You’ll study the basic concepts and standard methods of:

• mathematical notation and proof
• functions
• complex numbers and variables
• solution of equations
• resolution of inequalities
• sequences and series

This module will introduce you to the fundamental concepts of calculus, and you’ll develop some of their applications including basic ordinary differential equations.

You’ll be given an introductory treatment of vectors, matrices, geometry, and discrete maths, and you’ll be introduced to their application to real-world problems.

This module will present the place of mathematics and statistics in society, both historical and contemporary, while introducing some essential study skills. You’ll develop and practise personal and technical skills (for example, self study, teamwork, writing reports and making presentations).

This module will present some basic ideas and techniques of statistics while introducing some essential study skills (for example basic IT, note-taking, study skills for mathematics and statistics).

This module will present some basic ideas and techniques of statistics while introducing some essential study skills, allowing you to develop and practice personal and technical skills (for example, self study, teamwork, analysing data, writing reports and making presentations).

This module will introduce you to the basic ideas of linear algebra, such as matrices and determinants, vector spaces, bases, eigenvalues and eigenvectors. You’ll study various standard methods for solving ordinary differential equations and understand their relevance and the connections with linear algebra.

This module will present the basic ideas, techniques and results for calculus of two or more variables, including partial differentiation and integration over curves, surfaces and volumes.

This module will give a rigorous treatment of convergence of sequences and infinite series of real numbers and of continuity, differentiability and integrability of functions of a real variable, and will illustrate the importance of these concepts in the analysis of problems arising in applications.

This module will present the basic concepts of probability theory and statistical inference, and provide you with the tools to appropriately analyse a given data set and effectively communicate the results of such analysis.

You’ll be introduced to mathematical modelling in a wide variety of contexts. You’ll learn how to employ a variety of tools (including vectors and ODEs) in mathematical modelling.

This module will introduce you to R as both a data-science environment and as a general programming language. You’ll use R to import data and perform exploratory data analysis, including data visualisation. You’ll be introduced to basic concepts in scientific modelling, including parameter exploration, and you’ll be equipped for implementing and debugging simple models in R.

This module will demonstrate the central role linear algebra plays in applied mathematics. You’ll be provided with the tools to solve equations involving matrices. You’ll see how theoretical considerations lead to efficient computational techniques, and gain practical experience of solving linear algebra problems computationally.

This module will introduce and provide understanding of the least squares multiple regression model, general linear model, transformations and variable selection procedures, helping you to understand their importance in contemporary technology.

By the end of the module, you’ll be familiar with, and able to perform in R, multiple linear regression, generalised linear models (Poisson and Negative Binomial), generalised additive models, and penalised regression models.

This module will provide a broad introduction to analytical methods for solving partial differential equations. You’ll develop your understanding and technical skills in this area.

This module will equip you with a widely applicable toolkit of methods for mathematical modelling, with a focus on ordinary and partial differential equations. You’ll apply this toolkit to a range of modelling problems drawn from physics, biology, and other areas.

This module will give you a solid grounding in the fundamental concepts of algebraic structures, including (semi)groups, rings, and fields. As well as covering the basics of these structures, you’ll also explore other topics such as sets, equivalence relations and group actions.

Game theory is a mathematical framework and a powerful tool for analysing strategic decisions among rational decision makers. This module will equip you with the ability to model, analyse and predict outcomes in competitive and cooperative scenarios. You’ll gain a solid foundation in game theory and its applications to real-world problems, allowing you to explore how game theory can be applied to address global sustainability challenges, achieving United Nations Sustainable Development Goals.

This module will introduce you to the concepts of univariate and multivariate probability distributions and their properties. You’ll learn about generating functions and their applications. The module will present approaches to parameter estimation, focussing on maximum likelihood estimation and properties of estimators.

This module will provide you with the fundamental principles of statistical modelling through experimental design. You’ll derive the statistical models used in the analysis of balanced experimental designs and use them in the analysis of data sets. The fundamental principles of balance, replication, blocking, interactions, nesting and repeated measures are all covered.

This module will provide an overview of the fundamental tools used in survey design and analysis. You’ll learn how to apply the principles of survey design to create and carry out surveys, and you’ll develop skills in the analysis of survey data, as well as in the interpretation and presentation of results.

This module will expose you to a number of diverse topics in stochastic processes that can be used to model real systems. In addition to theoretical analysis, appropriate computational algorithms using R are introduced.

This module will introduce you to the basic theory and applications of:

• metric spaces
• normed vector spaces and Banach spaces
• inner product spaces and Hilbert spaces
• bounded linear operators on normed linear spaces

This module will motivate the need for numerical algorithms to approximate the solution of problems that cannot be solved with pen and paper. You’ll develop skills in performing detailed analysis of the performance of numerical methods, and continue to develop your skills in the implementation of numerical algorithms using Matlab.

This module will provide you with experience of the skills required to undertake project work, and to communicate the findings in written and oral form using a variety of sources, such as books, journals and the internet.

You’ll be introduced to ideas in mathematics and statistics that can be used to model real systems, with an emphasis on the valuation of financial derivatives.

The module places equal emphasis on deterministic analysis (calculus, differential equations) and stochastic analysis (Brownian motion, birth and death processes). In both cases, in addition to theoretical analysis, appropriate computational algorithms are introduced.

The first half of the module introduces general modelling and simulation tools, and the second half focuses on the specific application of valuing financial derivatives, including the celebrated Black-Scholes theory.

This module will present the main results in Functional Analysis, give you an introduction to linear operators on Banach and Hilbert spaces, and study applications to integral and differential equations.

This module will provide you with a range of applied statistical techniques that can be used in professional life. You’ll learn the fundamental principles of statistical modelling through experimental design and multivariate analysis.

This module will present you with the basic theory and practice of finite element methods and polynomial and piecewise polynomial approximation theory.

This module will introduce you to a range of modern statistical methods and practices used in industry, commerce and research, and you'll develop skills in their application and presentation.

This module will teach the application of mathematical models to a variety of general problems in biology, medicine, and ecology, with many applications drawn from marine population modelling.

You’ll see the application of ordinary differential equations to simple biological and medical problems, the use of mathematical modelling in biochemical reactions, and the application of partial differential equations in describing spatial processes such as cancer growth and pattern formation in embryonic development.

The marine population modelling applications will also introduce you to the use of difference models to represent population processes through applications to fisheries, and the use of coupled ODE system to describe ecosystems.

This module will demonstrate the central role network theory plays in mathematical modelling. You’ll see the intimate connection between linear algebra and graph theory, and use this connection to develop a sound theoretical understanding of network theory. You’ll apply the theory as a tool for revealing structure in networks, and apply the algorithms on a network using computer codes.

You’ll learn new statistical methodology and apply it to real data from medical research studies, with an emphasis on the interpretation of the statistical results in the context of the medical problem being investigated. This skill is necessary for the application of statistics to medical data and differs from the traditional, standard interpretation of statistical textbook problems.

You’ll be provided with experience and expertise in skills required to undertake a sustained and significant individual project in a mathematical or statistical area, using a variety of sources, such as books, journals and the internet, and to communicate the findings in written and oral form.

This module will provide a mathematical understanding of modern approaches to optimization and the calculus of variations.

This module will provide an overview of the fundamental tools used in survey design and analysis. You’ll learn how to apply the principles of survey design to create and carry out surveys, and you’ll develop skills in the analysis of survey data, as well as in the interpretation and presentation of results.

You’ll be introduced to ideas in mathematics and statistics that can be used to model real systems, with an emphasis on the valuation of financial derivatives.

The module places equal emphasis on deterministic analysis (calculus, differential equations) and stochastic analysis (Brownian motion, birth and death processes). In both cases, in addition to theoretical analysis, appropriate computational algorithms are introduced.

The first half of the module introduces general modelling and simulation tools, and the second half focuses on the specific application of valuing financial derivatives, including the celebrated Black-Scholes theory.

This module will present the main results in Functional Analysis, give you an introduction to linear operators on Banach and Hilbert spaces, and study applications to integral and differential equations.

This module will present you with the basic theory and practice of finite element methods and polynomial and piecewise polynomial approximation theory.

This module will teach the application of mathematical models to a variety of general problems in biology, medicine, and ecology, with many applications drawn from marine population modelling.

You’ll see the application of ordinary differential equations to simple biological and medical problems, the use of mathematical modelling in biochemical reactions, and the application of partial differential equations in describing spatial processes such as cancer growth and pattern formation in embryonic development.

The marine population modelling applications will also introduce you to the use of difference models to represent population processes through applications to fisheries, and the use of coupled ODE system to describe ecosystems.

This module will demonstrate the central role network theory plays in mathematical modelling. You’ll see the intimate connection between linear algebra and graph theory, and use this connection to develop a sound theoretical understanding of network theory. You’ll apply the theory as a tool for revealing structure in networks, and apply the algorithms on a network using computer codes.

You’ll learn new statistical methodology and apply it to real data from medical research studies, with an emphasis on the interpretation of the statistical results in the context of the medical problem being investigated. This skill is necessary for the application of statistics to medical data and differs from the traditional, standard interpretation of statistical textbook problems.

This module will provide you with the fundamental principles of statistical modelling through experimental design. You’ll derive the statistical models used in the analysis of balanced experimental designs and use them in the analysis of data sets. The fundamental principles of balance, replication, blocking, interactions, nesting and repeated measures are all covered.

This module covers all aspects of statistical consultancy skills necessary for being a successful statistician working in any research or customer environment. You will work on real-life problems in small groups and have the opportunity to interact with stakeholders researchers to formulate hypotheses.

This module will cover how to:

• engage with professionals working in business, industry and the public sector
• apply their statistical knowledge in different situations
• effectively communicate statistical results to non-statisticians

This module aims to provide you with a range of applied statistical techniques that can be used in professional life to analyse multivariate data. Both statistical and machine learning approaches are included.

You'll cover topics such as:

• graphical methods for investigating multivariate data
• logistic regression and discrimination
• linear and quadratic discriminant analysis
• non-parametric classification
• hierarchical and non-hierarchical clustering
• principal component analysis

Most people have an intuitive understanding of what risk is. The aim of this module is to formalise this understanding and develop models to quantify risk. Quantification of risk relies on many statistical methods. The emphasis in this course is the practical use of such methods.

You'll develop skills in communicating risk to risk managers as well as formulating practical risk questions that can influence policy decisions.

You can expect to learn about:

• the difference between uncertainty and variability
• quantifying uncertainty using methods such as bootstrapping and Bayesian inference
• selecting appropriate probability distributions based on given scenarios
• fitting probability distributions to data
• building risk models
• communicating your results as written reports

All theory will be implemented practically via computing sessions using the statistical software R. You'll learn to create bespoke functions in R to implement your models and use summary statistics and plots to communicate your results. 

This module will introduce you to Bayesian statistics and the modern Bayesian methods that are used in a variety of applications. Like with other modules, the focus is on real-life data and using statistical software packages for analysis.

You will gain experience in working with the following:

• visualising spatial data
• geospatial data, including methods for prediction
• bayesian modelling using software to implement Markov Chain Monte Carlo
• areal unit modelling

This module will develop your skills in data presentation and statistical communication. You will learn to develop data dashboards, which are increasingly used to allow key stakeholders (and the public) to gain key insights into data via interactive visualisation.

Topics covered will include:

• Creating a data dashboard in RStudio
• User interface design with respect to accessibility
• Creating interactive data visualisations which reflect a specific aim
• Reactive programming  in RStudio
• Static programming in R

This module provides you with the basic theories of machine learning and how to construct a machine model for a real dataset using R. You will also understand the ethical issues regarding data processing and management.

On completion of this module, you will be able to:

• clean data using RStudio and the tidyverse
• understand missing data and the role it plays
• understand ethical issues regarding data processing and management
• carry out single-value imputation
• carry out multiple imputed chained equations in R
• understand and implement artificial neural networks
• understand and implement support vector machines
• understand and implement tree-based classification and regression techniques
• understand and implement ensemble methods

This module aims to develop a more fundamental understanding of the mathematics of Machine Learning (ML) and of the ideas underpinning some classical algorithms in the field. Students will learn to critically interpret new algorithms in ML and to compare different techniques and the outputs they produce. By working on real world problems, students will be able to develop their coding skills.

To develop techniques for analysing the qualitative behaviour of solutions to ordinary differential equations and to introduce fundamental concepts associated with partial differential equations.

To develop expertise in asymptotic and integral methods, in particular for the solution of differential equations.

The module will enable you to develop a fundamental understanding of the mathematics of deep learning and the ideas underpinning traditional models and algorithms in the field. You'll be able to critically interpret algorithms in deep learning with particular reference to various strategies and training data augmentation and improving inference accuracy.