Mathematics

Gain an in-depth understanding of a key area of our research, such as geometry, analysis, algebra and number theory.

Key information

Award

BSc

Duration

3 years

full-time

Minimum entry

Three A-level offer: A* A* A

See full entry requirements

Applications : admissions ratio

12 : 1

Based on 2020 entry data

  • UCAS course code: G125
  • ECTS: 180
  • Start date: October 2022

Virtual Open Week: Imperial360 Live

Join our mailing list to find out when bookings open for our Virtual Open Week (Monday 21 to Saturday 26 June 2021).

Overview

Mathematics at Imperial aims to present a wide range of mathematical ideas in a way that develops your critical and intellectual abilities.

The Department is home to several Fellows of the Royal Society and international prize winners, and our degrees are built around our research expertise in four core areas:

  • Pure Mathematics
  • Applied Mathematics and Mathematical Physics
  • Mathematical Finance
  • Statistics

Mathematics students with lecturerYou will cover both topics that are a direct continuation of those at A-level and those that introduce you to new ways of thinking, such as the logical structure of arguments, the proper definition of mathematical objects, the design of sophisticated mathematical models, and the legitimacy of computations.

All of our courses have a similar curriculum for the first two years, covering key areas of mathematics such as algebra, differential equations, and probability and statistics.

Elective and more specialised modules start in your second year and enable you to deepen your knowledge of some areas while maintaining a broad understanding of mathematics.

On the BSc in Pure Mathematics, you will specialise in Pure Mathematics in your third year, when you take several modules in a variety of relevant topics such as Algebraic Number Theory, Functional Analysis, Topology and Probability Theory.

Your remaining optional modules can be chosen from our wide selection of topics in other areas of mathematics, many of which are linked to our cutting edge research.

Transfer between courses

Successful candidates will receive the same offer for any course they apply for within the Department, so you should apply to just one. There is no advantage in applying to multiple courses within Mathematics.

The high level of shared content in the first two years means it is usually possible to transfer between any of our maths courses during this time (within stated restrictions – which would include having taken the appropriate second year options). However, transfer onto the Year Abroad course must normally be done in your first year.

If you are an international student, transferring to a different course could have an impact on your student visa. Please visit our International Student Support webpage for further information.

Structure

Find out more about the limited circumstances in which we may need to make changes to or in relation to our courses, the type of changes we may make and how we will tell you about them.

Year 1

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

Year 2

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.

Year 3

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

Download the programme specification‌ [PDF] – this is the most up-to-date version available for this course. It may change for your year of entry. If/when changes to this course are approved by the College, we will update this document and the information on this course page.


I-Explore

Through I-Explore, you'll have the chance to deepen your knowledge in a brand new subject area, chosen from a huge range of for-credit modules.

All of our undergraduate courses include one module from I-Explore's wide selection. The module you choose will be fully integrated into your course's curriculum and count as credit towards your degree.

Find out more about I-Explore

Teaching and assessment

Teaching

  • Independent learning
  • Group Learning
  • Lectures
  • Tutorials
  • Problem-solving and group learning classes
  • Research Projects

Teaching, independent study and placement hours

 Year 1Year 2Year 3
Lectures, seminars and similar 330 hours 300 hours 240 hours
Independent study 1,170 hours 1,200 hours 1,260 hours
Placement
Based on the typical pathway through the course 
 

Assessment

  • Group assignments and projects
  • Individual Projects
  • Online tests and quizzes
  • Oral presentations
  • Poster presentations
  • Short, individual tests
  • Written examinations

Staff expertise

At Imperial, you will be taught by a range of teachers of all levels from Professors to PhD students, including some who undertake groundbreaking research and are regarded as experts in their field.

You may also experience peer teaching and be taught by specialists external to the College.

Associateship

As well as your main Imperial degree, you will also receive the award of the Associateship of the Royal College of Science (ARCS) on completion of this course.

The Royal College of Science is one of three historic Colleges that came together to form Imperial College London in 1907.

Find out more about our Associateships.

Compare this course

See how this course compares with similar courses at different institutions.

Discover Uni compares things like student satisfaction and what graduates do after they finish the course.

Entry requirements

We welcome students from all over the world and consider all applicants on an individual basis – see selection process below.

For advice on the requirements for the qualifications listed here please contact the Department (see Contact us).

We also accept a wide range of international qualifications. If the requirements for your qualifications are not listed here, please see our academic requirements by country page for guidance on which qualifications we accept.

A-levels

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.

International Baccalaureate

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.

Advanced Placements

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.

Other qualifications

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.

Admissions test

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.

Selection process

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

Foundation programmes

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:

ModuleStatus
Research and Academic Skills: Science and Society Compulsory
Academic English Compulsory
Biology Elective
Chemistry Elective
Mathematics Elective
Physics Elective
Information correct at time of publishing, but subject to change
Summary of the table's contents

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 

English language requirement (all applicants)

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.

Academic Technology Approval Scheme (ATAS)

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.

Competence standards

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

Tuition fees and funding

We charge tuition fees for every year that your course lasts. The fee you will be charged is based on your fee status, which is determined by government regulations.

Home rate of tuition

2022 entry

The fee for Home students is controlled by the UK government. It has not been confirmed for the 2022-23 academic year.

As a guide, the Home rate of tuition for the 2021-22 academic year was £9,250.

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.

 

Overseas rate of tuition

2022 entry

The fee for Overseas students is controlled by the College. It has not been confirmed for the 2022–23 academic year.

As a guide, the Overseas rate of tuition for the 2021–22 academic year was £32,000.

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.

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.

Accommodation and living costs

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.

Careers

The logical and analytical skills developed through a degree in mathematics are highly valued by a wide range of employers. Our graduates go on to a wide range of careers in industry, government and education, as well as international banking, computing, business, law and accountancy.

The MSci programmes in particular prepare you for research careers and are recognised throughout the European Union, where four-year undergraduate degrees tend to be the norm.

Recent graduates of the Department have become:

  • Quantitative Analyst, Multinational financial services company
  • Accountant, KPMG
  • Software Developer, Healthcare technology company
  • Technology Analyst, Goldman Sachs
  • E-Commerce Manager, UK-based financial services group

How to apply

UCAS key information

  • UCAS course code: G125
  • UCAS institution code: I50

UCAS Apply system

To apply to study at Imperial you must use the online application system managed by the Universities and Colleges Admissions Service (UCAS).

You can view this course on the UCAS website.

Application deadlines

All applications, other than those which include choices for medicine at Imperial, must be submitted to UCAS by 18.00 (UK time) on 15 January 2022 for entry in October 2022.

The deadline for applications including medicine courses at Imperial starting in 2022 is 18.00 (UK time) on 15 October 2021.

Track your application

Once you’ve submitted your application you can use UCAS Track to follow its progress and manage your choices.

Read more about how to apply

Further questions?

Find answers to your questions about admissions. Answers cover COVID-19, English language requirements, Visas and more.

Visit the FAQs

You may also be interested in the following related departments and the courses they offer:

Contact us

Mathematics student

Have a question?

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

Department of Mathematics

Panoramic view of the Queen's Lawn on South Kensington Campus

Take a virtual tour

Explore our South Kensington Campus and our halls of residence from your home.

Take a tour

Lecturer delivering a Schrödinger workshop

Events, talks and taster sessions

Register to meet us and find out more about studying at Imperial.

Find an event

Terms and conditions

There are some important pieces of information you should be aware of when applying to universities. We've put together this information in a dedicated section of our website.Makerspace

Read our terms and conditions for these areas: