Pure Mathematics
Obtain transferrable mathematical skills needed for employment and future research.
Develop your knowledge of pure mathematics alongside a range of transferrable skills
Develop research expertise in topics ranging from geometry and number theory to algebra and analysis
Design your own learning plan and tailor the course to your career interests
Course key facts
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Qualification
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MSc
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Duration
1 year, 2 years
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Start date
September 2025
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Study mode
Full-time, Part-time
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Fees
£14,400 Home
£35,700 Overseas
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Delivered by
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Location
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South Kensington
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Course overview
Advance your understanding of Pure Mathematics on this Master's course.
Carried out over one or two years, this course will train you in a range of mathematical skills in problem-solving, project work and presentation.
The flexible programme also allows you to pick from a range of optional modules to design your own learning plan.
It reflects key research interests in Pure Mathematics, including analysis, geometry and topology, number theory and algebra.
You'll also apply your knowledge from the course to an independent research project in an area of your choice.
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.
You'll choose eight modules that account for two-thirds of your overall grade.
Part-time students will choose four modules in the first year and four in the second year.
There are no mandatory core modules except the research project.
Taught modules
Explore the fundamental properties of probability, including probability measures. independent random variables and elements of Brownian motion.
Assess ideas of continuity and linear algebra, with a particular emphasis on vector spaces and linear maps.
Deepen your understanding of Fourier analysis and how the Fourier transform works.
Become familiar with the stochastic calculus in relation to non-linear filtering and modern numerical methods for solving the filtering problem.
Discover why Markov processes are widely used to model random evolutions and how the theory connects with many other subjects in mathematics.
Understand the curvature of a surface in 3-dimensional space and expand your knowledge of topological surfaces.
Build your understanding of algebraic curves and explore concepts including Meromorphic differentials and Abel's theorem.
Engage with algebraic topology and advance your knowledge of homology theory, fundamental groups and the Galois correspondence for covering spaces.
Learn to use algebraic and geometric ideas together, studying basic concepts from both perspectives and applying them to numerous examples.
Appreciate geodesics and curvature and the relationship between them and use these ideas to analyse how local geometric conditions can lead to global topological constraints.
Explore the foundations and examples of manifolds, including smooth manifolds, quotients, tangent spaces and vector bundles.
Delve into key aspects of differential topology, which is concerned with the topology of smooth manifolds.
Enhance your understanding of the theory of almost complex manifolds and complex manifolds, considering examples including Kähler manifolds and complex projective manifolds.
Further your appreciation of algebra and explore the basics of homological algebra, complexes and exact sequences.
Familiarise yourself with key concepts on this introduction to some of the more advanced topics in the theory of groups.
Examine Galois theory and why the formula for the solution to a quadratic equation is well-known, while no formula is possible for quintics.
Study the elementary theory of graphs and analyse why graphs are used in many areas of mathematics and other fields.
Explore the representations of groups and the character of a group representation.
Discover how computer theorem provers are maturing and improve your understanding of this area of mathematics by studying the Lean theorem prover.
Develop your knowledge further with this introduction to commutative algebra that looks into the prime and maximal ideals, the nilradical and the Jacobson radical.
Explore semisimple complex Lie algebras and the classification of irreducible representations.
Analyse a range of advanced algebra topics, incorporating aspects of number theory, geometry and topology.
Examine the properties of natural numbers and assess various theorems relating to number theory.
Gain an appreciation for algebraic number theory and advance your understanding of quadratic fields.
Explore the different types of elliptic curves and investigate the Mordell-Weil theorem.
Develop an understanding of partial differential equations (PDE) appearing in physics and geometry, and classical techniques to study them analytically.
Analyse the way in which we reason formally about mathematical structures and look at the ZFC axioms to develop the notion of cardinality.
Analyse geometric notions associated with domains in the plane and their boundaries, and how they are transformed under holomorphic mappings.
You'll also complete a research project based around a mathematical topic from the core course area.
This could include elements of analysis, algebra, combinatorics, geometry and number theory.
The project will be assessed by a written report and an oral examination.
Teaching and assessment
Balance of teaching and learning
Key
- Lectures, tutorials and self-study
- Research project
- 67% Lectures, tutorials and self-study
- 33% Research project
Teaching and learning methods
- Computing
- Independent research project
- Lectures
- Office hours
- Problem sheets
- Tutorials
Balance of assessment
Key
- Modules
- Research project
- 67% Modules
- 33% Research project
Assessment methods
- Coursework
- Dissertation
- Oral presentation
- Written examination
Entry requirements
We consider all applicants on an individual basis, welcoming students from all over the world.
How to apply
Apply online
You can submit one application form per year of entry. You can choose up to two courses.
Application deadlines – Round 1 closes on Thursday 16 January 2025
We operate a staged admissions process with several application rounds throughout the year.
Apply by 23.59 (UK time) on the closing date of an application round, to ensure you receive a response on your application by the relevant decision date.
Application rounds
Round 1
- Apply by Thursday 16 January 2025
- Decision by Thursday 6 March 2025
Round 2
- Apply by Thursday 27 March 2025
- Decision by Thursday 1 May 2025
Round 3
- Apply by Thursday 15 May 2025
- Decision by Thursday 17 July 2025
There is no application fee for MRes courses, Postgraduate Certificates, Postgraduate Diplomas, or courses such as PhDs and EngDs.
If you are applying for a taught Master’s course, you will need to pay an application fee before submitting your application.
The fee applies per application and not per course.
- £80 for all taught Master's applications, excluding those to the Imperial College Business School.
- £100 for all MSc applications to the Imperial College Business School.
- £150 for all MBA applications to the Imperial College Business School.
If you are facing financial hardship and are unable to pay the application fee, we encourage you to apply for our application fee waiver.
Find out more about how to apply for a Master's course, including references and personal statements.
An ATAS certificate is not required for students applying for this course.
Tuition fees
Home fee
Full-time
£14,400
Part-time
£7,200per year
You should expect and budget for your fees to increase each 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.
If you're a UK national, or EU national with settled or pre-settled status under the EU Settlement Scheme, you may be able to apply for a Postgraduate Master’s Loan from the UK government, if you meet certain criteria.
For courses starting on or after 1 August 2024, the maximum amount is £12,471. The loan is not means-tested and you can choose whether to put it towards your tuition fees or living costs.
The loan is not means-tested and you can choose whether to put it towards your tuition fees or living costs.
The Martingale Foundation are offering fully funded scholarships for eligible students on selected Mathematics courses.
Martingale Scholarships: Full details and how to apply
Closing date: 25 October 2023
Overseas fee
Full-time
£35,700
Part-time
£17,850per year
You should expect and budget for your fees to increase each 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.
If you're a UK national, or EU national with settled or pre-settled status under the EU Settlement Scheme, you may be able to apply for a Postgraduate Master’s Loan from the UK government, if you meet certain criteria.
For courses starting on or after 1 August 2024, the maximum amount is £12,471. The loan is not means-tested and you can choose whether to put it towards your tuition fees or living costs.
The loan is not means-tested and you can choose whether to put it towards your tuition fees or living costs.
The Martingale Foundation are offering fully funded scholarships for eligible students on selected Mathematics courses.
Martingale Scholarships: Full details and how to apply
Closing date: 25 October 2023
How will studying at Imperial help my career?
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
Course Director: Dr Travis Schedler
Visit the Department of Mathematics website.
Request info
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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