You will study eight courses and complete a main project under the supervision of a member of staff.
Theory of Error-Correcting Codes
The aim of this unit is to provide you with an introduction to the theory of error-correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.
Advanced Cipher Systems
Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed, as well as methods for obtaining confidentiality and authentication.
The main project (dissertation) accounts for 25% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.
Applications of Field Theory
You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.
Quantum Information Theory
‘Anybody who is not shocked by quantum theory has not understood it' (Niels Bohr). The aim of this unit is to provide you with a sufficient understanding of quantum theory in the spirit of the above quote. Many applications of the novel field of quantum information theory can be studied using undergraduate mathematics.
In this unit you will be introduced to the formal idea of an algorithm, when it is a good algorithm and techniques for constructing algorithms and checking that they work; explore connectivity and colourings of graphs, from an algorithmic perspective; and study how algebraic methods such as path algebras and cycle spaces may be used to solve network problems.
Advanced Financial Mathematics
In this unit you will investigate the validity of various linear and non-linear time series occurring in finance and extend the use of stochastic calculus to interest rate movements and credit rating;
The aim of this unit is to introduce some standard techniques and concepts of combinatorics, including: methods of counting including the principle of inclusion and exclusion; generating functions; probabilistic methods; and permutations, Ramsey theory.
Computational Number Theory
You will be provided with an introduction to many major methods currently used for testing/proving primality and for the factorisation of composite integers. The course will develop the mathematical theory that underlies these methods, as well as describing the methods themselves.
Several classes of computational complexity are introduced. You will discuss how to recognise when different problems have different computational hardness, and be able to deduce cryptographic properties of related algorithms and protocols.
On completion of the course graduates will have:
- knowledge and understanding of: the principles of communication through noisy channels using coding theory; the principles of cryptography as a tool for securing data; and the role and limitations of mathematics in the solution of problems arising in the real world
- a high level of ability in subject-specific skills, such as algebra and number theory
- developed the capacity to synthesise information from a number of sources with critical awareness
- critically analysed the strengths and weaknesses of solutions to problems in applications of mathematics
- the ability to clearly formulate problems and express technical content and conclusions in written form
- personal skills of time management, self-motivation, flexibility and adaptability.