This covers 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 introduces the fundamental concepts of calculus, and develops some of their applications including basic ordinary differential equations.

This module will present some basic ideas and techniques of statistics while introducing some essential study skills.

An introductory treatment of linear algebra and geometry.

This module will help you achieve a broad knowledge of the essence of computation and computational systems, as embodied by the notions of computable functions, formal languages and recursion, logic and computability and abstract machines.

This module will help you understand a broad knowledge of information systems and how information is created, used and disseminated within an information society.

This module will provide you with a solid foundation in the principles of computer programming. On completing this module you should have the necessary skills to be able to design, build and test a small system in a high-level language (Java in the current incarnation of the module).

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.

This module will present basic ideas, techniques and results for calculus of two and three variables, along with differentiation and integration over curves, surfaces and volumes of both scalar and vector fields.

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. It will illustrate the importance of these concepts in the analysis of problems arising in applications.

This module will further your skills in object-oriented programming, provide knowledge of key abstract data types along with their implementation and usage, and provide experience in the development of larger scale software and an introduction to design.

Your main goal is to be able to develop larger programs with specialised data structures and utilising APIs from a specification, and be able to ensure and show how the system they developed matches the specification.

This module will equip you with the tools to model and measure computation. To build on the module Machines, Languages and Computation, and develop further understanding of the mathematical foundations of computation. To foster an analytical and empirical appreciation of the behaviour of algorithms and the use of abstract data types.

This module will provide you with a critical appreciation and understanding of how to model user activities and the data to support them, together with how to implement systems and databases to support user activities.

In this module we'll introduce basic algebraic structures, with particular emphasis on those pertaining to finite dimensional linear spaces and deepen your understanding of linear mappings. We'll also provide an introduction to inner product spaces and bilinear forms.

In this module we’ll introduce you to analytical methods for solving ordinary and partial differential equations, so you'll develop an understanding along with technical skills in this area.

In this module you will be introduced 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 can’t be solved with pen and paper. You’ll develop your skills in performing detailed analysis of the performance of numerical methods and will continue to develop your skills in the implementation of numerical algorithms using R.

This module will extend and deepen your understanding of the analysis, design and implementation of software systems; to provide further experience in the activity of designing and implementing non-trivial systems; and to enable you to demonstrate practical competence in a group environment.

Your goal is the development in a group setting of significant systems from scratch aiming not just at any solution but a good solution, and to be introduced to more general Software Engineering topics.

This module will help to give you a broad appreciation of the scale and nature of the problems within Artificial Intelligence and to a detailed understanding of some of the fundamental techniques used to address those problems.

The module will provide familiarisation with the definition of programming language syntax and semantics, and the translation of these definitions into an implementation of a programming language.

This module will give you an understanding of the technologies used in the development of N-tier Internet-based applications.

The module aims to provide you with skills in basic functional programming and experience in integrated deployment of those skills.

The module will provide you with a good understanding of the issues in developing for mobile environments, approaches to handling these issues and skills in developing for a widespread mobile platform.

This module provides 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 will undertake an individual research project, researching a mathematical or statistical topic and writing a short report on it.

This module will allow you to demonstrate practical and documentary competence. You'll also be expected to give a demonstration of your work.

In this module you'll get an introduction to ideas in mathematics and statistics that can be used to model real systems, with an emphasis on the valuation of financial derivatives. This 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. You will also be introduced to linear operators on Banach and Hilbert spaces and study applications to integral and differential equations.

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

In this module you'll be introduced to the theory of Newtonian fluids and its application to flow problems and the dynamics of waves on water and in other contexts.

In this module you'll be presented with the basic theory and practice of finite element methods and polynomial and piecewise polynomial approximation theory.

In this module you'll be introduced to a range of modern statistical methods and practices used in industry, commerce and research, and you will develop skills in your application and presentation.

This module will demonstrate the central role network theory plays in mathematical modelling. It'll also show the intimate connection between linear algebra and graph theory and how to use this connection to develop a sound theoretical understanding of network theory. Finally, it'll apply this theory as a tool for revealing structure in networks.

In this module, you'll learn the application of mathematical models to a variety of problems in biology, medicine, and ecology. The module will show:

• the application of ordinary differential equations to simple biological and medical problems
• the use of mathematical modelling in biochemical reactions
• the application of partial differential equations in describing spatial processes such as cancer growth and pattern formation in embryonic development
• the use of delay-differential equations in physiological processes.

The marine population modelling element will introduce the use of difference models to represent population processes through applications to fisheries, and the use of coupled ODE system to represent ecosystems. Practical work will include example class case studies that will explore a real-world application of an ecosystem model.

This module will cover the application of classical statistical methods to data collected for health care research. There will be an emphasis on the use of real data and the interpretation of statistical analyses in the context of the research hypothesis under investigation. Topics covered will include:

• survival analysis
• experimental design and sampling
• categorical data analysis
• clinical measurement

This module will allow you to understand the mathematical structures arising in advanced functional programs as mediated by the following concepts: type classes and constructor classes, monoids, functors, applicative functors, monads and monad transformers, arrows, comonads, inductive and coinductive types, recursion patterns including folds and unfolds, continuations, and generalised algebraic data types.

This module aims to:

• enable you to understand the challenges of advanced software design and the issues associated with large-scale software architectures, frameworks, patterns and components
• develop your understanding of the tools and techniques that may be used for the automatic analysis and evaluation of software

Building on the previous material in software development, you'll extend and formalise your abilities in the area of computational complexity.

This module will allow you to understand the fundamentals of information access and information mining. The module will cover a range of techniques for extracting information from textual and non-textual resources, modelling the information content of resources, detecting patterns within information resources and making use of these patterns.