Conclusion
Following completion of this free OpenLearn course, Introduction to group theory, as well as being able to ‘understand some of the basic elements of group theory’ you should also find that your skills in producing convincing arguments and problem solving are improving.
You should now be able to:
- explain what is meant by a symmetry of a plane figure
- find the composite of two symmetries
- find the inverse of a symmetry
- determine whether a given set and binary operation form a group by checking group axioms
- describe the symmetries of some bounded three-dimensional figures.
This free OpenLearn course is an extract from the Open University course M208 Pure mathematics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .
If you feel you are ready to move on in your study of pure mathematics but don’t have time to study a full Open University course at this time, you might like to study one of the free OpenLearn courses Introduction to linear equations and matrices or Introduction to analysis. They are further adapted extracts from the Open University course M208 Pure mathematics.
Alternatively, if you are interested in applied mathematics, you might like to try the free OpenLearn courses Second-order differential equations and Dynamics. If you are interested in statistics, you might like to try the free OpenLearn courses, Modelling and estimation, Medical statistics and Bayesian statistics.