Never has the collection of data been more widespread than it is now. The extraction of information from massive, often complex and messy, datasets brings many challenges to fields such as statistics, mathematics and computing.

Develop the skills and understanding to apply modern statistical and data-science tools to gain insight from contemporary data sets. By addressing challenges from a variety of applications, such as social science, public health, industry and environmental science, you will learn how to perform and present an exploratory data analysis, deploy statistical approaches to analyse data and draw conclusions, as well as developing judgement to critically evaluate the appropriateness of chosen methods for real-world challenges.

Building on your knowledge of vectors and matrices, this module explores the elegant framework of linear algebra, a powerful mathematical toolkit with remarkably diverse applications across statistical analysis, advanced algebra, graph theory, and machine learning.

You'll develop a comprehensive understanding of fundamental concepts, including vector spaces and subspaces, linear maps, linear independence, orthogonality, and the spectral decomposition theorem.

Through individual exploration, small-group collaboration, and computational exercises, you'll gain both theoretical insight and practical skills. The module emphasises how these abstract concepts translate into powerful problem-solving techniques across multiple disciplines, preparing you for advanced studies while developing your analytical reasoning abilities.

This module provides you with a rigorous understanding of microeconomic principles that underpin sophisticated economic analysis and prepares you for further studies in economics. You will explore key microeconomic concepts including utility maximisation, profit maximisation, cost minimisation, market structures, externalities, information economics, public goods, general equilibrium theory, and welfare economics.

To succeed in this module, you will need problem-solving skills and to be proficient in algebra, elementary calculus and logical reasoning.

Statistics allows us to estimate trends and patterns in data and gives a principled way to quantify uncertainty in these estimates. The findings can lead to new insights and support decision-making in fields as diverse as cyber security, human behaviour, finance and economics, medicine, epidemiology, environmental sustainability and many more.

Dive into the behaviour of multivariate random variables and asymptotic probability theory, both of which are central to statistical inference. You will then be equipped to explore one of the most fundamental statistical models, the linear regression model, and learn how to apply general statistical inference techniques to multi-parameter statistical models. Statistical computing is embedded in the module, allowing you to investigate multivariate probability distributions, simulate random data, and implement statistical methods.

This module is designed to enhance your strategic thinking skills. You will learn how to use games to model real-world strategic situations, and how to analyse and solve these games in scenarios where players are intelligent and rational.

The module covers:

• normal form games
• extensive form games
• Bayesian games
• games with correlation devices
• repetitive games
• behavioural games

Additionally, you will have opportunities to play these games with your instructor and classmates. A basic understanding of algebra, calculus and economics is necessary for this module.

In this module you will extend the knowledge of macroeconomics that you developed in your first year. Although the primary focus of the module is on macroeconomic theory, this is taught within the context of current events in the international macroeconomic environment. The topics covered include classical and Keynesian views, unemployment, the government budget constraint, monetary and fiscal policy, intertemporal macroeconomics, economic policy in the open economy, unemployment and inflation, adaptive and rational expectations, policy effectiveness under rational expectations, the economics of independent central banks, and growth theory.

To succeed in this module, you will need to apply algebra, basic calculus, logical thinking, and problem-solving skills.

Machine learning is at the heart of modern AI systems, and it is a fundamentally mathematical subject. You will learn this mathematics by discovering how techniques are deployed in several AI systems, including the neural networks that have revolutionised the field.

You’ll start by building connections with previously encountered approaches through the unifying concept of a loss function of a parameter vector. For example, with a neural network model the vector input is the set of weights, and the loss function might be the prediction error on a dataset.

The goal is to find a vector input that produces a small loss; in the above example, this is known as training the neural net. You will learn and deploy some of the key mathematical ideas and numerical techniques, such as back propagation and stochastic gradient descent, that enable the automated iterative learning of a good vector input.

Many real-world problems give rise to integrals and ordinary differential equation (ODEs) that cannot be solved analytically. To start, you will be introduced to techniques for tackling such problems, beginning with fundamental numerical methods, such as the trapezium rule and Euler’s method, before progressing to more advanced techniques and quantifying the accuracy, stability and limitations of these methods. Alongside numerical approaches, you will also develop heuristic methods to characterise a system's limiting behaviour.

Many familiar phenomena, from the pulses of light down a fibre optic cable to the shudder of turbulence on a plane, involve multiple variables, such as time and position. Their mathematical description requires differentiation with respect to each of these independent variables, leading to partial differential equations (PDEs). You will learn how to formulate PDEs for complex, real-world problems and practice core techniques for solving them.

You will spend this year working in a graduate-level placement role. This is an ideal opportunity to gain experience in an industry or sector that you might be considering working in once you graduate.

Although it's up to you to find your placement we'll support you all the way. Our Careers Service will provide guidance on CVs, applications, interview techniques and creating a digital profile.

Building on the statistical techniques explored so far, you will gain an understanding of both the theoretical underpinnings and practical application of frequentist statistical inference. You will then be introduced to an alternative paradigm: Bayesian statistics.

The frequentist perspective views all probabilities in terms of the proportions of outcomes over repeated experimentation and has been the foundation of hypothesis testing and experimental design in years of data-driven science and research. Meanwhile, the increasingly popular Bayesian approach arises directly from Bayes theorem, avoiding hypothetical repeated sampling. As a result, Bayesian statistics is often more intuitive and easier to communicate and naturally takes all forms of uncertainty into account.

With this in mind, you will compare and contrast these two perspectives and their associated tools. You will learn to select and justify an appropriate methodology for inference and model selection, and to reason about the uncertainty in your findings within each paradigm.

This module will introduce you to the field of behavioural and experimental economics. It will equip you with the necessary skills to study how the standard rationality assumptions can be relaxed to account for psychological and cognitive biases as well as social preferences. Additionally, you will be introduced to the tool of experimentation in economics as a means of collecting data to test the various economic theories.

Some of the topics covered will include:

• behavioural finance
• rational emotions
• nudging
• choice under risk
• time preferences
• social preferences
• behavioural game theory

Understanding how data evolves over time is crucial across numerous sectors, from finance and engineering to climate science. Develop the tools to analyse temporal data, detect structural changes and build predictive models.

Using changepoint detection algorithms, you will learn how to identify abrupt changes in the mean or variance of a process, or parameters in a regression model. These methods will be introduced from a foundational perspective, developing both computational and mathematical understanding. You will then learn to handle temporal dependence by studying a popular range of time-series models, using these to generate insights about the data and produce forecasts. Throughout the module, you will learn to critically evaluate and compare models, whilst applying these techniques to real-world challenges.

Models of dynamical systems are fundamental to our understanding of the physical and natural world.

Explore a new class of model for the time evolution of a dynamical system and investigate Markov jump process models for real-world systems, such as the evolution of species populations in the wild and the spread of infectious diseases. Using these processes, you will learn how to simulate and study methods understanding their properties and behaviours. Unlike deterministic differential equation models, Markov jump processes are random, allowing for different behaviour every time they are simulated. You will discover how it is often possible to associate a jump process with a related differential equation approximation and that this can provide important insights into the behaviour of the jump process and the original real-world system.

Data science is transforming the role of information technology in society and in many sectors in which economists work. Machine learning and big data methods have gained popularity as tools in academic, government, industry, and beyond.

You will be introduced to big data and machine learning techniques with a focus on economic applications. These techniques are already significantly impacting the field of economics for modelling economic relationship, drawing causal inferences, and making predictions. They will soon become a standard toolbox for economists.

An introduction to a variety of methods that are useful for analysing environmental data, such as air temperatures, rainfall or wildfire locations. Spatial dependence is a key feature of many environmental datasets, and the Gaussian process will be introduced as a model for continuous spatial processes. You will learn about the properties of the Gaussian process and implement this model for spatial data analysis, before investigating methods for point-reference data, such as earthquake or wildfire locations.

You will also dip into natural hazard risk management, which seeks to mitigate the effects of events, such as flooding or storms, in a manner that is proportionate to the risk. You will learn basic concepts from extreme value theory, including the appropriate distributions for extremes, and how to use these as statistical models for estimating the probability of events more extreme than those in the dataset.

This module will introduce you to current economic research. Experts from a variety of fields will teach you in-depth about how economic research is conducted and its real-world applications. By the end of this module, you will be able to:

• Apply advanced economic methods and concepts to evaluate contemporary economic problems.
• Critically think about the issues raised by economic research, including their applications and limitations.
• Present the methods and conclusions of advanced economic research using a wide variety of presentational tools.
• Consolidate the core knowledge, methods, and analytical skills you have developed throughout your degree.

These skills will prepare you for a professional career in economics and related fields, as well as for further academic study.

This module builds on the foundations of monetary and fiscal policy analysis by placing policy decisions in a global context. The first part of the module emphasises the interpretation and analysis of macroeconomic data. You will learn how to apply empirical methods to understand fluctuations in output, employment, inflation, and trade balances.

The second part focuses on the design and coordination of monetary and fiscal policy in an interconnected world. Special attention will be given to the challenges that central banks and governments face in managing global shocks. The topics covered will include international policy spillovers, exchange rate regimes, capital flows, and the evolving role of institutions such as the IMF and the Bank of England. We will explore real-world applications and current policy debates throughout the module.

The study of graphs (mathematical objects used to model networks and pairwise relations between objects) is a cornerstone of discrete mathematics. Graphs can represent important real-world situations, and the study of algorithms for graph-theoretical problems has strong practical significance.

You will learn about structural and topological properties of graphs, including graph minors, planarity and colouring. We will introduce several theoretical tools, including matrices relating to graphs and the Tutte polynomial. We will also study fundamental algorithms for network exploration, routing and flows, with applications to the theory of connectivity and trees, considering implementation, proofs of correctness and efficiency of algorithms.

You will gain experience in following and constructing mathematical proofs, correctly and coherently using mathematical notation, and choosing and carrying out appropriate algorithms to solve problems. The module will enable you to develop an appreciation for a range of discrete mathematical techniques.

This module provides a comprehensive exploration of international trade and global business dynamics, connecting theoretical models with practical policy implications. You will examine core trade theories including the Ricardian model, Heckscher-Ohlin model, and heterogeneous firm models. The module also offers in-depth analyses of international factor mobility, trade policies, and globalisation trends.

On the international business side, you will study key topics such as global value chains, multinational firm strategies, international competitive advantage, and the economic impacts of outsourcing and offshoring. The module focuses on real-world applications, exploring how theoretical frameworks inform understanding of contemporary economic phenomena, including labour productivity, attitudes towards trade, the effects of immigration, and the evolving landscape of global economic interactions.

Lay the mathematical foundations necessary to model certain transactions in the world of finance. You will study some stochastic models for financial markets and investigate the pricing of European and American options and other financial products.

You will consider two discrete models, the binomial model and finite market model, and one continuous model. In particular, you’ll deduce the Black Scholes formula following an introduction to some probabilistic terminology, such as sigma algebras and martingales, and some financial terminology such as arbitrage opportunities and self-financing trading strategies. You will also gain a brief overview of Brownian motion.

AI is suddenly everywhere and the methods for training and using AI tools are fundamentally mathematical, and fascinating in their own right. By understanding what goes on ‘under the hood’ you will open up a plethora of exciting opportunities for both further study and employment.

We will introduce you to the deep learning architectures used in modern AI. You will investigate how different architectures work with different data types and tasks, and what the computationally specified architectures actually mean in a modelling sense.

However, deep neural nets need more than just an appropriate architecture; they need to be both trained and deployed. You’ll study the interesting maths at each of these stages: the most recent approaches to loss function minimisation, and the techniques to sequentially learn and adapt to new data and observations, a critical component of modern AI methods.

Public policy analysis is the study of government’s role in the economy. It involves examining both its normative and positive aspects. To gain a comprehensive understanding, we look at a combination of theories, empirical findings, and real-world examples.

We begin by focusing on public goods such as water, transportation, and other infrastructure that the government can provide directly or in collaboration with the private sector. This includes looking at the practice of regulators, as well as cost-benefit analysis. We evaluate the trade-off between efficiency and fairness, then examine state financing, including theories of optimal taxation and recent research on tax evasion and avoidance. Finally, we delve into the internal structure of government, exploring political economy and fiscal federalism.

Stochastic processes are fundamental to probability theory and statistics and appear in many places in both theory and practice. For example, they are used in finance to model stock prices and interest rates, in biology to model population dynamics and the spread of disease, and in physics to describe the motion of particles.

During this module, you will focus on the most basic stochastic processes and how they can be analysed, starting with the simple random walk. Based on a model of how a gambler's fortune changes over time, it questioned whether there are betting strategies that gamblers can use to guarantee a win. We will focus on Markov processes, which are natural generalisations of the simple random walk, and the most important class of stochastic processes. You will discover how to analyse Markov processes and how they are used to model queues and populations.

Statistics and machine learning share the goal of extracting patterns or trends from very large and complex datasets. These patterns are used to forecast or predict future behaviour or interpolate missing information. Learn about the similarities and differences between statistical inference and machine learning algorithms for supervised learning.

You will explore the class of generalised linear models, which is one of the most frequently used classes of supervised learning model. You will learn how to implement these models, how to interpret their output and how to check whether the model is an accurate representation of your dataset. Lastly, you will have the opportunity to see how these models can be extended to the case of the ‘large p, small n’ question. This phrase refers to the situation in which there are many more variables than there are samples, something which is now commonplace.