Mathematics with Computing BSc/MSci

Course content

What will you study on the BSc/MSci Mathematics with Computing?

The programme begins where your previous learning ends, developing your knowledge of the core areas of mathematics fundamental to further study. You will develop your analytic and problem solving skills, learning how to communicate effectively complex ideas.

You will learn to programme throughout your degree, starting in the first year. Additionally you will learn how to develop and study algorithms and determine their efficiency, and you will find out how computers can learn beyond what is programmed. Options in your third year allow you to specialise in computer graphics, artificial intelligence or in other areas, tailoring your development towards your own career choice.

The four-year MSci Mathematics with Computing allows you to specialise in your final year to study a huge variety of subjects, thereby letting you develop your own work in a number of cutting-edge areas.

BSc Modules

This module aims to provide an introduction to vector spaces and linear maps. The foundations are laid by studying basic manipulations of complex numbers, vectors and matrices. The underlying geometric meanings of these manipulations are emphasised and concrete examples are explored both by hand and with the help of computer software. Once the foundations have been developed, more advanced and abstract notions are studied for a deeper understanding.

Integration and differentiation are used to model situations in physics and engineering, as well as in other applications. In this module, we’ll look at how to describe these kinds of equations and you’ll be introduced to the importance of rigour in maths.

One of the fundamental concepts in maths is how unknown ideas are deduced from things that are known. This module takes a closer look at the logic behind argument and develops a keener understanding about the structures that underlie this. The module will develop your appreciation of the way mathematicians think about topics and how we critically analyse arguments.

We’ll begin to look at how maths is used to analyse information in this module. You will be introduced to some of the ideas behind how patterns and shapes can be deduced from given data and how we can use this information to model and estimate future trends.

This module has two components. First, the Algorithmic Complexity component introduces students to the theory of algorithms and data structures. Algorithms are at the core of every non-trivial computer program and application. Students will learn how to measure the efficiency of an algorithm in terms of its time and space requirements and distinguish between efficient and inefficient algorithmic solutions. General algorithmic design techniques as well as data structures for efficient data manipulation are taught. For this, we study fundamental problems such as sorting, searching, and discrete optimisation problems on graphs, strings and geometry.Second, the Machine Learning component introduces students to algorithmic approaches to learning from exemplar data. Students learn the process of representing training data within appropriate feature spaces for the purposes of classification. The major classifier types are taught before introducing students to specific instances of classifiers along with appropriate training protocols. Where classifiers have a relationship to statistical theory this is fully explored. Notions of structural risk with respect to model fitting are developed such that students are equipped with techniques for managing this in practical contexts.

Groups and Rings are structures used throughout maths to emulate objects like whole numbers or matrices. In this module you’ll be introduced to these structures and you’ll study their properties and what they look like. You’ll find that from very humble beginnings groups and rings lead to a deep and rich theory.

This module will begin by looking at what we really mean when we look at limits in mathematics and build on this to give you a greater understanding of series and calculus. The module builds on the ideas introduced in the level 4 modules about the need for rigour in maths. You will develop your ability to question mathematical arguments and to think logically about what definitions mean.

The HE Maths Curriculum Summit (2011) recently concluded that “problem-solving is the most useful skill a student can take with them when they leave university”. This module fosters this skill in you by building on the approaches developed throughout the programme to enhance your ability to approach problems in diverse areas of maths and solve them. You will learn how to approach a problem, analyse its properties and develop a strategy to solve it. Rowlett, P. (Ed.) (2011, January), HE Mathematics Curriculum Summit

This module builds on the topics covered in MSO2110 Groups and Rings. The module begins with a review of the material on rings encountered in the prerequisite and proceeds to build towards a study of fields, culminating in the development of Galois Theory. Students will develop their appreciation of the effect additional axioms have on the structure of rings by learning about commutative rings, Euclidean rings, integral domains, fields and other algebraic objects. In the second half of the module students will extend the work on fields and field extensions to develop Galois Theory.

Following from the previous module on mathematical analysis, this module will continue to develop your understanding of infinite and infinitesimal processes. You will also learn how extending the ideas developed here and in your previous module to complex numbers leads to a very different theory.

Maths is often called the universal language of science but communicating it can be difficult. With the continuing move to more diverse platforms such as social media this leads to even more challenges in communicating maths. In this module you will look at how maths is communicated, be it to specialists, non-specialists, school pupils or CEOs and how to motivate it for these diverse audiences.

This is your chance to study an area of maths that you’re interested in and write your own report on it. You can choose your topic yourself or from a list given by staff. If you choose this module then you will have the opportunity to publish your work as an article in a journal.

The aim of this module is to examine in depth the concepts and techniques needed in the construction of interactive graphics and visualisation systems covering advanced graphics programming techniques. It will cover theory and mathematics as required and It aims to provide students with practical experience via significant individual project work developing 2D and 3D programs using an industry standard environment.

The aim of the module is to introduce students to a range of AI theories and techniques, including the most commonly used. This will extend to the ability to implement these techniques, and the students will extend their own development skills.

This module builds on the discrete mathematics introduced in the second year to provide students with a range of methods for analysing and solving combinatorial problems, with applications across mathematics and to computer science, physics and beyond. It explores ideas of graph theory and design theory, and a range of techniques for solving counting problems both by hand and using computing. It also aims to develop students’ analytical and reasoning skills, and their ability to apply familiar techniques in unfamiliar settings.

Understanding and recognising patterns in data can be difficult when it comes from many different sources. In this module, you will begin to develop the techniques and tools that will enable you to study these kinds of relationships. You will develop a critical view of the pros and cons of the methods and the assumptions being made.

Simulating systems such as queuing times at hospitals, or traffic congestion in towns and cities is one of the most important tools used to inform management decisions. In this module, you will be introduced to mathematical simulation and you will learn how to develop models to study systems and improve efficiency.

This module introduces students to the main principles and ideas of functional analysis – a modern branch of mathematical analysis, largely influenced by progress in physics during the 20th century, such as quantum mechanics. The main object of study is a vector space, the elements of which are functions, so that the space is usually infinite-dimensional. Starting from simple geometric objects in vector spaces, the module will gradually introduce ideas from other areas of mathematics, such as topology, differentiation, integration, measure, optimisation, differential and integral equations. Functional analysis will help students to build a unified and beautiful picture about these topics, and achieve deeper understanding of various branches of mathematics and their applications.

Differential equations (DEs) are essential mathematical tools used to describe fundamental laws of nature. This module will equip you with general knowledge of the main types of these equations (ordinary and partial, linear and non-linear), which will be illustrated by examples from the natural sciences. Several techniques for solving differential equations will be presented, alongside a broad geometric understanding of possible solution behaviours.

MSci Modules

Vectors and matrices are the mathematical building blocks used in areas ranging from theoretical physics to computer graphics, as well as providing the basis for an understanding of how structures in maths interact. This module will introduce you to the methods and techniques used to analyse vectors and matrices.

Integration and differentiation are used to model situations in physics and engineering, as well as in other applications. In this module, we’ll look at how to describe these kinds of equations and you’ll be introduced to the importance of rigour in maths.

One of the fundamental concepts in maths is how unknown ideas are deduced from things that are known. This module takes a closer look at the logic behind argument and develops a keener understanding about the structures that underlie this. The module will develop your appreciation of the way mathematicians think about topics and how we critically analyse arguments.

We’ll begin to look at how maths is used to analyse information in this module. You will be introduced to some of the ideas behind how patterns and shapes can be deduced from given data and how we can use this information to model and estimate future trends.

This module has two components. First, the Algorithmic Complexity component introduces students to the theory of algorithms and data structures. Algorithms are at the core of every non-trivial computer program and application. Students will learn how to measure the efficiency of an algorithm in terms of its time and space requirements and distinguish between efficient and inefficient algorithmic solutions. General algorithmic design techniques as well as data structures for efficient data manipulation are taught. For this, we study fundamental problems such as sorting, searching, and discrete optimisation problems on graphs, strings and geometry.Second, the Machine Learning component introduces students to algorithmic approaches to learning from exemplar data. Students learn the process of representing training data within appropriate feature spaces for the purposes of classification. The major classifier types are taught before introducing students to specific instances of classifiers along with appropriate training protocols. Where classifiers have a relationship to statistical theory this is fully explored. Notions of structural risk with respect to model fitting are developed such that students are equipped with techniques for managing this in practical contexts.

Groups and Rings are structures used throughout maths to emulate objects like whole numbers or matrices. In this module you’ll be introduced to these structures and you’ll study their properties and what they look like. You’ll find that from very humble beginnings groups and rings lead to a deep and rich theory.

This module will begin by looking at what we really mean when we look at limits in mathematics and build on this to give you a greater understanding of series and calculus. The module builds on the ideas introduced in the level 4 modules about the need for rigour in maths. You will develop your ability to question mathematical arguments and to think logically about what definitions mean.

The HE Maths Curriculum Summit (2011) recently concluded that “problem-solving is the most useful skill a student can take with them when they leave university”. This module fosters this skill in you by building on the approaches developed throughout the programme to enhance your ability to approach problems in diverse areas of maths and solve them. You will learn how to approach a problem, analyse its properties and develop a strategy to solve it. Rowlett, P. (Ed.) (2011, January), HE Mathematics Curriculum Summit

This module will look at more advanced subjects in algebra. The module will further enhance your understanding of the often abstract nature of structures used in maths and how seemingly simple definitions lead to a great deal of rich and interesting ideas. The main thrust of this module will be Galois Theory, an important area that develops a deep relationship between groups and field.

Following from the previous module on mathematical analysis, this module will continue to develop your understanding of infinite and infinitesimal processes. You will also learn how extending the ideas developed here and in your previous module to complex numbers leads to a very different theory.

Maths is often called the universal language of science but communicating it can be difficult. With the continuing move to more diverse platforms such as social media this leads to even more challenges in communicating maths. In this module you will look at how maths is communicated, be it to specialists, non-specialists, school pupils or CEOs and how to motivate it for these diverse audiences.

This is your chance to study an area of maths that you’re interested in and write your own report on it