Special Topic - Number Theory

Description

Number Theory is the study of properties of the integers. Building on only basic knowledge of prime factorization and modular arithmetic (from MATH120) we will study further properties of the
whole numbers. The course will cover the following topics: Solutions of quadratic congruences, quadratic residues and the quadratic reciprocity law. The latter relates the question of whether p is a square mod q to whether q is a square mod p, for primes p and q and is a pivotal result that has motivated a lot of modern number theory. Representation of integers as sums of squares, in particular we’ll prove Fermat’s theorem that primes congruent to 1 mod 4 are a sum of two squares and Lagrange’s theorem that every integer is a sum of four squares. We will also study
quadratic Diophantine equations in some generality. We will study some other topics, such as distribution of primes if time permits.


For a full list of Honours courses, please refer to the School of Mathematics and Statistics Honours Booklet Mathematics and Statistics Honours Booklet