MA30810 - NUMBER THEORY

Module Identifier	MA30810
Module Title	NUMBER THEORY
Academic Year	2001/2002
Co-ordinator	Dr T McDonough
Semester	Semester 2
Pre-Requisite	MA21410
Course delivery	Lecture	19 x 1 hour lectures
	Seminars / Tutorials	3 x 1 hour example classes
Assessment	Exam	2 Hours (written examination)	100%
	Resit assessment	2 Hours (written examination)	100%

General description

The theory of numbers is one of the oldest branches of mathematics. It is concerned with a study of the most basic objects of mathematics - the integers. The module leads to a study of the topics (i) solution of polynomial congruences, (ii) the quadratic reciprocity law, (iii) multiplicative arithmetic functions, e.g. the sum of the factors as an integer.

Aims

To provide an introduction to some topics in classical number theory.

Learning outcomes

On completion of this module, a student should be able to:

examine consequences of the Euclidean algorithm and factorisation of integers into products of primes;
solve polynomial congruences;
derive consequences of quadratic residue law;
establish identities involving multiplicative functions;
provide formal proof of propositions.

Syllabus

1. Divisibility and Congruence
2. Classical Congruences
3. General Techniques for Solving Polynomial Congruences
4. Multiplicative Functions and Related Identities
5. Diophantine Equations

Reading Lists

Books
** Recommended Text
G A Jones & J M Jones. (1988) Elementary Number Theory. Springer 3540761977
** Supplementary Text
I Niven, H S Zuckerman & H L Montgomery. (1991) An Introduction the Theory of Numbers. Wiley 047154600?
G H Hardy & E M Wright. (1979) An Introduction to the Theory of Numbers. 5th. OUP 0198531702
H E Rose. (1994) A Course in Number Theory. Oxford Science Publications 0198534795
R B J T Allenby & E J Redfern. (1989) Introduction to Number Theory with Computing. Arnold 0713136618
H Rademacher. (1964) Lectures on Elementary Number Theory. Blaisdell X200628614
I M Vinogradov. (1954) Elements of Number Theory. Dover 54003691