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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. LearnÌýbasicÌýmodels, particularlyÌýdynamic general equilibrium modelling tools,Ìýand 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'llÌýlearn the fundamentals, apply them to real-worldÌýscenariosÌýand develop analytical skills through mathsÌýand 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, internationalÌýorganisationsÌýand historical and geographical determinants. ÌÇÐÄÔ­´´ topics like the International Monetary Fund (IMF), World Bank, climateÌýchangeÌýand trade policy. Analyse real-world development issues using economic theory.

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

Explore the history of economic development from ancient times to the 20th century. This module covers key themes and methodologies, providing a global perspective on economic growth and development.

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 onÌýcredit 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 andÌýperformanceÌýandÌýevaluate their empirical evidence.

Module description to be confirmed.

ExamineÌýlabourÌýmarket 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 UKÌýlabourÌýmarket and develop presentation and essay writing skills.

ÌÇÐÄÔ­´´ recent developments in macroeconomics, focusing on dynamic optimisation,Ìýreal businessÌýcycleÌýtheoryÌýand 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, dynamicÌýanalysisÌýand 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 marketÌýbehaviour. Explore the role of information in markets and build on your prior knowledge.ÌýÌÇÐÄÔ­´´Ìýadvanced theoretical concepts andÌýtheirÌýpractical applications, developing your analytical skills.

Gain a rigorous understanding of monetary economics, covering classical and modern theories. ÌÇÐÄÔ­´´ central banking, monetaryÌýpolicyÌýand 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, socialÌýinsuranceÌýand public goods. ÌÇÐÄÔ­´´ empirical research on current policy issues like inequality and poverty. Develop informed policy judgements and understand the impact of government actions.

During this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will progress to enhance your understanding of statistical methodology including the analysis of discrete and survival data. You will also be trained in the use of a high-level statistical computer program.

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.

The aim of Discrete Mathematics is the study of discrete and finite rather than continuous quantities. This includes counting problems, graphs and other quantities parametrised by integers.

As such Discrete Mathematics is of great importance for various branches of Pure Mathematics, Mathematical Physics, Statistics and Computer Sciences.

The course will cover a range of Discrete Mathematics topics, including:

• an introduction to advanced aspects of combinations and permutations
• ordinary and exponential generating functions
• recurrence relations and applications to counting problems
• graphs
• digraphs
• Eulerian and Hamiltonian trails
• planar graphs
• graph colouring
• trees
• minimum spanning tree algorithms

You can choose to undertake an independent research project, involving the application of techniques of economicÌýanalysis 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.

A metric space generalises the concept of distance familiar from Euclidean space. It provides a notion of continuity for functions between quite general spaces. The module covers:

• metric spaces
• topological spaces
• compactness
• separation properties like Hausdorffness and normality
• Urysohn’s lemma
• quotient and product topologies, and connectedness

Finally, Borel sets and measurable spaces are introduced.

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,ÌýintegrationÌýand optimisation. Apply these methods to economic and financial problems using software like Python andÌýJupyterÌýNotebook.

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 is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference.

You will explore the following topics in detail:

• sufficiency
• estimating equations
• likelihood ratio tests
• best-unbiased estimators

There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

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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.

This module will provide a general introduction to the analysis of data that arise sequentially in time. Several commonly occurring models will be discussed and their properties derived. Methods for model identification for real time series data will be described. Techniques for estimating the parameters of a model, assessing its fit and forecasting future values will be developed. You will gain experience of using a statistical package and interpreting its output.