Mathematics (Pure Mathematics)
Develop a broad understanding of mathematical theory and gain in-depth knowledge of pure mathematics.
Engage with mathematical ideas that will develop your critical and intellectual abilities and introduce new ways of thinking
Develop a broad understanding of mathematical theory, concepts and applications
Gain in-depth knowledge of pure mathematics, algebraic number theory, functional analysis, topology and probability
Course key facts
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Qualification
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BSc
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Duration
3 years
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Start date
October 2025
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UCAS course code
G125
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Study mode
Full-time
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Fees
£9,535 per year Home
£40,700 per year Overseas
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Delivered by
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Location
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South Kensington
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Applications: places
11 : 1 (2023)
Minimum entry standard
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A*A*A (A-level)
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39 points (International Baccalaureate)
Course overview
This course aims to present you with a wide range of mathematical ideas in a way that develops your critical and intellectual abilities.
You'll develop a broad understanding of mathematical theory and application and deepen your knowledge in areas that appeal to you.
You will engage with concepts that are both a direct continuation of those at A-level, and others that introduce you to new ways of thinking.
Your studies will cover the key areas of mathematics such as algebra, analysis, probability and statistics. You'll also explore topics such as the logical structure of arguments, the proper definition of mathematical objects, the design of sophisticated mathematical models, and the legitimacy of computations.
As part of the Pure Mathematics specialisation, you will examine a variety of relevant concepts including Algebraic Number Theory, Functional Analysis, Topology and Probability Theory.
You will also have the opportunity to choose from over 50 specialised modules – many of which are linked to our cutting-edge research and led by pre-eminent experts in their fields.
As a graduate in mathematics, you'll possess a set of logical and analytical skills that are highly valued by employers, enabling you to pursue opportunities across the commercial, government and education sectors.
Structure
This page is updated regularly to reflect the latest version of the curriculum. However, this information is subject to change.
Find out more about potential course changes.
Please note: it may not always be possible to take specific combinations of modules due to timetabling conflicts. For confirmation, please check with the relevant department.
In your first year, you will study the following core modules.
Core modules
Transition towards the way you will be expected to think about and approach mathematics during your degree, with emphasis on the importance of precise definitions and rigorous proofs.
Undertake a rigorous treatment of the concept of a limit, as applied to sequences, series and functions.
Generalise what you already know about systems of linear equations and matrices and view them in more abstract, and more geometric, frameworks of vector spaces and linear transformations.
Explore a selection of mathematical tools that will enable you to solve more complex problems in applied mathematics than you will have tackled previously.
Focus on probability concepts, within an axiomatic framework. There will be a strong emphasis on principles of modelling and data analysis and you will learn to use the formal language of probability.
Gain knowledge of programming in Python through illustrative examples, practice questions and assessment tasks, guided by computational principles and their underlying mathematical concepts.
Identify how mathematical ideas can be used to underpin a range of scientific problems and familiarise yourself with a mathematical framework that embraces multiple disciplines from engineering to economics and statistics.
Develop elementary research skills in mathematics while exploring your personal interests in a specific area of mathematics.
In your second year, you will study seven core modules, including the i-Explore module.
You will also select two optional modules.
Optional modules may be prerequisites for modules in later years. You will be advised about such dependencies before making your choices.
Core modules
Explore higher-dimensional derivatives, leading to the inverse and implicit function theorems, alongside metric and topological spaces as generalisations of n dimensional spaces, and limiting behaviour of sequences in such spaces.
Further your mathematical research and communication skills while developing transferable teamwork and presentation skills.
Study examples of groups and homomorphisms, along with applications of group theory and rings, a class of algebraic object equipped with both addition and multiplication.
Explore Lebesgue's theory of measure and integration, a powerful extension of the Riemann integral and an essential tool in all aspects of analysis and its applications, including probability, stochastic processes and PDEs.
Examine how to find matrices for a linear transformation which reflect its important features, culminating in the rational and Jordan canonical forms, and prove the fundamental Cayley-Hamilton Theorem.
Gain an understanding of advanced topics in calculus and ordinary differential equations, including an introduction to multi-dimensional vector calculus and differential operators.
Deepen your knowledge in a brand new subject area, chosen from a huge range of for-credit modules.
Optional modules
Foray into an ever-evolving interdisciplinary field in which concepts and methods from mathematics play a central role in the analysis of real-world systems from computing, science, and engineering.
Learn about partial differential equations and the concept of modelling in applied mathematics, with a focus on practical application.
Build a core of programming skills beyond those encountered in your first year through the object-oriented programming model, which is very widely used and taught in Python.
Investigate probability concepts that are useful in applications, particularly to statistics, focusing on the joint behaviour of several random variables.
Develop the traditional concepts of statistical inference, including maximum likelihood, hypothesis testing and interval estimation and apply them to the linear model that arises in many practical situations.
In your third year, you will be able to access a large selection of optional modules, including those 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.
Teaching and assessment
Balance of teaching and learning
Key
- Lectures, seminars and similar
- Independent study
Year 1
- 22% Lectures, seminars and similar
- 78% Independent study
Year 2
- 20% Lectures, seminars and similar
- 80% Independent study
Year 3
- 16% Lectures, seminars and similar
- 84% Independent study
Teaching and learning methods
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Independent learning
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Group learning
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Lectures
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Tutorials
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Problem solving
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Research projects
Balance of assessment
Key
- Coursework
- Examinations
Year 1
- 30% Coursework
- 70% Examinations
Year 2
- 20% Coursework
- 80% Examinations
Year 3
- 10% Coursework
- 90% Examinations
Assessment methods
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Group assignments and projects
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Individual projects
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Online tests and quizzes
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Oral presentations
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Poster presentations
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Short, individual tests
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Written examinations
Entry requirements
We consider all applicants on an individual basis, welcoming students from all over the world.
How to apply
Apply via UCAS
You can now submit your application via UCAS Hub. There you can add this course as one of your choices and track your application.
UCAS institution code: I50
Application deadlines – 29 January 2025 at 18.00 (UK time)
Admissions test (TMUA)
All applicants are strongly encouraged to sit the Test of Mathematics for University Admission (TMUA). If you submit your application on 23 December 2024 or earlier, you are required to take the TMUA.
Registration is now open for the January TMUA test sitting.
This is your last opportunity to sit the test for 2025 entry. Registration closes online on 23 December 2024 (21 November 2024 for candidates requiring access arrangements).
Key dates
October sitting (15 and 16 October 2024): Registration is now closed
January sitting (8 and 9 January 2025): Register online from 24 October to 23 December 2024 (candidates requiring access arrangements must register by 21 November 2024)
Take the test just once as only your first score will count.
Test fee bursary
Applications are open for the UAT-UK bursary which covers the full-test fee for candidates in financial need who are permanently living in the UK and planning to take the test at a UK test centre.
Full details of eligibility criteria and how to apply are available on the UAT-UK website.
Access arrangements
Access arrangements, for example, extra time or rest breaks, are available for students with learning difficulties, disabilities, and other medical conditions.
If this applies to you, you need to notify UAT-UK of your requirements before booking your test in one of Pearson VUE’s global network of test centres.
Once your access arrangements have been confirmed, you will be able to book your test online.
For candidates who apply after 23 December and are unable to sit the TMUA, conditional offers will typically require you to sit at least one Sixth Term Examination Paper (STEP).
Please note that the Mathematics Admissions Test (MAT) is no longer used by Imperial.
Test requirements for 2025 entry are transitional as we move from the MAT to TMUA, and these requirements may be modified for 2026 entry.
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.
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.
An ATAS certificate is not required for students applying for this course.
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.
Year abroad
Language requirement
Teaching is in the language of your host country, 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.
Please note the list of universities located abroad that the Department currently has partnerships with is illustrative.
Partnerships with universities are subject to continuous review and individual partnerships may or may not be renewed.
Tuition fees
Home fee
2025 entry
£9,535 per year
Important update for 2025 entry
The UK government has announced that, starting in April 2025, maximum tuition fees for Home undergraduate students in England will increase from £9,250 per year to £9,535. Find out more
Your fee is based on the year you enter the university, not your year of study. This means that if you repeat a year or resume your studies after an interruption, your fees will only increase by the amount linked to inflation.
Find out more about our tuition fees payment terms, including how inflationary increases are applied to your tuition fees in subsequent years of study.
Whether you pay the Home or Overseas fee depends on your fee status. This is assessed based on UK Government legislation and includes things like where you live and your nationality or residency status. Find out how we assess your fee status.
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.
The loan is paid directly to the university.
You will start repaying it only after you leave your course, have a job, and are earning above a certain amount.
Once the repayments start, the amount you pay each month depends on how much you earn, not on how much you owe in total.
Home students can apply for a means-tested Maintenance Loan to help with their living costs.
In November 2024, the UK government announced a 3.1% increase in English Maintenance Loans for 2025-26.
How you apply for student finance depends on whether you have studied before and where you’re from or normally live. Find out more on the UK government's website.
The Imperial Bursary is available to all Home undergraduate students with a household income below £70,000 per year.
The amount awarded is based on your household income, with up to £5,000/year available for students from the lowest income households.
It's money which you don't need to pay back, and it's paid on top of any government funding you may also receive.
It is available for each year of your course, as long as your annual household income remains below £70,000.
Overseas fee
2025 entry
£40,700 per year
Your fee is based on the year you enter the university, not your year of study. This means that if you repeat a year or resume your studies after an interruption, your fees will only increase by the amount linked to inflation.
Find out more about our tuition fees payment terms, including how inflationary increases are applied to your tuition fees in subsequent years of study.
Whether you pay the Home or Overseas fee depends on your fee status. This is assessed based on UK Government legislation and includes things like where you live and your nationality or residency status. Find out how we assess your fee status.
How will studying at Imperial help my career?
94% Of Imperial Mathematics graduates in work or further study*
- 94% Of Imperial Mathematics graduates in work or further study*
- 6%
85% Of Imperial Mathematics graduates in highly skilled work or further study*
- 85% Of Imperial Mathematics graduates in highly skilled work or further study*
- 15%
*2021-22 graduate outcomes data, published by HESA in 2024
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Gain transferable skills relevant to a career in industry, government and academia.
With specialised knowledge, you'll be highly sought after in a range of sectors.
International banking, computing, business, law and accountancy are just some of your options.
Other potential career paths could include financial services and healthcare technology.
Further links
Contact the department
- Telephone: +44 (0)20 7594 8484
- Email: ugmaths.admissions@imperial.ac.uk
Visit the Department of Mathematics website
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Request info
Learn more about studying at Imperial. Receive useful information about our life in our undergraduate community and download our latest Study Guide.
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Events, tasters and talks
Meet us and find out more about studying at Imperial.
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Course data
Terms and conditions
There are some important pieces of information you should be aware of when applying to Imperial. These include key information about your tuition fees, funding, visas, accommodation and more.
You can find further information about your course, including degree classifications, regulations, progression and awards in the programme specification for your course.
Programme specifications