Mathematics (MMath)

You'll cover the fundamentals, such as linear algebra and calculus. While calculus may already be familiar, you’ll gain a deeper understanding of the underlying ideas. Linear algebra begins with the algebra of vectors and matrices, before delving into more rigorous and abstract concepts, such as groups and fields.

You'll also get a taste of different areas of mathematics, such as:

• number theory
• probability and statistics
• dynamics
• operational research

This allows you to gain experience, before deciding what to do next.

Key modules continue to build your foundational knowledge. These include analysis and the techniques of partial differential equations and Fourier theory.

You'll also get a choice of modules to allow you to pursue a specific interest. Options include:

• Group Theory: this is one of the great simplifying and unifying ideas in modern mathematics. Group theory encodes symmetries algebraically.
• Fluid Dynamics: you’ll apply the techniques you’ve learned from complex numbers and multivariable calculus to model airflow over a wing or water flow through a propeller.

You can also choose options from financial mathematics. These cover how securities are evaluated, and how investment projects are appraised. You could learn about modelling of random processes though Markov chains and stochastic differential equations.

If you have chosen the statistics stream, you'll start specialising in statistics in your second year, learning about statistical distributions and modelling.

From pure mathematics you could study:

• Galois theory
• number theory
• infinite dimensional spaces
• algebraic invariants of a shape

Or, you could apply your statistical knowledge to the design of experiments or to simulating statistical events.

In applied mathematics you could:

• model black holes and cosmology
• model epidemics and biochemical reactions
• learn about Laplace and Fourier transforms
• study solutions of the Navier-Stokes equation

You could also choose from topics in optimisation, actuarial mathematics or modern applications of mathematics such as machine learning and social networks.

You’ll also carry out a project, choosing from:

• Maths and your Future: working in small teams to analyse data and apply your mathematical learning to a problem raised by a local or national employer
• Mathematical Investigation and Communication: learning independently about new areas of mathematics or applying your skills of modelling and computation
• Communicating and Teaching Mathematics: acting as an ambassador for mathematics in schools and gaining classroom experience

In the final year, you'll carry out an individually supervised year-long dissertation on a topic of your choice.

You'll also select from a wide range of advanced modules. You could learn key ideas from pure mathematics, such as homology or geometric group theory. You could choose to specialise in applications of mathematics, such as advanced general relativity or gravitational waves.

Alternatively, following the statistics pathway you could study topics such as machine learning, survival analysis and other modern applications of statistics.