Module Identifier MA30810  
Module Title NUMBER THEORY  
Academic Year 2000/2001  
Co-ordinator Dr T P McDonough  
Semester Semester 2  
Pre-Requisite MA21410  
Course delivery Lecture   19 x 1hour lectures  
  Seminars / Tutorials   3 x 1hour 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, (iv) representing numbers by forms, (only special quadratic forms are considered).

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

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

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

Reading Lists
** Recommended Text
G A Jones & J M Jones. Elementary Number Theory. Springer
** Supplementary Text
I Niven, H S Zuckerman & H L Montgomery. An Introductiono the Theory of Numbers. Wiley
G H Hardy & E M Wright. An Introduction to the Theory of Numbers. 5th edition. OUP
H E Rose. A Course in Number Theory. Oxford Science Publications
R B J T Allenby & E J Redfern. Introduction to Number Theory with Computing. Arnold
H Rademacher. Lectures on Elementary Number Theory. Blaisdell
I M Vinogradov. Elements of Number Theory. Dover