Mathematics (Pure Mathematics)
Develop a broad understanding of mathematical theory and gain in-depth knowledge of pure mathematics.
Course key facts
Qualification
BSc
Duration
3 years
Start date
October 2027
UCAS course code
G125
Study mode
Full-time
Fees
Course fees and funding
Delivered by
Location
-
South Kensington
-
Applications: places
14 : 1 (2025)
Minimum entry standard
A*A*A (A-level)
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.
Through I-Explore, you'll have the chance to deepen your knowledge in a brand new subject area, chosen from a huge range of for-credit modules.
All of our undergraduate courses include one module from I-Explore's wide selection. The module you choose will be fully integrated into your course's curriculum and count as credit towards your degree.
Optional modules
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.
Explore how variational principles can be applied to classical mechanics to develop methods that can be applied to an array of problems ranging from the double pendulum to the motion of relativistic particles.
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
- 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
- Special Relativity and Electromagnetism
- Applied Statistical Inference
- Statistical Theory
- Stochastic Simulation
- Survival Models
- Tensor Calculus and General Relativity
- 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
This is a general guide to how teaching and learning are usually balanced across this course. The methods used may change based on the modules you take.
Key
- Lectures, seminars and similar
- Independent study
Year 1
- 22% Title 1 goes here
- 78% Title 2 goes here
Year 2
- 20% Title 1 goes here
- 80% Title 2 goes here
Year 3
- 16% Title 1 goes here
- 84% Title 2 goes here
Teaching and learning methods
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Independent learning
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Group learning
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Lectures
-
Tutorials
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Problem solving
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Research projects
Balance of assessment
This is an example of how assessments are usually divided, based on a typical pathway through the course. The actual breakdown may vary depending on the modules you choose.
Key
- Coursework
- Examinations
Year 1
- 30% Title 1 goes here
- 70% Title 2 goes here
Year 2
- 20% Title 1 goes here
- 80% Title 2 goes here
Year 3
- 10% Title 1 goes here
- 90% Title 2 goes here
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.
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