Free course

Number theory

This free course is an introduction to Number Theory. Section 1 provides a brief introduction to the kinds of problem that arise in Number Theory. Section 2 reviews and provides a more formal approach to a powerful method of proof, mathematical induction. Section 3 introduces and makes precise the key notion of divisibility. The Division Algorithm, concerning the division of one integer by another, is used. Its consequences, both practical and theoretical, make it a cornerstone of number theory. Section 4 explores some of the basic properties of the prime numbers and introduces the sieve of Eratosthenes.

Course learning outcomes

After studying this course, you should 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.

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Course content