Mathematics

Number Theory

Module code: G5140
Level 4
15 credits in spring semester
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination

Number Theory introduces students to the mathematical properties of whole numbers and is sometimes called the “Queen of Mathematics”.

Learn how to define objects such as prime numbers, greatest common divisors and lowest common multiples, and rigorously prove properties about these objects.

You will encounter the work of mathematicians such as the Euclidean Algorithm and Fermat’s Last Theorem, and understand that number theory is crucial to solving problems today, for example how prime numbers keep credit card data safe online and how to determine the periods of time insect species spend underground.  

Module learning outcomes

• Understand the parallels between arithmetic of Z and arithmetic of polynomials over Z;
• Understand the notion of a Diophantine equation, and solve Diophantine equations;
• Apply theorems of modular arithmetic to a wide class of problems;
• Identify and classify algebraic group structures.