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In this Autumn semester module, you’ll be introduced to the basic mathematical concepts that underpin all degree programmes offered by the School of Mathematical Sciences. The major components are:

• mathematical fundamentals: logic; complex numbers; functions; set theory; introduction to cardinality; ordinary differential equations.
• linear algebra: systems of linear equations; introduction to matrices and matrix algebra.
• analysis: the real numbers; sequences; infinite series; limits and continuity of functions.
• programming in python: variables; logic and loops; functions; plotting graphs; debugging.

The overall aim of the module is to build on your existing mathematical knowledge, with an emphasis on developing mathematical skills, deepening understanding, and increasing confidence in applying a broad range of concepts and techniques. More specifically, the module introduces and provides practice in logical reasoning and rigorous mathematical thinking, particularly in relation to linear algebra and real analysis.

In this Spring semester module, you’ll build upon the basic mathematical concepts covered in ‘Core Mathematics 1’ and provides practice in logical reasoning and rigorous mathematical thinking, particularly in relation to linear algebra and real analysis. The major components are:

• linear algebra: vector spaces; linear maps; eigenvalues and eigenvectors.
• analysis: single-variable and multi-variable calculus (differential and integral).

Discover the big picture of the economy with this introductory macroeconomics course. Focus on the cyclical patterns of aggregate output and the interplay of real and monetary factors. Learn basic models, particularly dynamic general equilibrium modelling tools, and apply them to both theoretical and practical situations.ÌýDevelop your analytical and communication skills through essays and presentations.

Dive into the world of microeconomics, exploring how firms and households make decisions in various market conditions.ÌýYou'll learn the fundamentals, apply them to real-world scenarios and develop analytical skills through maths and diagrams. Engage in discussions and tutorials to enhance your understanding and communication skills.

Probability theory allows us to assess risk when calculating insurance premiums. It can help when making investment decisions. It can be used to estimate the impact that government policy will have on climate change or the spread of disease. In this module, you will study the theory and practice of discrete and continuous probability, including topics such as Bayes’ theorem, multivariate random variables, probability distributions and the central limit theorem.

Statistics is concerned with methods for collecting, organising, summarising, presenting and analysing data. It enables us to draw valid conclusions and make reasonable decisions based on statistical analysis. It can be used to answer a diverse range of questions in areas such as the pharmaceuticals industry, economic planning and finance. In this module you’ll study statistical inference and learn how to analyse, interpret and report data. Topics that you’ll learn about include, point estimators and confidence intervals, hypothesis testing, linear regression and goodness-of-fit tests.

This course introduces the theory and applications of functions of a complex variable, using an approach oriented towards methods and applications. You will also learn about functions of complex variables and study topics including, analyticity, Laurent series, contour integrals and residue calculus and its applications.

In this module you will further develop your understanding of the tools of real analysis. This provides you with a solid foundation for subsequent modules in metric spaces, numerical analysis and PDE modelling. You will study topics such as convergence, norms and topology of multidimensional space, convergence of sequences of functions and applications of differentiation and integration.

Explore factors influencing growth and development, focusing on economic policies, international organisations and historical and geographical determinants. ÌÇÐÄÔ­´´ topics like the International Monetary Fund (IMF), World Bank, climate change and trade policy. Analyse real-world development issues using economic theory.

Build on your econometric knowledge with advanced techniques. ÌÇÐÄÔ­´´ large sample theory, time series analysis and non-stationarity. Understand the theoretical properties of econometric models and their practical applications in economic analysis.

The aims of the module are to develop your understanding of experimental economics and the main approaches of behavioural economics. It will illustrate different types of experiment that can be undertaken in economics and enable you to understand their designs and purposes, and to assess their strengths and weaknesses.Ìý

This module covers:

• saving, focusing on how agents make intertemporal decisions about their savings and wealth accumulation
• saving puzzles and household portfolios, focusing on credit markets and credit markets' imperfections, and why do households hold different kinds of assets
• asset allocation and asset pricing, focusing on intertemporal portfolio selection, asset pricing and the equity premium puzzle
• bond markets and fixed income securities
• the term structure of interest rates
• the role of behavioural finance in explaining stock market puzzles

Analyse the organisation of firms and industries with a focus on market competition. ÌÇÐÄÔ­´´ various market structures, especially imperfect competition. Understand alternative theories of market structure and performance and evaluate their empirical evidence.

Examine labour market economics with a focus on policy implications and institutional arrangements. ÌÇÐÄÔ­´´ worker compensation schemes and their impact on productivity. Analyse theoretical and empirical aspects of the UK labour market and develop presentation and essay writing skills.

ÌÇÐÄÔ­´´ recent developments in macroeconomics, focusing on dynamic optimisation, real business cycle theory and economic growth. Apply these theories to policy issues and understand the techniques used by macroeconomic researchers.

Explore advanced mathematical techniques used in economic analysis. ÌÇÐÄÔ­´´ topics like optimisation, dynamic analysis and game theory. Develop a rigorous understanding of mathematical tools and their applications in economic theory.

Deepen your understanding of microeconomic theory with a focus on decision theory and market behaviour. Explore the role of information in markets and build on your prior knowledge.ÌýÌÇÐÄÔ­´´Â advanced theoretical concepts and their practical applications, developing your analytical skills.

Gain a rigorous understanding of monetary economics, covering classical and modern theories. ÌÇÐÄÔ­´´ central banking, monetary policy and the monetary transmission mechanism. Analyse recent developments and debates in monetary economics.

This module will acquaint you with some literature in theoretical and applied political economy. It provides an opportunity for interdisciplinary study within your Economics degree, and it will Enrich your study of economics with insights from political science and political philosophy.

Analyse the role of government in the economy, focusing on tax and welfare policies, social insurance and public goods. ÌÇÐÄÔ­´´ empirical research on current policy issues like inequality and poverty. Develop informed policy judgements and understand the impact of government actions.

This module provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. You’ll learn cryptography, including classical mono- and polyalphabetic ciphers.Ìý There will also be a focus on modern public key cryptography and digital signatures, their uses and applications.

You can choose to undertake an independent research project, involving the application of techniques of economic analysis to a research topic of your choice. For this module, you’ll write an economics research paper. You’ll be supported with writing an undergraduate dissertation in economics.

Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoner’s Dilemma. We look at tree-searching, including alpha-beta pruning, the ‘killer’ heuristic and its relatives. It then turns to mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.

This module will provide an introduction to international monetary issues, including the determination of exchange rates and international spill-over effects.Ìý

You will explore the concepts of discrete time Markov chains to understand how they used. We will also provide an introduction to probabilistic and stochastic modelling of investment strategies, and for the pricing of financial derivatives in risky markets.

You will gain well-rounded knowledge of contemporary issues which are of importance in research and workplace applications.

This module involves the application of mathematics to a variety of practical, open-ended problems - typical of those that mathematicians encounter in industry and commerce.

Specific projects are tackled through workshops and student-led group activities. The real-life nature of the problems requires you to develop skills in model development and refinement, report writing and teamwork. There are various streams within the module, for example:

• Pure Mathematics
• Applied Mathematics
• Data Analysis
• Mathematical Physics

This ensures that you can work in the area that you find most interesting.

This module is concerned with the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. Key topics to be covered include:

• Vector and matrix algebra ideas relevant to multivariate statistics, including the eigen and singular value decompositions
• Methods for dimension reduction including principal components analysis, canonical correlation analysis, and factor analysis
• Multivariate regression methods.
• Classification methods, such as linear discriminant analysis.
• Multivariate normal distributions and their use in multivariate analysis of variance tests
• Exploratory data analysis methods such as clustering tools, and multi-dimensional scaling, as well as other data visualisation techniques.
• Statistical software for conducting analysis of multivariate data

Learn programming tools widely used in economics. ÌÇÐÄÔ­´´ numerical methods like differentiation, integration and optimisation. Apply these methods to economic and financial problems using software like Python and Jupyter Notebook.

In this module a variety of techniques of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming.

These techniques have a wide range of applications to real world problems, in which a process or system needs to be made to perform optimally.

This module will develop your knowledge of discrete-time Markov chains by applying them to a range of stochastic models. You will be introduced to Poisson and birth-and-death processes. You will then move onto more extensive studies of epidemic models and queuing models, with introductions to component and system reliability.

Conduct an independent research project on a self-chosen economic topic. Apply economic analysis techniques and present your findings in an academic article. Develop your research, analytical and communication skills through this comprehensive project.

This module introduces measures (which generalise the notions of length and volume) and integrals (generalising the familiar version from calculus). As applications, we consider fractal sets, which often show unexpected properties.

The aim of this module is for you to acquire knowledge and experience of the Bayesian theory of statistical inference. You will develop an understanding of the mathematical basis of Bayesian inference and the core computational techniques used to implement Bayesian methodology in real life examples.ÌýYou will acquire knowledge and skills relevant to a professional statistician and/or data scientist.

This module will deepen and broaden your knowledge of statistics by introducing you to statistical theory and methodology for handling data with structural dependencies. This understanding is developed using temporal and other forms of dependence along with predictions for future or other events. You will acquire knowledge and skills of relevance to a professional and/or research statistician/data scientist.Ìý 

Modelling is a fundamental part of statistics, enabling us to analyse and interpret data to understand the world and make predictions.Ìý

This module studies statistical models for regression beyond linear models, including nonlinear regression, Gaussian Process regression and regression with binary and count data. These topics are the foundations of statistical machine learning and neural networks in AI. You will gain an understanding of the theoretical foundations of these areas along with the knowledge of how to implement the techniques in a computationally efficient manner to analyse data.Ìý 

Explore a range of graph theory topics, including an introduction to advanced aspects of combinations and permutations, graphs, digraphs, Eulerian and Hamiltonian trails, planar graphs, graph colouring, chromatic polynomials, trees and minimum spanning tree algorithms.

This module provides a self-contained account of the basic ideas of graph theory, which will enable you to acquire the necessary knowledge and skills to solve problems in the topic and to establish the grounding for further study in this area.

Scientific Computation and Numerical Analysis covers advanced numerical methods, and its analysis, for the approximate solution of important mathematical problems, such as solving partial differential equations (PDEs), finding solutions to overdetermined systems, rapidly solving large linear systems of equations, and finding matrix approximations. Methods discussed have important applications in modern-day society, including PDEs in engineering and applied sciences, Google's PageRank algorithm, model reduction and machine learning in data science. Specific techniques include:

• The finite element method (FEM) for PDEs, including weak formulations and its Galerkin discretization, and a priori error analysis
• Advanced methods for linear systems, including QR factorization, perturbation and conditioning theory, and the innovative Conjugate Gradient (CG) method
• Methods for low-rank approximation, including computation of eigenvalues, the singular value decomposition (SVD), and the fundamental Eckart-Young theory for best rank-k matrix approximation.'

Focus on econometric methods for policy evaluation and causal effect estimation. ÌÇÐÄÔ­´´ regression analysis, instrumental variables, difference-in-differences techniques and regression discontinuity. Apply these methods to cross-section and panel data to understand economic policies and outcomes.

Analyse economic policies using examples from environmental economics and international trade. ÌÇÐÄÔ­´´ climate change policies, discounting future outcomes and policy evaluation methods. Apply theoretical and empirical tools to make policy recommendations.

ÌÇÐÄÔ­´´ trade policy, economic policy for trade and international factor mobility, imperfect competition and trade distortions. Analyse the effects of trade policy interventions and understand the principles of optimal intervention. Learn about the political economy of protection and trade policy reform.

Gain advanced analytical tools to understand global economies. ÌÇÐÄÔ­´´ comparative advantage, economic integration and the impact of globalisation. Analyse trade benefits, economic inequalities and the role of international production and labour migration.ÌýDevelop theoretical and empirical skills to interpret trade dynamics.