Conclusion
Following completion of this free OpenLearn course, Number theory, as well as being able to ‘understand some of the basic elements of number theory’ you should also find that your skills and confidence in reading, understanding and writing mathematical arguments are improving.
You should now be able to:
- use, and understand the theoretical underpinnings of, mathematical induction
- understand and be able to apply the Generalised Principle of Mathematical Induction and the Second Principle of Mathematical Induction
- recognise the importance of the Division Algorithm, and be able to apply it in a variety of scenarios
- understand the term ‘prime number’, and be able to recall basic properties of integers relating to prime numbers
- find all prime numbers in a given range using the sieve of Eratosthenes.
This free OpenLearn course is an extract from the Open University course M303 Further 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 Group theory, Rings and polynomials and Metric spaces and continuity. They are further adapted extracts from the Open University course M303 Further pure mathematics.
If you are interested in applied mathematics, you might like to study the free OpenLearn courses Introduction to the calculus of variations, Linear programming – the basic ideas and Kinematics of fluids.
If you are interested in statistics, you might like to study the free OpenLearn courses Modelling events in time, Univariate continuous distribution theory and Point estimation.