This course covers a wide range of topics from both applied and applicable mathematics and is aimed at students who want to study the field in greater depth, in areas which are relevant to real life applications.
You will explore the mathematical techniques that are commonly used to solve problems in the real world, in particular in communication theory and in physics. As part of the course you will carry out an independent research investigation under the supervision of a member of staff. Popular dissertation topics chosen by students include projects in the areas of communication theory, mathematical physics, and financial mathematics.
The transferable skills gained on this course will open you up to a range of career options as well as provide a solid foundation for advanced research at PhD level.
- You will be provided with a solid mathematical foundation and knowledge and understanding of the subjects of cryptography and communications, preparing you for research or professional employment in this area.
- The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography. The academics who teach on this course include several leading researchers in these areas.
- The mathematical foundations needed for applications in communication theory and cryptography are covered including Algebra, Combinatorics Complexity Theory/Algorithms and Number Theory.
- You will have the opportunity to carry out your dissertation project in a cutting-edge research area; our dissertation supervisors are experts in their fields who publish regularly in internationally competitive journals and there are several joint projects with industrial partners and Royal Holloway staff.
- After completing the course students have a good foundation for the next step of their career both inside and outside academia.
Department research and industry highlights
The members of the Mathematics Department cover a range of research areas. There are particularly strong groups in information security, number theory, quantum theory, group theory and combinatorics. The Information Security Group has particularly strong links to industry.
Course content and structure
You will study eight courses and complete a main project under the supervision of a member of staff.
Core courses: 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.
Main project 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.
Additional courses: 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.
Network Algorithms 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;
Combinatorics 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.
Complexity Theory 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.
Assessment is carried out by a variety of methods including coursework, examinations and a dissertation. The examinations in May/June count for 75% of the final average and the dissertation, which has to be submitted in September, counts for the remaining 25%.
Employability & career opportunities
Our students have gone on to successful careers in a variety of industries, such as information security, IT consultancy, banking and finance, higher education and telecommunication. In recent years our graduates have entered into roles including Principal Information Security Consultant at Abbey National PLC; Senior Manager at Enterprise Risk Services, Deloitte & Touche; Global IT Security Director at Reuters; and Information Security Manager at London Underground.