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

Core modules

• Analysis 2
• Group Research Project
• Groups and Rings
• Lebesgue Measure and Integration
• Linear Algebra and Numerical Analysis
• Multi-variable Calculus and Differential Equations
• I-Explore module

Optional modules

You choose two modules from below.

• Network Science
• Partial Differential Equations in Action
• Principles of Programming
• Probability for Statistics
• Statistical Modelling 1

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

Optional modules

A large selection of optional modules are available in your third year, including modules specifically required for your stream of study. 

You will choose at least five modules from Group A to graduate with a Pure Mathematics degree. In addition, you will be able to choose a further three or four modules, depending on the number of ECTS credits awarded. This may include Group B modules, modules available in Year 2, and at most one offered by other departments.

Group A

• Algebra 3
• Algebraic Combinatorics
• Algebraic Number Theory
• Algebraic Topology
• Functional Analysis
• Galois Theory
• Geometric Complex Analysis
• Group Representation Theory
• Group Theory
• Markov Processes
• Mathematical Logic
• Number Theory
• Probability Theory

Group B

Group B modules are a number of examples of optional modules you may choose from in addition to the required modules (above) for this specialist degree.

• Advanced Topics in Partial Differential Equations
• Applied Complex Analysis
• Applied Probability
• Asymptotic Methods
• Bifurcation Theory
• Communicating Mathematics
• Computational Linear Algebra
• Computational Partial Differential Equations
• Consumer Credit Risk Modelling
• Dynamical Systems
• Dynamics of Games and Learning
• Finite Elements: Numerical Analysis and Implementation
• Fluid Dynamics 1
• Fluid Dynamics 2
• Function Spaces and Applications
• High Performance Computing
• Introduction to Geophysical Fluid Dynamics
• Mathematical Biology
• Mathematical Finance: An Introduction to Option Pricing
• Mathematics of Business and Economics
• Mathematics Research Project
• Methods for Data Science
• Numerical Solutions of Ordinary Differential Equations
• Quantum Mechanics 1
• Quantum Mechanics 2
• Scientific Computing
• Special Relativity and Electromagnetism
• Statistical Modelling 2
• Statistical Theory
• Stochastic Simulation
• Survival Models
• Tensor Calculus and General Relativity
• Theory of Complex Systems
• Time Series Analysis

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.

Imperial Horizons, Business School and modules from other departments

You may choose at most one module offered outside the Department through the Imperial Horizons programme (Imperial Horizons), the Business School (Business for Professional Engineers and Scientists), or another Department (subject to approval) for credit as part of your eight optional modules in your third year.

The Department of Mathematics approves a selection of the modules offered through these programmes, which means there are some modules you can take for credit.

Modules approved by the Department for credit are subject to change annually, but in the past have included modules such as:

• Finance and Financial Management
• Managing Innovation
• Music Technology
• Science, Politics and Human Identity

Minimum entry standards

Our minimum entry standard for 2022 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.

Typical offer range

As a guide, here are the typical offers made to at least 80% of A-level applicants for 2020 entry:

• Three A-level offer: A*A*A-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.

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 new 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 2022 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 2020 entry was 39-40 points overall.

Mathematics Higher Level for award in 2022

For entry in 2022, 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

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.

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:

• 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 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
  

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

2022 entry

£9,250 per year.

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.

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.

2022 entry

£34,000 per year.

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 Overseas 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.

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].

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.