PG Maths

Mathematics Postgraduate opportunities Prospectus 2013 entry www.ed.ac.uk

THE UNIVERSITY of EDINBURGH

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

Linking research and commerce Edinburgh 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 career With 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 destination Your 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 us Edinburgh 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

Contents Welcome to the School of Mathematics

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Facilities and resources

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Community

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Employability and graduate attributes

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Taught masters programmes

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Research at the School of Mathematics

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Research opportunities

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Funding

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How to apply

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Get in touch

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Campus map

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Thomas Jefferson American Founding Father and President (speaking to his son-in-law, Thomas Mann Randolph, as he began his studies in 1786)

Welcome to the University of Edinburgh/Contents

“You are now in a place where the best courses upon Earth are within your reach... such an opportunity you will never again have.”

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Welcome to the School of Mathematics 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.

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 heritage The 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 fields Our 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.

Facilities and resources 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.

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 support The 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 company In 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.

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.”

The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

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Welcome to the School of Mathematics/Facilities and resources www.ed.ac.uk

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Community We 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 School For 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 world Researchers 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 Khwaja PhD 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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The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

Institute for Academic Development All 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.

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.

Developing these broader professional skills and qualities means that our postgraduate students are always in high demand.

PhD 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.

For more information please visit www.ed.ac.uk/iad/postgraduates.

Careers Service The 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

Learn to teach

A solid start For 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 videoconferenced lectures, presented by staff from all participating universities.

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.

Community/Employability and graduate attributes

Employability and graduate attributes

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Taught masters programmes Financial Mathematics

Financial Modelling & Optimization

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MSc 1yr FT

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

Programme description

Programme description

This 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.

This 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.

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 structure This 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 opportunities Graduates have gone on to either work in major financial institutions or to continue their studies by joining PhD programmes.

Minimum entry requirements A 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 Director Dr Sotirios Sabanis E: S.Sabanis@ed.ac.uk T: +44 (0)131 650 5084 You may also be interested in: Finance & Investment or Banking & Risk (University of Edinburgh Business School Prospectus)

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 structure This 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 DerivativeFree 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 opportunities Graduates have gone on to either work in major financial institutions or to continue their studies by joining PhD programmes.

Minimum entry requirements A 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 2 yrs PT: UK/EU students £8,600 per year *Fees change annually. For the most up-to-date information about fees see www.ed.ac.uk/student-funding.

Programme Director Dr Sotirios Sabanis E: S.Sabanis@ed.ac.uk T: +44 (0)131 650 5084 You may also be interested in: Finance & Investment or Banking & Risk (University of Edinburgh Business School Prospectus)

The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

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www.ed.ac.uk/pg/645 MSc 1 yr FT (2 yrs PT available for UK/EU students)

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

Programme description

This 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.

This 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.

Programme structure This 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 opportunities The 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 requirements A 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 requirements See page 18

Tuition fees in 2012/13* 1 yr FT: UK/EU students £8,450; international students £17,200 2 yrs PT: UK/EU students £4,225 per year *Fees change annually. For the most up-to-date information about fees see www.ed.ac.uk/student-funding.

Programme Director Dr Julian Hall E: J.A.J.Hall@ed.ac.uk T: +44 (0)131 650 5075

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 structure This 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 opportunities This is the ideal programme if you wish to pursue an academic career.

Minimum entry requirements A 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 £5,750; international students £13,050 2 yrs PT: UK/EU students £2,875 per year *Fees change annually. For the most up-to-date information about fees see www.ed.ac.uk/student-funding.

Programme Director Professor Tom Lenagan E: T.Lenagan@ed.ac.uk T: +44 (0)131 650 5078

Mathematics

Taught masters programmes

Financial Operational Research

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Operational Research

Scientific Computing

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

MSc 1 yr FT

Programme description

Programme description

This 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.

This 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.

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 structure This 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 opportunities

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

Programme structure This 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.

The 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.

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.

Minimum entry requirements

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

A 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.

Career opportunities

Minimum entry requirements

Tuition fees in 2012/13*

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

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

English language requirements

2 yrs PT: UK/EU students £2,875 per year

See page 18

*Fees change annually. For the most up-to-date information about fees see www.ed.ac.uk/student-funding.

Tuition fees in 2012/13*

Programme Director

*Fees change annually. For the most up-to-date information about fees see www.ed.ac.uk/student-funding.

English language requirements See page 18

Dr Julian Hall E: J.A.J.Hall@ed.ac.uk T: +44 (0) 131 650 5075

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

Programme Director Dr Julian Hall E: J.A.J.Hall@ed.ac.uk T: +44 (0) 131 650 5075

The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

MSc 1 yr FT (2 yrs PT available for UK/EU students) Programme description This 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 structure This 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 opportunities This 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.

Minimum entry requirements A UK 2:1 degree, or its international equivalent (www.ed.ac.uk/international/ 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 *Fees change annually. For the most up-to-date information about fees see www.ed.ac.uk/student-funding.

Programme Director Dr Bruce Worton E: Bruce.Worton@ed.ac.uk T: +44 (0) 131 650 4884

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Taught masters programmes

Statistics & Operational Research

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Research at the School of Mathematics As 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 institutes In 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 ÂŁ3.5 million and ÂŁ5 million respectively, to establish the Centre for Analysis and Nonlinear Partial Differential Equations and the Centre for Numerical Algorithms and Intelligent Software.

The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

Algebra & Number Theory

Analysis

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

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.

Tuition fees in 2012/13* 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

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. Tuition fees in 2012/13* 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: g.law@ed.ac.uk You may also be interested in: Geometry & Topology and Algebra & Number Theory

*Fees change annually. For the most up-to-date information about fees see www.ed.ac.uk/student-funding.

E: g.law@ed.ac.uk You may also be interested in: Mathematical Physics and Geometry & Topology

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Contact: Mrs Gill Law, Postgraduate Research Administrator

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.

Research at the School of Mathematics/Research opportunities

Research opportunities

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Applied & Computational Mathematics

Geometry & Topology

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

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

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.

Tuition fees in 2012/13* 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: g.law@ed.ac.uk You may also be interested in: The Doctoral Training Centre in Neuroinformatics and Computational Neuroscience (Informatics Prospectus); Astrophysics (Physics & Astronomy Prospectus) or Geology & Geophysics (GeoSciences Prospectus)

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.

Research environment 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.

Tuition fees in 2012/13* 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: g.law@ed.ac.uk You may also be interested in: Mathematical Physics

The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

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

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

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.

Research environment 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 algebrogeometric 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.

Tuition fees in 2012/13* 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: g.law@ed.ac.uk You may also be interested in: Astrophysics (Physics & Astronomy Prospectus)

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.

Research environment 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.

Tuition fees in 2012/13* 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.

E: g.law@ed.ac.uk You may also be interested in: Management (University of Edinburgh Business School Prospectus)

www.ed.ac.uk

Contact: Mrs Gill Law, Postgraduate Research Administrator

Operational Research & Optimization

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Research opportunities

Mathematical Physics

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Probability & Stochastic Analysis

Statistics

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

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

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.

Tuition fees in 2012/13* 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: g.law@ed.ac.uk

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.

Tuition fees in 2012/13* 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: g.law@ed.ac.uk

The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

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Research opportunities www.ed.ac.uk

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Funding 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.

University of Edinburgh scholarships

Other sources of funding

China Scholarships Council/University of Edinburgh Scholarships

Commonwealth 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

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

The University of Edinburgh Graduate Discount Scheme We 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

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

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.”

The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

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

The Canada Student Loans Program The 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 Scotland This 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 Loans The 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

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.

Financial aid

Funding

Research council awards

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www.ed.ac.uk

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How to apply General requirements

Research degrees

Joining us from overseas

To 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.

The 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.

International 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.

Some programmes may vary, so check the entry requirements for the specific programme you wish to apply for.

Taught postgraduate programmes Before 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.

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 Jill.Douglas@ed.ac.uk or the Graduate Admission Officer, Dr Pieter Blue, at P.Blue@ed.ac.uk.

International agents The 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 requirements Students whose first language is not English must show evidence of one of the qualifications in the box below.

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)

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.

Cambridge CPE Grade B Cambridge CAE Grade C 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

The University of Edinburgh Mathematics Postgraduate opportunities Prospectus 2013 entry

For more information on our taught MSc programmes, email as follows: Financial Mathematics fimmsc@ed.ac.uk Financial Modelling & Optimization fmomsc@ed.ac.uk Mathematics pammsc@ed.ac.uk Operational Research ormsc@ed.ac.uk Scientific Computing scmsc@ed.ac.uk Statistics and Operational Research sormsc@ed.ac.uk For more information on postgraduate research, email pg@maths.ed.ac.uk.

Alternatively, contact: Gill Law Postgraduate Research Administrator E: G.Law@ed.ac.uk T: +44 (0)131 650 5085

Visit us Our 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.

Contact us

How to apply/Get in touch

Get in touch

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University building

School of Mathematics

Published by Communications and Marketing The University of Edinburgh Designed by Hamlin Daniels www.hamlindaniels.co.uk

Photography by Paul Dodds Yao Hui Norrie Russell Laurence Winram Printed by J Thomson Colour Printers www.jtcp.co.uk

Postgraduate Open Day: 23 November 2012

Semester 1: 16 September–20 December 2013

Induction Week: 9–13 September 2013

Semester 2: 13 January–23 May 2014

FSC This publication is available online at www.ed.ac.uk and can be made available in alternative formats on request.

Please contact Communications.Office@ed.ac.uk or call +44 (0)131 650 2252.

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