Courses / Module

NUMBER THEORY

Module code: MT444P
Credits: 5
Semester: 2
Department: MATHEMATICS AND STATISTICS
International:

	Overview
	Module Objective: To introduce students to classical analytic Number Theory. Topics to include some of the following: The arithmetic functions and identities. Algebraic and transcendental numbers. Continued fractions (including solving congruence equations by continued fractions, periodic continued fractions, Brounkner's Algorithm and Pell's equation). Approximation of irrationals by rationals (Liouville's theorem and construction of transcendental number). Quadratic residues, Euler's criterion and the Quadratic Reciprocity Law (with proof). Distribution of primes. Chebyshev's Theorem.

Overview

Module Objective:
To introduce students to classical analytic Number Theory.

Topics to include some of the following: The arithmetic functions and identities. Algebraic and transcendental numbers. Continued fractions (including solving congruence equations by continued fractions, periodic continued fractions, Brounkner's Algorithm and Pell's equation). Approximation of irrationals by rationals (Liouville's theorem and construction of transcendental number). Quadratic residues, Euler's criterion and the Quadratic Reciprocity Law (with proof). Distribution of primes. Chebyshev's Theorem.

	Learning Outcomes
	On successful completion of the module, students should be able to: Define the standard arithmetic functions and their properties. Define and find continued fractions. Prove and understand some of the theorems of classical number theory covered in the course. State, prove and apply the Quadratic Law of Reciprocity. Understand what is known regarding the distribution of primes. Use methods from the course to solve problems.

Learning Outcomes

Teaching & Learning methods

Assessment

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes Final in-house exam may be retaken with Department permission.

	Pre-Requisites
	Preferably MT241P or MT311S.

Timetable

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Courses / Module

NUMBER THEORY

Semester 1

Semester 2