Masters Degrees (Coding Theory)

Mathematics is at the heart of advances in science, engineering and technology, as well as being an indispensable problem-solving and decision-making tool in many other areas of life. This MSc course enables you to delve deeply into particular aspects of pure and applied mathematics, through a wide choice of modules in fascinating areas such as fractal geometry, coding theory and analytic theory. You’ll complete your MSc with a piece of independent study, exploring the history of modern geometry, advances in approximation theory, variational methods applied to eigenvalue problems, or algebraic graph theory and culminating in a dissertation on the topic of your choice.

Key features of the course

•Ideal for mathematically inclined scientists and engineers as well as mathematicians
•Extends your knowledge and refines your abilities to process information accurately, and critically analyse and communicate complex ideas
•Develops an enhanced skill set that will put you at an advantage in careers as diverse as mathematics, education, computer science, economics, engineering and finance.
•The most popular MSc in mathematics in the UK.
This qualification is eligible for a Postgraduate Loan available from Student Finance England. For more information, see Fees and funding

Course details

You can take a number of different routes towards your qualification - see the full module list for all options.

Modules

The modules in this qualification are categorised as entry, intermediate and dissertation. Check our website for start dates as some modules are not available for study every year.

Entry:

• Calculus of variations and advanced calculus (M820)
• Analytic number theory I (M823)

Intermediate:

• Nonlinear ordinary differential equations (M821)
• Applied complex variables (M828) - next available in October 2017 and following alternate years
• Analytic number theory II (M829) - next available in October 2018 and following alternate years
• Approximation theory (M832) - next available in October 2018 and following alternate years
• Advanced mathematical methods (M833) - next available in October 2017 and following alternate years
• Fractal geometry (M835) - next available in October 2017 and following alternate years
• Coding theory (M836) - next available in October 2018 and following alternate years
• Dissertation: Dissertation in mathematics (M840)

Module study order:

•You must normally pass at least one entry level module before studying an intermediate module.
•You must pass Analytic number theory I (M823) before studying Analytic number theory II (M829).
•You must normally pass four modules before studying the Dissertation in mathematics (M840).
•Some topics for the dissertation have prerequisite modules

Otherwise within each category modules may be studied in any order, and you may register for a module while studying a pre-requisite for that module (i.e. before you know whether you have passed the pre-requisite module or not).

To gain this qualification, you need 180 credits as follows:

150 credits from this list:

Optional modules

• Advanced mathematical methods (M833)
• Analytic number theory I (M823)
• Analytic number theory II (M829)
• Applied complex variables (M828)
• Approximation theory (M832)
• Calculus of variations and advanced calculus (M820)
• Coding theory (M836)
• Fractal geometry (M835)
• Nonlinear ordinary differential equations (M821)

Plus

Compulsory module

Dissertation in mathematics (M840)

The modules quoted in this description are currently available for study. However, as we review the curriculum on a regular basis, the exact selection may change over time.

Credit transfer

For this qualification, we do not allow you to count credit for study you have already done elsewhere.

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This highly focused MSc explores some of the mathematics behind modern secure information and communications systems, specialising in mathematics relevant for public key cryptography, coding theory and information theory. During the course critical awareness of problems in information transmission, data compression and cryptography is raised, and the mathematical techniques which are commonly used to solve these problems are explored.

The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography and our academic staff include several leading researchers in these areas. Students on the programme have the opportunity to carry out their dissertation projects in cutting-edge research areas and to be supervised by experts.

The transferable skills gained during the MSc will open up a range of career options as well as provide a solid foundation for advanced research at PhD level.

See the website https://www.royalholloway.ac.uk/mathematics/coursefinder/mscmathematicsofcryptographyandcommunications(msc).aspx

Why choose this course?

- You will be provided with a solid mathematical foundation and a knowledge and understanding of the subjects of cryptography and communications preparing you for research or professional employment in this area.

- 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 former 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 as well as complete a main project under the supervision of a member of staff.

Core courses:
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.

Channels
In this unit, you will investigate the problems of data compression and information transmission in both noiseless and noisy environments.

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.

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.

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:
- a suitable mathematical foundation for undertaking research or professional employment in cryptography and/or communications

- the appropriate background in information theory and coding theory enabling them to understand and be able to apply the theory of communication through noisy channels

- the appropriate background in algebra and number theory to develop an understanding of modern public key cryptosystems

- a critical awareness of problems in information transmission and data compression, and the mathematical techniques which are commonly used to solve these problems

- a critical awareness of problems in cryptography and the mathematical techniques which are commonly used to provide solutions to these problems

- a range of transferable skills including familiarity with a computer algebra package, experience with independent research and managing the writing of a dissertation.

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%.

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.

How to apply

Applications for entry to all our full-time postgraduate degrees can be made online https://www.royalholloway.ac.uk/studyhere/postgraduate/applying/howtoapply.aspx .

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The ALGANT Master program provides a study and research track in pure mathematics, with a strong focus on algebra, geometry and number theory. This track may be completed throughout Europe and the world, thanks to a partnership between leading research universities. The ALGANT course introduces students to the latest developments within these subjects, and provides the best possible preparation for their forthcoming doctoral studies.

The ALGANT program consists mainly of advanced courses within the field of mathematics and of a research project or internship leading to a Master thesis. Courses are offered in: algebraic geometry, algebraic and geometric topology, algebraic and analytic number theory, coding theory, combinatorics, complex function theory, cryptology, elliptic curves, manifolds. Students are encouraged to participate actively in seminars.

The university partners offer compatible basic preparation in the first year (level 1), which then leads to a complementary offer for more specialized courses in the second year (level 2). 

Program structure

Year 1 (courses in French)

Semester 1

• Modules and quadratic spaces (9 ECTS)
• Group theory (6 ECTS)
• Complex analysis (9 ECTS)
• Functional analysis (6 ECTS)

Semester 2

• Geometry (6 ECTS)
• Number theory (6 ECTS)
• Spectral theory and distributions (6 ECTS)
• Probability and statistics (6 ECTS)
• Cryptology (6 ECTS)
• Algebra and formal computations (6 ECTS)

Year 2 (courses in English)

Semester 1

• Number theory (9 ECTS)
• Algorithmic number theory (6 ECTS)
• Geometry (9 ECTS)
• Elliptic curves (6 ECTS)
• Algebraic geometry (9 ECTS)
• Analytic number theory: advanced course 1 (6 ECTS)

Semester 2

• Cohomology of groups: advanced course 2 (6 ECTS)
• The key role of certain inequalities at the interface between complex geometry (6 ECTS)

Strengths of this Master program

• Courses given by academic experts within the field of mathematics.
• Individually tailored study tracks.
• Top-quality scientific environment and facilities provided by leading global research institutes, e.g. Institut de Mathématiques de Bordeaux.
• Supported by the International Master program of the Bordeaux Initiative of Excellence.

After this Master program?

Students who successfully complete the ALGANT program will be well equipped to pursue a career in research by preparing a Ph.D.

Graduates may also directly apply for positions as highly trained mathematicians, especially in the areas of cryptography, information security and numerical communications.

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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.

See the website https://www.royalholloway.ac.uk/mathematics/coursefinder/mscmathematicsforapplications.aspx

Why choose this course?

- 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

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.

How to apply

Applications for entry to all our full-time postgraduate degrees can be made online https://www.royalholloway.ac.uk/studyhere/postgraduate/applying/howtoapply.aspx .

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Audiovisual experiences are key drivers, not just for entertainment but also for business, security and technology development. Video accounts for around 80 per cent of all internet traffic and some mobile network operators have predicted that wireless traffic will double every year for the next 10 years - driven primarily by video. Visual information processing also plays a major role underpinning other industries such as healthcare, security, robotics and autonomous systems.

This challenging, one-year taught Master’s degree covers a range of advanced topics drawn from the field of multimedia signal processing and communications. The programme covers the properties and limitations of modern communication channels and networks, alongside the coding and compression methods required for efficient and reliable wired and wireless audio-visual transmission. It provides students with an excellent opportunity to acquire the necessary skills to enter careers in one of the most dynamic and exciting fields in ICT.

The programme builds on the research strengths of the Visual Information Laboratory and the Communication Systems and Networks Group within the Faculty of Engineering at Bristol. Both groups are highly regarded for combining fundamental research with strong industrial collaboration and their innovative research has resulted in ground-breaking technology in the areas of image and video analysis, coding and communications. Both groups also offer extensive, state-of-the-art research facilities.

This MSc provides in-depth training in design, analysis and management skills relevant to the theory and practice of the communication networks industry. The programme is accredited by the Institution of Engineering and Technology until 2018, and is one of only a handful of accredited programmes in this field in the UK.

Programme structure

Your course will cover the following core subjects:
Semester One (50 credits)
-Coding theory
-Communication systems
-Digital filters and spectral analysis
-Mobile communications
-Networking protocol principles

Semester Two (70 credits)
-Digital signal processing systems
-Speech and audio processing
-Optimum signal processing
-Biomedical imaging
-Image and video coding
-Engineering research skills

Research project
You will complete a substantial research project, starting during Semester Two and completed during the summer. This may be based at the University or with industrial partners.

Careers

This one-year MSc programme covers all aspects of current and future image and video communications and associated signal processing technologies. It will prepare you for a diverse range of exciting careers, not only in the communications field, but also in other areas such as management consultancy, project management, finance and government agencies.

Our graduates have gone on to have rewarding careers in some of the leading multinational communications companies, such as Huawei, China Telecom, Toshiba, China Mobile and Intel. Some graduates follow a more research-oriented career path with a number of students going on to study for PhDs at leading universities.

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This MSc covers a range of advanced topics drawn from wireless communications and communications-related signal processing, including associated enabling technologies. It provides an excellent opportunity to develop the skills required for careers in some of the most dynamic fields in wireless communications.

This programme builds on the internationally recognised research strengths of the Communications Systems and Networks group within the Smart Internet Lab. This group conducts pioneering research in a number of key fundamental and experimental work areas, including spatial channel measurements and predictions, information theory, advanced wireless access (cellular and WLAN) and RF technologies. The group has well-equipped laboratories with state-of-the-art test and measurement equipment and first-class computational facilities.

The MSc provides in-depth training in design, analysis and management skills relevant to the theory and practice of the wireless communications industry. This degree is accredited by the Institute of Engineering and Technology (IET) until 2018, and is one of only a handful of accredited programmes in this field in the UK.

Programme structure

Your course will cover the following core subjects:
Semester One (60 credits)
-Coding theory
-Radio frequency engineering
-Communication systems
-Mobile communications
-Networking protocol principles
-Digital filters and spectral analysis

Semester Two (60 credits)
-Advanced mobile radio techniques
-Antennas and electromagnetic compatibility
-Broadband wireless communications
-Digital signal processing systems
-Engineering research skills
-Research project (60 credits)

You will carry out a substantial research project, starting during Semester Two and completing during the summer. This may be based at the University or with industrial partners.

Careers

This is a challenging one-year taught Master’s degree, covering all aspects of current and future wireless communication systems and associated signal processing technologies. It will prepare you for a diverse range of exciting careers - not only in the communications field, but also in other areas such as management consultancy, project management, finance and government agencies.

Our graduates have gone on to have rewarding careers in some of the leading multinational communications companies, such as Huawei, China Telecom, Toshiba, China Mobile and Intel. Some graduates follow a more research-oriented career path, with a number of students going on to study for PhDs at leading universities.

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This programme offers you the chance to study a range of modules in pure and applicable mathematics, giving you the opportunity to increase your knowledge and abilities in these areas. Depending on your choices, you will take either 7 or 8 modules, allowing you to study several different topics in depth, and to focus on the areas that interest you most. Over 2 years you will also learn the methods of mathematical research: how to read mathematical papers and how to communicate mathematics, both in written form for your project dissertation, and orally when you give presentations about your project.

You will acquire the skills to pursue your interest in the subject, either formally with a research degree, or informally with independent reading. You will come to us as someone with a mathematics degree; you will graduate as a mathematician.

Why study this course at Birkbeck?

Offers modules in group theory, graph theory, combinatorics and applicable mathematics such as coding theory and cryptography.
Specially designed for part-time students: delivered via high-quality, face-to-face teaching in the evenings, so that you can fit study around daytime commitments.
You complete a project in your chosen area of mathematics, with guidance from an expert supervisor.
Birkbeck's mathematicians are all active researchers, mostly in the areas of algebra and combinatorics. We've developed this exciting course around those research strengths.
Birkbeck has a library and several workstation rooms. You can also use several local university libraries, including the collection of the London Mathematical Society, a 5-minute walk from Birkbeck's main building.

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Modules

To gain this qualification, you need 180 credits as follows:

Stage 1

60 credits from List A:

List A: optional modules

• Advanced routing - CCNP 1 (T824)
• Capacities for managing development (T878)
• Conflict and development (T879)
• Development: context and practice (T877)
• Environmental monitoring and protection (T868)
• Finite element analysis: basic principles and applications (T804)
• Institutional development (TU872)
• Making environmental decisions (T891)
• Managing for sustainability (T867)
• Managing systemic change: inquiry, action and interaction (TU812)
• Managing technological innovation (T848)
• Manufacture materials design (T805)
• Multilayer switching - CCNP 3 (T826)
• Network security (T828)
• Optimising networks - CCNP 4 (T827)
• Problem solving and improvement: quality and other approaches (T889)
• Strategic capabilities for technological innovation (T849)
• Thinking strategically: systems tools for managing change (TU811)

Plus 30 credits from List B:

List B: optional modules

• Advanced mathematical methods (M833)
• Advanced routing - CCNP 1 (T824)
• Analytic number theory I (M823)
• Analytic number theory II (M829)
• Applied complex variables (M828)
• Approximation theory (M832)
• Calculus of variations and advanced calculus (M820)
• Capacities for managing development (T878)
• Coding theory (M836)
• Conflict and development (T879)
• Data management (M816)
• Developing research skills in science (S825)
• Development: context and practice (T877)
• Digital forensics (M812)
• Environmental monitoring and protection (T868)
• Finite element analysis: basic principles and applications (T804)
• Fractal geometry (M835)
• Information security (M811)
• Institutional development (TU872)
• Making environmental decisions (T891)
• Managing for sustainability (T867)
• Managing systemic change: inquiry, action and interaction (TU812)
• Managing technological innovation (T848)
• Manufacture materials design (T805)
• Multilayer switching - CCNP 3 (T826)
• Network security (T828)
• Nonlinear ordinary differential equations (M821)
• Optimising networks - CCNP 4 (T827)
• Problem solving and improvement: quality and other approaches (T889)
• Project management (M815)
• Researching mathematics learning (ME825)*
• Software development (M813)
• Software engineering (M814)
• Space science (S818) NEW1
• Strategic capabilities for technological innovation (T849)
• Thinking strategically: systems tools for managing change (TU811)

* 60-credit module of which only 30 credits count towards this qualification

Plus 30 credits from:

Compulsory module

Team engineering (T885)

Stage 2

60 credits from:

Compulsory module

Research project (T802)

The modules quoted in this description are currently available for study. However, as we review the curriculum on a regular basis, the exact selection may change over time.

Credit transfer

Credit transfer is not permitted for the MSc except for any awarded as part of the Postgraduate Diploma in Engineering.
For further advice and guidance, please email us.

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In this MRes Mathematical Sciences course, you will gain deep knowledge of a chosen topic in mathematics or statistics and develop your research skills in project planning, reviewing literature, group discussions, research presentations and writing publications.

You can choose to work with experts from a range of areas including quantum cryptography, graph theory, statistical analysis, bioinformatics and mathematical modelling.

You will take three taught modules each providing you with the underpinning theory to support your research work.

Modules:

• Computational Statistics and Data Analysis
• Applied Statistics
• Statistical Modelling
• Mathematical Recipes
• Topics in Mathematical Biology
• Linear Systems
• Topics in Applied Mathematics#
• Numerical Analysis and Dynamical Systems
• Topics in Pure Mathematics
• Coding Theory and Cryptography
• Research Methods
• Research Project

COME VISIT US ON OUR NEXT OPEN DAY!

Visit us on campus throughout the year, find and register for our next open event on http://www.ntu.ac.uk/pgevents.

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The Department of Mathematics offers graduate courses leading to M.Sc., and eventually to Ph.D., degree in Mathematics. The Master of Science program aims to provide a sound foundation for the students who wish to pursue a research career in mathematics as well as other related areas. The department emphasizes both pure and applied mathematics. Research in the department covers algebra, number theory, combinatorics, differential equations, functional analysis, abstract harmonic analysis, mathematical physics, stochastic analysis, biomathematics and topology.

Current faculty projects and research interests:

• Ring Theory and Module Theory, especially Krull dimension, torsion theories, and localization

• Algebraic Theory of Lattices, especially their dimensions (Krull, Goldie, Gabriel, etc.) with applications to Grothendieck categories and module categories equipped with torsion theories

• Field Theory, especially Galois Theory, Cogalois Theory, and Galois cohomology

• Algebraic Number Theory, especially rings of algebraic integers

• Iwasawa Theory of Galois representations and their deformations Euler and Kolyvagin systems, Equivariant Tamagawa Number
Conjecture

• Combinatorial design theory, in particular metamorphosis of designs, perfect hexagon triple systems

• Graph theory, in particular number of cycles in 2-factorizations of complete graphs

• Coding theory, especially relation of designs to codes

• Random graphs, in particular, random proximity catch graphs and digraphs

• Partial Differential Equations

• Nonlinear Problems of Mathematical Physics

• Dissipative Dynamical Systems

• Scattering of classical and quantum waves

• Wavelet analysis

• Molecular dynamics

• Banach algebras, especially the structure of the second Arens duals of Banach algebras

• Abstract Harmonic Analysis, especially the Fourier and Fourier-Stieltjes algebras associated to a locally compact group

• Geometry of Banach spaces, especially vector measures, spaces of vector valued continuous functions, fixed point theory, isomorphic properties of Banach spaces

• Differential geometric, topologic, and algebraic methods used in quantum mechanics

• Geometric phases and dynamical invariants

• Supersymmetry and its generalizations

• Pseudo-Hermitian quantum mechanics

• Quantum cosmology

• Numerical Linear Algebra

• Numerical Optimization

• Perturbation Theory of Eigenvalues

• Eigenvalue Optimization

• Mathematical finance

• Stochastic optimal control and dynamic programming

• Stochastic flows and random velocity fields

• Lyapunov exponents of flows

• Unicast and multicast data traffic in telecommunications

• Probabilistic Inference

• Inference on Random Graphs (with emphasis on modeling email and internet traffic and clustering analysis)

• Graph Theory (probabilistic investigation of graphs emerging from computational geometry)

• Statistics (analysis of spatial data and spatial point patterns with applications in epidemiology and ecology and statistical methods for medical data and image analysis)

• Classification and Pattern Recognition (with applications in mine field and face detection)

• Arithmetical Algebraic Geometry, Arakelov geometry, Mixed Tate motives

• p-adic methods in arithmetical algebraic geometry, Ramification theory of arithmetic varieties

• Topology of low-dimensional manifolds, in particular Lefschetz fibrations, symplectic and contact structures, Stein fillings

• Symplectic topology and geometry, Seiberg-Witten theory, Floer homology

• Foliation and Lamination Theory, Minimal Surfaces, and Hyperbolic Geometry

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Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Mathematics at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).

The MSc Mathematics course has been designed for students who wish to build on their BSc, extending their range of mathematics expertise across a broader spread of topics, and demonstrating their literature research skills through an extended dissertation.

Such a qualification will mark graduates out as having a broader and deeper understanding of mathematics, and the skills required to pursue a significant project with a high level of independence, presenting their results in a written report. This will give MSc Mathematics graduates an edge in the ever more competitive jobs market.

On the Mathematics course you will study different elements of mathematics in a broad sense - including mathematical elements of computing if desired - in addition to developing your research, project management, and written communication skills through a project you will undertake. As a student of MSc in Mathematics, you will be fully supported to ensure that your project further develops an excellent foundation for your future career plans.

Modules

Modules on the MSc Mathematics include:

• Algebraic coding theory

• Biomathematics

• Black-Scholes theory

• Data science

• Differential geometry

• Fourier analysis

• Ito calculus

• Lie theory

• Numerical analysis

• Partial differential equations

• Stochastic processes

• Statistical mechanics

• Topology

Please visit our website for a full description of modules for the MSc Mathematics.

On top of the Mathematics modules you study, you will also complete a dissertation as part of your studies.

Facilities

The Aubrey Truman Reading Room, located in the centre of the Department of Mathematics, houses the departmental library and computers for student use. It is a popular venue for students to work independently on the regular example sheets set by their lecturers, and to discuss Mathematics together.

Our main university library, Information Services and Systems (ISS), contains a notably extensive collection of Mathematics books.

Mathematics students will benefit from the £31m Computational Foundry for computer and mathematical sciences which will provide the most up-to-date and high quality teaching facilities featuring world-leading experimental set-ups, devices and prototypes to accelerate innovation and ensure students will be ready for exciting and successful careers. (From September 2018)

Careers

The ability to think rationally and to process data clearly and accurately are highly valued by employers. Mathematics graduates earn on average 50% more than most other graduates. The most popular areas are the actuarial profession, the financial sector, IT, computer programming and systems administration, and opportunities within business and industry where employers need mathematicians for research and development, statistically analysis, marketing and sales.

Some of our Mathematics students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where Mathematics graduates will find plenty of career opportunities.

Research

The results of the Research Excellence Framework (REF) 2014 show that our research environment (how the Department supports research staff and students) and the impact of our research (its value to society) were both judged to be 100% world leading or internationally excellent.

All academic staff in Mathematics are active researchers and the department has a thriving research culture.

http://www.swansea.ac.uk/postgraduate/taught/science/mscmathematics/

Student Profile

"Further to my studies at Swansea University as a Master of Science graduate in Financial Mathematics, I am currently working at Deutsche Bank in London as part of the Structured Financial Services team providing client services for corporate lending and debt portfolios. The complex nature of the Mathematics course has helped me become a logical decision maker and a highly skilled problem solver. These transferable skills are very useful in the world of Finance since the role is highly challenging working towards deadlines and structured transaction targets. My studies at Swansea University have also enriched me with leadership, motivational skills and have enhanced my communication skills. I work in a close team of 10 people within a large department which encourages a culture that strives towards learning and effective teamwork. I thoroughly enjoyed my time at Swansea University and cherish the many fond memories. I am so pleased to be expanding my horizon within a major financial centre."

Rhian Ivey, BSc Mathematics, MSc Mathematics and Computing for Finance

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If you want to study for a mathematics-related MSc course but don’t meet the full academic entry requirements, this programme will equip you with the mathematical knowledge and skills you need.

You’ll choose from a range of undergraduate modules offered in the School of Mathematics, building a programme which fills the gaps in your knowledge and prepares you for postgraduate study in your chosen field. If you complete the GradDip and meet the required performance standard, you’ll be eligible to apply for a number of related MSc courses in the next academic year.

You could develop your understanding of graph theory or quantum mechanics, algebra or calculus, financial statistics or coding theory among many others in a supportive and stimulating research environment.

Course content

The programme is highly flexible and there are no compulsory modules, meaning you can build your own programme of study that suits your interests as well as the MSc programme you want to study after the GradDip. Your choices will be checked and approved by the Programme Leader, who might also suggest different choices according to your background.

Around half of the total number of credits you study should come from level 3 modules, including no more than one project module. You’ll need to pass at least 100 credits – including at least 60 credits at level 3 – and have an overall average of at least 40 to graduate with the GradDip.

For more information on typical modules, read Mathematics GradDip in the course catalogue

Learning and teaching

The flexibility of this programme means that you can choose from modules that use a wide range of teaching and learning methods. These could include example classes, practicals, lectures, seminars, workshops and tutorials among many others.

However, independent study is another vital element of the programme which allows you to develop your skills and prepare for taught sessions.

Assessment

You’ll also come across a variety of assessment methods which could include exams as well as problem sheets, essays, practicals, class tests and other forms of coursework.

Career opportunities

The GradDip is a stepping stone to a postgraduate qualification. If you complete the programme successfully, you’ll be eligible for entry onto a number of related MSc programmes in the following academic year.

Mathematicians can choose from a wide range of career options in diverse employment sectors, from software development and system modelling to finance, risk management and general and management positions in sectors such as manufacturing and retail.

Once you’ve completed a postgraduate qualification, you may be able to benefit from new opportunities at more senior levels, or even prepare for further research at PhD level.

Careers support

We encourage you to prepare for your career from day one. That’s one of the reasons Leeds graduates are so sought after by employers.

The Careers Centre and staff in your faculty provide a range of help and advice to help you plan your career and make well-informed decisions along the way, even after you graduate. Find out more at the Careers website.

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In what way does society influence the way that we use language? And conversely, how far does the way we use language influence society? Can language use impact the class system? Sexism? Mental health?

On our MA Sociolinguistics, you address questions like these through exploration of the stylistic, cognitive and functional aspects of language variation and change. We familiarise you with the foundations of contemporary sociolinguistics, including:
-Language variation and change
-Ethnography of speaking
-Multilingualism
-Discourse

We additionally offer modules in some of the most prominent sub-disciplines in linguistics such as variation theory, socio-pragmatics, conversation analysis, language contact, language and gender, and language rights.

You also gain first-hand experience of interview, questionnaire and observation data and learn quantitative and qualitative methodologies for coding and analysing sociolinguistic interview and questionnaire data.

We are one of the largest and most prestigious language and linguistics departments in the world, a place where talented students become part of an academic community in which the majority of research is rated ‘world-leading’ or ‘internationally excellent’ (REF 2014), placing us firmly within the top 10 departments in the UK and ranked among the top 150 departments on the planet according to the QS World [University] Rankings [2016] for linguistics.

If you want a global outlook, are interested in human communication, and want to study for a degree with real-world practical value in a world-class department, welcome to Essex.

Our expert staff

Our staff maintain excellent student-staff ratios with capped language-specific seminars.

In sociolinguistics, Peter Patrick, Rebecca Clift, Enam Al Wer and Vineeta Chand all work on different aspects of how language varies, and investigate which factors cause such variation. Peter is also involved in language rights, and offers expert opinions in asylum cases where language is used to determine origin.

Specialist facilities

-An exciting programme of research seminars and other events
-Our Languages for All programme offers you the opportunity to study an additional language alongside your course at no extra cost
-Our ‘Visual World’ Experimental Lab records response times and eye movements when individuals are presented with pictures and videos
-Our Eye-Tracking Lab monitors eye movement of individuals performing tasks
-Our Psycholinguistics Lab measures how long it takes individuals to react to words, texts and sounds
-Our Linguistics Lab has specialist equipment to analyse sound
-Our Albert Sloman Library houses a strong collection of books, journals, electronic resources and major archives

Your future

Our course can lead to careers in areas such as academic research, publishing, journalism, administration, public service and teaching. You develop key employability skills including research design, data analysis, thinking analytically, report writing and public speaking.

We work with the University’s Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

Within our Department of Language and Linguistics, we also offer supervision for PhD and MPhil. We offer supervision in areas including language acquisition, language learning and language teaching, culture and communication, psycholinguistics, language disorders, sociolinguistics, and theoretical and descriptive linguistics.

Our graduates are successful in a wide variety of career paths. They leave Essex with a unique set of skills and experience that are in demand by employers.

Example structure

-Variationist Sociolinguistic Theory
-Sociolinguistic Methods 1: Data Collection
-Sociolinguistic Methods: Data Coding and Analysis
-MA Dissertation
-Assignment Writing and Dissertation Preparation
-Sociocultural Linguistics
-Advanced Phonology (optional)
-First Language Acquisition (optional)
-Phonological Development (optional)
-Second Language Acquisition and Linguistics Theory (optional)
-American Languages (optional)
-Varieties of English (optional)
-Sentence Processing (optional)
-Language Rights (optional)
-Semantics (optional)
-Language Learning (optional)
-English Syntax 1 (optional)
-Individual Differences in L2 Learning (optional)
-Syntactic Theory I (optional)
-Experimental Design and Analysis (optional)
-Research Methods I (optional)
-English Syntax 2 (optional)
-Syntactic Theory II (optional)
-The Role of Age in Bilingual Development (optional)
-Variation in English II (optional)
-Research Methods II (optional)
-Graduate Research Assignment (optional)
-Language Attrition (optional)
-Language in Context: From Pragmatics to Conversation Analysis (optional)
-Intercultural Communication: communicating across languages and cultures (optional)

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If you are interested in the possibility of a research degree (PhD or Research Masters) in the School of Mathematical Sciences, we encourage you to become familiar with the range of research activity and expertise in the School. In particular, we would encourage you to approach or contact members of the academic staff whose research area may be of particular interest.

The research of the School covers a wide range of areas including:

Analysis (Infinite-dimensional analysis, Functional Analysis, Potential Theory)
Algebra (Matrix Theory, K-theory, Quadratic and Hermitian Forms)
Discrete Mathematics (Coding, Cryptography, Number Theory)
Applied Mathematics (Fluid Dynamics, Computational Science, Meteorology, Biomathematics, Information Theory)
Theoretical Physics (Astrophysics, General Relativity, Quantum Gravity, Statistical Mechanics, Quantum Field Theory)
Statistics (Bayesian Statistics, Pharmaceutical, Medical and Educational Statistics, Environmental and ecological modelling, Epidemiology, Econometrics).

Please see our School Website for more details:
http://www.ucd.ie/mathstat

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Applied linguistics addresses real-life language problems through insights gained from current linguistic theory, psychology and education.

Our MA is designed for people who want to know more about how foreign or second languages (particularly English) are learned, and how different kinds of classroom practice might affect proficiency. You explore different approaches to understanding language and language acquisition, and the methods that can be used to investigate language learning and teaching. You select a mixture of modules on language learning and its application to classroom practices.

You can choose areas of special study from a wide range of options, including:
-Teaching speaking and listening skills to language learners
-Psychological factors in second language learning
-Computer-assisted language-learning
-Literature and language-learning
-Age and bilingual development

You'll also be part of our Centre for Research in Language Development throughout the Lifespan (LaDeLi), a unique research centre specialising in all aspects of language learning and development.

We are one of the largest and most prestigious language and linguistics departments in the world, a place where talented students become part of an academic community in which the majority of research is rated ‘world-leading’ or ‘internationally excellent’, placing us firmly within the top 10 departments in the UK and among the top 150 departments on the planet (QS World University Rankings 2016).

If you want a global outlook, are interested in human communication, and want to study for a degree with real-world practical value in a world-class department, welcome to Essex.

This course is also available on a part-time basis.

Our expert staff

Our staff maintain excellent student-staff ratios with capped language-specific seminars.

In applied linguistics, Florence Myles, Monika Schmid, Sophia Skoufaki, Karen Roehr-Brackin, Adela Gánem-Gutiérrez, and Roger Hawkins focus on the learning of second and further languages, whilst Julian Good, Christina Gkonou and Tracey Costley focus on issues to do with the classroom teaching of English as a foreign language.

Specialist facilities

-An exciting programme of research seminars and other events
-Our Languages for All programme offers you the opportunity to study an additional language alongside your course at no extra cost
-Our ‘Visual World’ Experimental Lab records response times and eye movements when individuals are presented with pictures and videos
-Our Eye-Tracking Lab monitors eye movement of individuals performing tasks
-Our Psycholinguistics Lab measures how long it takes individuals to react to words, texts and sounds
-Our Linguistics Lab has specialist equipment to analyse sound
-Our Albert Sloman Library houses a strong collection of books, journals, electronic resources and major archives

Your future

Our course can lead to careers in areas such as academic research, publishing, journalism, administration, public service and teaching. You develop key employability skills including research design, data analysis, thinking analytically, report writing and public speaking.

We work with the University’s Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

Within our Department of Language and Linguistics, we also offer supervision for PhD and MPhil. We offer supervision in areas including language acquisition, language learning and language teaching, culture and communication, psycholinguistics, language disorders, sociolinguistics, and theoretical and descriptive linguistics.

Our graduates are successful in a wide variety of career paths. They leave Essex with a unique set of skills and experience that are in demand by employers.

Example structure

Postgraduate study is the chance to take your education to the next level. The combination of compulsory and optional modules means our courses help you develop extensive knowledge in your chosen discipline, whilst providing plenty of freedom to pursue your own interests. Our research-led teaching is continually evolving to address the latest challenges and breakthroughs in the field, therefore to ensure your course is as relevant and up-to-date as possible your core module structure may be subject to change.

MA Applied Linguistics
-MA Dissertation
-Assignment Writing and Dissertation Preparation
-Language Learning
-Research Methods I
-Research Methods II
-Advanced Phonology (optional)
-First Language Acquisition (optional)
-Phonological Development (optional)
-Second Language Vocabulary: Learning, Teaching and Use (optional)
-Topics in the Psychology of Language Learning and Teaching (optional)
-Second Language Acquisition and Linguistics Theory (optional)
-American Languages (optional)
-Varieties of English (optional)
-Sentence Processing (optional)
-Language Rights (optional)
-Semantics (optional)
-Literature and Language Teaching (optional)
-English Syntax 1 (optional)
-Description of Language for TEFL/ELT and Applied Linguistics (optional)
-Individual Differences in L2 Learning (optional)
-Syntactic Theory I (optional)
-Variationist Sociolinguistic Theory (optional)
-Experimental Design and Analysis (optional)
-Materials Design and Evaluation (optional)
-Sociolinguistic Methods 1: Data Collection (optional)
-English Syntax 2 (optional)
-Syntactic Theory II (optional)
-Teaching, Listening and Speaking (optional)
-Sociocultural Linguistics (optional)
-The Role of Age in Bilingual Development (optional)
-Variation in English II (optional)
-Sociolinguistic Methods: Data Coding and Analysis (optional)
-Graduate Research Assignment (optional)
-Language Attrition (optional)
-Teaching Practice I (optional)
-Approaches, Methods and Teacher Development for TEFL/TESOL (optional)
-Language in Context: From Pragmatics to Conversation Analysis (optional)
-Teaching Reading and Writing in TEFL/TESOL (optional)
-Intercultural Communication: communicating across languages and cultures (optional)

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