pg maths

Postgraduate opportunities Prospectus 2013 entry

Mathematics

www.ed.ac.uk

Welcome to the University of Edinburgh:Influencing the world since 1583

THE UNIVERSITY of EDINBURGH

Our proud history and alumni ambassadors For more than 400 years our people have been making their mark on the world. They’ve explored space, revolutionised surgery, won Nobel

Prizes, published era-defining books, run the country, paved the way for life-saving breakthroughs and laid the foundations for solving the

mysteries of the universe. By choosing further study or research at Edinburgh you will be joining a community of scholars who have been at

the forefront of knowledge since 1583.

We are associated with 15 Nobel Prize winners, including physicists Charles Barkla and Max Born, medical researcher Peter Doherty,

economist Sir James Mirrlees and biologist Sir Paul Nurse. Our famous alumni include NASA astronaut Piers Sellers, former

MI5 Director-General Dame Stella Rimington, Olympians Sir Chris Hoy and Katherine Grainger and historical greats such as philosopher

David Hume, physicist and mathematician James Clerk Maxwell, inventor Alexander Graham Bell and Sherlock Holmes creator Sir Arthur

Conan Doyle.

Teaching and research excellence We are consistently ranked as one of the world’s top 50* universities. As host to more than 30,000 students from some 130 countries,

studying across 100 academic disciplines, the University of Edinburgh continues to attract the world’s greatest minds. World-leading

research is produced by 96 per cent** of our academic departments, placing Edinburgh in the top five in the UK for research. Our excellent

teaching was also confirmed in the latest report from the Quality Assurance Agency, which awarded us the highest rating possible for the

quality of the student learning experience.

Collaborations and international partnerships As an internationally renowned centre of academic excellence, Edinburgh is the site of many world-class research collaborations. Our

postgraduate students are crucial to our continued success and development and, along with our staff, they forge research links through regular

travel and overseas exchanges. We take pride in our partnerships with other institutions such as the California Institute of Technology, Stanford

University, the University of Melbourne, Peking University, the University of Delhi and the University of KwaZulu-Natal – to name but a few.

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The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

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ContentsWelcome to the School of Mathematics 2

Facilities and resources 2

Community 4

Employability and graduate attributes 5

Taught masters programmes 6

Research at the School of Mathematics 10

Research opportunities 11

Funding 16

How to apply 18

Get in touch 19

Campus map 20

“You are now in a place where the best courses upon Earth are within

your reach... such an opportunity you will never again have.”

Thomas Jefferson

American Founding Father and President (speaking to his son-in-law,

Thomas Mann Randolph, as he began his studies in 1786)

Linking research and commerceEdinburgh was one of the first UK universities to actively develop commercial links with industry, government and the professions.

Edinburgh Research and Innovation (ERI) has continued, for the past four decades, to develop the promotion and commercialisation

of the University’s research excellence. ERI assists our postgraduates in taking a first step to market, whether it is through collaborative

research, licensing technology or providing consultancy services.

Enhancing your careerWith the best track record for graduate employment in the Russell Group, the University of Edinburgh is committed to embedding

employability into the teaching and learning experience. From offering access to volunteering schemes to providing support from our

sector-leading Careers Service, the University gives students myriad opportunities to develop the skills, knowledge and experience to give

them the edge in a competitive job market.

An inspiring destinationYour first-class education will take place in one of Europe’s most striking capital cities, which is regularly voted one of the best places in the

world to live. Edinburgh enjoys a solid reputation as a centre for innovation, whether as home to the 18th-century Scottish Enlightenment or

as a modern source of pioneering science, medicine and technology. You couldn’t ask for a more inspiring setting in which to further your

knowledge and broaden your horizons.

Join usEdinburgh offers unparalleled academic breadth and diversity, making it a vibrant, challenging and stimulating environment for postgraduate

study. Whether you plan to change direction, enhance your existing career or develop in-depth knowledge of your area of study, the

University of Edinburgh provides a world-class learning experience.

*Times Higher Education World University Rankings ** Research Assessment Exercise 2008

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Students can use more than 1,200 computers

in suites distributed across the University’s sites,

and many are accessible by swipe card 24

hours a day. In addition, if you are a research

student you will have your own desk with

desktop computer.

Software supportThe School of Mathematics provides all

postgraduates with access to software

packages such as Maple, Matlab and

Mathematica. Research students are allocated

parallel computing time on ‘Eddie’ – the Edinburgh Compute and Data Facility. It is also possible to arrange use of the BlueGene/Q

supercomputer facility if your research requires it.

In good companyIn a discipline that is as much about equations as equipment, you can be certain of thriving in a rich academic setting for your studies. Our School is one of the country’s largest research communities in its own right, but you will also benefit from Edinburgh’s high-level collaborations, both regional and international.

Research students will have a primary and

secondary supervisor and the opportunity to

network with a large and varied peer group.

You will be carrying out your research in the

company of eminent figures, many of whom

are considered leaders in their fields, and

you will be exposed to a steady stream of

distinguished researchers from all over

the world.

Welcome to the School of Mathematics

Facilities and resources

We have an outstanding reputation for

teaching and research. We were judged

‘excellent’ in the most recent Teaching

Quality Assessment and, in the 2008 Research

Assessment Exercise, we were ranked among

the top five in the UK by volume of research

activity in the highest categories (4* and 3*).

Rich heritageThe School also boasts a rich heritage in

pioneering mathematics. Our base, the James

Clerk Maxwell Building, is named after one of

the most celebrated mathematicians to study

and teach at the University. The 19th-century

scientist is most famous for developing classical

electromagnetic theory. Nobel Prize winning

physicist Max Born was Tait Professor of

Mathematical Physics here, from 1936 to 1953.

Leaders in their fieldsOur status as one of the most prestigious

schools in the UK for mathematics attracts

highly respected staff. Among the 50 current

academic staff of the School of Mathematics

many are leaders in their fields and regularly

recognised with international awards.

The School is home to three Fellows of the

Royal Society, eight Fellows of the Royal Society

of Edinburgh and seven Leverhulme Prize or

Fellowship holders. Abel Prize winner and Fields

medallist Sir Michael Atiyah is an Honorary

Professor, and Professor Agata Smoktunowicz,

of the Algebra and Number Theory Group, is a

recent recipient of the European Mathematical

Society Prize.

By joining the University of Edinburgh’s School of Mathematics, you’ll follow in the footsteps of some of history’s most pioneering mathematicians and study alongside some of the most exciting minds working in the field today. Whether you wish to follow a taught masters programme or pursue your own line of investigation, our School offers a dynamic academic environment, supported by excellent facilities.

As a postgraduate student you will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs (EPCC) to generous library provision for research at such a leading level, including the new King’s Buildings Library and the mathematics-focused James Clerk Maxwell Library.

Michel Zedler

MSc Operational Research

“I experienced an egalitarian professor–student relationship and felt that student feedback was considered carefully. A number of

external guest lecturers from diverse backgrounds in industry and academia enriched the programme with their expertise. The

overall productive learning atmosphere was further improved by group assignments that channelled skill transfer between

students. I have won some lifetime friends.”

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CommunityWe are a vibrant community of about 50 staff supervising 60 students, and while you will be immersed in academic discourse at the highest level, we also offer plenty of opportunities to have fun, through a full calendar of social events.

Mathematics need never be a solitary

discipline, when there is the daily bustle of the

common room, subject-specific clubs, the

weekly postgraduate colloquium – where

students give talks and share cake – and many

annual events including a residential excursion

to Firbush Point on the banks of Loch Tay in the

Highlands, where everything from cycling to

canoeing is on offer.

Graduate SchoolFor research students our Graduate School

offers a busy schedule of activities ranging

from formal seminars to social events. The

Graduate School runs its own website and

YouTube channel, which features

self-produced videos of lectures.

Share your work with the worldResearchers are encouraged to travel and

participate in conferences and seminars. You’ll

also be in the right place in Edinburgh to meet

distinguished researchers from all over the

world who are attracted to conferences held at

the School and the various collaborative

centres based here. You will find opportunities

for networking that could have far-reaching

effects on your career in mathematics.

Sarah Farid KhwajaPhD Mathematics

“The school is very supportive in

organising social events to help

networking. Edinburgh is an

international university that attracts

students from different countries and

I made many friends during my first

month in Edinburgh, who have given

me a different perspective of the

world. I’ve also been able to make

useful contacts with academics

within the University and with

external experts in the field.”

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Employability and graduate attributes While your research will build your knowledge and skills in your particular area, throughout your degree you’ll also gain expertise and confidence in a number of related areas, such as public speaking, presentation and written communication. This personal and professional development, supported by services offered by the School and the University, will give you an edge when applying for academic or commercial roles.

Institute for Academic DevelopmentAll of our postgraduate students have the

opportunity to benefit from the University’s

Institute for Academic Development (IAD),

which provides information, events and

courses to develop the skills you will need now

and in the future.

The IAD offers one of the most established

university research and career skills training

packages in the UK. Our IAD experts will help

you gain the skills, knowledge and confidence

needed to move onto the next stage in your

career, be that in a professional sector or

within academia.

The Institute provides PhD researchers and

masters by research students with dedicated

training in topics such as research

management; personal effectiveness;

communication skills; public engagement,

networking and team working; leadership and

career management. You can gain expertise in

information technology and presentation skills;

confidence in undertaking independent and

creative research; the ability to critically

evaluate source materials; and the capacity to

construct intellectually rigorous arguments.

For taught postgraduates, the IAD provides a

growing range of tailored study-related and

transferable skills workshops, plus online

advice and learning resources. These are all

designed to help you settle into postgraduate

life, succeed during your studies, and move

confidently onwards to the next stage of

your career.

Developing these broader professional skills

and qualities means that our postgraduate

students are always in high demand.

For more information please visit

www.ed.ac.uk/iad/postgraduates.

Careers ServiceThe University’s award-winning Careers Service

aims to expand the horizons of all our

students, enabling you to make informed

career decisions and progress towards high

personal and professional achievement,

whether in work or in further study. Our goal is

to offer you a world-class service. Our teams

of subject-specific expert advisers are here to

help at any time in your programme of study.

We offer impartial guidance and information,

and draw on our relationships with a wide

range of employing and training organisations.

For more information on the full range of

services available, including access to

vacancies, advice on starting your own

business, getting published, working

internationally or even volunteering, visit

the postgraduate section of our website at

www.ed.ac.uk/careers.

Learn to teachPhD students are given leadership roles within

the School, and you’ll be expected to spend

some of your time conducting undergraduate

tutorials. And we will help you: the University

offers courses in public speaking and other

teaching skills, and you’ll be able to draw on

the support of your peers and supervisors in

research group meetings.

A solid startFor research students, a strong foundation in

the fundamentals of your chosen field is

essential and in the early part of your studies

you will be offered taught courses through

the Scottish Mathematical Sciences Training

Centre, a consortium of seven mathematics

departments. You’ll take part in video-

conferenced lectures, presented by staff

from all participating universities.


Taught masters programmes

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FinanCial MaThEMaTiCS www.ed.ac.uk/pg/118 MSc 1yr FT

Programme descriptionThis masters is run jointly with Heriot-Watt University. It provides you with expertise in financial mathematics, including stochastic calculus, and a range of practical techniques for analysing financial markets. You will also learn quantitative skills for developing and managing risk that are in high demand since the recent financial crisis.

Adding depth to your learning, our work placement programme puts you at the heart of organisations such as Aberdeen Asset Management, Barrie & Hibbert and Lloyds Banking Group.

Programme structureThis programme involves two taught semesters of compulsory and optional courses, followed by a dissertation project.

Compulsory courses: Discrete-Time Finance, Stochastic Analysis in Finance I, Financial Markets, Derivatives Markets, Special Topics 1, Derivative Pricing and Financial Modelling, Stochastic Analysis in Finance II, Special Topics 2, Credit Risk Management.

Optional courses: Financial Risk Management, Statistical Methods, Simulation, Mathematical Programming, Financial Econometrics, Numerical Techniques for PDE, Time Series Analysis, Modern Portfolio Theory, Optimization Methods in Finance.

Career opportunitiesGraduates have gone on to either work in major financial institutions or to continue their studies by joining PhD programmes.

Minimum entry requirementsA UK 2:1 degree, or its international equivalent (www.ed.ac.uk/international/

country), in mathematics or a mathematical subject such as statistics, physics

or engineering.

English language requirements

See page 18

Tuition fees in 2012/13*1 yr FT: UK/EU students £17,200; international students £20,000

*Fees change annually. For the most up-to-date information about fees see

www.ed.ac.uk/student-funding.

Programme DirectorDr Sotirios Sabanis E: [email protected] T: +44 (0)131 650 5084

FinanCial ModElling & oPTiMizaTion www.ed.ac.uk/pg/640

MSc 1 yr FT (2 yrs PT available for UK/EU students)

Programme descriptionThis programme gives you a flexible syllabus to suit the demands of employers that use modern financial tools and optimization techniques, in areas such as the financial sector and energy markets.

We will give you sound knowledge in financial derivative pricing, portfolio optimization and financial risk management. We’ll also provide you with the skills to solve some of today’s financial problems, which have themselves been caused by modern financial instruments. This expertise includes modern probability theory, applied statistics, stochastic analysis and optimization.

Adding depth to your learning, our work placement programme puts you at the heart of financial organisations such as Aberdeen Asset Management, Barrie & Hibbert and Lloyds Banking Group.

Programme structureThis programme involves two taught semesters of compulsory and optional courses, followed by a dissertation project.

Compulsory courses: Discrete-Time Finance; Stochastic Analysis in Finance I; Fundamentals of Optimization; Research-Linked Topics; Finance, Risk and Uncertainty; Risk-Neutral Asset Pricing; Stochastic Analysis in Finance II; Simulation; Optimization Methods in Finance.

Optional Courses: Nonlinear Optimization; Large Scale Optimization; Stochastic Optimization; Combinatorial Optimization; Global and Derivative-Free Optimization; Introduction to Java Programming; Parallel Numerical Algorithms (advanced programming course offered by EPCC); Dynamic & Integer Programming; Game Theory; Stochastic Modelling; Credit Scoring and Data Mining; Financial Risk Management; Risk Analysis.

Career opportunitiesGraduates have gone on to either work in major financial institutions or to continue their studies by joining PhD programmes.


country), in mathematics or a mathematical subject such as statistics, physics or

engineering.


See page 18


2 yrs PT: UK/EU students £8,600 per year



Programme DirectorDr Sotirios Sabanis E: [email protected] T: +44 (0)131 650 5084

You may also be interested in: Finance & Investment or Banking & Risk (University of Edinburgh Business School Prospectus)

You may also be interested in: Finance & Investment or Banking & Risk (University of Edinburgh Business School Prospectus)

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Programme descriptionThis programme will show you how to use mathematical techniques to model and solve real-life financial problems. Operational research is an important skill that is in high demand in the finance industry.

Programme structureThis programme involves two taught semesters of compulsory and optional courses followed by your dissertation project.

Compulsory courses: Computing for OR; Dynamic and Integer Programming; Game Theory; Methodology, Modelling & Consulting Skills; Fundamentals of Optimization; Financial Mathematics and Investment; Financial Risk Management; Simulation; Stochastic Modelling.

Optional courses: These are generally grouped into the following areas: finance, risk, industry, statistics and optimization. Many dissertation projects are carried out as part of an external placement in industry.

Career opportunitiesThe skills you will learn are in demand by a vast range of organisations, for example professional consultancy firms, big companies with operational research departments such as airlines or telecommunications providers, smaller financial firms and the public sector. Recent graduates have joined Cap Gemini, British Airways, Orange, Barrie & Hibbert and HM Revenue & Customs.

Minimum entry requirementsA UK 2:1 degree, or its international equivalent (www.ed.ac.uk/

international/country), in a numerate discipline, for example

mathematics, engineering, computer science, physical or biological

sciences, economics or business.

English language requirementsSee page 18





Programme DirectorDr Julian Hall E: [email protected] T: +44 (0)131 650 5075

MaThEMaTiCS www.ed.ac.uk/pg/645


Programme descriptionThis programme is the ideal preparation for a career that involves the use of advanced mathematics or for a doctoral degree in mathematics. We will introduce you to abstract thinking and logical analysis and develop your skills in advanced techniques in pure and applied mathematics.

You will study key areas including analysis, algebra, geometry, probability theory, statistics, partial differential equations and numerical methods. We will also develop your project management and communication skills.

Programme structureThis programme consists of two taught semesters of courses followed by your dissertation project. You have a wide range of options, including courses from the Scottish Mathematical Sciences Training Centre, which selects teaching staff from various Scottish universities. Some of these are taught by video conference.

Career opportunitiesThis is the ideal programme if you wish to pursue an academic career.


country), in mathematics or a mathematical subject such as statistics, physics

or engineering.


See page 18

Tuition fees in 2012/13*

1 yr FT: UK/EU students £5,750; international students £13,050




Programme DirectorProfessor Tom Lenagan E: [email protected] T: +44 (0)131 650 5078


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Programme descriptionThis programme will show you how to use mathematical techniques to tackle real-life problems ranging from scheduling flights and routing mobile phone calls to managing investments and minimising risks. Operational research is an important skill that is in high demand.

Our intensive programme allows you to specialise in an area that best suits your career goals. You can choose operational research, operational research with risk, or operational research with computational optimization.

Programme structureThis programme involves two taught semesters of compulsory and optional courses followed by your dissertation project.

Compulsory courses: Fundamentals of Optimization; Computing for OR; Dynamic and Integer Programming; Game Theory; Methodology, Modelling & Consulting Skills; Probability and Statistics; Simulation; Stochastic Modelling.

Optional courses are generally grouped into the following areas: finance, risk, and industry, statistics and optimization.

Many dissertation projects are carried out as part of an external placement in industry.

Career opportunitiesThe skills you will learn are in demand by a vast range of high-profile organisations, for example professional consultancy firms, big companies with operational research departments such as airlines or telecommunications providers, smaller financial firms and the public sector. Recent graduates have joined Cap Gemini, British Airways, Orange, Barrie & Hibbert and HM Revenue & Customs.


country), in a numerate discipline, for example mathematics, engineering,

computer science, physical or biological sciences, economics or business.


See page 18


1 yr FT: UK/EU students £5,750; international students £14,400




Programme DirectorDr Julian Hall E: [email protected] T: +44 (0) 131 650 5075

SCiEnTiFiC CoMPUTingwww.ed.ac.uk/pg/703

MSc 1 yr FT

Programme descriptionThis programme starts by developing your expertise in design, implementation and mathematical analysis of numerical algorithms for ordinary and partial differential equations, linear algebra, and convex and non-convex optimization. This theory is backed up with training in advanced computing languages, such as CUDA, and experience with the latest high performance computing hardware, including GPUs and cloud computing. You’ll also benefit from unrivalled parallel computing facilities.

You will use the theory and software to analyse molecular dynamics, social networks, atmospheric and oceanographic waves and astronomical many-body interactions so you can carry out your own analysis for the scientific developments of tomorrow.

Programme structureThis programme comprises two semesters of core and optional courses followed by your dissertation project.

Compulsory courses: Numerical Ordinary Differential Equations; Numerical Linear Algebra; Fundamentals of Optimization; Computer Programming for Scientific Computing; HPC Architecture; Numerical Partial Differential Equations; Nonlinear Optimization; and either Parallel Numerical Algorithms or Design and Analysis of Parallel Algorithms.

Optional courses: Large Scale Optimization; Stochastic Optimization; Combinatorial Optimization; Data Mining and Exploration; Extreme Computing; Information Theory; Machine Learning for Pattern Recognition; Fundamental Concepts in High Performance Computing; Message Passing Algorithms; Object Oriented Programming for HPC.

Career opportunitiesThis programme is perfect preparation for a career in a broad range of hi-tech industries, or in academic research.


country), in a numerate discipline, such as mathematics, engineering, computer

science or physical sciences. Previous experience with computing programming is

assumed: suitable languages including C, C++, Fortran and Matlab.

English language requirementsSee page 18




Programme DirectorDr Julian Hall E: [email protected] T: +44 (0) 131 650 5075

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Programme descriptionThis programme facilitates the professional development of students in the theory and practice of statistics and operational research (OR), providing the foundations for a successful career.

It is relevant in preparing students to work in areas such as the medical and health industry, the government, the financial sector and any other area where modern statistical tools and OR techniques are used. It provides a sound foundation and develops wider skills required for solving problems, working in teams and managing time.

Students will be able to identify appropriate statistical or operational techniques, which can be applied to practical problems.

Students will acquire the core skills of Java programming and use the packages R for Statistics and Simul8 for simulation. In addition, students will acquire the ability to use high-level applications in Excel.

Programme structureThis MSc consists of traditional lecture-based courses and practical lab-based courses. Assessment will be given by means of exams, written reports and programming assignments. An industrial or academic project is written up as a dissertation.

Compulsory courses: Statistical Theory; Statistical Regression Models; Simulation; Methodology, Modelling and Consulting Skills; Computing for Statistics; Stochastic Modelling; Dynamic and Integer Programming; Likelihood and Generalised Linear Models; Fundamentals of Optimization.

Optional courses: Stochastic Optimization; Combinatorial Optimization; Operational Research in the Airline Industry; Operational Research in the Telecommunications; Large Scale Optimization; Time Series Analysis and Forecasting; Risk Analysis; Data Analysis; Machine Learning & Pattern Recognition (Level 11); Clinical Trials; Genetic Epidemiology; Stochastic Models in Biology; Credit Scoring and Data Mining; The Analysis of Survival Data; Categorical Data Analysis; Nonparametric Regression; Computing for Operational Research.

Career opportunitiesThis programme is ideal for students who wish to apply their statistics and operational research knowledge within a wide range of sectors including the medical and health sector, government, and finance. The advanced problem solving skills you’ll develop will be highly prized by many employers.


country), with a significant Mathematics and Statistics component.

English language requirements See page 18

Tuition fees for 2012/2013*1 yr FT: UK/EU students £5,750; international students £14,400

2 yrs PT: UK/EU students £2,875



Programme Director

Dr Bruce Worton E: [email protected] T: +44 (0) 131 650 4884


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Research at the School of MathematicsAs one of the best in the UK for mathematics research, we can provide a truly stimulating and inspiring environment for beginning your research career.

We carry out research in the following areas:

Algebra and Number Theory; Computational

Mathematics; Geometry & Topology;

Mathematical Physics; Operational Research &

Optimization; Probability & Stochastic Analysis;

and Statistics.

Centres and institutesIn 2005, we set up the Maxwell Institute for

Mathematical Sciences in collaboration with

Heriot-Watt University. The Institute pools

research from both universities to offer a

research and postgraduate training

environment that can attract the best

mathematics talent from around the world.

With Heriot-Watt University we also created

the International Centre for Mathematical

Sciences (ICMS). This research institute works to

develop mathematical sciences in new

directions, support and develop mathematics

that is relevant and in demand from other

sciences, industry and commerce and foster

collaboration between mathematics

departments across Scotland.

We have been granted two EPSRC Science and

Innovation Awards, worth £3.5 million and £5

million respectively, to establish the Centre for

Analysis and Nonlinear Partial Differential

Equations and the Centre for Numerical

Algorithms and Intelligent Software.

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Research opportunities

algEbra & nUMbEr ThEory www.ed.ac.uk/pg/509

PhD 3 yrs FT (6 yrs PT available for UK/EU students)

Our pure mathematics work was ranked by the latest Research

Assessment Exercise among the UK’s top five in this field for volume of

top-category research.

Our credentials have also been proven by recent accolades: many of

our staff are the holders of prestigious awards, including the European

Mathematical Society Prize, the Whitehead Prize of the London

Mathematical Society, the Waclaw Sierpinski Prize of the Polish

Academy of Sciences and the Berwick Prize of the London

Mathematical Society. Our lecturers have also presented at the

International Congress of Mathematicians, and one is currently an

EPSRC Leadership Fellow.

Research

The research carried out by the Algebra and Number Theory group

centres on four areas: non-commutative ring theory, especially

problems concerning nil rings, the Jacobson radical, prime and primitive

rings, and combinatorial problems in ring theory including growth of

algebras (Gelfand–Kirillov dimension); non-commutative algebraic

geometry, in particular representation theory of noetherian rings and

quantum algebras, and the growth properties of finitely-generated

algebras over fields, especially on the notion of the Gelfand–Kirillov

dimension of an algebra; number theory, focusing on the study of

algebraic integers which are confined in some way; and representation

theory and its applications to algebraic geometry and combinatorics.

Much of our research is closely related to the areas of geometry &

topology and mathematical physics, and you can benefit from close

links we maintain with these groups.

Active seminar programme

Through the School’s membership of the Maxwell Institute, we present

regular seminars, and run our own informal seminars and colloquia. We

also serve on editorial boards of various international journals. Most

importantly, many of our recent PhD students have gone on to

postdoctoral positions throughout the world.


PhD 3 yrs FT: UK/EU students £3,828; international students £11,450

per year

PhD 6 yrs PT: UK/EU students £1,914 per year

*Fees change annually. For the most up-to-date information about fees

see www.ed.ac.uk/student-funding.

Contact: Mrs Gill Law, Postgraduate Research Administrator

E: [email protected]

analySiSwww.ed.ac.uk/pg/510


Our group is one of the top two centres in the UK for research in the

field of analysis. Your passion for this highly specialised discipline will be

richly rewarded by world-leading academic staff, a rich seminar and

working group programme and a qualification that shows you have the

ability to approach research at the most advanced level.

Research

We have a unique focus on the intersection of classical Euclidian

harmonic analysis and partial differential equations. Our specialisms

are: PDEs – elliptic and parabolic problems, especially in relation to

rough domains and minimal regularity; nonlinear hyperbolic equations

and systems, especially in relation to black holes and general relativity;

and nonlinear hyperbolic and dispersive problems in mathematical

physics and mathematical biology, null form estimates, kinetic

equations and chemotaxis. We also look at the connections between

harmonic analysis and geometry, number theory and combinatronics,

and stochastic analysis.

Additional resources

In addition to the School’s excellent facilities, as part of the Analysis

group you will have access to the Centre for Analysis and Nonlinear

PDEs (CANPDE). Established in 2007, the Centre is a joint project of

Edinburgh and Heriot-Watt under the umbrella of the Maxwell Institute.

Through seminars, mini-symposia and workshops, it aims to stimulate

and support development of research in theoretical nonlinear PDEs.



per year






You will carry out your research within one of eight research groups: communities of research staff and students with access to specialist facilities and subject-specific funding.

You may also be interested in:

Mathematical Physics and Geometry & Topology


Geometry & Topology and Algebra & Number Theory


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aPPliEd & CoMPUTaTional MaThEMaTiCS www.ed.ac.uk/pg/511


The Applied and Computational Mathematics group combines expertise

in dynamics, classical and statistical mechanics and advanced scientific

computing techniques, to develop techniques for applications such as

stellar and molecular dynamics, geophysical and astrophysical fluid

dynamics and optoelectronics.

If you have a passion for applied mathematics, our facilities, people

and environment will help you develop the full potential of your

research ideas.

You’ll have access to the EPCC, one of Europe’s leading supercomputing

centres, and membership of the Centre for Numerical Algorithms and

Intelligent Software (NAIS), a cross-institutional collaboration that aims

to increase your research networks.

Research environment

Our research interests are varied and include stellar dynamics,

astronomical fluid dynamics, multiscale modelling and analysis,

molecular dynamics, mathematical meteorology, Hamiltonian dynamics,

nonlinear waves in fluids and solids, unsteady free boundary problems,

optoelectronics, signal processing, exponential asympotics and

homogenisation theory.

Valuable connections

Having access to a broad community of researchers means that your

work will be well distributed and recognised. We joined with two other

Scottish universities (Heriot-Watt and Strathclyde) in 2009 to create

NAIS. Through this collaboration, you’ll create stronger networks with

researchers across Scotland and have access to substantial training and

visitor and workshop programmes in numerical analysis, computer

science and high performance computing software development.



per year






gEoMETry & ToPology www.ed.ac.uk/pg/512


Our research group has strong links with the Mathematical Physics

research group. You’ll find this invaluable as a research student, as

opportunities to discuss your work and expand your thinking abound.

Working within one of the largest mathematics groups in the UK, you’ll

be completing your degree in an environment that hums with a busy

graduate school life, and you will have the chance to make your mark in

seminars, workshops, clubs and outings.


Our interests include differential and algebraic geometry, algebraic and

geometric topology, twistor theory and integrable systems. The field of

algebraic geometry, in particular, is highly dynamic, reflecting its

application to the rapidly increasing use of computer aided design in a

variety of careers.

Opportunities for travel

While we can offer a large community of researchers under one roof,

we believe in encouraging you to gain as broad a perspective as

possible. The best way to do this is to involve yourself in the international

dialogue on your research area, through attending conferences and

symposia, and visiting your peers in centres of research worldwide.

Throughout your studies, you’ll be given opportunities to travel to events

and institutions that will allow you to gain this perspective, and open up

new areas of investigation.


PhD 3 yrs FT: UK/EU students £3,828; international students £11,450 per

year







The Doctoral Training Centre in Neuroinformatics and Computational

Neuroscience (Informatics Prospectus); Astrophysics (Physics &

Astronomy Prospectus) or Geology & Geophysics (GeoSciences

Prospectus)


Mathematical Physics

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MaThEMaTiCal PhySiCS www.ed.ac.uk/pg/513


We are a multidisciplinary research group with close connections with

the School’s Algebra and Geometry & Topology groups. You will benefit

from being not only in one of the largest mathematics research groups

in the UK but also part of the Edinburgh Mathematical Physics Group

– a joint research institute formed in 1999 with Heriot-Watt University

through the Maxwell Institute.


Our group pursues wide-ranging interests spanning a number of

disciplines. A central goal is to understand the principles behind

quantum gravity, through the study of black holes, cosmologies and

spacetime singularities, and via the use of holography and the interplay

with quantum gauge field theory through the gauge/gravity

correspondence. Particularly fruitful areas of research in the group are

the geometry of higher-dimensional black holes and their near-horizon

geometries in the context of higher-dimensional generalisations of

General Relativity.

We are fascinated by the various manifestations of supersymmetry,

which has led us to study gauge theoretic moduli spaces, often via

integrable systems techniques, displaying a beautiful interplay between

the algebraic geometry of curves and their associated function theory.

This research has led to computer implementations of various algebro-

geometric constructions. Recently we have made progress in some

purely mathematical problems suggested by the gauge/gravity

correspondence: namely, the classification of certain exotic algebraic

structures related to superconformal field theories, as well as that of

certain types of homogeneous supergravity backgrounds.

An environment of excellence

As well as experiencing a vibrant research environment that brings you

into contact with a broad group of your peers, your membership of the

Edinburgh Mathematical Physics Group will give you access to a

dynamic programme of seminars, lecture courses and other

presentations. There is a dedicated website and blog, and a

comprehensive range of graduate activities.



per year






oPEraTional rESEarCh & oPTiMizaTion www.ed.ac.uk/pg/514


As a member of the Operational Research and Optimization group you

will also be part of the Edinburgh Research Group in Optimization

(ERGO), a wider association, with our group as the focus, which includes

academics at the universities of Dundee and Oxford as well as

commercial organisations. Through its regular seminar series, this

network provides interaction with a broad array of local and

international institutions and industrial bodies interested in the

development of operational research and optimization. As a result,

you’ll establish valuable relationships that will help you take your

research to its optimum level.


Our group has as its primary focus the mathematical and computing

aspects of optimization. Core technology in optimization is the solution

for large sparse linear and quadratic problems, and we are able to

provide world-class expertise in the two main solution methods for

these: the simplex method and the interior point method.

We have interests in global optimization, decomposition methods,

parallel computing, industrial applications of optimization and

stochastic optimization. Our current researchers are exploring the

following areas: parameter uncertainty in queueing theory and revenue

management; algorithms for linear and nonlinear nonconvex smooth

optimization problems; optimization methods for linear, quadratic and

nonlinear programming; decomposition methods for large-scale

nonlinear nonconvex constrained optimization; bundle methods;

warmstarts for interior point methods; pooling problems;

computational techniques for solving large-scale linear programming

problems; applications of optimization in the chemical, oil and

electricity industries; and efficient gradient methods for large-scale

convex and nonconvex optimization problems.

An environment of excellence

Being part of the Operational Research and Optimization group and

ERGO will give you the opportunity to meet and confer with academics

worldwide – we’re currently interacting with researchers in Italy, Norway,

China, France, Spain and Turkey. Two of our visiting professors are world

leaders in continuous optimization. In addition, researchers from our

group are regularly invited to give addresses and organise workshops at

major optimization conferences, join international conference

committees and sit on assessment panels for European grants.



per year







Astrophysics (Physics & Astronomy Prospectus)

You may also be interested in: Management

(University of Edinburgh Business School Prospectus)


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ProbabiliTy & SToChaSTiC analySiS www.ed.ac.uk/pg/515


Our research group operates in what is perhaps the most widely applied

area of mathematics. The financial sector, in particular, is a major focus

of our research, and graduates with the right research experience can

make their way into highly rewarding roles in industry. As part of our

small, specialised group, you’ll enjoy a research environment that

features a balance between theory and practice, access to one of the

most powerful computing facilities in the UK and strong links with

relevant industries.

Research

Our research focuses on the following themes: stochastic differential

equations and stochastic partial differential equations (PDEs) and their

applications in nonlinear filtering and stochastic control; applications of

stochastic analysis of PDEs, stochastic PDEs and stochastic differential

equations (accelerated numerical methods in particular).

We’re also involved in the applications of probability theory, mainly to

mathematical finance, particularly stochastic volatility models,

equivalent martingale measures and incomplete markets. Other

applications include engineering, signal procession and biological

sciences.

Financial industry links

With the financial sector being the major commercial employer of our

graduates, our involvement with the Scottish Financial Risk Academy,

established in conjunction with Heriot-Watt University, offers valuable

industry links and training. You can benefit from short project

internships with leading financial institutions, visits from leading risk

scholars, and a series of knowledge exchange courses and events.

Unparalleled computing

As part of the Probability & Stochastic Analysis group, you’ll have access

to EPCC, one of Europe’s leading supercomputing facilities. EPCC

enables high-level grid computing, data integration, and computer

simulation and process optimization. We offer training in all the relevant

programs you need to achieve your research aims.

Rewarding career options

Many of our graduates take up lucrative positions with high-profile

financial companies. A large number also pursue careers in academia,

while others apply their skills in engineering or biological sciences.



year






STaTiSTiCS www.ed.ac.uk/pg/516


Our society revolves around variation, uncertainty and risk. By gaining a

greater understanding of these variables through the study of statistics,

we are able to create systems and techniques that benefit areas as

diverse as science, the law and finance. The Statistics group explores a

wide range of statistical theory and practice, often applying its findings

in collaboration with researchers in related fields, such as Informatics

and Biomathematics.

Research

Our work is balanced between classical and Bayesian statistics. Our

particular areas of interest include hierarchical multivariate random

effects models, wavelets, nonparametric regression and resampling.

While the group has a strong theoretical base, we are also heavily

involved in specific application areas, particularly forensic science, the

law, agriculture, and functional genomics data, such as gene expression

microarrays.

Strong links for collaboration

As a research student, you’ll find a wealth of expertise available to you

via our links with theorists and practitioners in related fields. The

University’s School of Informatics, for instance, is the largest and most

prestigious in the UK, and features a Machine Learning research group

whose work is linked to some forms of statistical research. In addition,

the Scottish Government-backed research provider Biomathematics and

Statistics Scotland is an associated research institute of the University.

With its main base in our building, it provides access to other researchers

with an interest in statistical genomics and bioinformatics, process and

systems modelling and statistical methodology.

If your research is in the expanding area of forensic statistics, you’ll

benefit from our link with the Joseph Bell Centre for Forensic Statistics

and Legal Reasoning. The centre applies and teaches statistical

techniques for interpreting evidence, such as binomial probabilities,

conditional probability and Bayes’ Theorem.

Careers in statistics

You’ll gain a qualification that is highly regarded in both academia and

industry. Future career options are diverse, with past students finding

positions in academic institutions, forensics, finance, the law and

biological and agricultural organisations.



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Funding

University of Edinburgh scholarships

China Scholarships Council/University of Edinburgh Scholarships A number of scholarships for PhD study to candidates who are citizens and

residents of China. www.ed.ac.uk/student-funding/china-council

College of Science & Engineering Scholarships The College of Science & Engineering has funds from endowments and donations

that are available to provide funding for studentships. Individual Schools also

receive considerable support from other organisations such as charities, trusts

and industrial sponsors.

Edinburgh Global Masters Scholarships A number of scholarships available to international students for masters study.

www.ed.ac.uk/student-funding/masters

Edinburgh Global Research Scholarships These scholarships are designed to attract high-quality international research

students to the University. www.ed.ac.uk/student-funding/global-research

Edinburgh Santander Masters Scholarships Several scholarships are available to students from a number of countries for

masters study. www.ed.ac.uk/student-funding/santander

Edinburgh UK/EU Masters Scholarships Scholarships for UK and EU students who have been accepted on a full-time

masters degree programme. www.ed.ac.uk/student-funding/uk-masters

Principal’s Career Development PhD Scholarships A number of awards, open to UK, EU and international PhD students.

www.ed.ac.uk/student-funding/development

Principal’s Indian Masters Scholarships 15 scholarships are available to students from India for masters study.

www.ed.ac.uk/student-funding/masters-india

School of Mathematics Studentships A number of full and partial scholarships and studentships for MPhil and PhD

students. www.maths.ed.ac.uk/pg/prosp.shtml

Other sources of funding

Commonwealth Scholarships For students who are resident in any Commonwealth country, other than the UK.

www.dfid.gov.uk/cscuk

Fulbright Scholarships Scholarships open to US graduate students in any subject wishing to study in the

UK. www.iie.org/fulbright

Marshall Scholarships Open to outstanding US students wishing to study at any UK university for at least

two years. www.marshallscholarship.org

Scotland’s Saltire Scholarships A number of scholarships open to citizens of Canada, China, India and the US,

undertaking masters-level study in Scotland.

www.ed.ac.uk/student-funding/saltire

A large number of scholarships, loans and other funding schemes are available for your postgraduate studies. You can find the full range at www.ed.ac.uk/student-funding.

Awards are offered by the School of Mathematics, the College of Science & Engineering, the University of Edinburgh, the Scottish, British and

international governments and funding bodies.

Below we list a selection of potential sources of financial support for postgraduate students applying to the School of Mathematics. Where an entry

does not include a web address, please use the web link above to navigate to the particular award.

The University of Edinburgh Graduate Discount SchemeWe offer a 10 per cent discount on postgraduate fees for all alumni who have graduated with an undergraduate degree from the University. www.ed.ac.uk/student-funding/discounts

Robert Starr

MSc High Performance Computing

Scotland’s Saltire Scholarship

“The Scottish Government’s initiative to attract international

students from Canada, China, India and the US through the

Saltire Scholarship Scheme as well as the University of

Edinburgh’s help and support for international students has

helped provide me with an opportunity that I would never

have conceived prior to starting my studies at Edinburgh.”

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Research council awards

Research councils offer awards to masters, MPhil and PhD students in most of the Schools within the University of Edinburgh. All studentship applications from the research councils must be made through the University, through your School or College office. Awards can be made for both taught and research programmes.

Normally only those UK/EU students who have been resident in the UK for the preceding three years are eligible for a full award. For some awards, candidates who are EU nationals and are resident in the UK may be eligible for a fees-only award. www.ed.ac.uk/student-funding/research-councils

Financial aid

The Canada Student Loans ProgramThe University is eligible to certify Canadian student loan applications. Full details

on eligibility and how to apply can be found online.

www.ed.ac.uk/student-funding/canadian-loans

The Student Awards Agency for ScotlandThis department of the Scottish Government has offered loans to postgraduate

students in the past. At time of going to press arrangements for study in

2013/14 were under review.

www.saas.gov.uk

US Student LoansThe University is eligible to certify loan applications for US loan students.

Full details on eligibility and how to apply can be found online.

www.ed.ac.uk/student-funding/us-loans


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How to applyGeneral requirementsTo apply for any postgraduate degree, you will

in most cases need a UK degree with a 1st or

2:1 classification, or its international equivalent

(www.ed.ac.uk/international/country),

generally in a related area.

Some programmes may vary, so check the

entry requirements for the specific programme

you wish to apply for.

Taught postgraduate programmesBefore you apply, we strongly advise you to

contact us to discuss the programmes you

wish to explore, the courses you wish to cover

and even, if possible, any areas of interest for

your research dissertation. You should then

apply for our programmes online, using the

degree finder: www.ed.ac.uk/pg/degrees.

In the first instance contact the Programme

Director for the programme you are

interested in.

Research degreesThe first step in applying for a research degree

is to explore our areas of research and

determine which best suits your skills and

interests. After checking the dates for research

applications (available online), you should

contact your potential supervisor to discuss

whether they are happy to supervise your work.

Check to see if a separate application is needed

for funding, then apply online, using the degree

finder: www.ed.ac.uk/pg/degrees.

Any research area in the School of Mathematics

will require you to have a solid undergraduate

degree in a related field. If your background is

not directly related to mathematics, you may

still be considered – your potential supervisor

can advise you on this.

You can also contact the Graduate School

Administrative Officer, Jill Douglas, at

[email protected] or the Graduate

Admission Officer, Dr Pieter Blue, at

[email protected].

Joining us from overseasInternational applicants are advised to check

the University’s website to find out more about

their visa options and our Integrated English for

Academic Purposes (IEAP) programme. Please

visit www.ed.ac.uk/international/ieap.

International agentsThe University has certified representative

agents in the following locations: Brunei,

Canada, China, Gulf Region, Hong Kong, India,

Japan, Jordan, Korea, Malaysia, Mexico, Nigeria,

Norway, Russia, Saudi Arabia, Singapore, South

Africa, South Korea, Taiwan, Thailand, Turkey,

Zambia and Zimbabwe. International

applicants can use an agent to help guide

them through the application process if

necessary. Contact details for all our agents

can be found at www.ed.ac.uk/studying/

international/agents.

English language requirementsStudents whose first language is not English must show evidence of one of the qualifications in the box below.

Abbreviations: IELTS − International English Language Testing System; TOEFL iBT − Test of English as a Foreign Language Internet-Based Test; CPE − Certificate of Proficiency in English; CAE − Certificate in Advanced English

IELTS 6.5 (with no score lower than 6.0 in each section)

TOEFL iBT Total 92 (with no score lower than 20 in each section).

Pearson Test of English 61 (with no score lower than 56 in each of the ‘Communicative Skills’ sections - ‘Enabling Skills’ section scores are not considered)

Cambridge CPE Grade B

Cambridge CAE Grade C

Please note:

• English language requirements can be affected by government policy so please ensure you

visit our website for the latest details. www.ed.ac.uk/english-requirements/pg/cse

• Your English language certificate must be no more than two years old at the beginning of

your degree programme.

• A degree from an English-speaking university may be accepted in some circumstances.

• Cambridge tests are accepted only for applicants who do not need Tier 4 visas to

enter the UK.

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Contact usFor more information on our taught MSc

programmes, email as follows:

Financial Mathematics

[email protected]

Financial Modelling & Optimization

[email protected]

Mathematics

[email protected]

Operational Research

[email protected]

Scientific Computing

[email protected]

Statistics and Operational Research

[email protected]

For more information on postgraduate

research, email [email protected].

Alternatively, contact:

Gill Law

Postgraduate Research Administrator


T: +44 (0)131 650 5085

Visit usOur postgraduate Open Day is your

opportunity to come and meet current staff

and students. Our next campus-based Open

Day takes place on Friday 23 November 2012.

For further details, please visit

www.ed.ac.uk/postgraduate-open-day.

We also run online information sessions for

prospective postgraduate students throughout

the year. To find out more, visit

www.ed.ac.uk/pg/open-day/online-events.

Get in touch


20

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© The University of Edinburgh 2012. No part of this publication may be reproduced without written permission of the University.The University is a charitable body, registered in Scotland, with registration number SC005336.

Semester 1:

16 September–20 December 2013

Semester 2:

13 January–23 May 2014

Postgraduate Open Day:

23 November 2012

Induction Week:

9–13 September 2013

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