Groups and geometry
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| Examination | No residential school |
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This course is available for study in the countries shown. Fees may vary by country.
Summary
This course covers the construction, recognition and classification of geometric entities (tilings, friezes, wallpaper patterns, regular solids, crystal structures) and algebraic entities (symmetry groups, cyclic and abelian groups, and other groups of low order). The geometry and algebra are strongly interconnected: the geometric classification is done in terms of symmetry groups. After revising the basics and introducing tilings and friezes, Groups teaches you to construct and classify cyclic groups; the finitely presented abelian groups; and certain other groups. Geometry continues the study of geometric objects using their symmetry groups. You need a good understanding of the basics of group theory, linear algebra and algebraic manipulation, as in Pure mathematics (M208).
Course content
The geometric structures studied in this course are all in the context of Euclidean two- or three-dimensional space (inversive, non-Euclidean and projective geometries are not covered).
After an introductory section the texts divide into a Geometry stream and a Groups stream. In the Groups stream you will learn how to construct the cyclic groups (groups generated by a single element) and the finite Abelian groups (commutative groups containing finitely many elements), and you will also learn how to use a classification algorithm for the latter so that, given information about the relationships between generating elements, you can completely characterise the group. The stream ends with an introduction to the problem of classifying groups that are not given to be Abelian.
In the Geometry stream you will see how to classify the seven types of frieze pattern and the seventeen types of wallpaper pattern, and learn how to classify certain types of repeating tiling of the plane. You will also use symmetry groups to develop a powerful method of counting and listing the ‘essentially different’ colourings of a geometric object. The stream ends with an introduction to the study of similar structures in three dimensions.
Entry
This is a Level 3 course. Level 3 courses build on study skills and subject knowledge acquired from previous studies at Levels 1 and 2. They are intended only for students who have recent experience of higher education in a related subject, preferably with the OU. Although the course is self-contained and all the essential material is revised in the introductory section, you are likely to find it hard going if you are not at all familiar with group-theoretic and geometric thinking. You could get the necessary background from our Level 2 mathematics course Pure mathematics (M208). Students are more likely to complete this course successfully if they have acquired their prerequisite knowledge through passing M208. The introductory block of M336 revises the essential material from M208, but on the assumption that you have seen it before. Your regional or national centre will be able to tell you where you can see reference copies of M208. To help you decide whether or not you are ready to start M336 we have devised a diagnostic quiz, which is available in PDF format from the Pure Maths website.
If you have any doubt about the suitability of the course, please contact our Student Registration & Enquiry Service.
Qualifications
M336 is an optional course in our
- BA/BSc (Honours) Computing and Mathematical Sciences (B14)
- BA/BSc (Honours) Mathematics (B31)
- BA/BSc (Honours) Mathematics and Statistics (B36)
- BSc (Honours) Mathematics and its Learning (B46)
- Diploma in Statistics (D44)
It can also count towards most of our other degrees at bachelors level, where it is equally appropriate to a BA or BSc. 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 visual nature of the geometry part of the course is evident in the many diagrams, in the tiling and frieze cards and overlays, and in the DVDs. We can provide transcripts of the audio and video materials. The course materials are available in Adobe Portable Document Format (PDF). Some Adobe PDF components may not be available or fully accessible using a screen reader and mathematical, scientific, and foreign language materials may be particularly difficult to read in this way. Large print versions of the course material can be provided on request. Our Services for disabled students website has the latest information about availability.
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 books, other printed materials, CD and DVD, course website.
You will need
DVD player and CD player.
You require internet access at least once a week during the course to download course resources and keep up to date with course news.
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.
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. We may also be able to offer group tutorials or day schools that you are encouraged, but not obliged, to attend. Where your tutorials are held will depend on the distribution of students taking the course. 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.
Please note that TMAs for all undergraduate mathematics and statistics courses must be submitted on paper as – due to technical reasons – we are unable to accept TMAs via our eTMA system.
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’. In M336 this rule can apply to one assignment only. You will be given more detailed information when you begin the course.
Professional recognition
This course may help you to gain recognition from a professional body. You can download our Recognition leaflets 3.3 Professional Engineering Institutions, and 3.6 Institute of Mathematics and its Applications or ask our Student Registration & Enquiry Service for a copy.
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 2010. We expect it to be available at the same time in alternate years.
How to register
To register a place on this course return to the top of the page and use the Click to register button. For more information and advice about registration see OU Study Explained.
About this page
An undergraduate course in Mathematics and Statistics.
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Student Reviews
Great course for group theory. Whilst an abstract subject the course presents it clearly and enjoyably. The geometry is also ...
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This was a fun course. It has enough interesting bits to make it challenging and other parts that tie back ...
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