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 2021 entry is A*A*A overall, to include:

• A* in Mathematics
• A* in Further Mathematics
• A in another subject (Chemistry and Physics are preferred)

General Studies and Critical Thinking are not accepted.

Typical offer range

As a guide, here are the typical offers made to at least 80% of A-level applicants for 2019 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

There is no formal language requirement our Year in Europe degree, however applicants may be required to demonstrate a basic competence in a required language.

These requirements are different to entry requirements, as you will often have the opportunity to work towards the necessary criteria in your time at university, up to the third year of this course.

As a guide a basic competency would equate to:

• A Level Grade C
• AS Level Grade B
• GCSE Grade A

If you can demonstrate that you are fluent in the language you do not need a formal language qualification.

Language courses are available in the College for all students, and are ideal for those who need to improve their standard.

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 2021 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 2019 entry was 39-40 points overall.

Language requirement

There is no formal language requirement our Year in Europe degree, however applicants may be required to demonstrate a basic competence in a required language.

These requirements are different to entry requirements, as you will often have the opportunity to work towards the necessary criteria in your time at university, up to the third year of this course.

As a guide a basic competency would equate to:

• A Level Grade C
• AS Level Grade B
• GCSE Grade A

If you can demonstrate that you are fluent in the language you do not need a formal language qualification.

Language courses are available in the College for all students, and are ideal for those who need to improve their standard.

Mathematics Higher Level for award in 2021

For entry in 2021, 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 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

You may also require a relevant language qualification for this year abroad degree.

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 prior 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.

Interview policy

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.

Pilot admissions schemes (Home students)

From 2020 entry, we will be using information about our applicants in a number of new pilot admissions schemes, to consider the wider context of Home students from groups underrepresented at the College.

More about pilot admissions schemes

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:

• 70% 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 Mathematics, international students studying Warwick IFP Science and Engineering must achieve:

• 70% overall
• 80% Mathematics
• 80% Chemistry or Physics

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

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

• Life Sciences 
• Computer Science 
• Mathematics & Statistics 
• Economics 
• Physical Sciences 
• Engineering 

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

2021 entry

£9,250 per year.

Year in Europe

£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 2022 will apply to fees for the academic year 2022–2023.

Fee status

Whether you pay the Home fee 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.

EU/EEA/Swiss students

The Government has confirmed that EU/EEA/Swiss students who begin a course before the 31 July 2021 will be eligible to pay the same fee as Home students and have access to student finance for the duration of their course, as long as they meet certain requirements which are unchanged from previous years. This includes students who begin the course remotely.

EU/EEA/Swiss students starting a course on or after 1 August 2021 will no longer be eligible for the Home fee rate and so will be charged the Overseas fee. Please note we do not expect this to apply to Irish students or students benefitting from Citizens' rights under the EU Withdrawal Agreement, EEA EFTA Separation Agreement or Swiss Citizens’ Rights Agreement respectively. However, we are currently awaiting the formal publication of the amended Fees and Awards regulations.

The UK Council for International Student Affairs (UKCISA) website has useful information on the conditions you currently need to meet to be entitled to pay tuition fees at the Home rate for study on a higher education course in England and reflect the regulations as they currently stand (not the amended regulations which are subject to publication). 

UKCISA has also provided some information in response to Questions for students starting their course from the 1 August 2021.

For regular updates for EU students, please see our Imperial and the EU webpages.

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.

2021 entry

£9,250 per year.

Year in Europe

£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 2022 will apply to fees for the academic year 2022–2023.

Fee status

Whether you pay the Home fee 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.

EU/EEA/Swiss students

The Government has confirmed that EU/EEA/Swiss students who begin a course before the 31 July 2021 will be eligible to pay the same fee as Home students and have access to student finance for the duration of their course, as long as they meet certain requirements which are unchanged from previous years. This includes students who begin the course remotely.

EU/EEA/Swiss students starting a course on or after 1 August 2021 will no longer be eligible for the Home fee rate and so will be charged the Overseas fee. Please note we do not expect this to apply to Irish students or students benefitting from Citizens' rights under the EU Withdrawal Agreement, EEA EFTA Separation Agreement or Swiss Citizens’ Rights Agreement respectively. However, we are currently awaiting the formal publication of the amended Fees and Awards regulations.

The UK Council for International Student Affairs (UKCISA) website has useful information on the conditions you currently need to meet to be entitled to pay tuition fees at the Home rate for study on a higher education course in England and reflect the regulations as they currently stand (not the amended regulations which are subject to publication). 

UKCISA has also provided some information in response to Questions for students starting their course from the 1 August 2021.

For regular updates for EU students, please see our Imperial and the EU webpages.

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.

2021 entry

£9,250 per year.

Year in Europe

£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 2022 will apply to fees for the academic year 2022–2023.

Fee status

Whether you pay the Home fee 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.

EU/EEA/Swiss students

The Government has confirmed that EU/EEA/Swiss students who begin a course before the 31 July 2021 will be eligible to pay the same fee as Home students and have access to student finance for the duration of their course, as long as they meet certain requirements which are unchanged from previous years. This includes students who begin the course remotely.

EU/EEA/Swiss students starting a course on or after 1 August 2021 will no longer be eligible for the Home fee rate and so will be charged the Overseas fee. Please note we do not expect this to apply to Irish students or students benefitting from Citizens' rights under the EU Withdrawal Agreement, EEA EFTA Separation Agreement or Swiss Citizens’ Rights Agreement respectively. However, we are currently awaiting the formal publication of the amended Fees and Awards regulations.

The UK Council for International Student Affairs (UKCISA) website has useful information on the conditions you currently need to meet to be entitled to pay tuition fees at the Home rate for study on a higher education course in England and reflect the regulations as they currently stand (not the amended regulations which are subject to publication). 

UKCISA has also provided some information in response to Questions for students starting their course from the 1 August 2021.

For regular updates for EU students, please see our Imperial and the EU webpages.

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.

2021 entry

£9,250 per year.

Year in Europe

£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 2022 will apply to fees for the academic year 2022–2023.

Fee status

Whether you pay the Home fee 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.

EU/EEA/Swiss students

The Government has confirmed that EU/EEA/Swiss students who begin a course before the 31 July 2021 will be eligible to pay the same fee as Home students and have access to student finance for the duration of their course, as long as they meet certain requirements which are unchanged from previous years. This includes students who begin the course remotely.

EU/EEA/Swiss students starting a course on or after 1 August 2021 will no longer be eligible for the Home fee rate and so will be charged the Overseas fee. Please note we do not expect this to apply to Irish students or students benefitting from Citizens' rights under the EU Withdrawal Agreement, EEA EFTA Separation Agreement or Swiss Citizens’ Rights Agreement respectively. However, we are currently awaiting the formal publication of the amended Fees and Awards regulations.

The UK Council for International Student Affairs (UKCISA) website has useful information on the conditions you currently need to meet to be entitled to pay tuition fees at the Home rate for study on a higher education course in England and reflect the regulations as they currently stand (not the amended regulations which are subject to publication). 

UKCISA has also provided some information in response to Questions for students starting their course from the 1 August 2021.

For regular updates for EU students, please see our Imperial and the EU webpages.

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.