Mathematical Sciences MPhil, PhD

Entry requirements
2:1 +
Full-time
3 years (PhD), 2 years (MPhil)
Part-time
6 years (PhD), 4 years (MPhil)
Start date
January, April, July, October 2019
UK / EU fee
TBC
International fee
£16,900
Location
Loughborough

Overview

Our Mathematical Sciences department is committed to driving forward innovation across the teaching and research of both pure and applied mathematics.

The Department of Mathematical Sciences attracts staff and students from all over the world, making it a diverse and stimulating environment in which to study. Active in high quality research across the broad spectrum of mathematics, the Department has an international reputation, with four fifths of research rated internationally-leading (or better) in REF 2014.

Our Department undertakes research in both pure and applied mathematics and is located in the newly-refurbished Schofield Building. The department consists of around 35 members of staff and 50 PhD students from all over the world.

The Department’s work is complemented and underpinned by senior visiting academics, research associates and a large support team.

Our programmes reflect our strengths, and in some cases represent established collaborative training ventures with industrial partners. Our graduates go on to work with companies such as BAE Systems, Citigroup, Experian, GE Aviation, Mercedes Benz, Nuclear Labs USA and PwC.

It is also part of the London Mathematical Society’s Good Practice Scheme, which supports mathematics departments interested in embedding equal opportunities for women within their working practices.

Where you'll study

Our Department undertakes research in both pure and applied mathematics and is located in the newly-refurbished Schofield Building. You will have access to spacious study areas, with the latest audio-visual equipment to support teaching and research.

Research areas

Dynamical Systems

This group studies a wide range of aspects of dynamical systems theory, such as Hamiltonian and dissipative dynamics, dynamical chaos in classical and quantum systems, dynamics of multi-scale systems, ergodic theory, random matrix theory, and bifurcation theory.

Applications include problems of celestial mechanics, plasma physics, semi-classical methods, atomic physics, and the dynamics of chemical reactions.

You can find further details here - Dynamical Systems

Geometry and Mathematical Physics

The theory of integrable systems studies differential equations which are, in a sense, exactly solvable and possess regular behaviour. Such systems play a fundamental role in mathematical physics providing an approximation to various models of applied interest.

Dating back to Newton, Euler and Jacobi, the theory of integrable systems now plays a unifying role in mathematics bringing together algebra, geometry and analysis. The research of the group includes both classical and quantum integrable systems in relation to representation theory and special functions, as well as algebraic, differential and symplectic geometry.

You can find further details here - Geometry and Mathematical Physics

Global Analysis and PDEs

Global analysis and the theory of partial differential equations (PDEs) are classical fields of mathematics that have a wide range of applications, for instance in number theory, group theory, geometry and topology. They also have important applications outside of mathematics in physics, engineering and chemistry.

The Global Analysis and PDEs Research Group is rooted in pure mathematics and focuses on geometric and topological aspects of analysis. The interests of the group include spectral and scattering theory on manifolds, regularity and existence of global solutions to pseudo-differential equations and boundary value problems, topological questions related to generalisations of the Atiyah-Singer index theorem, applications of theory of PDE to approximation theory, as well as other topics.

You can find further details here - Global Analysis and PDEs

Linear and Nonlinear Waves

The group’s interests are in wave motion in a variety of physical situations including geophysical fluid dynamics, water waves, solid mechanics, Bose-Einstein condensates, electromagnetism and acoustics. The group develop and apply exact, numerical, asymptotic and perturbation techniques to pursue research on linear and nonlinear waves with a focus on solitary waves and soliton theory, stochastic wave systems, wave generation, and diffraction and scattering by obstacles.

You can find further details here - Linear and Nonlinear Waves

Mathematical Modelling

Members of the group apply a variety of techniques from applied mathematics to diverse problems in medicine, biology, fluid dynamics, materials and soft matter science. The biological systems studied range from intracellular processes to those at the scale of organisms and populations. The fluid flows studied range from environmental buoyancy-driven flows to technologically important micro- and nano-fluidic flows.

The modelling of materials involves the use of mathematical and computational techniques to solve a wide and varied class of problems. This includes nanoscale devices where the fate of individual atoms is important. It spans length scales and time scale that vary over many orders of magnitude and involves the solution of equations that range from continuum to quantum mechanical descriptions.

You can find further details here - Mathematical Modelling

Stochastic Analysis

Stochastic analysis is currently a very active and important basic research area in mathematics. Rooted in probability and measure theory and beginning with the fundamental work of Wiener, Kolmogorov, Levy and Ito, stochastic analysis has intrinsic and deep connections and many applications in analysis and partial differential equations, geometry, dynamical systems, physics, geophysics, engineering, biology etc. in which many problems are modelled by stochastic differential equations or stochastic partial differential equations.

Stochastic analysis has become the basic mathematics for mathematical finance thanks to the pioneering idea of Black, Scholes and Merton. It has been a main research area in probability theory in recent years and the trend is still increasing. In our group, the research topics include: stochastic analysis, in particular interactions with analysis; stochastic methods in (nonlinear) partial differential equations and mathematical physics; stochastic dynamical systems; stochastic differential equations; stochastic partial differential equations; infinite-dimensional analysis; stochastic analysis on geometric spaces; Markov processes and Dirichlet forms; quantum stochastic analysis; rough path; Schramm Loewner evolution; and mathematics of finance.

You can find further details here - Stochastic Analysis

Your personal and professional development

Support from your supervisor

You will have at least two academic supervisors who will guide you in your research. You’ll also be provided with a desk, computer, photocopying facilities and can apply for funds for conference attendance.

Skills and experience

A PhD programme will give you the opportunity to develop new and highly sought after skills which can set you up for a range of careers. It’s a chance to make a novel contribution to knowledge, to become a world expert in a particular field, and it can open a range of doors with different employers. You'll also enhance your interpersonal skills, such as networking and relationship building, which will be invaluable in your future career.

In addition to the University’s extensive training provision, you’ll also enjoy a dynamic research atmosphere with regular workshops, international visitors and a wide range of research seminars to which you’ll be invited to make presentations.

Entry requirements

Our entry requirements are listed using standard UK undergraduate degree classifications i.e. first-class honours, upper second-class honours and lower second-class honours. To learn the equivalent for your country, please choose it from the dropdown below.

Entry requirements for United Kingdom

Applicants should have a 1st class or good 2:1 degree in mathematics or a related discipline.

IELTS: overall 6.5 with minimum 6.0 in each component.

Algeria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Algeria 17/20 15/20 12.5/20

Argentina

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Argentina 8.5 7.5 6.0

Australia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Australia - honours degree (AQF level 8) First class Upper second, H2A Lower second, 2B
Australia - ordinary degree (AQF level 7) High Distinction 85% Distinction 80% Distinction 75%

Azerbaijan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Azerbaijan 4.5 or 90% 4 or 80% 3.5 or 70%

Bahrain

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bahrain - GPA 4.0 scale 3.5 3.0 2.8

Bangladesh

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bangladesh – BUET or 'Good Private' University - 4 year degree 1st (70%) 2nd (60%) 2nd (55%)
Other universities 1st (80%) 1st (70%) 2nd - (60%)

Belarus

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Belarus 9 8 6.5

Belgium

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Belgium 80% (Magna Cum Laude)/17 70% (Cum Laude)/14 60%/12

Brazil

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Brazil 8.5/A 7.5/B 6.0/C

Brunei

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Brunei First Upper Second (60%/B/3.1) Lower Second (50%/C/2.7)

Bulgaria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Bulgaria 6 5 4

Cameroon

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Cameroon 1st or 15/20 or GPA 3.7 2:1 or 14/20 or Bien (GPA 3.4) 2:2 or 12.5/20 or Assez Bien (GPA 3.1)

Canada

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Canada - GPA 4.0/percentage scale 3.5/85% 3.0/75% 2.8/68%
Canada - out of 9 8 7 5
Canada - out of 12 10 8 6

Chile

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Chile 6.0 5.0 4.5

China

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
ShanghaiRanking 1-250 85% 80% 77%
ShanghaiRanking 251 - 500 89% 83% 80%
ShanghaiRanking 501+ 92% 86% 82%

Further information

Colombia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Colombia 4.5 3.5 3.0

Croatia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Croatia 4.5 3.8 3.0

Cuba

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Cuba 5 4 3

Cyprus

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Cyprus 8.5 7.0 6.5

Czech Republic

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Czech Republic 1.2 2.2 2.7

Denmark

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Denmark 12 10 7

Ecuador

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Ecuador 8.5 (85%) 7.5 (75%) 6 (60%)

Egypt

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Egypt 3.7 3.2 2.7

Finland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Finland - out of 3 3 2 1
Finland - out of 5 4.5 3 2.5

France

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
France 14 12 11

Germany

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Germany 1.5 2.5 3.0

Ghana

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Ghana First Upper second/60% Lower second/50%

Greece

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Greece 8.5 7.0 6.5

Hong Kong

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Hong Kong GPA 4.0 scale 3.5 3.0 2.8

India

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Institutions listed on the Indian Ranking of Higher Educational Institutions Framework 65% (First) 60% (First) 55% (Upper second)
All other Indian institutions 70% (First with distinction) 65% (First) 60% (First)

Indonesia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Indonesia 3.7 (4.0) 3.3 (3.7) 3 (3.3)

Iran

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Iran 18 16 14

Iraq

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Iraq 85% 80% 75%

Ireland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Republic of Ireland First (70%) Upper second (60%) Lower second (50%)

Israel

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Israel 90% 80% 75%

Italy

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Italy 109/110 104/110 (or 27) 100/110 (or 26)

Japan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Japan 85% 80% or B or 3.0 70% or C or 2.0

Jordan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Jordan - GPA 4.0 scale 3.5 3 or 3.5/5 or 75% 2.8 or 65%

Kazakhstan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Kazakhstan - GPA 5.0/percentage scale 4.5 or 90% 4 or 85% 3.5 or 80%
Kazakhstan - GPA 4.33 scale 3.9 3.7 3.2
Kazakhstan - GPA 4.0 scale 3.7 3.4 3

Kenya

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Kenya First / 70% / A Upper second / 60% / B Lower second / 50% / C

Kosovo

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Kosovo 10 9 8

Kuwait

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Kuwait GPA 4.0 scale 3.6 3.0 2.8

Lebanon

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Lebanon - American 90% (3.5) 80% (3.2) 70% (2.8)
Lebanon - French 18 15 12

Libya

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
BSc Engineering, Architecture, Medicine 85 (4.0) 80 (3.0) 75 (2.5)
Other bachelor's degree from a university 90 (4.0) 85% (3.6) 80% (3.0)
Master's degree Master's Master's Master's

Lithuania

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Lithuania 9 8 7

Macau

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Macau 1st or GPA 3.7 2:1 or GPA 3.0 2:2 or GPA 2.5

Macedonia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Macedonia 10 9 8

Malawi

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
MSc Degree 75% 70% 65%
BSc Degree - 80% 80%

Malaysia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Malaysia - classification First Class 2.1 2.2
Malaysia - GPA 4.0 scale 3.5 3.0 2.8

Mexico

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Mexico 9 8 7

Morocco

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Morocco 17 15 13

Namibia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Namibia 80% or A 70% or B 60% or C

Netherlands

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Netherlands 8 7 6

New Zealand

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
New Zealand First (A/A+) Upper second (B+/A-) Lower second (B-/B)

Nigeria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Nigeria 7 point Scale 6 5 4
Nigeria 5 point scale 4.5 3.8 3.5
Nigeria 4 point scale 3.5 3 2.5

Norway

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Norway A (1.5) B (2.5) C (3.2)

Oman

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Oman GPA 4.0 scale 3.5 3.0 2.8

Pakistan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Pakistan Public Universities (Tech or Eng) 4 Year degree only First with distinction (75%) / 4.0 First (65%) / 3.2 Second (59%) / 2.6
Pakistan Private Universities (Tech or Eng) 4 Year degree only First with Distinction (85%) First (75%) First (65%)
Pakistan master's (2 or 3 year bachelor's plus master's) First Second (55%) Second

Palestine

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Palestine A / 90% / 3.7 B+ / 85% / 3.3 B / 80% / 3.0

Peru

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Peru 16 14 12

Philippines

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Philippines - degree from prestigious state universities or Centres of Excellence (COE) Summa Cum Laude 4.0 / 96% / 1.0 Magna cum Laude 3.5 / 92% / 1.5 Cum Laude 3.0 / 87%/ 2.0

Poland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Poland 5 (Very good) 4 (Good) 3.5

Portugal

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Portugal 18 16 14

Qatar

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Qatar GPA 4.0 scale 3.5 3.0 2.8

Romania

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Romania 8.5 7.5 6.5

Russia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Russia 4.5 4.0 3.5

Rwanda

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Rwanda - 2:1 or 16/20 or 70% 2:2 or 14/20 or 60%

Saudi Arabia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Saudi Arabia GPA 4.0 scale 3.5 3.0 2.8
Saudi Arabia GPA 5.0 scale 4.5 3.75 3.5

Singapore

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Singapore - classification First Upper second Lower second
Singapore - GPA 4.0 scale 3.7 3.0 2.7
Singapore - GPA 5.0 scale 4.5 3.5 3.0

Slovenia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Slovenia 9.5 8.5 7

South Africa

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
South Africa - classification 1st 2:1 2:2
South Africa - percentage scale 75-100% 70-74% 60-69%

South Korea

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
South Korea 4.0 / A 3.0 / B 2.5 / C+

Spain

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Spain 9.0 7.5 6.5
Spain - UCM grading 3.0 2.0 1.5

Sri Lanka

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Sri Lanka 70% 60% 55%

Sudan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Sudan (North and South) 1st or 70% or B+ 2:1 or 66% Mid 2:2 or 60% or B

Switzerland

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Switzerland 6 5 4

Syria

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Syria - state universities 85% 75% 65%
Syria - private universities 95% 85% 75%

Taiwan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Taiwan - prestigious national universities 80% 75% 73%
Taiwan - excellent universities 83% 78% 75%
Taiwan - good universities 88% 83% 80%

Tanzania

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Tanzania 1st 2:1 2:2

Thailand

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Thailand GPA 4.0 scale 3.5 3.0 2.8

Tunisia

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Tunisia 15 (tres bien) 13 (bien) 11 (assez bien)

Turkey

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Turkey 3.5 2.8 2.2

Turkmenistan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Turkmenistan - 4.5 4

Uganda

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Uganda First Upper second Lower second

Ukraine

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Ukraine 5 4.5 4

United Arab Emirates

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
United Arab Emirates GPA 4.0 scale 3.5 3.0 2.8

United States of America

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
United States of America GPA 4.0 scale 3.5 3.2 2.8

Uzbekistan

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Uzbekistan 90% / 85% 80% / 75% 75% / 65%

Venezuela

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Venezuela - out of 20 - 16 14
Venezuela - out of 9 - 7 6.5

Vietnam

First-class honours (70%) Upper second-class honours (60%) Lower second-class honours (50%)
Vietnam 8.0 7.0 6.0

English language requirements

Applicants must meet the minimum English Language requirements. Further details are available on the International website.

Fees and funding

UK / EU fee

Full-time degree per annum
TBC

International fee

Full-time degree per annum
£16,900

Starting your studies in the 2018/19 academic year?

If your start date is October 2018, January 2019, or April 2019 your tuition fees for this academic year will be at the 2018/19 rates.

Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment.

Bursaries Student loans Centre for Doctoral Training Awards Grants Scholarships

How to apply

If you can't find a suitable PhD opportunity that fits your interests and experience from our funded (studentships) and unfunded opportunities, you can submit a research proposal to the Department of Mathematical Sciences in the hope of finding a supervisor who will work with you on your dream project.

If you wish to apply for a PhD through this method, you do not need to submit a detailed research proposal with your application, but you should indicate which area of research you wish to pursue and/or names of staff members you are interested in working with.

Apply now