Core modules

• Introduction to University Mathematics
• Analysis 1
• Linear Algebra and Groups
• Calculus and Applications
• Probability and Statistics
• Introduction to Computation
• An Introduction to Applied Mathematics
• Individual Research Project
• Language Classes (if required)

Language module

You will have a meeting with the Centre for Languages, Culture and Communication soon after beginning your degree at Imperial to establish your ability in the relevant language.

There are different levels of language modules available depending on your ability, and you are normally expected to pass level three by the end of your second year. Some students will not be required to take language classes, for instance if you are fluent in a relevant langauge.

Your language module will be taken for credit but not counted toward your final degree grade.

List of language modules

Core modules

• Linear Algebra and Numerical Analysis
• Analysis 2
• Multi-variable Calculus and Differential Equations
• Group Research Project
• I-Explore module
• Language Classes (if required)

Optional modules

You choose four modules from below.

• Groups and Rings
• Lebesgue Measure and Integration
• Probability for Statistics
• Statistical Modelling 1
• Network Science
• Partial Differential Equations in Action
• Principles of Programming

Optional modules may be prerequisites for modules in later years. You will be advised about such dependencies before making your choices.

Language module

You will have a meeting with the Centre for Languages, Culture and Communication soon after beginning your degree at Imperial to establish your ability in the relevant language.

There are different levels of language modules available depending on your ability, and you are normally expected to pass level three by the end of your second year. Some students will not be required to take language classes, for instance if you are fluent in a relevant langauge.

Your language module will be taken for credit but not counted toward your final degree grade.

List of language modules

If you are required to take a language module as part of the Year Abroad requirements, this will most likely be taken as the required I-Explore module.

Opportunities

The third year consists of an agreed programme of study at an approved university in either France, Germany, Spain, Switzerland or the USA. We currently have exchange agreements with:

• University of Grenoble, France
• Humboldt University, Germany
• Autonomous University of Madrid, Spain
• EPF Lausanne, Switzerland
• ETH Zurich, Switzerland
• MIT, USA

This is an integrated year abroad so the grades you achieve will count directly towards your Imperial degree.

Conditions

Language proficiency

Teaching is in the language of your host country in France, Germany and Spain, so you will need to reach an acceptable proficiency in the relevant language before you go. Free language classes are available at the College to help you prepare.

Availability

There are limited places available on the Year Abroad programme, which means that competition for selection is strong and a placement cannot be guaranteed.

Normally only students who are on track for at least a 2:1 will be eligible for placements in France and Germany. Only students on track to achieve a 1st will be eligible for placements in Singapore and the USA.

Other

• Please note the above is an illustrative list of universities located abroad which the Department is currently partnered with. Partnerships with universities are subject to continuous review and individual partnerships may or may not be renewed.
• There may be limitations placed upon your ability to live and study in these locations. If applicable you will need to successfully apply for the relevant visa. This applies to all students, including Home students, in light of the UK's decision to leave the European Union. Find the latest information on Imperial and the EU.
  • Study abroad placements in Europe are currently available through the Erasmus scheme. Imperial College now has approval to continue implementing its 2020-21 Erasmus project into 2021-22. Find the latest information on the Erasmus scheme.
  • This department is taking part in the Imperial College London–Massachusetts Institute of Technology (MIT) student exchange pilot. Find out more about the study abroad opportunities that will be created through this two-year pilot, which launched in 2018.

Core module

• Mathematics Research Project

Optional modules

You choose six optional modules from Group A in your fourth year.

Group A

• Advanced Dynamical Systems
• Advanced Topics in Partial Differential Equations
• Algebra 3
• Algebra 4
• Algebraic Combinatorics
• Algebraic Number Theory
• Algebraic Topology
• Analytic Methods in Partial Differential Equations
• Applied Complex Analysis
• Applied Probability
• Asymptotic Methods
• Bifurcation Theory
• Computational Linear Algebra
• Computational Partial Differential Equations
• Consumer Credit Risk Modelling
• Differential Topology
• Dynamical Systems
• Dynamics of Games and Learning
• Elliptic Curves
• Finite Elements: Numerical Analysis and Implementation
• Fluid Dynamics 1
• Fluid Dynamics 2
• Function Spaces and Applications
• Functional Analysis
• Galois Theory
• Geometric Complex Analysis
• Group Representation Theory
• Group Theory
• High Performance Computing
• Hydrodynamic Stability
• Infinite Groups
• Introduction to Geophysical Fluid Dynamics
• Markov Processes
• Mathematical Biology
• Mathematical Finance: An Introduction to Option Pricing
• Mathematical Logic
• Mathematics Research Project
• Methods for Data Science
• Modular Representation Theory
• Number Theory
• Numerical Solutions of Ordinary Differential Equations
• Probability Theory
• Quantum Mechanics 1
• Quantum Mechanics 2
• Random Dynamical Systems and Ergodic Theory
• Scientific Computing
• Special Relativity and Electromagnetism
• Statistical Modelling 2
• Statistical Theory
• Stochastic Differential Equations
• Stochastic Simulation
• Survival Models
• Tensor Calculus and General Relativity
• Theory of Complex Systems
• Time Series Analysis
• Vortex Dynamics

The list gives you an idea of the optional modules that you may be able to choose from, not the exact modules that will be offered. You may only take the same module once, even if offered in different years and at different levels. Modules from other departments may be allowed with permission.

Minimum entry standards

Our minimum entry standard for 2023 entry is A*A*A overall, to include:

• A* in Mathematics
• A* in Further Mathematics
• A in another subject

General Studies and Critical Thinking are not accepted.

Students taking English exam board science A-levels will be required to pass the practical endorsement.

Typical offer range

As a guide, here are the typical offers made to at least 80% of A-level applicants for 2021 entry:

• Three A-level offer: A*A*A
• Four A-level offer: A*A*AA

Practical endorsement (practical science assessment)

If you are made an offer you will be required to achieve a pass in the practical endorsement in all science subjects that form part of the offer.

The practical endorsement is part of the reformed English linear A-levels.

Language requirement

GCSE grade B/6 in an appropriate modern foreign language

Further Mathematics

We are able to make special cases for students who are from schools that do not offer Further Mathematics A-level, and encourage applications from them. We are often guided by performance in MAT when making these special cases. You should ask your teacher to clearly indicate this in your UCAS application form. If your school offers Further Mathematics AS but not A level, then we expect that you should be taking it.

Additional Mathematics support

Our A-level Mathematics online course covers a range of key topic areas to help you gain a deeper understanding of the skills and techniques required to succeed in your A-level Mathematics exams.

This optional course has been built around the A-level syllabus with the aim of developing your thinking skills, fluency and confidence.

Please note: this course is not compulsory and does not form part of the entry requirements for this course. It is available free of charge via the EdX website. It is self-paced so you can start it at any time.

Minimum entry standards

Our minimum entry standard for 2023 entry is 39 points overall, to include:

• 7 in Mathematics at higher level
• 6 in another subject at higher level

Typical offer range

As a guide, the typical offer made to at least 80% of IB applicants for 2021 entry was 39-40 points overall.

Language requirement

An appropriate modern foreign language grade 2 higher level, or grade 3 standard level.

Mathematics Higher Level

The Mathematics Analysis and Approaches or the Applications and Interpretation syllabi will be accepted at higher level, but Analysis and Approaches is preferred.

Additional Mathematics support

We have recently launched an A-level Mathematics online course, which is available free of charge via the EdX website.

Although this optional course has been built around the A-level syllabus, it is relevant to your curriculum too.

Please note: this course is not compulsory and does not form part of the entry requirements for this course. It is self-paced so you can start it at any time.

The grades detailed below are the minimum requirements for students offering only Advanced Placements as their exams for entry to Imperial.

If you are studying a High School Diploma that is accepted by Imperial alongside Advanced Placements, requirements may apply to both your Diploma and Advanced Placements.

Please consult our country index to check whether we accept your High School Diploma programme for admission.

Our minimum requirement for this course is grades 5, 5, 5 to include:

• 5 in Calculus BC
• 5 in Chemistry, Physics C (Electricity and Magnetism, or Mechanics), Statistics or Computer Science
• 5 in another subject

Language requirement

An appropriate modern foreign language grade 2 Advanced Placement, or grade B in year 12 of a USA High School Graduation Diploma.

Additional Mathematics support

We have recently launched an A-level Mathematics online course, which is available free of charge via the EdX website.

Although this optional course has been built around the A-level syllabus, it is relevant to your curriculum too.

Please note: this course is not compulsory and does not form part of the entry requirements for this course. It is self-paced so you can start it at any time.

Places will also be available to those with other equivalent qualifications, e.g. Abitur, Diploma Di Esame Di Stato, European Baccalaureate, Scottish Highers, Titullo de Bachiller, and to applicants with appropriate educational experience or other competencies. See admission of students with other competencies.

Mathematics Admissions Test (MAT)

All candidates who apply up to 15 October are required to sit the Mathematics Admissions Test (MAT). The MAT allows us to have a common measure with which to benchmark all our applicants, regardless of which qualifications they are taking as well or those they already have.

The MAT is a paper-based, subject-specific admissions test which lasts 2.5 hours and takes place in early November. 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 may request their MAT result from April onwards the year after their test sitting. A request must be made in writing to ugmaths.admissions@imperial.ac.uk and confirm your full name, UCAS ID and MAT registration number.

Sixth Term Examination Paper (STEP)

Conditional offers to post-15 applicants who were unable to take MAT will include a STEP requirement. This may also be applied to conditional offers to applicants taking other qualification types.

Our minimum STEP offer is a Grade 2 in either the STEP II or STEP III papers. Both the grade and the number of papers may be increased in some cases.

In addition, some MAT candidates who have a borderline mark may be considered for a STEP offer and that offer may also be increased. Find out more about STEP (Sixth Term Examination Paper), which is also administered by ATS.

Assessing your application

Admissions Tutors consider all the evidence available during our rigorous selection process and the College flags key information providing assessors with a more complete picture of the educational and social circumstances relevant to the applicant. Some applicants may be set lower offers and some more challenging ones.

Interviews

We don't currently use interviews as part of our regular admissions process.

We may consider students for interview where there are mitigating circumstances that need investigating, or where the background of the student means that their application requires further consideration. In these cases, our conditional offer may change as a result of the interview, and as with all candidates, each application is considered on its individual merits.

A foundation course is a one-year preparation course, designed for international students, which leads to undergraduate programmes in the UK. Foundation programmes are normally for school-leavers who have studied a non-British curriculum but wish to pursue a degree at a UK university.

Foundation programmes are offered by many UK universities, but only two would be considered for entry to Imperial: 

1. UCL’s Undergraduate Preparatory Certificate for Science and Engineering (UPCSE), and 
2. Warwick’s International Foundation Programme (IFP) in Science & Engineering

UCL UPCSE

A year-long programme for international students whose school leaving qualifications do not allow them direct entry to UK universities. Students must complete four modules across the year – two compulsory and two elective modules:

To be considered for admission to Mathematics, international students studying UCL UPCSE must achieve:

• 80% overall
• 80% Mathematics
• 80% Chemistry or Physics

Grade 2 in Step 2 or Step 3 may also be required

Warwick IFP Science and Engineering

A year-long programme for international students whose school leaving qualifications do not allow them direct entry to UK universities. 

To be considered for admission to the Department of Computing, international students studying Warwick IFP Science and Engineering must achieve:

• 80% overall
• 80% Mathematics, Physics and Computer Science or 80% Mathematics, Statistics and Further Mathematics, and Computer Science or 80% Mathematics, Statistics and Further Mathematics, and Mathematical Modelling and Interdisciplinary Mathematics
• A modern foreign language at Common European Framework of Reference for Languages (CEFR) A2+

To meet these requirements, students should choose from the following IFP pathways:

• Computer Science 
• Mathematics & Statistics 
• Engineering 

We want to make sure that the Imperial learning community is as diverse as the society we serve. So to make our admissions process as fair as possible, we have introduced admissions schemes for Home students that allow us to consider your application in the full context of any additional barriers you may face.

Find out if you meet the eligibility criteria for our contextual admissions schemes. 

If you meet the minimum contextualised Maths Admission Test (MAT) score, the Department of Mathematics will guarantee you an offer at the Department’s minimum of of A*A*A at A-level or an equivalent level qualification.

Read more about the contextual admissions scheme in this department and others.

All candidates must demonstrate a minimum level of English language proficiency for admission to the College.

For admission to this course, you must achieve the higher College requirement in the appropriate English language qualification. For details of the minimum grades required to achieve this requirement, please see the English language requirements for undergraduate applicants.

An ATAS certificate is not required for overseas students who apply for this course.

For more information about the Academic Technology Approval Scheme (ATAS), please see the International Student Support website.

View our terms and conditions on visas.

Our competence standards highlight the core skills students should be able to demonstrate by the end of this course.

View the Department of Mathematics' competence standards [PDF]

We believe in providing the widest practicable access to all of our degree programmes and will make reasonable adjustments wherever possible to support your study. For more information, please contact the Department using the contact details below.

Department of Mathematics

T: +44 (0)20 7594 8484
E: ugmaths.admissions@imperial.ac.uk

2023 entry

£9,250 per year.

Please note, this fee is set by the UK government and is subject to change until it has passed into legislation. We will update this page when this happens.

Year in Europe

For the 2022-23 year in Europe, the fee was £1,385 for that year.

Read more about funding for year abroad placements.

For each subsequent year, you should expect and budget for your tuition fee to increase by an amount in line with inflation. The measure of inflation used will be the Retail Price Index (RPIX) value, taken from April in the calendar year in which the academic session starts.

For example, the RPIX value in April 2023 will apply to fees for the academic year 2023–2024.

Fee status

Whether you pay the Home fee or not depends on your fee status.

Your fee status is assessed based on UK Government legislation and includes things like where you live and your nationality or residency status.

Find out more about how we assess your fee status.

Home fee eligibility

You can find the conditions you need to meet to pay the Home rate of tuition fees from the UK Council for International Student Affairs (UKCISA). These apply to higher education courses in England and reflect the regulations as they currently stand, noting that these are subject to amendment.

Because of the UK’s exit from the European Union, some frameworks of eligibility have been amended. Individuals affected by the amended frameworks should refer to the UKCISA publication, Who pays ‘home’ fees for higher education in England [PDF].

Government funding

If you're a Home student, you can apply for a Tuition Fee Loan from the UK government to cover the entire cost of tuition for every year of your course.

You can also apply for a means-tested Maintenance Loan to help towards your living costs.

2023 entry

The fee for Overseas students has not been confirmed for the 2023-24 academic year. The fee is controlled by the College and we will update this page when it is announced.

As a guide, the Overseas fee for 2022-23 was £34,000.

Year in Europe

For the 2022-23 year in Europe, the fee was 100% of the relevant fee for that year.

Read more about funding for year abroad placements.

For each subsequent year, you should expect and budget for your tuition fee to increase by an amount in line with inflation. The measure of inflation used will be the Retail Price Index (RPIX) value, taken from April in the calendar year in which the academic session starts. For example, the RPIX value in April 2023 will apply to fees for the academic year 2023–2024.

Fee status

Whether you pay the Overseas fee or not depends on your fee status.

Your fee status is assessed based on UK Government legislation and includes things like where you live and your nationality or residency status.

Find out more about how we assess your fee status.

Home fee eligibility

You can find the conditions you need to meet to pay the Home rate of tuition fees from the UK Council for International Student Affairs (UKCISA). These apply to higher education courses in England and reflect the regulations as they currently stand, noting that these are subject to amendment.

Because of the UK’s exit from the European Union, some frameworks of eligibility have been amended. Individuals affected by the amended frameworks should refer to the UKCISA publication, Who pays ‘home’ fees for higher education in England [PDF].

This section outlines additional costs relevant to this course. These are not included in your tuition fees. It's possible that all, or only some, of these will be relevant to you.

Figures are approximated, usually based on costs in the most recent academic year. They are likely to change each year but it's useful for you to be aware of the things you may have to pay for. This can help you budget for life at Imperial.

Mandatory costs are those that you will need to pay to fully participate in and complete your studies. Optional costs are not essential to your studies so you can opt-out of these.

Placements and year abroad

If you are undertaking a placement or year abroad, you may have to consider the costs involved. These will vary, depending on the location of your year abroad or placement.

Costs may include flights, transport, visas, travel insurance, health insurance and living expenses such as accommodation.

Find out more about the types of placement costs

Student status with the Year Abroad

If you spend an academic year abroad, you will retain your student status at Imperial so that you will normally remain eligible for the same loans and grants that you would receive in the UK. As an exchange student, you will not pay tuition fees to the host institution abroad.

Living costs, including accommodation, are not included in your tuition fees.

Most Imperial undergraduates choose to live in our halls of residence in their first year. You can compare costs across different accommodation options.

Read our rough guide to university spending in London.