Financial Mathematics MSc

Key information

Duration:
1 year full time
Start date:
September 2018
Apply by:
1 August (International), 1 September (UK/EU)

Understand the main aspects of quantitative finance – including general finance theory, finance models and programming for graduates with a science, engineering and mathematics background.

Our course has been developed drawing on expertise from industry professionals. You cover topics such as:

  • interest-rate theory
  • arbitrage theory
  • GARCH models
  • corporate finance
  • option pricing models and numerical analysis
  • programming in C and Java
  • the use of mathematical computing software.

Why choose this course?

  • This course builds on Sussex’s strong foundation of interdisciplinary study – you’ll be taught by faculty from the Department of Mathematics and the Department of Business and Management.
  • Our courses are designed to meet employer demands – you’ll gain the knowledge and skills to compete effectively in the fast-paced world of work.
  • You have a choice between practice- and research-oriented study, working with experts in their fields.
Our students will learn the latest mathematical techniques and technical skills to start a successful career in the financial industry.”Dr Bertram Düring
Senior Lecturer in Mathematics

Entry requirements

Degree requirements

You should normally have a lower second-class (2.2) undergraduate honours degree or above.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please select your country from the list.

Argentina

Degree requirements

Licenciado/Titulo with a final mark of 6.0-7.0 depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Australia

Degree requirements

Bachelors degree with second-class lower division.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Azerbaijan

Degree requirements

Magistr or Specialist Diploma with a minimum average mark of at least 4 or 81%

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Bahrain

Degree requirements

Bachelors degree with CGPA 2.5/4.0 (Grade C+).

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Bangladesh

Degree requirements

Masters degree with CGPA of at least 3.0/4.0.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Brazil

Degree requirements

Bacharel, Licenciado or professional title with a final mark of at least 7.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Brunei

Degree requirements

Bachelors (Honours) degree with second class lower division or GPA 2.7/4.0.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Canada

Degree requirements

Bachelors degree with CGPA 3.0/4.0 (grade B).

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Chile

Degree requirements

Licenciado with a final mark of 4.5-5.0/7 depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

China

Degree requirements

Bachelors degree with an overall mark of 65%-80% depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Colombia

Degree requirements

Licenciado with ‘Acreditacion de alta calidad’ and a GPA of 3.0.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Cyprus

Degree requirements

Bachelors degree or Ptychion with a final mark of at least 6.5.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Ecuador

Degree requirements

Licenciado with a final mark of at least 15/20.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Egypt

Degree requirements

Bachelors degree from a university with an overall grade of 70%

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

France

Degree requirements

Licence with mention assez bien or Maîtrise with final mark of at least 12.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Germany

Degree requirements

Bachelors degree or Magister Artium with a final mark of 2.7 or better.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Ghana

Degree requirements

Bachelors degree from a public university with second-class lower division.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Greece

Degree requirements

Ptychion from an AEI with a final mark of at least 6.5.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Hong Kong

Degree requirements

Bachelors (Honours) degree with second-class lower division.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

India

Degree requirements

Bachelors degree with an overall mark of 50-65% depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Indonesia

Degree requirements

Bachelors degree from an 'A' accredited university with GPA 2.8/4.0. 

Bachelors degree from a 'B' accredited university with GPA 3.0/4.0.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Iran

Degree requirements

Bachelors degree (Licence or Karshenasi) with a final mark of at least 14.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Italy

Degree requirements

Diploma di Laurea with an overall mark of at least 101.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Japan

Degree requirements

Bachelors degree with a minimum C/GPA of at least 3.0/4.0 or equivalent.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Jordan

Degree requirements

Bachelors degree with CGPA of at least 2.8/4.0.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Kazakhstan

Degree requirements

Bachelors degree with an overall mark of 3.75 or better (on a scale of 1-5)/GPA 2,67.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Kenya

Degree requirements

Bachelors (Honours) degree with second-class lower division.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Kuwait

Degree requirements

Bachelors degree with CGPA of at least 2.8/4.0 or B.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Lebanon

Degree requirements

Bachelors degree with CGPA 3.0/4.0 or 13/20.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Malawi

Degree requirements

Masters degree, depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Malaysia

Degree requirements

Bachelors degree with CGPA of at least 2.7/4.0

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Mexico

Degree requirements

Licenciado with a final mark of at least 7.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Nepal

Degree requirements

Masters degree with overall mark of 70%

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Nigeria

Degree requirements

Bachelors degree with second-class lower division or CGPA of at least 3.0/5.0.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Norway

Degree requirements

Bachelors degree with an overall grade of C.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Oman

Degree requirements

Bachelors degree with CGPA of at least 2.8/4.0.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Pakistan

Degree requirements

Four-year bachelors degree with overall grade of 65% or Masters with 55%

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Palestine

Degree requirements

Bachelors degree with GPA of at least 3.0/4.0 or B.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Paraguay

Degree requirements

Bachelors with a final mark of at least 7/10.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Peru

Degree requirements

Licenciado with a final mark of 12/20 depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Philippines

Degree requirements

Masters degree with 1.75/5.0 (where 1 is the highest) or 3.5/4.0

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Qatar

Degree requirements

Bachelors degree with an overall CPGA of at least 2.8 (on a scale of 4).

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Russia

Degree requirements

Magistr or Specialist Diploma with a minimum average mark of at least 4.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Saudi Arabia

Degree requirements

Bachelors degree with a CGPA 3.0/5.0 or 2.8/4.0.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Singapore

Degree requirements

Bachelors (Honours) degree with second-class lower division or CAP 3.5.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

South Africa

Degree requirements

Bachelors (honours) degree with second-class division 2.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

South Korea

Degree requirements

Bachelors degree with a CGPA of at least 3.0/4.0 or B.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Spain

Degree requirements

Licenciado with a final mark of at least 2/4.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Sri Lanka

Degree requirements

Bachelors Special degree with lower second honours.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Switzerland

Degree requirements

Licence or Diplôme with 4.5/6 or 7/10.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Taiwan

Degree requirements

Bachelors degree with overall mark of 70%-85% depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Thailand

Degree requirements

Bachelors degree with CGPA of at least 2.8/4.0 or equivalent.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Turkey

Degree requirements

Lisans Diplomasi with CGPA of at least 3.0/4.0 or equivalent depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

United Arab Emirates

Degree requirements

Bachelors degree with CGPA of at least 2.8/4.0 or equivalent.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

USA

Degree requirements

Bachelors degree with CGPA 3.0/4.0 depending on your university.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Vietnam

Degree requirements

Bachelors degree (with a Graduate Thesis/research component) with CGPA of at least 3.0/4.0 or 7.0/10.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Zambia

Degree requirements

Masters degree with GPA of 2.0/2.5 or equivalent.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

Zimbabwe

Degree requirements

Bachelors (Honours) degree with second-class lower division.

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

Please note

Our entry requirements are guidelines and we assess all applications on a case-by-case basis.

My country is not listed

If your country is not listed, you need to contact us and find out the qualification level you should have for this course. Contact us at pg.enquiries@sussex.ac.uk

Subject-specific requirements

Your qualification should have a high mathematics content, demonstrating knowledge in calculus, probability and statistics, differential equations and some numerical analysis/ scientific computation / programming / modelling. You are suited to this course if your qualification is in mathematics, finance, economics, business, science, engineering or computing. You may also be considered for the course if you have other professional qualifications or experience of equivalent standing.

English language requirements

IELTS (Academic)

Lower level (6.0 overall, including at least 6.0 in each component).

Check your IELTS qualification meets all of our entry requirements and find out more about IELTS

Alternative English language qualifications

Proficiency tests

Cambridge Advanced Certificate in English (CAE)

For tests taken before January 2015: grade B or above.

For tests taken after January 2015: 169 overall, including at least 169 in each skill.

We would normally expect the CAE test to have been taken within two years before the start of your course.

You cannot combine scores from more than one sitting of the test. Find out more about Cambridge English: Advanced

Cambridge Certificate of Proficiency in English (CPE)

For tests taken before January 2015: grade C or above.

For tests taken after January 2015: 169 overall, including at least 169 in each skill.

We would normally expect the CPE test to have been taken within two years before the start of your course.

You cannot combine scores from more than one sitting of the test. Find out more about Cambridge English: Proficiency

Pearson (PTE Academic)

56 overall, including at least 56 in all four skills.

PTE (Academic) scores are valid for two years from the test date. Your score must be valid when you begin your Sussex course. You cannot combine scores from more than one sitting of the test. Find out more about Pearson (PTE Academic)

TOEFL (iBT)

80 overall, including at least 19 in Listening, 19 in Reading, 21 in Speaking, 21 in Writing.

TOEFL (iBT) scores are valid for two years from the test date. Your score must be valid when you begin your Sussex course. You cannot combine scores from more than one sitting of the test. Find out more about TOEFL (iBT)

The TOEFL Institution Code for the University of Sussex is 9166.

English language qualifications

AS/A-level (GCE)

Grade C or above in English Language.

Hong Kong Advanced Level Examination (HKALE)/ AS or A Level: grade C or above in Use of English.

French Baccalaureat

A score of 12 or above in English.

GCE O-level

Grade C or above in English.

Brunei/Cambridge GCE O-level in English: grades 1-6.

Singapore/Cambridge GCE O-level in English: grades 1-6.

GCSE or IGCSE

Grade C or above in English as a First Language (Grade 5 or above in GCSE from 2017).

Grade B or above in English as a Second Language.

German Abitur

A score of 12 or above in English.

Ghana Senior Secondary School Certificate

If awarded before 1993: grades 1-6 in English language.

If awarded between 1993 and 2005: grades A-D in English language.

Hong Kong Diploma of Secondary Education (HKDSE)

 Level 4, including at least 3 in each component in English Language.

Indian School Certificate (Standard XII)

The Indian School Certificate is accepted at the grades below when awarded by the following examination boards:

Central Board of Secondary Education (CBSE) – English Core only: 70%

Council for Indian School Certificate Examinations (CISCE) - English: 70% 

International Baccalaureate Diploma (IB)

English A or English B at grade 5 or above.

Malaysian Certificate of Education (SPM) 119/GCE O-level

If taken before the end of 2008: grades 1-5 in English Language.

If taken from 2009 onwards: grade C or above in English Language.

The qualification must be jointly awarded by the University of Cambridge Local Examinations Syndicate (UCLES).

West African Senior School Certificate

Grades 1-6 in English language when awarded by the West African Examinations Council (WAEC) or the National Examinations Council (NECO).

Country exceptions

Select to see the list of exempt English-speaking countries

If you are a national of one of the countries below, or if you have recently completed a qualification equivalent to a UK Bachelors degree or higher in one of these countries, you will normally meet our English requirement. Note that qualifications obtained by distance learning or awarded by studying outside these countries cannot be accepted for English language purposes.

You will normally be expected to have completed the qualification within two years before starting your course at Sussex. If the qualification was obtained earlier than this, we would expect you to be able to demonstrate that you have maintained a good level of English, for example by living in an English-speaking country or working in an occupation that required you to use English regularly and to a high level.

Please note that this list is determined by the UK’s Home Office, not by the University of Sussex.

List of exempt countries: 

  • Antigua and Barbuda
  • Australia
  • Bahamas
  • Barbados
  • Belize
  • Canada**
  • Dominica
  • Grenada
  • Guyana
  • Ireland
  • Jamaica
  • New Zealand
  • St Kitts and Nevis
  • St Lucia
  • St Vincent and the Grenadines
  • Trinidad and Tobago
  • United Kingdom
  • USA

** Canada: you must be a national of Canada; other nationals not on this list who have a degree from a Canadian institution will not normally be exempt from needing to provide evidence of English.

English language support

If you don’t meet the English language requirements for your degree, you may be able to take a pre-sessional course

Visas and immigration

Find out how to apply for a student visa

Admissions information for applicants

How to apply

You apply to Sussex using our postgraduate application system

Personal statement

Yes. You must submit a personal statement as part of your application. 

Find out how to write a personal statement

If your qualifications aren’t listed or you have a question about entry requirements, email pg.enquiries@sussex.ac.uk

Application deadlines

1 August (International), 1 September (UK/EU)

Our experts

Dr Bertram Duering

Dr Bertram Duering

Reader in Mathematics

Research interests

Applied Mathematics, Financial Mathematics, Interacting particle systems, Kinetic theory, Mathematical modelling, Nonlinear partial differential equations, Numerical Analysis, Optimal Control, Partial Differential Equations

View Bertram Duering's profile

Dr Max Jensen

Dr Max Jensen

Senior Lecturer In Mathematics

Research interests

Financial Mathematics, Numerical Analysis, Optimal Control, Partial Differential Equations

View Max Jensen's profile

Prof Anotida Madzvamuse

Prof Anotida Madzvamuse

Professor of Mathematical&ComputationalBiology'RSW Research Merit Award Holder'

Research interests

computational biology, Coupled bulk-surface models, Dynein transport models, evolving surface finite element, Keratin spatio-temporal models, Mathematical Biology, Mathematical modelling, moving grid finite element, Optimal control of Geometric PDES, Parameter Identification, Pattern Formation, Reaction-diffusion, Scientific Computing

View Anotida Madzvamuse's profile

Prof Enrico Scalas

Prof Enrico Scalas

Professor Of Statistics & Probability

Research interests

Econophysics, Financial Mathematics, Mathematical Statistics, Monte Carlo simulations, Probability Theory, Statistical Mechanics, Stochastic Processes

View Enrico Scalas's profile

Dr Qi Tang

Dr Qi Tang

Reader in Mathematics

Research interests

Big Data Analytics, Finance, Stochastic integral-differential equations

View Qi Tang's profile

Course enquiries

+44 (0)1273 873254
mps@​sussex.ac.uk

Find out about the Department of Mathematics

Fees and scholarships

How much does it cost?

Fees

UK/EU students:
£10,600 per year
Channel Islands and Isle of Man students:
£10,600 per year
International students:
£17,900 per year

Note that your fees may be subject to an increase on an annual basis.

Living costs

Find out typical living costs for studying at Sussex

How can I fund my course?

Postgraduate Masters loans

You can borrow up to £10,280 to help with fees and living costs if your course starts on or after 1 August 2017. Loans are available from the Student Loans Company if you’re from the UK or if you’re an EU national studying for a Masters.

Find out more about Postgraduate Masters Loans

Scholarships

Our aim is to ensure that every student who wants to study with us is able to despite financial barriers, so that we continue to attract talented and unique individuals.

How Masters scholarships make studying more affordable

Working while you study

Our Careers and Employability Centre can help you find part-time work while you study. Find out more about career development and part-time work

Careers

Our graduates have found jobs in banking (investment funds and hedge funds) and financial software companies.

Graduate destinations

100% of students from the Department of Mathematics were in work or further study six months after graduating. Recent graduates have gone on to jobs including:

  • accountant, Ernst & Young
  • graduate analyst, Invesco
  • performance analyst, Legal and General Investment Management.

(EPI, Destinations of Leavers from Higher Education Survey 2015 for postgraduates)

The mix of theoretical and practical study, from monetary theory and econometrics to MATLAB and C++ programming, helped me to succeed in finding a job in the financial market.”Ryan Horne
Trading Analyst Services Department
Orc Software

Dissertation (Financial Mathematics)

  • 60 credits
  • All Year Teaching, Year 1 credits

You are expected to carry out independant study and research of a designated topic, and complete a report on the subject over the summer of the year of study

Corporate and International Finance

  • 15 credits
  • Autumn Semester, Year 1 credits

This module covers the most important topics in corporate finance such as: capital investment decision-taking; financing andcapital structure; risk management; and portfolio theory. You will then analyse issues in international finance including: models of exchange rates; efficiency in foreign exchange markets; monetary unions; and international financial crises.

Financial and Time Series Econometrics

  • 15 credits
  • Spring Semester, Year 1 credits

The primary aim of this module is for you to become familiar with a variety of applied time-series econometric techniques, enabling the confident and independent use of these techniques.

An important emphasis of the module is to provide you with 'hands-on' experience of econometric analysis through using a variety of economic data sets.

Financial computing with MATLAB

  • 15 credits
  • Autumn Semester, Year 1 credits

From basic skills of MATLAB you will progress to be able to handle some financial data processing abilities.

Financial Mathematics

  • 15 credits
  • Autumn Semester, Year 1 credits

You will study generalized cash flows, time value of money, real and money interest rates, compound interest functions, quations of value, loan repayment schemes, investment project evaluation and comparison, bonds, term structure of interest rates, some simple stochastic interest rate models and project writing.

Financial Portfolio Analysis

  • 15 credits
  • Spring Semester, Year 1 credits

You will study valuation, options, asset pricing models, the Black-Scholes model, Hedging and related MatLab programming. These topics form the most essential knowledge for you if you intend to start working in the financial fields. They are complex application problems. Your understanding of mathematics should be good enough to understand the modelling and reasoning skills required. The programming element of this module makes complicated computations manageable and presentable.

Mathematical Models in Finance and Industry

  • 15 credits
  • Spring Semester, Year 1 credits

Topics include: partial differential equations (and methods for their solution) and how they arise in real-world problems in industry and finance. For example: advection/diffusion of pollutants, pricing of financial options.

Advanced Numerical Analysis

  • 15 credits
  • Autumn Semester, Year 1 credits

This module will cover topics including:

  • Iterative methods for linear systems: Jacobi and Gauss-Seidel, conjugate gradient, GMRES and Krylov methods
  • Iterative methods for nonlinear systems: fixed point iteration, Newton's method and Inexact Newton
  • Optimisation: simplex methods, descent methods, convex optimisation and non-convenx optimisation
  • Eigenvalue problems: power method, Von Mises method, Jacobi iteration and special matrices
  • Numerical methods for ordinary differential equations: existence of solutions for ODE's, Euler's method, Lindelöf-Picard method, continuous dependence and stability of ODE's
  • Basic methods: forward and backward Euler, stability, convergence, midpoint and trapezoidal methods (order of convergence, truncation error, stability convergence, absolute stability and A-stability)
  • Runge-Kutta methods: one step methods, predictor-corrector methods, explicit RK2 and RK4 as basic examples, and general theory of RK methods such as truncation, consitency, stability and convergence 
  • Linear multistep methods: multistep methods, truncation, consistency, stability, convergence, difference equaitons, Dahlquist's barriers, Adams family and backward difference formulas
  • Boundary value problems in 1d, shooting methods, finite difference methods, convergence analysis, Galerkin methods and convergence analysis

Advanced Partial Differential Equations

  • 15 credits
  • Spring Semester, Year 1 credits

You will be introduced to modern theory of linear and nonlinear Partial Differential Equations. Starting from the theory of Sobolev spaces and relevant concepts in linear operator theory, which provides the functional analytic framework, you will treat the linear second-order elliptic, parabolic, and hyperbolic equations (Lax-Milgram theorem, existence of weak solutions, regularity, maximum principles), e.g., the potential, diffusion, and wave equations that arise in inhomogeneous media.

The emphasis will be on the solvability of equations with different initial/boundary conditions, as well as the general qualitative properties of their solutions. They then turn to the study of nonlinear PDE, focusing on calculus of variation.

Commodity and Energy Markets

  • 15 credits
  • Spring Semester, Year 1 credits

You study and analyse the commodity markets, looking at distinctive features, complex price risks, and widespread valuation and hedging challenges.

You look at how techniques and tools from the traditional financial markets are adapted and extended and examine fundamental commodity concepts such as:

  • contango
  • backwardation
  • physical delivery and storage
  • seasonality and other prominent features of the behaviour of commodity spot and forward prices.

You study:

  • the links with supply and demand and the relationship between the physical and financial markets
  • quantitative techniques for modelling commodity price dynamics
  • pricing and hedging derivative products
  • applications to real-world problems and decisions (such as physical asset valuation, investment, operation or hedging)
  • energy, agriculturals, and metals
  • electricity and carbon emissions, with links to energy and environmental policy.

Continuum Mechanics

  • 15 credits
  • Spring Semester, Year 1 credits

Topics include: 

  • kinematics (Eulerian and Lagrangian descriptions, velocity, acceleration, rate of change of physical quantities, material derivatives, streamlines)
  • deformation (stress and strain tensors, Hooke's law, equilibrium equations)
  • conservation laws for mass, momentum and energy
  • phase/group velocities of travelling wave solutions
  • models of fluid and solid mechanics.

Cryptography

  • 15 credits
  • Autumn Semester, Year 1 credits

You will cover the following areas: 

  • symmetric-key cryptosystems
  • hash functions and message authentication codes
  • public-key cryptosystems
  • complexity theory and one-way functions
  • primality and randomised algorithms
  • random number generation
  • elliptic curve cryptography
  • attacks on cryptosystems
  • quantum cryptography
  • cryptographic standards.

Dynamical Systems

  • 15 credits
  • Spring Semester, Year 1 credits

General dynamical systems:

  • semiflow
  • stability and attraction
  • omega-limit set
  • global attractor.

Ordinary Differential Equations:

  • linear systems
  • Lyapunov function
  • linearised systems around fixed points
  • two-dimensional systems
  • periodic orbit.

Discrete systems (iterations):

  • linear systems
  • linearised systems around fixed points
  • chaos.

Financial Invest & Corp Risk Analysis

  • 15 credits
  • Spring Semester, Year 1 credits

In this module, we introduce the three main risk concepts in the investment and corporate risk management field: market risk (times series), credit risk (financial rating) and operational risk (evaluation and reporting techniques), using Basel Regulations as guidelines.

We then introduce the mathematical tools required to quantify, describe and analyse these risks quantitatively (including graphic representation, bootstrapping, calculation of transition matrices, ARCH/GARCH models, VaR, Monte-Carlo simulation)

We also introduce some programming tools in Excel and MatLab on how to deal with these problems.

Finite Element Analysis

  • 15 credits
  • Spring Semester, Year 1 credits

Topics include:

  • introduction to finite-element modelling methods and software
  • preparation of the graphical interface
  • setting up a model
  • mesh generation
  • stress analysis
  • nodal analysis and dynamic modelling
  • interfacing with other packages and the use of exchangeable formats
  • checking a solution
  • debugging and validation of the modelling process.

Functional Analysis

  • 15 credits
  • Autumn Semester, Year 1 credits

In this module, you cover:

  • Banach spaces, Banach fixed-point theorem, Baire's theorem
  • bounded linear operators and on Banach spaces, continuous linear functionals, Banach-Steinhaus uniform boundedness principle
  • open mapping and closed graph theorems, Hahn-Banach theorem
  • Hilbert spaces, orthogonal expansions, Riesz representation theorem.

Introduction to Mathematical Biology

  • 15 credits
  • Autumn Semester, Year 1 credits

The module will introduce you to the concepts of mathematical modelling with applications to biological, ecological and medical phenomena. The main topics will include:

  • continuous populations models for single species
  • discrete population models for single species
  • phase plane analysis
  • interacting populations (continuous models)
  • enzyme kinetics
  • dynamics of infectious diseases and epidemics.

Linear Statistical Models

  • 15 credits
  • Autumn Semester, Year 1 credits

Topics include:

  • full-rank model (multiple and polynomial regression), estimation of parameters, analysis of variance and covariance
  • model checking
  • comparing models, model selection
  • transformation of response and regressor variables
  • models of less than full rank (experimental design), analysis of variance, hypothesis testing, contrasts
  • simple examples of experimental designs, introduction to factorial experiments
  • use of a computer statistical package to analyse real data sets.

Measure and Integration

  • 15 credits
  • Autumn Semester, Year 1 credits

In this module, you cover:

  • countably additive measures, sigma-algebras, Borel sets, measure spaces
  • outer measures and Caratheodory's construction of measures
  • construction and properties of Lebesgue measure in Euclidean spaces
  • measurable and integrable functions, Lebesgue integration theory on measure spaces, L^p spaces and their properties
  • convergence theorems: monotone convergence, dominated convergence, Fatou's lemma
  • application of limit theorems to continuity and differentiability of integrals depending on a parameter
  • properties of finite measure spaces and probability theory.

Monte Carlo Simulations

  • 15 credits
  • Spring Semester, Year 1 credits

The module will cover topics including:

  • Introduction to R 
  • Pseudo-random number generation 
  • Generation of random variates 
  • Variance reduction 
  • Markov-chain Monte Carlo and its foundations 
  • How to analyse Monte Carlo simulations 
  • Application to physics: the Ising model 
  • Application to statistics: goodness-of-fit tests

Numerical Solution of Partial Differential Equations

  • 15 credits
  • Spring Semester, Year 1 credits
Topics covered include: variational formulation of boundary value problems; function spaces; abstract variational problems; Lax-Milgram Theorem; Galerkin method; finite element method; examples of finite elements; and error analysis.

Object Oriented Programming

  • 15 credits
  • Autumn Semester, Year 1 credits

You will be introduced to object-oriented programming, and in particular to understanding, writing, modifying, debugging and assessing the design quality of simple Java applications.

You do not need any previous programming experience to take this module, as it is suitable for absolute beginners.

Optimal Control of Partial Differential Equations

  • 15 credits
  • Spring Semester, Year 1 credits

You will be introduced to optimal control problems for partial differential equations. Starting from basic concepts in finite dimensions (existence, optimality conditions, adjoint, Lagrange functional and KKT system) you will study the theory of linear-quadratic elliptic optimal control problems (weak solutions, existence of optimal controls, adjoint operators, necessary optimality conditions, Langrange functional and adjoint as Langrangian multiplier) as well as basic numerical methods for your solution (gradient method, projected gradient method and active set strategy). The extension to semi-linear elliptic control problems will also be considered.

Partial Differential Equations

  • 15 credits
  • Autumn Semester, Year 1 credits

Topics include: 

  • second-order partial differential equations (wave equation, heat equation, Laplace equation)
  • D'Alembert's solution
  • separation of variables
  • Duhamel's principle
  • energy method
  • Maximum principle
  • Green's identities.

Perturbation theory and calculus of variations

  • 15 credits
  • Spring Semester, Year 1 credits

The aim of this module is to introduce you to a variety of techniques primarily involving ordinary differential equations, that have applications in various branches of applied mathematics. No particular application is emphasised.

Topics covered include –

Dimensional analysis and scaling:

  • physical quantities and their measurement
  • dimensions
  • change of units
  • physical laws
  • Buckingham Pi Theorem
  • scaling.

Regular perturbation methods:

  • direct method applied to algebraic equations and initial value problems (IVP)
  • Poincar method for periodic solutions
  • validity of approximations.

Singular perturbation methods:

  • finding approximate solutions to algebraic solutions
  • finding approximate solutions to boundary value problems (BVP) including boundary layers and matching.

Calculus of Variations:

  • necessary conditions for a function to be an extremal of a fixed or free end point problem involving a functional of integral form
  • isoperimetric problems.

Probability Models

  • 15 credits
  • Autumn Semester, Year 1 credits

You cover topics including:

  • short revision of probability theory
  • expectation and conditional expectation
  • convergence of random variables, in particular laws of large numbers, moment generating functions, and central limit theorem
  • stochastic processes in discrete time in particular Markov chains, including random walk, martingales in discrete time, Doob's optional stopping theorem, and martingale convergence theorem.

Programming in C++

  • 15 credits
  • Autumn Semester, Year 1 credits

After a review of the basic concepts of the C++ language, you are introduced to object oriented programming in C++ and its application to scientific computing. This includes writing and using classes and templates, operator overloading, inheritance, exceptions and error handling. In addition, Eigen, a powerful library for linear algebra is introduced. The results of programs are displayed using the graphics interface dislin.

Random processes

  • 15 credits
  • Spring Semester, Year 1 credits

Topics covered include:

Rationalisation:
After the introduction of the Poisson process, birth and death processes as well as epidemics models can be presented in full generality as applications of the pooled Poisson process. At the same time, you will be introduced to the Kolmogorov equations and to the techniques for solving them. Renewal theory is needed to better understand queues, and, for this reason, it is discussed before queues.
Modernisation:
A modern introductory course on stochastic processes must include at least a section on compound renewal processes (with a focus on the compound Poisson process) as well as a chapter on the Wiener process and on Ito stochastic calculus. This is necessary given the importance this process has in several applications from finance to physics. Modernisation is achieved by including a new introductory chapter divided into three parts.

Poisson processes:

  • density and distribution of inter-event time
  • pooled Poisson process
  • breaking down a Poisson process
  • applications of the Poisson process, e.g. birth-and-death processes, the Kolmogorov equations

Renewal processes:

  • the ordinary renewal process
  • the equilibrium renewal process
  • the compound renewal process
  • applications of renewal processes, queues.

Wiener processes:

  • definition and properties
  • introduction to stochastic integrals
  • introduction to stochastic differential equations.

Statistical Inference

  • 15 credits
  • Spring Semester, Year 1 credits

Topology and Advanced Analysis

  • 15 credits
  • Autumn Semester, Year 1 credits

Topics that will be covered in this module include:

  • Topological spaces
  • Base and sub-base
  • Separation axioms
  • Continuity
  • Metrisability
  • Completeness
  • Compactness and Coverings
  • Total Boundedness
  • Lebesgue numbers and Epsilon-nets
  • Sequential Compactness
  • Arzela-Ascoli Theorem
  • Montel's theorem
  • Infinite Products
  • Box and Product Topologies
  • Tychonov Theorem
  • Banach-Alaoglu theorem.
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