Elements of Number Theory

Module code: MA1104

Elementary Number Theory will provide an introduction into the thinking and reasoning of pure mathematics.

Number theory is one of the oldest and most fundamental branches of pure mathematics. It studies the properties of integers, focusing on prime numbers - numbers larger than 1 but only divisible by 1 and themselves. These form the `building blocks’ of all numbers, similar to atoms being the building blocks of molecules.

G. H. Hardy, one of the greatest number theorists of the twentieth century, wrote in A Mathematician’s Apology that he had ‘never done anything useful’. However, there are many fascinating applications of number theory to real-world problems, most notably to cryptography. For example, the RSA cryptosystem, based on modular arithmetic and prime numbers, is at the heart of many modern public key methods. In this module, as well as covering the basics of number theory, you‘ll study its applications.


  • 33 hours of lectures
  • 2 hours of seminars
  • 11 hours of tutorials
  • 104 hours of guided independent study


  • Coursework (60%)
  • Class test (40%)