Applied Mathematics
Equipping students with a range of transferable skills in mathematical modelling, analysis and computation for employment in industry and future research.
Equipping students with a range of transferable skills in mathematical modelling, analysis and computation for employment in industry and future research
Tailor your module choices to your interests
Tackle state-of-the-art problems in applied mathematics on a substantial research project
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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Minimum entry standard
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2:1 in mathematics, applied mathematics, engineering or physics
Course overview
This course provides training in many different areas of applied mathematics, equipping you with a range of mathematical, modelling and presentation skills for problem-solving and research.
This course is delivered in small classes, with a broad choice modules from the foundational to highly specialised, allowing you to tailor the course to your interests and background.
Starting from 2024, we offer a programme stream on Scientific Computing & Machine Learning (SCML) as part of our world-class Applied Mathematics MSc. This stream is for students who want to develop core expertise at the interface between modern computational mathematics and data-driven modelling.
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.
The taught element of the course, beginning in the autumn term and continuing into the spring term, consists of 8 modules and makes up two-thirds of the course. Students on the standard stream can choose from the full list of modules in any combination from Group A and/or Group B.
You are assessed through coursework during term time, and exams in May and June. The taught courses cover a range of topics in applied mathematics, including applied and stochastic analysis, analytical (e.g., complex and asymptotic) methods, numerical analysis and scientific computation, fluid dynamics, mathematical physics, bio-mathematics, data and optimisation methods, and more.
Part-time students will choose 4 modules in the first year and 4 in the second year.
Scientific Computing & Machine Learning (SCML) stream
You can apply either directly to the SCML stream in your application to Imperial, or by the end of Term 1, after you have decided on your modules and research project. Entry to the SCML stream can be limited, depending on aligned project availability.
To follow our new SCML stream, you must choose at least 4 out of your 8 modules from Group A. The remaining 4 modules can be in any combination from either Group A and/or Group B.
Optional modules: Group A
Develop a foundation in the analysis and implementation of numerical methods to obtain solutions to nonlinear differential equations.
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.
Develop a deep understanding of the finite element method by spanning both its analysis and implementation.
Study the theory and applications of stochastic differential equations and touch on issues including stochastic optimal control, and the applications of SDEs to partial differential equations.
Discover more about machine and deep learning as you gain an insight into the impact of optimisation algorithms and network architecture through mathematical tools.
Learn how to visualise and explore data in R, and understand the fundamental concepts and challenges of learning from data.
Gain a thorough grounding in optimisation models, theory, algorithms and software
Engage with the efficient algorithms deployed to solve mathematical problems using computation and become comfortable with Python.
Optional modules: Group B
Conduct in-depth study of an advanced topic in the theory of dynamical systems, looking at exciting recent research.
Analyse boundary value problems for elliptic and parabolic PDEs using the variational approach.
Develop an understanding of partial differential equations (PDE) appearing in physics and geometry, and classical techniques to study them analytically.
Further your knowledge of mathematical techniques including the Wiener-Hopf method, Plemelj formulae, Hilbert problem, and Orthogonal polynomials.
Broaden your knowledge on asymptotic methods and learn more about the techniques introduced that find wide applications in engineering and natural sciences.
Advance your understanding of bifurcation theory, the study of how the behaviour of dynamical systems changes when parameters are varied.
Build your understanding of key elements of classical dynamics including the calculus of variations, Lagrangian Mechanics and Hamiltonian Mechanics.
Examine the foundations of discrete-time dynamical systems and discover why they are so important to areas such as finance, physics, biology and social sciences.
Explore modelling learning through the dynamics of games and analyse learning models used by technology companies.
Be presented with a derivation of the Navier-Stokes 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 Navier-Stokes formulation and learn how to solve Prandtl’s boundary-layer equations.
Broaden your knowledge of basic function spaces and the basic methodologies needed to undertake the analysis of partial differential equations.
Become familiar with concepts in geometric mechanics including Fermat’s principle and subsequent developments in the field.
Examine basic concepts and techniques of modern hydrodynamic stability theory and learn how to predict hydrodynamic instabilities in a variety of fluid flows.
Advance your knowledge of fluid-dynamics 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.
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 1 and further your understanding of key areas of contemporary physics.
Assess the theory and applications of random dynamical systems and ergodic theory before exploring more advanced developments in this field.
Discover how advances in modern theoretical physics are being made and become familiar with the classical theory of fields.
Investigate principles and applications of statistical mechanics, with a special emphasis on phase transitions.
Examine the use of valuations, hedging and risk management of financial options by utilising stochastic differential equations.
Advance your understanding of Tensor calculus and explore concepts including Riemannian geometry, Einstein's field equations and the Newtonian approximation.
Analyse the theory of partial differential equations and its related concepts, and build familiarity with conservation laws.
Focus on the dynamics of vorticity in an ideal fluid in two and three dimensions and explore various techniques in dynamical systems theory.
As well as attending taught courses, you undertake independent work on a written project. A list of projects and supervisors is issued in November. You agree a topic with a supervisor towards the end of the first term, and begin working on your project in the second term. The bulk of the project is completed during the summer, with a submission deadline in September.
If you enter the Scientific Computing & Machine Learning stream, you will develop a research project aligned with the stream.
You will be assessed on your written thesis (dissertation) and a presentation, followed by questions from two academic staff. You will also receive feedback on poster presentations and research proposals during the course.
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
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Group tutorials
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Independent research project
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Individual student/lecturer consultations
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Lectures
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Problem classes / problem sheets
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Research seminars
Balance of assessment
Key
- Modules
- Research project
- 67% Modules
- 33% Research project
Assessment methods
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Coursework
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Dissertation
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Examination
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Oral assessment
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Practical
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
- Applications open on Friday 27 September 2024
- Applications close on Thursday 16 January 2025
- Decision by Thursday 6 March 2025
Round 2
- Applications open on Friday 17 January 2025
- Applications close on Thursday 27 March 2025
- Decision by Thursday 1 May 2025
Round 3
- Applications open on Friday 28 March 2025
- Applications close on Thursday 15 May 2025
- Decision by Thursday 17 July 2025
Round 4
- Applications open on Friday 16 May 2025
- Applications close on Friday 4 July 2025
- Decision by Thursday 31 July 2025
You may be invited to attend an interview with our staff as part of your application.
Details of this will be sent to you following your application.
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.
If you are selecting MSc Applied Mathematics as a second course choice in your application to Imperial, please note we will only consider your application if your first choice course is MSc Pure Mathematics.
Applications are made via our portal My Imperial.
To take the SCML stream, you can either:
- apply directly to the SCML stream, or
- apply to the generic MSc Applied Mathematics stream, and then wait until the end of Term 1 to confirm your decision.
Entry to the SCML stream can be limited, depending on aligned project availability.
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 Martingale Foundation are offering fully funded scholarships for eligible students on selected Mathematics courses.
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 Martingale Foundation are offering fully funded scholarships for eligible students on selected Mathematics courses.
How will studying at Imperial help my career?
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The solid training and exposure to cutting-edge activity in applied mathematics provides the necessary background for further postgraduate study in applied mathematics, or closely related areas such as engineering and physics.
The unique skills you will gain across mathematical foundations, modern computational mathematics, and machine learning are the starting point for an exciting career in industry, finance, big tech, and academia.
Further links
Contact the department
Course Director: Dr Dante Kalise
Visit the Department of Mathematics website.
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Request info
Find out more about studying at Imperial. Receive updates about life in our community, including event invites 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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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