入学要求 Requirement：
First degree : UK Upper Second Class Honours degree (2:1). or equivalent, with Mathematics as a main field of study and good marks in relevant courses.
Alternative entry requirements : Exceptionally, at the discretion of the course director, qualifications in other subjects (for example, physics or computer science) or degrees of lower classification may be considered.
Applicants come from a diverse range of backgrounds and we accept a broad range of qualifications but a solid foundation in mathematics is needed.
英语要求English language requirements：
IELTS 6.5, TOEFL (iBT) 88, or equivalent, for non-native English speaking applicants.
Students from overseas should visit the International pages for information on the entry requirements from their country and further information on English language requirements. Royal Holloway International offers a Pre-Master’s Diploma for International Students and English language pre-sessional courses, allowing students the opportunity to develop their study skills and English language before starting their postgraduate degree.
学费 Tuition Fee：2011/2012 12,210pounds
课程特征Course Features
Course overview
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.
课程内容 Course Content：
You will study three core units and five elective units as well as complete a main project under the supervision of a member of staff.
Core course units:
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.
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.
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.
Elective course units:
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.
Aerodynamics and Geophysical Fluid Dynamics
This unit aims to show how the mathematical models of fluid flow (the Navier-Stokes equation and others) are successful in describing how aircraft are able to fly, and how the motions of the atmosphere and the oceans are caused.
Advanced Electromagnetism and Special Relativity
This unit aims to show how Maxwell’s equations lead to electromagnetic waves and indirectly to the special theory of relativity; how electromagnetic fields propagate with the speed of light; how to derive the laws of optics from these equations; and how the laws of special relativity lead to time dilation and length contraction.
Magnetohydrodynamics
You will be introduced to the study of the motion of conducting fluids in the presence of a magnetic field. Practical applications and a discussion of the structure of sunspots and the origin of the Earth’s magnetic field will be given.
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.
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.
Public Key Cryptography
This course introduces some of the mathematical ideas essential for an understanding of public key cryptography, such as discrete logarithms, lattices and elliptic curves. Several important public key cryptosystems are studied, such as RSA, Rabin, ElGamal Encryption, Schnorr signatures; and modern notions of security and attack models for public key cryptosystems are discussed.
Permutations and Counting with Groups
Since symmetries can be described as permutations, you will study the basic properties of permutations. By introducing the notion of a group, we are able to capture and investigate algebraically all the symmetries of a given structure. We proceed to develop the basic theory of finite groups, emphasising concrete examples which are often geometrical in nature.
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.
教学与评估 Teaching and Assessment：
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%
其它信息 Other Information：
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.