraduate course in Mathematics and Statistics.
Study explained
- Course
- - a module of study that can count towards a qualification.
- Credit points
- - show how much study is required to complete a course or qualification. One credit point represents roughly 10 hours of study.
- Financial support
- - find out if you qualify for support with your fees with our eligibility checker.
- Study explained
- - all you need to know about studying with the OU.
Student Reviews
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