Pre-requisite: MAST4001 (Algebraic Methods) or MAST4005 (Linear Mathematics)
OverviewThe security of our phone calls, bank transfers, etc. all rely on one area of Mathematics: Number Theory. This module is an elementary introduction to this wide area and focuses on solving Diophantine equations. In particular, we discuss (without proof) Fermat's Last Theorem, arguably one of the most spectacular mathematical achievements of the twentieth century. Outline syllabus includes: Modular Arithmetic; Prime Numbers; Introduction to Cryptography; Quadratic Residues; Diophantine Equations.
This module appears in:
Method of assessment
80% Examination, 20% Coursework
D.M. Burton, Elementary Number Theory, McGraw-Hill, 2010.
G.A. Jones and J.M. Jones, Elementary Number Theory, Springer, 1998.
W. Stein, Elementary Number Theory: Primes, Congruences, and Secrets, Undergraduate Texts in Mathematics, Springer, 2009.
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within Number Theory;
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the following areas: integers, prime numbers, congruences, arithmetic functions, quadratic residues, Diophantine equations;
3 apply the concepts and principles in Number Theory in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques;
4 make appropriate use of Maple.
The intended generic learning outcomes. On successfully completing the module students will be able to:
Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently.
8 demonstrate an increased level of skill in numeracy and computation.