Module description
Syllabus:
Review of divisibility, prime numbers and congruences. Residue class rings, Euler’s φ-function, primitive roots. Quadratic residues and quadratic reciprocity law. Irrational and transcendental numbers. Sums of squares. Some Diophantine equations. If time permits we will also learn about the ‘AKS’ algorithm for primality testing.
Prerequisites:
Introduction to Algebra (4CCM121A or 5CCM121B)
Assessment details
Written examination and class test.
Exercises or quizzes will be set each week to be handed in the following week. These problems will be discussed in the tutorials and solutions will be available.
Educational aims & objectives
The aim of this module is to give an introduction to elementary number theory and to further develop the algebraic techniques met in ‘Introduction to Abstract Algebra’. By introducing several new concepts in the concrete setting of rational integers, this module is a good preparation for more demanding modules in number theory and algebra.
Teaching pattern
Three hours of lectures and one hour of tutorial per week throughout the term
Suggested reading list
Indicative reading list - link to Leganto system where you can search with module code for lists