Mathematics
Deepen your understanding of mathematics and enrich your studies on an optional year abroad
Mathematics with a Year Abroad
Deepen your understanding of mathematics and enrich your studies on an optional year abroad
Engage with mathematical ideas that will develop your critical and intellectual abilities and introduce new ways of thinking
Choose from over 50 specialised modules and deepen your knowledge in the areas that most appeal to you
Enrich your study of mathematics with an integrated year of Master’s level study, or a year abroad at a leading global university
Course key facts

Qualification

MSci


Duration
4 years

Start date
October 2023

UCAS course code
G103

Study mode
Fulltime

Fees
£9,250 Home
£36,700 Overseas

Delivered by

Location

South Kensington


Applications: places
14 : 1 (2021)
Minimum entry standard 2023

A*A*A (Alevel)

39 points (International Baccalaureate)

Qualification

MSci


Duration
4 years

Start date
October 2023

UCAS course code
G104

Study mode
Fulltime

Fees
£9,250 Home
£36,700 Overseas

Delivered by

Location

South Kensington


Applications: places
14 : 1 (2021)
Minimum entry standard 2023

A*A*A (Alevel)

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 will engage with concepts that are both a direct continuation of those at Alevel, 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.
This course will enable you to develop a broad understanding of mathematical theory and application, while also providing opportunities to deepen your knowledge in the mathematical areas that most appeal to you.
You will be able to select from over 50 specialised modules, many of which are linked to our cuttingedge research and led by preeminent experts in their fields.
The MSci Mathematics course builds on the BSc with an integrated year taught at Master's level, in which you complete advanced modules and a research project.
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.
This course aims to present you with a wide range of mathematical ideas in a way that develops your critical and intellectual abilities.
You will engage with concepts that are both a direct continuation of those at Alevel, 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.
This course will enable you to develop a broad understanding of mathematical theory and application, while also providing opportunities to deepen your knowledge in the mathematical areas that most appeal to you.
You will be able to select from over 50 specialised modules, many of which are linked to our cuttingedge research and led by preeminent experts in their fields.
You also have the chance to complete an integrated year abroad during your third year at one of our partner universities, where you can challenge yourself in a different academic and cultural environment. You will then return to Imperial to complete your studies during your fourth and final year.
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.
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 five core modules.
You will also select four 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
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 CayleyHamilton Theorem.
Explore higherdimensional 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.
Gain an understanding of advanced topics in calculus and ordinary differential equations, including an introduction to multidimensional vector calculus and differential operators.
Further your mathematical research and communication skills while developing transferable teamwork and presentation skills.
Deepen your knowledge in a brand new subject area, chosen from a huge range of forcredit modules.
Optional modules
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.
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.
Foray into an everevolving interdisciplinary field in which concepts and methods from mathematics play a central role in the analysis of realworld 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 objectoriented programming model, which is very widely used and taught in Python.
In your third year, you will be able to access a large selection of optional modules to study the areas that are most interesting to you.
You will choose at least seven optional modules. In addition, you will be able to choose a further one or two modules, depending on the number of ECTS credits awarded. This may include modules available in Year 2, and at most one offered by other departments.
The following 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.
Optional modules
Analyse boundary value problems for elliptic and parabolic PDEs using the variational approach.
Further your appreciation of algebra and explore the basics of homological algebra, complexes and exact sequences.
Module description coming soon.
Discover algebraic number theory, with emphasis on quadratic fields. In such fields, the familiar unique factorisation enjoyed by the integers may fail, but the extent of the failure is measured by the class group.
Engage with algebraic topology and advance your knowledge of homology theory, fundamental groups and the Galois correspondence for covering spaces.
Further your knowledge of mathematical techniques including the WienerHopf method, Plemelj formulae, Hilbert problem, Orthogonal polynomials, the GrammSchmidt process, and the Rodrigues formula.
Gain an understanding of the basics of stochastic processes and how they can be applied. Lay the groundwork for further deep work, especially in such areas as genetics, industrial applications, and medicine.
Study a range of asymptotic series and expansions, including the asymptotic expansion of integrals, the Laplace method and Watson's lemma.
Advance your understanding of bifurcation theory, the study of how the behaviour of dynamical systems (ODEs, maps) changes when parameters are varied.
Module description coming soon.
Assess the different methods used to solve linear systems and other linear algebra computations, with a focus on both mathematical analysis and practical applications.
Investigate a variety of computational approaches for solving partial differential equations, including finite difference methods, finite volume and spectral methods.
Module description coming soon.
Examine the foundations of discretetime dynamical systems and discover why they are so important to areas such as finance, physics, biology and social sciences.
Explore modelling learning through studying the dynamics of games and analyse learning models used by technology companies.
Develop a deep understanding of the finite element method by spanning both its analysis and implementation.
Be presented with a derivation of the NavierStokes and learn techniques to simplify and solve the equation with the purpose of describing the motion of fluids at different conditions.
Seek out simplifications in the NavierStokes formulation and learn how to solve Prandtl’s boundarylayer equations.
Broaden your knowledge of basic function spaces and the basic methodologies needed to undertake the analysis of partial differential equations.
Assess ideas of continuity and linear algebra, with a particular emphasis on vector spaces and linear maps.
Learn why the formula for the solution to a quadratic equation and similar formulae for cubic and quartic equations are wellknown but no formula is possible for quintics.
Module description coming soon.
Explore the representations of groups and the character of a group representation.
Familiarise yourself with key concepts on this introduction to some of the more advanced topics in the theory of groups.
Develop intermediate proficiency in the use of the C++ programming language, as well as the skills to write efficient parallel programs and use of software engineering tools and best practices.
Advance your knowledge of fluiddynamics relating to geophysics through a mix of theory and applications.
Discover why Markov processes are widely used to model random evolutions and how the theory connects with many other subjects in mathematics.
Learn how to describe the application of mathematical models to biological phenomena and give consideration to problems typical of particular organisms and environments.
Engage with the mathematical modelling of derivatives securities, which focuses on the pricing and hedging of derivatives using a probabilistic representation of market uncertainty.
Module description coming soon.
Module description coming soon.
Module description coming soon.
Learn how to visualise and explore data in R, and understand the fundamental concepts and challenges of learning from data.
Focus on the properties of natural numbers, and in particular of prime numbers, which can be proved by elementary methods.
Explore a range of techniques for solving ordinary differential equations, including the RungeKutta, extrapolation and linear multistep methods.
Explore the fundamental properties of probability, including probability measures. independent random variables and elements of Brownian motion.
Untangle the theory of quantum mechanics and discover why it provides the basis for many areas of contemporary physics.
Build on topics covered in Quantum Mechanics I and further your understanding of key areas of contemporary physics.
Engage with the efficient algorithms deployed to solve mathematical problems using computation and become comfortable with the Python programming language.
Discover how advances in modern theoretical physics are being made and become familiar with the classical theory of fields.
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.
Familiarise with the criteria and the theoretical results necessary to develop and evaluate optimum statistical procedures in hypothesis testing, point and interval estimation.
Build an uptodate understanding of computational simulation methods, covering areas from basic random variate generation to the Monte Carlo methodology.
Examine survival models that are fundamental to actuarial work, as well as being a key concept in medical statistics, with particular emphasis on actuarial applications.
Advance your understanding of Tensor calculus and explore concepts including Riemannian geometry, Einstein's field equations and the Newtonian approximation.
Module description coming soon.
Learn the basic statistical concepts and reasoning relevant to atmospheric science and gain experience in the proper use of statistical methods for the analysis of weather and climate data.
In your fourth year, you will complete a compulsory mathematics research project.
You will also complete six optional modules.
Optional modules
 Advanced Dynamical Systems
 Algebra 4
 Analytic Methods in Partial Differential Equations
 Differential Topology
 Hydrodynamic Stability
 Infinite Groups
 Modular Representation Theory
 Random Dynamical Systems and Ergodic Theory
 Stochastic Differential Equations
 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.
In your first year, you will study seven core modules, in addition to language classes if required.
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.
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 language.
Your language module will be taken for credit but not counted toward your final degree grade.
In your second year, you will study five core modules.
You will also select four 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
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 CayleyHamilton Theorem.
Explore higherdimensional 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.
Gain an understanding of advanced topics in calculus and ordinary differential equations, including an introduction to multidimensional vector calculus and differential operators.
Further your mathematical research and communication skills while developing transferable teamwork and presentation skills.
Deepen your knowledge in a brand new subject area, chosen from a huge range of forcredit modules.
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 language.
Your language module will be taken for credit but not counted toward your final degree grade.
Optional modules
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.
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.
Foray into an everevolving interdisciplinary field in which concepts and methods from mathematics play a central role in the analysis of realworld 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 objectoriented programming model, which is very widely used and taught in Python.
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.
In your fourth year, you will complete a compulsory mathematics research project.
You will also complete six optional modules.
Optional modules
 Advanced Dynamical Systems
 Algebra 4
 Analytic Methods in Partial Differential Equations
 Differential Topology
 Hydrodynamic Stability
 Infinite Groups
 Modular Representation Theory
 Random Dynamical Systems and Ergodic Theory
 Stochastic Differential Equations
 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.
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
Year 4
 12% Lectures, seminars and similar
 88% Independent study
Teaching and learning methods
 Independent learning
 Group learning
 Lectures
 Tutorials
 Problem solving
 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
Year 4
 10% Coursework
 90% Examinations
Assessment methods
 Group assignments and projects
 Individual projects
 Online tests and quizzes
 Oral presentations
 Poster presentations
 Short, individual tests
 Written examinations
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 4
 12% Lectures, seminars and similar
 88% Independent study
Teaching and learning methods
 Independent learning
 Group learning
 Lectures
 Tutorials
 Problem solving
 Research projects
Balance of assessment
Key
 Coursework
 Examinations
Year 1
 30% Coursework
 70% Examinations
Year 2
 20% Coursework
 80% Examinations
Year 4
 10% Coursework
 90% Examinations
Assessment methods
 Group assignments and projects
 Individual projects
 Online tests and quizzes
 Oral presentations
 Poster presentations
 Short, individual tests
 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 start your application via UCAS Hub. There you can add this course as one of your choices and track your application.
Applications for 2023 entry are closed
Application deadlines — 25 January 2023 at 18.00 (UK time)
Applications for 2023 entry are closed
Application deadlines — 25 January 2023 at 18.00 (UK time)
Mathematics Admissions Test (MAT)
All candidates who apply up 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 paperbased, subjectspecific 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 post15 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.
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
2023 entry
£9,250 per year
Year in Europe
2023 entry
£1,385 for that year
Your fee is based on the year you enter the College, 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.
You can also apply for a meanstested Maintenance Loan to help towards your living costs.
Overseas fee
2023 entry
£36,700 per year
Year in Europe
2023 entry
100% of the fee for that year
Your fee is based on the year you enter the College, 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.
Your future 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
 Telephone: +44 (0)20 7594 8484
 Email: ugmaths.admissions@imperial.ac.uk
Visit the Department of Mathematics website
Request info
Learn more about studying at Imperial. Receive useful information about our life in our undergraduate community and download our latest Study Guide.
Request info
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