Discrete Mathematics - MAST7015

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Module delivery information

This module is not currently running in 2023 to 2024.

Overview

Discrete mathematics has found new applications in the encoding of information. Online banking requires the encoding of information to protect it from eavesdroppers. Digital television signals are subject to distortion by noise, so information must be encoded in a way that allows for the correction of this noise contamination. Different methods are used to encode information in these scenarios, but they are each based on results in abstract algebra. This module will provide a self-contained introduction to this general area of mathematics.
Syllabus: Modular arithmetic, polynomials and finite fields. Applications to
• orthogonal Latin squares,
• cryptography, including introduction to classical ciphers and public key ciphers such as RSA,
• "coin-tossing over a telephone",
• linear feedback shift registers and m-sequences,
• cyclic codes including Hamming,
At level 7, topics will be studied and assessed to greater depth.

Details

Contact hours

Total contact hours: 42
Private study hours: 108
Total study hours: 150

Method of assessment

80% examination, 20% coursework

N L Biggs, Discrete Mathematics, Oxford University Press, 2nd edition, 2002
D Welsh, Codes and Cryptography, Oxford University Press, 1988
R Hill, A First Course in Coding Theory, Oxford University Press, 1980

See the library reading list for this module (Canterbury)

Learning outcomes

The intended subject specific learning outcomes. On successfully completing the level 7 module students will be able to:
1 demonstrate systematic understanding of the theory and practice of finite fields and their application to Latin squares, cryptography, m-sequences, cyclic codes and
further error-correcting codes;
2 demonstrate the capability to solve complex problems using a very good level of skill in calculation and manipulation of the material in the following areas: modular
arithmetic, factorising polynomials, construction of finite fields, Latin squares, classical and public key ciphers including RSA, m-sequences, cyclic codes;
3 apply a range of concepts and principles of discrete mathematics in loosely defined contexts, showing good judgment in the selection and application of tools and
techniques.

The intended generic learning outcomes. On successfully completing the level 7 module students will be able to:
1 work competently and independently, be aware of their own strengths and understand when help is needed;
2 demonstrate a high level of capability in developing and evaluating logical arguments;
3 communicate arguments confidently with the effective and accurate conveyance of conclusions ;
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 effective use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material effectively;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.

Notes

1. ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
2. The named convenor is the convenor for the current academic session.