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The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications. Read more
The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications. It is the medium for expressing knowledge about many physical phenomena and is concerned with patterns, systems, and structures unrestricted by any specific application, but also allows for applications across many disciplines.

Why this programme

-The University of Glasgow’s School of Mathematics and Statistics is ranked 4th in Scotland (Complete University Guide 2015).
-The School has a strong international reputation in pure and applied mathematics research and our PGT programmes in Mathematics offer a large range of courses ranging from pure algebra and analysis to courses on mathematical biology and fluids.
-You will be taught by experts across a wide range of pure and applied mathematics and you will develop a mature understanding of fundamental theories and analytical skills applicable to many situations.
-You will participate in an extensive and varied seminar programme, are taught by internationally renowned lecturers and experience a wide variety of projects.
-Our students graduate with a varied skill set, including core professional skills, and a portfolio of substantive applied and practical work.
-With a 94% overall student satisfaction in the National Student Survey 2014, the School of Mathematics and Statistics combines both teaching excellence and a supportive learning environment.

Programme structure

Modes of delivery of the Masters in Mathematics/Applied Mathematics include lectures, laboratory classes, seminars and tutorials and allow students the opportunity to take part in project work.

If you are studying for the MSc you will take a total of 120 credits from a mixture of Level-4 Honours courses, Level-M courses and courses delivered by the Scottish Mathematical Sciences Training Centre (SMSTC).

You will take courses worth a minimum of 90 credits from Level-M courses and those delivered by the SMSTC. The remaining 30 credits may be chosen from final-year Level-H courses. The Level-M courses offered in a particular session will depend on student demand. Below are courses currently offered at these levels, but the options may vary from year to year.

Level-H courses (10 or 20 credits)
-Algebraic & geometric topology
-Continuum mechanics & elasticity
-Differential geometry
-Fluid mechanics
-Functional analysis
-Further complex analysis
-Galois theory
-Mathematical biology
-Mathematical physics
-Numerical methods
-Number theory
-Partial differential equations
-Topics in algebra

Level-M courses (20 credits)
-Advanced algebraic & geometric topology
-Advanced differential geometry & topology
-Advanced functional analysis
-Advanced methods in differential equations
-Advanced numerical methods
-Biological & physiological fluid mechanics
-Commutative algebra & algebraic geometry
-Elasticity
-Fourier analysis
-Further topics in group theory
-Lie groups, lie algebras & their representations
-Magnetohydrodynamics
-Operator algebras
-Solitons
-Special relativity & classical field theory

SMSTC courses (20 credits)
-Algebra 1
-Algebra 2
-Applied analysis and PDEs 1
-Applied analysis and PDEs 2
-Applied mathematical methods 1
-Applied mathematical methods 2
-Geometry and topology 1
-Geometry and topology 2
-Mathematical modelling 1
-Mathematical modelling 2
-Pure analysis 1
-Pure analysis 2.

The project titles are offered each year by academic staff and so change annually

Career prospects

Career opportunities are diverse and varied and include academia, teaching, industry and finance.

Graduates of this programme have gone on to positions such as:
-Maths Tutor at a university.

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Studying Mathematics at postgraduate level gives you a chance to begin your own research, develop your own creativity and be part of a long tradition of people investigating analytic, geometric and algebraic ideas. Read more
Studying Mathematics at postgraduate level gives you a chance to begin your own research, develop your own creativity and be part of a long tradition of people investigating analytic, geometric and algebraic ideas.

If your mathematical background is insufficient for direct entry to the MSc in Mathematics and its Applications, you may apply for this course. The first year of this Master's programme gives you a strong background in mathematics, equivalent to the Graduate Diploma in Mathematics, with second year studies following the MSc in Mathematics and its Applications.

Visit the website https://www.kent.ac.uk/courses/postgraduate/148/international-masters-in-mathematics-and-its-applications

About the School of Mathematics, Statistics and Actuarial Science (SMSAS)

The School has a strong reputation for world-class research and a well-established system of support and training, with a high level of contact between staff and research students. Postgraduate students develop analytical, communication and research skills. Developing computational skills and applying them to mathematical problems forms a significant part of the postgraduate training in the School.

The Mathematics Group at Kent ranked highly in the most recent Research Assessment Exercise. With 100% of the Applied Mathematics Group submitted, all research outputs were judged to be of international quality and 12.5% was rated 4*. For the Pure Mathematics Group, a large proportion of the outputs demonstrated international excellence.

The Mathematics Group also has an excellent track record of winning research grants from the Engineering and Physical Sciences Research Council (EPSRC), the Royal Society, the EU, the London Mathematical Society and the Leverhulme Trust.

Course structure

At least one modern application of mathematics is studied in-depth by each student. Mathematical computing and open-ended project work forms an integral part of the learning experience. You strengthen your grounding in the subject and gain a sound grasp of the wider relevance and application of mathematics.

There are opportunities for outreach and engagement with the public on mathematics.

Modules

The following modules are indicative of those offered on this programme. This list is based on the current curriculum and may change year to year in response to new curriculum developments and innovation. Most programmes will require you to study a combination of compulsory and optional modules. You may also have the option to take modules from other programmes so that you may customise your programme and explore other subject areas that interest you.

MA552 - Analysis (15 credits)
MA553 - Linear Algebra (15 credits)
MA588 - Mathematical Techniques and Differential Equations (15 credits)
MA591 - Nonlinear Systems and Mathematical Biology (15 credits)
MA593 - Topics in Modern Applied Mathematics (30 credits)
MA549 - Discrete Mathematics (15 credits)
MA572 - Complex Analysis (15 credits)
MA563 - Calculus of Variations (15 credits)
MA587 - Numerical Solution of Differential Equations (15 credits)
MA577 - Elements of Abstract Analysis (15 credits)
MA576 - Groups and Representations (15 credits)
MA574 - Polynomials in Several Variables (15 credits)
MA961 - Mathematical Inquiry and Communication (30 credits)
MA962 - Geometric Integration (15 credits)
MA964 - Applied Algebraic Topology (15 credits)
MA965 - Symmetries, Groups and Invariants (15 credits)
MA968 - Mathematics and Music (15 credits)
MA969 - Applied Differential Geometry (15 credits)
MA970 - Nonlinear Analysis and Optimisation (15 credits)
MA971 - Introduction to Functional Analysis (15 credits)
MA972 - Algebraic Curves in Nature (15 credits)
MA973 - Basic Differential Algebra (15 credits)
CB600 - Games and Networks (15 credits)
MA562 - Nonlinear Waves and Solitons (15 credits)
MA960 - Dissertation (60 credits)

Assessment

Closed book examinations, take-home problem assignments and computer lab assignments (depending on the module).

Programme aims

This programme aims to:

- provide a Master’s level mathematical education of excellent quality, informed by research and scholarship

- provide an opportunity to enhance your mathematical creativity, problem-solving skills and advanced computational skills

- provide an opportunity for you to enhance your oral communication, project design and basic research skills

- provide an opportunity for you to experience and engage with a creative, research-active professional mathematical environment

- produce graduates of value to the region and nation by offering you opportunities to learn about mathematics in the context of its application.

Study support

Postgraduate resources
The University’s Templeman Library houses a comprehensive collection of books and research periodicals. Online access to a wide variety of journals is available through services such as ScienceDirect and SpringerLink. The School has licences for major numerical and computer algebra software packages. Postgraduates are provided with computers in shared offices in the School. The School has two dedicated terminal rooms for taught postgraduate students to use for lectures and self-study.

Support
The School has a well-established system of support and training, with a high level of contact between staff and research students. There are two weekly seminar series: The Mathematics Colloquium at Kent attracts international speakers discussing recent advances in their subject; the Friday seminar series features in-house speakers and visitors talking about their latest work. These are supplemented by weekly discussion groups. The School is a member of the EPSRC-funded London Taught Course Centre for PhD students in the mathematical sciences, and students can participate in the courses and workshops offered by the Centre. The School offers conference grants to enable research students to present their work at national and international conferences.

Dynamic publishing culture
Staff publish regularly and widely in journals, conference proceedings and books. Among others, they have recently contributed to: Advances in Mathematics; Algebra and Representation Theory; Journal of Physics A; Journal of Symbolic Computations; Journal of Topology and Analysis. Details of recently published books can be found within the staff research interests section.

Global Skills Award
All students registered for a taught Master's programme are eligible to apply for a place on our Global Skills Award Programme (http://www.kent.ac.uk/graduateschool/skills/programmes/gsa.html). The programme is designed to broaden your understanding of global issues and current affairs as well as to develop personal skills which will enhance your employability.

Careers

A postgraduate degree in Mathematics is a flexible and valuable qualification that gives you a competitive advantage in a wide range of mathematically oriented careers. Our programmes enable you to develop the skills and capabilities that employers are looking for including problem-solving, independent thought, report-writing, project management, leadership skills, teamworking and good communication.

Many of our graduates have gone on to work in international organisations, the financial sector, and business. Others have found postgraduate research places at Kent and other universities.

Find out how to apply here - https://www.kent.ac.uk/courses/postgraduate/apply/

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This course aims to bring you, in 12 months, to a position where you can embark with confidence on a wide range of careers, including taking a PhD in Mathematics or related disciplines. Read more
This course aims to bring you, in 12 months, to a position where you can embark with confidence on a wide range of careers, including taking a PhD in Mathematics or related disciplines. There is a wide range of taught modules on offer, and you will also produce a dissertation on a topic of current research interest taken from your choice of a wide range of subjects offered.

Course structure and overview

-Six taught modules in October-May.
-A dissertation in June-September.

Modules: Six of available options
In previous years, optional modules available included:

Modules in Pure Mathematics:
-Algebraic Topology IV
-Codes and Cryptography III
-Differential Geometry III
-Galois Theory III
-Geometry III and IV
-Number Theory III and IV
-Riemannian Geometry IV
-Topology III
-Elliptic Functions IV

Modules in Probability and Statistics:
-Mathematical Finance III and IV
-Decision Theory III
-Operations Research III
-Probability III and IV
-Statistical Methods III
-Topics in Statistics III and IV

Modules in Applications of Mathematics:
-Advanced Quantum Theory IV
-Dynamical Systems III
-General Relativity III and IV
-Mathematical Biology III
-Numerical Differential Equations III and IV
-Partial Differential Equations III and IV
-Quantum Information III
-Quantum Mechanics III
-Statistical Mechanics III and IV

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Take advantage of one of our 100 Master’s Scholarships or College of Science Postgraduate Scholarships to study High Performance and Scientific Computing at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Read more
Take advantage of one of our 100 Master’s Scholarships or College of Science Postgraduate Scholarships to study High Performance and Scientific Computing at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Postgraduate loans are also available to English and Welsh domiciled students. For more information on fees and funding please visit our website.

The MSc in High Performance and Scientific Computing is for you if you are a graduate in a scientific or engineering discipline and want to specialise in applications of High Performance computing in your chosen scientific area. During your studies in High Performance and Scientific Computing you will develop your computational and scientific knowledge and skills in tandem helping emphasise their inter-dependence.

On the course in High Performance and Scientific Computing you will develop a solid knowledge base of high performance computing tools and concepts with a flexibility in terms of techniques and applications. As s student of the MSc High Performance and Scientific Computing you will take core computational modules in addition to specialising in high performance computing applications in a scientific discipline that defines the route you have chosen (Biosciences, Computer Science, Geography or Physics). You will also be encouraged to take at least one module in a related discipline.

Modules of High Performance and Scientific Computing MSc

The modules you study on the High Performance and Scientific Computing MSc depend on the route you choose and routes are as follows:

Biosciences route (High Performance and Scientific Computing MSc):

Graphics Processor Programming
High Performance Computing in C/C++
Operating Systems and Architectures
Software Testing
Programming in C/C++
Conservation of Aquatic Resources or Environmental Impact Assessment
Ecosystems
Research Project in Environmental Biology
+ 10 credits from optional modules

Computer Science route (High Performance and Scientific Computing MSc):

Graphics Processor Programming
High Performance Computing in C/C++
Operating Systems and Architectures
Software Testing
Programming in C/C++
Partial Differential Equations
Numerics of ODEs and PDEs
Software Engineering
Data Visualization
MSc Project
+ 30 credits from optional modules

Geography route (High Performance and Scientific Computing MSc):

Graphics Processor Programming
High Performance Computing in C/C++
Operating Systems and Architectures
Software Testing
Programming in C/C++
Partial Differential Equations
Numerics of ODEs and PDEs
Modelling Earth Systems or Satellite Remote Sensing or Climate Change – Past, Present and Future or Geographical Information Systems
Research Project
+ 10 credits from optional modules

Physics route (High Performance and Scientific Computing MSc):

Graphics Processor Programming
High Performance Computing in C/C++
Operating Systems and Architectures
Software Testing
Programming in C/C++
Partial Differential Equations
Numerics of ODEs and PDEs
Monte Carlo Methods
Quantum Information Processing
Phase Transitions and Critical Phenomena
Physics Project
+ 20 credits from optional modules

Optional Modules (High Performance and Scientific Computing MSc):

Software Engineering
Data Visualization
Monte Carlo Methods
Quantum Information Processing
Phase Transitions and Critical Phenomena
Modelling Earth Systems
Satellite Remote Sensing
Climate Change – Past, Present and Future
Geographical Information Systems
Conservation of Aquatic Resources
Environmental Impact Assessment
Ecosystems

Facilities

Students of the High Performance and Scientific Computing programme will benefit from the Department that is well-resourced to support research. Swansea physics graduates are more fortunate than most, gaining unique insights into exciting cutting-edge areas of physics due to the specialized research interests of all the teaching staff. This combined with a great staff-student ratio enables individual supervision in advanced final year research projects. Projects range from superconductivity and nano-technology to superstring theory and anti-matter. The success of this programme is apparent in the large proportion of our M.Phys. students who seek to continue with postgraduate programmes in research.

Specialist equipment includes:

a low-energy positron beam with a highfield superconducting magnet for the study of positronium
a number of CW and pulsed laser systems
scanning tunnelling electron and nearfield optical microscopes
a Raman microscope
a 72 CPU parallel cluster
access to the IBM-built ‘Blue C’ Supercomputer at Swansea University and is part of the shared use of the teraflop QCDOC facility based in Edinburgh

The Physics laboratories and teaching rooms were refurbished during 2012 and were officially opened by Professor Lyn Evans, Project Leader of the Large Hadron Collider at CERN. This major refurbishment was made possible through the University’s capital programme, the College of Science, and a generous bequest made to the Physics Department by Dr Gething Morgan Lewis FRSE, an eminent physicist who grew up in Ystalyfera in the Swansea Valley and was educated at Brecon College.

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From geometry, analysis, partial differential equations and mathematical physics to fluid dynamics, meteorology and modelling in life sciences – our Masters in Mathematics offers you an extraordinary range of research opportunities that lie at the heart of tackling the key scientific questions of our age. Read more
From geometry, analysis, partial differential equations and mathematical physics to fluid dynamics, meteorology and modelling in life sciences – our Masters in Mathematics offers you an extraordinary range of research opportunities that lie at the heart of tackling the key scientific questions of our age.

PROGRAMME OVERVIEW

This programme reflects and benefits from the strong research activities of the Department of Mathematics.

The taught modules and dissertation topics are closely aligned with the interests of the Department’s four research groups:
-Mathematics of Life and Social Sciences
-Dynamical Systems and Partial Differential Equations
-Fields, Strings and Geometry
-Fluids, Meteorology and Symmetry

During the first two semesters you will take a range of taught modules from an extensive list of options, followed by an extended research project conducted over the summer under the supervision of a member of the department, culminating in the writing of a dissertation.

PROGRAMME STRUCTURE

This programme is studied full-time over one academic year. It consists of eight taught modules and a dissertation. The following modules are indicative, reflecting the information available at the time of publication. Please note that not all modules described are compulsory and may be subject to teaching availability and/or student demand.
-Maths of Weather
-Graphs and Networks
-Manifolds and Topology
-Quantum Mechanics
-Numerical Solutions of PDEs
-Functional Analysis and Partial Differential Equations
-Nonlinear Wave Equations
-Representation Theory
-Advanced Techniques in Mathematics
-Lie Algebras
-Nonlinear Patterns
-Geometric Mechanics
-Relativity
-Ecological and Epidemiological Modelling
-Mathematical Biology and Physiology
-Topology
-Non-Commutative Algebra
-Dissertation

CAREERS

Mathematics is not only central to science, technology and finance-related fields, but the logical insight, analytical skills and intellectual discipline gained from a mathematical education are highly sought after in a broad range of other areas such as law, business and management.

There is also a strong demand for new mathematics teachers to meet the ongoing shortage in schools.

As well as being designed to meet the needs of future employers, our MSc programme also provides a solid foundation from which to pursue further research in mathematics or one of the many areas to which mathematical ideas and techniques are applied.

EDUCATIONAL AIMS OF THE PROGRAMME

-To provide graduates with a strong background in advanced mathematical theory and its applications to the solution of real problems
-To develop students understanding of core areas in advanced mathematics including standard tools for the solution of real life applied mathematical problems
-To develop the skill of formulating a mathematical problem from a purely verbal description
-To develop the skill of writing a sophisticated mathematical report and, additionally, in presenting the results in the form of an oral presentation
-To lay a foundation for carrying out mathematical research leading to a research degree and/or a career as a professional mathematician in an academic or non-academic setting

PROGRAMME LEARNING OUTCOMES

Knowledge and understanding
-Knowledge of the core theory and methods of advanced pure and applied mathematics and how to apply that theory to real life problems
-An in-depth study of a specific problem arising in a research context

Intellectual / cognitive skills
-Ability to demonstrate knowledge of key techniques in advanced mathematics and to apply those techniques in problem solving
-Ability to formulate a mathematical description of a problem that may be described only verbally
-An understanding of possible shortcomings of mathematical descriptions of reality
-An ability to use software such as MATLAB and IT facilities more generally including research databases such as MathSciNet and Web of Knowledge

Professional practical skills
-Fluency in advanced mathematical theory
-The ability to interpret the results of the application of that theory
-An awareness of any weaknesses in the assumptions being made and of possible shortcomings with model predictions
-The skill of writing an extended and sophisticated mathematical report and of verbally summarising its content to specialist and/or non-specialist audiences

Key / transferable skills
-Ability to reason logically and creatively
-Effective oral presentation skills
-Written report writing skills
-Skills in independent learning
-Time management
-Use of information and technology

GLOBAL OPPORTUNITIES

We often give our students the opportunity to acquire international experience during their degrees by taking advantage of our exchange agreements with overseas universities.

In addition to the hugely enjoyable and satisfying experience, time spent abroad adds a distinctive element to your CV.

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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. Read more
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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Joining the Department as a postgraduate is certainly a good move. The Department maintains strong research in both pure and applied mathematics, as well as the traditional core of a mathematics department. Read more
Joining the Department as a postgraduate is certainly a good move. The Department maintains strong research in both pure and applied mathematics, as well as the traditional core of a mathematics department. What makes our Department different is the equally strong research in fluid mechanics, scientific computation and statistics.

The quality of research at the postgraduate level is reflected in the scholarly achievements of faculty members, many of whom are recognized as leading authorities in their fields. Research programs often involve collaboration with scholars at an international level, especially in the European, North American and Chinese universities. Renowned academics also take part in the Department's regular colloquia and seminars. The faculty comprises several groups: Pure Mathematics, Applied Mathematics, Probability and Statistics.

Mathematics permeates almost every discipline of science and technology. We believe our comprehensive approach enables inspiring interaction among different faculty members and helps generate new mathematical tools to meet the scientific and technological challenges facing our fast-changing world.

The MPhil program seeks to strengthen students' general background in mathematics and mathematical sciences, and to expose students to the environment and scope of mathematical research. Submission and successful defense of a thesis based on original research are required.

Research Foci

Algebra and Number Theory
The theory of Lie groups, Lie algebras and their representations play an important role in many of the recent development in mathematics and in the interaction of mathematics with physics. Our research includes representation theory of reductive groups, Kac-Moody algebras, quantum groups, and conformal field theory. Number theory has a long and distinguished history, and the concepts and problems relating to the theory have been instrumental in the foundation of a large part of mathematics. Number theory has flourished in recent years, as made evident by the proof of Fermat's Last Theorem. Our research specializes in automorphic forms.

Analysis and Differential Equations
The analysis of real and complex functions plays a fundamental role in mathematics. This is a classical yet still vibrant subject that has a wide range of applications. Differential equations are used to describe many scientific, engineering and economic problems. The theoretical and numerical study of such equations is crucial in understanding and solving problems. Our research areas include complex analysis, exponential asymptotics, functional analysis, nonlinear equations and dynamical systems, and integrable systems.

Geometry and Topology
Geometry and topology provide an essential language describing all kinds of structures in Nature. The subject has been vastly enriched by close interaction with other mathematical fields and with fields of science such as physics, astronomy and mechanics. The result has led to great advances in the subject, as highlighted by the proof of the Poincaré conjecture. Active research areas in the Department include algebraic geometry, differential geometry, low-dimensional topology, equivariant topology, combinatorial topology, and geometrical structures in mathematical physics.

Numerical Analysis
The focus is on the development of advance algorithms and efficient computational schemes. Current research areas include: parallel algorithms, heterogeneous network computing, graph theory, image processing, computational fluid dynamics, singular problems, adaptive grid method, rarefied flow simulations.

Applied Sciences
The applications of mathematics to interdisciplinary science areas include: material science, multiscale modeling, mutliphase flows, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, astrophysics and space science.

Probability and Statistics
Statistics, the science of collecting, analyzing, interpreting, and presenting data, is an essential tool in a wide variety of academic disciplines as well as for business, government, medicine and industry. Our research is conducted in four categories. Time Series and Dependent Data: inference from nonstationarity, nonlinearity, long-memory behavior, and continuous time models. Resampling Methodology: block bootstrap, bootstrap for censored data, and Edgeworth and saddle point approximations. Stochastic Processes and Stochastic Analysis: filtering, diffusion and Markov processes, and stochastic approximation and control. Survival Analysis: survival function and errors in variables for general linear models. Probability current research includes limit theory.

Financial Mathematics
This is one of the fastest growing research fields in applied mathematics. International banking and financial firms around the globe are hiring science PhDs who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks. The trend has been accelerating in recent years on numerous fronts, driven both by substantial theoretical advances as well as by a practical need in the industry to develop effective methods to price and hedge increasingly complex financial instruments. Current research areas include pricing models for exotic options, the development of pricing algorithms for complex financial derivatives, credit derivatives, risk management, stochastic analysis of interest rates and related models.

Facilities

The Department enjoys a range of up-to-date facilities and equipment for teaching and research purposes. It has two computer laboratories and a Math Support Center equipped with 100 desktop computers for undergraduate and postgraduate students. The Department also provides an electronic homework system and a storage cloud system to enhance teaching and learning.

To assist computations that require a large amount of processing power in the research area of scientific computation, a High Performance Computing (HPC) laboratory equipped with more than 200 high-speed workstations and servers has been set up. With advanced parallel computing technologies, these powerful computers are capable of delivering 17.2 TFLOPS processing power to solve computationally intensive problems in our innovative research projects. Such equipment helps our faculty and postgraduate students to stay at the forefront of their fields. Research projects in areas such as astrophysics, computational fluid dynamics, financial mathematics, mathematical modeling and simulation in materials science, molecular simulation, numerical ocean modeling, numerical weather prediction and numerical methods for micromagnetics simulations all benefit from our powerful computing facilities.

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Graduate courses are offered in algebra, real analysis, complex analysis, numerical analysis, linear and nonlinear functional analysis, algebraic topology, combinatorics, differential geometry, ordinary differential equations, partial differential equations, probability, statistics, mathematical finance. Read more
Graduate courses are offered in algebra, real analysis, complex analysis, numerical analysis, linear and nonlinear functional analysis, algebraic topology, combinatorics, differential geometry, ordinary differential equations, partial differential equations, probability, statistics, mathematical finance. Advanced courses in these and related areas, leading to research topics, are also offered.

People

At the heart of all of our programs is our exceptional faculty, men and women who are leading scholars in their fields and dedicated mentors in the classroom.

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This programme develops mathematical modelling skills and provides mathematical techniques required by industry. The period October to June is devoted to lectures, tutorials and practical sessions comprising the core modules. Read more
This programme develops mathematical modelling skills and provides mathematical techniques required by industry.

The period October to June is devoted to lectures, tutorials and practical sessions comprising the core modules.

This is followed by a period of about 14 weeks devoted to an individual project either in an industrial or engineering company or at the University.

Core study areas include mathematical modelling, regular and chaotic dynamics, programming and numerical methods, advanced reliability, availability and maintainability, elements of partial differential equations, static and dynamic optimisation and fluid mechanics.

See the website http://www.lboro.ac.uk/study/postgraduate/programmes/departments/mathematics/industrial-maths-modelling/

Programme modules

Compulsory Modules:
Semester 1
- Mathematical Modelling I
- Regular and Chaotic Dynamics
- Programming and Numerical Methods
- Advanced Reliability, Availability and Maintainability

Semester 2
- Mathematical Modelling II
- Elements of Partial Differential Equations
- Static and Dynamic Optimisation
- Fluid Mechanics

Assessment

A combination of written examinations, reports, individual and group projects, and verbal presentations.

Careers and further Study

Graduate employment over a wide range of industries encompassing aerospace, automotive electronics, and computer interests as well as software houses, insurance companies, and research establishments and institutions.

Scholarships and sponsorships

A limited number of scholarships are available for this programme as well as the loyalty bonus scheme which reduces fees for Loughborough graduates.

Why choose mathematics at Loughborough?

Mathematics at Loughborough has a long history of innovation in teaching, and we have a firm research base with strengths in both pure and applied mathematics as well as mathematics education.

The Department comprises more than 34 academic staff, whose work is complemented and underpinned by senior visiting academics, research associates and a large support team.

The programmes on offer reflect our acknowledged strengths in pure and applied research in mathematics, and in some cases represent established collaborative training ventures with industrial partners.

- Mathematics Education Centre (MEC)
The Mathematics Education Centre (MEC) at Loughborough University is an internationally renowned centre of research, teaching, learning and support. It is a key player in many high-profile national initiatives.
With a growing number of academic staff and research students, the MEC provides a vibrant, supportive community with a wealth of experience upon which to draw.
We encourage inquiries from students who are interested in engaging in research into aspects of learning and teaching mathematics at Masters, PhD and Post Doc levels. Career prospects With 100% of our graduates in employment and/or further study six months after graduating, career prospects are excellent. Graduates go on to work with companies such as BAE Systems, Citigroup, Experian, GE Aviation, Mercedes Benz, Nuclear Labs USA and PwC.

- Career prospects
With 100% of our graduates in employment and/or further study six months after graduating, career prospects are excellent. Graduates
go on to work with companies such as BAE Systems, Citigroup, Experian, GE Aviation, Mercedes Benz, Nuclear Labs USA and PwC.

Find out how to apply here http://www.lboro.ac.uk/study/postgraduate/programmes/departments/mathematics/industrial-maths-modelling/

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You can study this Mathematical Sciences MSc programme full-time or part-time. It offers students the opportunity to specialise in a broad range of areas across pure and applied mathematics, statistics and probability, and theoretical physics. Read more
You can study this Mathematical Sciences MSc programme full-time or part-time. It offers students the opportunity to specialise in a broad range of areas across pure and applied mathematics, statistics and probability, and theoretical physics.

The topics we cover include:

- advanced probability theory
- algebra
- asymptotic methods
- geometry
- mathematical biology
- partial differential equations
- quantum field theory
- singularity theory
- stochastic analysis
- standard model/string theory.

By completing the first semester you qualify for the PG certificate. By completing the second, you qualify for the PG Diploma. Then, by completing your dissertation, you qualify for the MSc.

Key Facts

REF 2014
92% of our research impact judged at outstanding and very considerable, 28% improvement in overall research at 4* and 3*.

Facilities
A dedicated student resource suite is available in the Department, with computer and reading rooms and a social area.

Why Department of Mathematical Sciences?

Range and depth of study options

We offer a very wide range of modules, from advanced algebra and geometry, to partial differential equations, probability theory, stochastic analysis, and mathematical physics. With these you can tailor your programme to specialise in one of these areas, or gain a broad understanding of several. This allows you to build up the required background for the project and dissertation modules, which offer the opportunity to undertake an in-depth study of a topic of your choice, supervised by a leading expert in the field.

Exceptional employability

At Liverpool, we listen to employers’ needs. Alongside key problem solving skills, employers require strong communication skills. These are integral to this programme. Graduates go on to research degrees, or become business and finance professionals, or to work in management training, information technology, further education or training (including teacher training) and scientific research and development.

Teaching quality

We are proud of our record on teaching quality, with five members of the Department having received the prestigious Sir Alastair Pilkington Award for Teaching. We care about each student and you will find the staff friendly and approachable.

Accessibility

We take students from a wide variety of educational backgrounds and we work hard to give everyone the opportunity to shine.

Supportive atmosphere

We provide high quality supervision and teaching, computer labs, and and you will benefit from the friendly and supportive atmosphere in the Department, as evidenced by student feedback available on our university website. A common room and kitchen for the exclusive use of the Department’s students, and a lively maths society help to foster a friendly and supportive environment.

Career prospects

The excellent University Careers Service is open to all postgraduates. Graduates of the MSc and PhD programmes move on to many different careers. Recent graduates have moved into fast track teacher programmes, jobs in finance (actuarial, banking, insurance), software development, drugs testing and defence work, as well as University postdoctoral or lecturing posts. The MSc programme is of course a natural route into doctoral study in Mathematics and related fields, both at Liverpool and elsewhere. Some of our PhD students move on to postdoctoral positions and to academic teaching jobs and jobs in research institutes, both in the UK and elsewhere.

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Take advantage of one of our 100 Master’s Scholarships to study Stochastic Processes. Theory and Application at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Read more
Take advantage of one of our 100 Master’s Scholarships to study Stochastic Processes: Theory and Application at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Postgraduate loans are also available to English and Welsh domiciled students. For more information on fees and funding please visit our website.

The MRes in Stochastic Processes: Theory and Application is delivered through optional modules for the taught element followed by a large research project that contributes to the field in an explicit way, rather than merely applying existing knowledge.

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields.

The Department’s research groups include:

Algebra and Topology Group
Areas of interest include: Noncommutative geometry, Categorical methods in algebra and topology, Homotopy theory and homological algebra and others.

Analysis and Nonlinear Partial Differential Equations Group
Areas of interest include: Reaction-diffusion and reaction-diffusion-convection equations and systems, Navier–Stokes equations in fluid dynamic, Complexity in the calculus of variations and others.

Stochastic Analysis Group
Areas of interest include: Functional inequalities and applications, Lévy-type processes, Stochastic modelling of fractal, multi-fractal and multi-scale systems, Infinite dimensional stochastic analysis and others.

Mathematical Methods in Biology and Life Sciences Group
Areas of interest include: Mathematical pharmacology; heat and mass transfer models for plant cooling; modelling cellular signal transduction dynamics; mathematical oncology: multi-scale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies; multi-scale analysis of individual-based models; spreading speeds and travelling waves in ecology; high performance computing.

Key Features

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields.

Course Content

As a student on the MRes Stochastic Processes programme you will study a range of topics for the taught element including:

Stochastic Calculus based on Brownian Motion
Levy processes and more general jump processes
The advanced Black-Scholes theory
Theory and numerics of parabolic differential equations
Java programming

The Stochastic Processes: Theory and Application course consists of a taught part (60 credits) and a research project (120 credits). Students will have a personal supervisor for their research project from the start of their studies.

Research projects could be of a theoretical mathematical nature, or they could be more applied, for example in financial mathematics or actuarial studies. Some of the research projects will be of an interdisciplinary character in collaboration with some of Swansea's world class engineers. For such projects it is likely that EPSRC funding would be available.

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.

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, statistical analysis, marketing and sales.

Some of our students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where maths 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.

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Accurate and efficient scientific computations lie at the heart of most cross-discipline collaborations. It is key that such computations are performed in a stable, efficient manner and that the numerics converge to the true solutions, dynamics of the physics, chemistry or biology in the problem. Read more
Accurate and efficient scientific computations lie at the heart of most cross-discipline collaborations. It is key that such computations are performed in a stable, efficient manner and that the numerics converge to the true solutions, dynamics of the physics, chemistry or biology in the problem.

The programme closely follows the structure of our Applied Mathematical Sciences MSc and will equip you with the skill to perform efficient accurate computer simulations in a wide variety of applied mathematics, physics, chemical and industrial problems.

The MSc, has at its core, fundamental courses in pure mathematics and students will be able to take options from both pure and applied mathematics.

Students will take a total of 8 courses, 4 in each of the 1st and 2nd Semesters followed by a 3-month Project in the summer. A typical distribution for this programme is as follows:

Core courses

Modelling and Tools;
Functional Analysis;
Partial Differential Equations;
Pure Mathematics (recommended).

Optional Courses

Mathematical Ecology;
Optimization;
Numerical Analysis of ODEs;
Applied Mathematics;
Dynamical Systems;
Stochastic Simulation;
Applied Linear Algebra;
Partial Differential Equations;
Numerical Analysis;
Bayesian Inference and Computational Methods;
Geometry.

Typical project subjects

Domain Decomposition;
Mathematical Modelling of Crime;
The Geometry of Point Particles;
Can we Trust Eigenvalues on a Computer?;
Braess Paradox;
The Ising Model: Exact and Numerical Results;
Banach Alegbras.

The final part of the MSc is an extended project in computational mathematics, giving the opportunity to investigate a topic in some depth guided by leading research academics from our 5-rated mathematics and statistics groups.

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The LLM Gender, Conflict and Human Rights draws on the established research excellence of the Transitional Justice Institute to deliver a world-leading masters programme in the field. Read more
The LLM Gender, Conflict and Human Rights draws on the established research excellence of the Transitional Justice Institute to deliver a world-leading masters programme in the field.

Key benefits

• Opportunity to undertake an LLM programme with a specific focus on gender and transitional justice – the only LLM programme of its type in the UK or Ireland;

• Teaching is delivered by active researchers in the TJI, many of whom have received international recognition for their work;

• Gain unique insights into the differential legal protection of human rights of women and men in transitional contexts, while studying in a society currently in a process of transition;

• Take advantage of the opportunities to specialise in identified areas e.g. human rights, transitional justice, peace and conflict research in divided societies;

• Enhance the skills you need for working with gender and human rights in a range of sectors;

• Internship opportunities with a range of organizations including the Northern Ireland Human Rights Commission, Disability Action (Centre on Human Rights), Human Rights Consortium, Law Centre (NI) and Northern Ireland Council for Ethnic Minorities (NICEM), all based in Belfast;

• Extensive events programme (TJI Seminar Series, International Conferences) and distinguished Visiting Scholars programme.

• Excellent library facilities on campus. Students also have sole access to a dedicated LLM computer suite;

• Fully equipped LLM teaching rooms with integrated audio visual and video conferencing facilities.

Visit the website: https://www.ulster.ac.uk/courses/course-finder/201617/gender-conflict-and-human-rights-9079

Course detail

- Description -

This programme has been developed to enable students to:

• Gain a systematic understanding, in-depth knowledge and critical awareness of the differential experiences of women and men of human rights norms and institutions, especially in conflict and post-conflict situations;
• Understand foundational concepts in gender theory and their application to human rights, international law and transitional justice
• Develop skills highly relevant to legal practice, and to gender policy, research and advocacy roles in the voluntary, public and private sectors in the UK, Ireland and beyond;
• Successful completion may also open up further study and research options.

- Work placement / study abroad -

The LLM offers a range of internships with local human rights organisations.

Career options

Previous graduates have gone onto positions in the local human rights sector and public sector in Northern Ireland, to legal practice in areas related to the LLM and to PhD research. Further, previous graduates have secured work in the United Nations and in international non-governmental organisations.

How to apply: https://www.ulster.ac.uk/apply/how-to-apply#pg

Why study at Ulster?

1. Over 92% of our graduates are in work or further study six months after graduation.
2. We are a top UK university for providing courses with a period of work placement.
3. Our teaching and the learning experience we deliver are rated at the highest level by the Quality Assurance Agency.
4. We are an international university with more than 2,000 international students from over 80 countries and Alumni from 121 countries.
5. More than 4,000 students from over 50 countries have successfully completed eLearning courses at Ulster University.

Flexible payment

To help spread the cost of your studies, tuition fees can be paid back in monthly instalments while you learn. If you study for a one-year, full-time master’s, you can pay your fees up-front, in one lump sum, or in either five or ten equal monthly payments. If you study for a master’s on a part-time basis (e.g. over three years), you can pay each year’s fees up-front or in five or ten equal monthly payments each year. This flexibility allows you to spread the payment of your fees over each academic year. Find out more by visiting http://www.ulster.ac.uk/learnyourway

Scholarships

A comprehensive range of financial scholarships, awards and prizes are available to undergraduate, postgraduate and research students. Scholarships recognise the many ways in which our students are outstanding in their subject. Individuals may be able to apply directly or may automatically be nominated for awards. Visit the website: https://www.ulster.ac.uk/apply/fees-and-finance/scholarships

English Language Tuition

CELT offers courses and consultations in English language and study skills to Ulster University students of all subjects, levels and nationalities. Students and researchers for whom English is an additional language can access free CELT support throughout the academic year: https://www.ulster.ac.uk/international/english-language-support

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The academic staff in the Applied Computing Department (ACD) are all engaged in research and publications. Considering its modest size, ACD has successfully attracted research funding from various sources in the UK and the EU, including industry, research councils, HEA and EU framework projects such as FP6. Read more

Research programme

The academic staff in the Applied Computing Department (ACD) are all engaged in research and publications. Considering its modest size, ACD has successfully attracted research funding from various sources in the UK and the EU, including industry, research councils, HEA and EU framework projects such as FP6. Furthermore, ACD has been working and collaborating with many European research institutions.

For the academic year 2012-2013, 2 DPhil and 6 MSc students (1 in Mathematics) have graduated, four of whom graduated with Distinction. The 2 DPhil students have made it for the March graduation and we expect to have 3 or 4 more completing their DPhil research programmes for the next graduation. One of our new MPhil/DPhil students in Computing joined the Department last October, and 3 other MPhil/DPhil students have joined us since. Over the last few years, the number of research students in ACD has grown steadily to (currently) 29 PhD and 2 Master’s research students.

We have had over 20 refereed conference and journal papers published during the last 12 months, and two of the papers have been awarded best paper awards.

ACD supports diverse research topics addressing varied applied computing technologies such as:

- Image processing and pattern recognition with applications in biometric-based person identification, image super-resolution, digital watermarking and steganography, content-based image / video indexing and retrieval, biomedical image analysis.
- Multi-factor authentication and security algorithms.
- Wireless networks technologies (Multi-frequency Software-Defined / Cognitive Radios, convergence and integration of different wireless technologies and standards such as WiFi and WiMax, IPv4 and IPv6, wireless mesh technologies, intrusion detection and prevention, efficiency and stability of ad hoc networks).
- Hybrid navigation and localisation integrations for mobile handsets, including using Cellular and WiFi in conjunction with GPS and Glonass for seamless positioning indoors, Multiplexed receive chain of GPS/Glonass with on-board handset Bluetooth/WiFi, GNSS signals multiplexing for real time simulation.
- Cloud computing, including the readiness of mobile operating systems for cloud services and focusing on techniques for fast computing handovers, efficient virtualisation and optimised security algorithms.
- Data mining techniques, including database systems, the application of data mining techniques in image and biological data, human-computer interaction and visual languages.
- Research and development of Apps for mobile devices and smart TVs, particularly for application in the areas of education and healthcare.
- Differential geometry – Einstein metrics, quasi-Einstein metrics, Ricci solitons, numerical methods in differential geometry.

As well as researching the chosen subject, our students engage in delivering seminars weekly, attending conferences and workshops, attending online webinars and discussion forums, attending training and focused group studies, supervising tutorial and laboratory sessions for undergraduate students, peer reviews and final year project supervision, among a host of technical and networking activities to enhance their skills and techniques.

Find out more about our Department of Applied Computing on http://www.buckingham.ac.uk/appliedcomputing.
Apply here http://www.buckingham.ac.uk/sciences/msc/computingresearch.

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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. Read more
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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