MAU23101 Introduction to number theory

Module Code	MAU23101
Module Title	Introduction to number theory
Semester taught	Semester 1
ECTS Credits	5
Module Lecturer
Module Prerequisites	N/A

This module is examined in a 2-hour examination at the end of Semester 1.
Continuous assessment contributes 15% towards the overall mark.
The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

11 weeks of teaching with 3 lectures per week.

On successful completion of this module, students will be able to

State and prove some standard theorems in number theory.
Use standard theorems to solve problems in number theory including some classes of Diophantine equations.

Divisibility and factorisation of integers: prime numbers, gcd and lcm, Euclidean algorithm, Bézout's theorem, multiplicative functions such as sums of divisors.
Arithmetic in the ring Z/nZ and the field Z/pZ, Euler's totient function, Chinese remainder theorem, multiplicative order and primitive roots.
Sums of squares, quadratic forms, discriminant, class number.
Continued fractions, expansion of rationals and quadratic irrationals, Diophantine approximation, Pell-Fermat equations.