Courses / Module

ELEMENTARY NUMBER THEORY

Module code: MT311S
Credits: 5
Semester: 1
Department: MATHEMATICS AND STATISTICS
International:

	Overview
	Module objective: To introduce the student to elementary Number Theory. Induction. The division algorithm and the Euclidean algorithm in Z. The fundamental theorem of arithmetic. The integers modulo n. Fermat's Little Theorem, Euler phi function, Euler's generalisation of Fermat's Little Theorem. Wilson's Theorem. Solving Linear Diophantine equations. Solving systems of linear congruences using the Chinese Remainder Theorem. Legendre symbols, quadratic residues, quadratic Law of Reciprocity. Primitive roots. Successive squaring mod n for fast multiplication. Computation using mathematical/statistical software.

Overview

Module objective: To introduce the student to elementary Number Theory.

Induction. The division algorithm and the Euclidean algorithm in Z. The fundamental theorem of arithmetic. The integers modulo n. Fermat's Little Theorem, Euler phi function, Euler's generalisation of Fermat's Little Theorem. Wilson's Theorem. Solving Linear Diophantine equations. Solving systems of linear congruences using the Chinese Remainder Theorem.
Legendre symbols, quadratic residues, quadratic Law of Reciprocity. Primitive roots. Successive squaring mod n for fast multiplication.
Computation using mathematical/statistical software.

	Learning Outcomes
	On successful completion of the module, students should be able to: Solve systems of linear congruences. Prove and apply the classical theorems of elementary number theory. Define the Legendre symbol and determine whether a number is a quadratic residue. Find primitive roots. Use the methods from the course to solve problems. State accurately any definitions given in the course. State, prove and apply any theorems given in the course.

Learning Outcomes

Teaching & Learning methods

Assessment

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes Continuous assessment mark is carried forward to the Autumn. University scheduled written examination (Autumn): 120 minutes, On-campus

	Pre-Requisites
	Basic manipulative skills.

Timetable

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Courses / Module

ELEMENTARY NUMBER THEORY

Semester 1

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