The University of Southampton
Mathematical SciencesPostgraduate study

PhD (Integrated) in Mathematical Sciences (4 years)

This is a programme whose regulations fall under those for an Integrated PhD as outlined in the University Calendar.  Candidates are required to undertake the scheme of study over a period of four years full-time registration, to pass the required examinations, and to submit a thesis not more than 12 months later than the end of the fourth year of study. In exceptional circumstances the Faculty Graduate School directorate may approve a later date for submission. If part-time candidates are permitted, they are required to submit a thesis not more than 12 months later than the end of the seventh year of study.


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In the first year, students follow a taught programme of Level 7 modules selected from across a range to be approved by the programme director in consultation with the supervisory team.  Following successful completion of the taught element, students embark on their individual research programme. In all years, the programme provides an integrated series of training modules to help students to develop professional and personal skills as well as scientific expertise.

The research work of each student will be closely supervised and supported, particularly during the research phase of the programme. The student will be monitored according to the progression milestones in the regulations for the Integrated PhD in a Named Subject and the Code of Practice for Research Candidature and Supervision.

View the programme specification document for this course

Programme Structure

All students will complete a one-year Masters level project chosen to prepare them for research. This will be delivered and assessed via the core module MATH6144 (15 ECTS/ 30 CATS).

Students will take a number of modules (comprising an additional 45 ECTS/90 CATS) from a range of modules, at least 30 ECTS/60 CATS of these must be at level 7. Up to 15 ECTS/30 CATS may be chosen from approved alternative modules in related cognate areas.

The selection of modules, dependent on existing knowledge and qualifications, will be chosen by the student in consultation with the supervisory team, and must be approved by the Doctoral Programme Director.

Entry Requirements

Typical entry requirements

International applications

In addition to the academic requirement those applicants for whom English is a second language may be required to demonstrate that they have achieved the equivalent of an IELTS score of at least 6.5 overall, with at least 6.0 in each component.

Mature applicants

Mature applicants are warmly encouraged to apply.

Accreditation of Prior (Experiential) Learning (AP(E)L)

The programme is not designed to provide for admission through AP(E)L.

English Language Proficiency (IELTS)
6.5 6.0 6.0 6.0 6.0
Selection process

Applicants must satisfy the general entry requirements as laid out in the Code of Practice for Research Candidature and Supervision and in particular they must have a first or upper second-class honours degree or equivalent in a discipline which provides relevant quantitative training (e.g. computer science, economics, engineering, mathematics, physics, and statistics).

This page contains specific entry requirements for this course. Find out about equivalent entry requirements and qualifications for your country.


Typical course content

All students will complete a one-year Masters level project chosen to prepare them for research.

Year 1

MMath Project

Modules are grouped into the following groups: Actuarial Sciences Pure and Applied Mathematics Operational Research Statistics Students are required to select 90 credits from one of these groups.

Actuarial Sciences

Actuarial Mathematics I
Financial Mathematics
Mathematical Finance
Actuarial Mathematics II
Stochastic Processes
Accounting and Finance for Actuarial Science

Pure and Applied Mathematics

Intro To Semigroup Theory
Differential Geometry and Lie Groups
Homotopy and Homology
Geometric Group Theory
Complex Function Theory
Gravitational Waves

Operational Research

Statistical Methods
Stochastic OR Methods
Case Studies
Multivariate Statistics for Data Mining
Deterministic OR Methods
Visual Basic for Applications


Statistical Computing
Statistical Theory and Linear Models
Bayesian Methods
Topics in Statistics
Applied Statistical Modelling
Clinical Trials

These modules are only indicative examples of the options available. There is a wide array of option modules to choose from, subject to availability.

Please note: This specification provides a concise summary of the main features of the programme and the learning outcomes that a typical student might reasonably be expected to achieve and demonstrate if s/he takes full advantage of the learning opportunities that are provided. More detailed information can be found in the programme handbook (or other appropriate guide or website).

Fees & funding

Tuition fees

Fees for postgraduate taught courses vary across the University. All fees are listed for UK, EU and international full-time and part-time students alphabetically by course name.

View the full list of course fees


Scholarships, bursaries, sponsorships or grants may be available to support you through your course. Funding opportunities available to you are linked to your subject area and/or your country of origin. These can be from the University of Southampton or other sources.

Explore funding opportunities

Costs associated with this course

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

There will also be further costs for the following, not purchasable from the University:

EquipmentApproved Calculators Candidates may use calculators in the examination room only as specified by the University and as permitted by the rubric of individual examination papers. The University approved model is Casio FX-570 This may be purchased from any source and no longer needs to carry the Universi-ty logo.
StationeryYou will be expected to provide your own day-to-day stationery items, e.g. pens, pencils, note-books, etc. Any specialist stationery items will be specified under the Additional Costs tab of the relevant module profile.
BooksWhere a module specifies core texts these should generally be available on the reserve list in the library. However due to demand, students may prefer to buy their own copies. These can be purchased from any source. Some modules suggest reading texts as optional background reading. The library may hold copies of such texts, or alternatively you may wish to purchase your own copies. Although not essential reading, you may benefit from the additional reading materials for the module.
OtherComputer Discs You may find it useful to purchase some USB memory sticks or other devices to store your per-sonal files. However these standalone devices may fail and therefore you should always take backups. As a student enrolled at the University you will be able to safe your own computer files on an account so that you can access them from multiple University computers. This is also con-sidered a safe way of keeping backups of all your files.
OtherSoftware Licenses Some modules may involve lab sessions or coursework where you practice certain specialised software products. The University will enable you to have access to such software without the need for you to pay for a software license.
OtherHardware You will be able to use University computers at various locations including the Library to write reports or interact with software programmes as necessary. It may be very useful for you to use your own laptop device for certain tasks if you want to work at your own preferred locations such as your home, but be aware that in case this device gets damaged you may lose valuable files – therefore it is important to always safe your work on your University student account as a backup in addition to saving any work on separate hardware devices in case you don’t have im-mediate access to your University account. Reporting failure of your own laptop is not a valid excuse to being late with e.g. a coursework submission!
Printing and copyingIn the majority of cases, coursework such as essays; projects; dissertations is likely to be submit-ted on line. However, there are some items where it is not possible to submit on line and stu-dents will be asked to provide a printed copy. A list of the University printing costs can be found here: For students undertaking modules with a high mathematical content, some assessed work will be submitted in handwritten hard copy format. Students are advised that they will need to bear the costs of the required stationery.
PlacementsYou may be offered the opportunity at the end of the taught programme to undertake a three month long summer project relevant to your programme. This may be in collaboration with an organisation. How expenses for traveling and accommodation are covered is dependent on the particular case and you may want to discuss this during semester 2 with the AU Industrial Liaison Officer.
OtherOptional Visits (e.g. museums, galleries) Some modules may include optional visits to a museum, galleries, businesses, etc. You will normally be expected to cover the cost of travel and admission, unless otherwise specified in the module profile.

In some cases you'll be able to choose modules (which may have different costs associated with that module) which will change the overall cost of a programme to you. Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at

Career Opportunities

With leading academics, a multidisciplinary approach and a superb record for the quality of our teaching and our research, Mathematical Sciences offers a vibrant and supportive environment for postgraduate students.

Mathematical Sciences has one of the broadest communities of mathematicians in the UK, spanning pure and applied mathematics, statistics and operational research. Our research includes internationally-recognised projects with partners in engineering, physical and biological sciences and social sciences. We place great importance on the development of graduate skills vital for future employment by adding transferrable skills into learning and teaching.

A PhD is recognised by employers across a wide range of sectors. Our postgraduate research students are highly sought after by other universities, business and industry, NGOs and governments worldwide.

Learning & Assessment

Study locations

Highfield Campus

Highfield Campus

Mathematics is based on the University's Highfield Campus in Building ...Find out more

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