Functional analysis
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| 4 Tutor-marked assignments (TMAs) | |
| Examination | No residential school |
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No current presentation - see Future availability |
| This course is expected to run until February 2014. | |||
Summary
Twentieth century mathematics places emphasis on classes of functions, rather than special properties of individual functions. Functions are considered as elements of a set and these sets can usually be given the additional structure of a linear and topological space. The interplay of these structures gives the subject its characteristic flavour. Along with the set of functions, this course considers sets of mappings from the set into various other sets, particularly, linear mappings onto the set itself (operators) and into complex numbers (linear functionals).
Course content
This MSc in Mathematics course does not consider any of the many applications of the theory, which include approximations, optimisation, classical and quantum mechanics, statistical mechanics, infinite group representations and harmonic analysis, and partial differential equations.
The course is based on the set book Elements of Functional Analysis by I. J. Maddox. We follow that text chapter by chapter, omitting the last one.
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 must have a good working knowledge of convergence, continuity, complex functions and Cauchy’s theorem, elementary set theory and mappings, topological spaces (particularly metric spaces), compactness, vector spaces and linear maps between them. An adequate preparation would be our undergraduate-level courses Pure mathematics (M208) (or the discontinued course M203) and Complex analysis (M337) (or the discontinued courses M332 and M386). If you have any doubt about the suitability of the course, please contact our Student Registration & Enquiry Service.
Qualifications
M826 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
You need to be able to read small print and diagrams.
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.
Computing requirements
This course includes online computer activities – you can access these using a web browser that can play Flash and Shockwave.
You will need internet access and a computer. If you have purchased a new 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.
Materials to buy
Students have to buy one Set Book which is only available from The Open University. Please phone +44 01908 659048 for information.
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 M826 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
This course is available every other year and the next presentation will be 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
I didn't enjoy this course at all, and spent most of it having no idea what was going on. I ...
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Perhaps the problem here is that M826 is not meant to be a course on 'Hilbert Spaces and its applications'. ...
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It is difficult to provide a cartoon of functional analysis, probably the most abstract subject in the MSc syllabus. Very ...
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