Mathematics (Pure Mathematics)

Study mode:On campus Study type:Full-time Languages: English
Local:$ 11.1 k / Year(s) Foreign:$ 29 k / Year(s) Deadline: Jan 15, 2024
11 place StudyQA ranking:3098 Duration:3 years You need IELTS certificate

Photos of university / #imperialcollege

All  Mathematics students follow broadly the same programme of study in years one and two of their degree programmes. The specialist degree programmes are then tailored from year three onwards. Students studying the straight Mathematics programme can tailor their optional choices according to their own interests and therefore specialise in any way they choose.

We regularly revise our degree courses to keep them up to date and interesting. We also regularly review the structure of our course units to take account of changes happening in schools and the patterns of subjects offered by prospective undergraduates.

The programme of study consists mainly of half-unit, one-term components, eight of which are taken in each year. Most of these components are lecture courses that are examined primarily by written papers in the summer term. Others are examined wholly by submission of projects.

Teaching is in the form of lectures, problem classes and small study groups. You will also have a personal tutor for regular consultation about academic and personal matters.


Eight lecture courses are available, each of half-unit weighting. Currently, these are as follows:

  • Analysis I
  • Algebra I
  • Foundations of Analysis
  • Geometry and Linear Algebra
  • Mathematical Methods I
  • Mathematical Methods II
  • Mechanics
  • Probability and Statistics I

There is a practical course on Computation running through the first year programme, currently using Maple and Matlab. This is examined primarily by project.

Towards the end of the first year, you will complete an individual poster project, whose subject can be chosen from a range of topics suggested by a series of inspirational lectures. All posters are then exhibited together and you will explain your work to circulating staff and students, obtaining credit both for content and exposition.

All courses, computation and the project must normally be passed for progression to the second year of the programme.


There are currently 10 examined courses, of which you take eight. Seven courses are compulsory:

  • Algebra II
  • Complex Analysis
  • Differential Equations
  • Real Analysis
  • Multivariable Calculus
  • Introduction to Numerical Theory
  • Probability and Statistics II

You then choose one course from the following options:

  • Non-linear Waves
  • Metric Spaces and Topology
  • Statistical Modelling I

After examinations in the third term there is a group project that involves written and oral elements. The groups and the project allocation are arranged by the Department.

All courses and the project must normally be passed for progression to the third year of the programme.


A large selection of courses is available, each of half-unit weighting. These are in the areas of pure mathematics, mathematical physics, applied mathematics, mathematical methods, numerical analysis and statistics.

Some project courses and non-mathematical options from outside the Department are also available.


  • Philosophy I
  • Controversies and Ethical Dilemmas in Science and Technology
  • European History: 1870 – 1989
  • Politics
  • History of Science
  • Global History of Twentieth Century Things
  • History of Medicine
  • Music and Western Civilisation
  • Communicating Science: The Public and the Media
  • Humanities Essay
  • Creative Writing
  • Music Technology
  • Philosophies of Science: Theory, Society and Communications

Business School

  • Finance and Financial Management
  • Innovation Management
  • Managerial Economics

A key feature of our third and fourth year courses is flexibility. Some students remain broad in their interests, while others prefer to specialise. This is subject to timetabling restrictions and departmental approval. We provide a wide choice of courses so that our students have a range of options in which to specialise.

Below is the list of third and fourth year courses running in 2012-2013. Please note: not all course modules are offered at every session and the list described here is subject to change. Courses marked *are available at both third and fourth year.

Applied mathematics/mathematical physics/numerical analysis


  • Fluid Dynamics I *
  • Fluid Dynamics II *
  • Introduction to Geophysical Fluid Dynamics *
  • Hydrodynamic Stability
  • Vortex Dynamics
  • Asymptotic Analysis *


  • Dynamical Systems *
  • Chaos and Fractals *
  • Bifurcation Theory *
  • Ergodic Theory: Seminar Course
  • Advanced Dynamical Systems: Seminar Course
  • Geometric Mechanics I: Dynamics and Symmetry *
  • Geometric Mechanics II: Rotating, Translating and Rolling *
  • Integrable Systems


  • Mathematical Finance *


  • Mathematical Biology I: Molecular Topology and Stereochemistry *
  • Mathematical Biology of the Cell *

Mathematical physics:

  • Mathematical Physics I: Quantum Mechanics *
  • Special Relativity and Electromagnetism *
  • Tensor Calculus and General Relativity *
  • Partial Differential Equations *
  • Methods of Mathematical Physics *
  • Mathematical Physics II: Statistical Mechanics
  • Applied Stochastic Processes

Numerical analysis/computation:

  • Numerical Solution of Ordinary Differential Equations *
  • Computational Partial Differential Equations I *
  • Scientific Computation *

Pure mathematics


  • Probability *
  • Functional Analysis *
  • Fourier Analysis and Theory of Distributions *
  • Measure and Integration *
  • Analytic Methods in Partial Differential Equations
  • Stochastic Filtering
  • Introduction to Infinite Dimensional Analysis


  • Geometry of Curves and Surfaces *
  • Geometry I: Algebraic Curves *
  • Geometry II: Algebraic Topology *
  • Computational Algebra and Geometry *
  • Riemannian Geometry
  • Manifolds
  • Differential Topology
  • Complex Manifolds

Algebra and discrete mathematics:

  • Algebra III *
  • Group Theory *
  • Galois Theory *
  • Group Representation Theory *
  • Algebraic Combinatorics *
  • Groups and Representations
  • Lie Algebras
  • Commutative Algebra

Number theory:

  • Number Theory *
  • Algebraic Number Theory *
  • Analytic Number Theory *
  • Number Theory: Elliptic Curves


  • Statistical Theory I *
  • Statistical Modelling II *
  • Applied Probability *
  • Statistical Pattern Recognition *
  • Time Series *
  • Stochastic Simulation *
  • Games, Risks and Decisions *
  • Survival Models and Actuarial Applications *
  • Credit Scoring I *
  • Credit Scoring II *


Applicants for our courses are high-achieving students, with good qualifications and predicted grades.

Applicants to all our Mathematics courses (except joint Mathematics and Computer Science courses) must therefore sit an admissions test to allow us to have a common measure with which to benchmark all of our applicants, regardless of which qualifications they have, or have already achieved.

All UK and international applicants to our undergraduate Mathematics courses for 2014 entry must sit the Mathematics Admissions Test (MAT) as part of their application to Imperial.

The MAT is a paper-based, subject-specific admissions test which lasts 2.5 hours. For more information about the test, visit the Admission Testing Service's website. You must register for the test before taking it. Find out how to register for the test.

Applicants who are not able to take the Mathematics Admissions Test (MAT) will need to sit a Sixth Term Examination Paper (STEP). Such applicants must make it clear on their UCAS applications that they are taking either STEP II or STEP III.  They may be made our standard offer, with the additional requirement of a Grade 2 in either of these STEP papers.

In addition, candidates who have a borderline mark in their MAT paper may be considered for a STEP offer if they have indicated that they are taking STEP II or III on their UCAS form. Find out more about STEP (Sixth Term Examination Paper), which is also administered by ATS.


You are recommended to take an A-level combination that includes both Mathematics and Further Mathematics. Competition for places is intense, so your application will be stronger if you are studying subjects with a high mathematical content.

For Mathematics degrees (except joint Mathematics and Computer Science) the normal minimum entry requirement is:

  • A* in A-level Mathematics
  • A* in Further Mathematics
  • A in one other A-level (though not essential, strong candidates take Physics and/or Chemistry)

Although we do not require passes in specific subjects at GCSE level, we do expect candidates to have a broad education. This can be shown by passes in a suitable range of subjects at that level, and we would normally expect at least five of these to be at grade A or A*.

President's Undergraduate Scholarships

The President's Undergraduate Scholarships are the most prestigious awards the College has to offer. They are designed to reward students who demonstrate the highest academic excellence and potential.

They are funded entirely by philanthropic donations from generous alumni and supporters of the College. Scholars are invited to serve as ambassadors for the College.

There are 112 President's Undergraduate Scholarships available for students starting their studies in 2015–16.

Academic departments are responsible for nominating scholarship recipients as part of the admission process. All first time undergraduate applicants who have applied to the College by 15 October will be considered for these awards. 

Student Status Eligibility Open pre-enrolment only

Value £3,000 one off scholarship payment upon enrolment

All applicants are reviewed by their academic departments as part of the admission process and nominated on the basis of academic excellence and potential.

Duration 1 year

Selection Process

There is no seperate application process for these awards. Selection will be determined by departments' usual admissions processes.

Scholarships and bursaries

Both scholarships and bursaries are sources of funding offered by Imperial. In general, undergraduate scholarships are for those who are both academically excellent and/or in financial need, whereas postgraduate scholarships are primarily awarded based on academic excellence.

Bursaries are awarded based solely on financial circumstances.

Before applying

  1. You must quote your College Identifier (CID) number when corresponding with the College.

  2. The scholarships we offer are limited and highly competitive. You must have sufficient funding in place before enrolling on your course.

  3. Unless otherwise stated, the scholarships advertised are only available to prospective students applying for full-time courses.

  4. The award period will generally commence on the first day of the academic year which you have applied for (e.g. 1 October 2012).

  5. Scholarship applications will only be considered following an offer of admission. Only if you fulfil all the eligibility criteria (that is, if you meet the requirements) of the scholarship, will you be considered.

  6. If there is no separate scholarship application form to be submitted, we will use your admission application form and references provided. These documents may therefore also be passed to stakeholders involved in the selection process.

  7. Please do not send in supporting documents unless the scholarship application process specifically asks you to do so.

  8. Funding deadlines are strictly adhered to and any application received after the closing date will not be accepted.

Successful award recipients

9. Agreeing to these terms and conditions and supplying your UK bank details

a) All scholarship and bursary payments will be made to the UK bank account details held on your Student e-Service account. You are able to log into your Student e-Service account and make changes to your bank details at any time after you’ve accepted your admissions offer.
b) By submitting your bank details via the Student Funding tab in Imperial’s Student e-Service portal, and/or bursary form, you are confirming that you agree with the terms and conditions of the award.
c) It may take a few weeks to set up your bursary payments and your UK bank account (if applicable); therefore you should bring sufficient funds to cover your living expenses during this time. Initial payment dates may vary; it is your responsibility to ensure you are aware of when payments will be made.
d) The award is subject to you fulfilling any outstanding conditions of admission.
e) Funds will only be released in line with your registration at College and you will need to ensure your bank details are up to date.
f) Payment Dates: Payments are normally made on the 7th day of each month; bank details should be updated before the 24th day of the preceding month to ensure payment is not delayed. Undergraduate payments will commence from 7th November. Postgraduate payments will commence on the 7th of the month following your registration.

10. Please make sure that you have completed all the steps necessary to register for the academic year in which you wish to receive payment. Please note that new award holders will also need to have fulfilled all of their conditions of offer before they are able to register.

11. All Imperial scholarships are subject to satisfactory academic progression. If the duration of your scholarship is longer than 12 months, it will be renewable annually.

12. Awards will not generally be made to those already holding a full scholarship from another source; please inform Student Financial Support, and/or any other department which has offered you an award, immediately if you are granted more than one award, even if you have already accepted our award. If you wish to hold several partial awards concurrently, this will be considered on a case-by-case basis.

13. Scholarships are not generally awarded to students who are writing-up.

14. Applicants wishing to study at UK partner institutions are not eligible for Imperial College London scholarships.

15. Undergraduate Financial Support / Imperial Bursary Package

a) To be eligible to receive an Imperial Bursary you must have been assessed for means tested funding from Student Finance England (or equivalent funding authority) and have a household income below the Imperial household income threshold for your cohort. You must contact us if this is not the case. Any previous study may affect your entitlement.
b) The College reviews household income information (which it receives from Student Finance England, etc.) on a continuous basis. A change in your household income may result in a change in your Imperial Bursary. Any overpayments will be reclaimed.
c) The Imperial Bursary is available for each year of your course excluding repeat years of study and NHS funded years for Medical courses. If you change from a 3 year to a 4 year course at Imperial you will be awarded a further year’s bursary. You should contact us about any course changes as soon as possible.
d) Students on paid placements might not be eligible for the Imperial Bursary.
e) To be eligible for the Imperial Bursary, we must receive your household income from the Student Loans Company by 1 May following the start of your academic year.

16. If you have been offered funding by the Research Councils, please ensure that you have read the most up-to-date postgraduate funding guide; you will need to adhere to the terms and conditions laid out there.

17. Deferrals, withdrawals and interruption of studies

a) You must inform the Student Financial Support team immediately of any interruptions to your study, particularly if they are likely to affect your attendance and registration status at College.
b) If you withdraw from your course or take an interruption of study (IOS) you must notify us immediately by contacting us here. If you take an IOS your bursary will be postponed until you re-register.
c) Bursaries and scholarships are not transferable. If you transfer to another institution or withdraw from the College, any payments due to you will be cancelled and any overpayments are recoverable.
d) We will not provide scholarship or bursary support for any period of repeat study.
e) Awards cannot be deferred.

18. Student Financial Support may at any time, at their discretion, withdraw or recover an award for breach of any of the above conditions.

19. The College reserves the right to place a limit on financial support where a student is in receipt of other funding.

20. Information on students is shared within the Imperial College community and donors (where applicable and relevant to your award) in accordance with the Data Protection Act 1998.

a) Where awards have specific eligibility criteria (e.g. satisfactory academic progression), supporting evidence may be shared with named donors in order to verify continued eligibility.
b) Award recipients may be expected to meet with donors.

21. If you are in receipt of an award to study that is restricted to students on the basis of nationality or residency; please note that, in accordance with the Equality Act 2010, you must not intend to exercise in Great Britain skills you have obtained as a result of your training at the College and you must not be ordinarily resident in an EEA state.

22. These terms and conditions are the formal rules which regulate centrally funded awards. As such, there are no appeal procedures associated with funding from the Student Financial Support team.

Thermo Fisher Scholarship

Student Status EligibilityValue Required    
Open pre-enrolment only
Value - $5000
Number AvailableValue Required - 8
Further Eligibility Criteria InformationValue Required    
This scholarship is available to HOME applicants who have received a conditional firm or unconditional offer from Imperial College by the published deadline. Only available to Chemical Engineering, Bioengineering, Earth, Science and Engineering, Materials, Mechanical Engineering, Chemistry, Life Sciences and Mathematics students only.
Your household income must also have been assessed to be £60,000 or less by your government funding authority (e.g. Student Loans Company).
 Duration Value Required    
Maximum of 4 years
Application Deadline DateValue Required    

How to apply
 There is no separate application form that you need to complete in order to apply for this scholarship. 
  Your department will assess your academic merit from your UCAS form and your predicted A-Level results, and will select the best candidate as the scholar.  Each Department will be allocated one award. 
Value of the Award
The successful Scholars will receive a cash bursary (the equivalent in £GBP) of $5,000 per annum. The award is for a maximum of 4 years, excluding repeat periods of study.

Outcome of the Award
The successful candidate will be notified by email no later than 4 July 2015.  If you have not heard from us by this date please assume you have been unsuccessful in your application.
Please note that the successful scholar will be expected to meet informally with the donors on occasions, and will be required to submit a short statement of progress each year that will be shared with the donors.
This award is for students starting in the academic year 2015-16 and cannot be deferred.

Similar programs:
Study mode:Blended Languages: English
Local:$ 11.1 k / Year(s) Foreign:$ 32.1 k / Year(s)
Deadline: Jan 15, 2024 11 place StudyQA ranking: 2380 You need IELTS certificate
Study mode:Blended Languages: English
Local:$ 11.1 k / Year(s) Foreign:$ 32.1 k / Year(s)
Deadline: Jan 15, 2024 11 place StudyQA ranking: 1720 You need IELTS certificate
Study mode:On campus Languages: English
Local:$ 9 k / Year(s) Foreign:$ 10.4 k / Year(s)
601–800 place StudyQA ranking: 1008 You need IELTS certificate
Study mode:On campus Languages: English
Local:$ 2.06 k / Year(s) Foreign:$ 12.6 k / Year(s)
Deadline: Jan 15, 2024 201–250 place StudyQA ranking: 932 You need IELTS certificate
Study mode:On campus Languages: English
Local:$ 10.6 k / Year(s) Foreign:$ 14.4 k / Year(s)
Deadline: Jan 15, 2024 200 place StudyQA ranking: 1522 You need IELTS certificate
Study mode:On campus Languages: English
Local:$ 2.06 k / Year(s) Foreign:$ 12.6 k / Year(s)
Deadline: Jan 15, 2024 201–250 place StudyQA ranking: 1147 You need IELTS certificate
Study mode:On campus Languages: English
Local:$ 9 k / Year(s) Foreign:$ 12 k / Year(s)
Deadline: Jan 15, 2024 301–350 place StudyQA ranking: 839 You need IELTS certificate
Study mode:On campus Languages: English
Local:$ 9 k / Year(s) Foreign:$ 12 k / Year(s)
Deadline: Jan 15, 2024 301–350 place StudyQA ranking: 855 You need IELTS certificate