School of Mathematics
FACULTY OF MATHEMATICS
AND PHYSICAL SCIENCES
POSTGRADUATE
STUDY TAUGHT
MASTERS AND
PHD RESEARCH
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
For current information on courses, fees and entry requirements
please visit our website at www.maths.leeds.ac.uk
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in this brochure is accurate at the date of publication the University
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© The University of Leeds 2015. All rights reserved. Reproduction in whole
or in part is forbidden without the permission of the publishers.
CONTENTS
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Welcome to the School
Student Life
Research in the School of Mathematics
Taught Masters Courses
Graduate Diploma
PhD Research Programmes
Doctoral Training Programmes
The University and City
We Welcome International Students
Accommodation
Entry Requirements
Application Process
Contact Us
THE SCHOOL
OF MATHEMATICS
The School comprises of three departments, Applied
Mathematics, Pure Mathematics and Statistics, each with an
enviable reputation for research. Together they form one of
the largest research schools of mathematicians in the UK, with
around 70 academic staff, 20 postdoctoral fellows and over
100 postgraduate students.
We are located at the centre of the
campus, here at the University of
Leeds, with our own teaching space,
tutorial rooms and study areas, ranging
from a relaxed seating area to a quiet
reading room, as well as two computer
clusters and dedicated office space for
postgraduate students. We also have
a well equipped Research Visitors’
Centre to support the needs of eminent
academic staff from all over the world
who spend significant periods of
time at Leeds working on high-level
collaborative research programmes.
I looked around at several universities and
Leeds was one of my favourites as they had
modules in statistics and also in finance.
There is a wide variety of module choice,
so you can pick the modules which you like.
JAMES BERTSCHY, MSC STATISTICS
3
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
STUDENT LIFE
All students are
encouraged to take
part in the life of
the School and to
contribute to the
range of academic
and social activities
available
The School warmly welcomes postgraduate students onto a
range of Masters courses and PhD programmes. We take pride
in the calibre of our staff, in the quality of our teaching and in the
successes of our students as they develop their career potential
within a stimulating and supportive academic environment.
All students are encouraged to take part
in the life of the School and to contribute
to the range of academic and social
activities available. Our students come
from a wide range of nationalities and
backgrounds which ensures a lively and
exhilarating international environment in
which to study.
All PhD students are provided with high
quality office accommodation as well as
access to state-of-the-art workstations with
either a Linux or Windows platform. The
University supports a wireless network
and a Virtual Private Network (VPN) that
allows students to connect when working
off campus.
As a student you will also have access
to specialised facilities for your research
area. The University is a member of the
White Rose Consortium, which gives the
School access to the White Rose Grid, a
research infrastructure providing massive
parallel computing power. The School of
Mathematics also has a video conferencing
room that is devoted to teaching graduate
students in mathematics across a network
of 19 UK universities.
PhD students can take advantage of the
broader generic skills training offered
through the Faculty Graduate School,
which provides courses to help develop
research, interpersonal and life skills. The
Graduate School also helps to promote
the interaction between PhD students
in different Schools/Departments and
ensures best practice in the support and
development of our postgraduate students.
RESEARCH
5
The quality of the School’s research was recognised in the 2014 Research Excellence
Framework (REF), where 85% of the work submitted was classed as ‘world leading’ or
‘internationally excellent’, placing it in the top ten mathematics departments in the UK
in terms of research quality, impact and power.
Research and study in the
School of Mathematics go hand
in hand. As our students develop their
own understanding of a
diverse range of mathematical
topics and skills to progress their
careers in both academic and
commercial sectors they themselves
contribute to the development of
mathematical knowledge.
Our research is wide-ranging and
increasingly interdisciplinary with
academic staff actively collaborating
with other departments, other
universities, and with industry and
public services in this country and
all around the world. There are a
number of areas of research which are
recognised by the University as ‘Peaks
of Excellence’, including Algebra and
Logic, Astrophysical and Geophysical
Fluid Dynamics and Polymers and
Complex Fluids.
DR STEPHEN GRIFFITHS,
APPLIED MATHEMATICS
PROFESSOR PAUL MARTIN,
PURE MATHEMATICS
DR ARIEF GUSNANTO
STATISTICS
My research lies within the mathematical
geosciences, and is mainly oriented
towards the fluid dynamics of the Earth’s
atmosphere and ocean. My aims are
to understand observed dynamical
phenomena, either by numerical
simulations or through mathematical
analysis of simplified theoretical models.
Particular interests are:
Group representation theory is a
remarkably rich and exciting area
of mathematics, with a wealth of
applications in Physics and the
wider sciences. The topic has been
the subject of intensive study by
researchers over many years, and this
intense activity continues. However,
again motivated in part by applications,
the subject has recently been widened
by a succession of generalisations of the
notion of `group’ to different algebraic
systems. One overarching such
generalisation is the notion of a diagram
category. Accordingly this project
concerns representation theory of such
objects. It turns out that many of the
powerful techniques of representation
theory developed to address groups
and algebras may be generalised to
apply to diagram categories, and this
relatively young branch of the field has
many exciting open problems, including
applications back in the original area of
group representation theory itself.
Why do some people have a disease
while others don’t? If my parents have
had a heart attack do I have a higher
chance of having one? In DNA, which
genes predispose an individual to
the disease? These are some of the
questions that I am trying to tackle
in my research. The long-term goal
is to gain a better understanding of
which genetic variations in our DNA
increase the risk of disease, and how.
More specifically, which single DNA
substitutions are associated with certain
types of cancer? What regions in the
genome are involved in the mechanism
of developing leukemia, etc? Statistical
modelling and inference on data from
biological and medical experiments play
a crucial part in identifying the ‘signal’ of
interest and validating the results.
■Instability
theory: analytical and
numerical modelling of linear and
nonlinear instabilities in rotating,
stratified shear flows.
■Nonlinear
waves: analytical and
numerical modelling of coupled
nonlinear wave equations.
■Waves
in the atmosphere and ocean:
equatorial waves; internal waves;
ocean tides; paleotides.
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
TAUGHT
MASTERS COURSES
We offer six MSc courses on a full-time basis over 12 months. Each course starts with two
semesters of taught modules, examined in January and June. There is then an intensive
summer project where a chosen topic in mathematics is studied in depth.
■MSc
Atmosphere-Ocean Dynamics
■MSc
Mathematics
■MSc
Mathematics and
Computer Science
■MSc
Statistics
■MSc
Medical Statistics
■MSc
Statistics with
Applications to Finance
These programmes consist of both
compulsory and optional modules
which provide the opportunity to cover
a range of mainstream and advanced
topics and innovative methods,
selected from the research interests
of the School of Mathematics. The
choice of modules is dependent
on background, and subject to the
agreement of the Course Co-ordinator.
Each of these courses provides a
pathway to progress on to a wide
range of appealing PhD topics and
may be combined with a subsequent
PhD programme (subject to entry
requirements). Across statistics, pure
and applied mathematics there
is ample scope to pursue a varied
range of research topics.
We also offer jointly with Leeds
University Business School (LUBS)
the following courses.
■MSc
Financial Mathematics
■MSc
Actuarial Finance
For these courses please make
enquiries to:
Postgraduate Admissions Office
Leeds University Business School
E: masters@lubs.leeds.ac.uk
Tel: +44 (0) 113 343 4908
WHY STUDY A
MASTERS AT LEEDS?
■Research-led
teaching delivered
by experts in their field
■Wide
choice of modules and
options to specialise
■Emergence
of data mining and
analysis means demand for
statisticians is growing across
a wide range of professions
■An
■Opportunities
■Degrees
On graduation you will have an excellent
grounding for research in your chosen
area of mathematics, or the necessary
background to excel in industries which
require mathematical skills.
international university with
a first-class study environment
which are recognised
by employers around the world
for their quality
■Numeracy
is an attribute keenly
sought after by employers
exist to pursue further
research as a PhD student
There are career opportunities in a wide
range of professions in the commercial,
environmental, government and
financial services sectors, charitable
organisations, market research, medical
and pharmaceutical organisations,
computer and gaming industries,
forensic and police investigation and
teaching mathematics within higher
education.
It is really coming together brilliantly between the Maths department’s
Hydrodynamic Stability course and the more general applications
in the Earth and Environment department’s atmospheric course. In
Earth and Environment we really get to see how concepts can be
applied to the atmosphere and ocean, and then in the maths lectures
we get the more rigorous formulation of the concepts.
LEIGHTON REGAYRE, MSC ATMOSPHERE-OCEAN DYNAMICS
MSC ATMOSPHERE
OCEAN DYNAMICS
This course is designed for students from a mathematical background who wish to apply their
skills to understanding the complex behaviour of Earth’s atmosphere and oceans.
This is an exciting interdisciplinary subject, of increasing importance to a society seeking
to understand climate change.
Training is offered in both modern
applied mathematics and atmosphereocean science, combining teaching
resources from the School of
Mathematics and the School of Earth
and Environment. The latter are
provided by members of the School’s
Institute for Climate and Atmospheric
Science, part of the National Centre for
Atmospheric Science.
COURSE CONTENT
Topics are drawn from four
broad areas:
■Applied
mathematics: asymptotic
methods, fluid dynamics,
mathematical theory of waves and
stability of flows.
■Numerical
methods and computing:
discretization of ordinary and partial
differential equations, algorithms for
linear algebra, direct use of numerical
weather and climate models.
■Atmospheric
dynamics: structure
of the atmosphere, dynamics
of weather systems and atmospheric
waves.
■Ocean
dynamics: the large-scale
ocean circulation, surface waves
and tides.
COURSE STRUCTURE
The course is made up of two parts,
a research project and a set of taught
modules. The research project is
undertaken over the summer, under
the supervision of a member of staff,
and involves an in-depth investigation
of a chosen subject in atmosphereocean dynamics. The taught modules
involve lectures and some computer
workshops. Beyond a compulsory core
of atmosphere-ocean fluid dynamics,
you may choose from a range of
modules to suit your interests.
EXAMPLE MODULES
OFFERED BY THE SCHOOL
OF MATHEMATICS:
■Mathematical
■Numerical
■Fluid
Methods
Methods
Dynamics
■Geophysical
■Linear
Fluid Dynamics
and Nonlinear Waves
■Nonlinear
Dynamics
EXAMPLE MODULES
OFFERED BY THE
SCHOOL OF EARTH
AND ENVIRONMENT:
■Atmosphere
and Ocean Dynamics
■Atmosphere-Ocean
Climate
Change Processes
■Dynamics
of Weather Systems
■Practical
Weather Forecasting
■Weather,
Climate and Air Quality
CAREER OPPORTUNITIES
You will be prepared for postgraduate
research in applied mathematics
or atmosphere-ocean science, or
employment in the environmental
sector. However, given the
interdisciplinary nature of the
programme, you will develop expertise
and skills in a number of different
areas, and will therefore be attractive to
a wider range of employers.
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
MSC MATHEMATICS
This programme provides a solid training in mainstream mathematics
and will give you an insight into modern developments in mathematics.
It is designed to build on existing
mathematical skills and allows
students from a wide range of
backgrounds to both broaden and
deepen their understanding of their
chosen branch of mathematics.
The course allows specialisation in
areas of pure mathematics, applied
mathematics or statistics and offers the
flexibility to cover a range of areas or to
concentrate in one specific area.
MODULES TYPICALLY
AVAILABLE INCLUDE:
The course is ideal for those who wish
to take their studies of mathematics
beyond the BSc level, for interest
or to develop future employment
opportunities. It also provides an
excellent preparation for research for
an MPhil or PhD. At Leeds we have
a range of research opportunities
available and in some cases you can
progress to a PhD on the basis of a
specified performance in the MSc.
■Analysis
■Algebra
There is strength in the School
in Noncommutative Algebra and
Representation Theory. Building
on the wide range of BSc modules,
a masters level module is typically
offered either in Galois theory, or
in Commutative Algebra and
Algebraic Geometry.
Two modules take you from BSc
analysis through measure theory,
Banach spaces and Banach
algebras.
■Logic
Members of the very strong Logic
Group at Leeds give at least two
modules, for example on Models and
Sets, and Proof and Computation.
Geometry 2
This module looks at further study
of curves and surfaces, in particular,
to understand what properties of
curves and surfaces are intrinsic,
extrinsic, local, or global, and to give
some applications.
■Differential
■Advanced
Mathematical Biology
The physical sciences are
underpinned by mathematics, both
as a structure or language for the
concise statement of the laws of
nature, and as a tool for developing
an understanding of new phenomena
by modelling analysis. This module
introduces you to some areas of
mathematical biology and medicine.
Series
In time series, measurements
are made at a succession of
times, and it is the dependence
between measurements taken at
different times which is important.
The module will concentrate on
techniques for model identification,
parameter estimation, diagnostic
checking and forecasting.
■Time
in Actuarial Science
The module provides a grounding
in stochastic processes and survival
models and their application in
actuarial science.
■Models
Polymeric Fluids
Firstly it gives an introduction to
the ‘phenomenology’ of the subject
– what kind of things do these
fluids do when they flow? Then, the
module focuses on a particular class
of fluids, those containing polymer
molecules.
■Advanced
Fluid Dynamics
This considers many of the
most fascinating astrophysical
phenomena, in stars, planets and
accretion discs. In particular, it
considers the extension of classical
fluid dynamics to electrically
conducting plasmas, the state of
nearly all astrophysical bodies
■Astrophysical
MSC MATHEMATICS AND
COMPUTER SCIENCE
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This interdisciplinary Masters degree combines teaching and research from the School of
Mathematics and the School of Computing. You will be introduced to sophisticated techniques
at the forefront of mathematics and computer science.
The programme follows two main
strands, based on the complementary
research strengths of both Schools.
ALGORITHMS AND
COMPLEXITY THEORY
This concerns the efficiency of
algorithms for solving computational
problems, and identifies hierarchies of
computational difficulty. This subject
has applications in many areas, such
as distributed computing, algorithmic
tools to manage transport infrastructure,
health informatics, artificial intelligence,
and computational biology.
NUMERICAL METHODS &
PARALLEL COMPUTING
Many problems, in mathematics,
physics, astrophysics and biology
cannot be solved using analytical
techniques and require the application
of numerical algorithms for progress.
The development and optimisation
of these algorithms coupled to the
recent increase in computing power
via the availability of massively parallel
machines has led to great advances
in many fields of computational
mathematics. This subject has
applications in many areas, such as
combustion, lubrication, atmospheric
dispersion, river and harbour flows, and
many more.
COURSE CONTENT
You will study a selection of optional
taught modules. It is advisable to choose
a coherent group of modules, but you can
mix from the two groups, and sometimes
choose other modules (subject to
approval). You will also undertake a
substantial research project over the
summer linked to the themes of the
programme or on a topic of your choice.
EXAMPLE MODULES
RELATED TO ALGORITHMS
AND COMPLEXITY THEORY:
■Advanced
Distributed Systems
■Advanced
Models and Sets
■Advanced
Proof and Computation
■Algorithms
■Coding
Theory
■Combinatorics
■ Graph
Theory: Structure and Algorithms
■Knowledge
Representation and
Machine Learning
■Scheduling
EXAMPLE MODULES
RELATED TO NUMERICAL
METHODS:
■Advanced
Mathematical Methods
■Advanced
Dynamical Systems
■Advanced
Polymeric Fluids
■Cloud
Computing
■Scientific
Computation
■Scientific
Visualisation
■Systems
Programming
STRONG LINKS
WITH INDUSTRY
In collaboration with both industrial
and academic partners, our research
has resulted in computational
techniques, and software, that has been
widely applied. Our industry links are
extensive and include companies such
as Google, Yahoo, Akamai, Microsoft,
and Tracsis, as well as the NHS.
CAREER OPPORTUNITIES
This MSc will provide you with both
technical and transferable skills that are
valued by industry. It will also provide
you with an excellent background
if you wish to embark on a PhD in
mathematics or in computer science. Statistics is an important area of study within
mathematics, and an important tool within a wide
range of subjects across the sciences and social
sciences, from biology, medicine and engineering,
through to the environmental sciences, geography,
psychology and sociology.
ROYAL STATISTICAL SOCIETY
MSC STATISTICS
This is a flexible course that combines in-depth training in mainstream advanced statistical
modelling with a broad range of specialisations, including financial mathematics, statistical
bioinformatics, shape analysis and risk management.
The course will give you the chance to
broaden your understanding of statistics
and develop skills across a range of
statistical techniques required for a
career in statistics or further academic
research.
MODULES TYPICALLY
AVAILABLE INCLUDE:
Computing
An introduction to methods of
statistical computing essential
for the applied statistician, with
an emphasis on sampling-based
methods such as Markov chain
Monte Carlo.
■Statistical
and DNA
Modern biological experiments
produce large data sets involving
information related to DNA. This
module gives the basic biological
background before looking at a
range of data types and methods
to analyse them.
■Statistics
Theory
We often use statistical tests and
estimators without fully exploring
the theoretical basis for their use.
Here, we look more deeply into
the mathematics behind statistical
inference and compare the two main
approaches to statistics: Frequentist
and Bayesian inference.
■Statistical
Linear and
Additive Models
Linear regression relates a response
or outcome variable to a number of
predictor or input variables in certain
situations. We see how to extend
these ideas to wider regression
frameworks, the generalised linear
and generalised additive models,
with a wide range of applications.
■Generalised
Statistics and Causality
Bayesian statistics gives us a
rigorous framework to combine
prior beliefs and expectations with
observed data from many sources –
a process that we all do informally.
This framework also opens up many
opportunities for analyses of complex
problems that cannot be adequately
handled using traditional statistical
techniques.
■Bayesian
Learning Skills
A practical introduction to
research methods including
literature searching, writing styles,
mathematical typesetting and giving
presentations.
■Independent
and Cluster Analysis
Modern data sets typically include
many different measurements on
each individual studied. We explore
how to analyse this kind of data,
taking a holistic approach rather
than dealing with each variable
separately.
■Multivariate
I chose Leeds because the statistics course is accredited by the
Royal Statistical Society which means if you get the qualification you
become a graduate statistician and can go on to get a chartered
statistician qualification. I also thought the courses sounded quite
flexible because you can study general statistics or take a more
financial or medical statistics route.
LAURA MANDEFIELD, MSC STATISTICS
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MSC MEDICAL STATISTICS
Statistical evaluation of evidence is critical in the search for new medicines and healthcare
treatments. This degree programme blends theoretical and applied statistical disciplines with
a specialisation in medical applications.
The programme combines taught
modules with a summer project and
utilises existing links with individual
clinicians, medical research groups in
the University of Leeds, Leeds NHS
trust, and the Department of Health’s
Information Centre in Leeds.
The course covers modern developments
in statistics and provides the opportunity
to undertake data analysis for a wide
variety of statistical problems. It aims
to build an appreciation of theoretical
and practical perspectives on issues in
medical statistics, whilst developing the
ability to select and apply appropriate
statistical methods for the analysis of
medical data.
Options within the course vary from
mainstream topics in statistical
methodology to more specialised areas
such as epidemiology and biostatistics.
MODULES TYPICALLY
AVAILABLE INCLUDE:
■ Introduction
to Clinical Trials
An outline of the statistical principles of
clinical trial design, conduct, analysis
and reporting. The emphasis will be on
understanding the practical issues that
arise through real examples backed up
with the relevant theory.
■ Core
Epidemiology
Advanced Epidemiology
Epidemiological studies investigate
patterns of disease occurrence,
looking for key risk factors and ways
of preventing the spread of disease.
Such studies depend on databases
of medical conditions in a population
and hence different statistical methods
are needed than those used to analyse
a carefully designed clinical trial. This
module looks at a wide range of tools
needed for a medical statistician to
conduct an epidemiological study.
■ Introduction
to Modelling
This module will provide a
comprehensive understanding of the
principles (model theory, limitations,
assumptions) underpinning the use
of (generalised) linear modelling in
medicine and health.
■ Statistical
Computing
The use of computers in mathematics
and statistics has opened up a wide
range of techniques for studying
otherwise intractable problems and
for analysing very large data sets.
This module gives an overview of the
foundations and basic methods in
statistical computing.
CAREER OPPORTUNITIES
As a medical statistics graduate you
will have specialist knowledge that will
help you progress your career into areas
such as medical or epidemiological
research. There are several aims to
medical research, all of which involve
a significant amount of statistics,
monitoring and surveillance of health
and disease, establishing causes of
disease or factors associated with
death or disease, detecting disease,
preventing death or disease and
evaluating treatments for disease.
Medical statisticians looking to follow
a career in medical research are
mainly employed by pharmaceutical
companies, university medical schools,
research units and the NHS.
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
MSC STATISTICS WITH
APPLICATIONS TO FINANCE
This degree programme is suitable for students from a wide range of backgrounds
providing a broader understanding of statistics related to financial applications.
The course consists of modules which
cover mainstream topics in statistical
methodology and more specialised
topics in statistical finance, reflecting
the specific research interests of
academic staff within the School.
MODULES TYPICALLY
AVAILABLE INCLUDE:
Time Finance
Continuous time models play a
central role in pricing of financial
assets under more challenging
circumstances than can be
handled with discrete time models.
■Continuous
Financial Modelling
Financial investments such as
stocks and shares are risky: their
value can go down as well as up.
To compensate for the risk in a fair
market, a discount is needed. This
module will develop the necessary
probabilistic tools to enable investors
to value such assets.
■Stochastic
Regression and Robustness
In many areas of science and
social study, several variables or
measurements are taken from each
member of a sample. This module
will examine ways of predicting one
particular variable from the remaining
measurements using the linear
regression model.
■Linear
Time Finance
This module develops a
general methodology for the
pricing of financial assets in risky
financial markets based
on discrete time models.
■Discrete
Series and Spectral Analysis
In time series, measurements are
made at a succession of times,
and it is the dependence between
measurements taken at different
times which is important. We
concentrate on techniques for
model identification, parameter
estimation and forecasting future
values of the time series.
■Time
Management
This module gives comprehensive
coverage of mathematical and
practical approaches to financial
risk management. Avoiding the
disastrous consequences of badly
managed risk requires detailed
mathematical knowledge of how
to quantify financial risk and
stress-test a hedge.
■Risk
FOR FURTHER INFORMATION
On all our taught Masters courses visit: www.maths.leeds.ac.uk/postgraduate-taught
Details of individual academic staff and their research interests can be found at: www.maths.leeds.ac.uk/people
On related research areas: The Astrophysical and Geophysical Fluids Group within the School of Mathematics:
http://www.maths.leeds.ac.uk/research/groups/astrophysical-and-geophysical-fluids.html
The Institute for Climate and Atmospheric Science within the School of Earth and Environment:
www.see.leeds.ac.uk/research/icas
The School of Computing: www.engineering.leeds.ac.uk/comp/research
13
GRADUATE DIPLOMA
The Graduate Diploma is aimed at students who would like to study for a mathematics
related MSc course but who do not meet the full academic entry requirements. There
are two programmes available: Graduate Diploma in Mathematics and a Graduate Diploma in
Financial and Actuarial Mathematics
Each one leads on to a number of
related MSc courses within the same
field of study and on completion of the
Graduate Diploma students who meet
the required performance level will be
eligible for entry onto a related MSc
courses, in the following academic year.
The programme will consist of a
selection of undergraduate modules
at level 2 and 3, from the School of
Mathematics and possibly from other
schools, as applicable, depending on
which MSc programme students wish
to prepare for.
The programmes will help you to
develop the required understanding
of those specific areas of mathematics
relevant to the appropriate MSc course
to be studied, as well as gaining a
good level of skill in calculation and
manipulation within those specific
areas of mathematics
You will learn to apply concepts and
principles in well-defined contexts,
showing judgement in the selection and
application of tools and techniques,
and gain an understanding of complex
logical arguments, identifying the
assumptions and conclusions made.
Candidates will be required to study
120-125 credits from a wide selection
of optional module which can include:
The modules shown below are a typical
example taken from the wide choice
that are available.
Further details can be found at:
www.maths.leeds.ac.uk/graddiploma
GRADUATE DIPLOMA
IN MATHEMATICS
■Coding
Theory
■Differential
Geometry
■Environmental
■Financial
■Fluid
Statistics
Mathematics Dynamics
■Geometry
■Hilbert
of Curves and Surfaces Spaces and Fourier Analysis
■Introduction
to Markov Processes
■Mathematical
■Special
Biology
Relativity
GRADUATE DIPLOMA IN
FINANCIAL AND ACTUARIAL
MATHEMATICS
■Corporate
Finance
■International
■Financial
Mathematics
■Numerical
■Statistical
■Actuarial
Business Finance
Analysis
Modelling
Mathematics
■Stochastic
Financial Modelling
■Multivariate
Analysis
CAREER OPPORTUNITIES
Mathematicians have a wide range of
career options to choose from, across
diverse employment sectors. From
the more specialised roles in software
development and system modelling,
through professional practice in
finance and risk management to the
broader, more general, management
positions in the manufacturing and
retail sectors, the variety and breadth of
career opportunities are limited only by
the personal preference of the individual.
The Graduate Diploma is a stepping
stone to a postgraduate qualification,
which can provide additional
employment opportunities, at a more
senior level and also a route into further
study at PhD level. THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
What’s quite unique about Leeds is that the mathematical logic is
very diverse. Most places which do it in the UK just pick one or two
aspects of mathematical logic but in Leeds we have all three areas:
model theory, proof theory and computability theory.
DAVID BRADLEY-WILLIAMS,
PHD PURE MATHEMATICS
PHD RESEARCH
PROGRAMMES
DEPARTMENT OF
APPLIED MATHEMATICS
DEPARTMENT OF
PURE MATHEMATICS
Much of applied mathematics is
concerned with solving challenging
equations that describe interesting
and important problems, and there
is ample scope for a wide range of
appealing PhD topics.
The Department of Pure Mathematics
is one of the largest and most active
centres for pure mathematics research
in the UK with research groups of
international standing in four of the
most vital areas of mathematics:
As well as conducting research
in the foundations of applied
mathematics, the Department also
undertakes research in a variety
of multidisciplinary settings. It has
excellent connections with many
other disciplines, including pure
mathematics and statistics within
the School of Mathematics, and
astronomy, biology, computer
science, earth sciences, engineering,
environment, food science and
physics within the University,
as well as links with industry.
Current research falls into the
following main areas:
■Applied
■Algebra
■Differential
Geometry
■Analysis
■Mathematical
Logic
There is extensive interaction between
these research groups, and with the
Departments of Applied Mathematics
and Statistics. The Department hosts
the Leeds Algebra Group and Leeds
Logic Group which are recognised as
‘Gold Peaks of Excellence’ within the
University. These peaks reflect the
wealth of expertise, external recognition
and reputation for international
excellence and world-leading research
in the Department.
Nonlinear Dynamics
■Astrophysical
and
Geophysical Fluids
■Computational
Partial
Differential Equations
■Integrable
Systems and
Mathematical Physics
■Mathematical
Biology
and Medicine
■Polymers
and
Industrial Mathematics
There are weekly seminars for research
students across algebraic, geometric,
functional analysis and logic disciplines.
As well as these weekly seminars there
is a less specialised Departmental
Colloquium which meets once or twice
a term, and a weekly seminar course
each year in each of the four major
research areas.
15
DEPARTMENT
OF STATISTICS
The Department of Statistics has a strong
profile across a wide range of areas in
both theoretical and applied statistics and
probability.
A distinctive feature is its internationally
recognised expertise in shape analysis
and related areas. Building on
these strengths the Department has
established a Centre for Statistical
Bioinformatics to encourage high profile
interdisciplinary collaboration.
The Department organises the Leeds
Annual Statistics Research (LASR)
Workshop, which is a well-established
international event, celebrating its
34th anniversary in 2015. Over
recent years, the theme of the
workshop has reflected the growing
departmental interest in image and
shape analysis and bioinformatics.
There is also collaboration with other
subject areas across the University
including environmental sciences,
transport studies, mining and mineral
engineering, biochemistry, epidemiology
and biostatistics.
The department also undertakes work
in financial mathematics. Working
closely with Leeds University Business
School, their research is predominantly
in stochastic analysis, stochastic
control, random dynamical systems,
financial economics, mathematical
economics and computer science. The
research often combines several fields,
providing novel approaches to capture
the interdependence between investor
behaviour and market dynamics.
Training opportunities for research
students include the regular departmental
seminars plus local and national meetings
of the Royal Statistical Society. There
is also a Postgraduate seminar series
which gives students the opportunity to
present their own work. Students are also
encouraged to attend suitable national
and international conferences.
Students can reinforce their
background in statistics by attending
some of the Department’s extensive
range of final year undergraduate
and taught postgraduate modules.
Week-long graduate training courses
are also organised nationally by the
Academy for PhD Training in Statistics
(APTS). Where appropriate, there
are opportunities to get involved in
statistical consultancy; this provides
both practical statistical training and
the chance to develop more general
interpersonal skills.
Key research areas include:
■Image
and Shape Analysis,
Spatio-Temporal Modelling
■Modern
Data Analysis
■Statistical
Bioinformatics
■Probability,
Stochastic Modelling
and Financial Mathematics
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
DOCTORAL TRAINING
PROGRAMMES
Doctoral training programmes provide structured PhD training and focus on multi-disciplinary
challenges in modern science, with groups of students working as a cohort in a defined scientific
area. Each programme varies in structure; however studentships typically last for four years
with opportunities to learn theoretical and experimental skills through lectures during the first
year. PhD projects usually include collaborative supervision.
EPSRC CDT: CENTRE FOR
DOCTORAL TRAINING IN
FLUID DYNAMICS
Fluid dynamics sits at the centre of our
lives. The weather we experience, the
products we use, the food we eat, cars
we drive, medical care we receive all
depend on fluid dynamics.
The ability to measure, model and
predict fluid flows is therefore critically
important to the innovation of processes
and products across almost all
industries, and to the monitoring and
prediction of environmental processes.
Our EPSRC Centre for Doctoral
Training in Fluid Dynamics will tackle
fundamental and applied problems
providing students from a wide range
of academic backgrounds with the
opportunity to undertake cutting-edge,
multidisciplinary research.
ENTRY REQUIREMENTS
A degree equivalent to a UK first
class honours (or in exceptional
circumstances, a high upper second
class) in a science or engineering
discipline.
Non-native English speakers require an
English language qualification, such as
n IELTS
(6.5 with no element less than 6.0) or
n TOEFL
(92 with no component under 23).
To find out more go to
www.fluid-dynamics.leeds.ac.uk
17
EPSRC: CENTRE FOR
DOCTORAL TRAINING
IN SOFT MATTER AND
FUNCTIONAL INTERFACES
Soft matter can be found throughout
industrial and technological
applications. Whether it’s packaging,
adhesives, detergents, cosmetics,
medicines, fuels, rubber tyres, or paints,
a scientific understanding of soft matter
is central and essential to designing and
optimising these products
This fully funded 4-year PhD
studentship allows you to take part in a
comprehensive training programme and
choose from wide choice of cuttingedge, innovative research projects
across the full range of science for Soft
Matter and Functional Interfaces.
The Soft Matter and Functional
Interfaces (SOFI) CDT provides
industrially-integrated, postgraduate
training in research, enterprise and
innovation for future leaders in the
soft matter industrial sector. SOFI CDT
combines expertise from Durham,
Leeds and Edinburgh universities,
industry and central facilities.
ENTRY REQUIREMENTS
Applicants must have a good first
degree (2.1 honours or higher) in
an appropriate physical science
subject, food science, mathematics or
engineering.
Non-native English speakers require an
English language qualification, such as
n IELTS
(6.5 with no element less than 6.0) or
n TOEFL
(92 with no component under 23).
For more information see
www.dur.ac.uk/soft.matter/cdt
During my
undergraduate
degree I developed
an interest in applied
mathematics and was
recommended the
CDT in Fluid Dynamics
by my previous
supervisor, due to the
range in projects that
would be offered and
the multi-disciplinary
approach amongst
the cohort. I also feel
that the CDT offers
excellent experience
in applications of
academic research
in both academia
and industry.
HANNAH KRECZAK, CDT FLUID DYNAMICS
FORMER UNIVERSITY OF LEEDS
UNDERGRADUATE MATHS STUDENT
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
THE UNIVERSITY
The University of Leeds has an international reputation and is a member
of the prestigious Russell Group of research-led universities.
It is well known worldwide for the
quality of its education and research,
making it one of the most popular
universities in the UK. Degrees from
Leeds are recognised by employers and
universities globally.
There are around 24,000
undergraduate and 6,000 postgraduate
students at the University. Despite its
size, the University has a friendly and
supportive environment as students are
taught within smaller Schools ensuring
more personal surroundings for study.
Within the Schools you will find modern,
well-equipped lecture theatres and
laboratories. On campus, we have an
internationally-renowned academic
library featuring a collection of
2,600,000 books and 9,000 periodicals,
with access to electronic resources,
including networked databases and
electronic journals. The Edward Boyle
library is located next door to the School
of Mathematics providing additional
study space, as well as computer
clusters housing over 230 PCs for
individual use.
In your spare time you will find the
University has a lot to offer including
great sports facilities. The Sports
Centre offers a range of activities from
beginners to competitive level and the
new swimming pool, with its impressive
design provides a 200 station fitness
suite, together with a sauna and steam
room. With playing fields for hockey,
cricket, football and rugby a short
distance away we can meet all your
sporting aspirations.
The University also boasts a thriving
Student Union (LUU) with a range of
shops, bars and eateries. The Union is
renowned for organising a wide range
of entertainment and events. There are
also over 200 student societies that you
can get involved with.
LUU regularly wins awards which have
recently included the National Union
of Students (NUS) ‘Higher Education
Union of the Year’ award, where it was
selected from over 60 students’ unions
across the UK.
Best university
destination in
the UK Voted by
The Independent
THE CITY
19
Leeds is a key multi-cultural hub in the North of England with
a vibrant mix of culture, commerce and style.
It is one of the most exciting and
cosmopolitan cities in the UK and many
students enjoy their time here so much
that they stay on to live and work in the
city after graduation.
The city is well known for its shopping
and you can find a range of stores from
small boutiques, with designer labels,
to huge shopping malls. Leeds also
offers an extensive choice of places
to eat and drink. All culinary tastes
are catered for, from Italian to Thai,
Caribbean to vegetarian. Nightlife in
and around the city is also known for its
diversity and popularity, offering a range
of cafes, bars and clubs.
Leeds is one of the greenest cities in
Britain, with more parkland than any other
European city and benefits from being
close to the awe-inspiring scenery of the
Yorkshire Dales where you can pursue a
huge selection of outdoor activities.
WE WELCOME
INTERNATIONAL STUDENTS
The University of Leeds is a truly international university. We have links with over 600
institutions worldwide and up to 5,000 international students study with us each year.
We are one of the UK’s top universities,
world-famous for our teaching and
research and situated in the heart of a
vibrant and multicultural city.
The University has a dedicated
International Centre which will provide
support and advice throughout your
time at Leeds University. The Centre
can provide help from managing your
money, to your health and welfare. Visit
www.leeds.ac.uk/international for more
information.
I ended up with a really enthusiastic supervisor. I have had access to
the high level super computers and the computer clusters and all the
facilities that I have needed to do applied maths.
NICKOLAI BERKOFF, PHD APPLIED MATHEMATICS
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
ACCOMMODATION
All our accommodation is within easy reach of the University and city centre.
Some residences are on campus,
others within walking distance,
and those residences further away
are close to bus routes, shops and
places to eat. We have a wide range
of properties, so there is something
to suit every budget. If you are a
full-time international Masters or
research postgraduate student (i.e.
you pay fees at the international rate)
you are guaranteed a single place
in University accommodation during
your first year at Leeds, provided
that you apply for accommodation
following our online procedure.
If you are a UK or EU postgraduate
student you need to follow the same
application process as for international
postgraduates. We cannot guarantee
you a place but we will do our best to
find you suitable accommodation in one
of our residences. There are usually a
number of vacancies available every
year to UK and EU postgraduates, so it
is worth applying.
Before you can apply for accommodation
you must formally accept your
conditional or unconditional offer from
Leeds. Accepting your offer will give you
access to our online application system.
Apply online at www.leeds.ac.uk/
accommodation/apply
Accommodation Services University of
Leeds Leeds, LS2 9JT, UK
Tel: +44 (0)113 343 7777
Fax: +44 (0)113 343 6077
E-mail: accom@leeds.ac.uk
www.leeds.ac.uk/accommodation
21
ENTRY REQUIREMENTS
For all taught masters and PhD study, except MSc Mathematics and Computer
Science, a minimum of a BSc upper second class (2.1) honours degree or equivalent
is required, in a subject relevant to the programme of study.
MSC MATHEMATICS AND
COMPUTER SCIENCE:
GRADUATE DIPLOMA
IN MATHEMATICS
A first or upper second class (2.1) BSc
degree in mathematics or computer
science (with a substantial mathematics
component) or equivalent. We will
also consider students who hold other
degrees with a substantial mathematics
component. English Language
Requirements: A pass at GCSE level
English Language (grade C or above).
An undergraduate degree in
mathematics or related subject
(e.g. BSc in Statistics, Engineering,
Physics, Computer Science, etc.)
with a minimum of a 2:2 or equivalent,
and adequate performance on
mathematics modules.
GRADUATE DIPLOMA
IN FINANCIAL AND
ACTUARIAL MATHEMATICS
Undergraduate degree in mathematical,
physical or social sciences (e.g. BSc
in Mathematics, Engineering, Physics,
Computer Science, Accounting,
Management, Finance, Economics etc)
with a minimum of 2:2.
Candidates whose first language is not English will require an appropriate English language qualification.
MASTERS REQUIREMENTS
■IELTS
(academic) 6.5 with at least
6.0 in all components
■Internet
Based TOEFL (iBT) of at least
92 overall with no less than 21 in
listening and reading, 23 in speaking
and 22 in writing
■Pearson
Test of English (PTE)
academic score of 64 with at
least 60 in all components.
■Internet
■Pearson
PHD REQUIREMENTS
■IELTS
(academic) 6.0 with at least
5.5 in all components
Based TOEFL (iBT) 87 (with
not less than 20 listening, 20 reading,
21 writing, 22 speaking)
Test of English Academic: an
overall score of 59, with not less than
59 in any of the four skills
THE SCHOOL OF MATHEMATICS – POSTGRADUATE STUDY
THE APPLICATION OPEN
DAYS
PROCESS
Whether you are applying for a taught Masters course or a
PhD programme there are three steps that you need to take.
1 Consider which programme
of study you want to apply for.
For PhD research degrees you
should take a look at the research
areas and projects shown on the
School of Mathematics website
www.maths.leeds.ac.uk
2.Complete an application
form online:
For Masters courses:
www.leeds.ac.uk/students/apply.htm
For PhD programmes:
www.leeds.ac.uk/pgr/apply
Applications for Masters courses
should be made before the first week
in August if you wish to start your
study in September/October of that
year. We strongly recommend that you
apply before June to allow sufficient
time for paperwork to be completed.
Applications for PhD programmes
can be made at any time, but
there are deadlines associated
with applying for associated
scholarships – please contact the
School for further information.
Please make sure you state your
choice of research area(s) in order of
preference on the application form.
You are also welcome to indicate
specific research projects of interest.
3.Provide supporting
documentation.
In addition to your application form
we will require:
Your degree qualifications
Transcripts of your academic
records showing detailed marks in
courses you have taken
A minimum of two academic
references in support of your
application
Please email the above (as scanned
documents) or send by post to the
relevant contact shown to the right.
Each year the School of
Mathematics holds two
postgraduate open days.
These offer a great opportunity to visit
Leeds and the School, and to meet staff
and current students. To find out more
about these or any other aspect of the
application process, please contact us.
CONTACT
TAUGHT MASTERS
Taught Postgraduate Admissions Office
School of Mathematics
University of Leeds
LEEDS
LS2 9JT
E: maths-msc@leeds.ac.uk
T: +44 (0) 113 343 5111
F: +44 (0) 113 343 5090
PHD RESEARCH
Research Postgraduate
Admissions Office
School of Mathematics
University of Leeds
LEEDS
LS2 9JT
E: maths-phd@leeds.ac.uk
T: +44 (0) 113 343 5102
F: +44 (0) 113 343 5090
23
FOR CURRENT INFORMATION
PLEASE VISIT OUR WEBSITE AT
WWW.MATHS.LEEDS.AC.UK
The University endeavours to ensure that
the information contained in this brochure
is accurate at the date of publication and
does not accept liability for any inaccuracies
contained within it. Where circumstances
change outside the reasonable control of the
University, we reserve the right to change
or cancel parts of, or entire, programmes of
study or services at any time without liability,
even after students have registered at the
University. The University’s contract with its
students does not confer third party benefits
for the purposes of the Contract (Rights of
Third Parties) Act 1999.
School of Mathematics
University of Leeds
Woodhouse Lane
Leeds LS2 9JT
Tel. +44 (0) 113 343 5102
www.maths.leeds.ac.uk
School of Mathematics
University of Leeds
Woodhouse Lane
Leeds LS2 9JT
Tel. +44 (0) 113 343 5102
www.maths.leeds.ac.uk