Pure Mathematics
  • Undergraduate
  • BSc

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

  • Qualification

    • BSc

  • Duration

    3 years

  • Start date

    October 2023

  • UCAS course code

    G125

  • Study mode

    Full-time

  • Fees

    • £9,250 Home

    • £36,700 Overseas

  • Delivered by

  • Location

    • South Kensington

  • Applications: places

    14 : 1 (2021)

Minimum entry standard 2023

  • A*A*A (A-level)

  • 39 points (International Baccalaureate)

View full entry requirements

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.

In your first year, you will study the following core modules.

Core modules

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

Optional modules

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

  • A person studying independently
    Independent learning
  • A group of people interacting
    Group learning
  • Person at lectern giving speech
    Lectures
  • Four students sitting in a tutorial
    Tutorials
  • Person participating in classroom discussion.
    Problem solving
  • Individual research project
    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

  • Group assignments and projects
  • Person completing coursework
    Individual projects
  • Online tests and quizzes
  • Oral presentations
  • Poster project
    Poster presentations
  • Short, individual tests
  • A person completing a written exam
    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)

Tuition fees

Home fee

2023 entry

£9,250 per year

Overseas fee

2023 entry

£36,700 per year

Your future career

Person in a bubble surrounded by 4 skills

Gain transferable skills relevant to a career in industry, government and academia.

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With specialised knowledge, you'll be highly sought after in a range of sectors.

Laptop displays finance statistics

International banking, computing, business, law and accountancy are just some of your options.

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Other potential career paths could include financial services and healthcare technology.

Course data

Compare this course

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.

Read our terms and conditions

You can find further information about your course, including degree classifications, regulations, progression and awards in the programme specification for your course.

Programme specifications