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.
Introduction to Algebra (4CCM121A or 5CCM121B)
Semester 1 only students will be set an alternative assessment in lieu of in-person exams in January. Full year students will complete the standard assessment.
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.
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