The first year of study contains an introduction to all the main areas of mathematics. In the second year you build on these foundations to gain more specialist knowledge and have the opportunity to work on a real industrial case-study to apply your knowledge. The final year is devoted to advanced courses in pure mathematics, applied mathematics and statistics alongside completing your specialist project.
Course structure
Year 1 core modules
Analysis I
The module gives a solid foundation to the properties of the real numbers and of continuous functions of one real variable. You develop the mathematical skills and techniques of fundamental operations with limits, and develop skills in using mathematical terminology and style of reasoning in order to solve problems.
Lectures introduce techniques and underlying principles. Problem-solving seminars based on weekly worksheets provide the opportunity for you to demonstrate understanding and develop competence in the application of these.
Analysis II
This module deepens your mathematical knowledge in analysis to include the techniques of differentiation and integration in one real variable. The fundamental functions (exp, log, sin, cos, tan) are defined accurately and their properties outlined. Important applications like finding local extrema of functions, approximation through Taylor expansion, or the solution of elementary ODEs is presented, their mathematical eligibility proven, and their execution practised.
Lectures are used to introduce techniques and underlying principles. Problem-solving seminars based on weekly worksheets provide the opportunity for you to demonstrate understanding and develop competence in the application of these.
Exploring Mathematics
The module provides a general introduction to problem solving. You develop personal and team-working skills and the importance of communicating mathematics in both written and oral form. You develop your reflective and professional skills, gaining recognition of the benefits with respect to your academic progress and subsequent lifelong learning.
A group-based learning approach is adopted and where appropriate, supporting lectures/seminars introduce techniques and underlying principles. IT laboratory sessions are used to introduce you to specialist software.
Linear Algebra 1
This module gives a solid foundation to Linear Algebra topics. You develop the mathematical skills and techniques of fundamental operations of vectors and matrices, and skills in selecting and applying Linear Algebra techniques to solve problems.
Lectures are used to introduce techniques and underlying principles. Problem-solving tutorials provide the opportunity for you to demonstrate understanding and develop competence in the application of these.
Linear Algebra 2
This module deepens your mathematical knowledge in Linear Algebra to include Eigenvalues and Eigenvectors, and extend your base of techniques to solve a variety of problems. The emphasis is on developing competence in the identification of the most appropriate method to solve a given problem and its subsequent application.
Lectures are used to introduce techniques and underlying principles. Problem-solving tutorials provide the opportunity for you to demonstrate understanding and develop competence in the application of these.
Probability and Statistics
You are introduced to the concepts of statistics and probability. You develop a conceptual understanding of basic statistical and probability methods, supported by the use of a statistical computer package.
Lectures are used to introduce techniques and underlying principles. Problem-solving seminars/laboratory sessions provide the opportunity for you to demonstrate understanding and develop competence in the application of these.
Year 2 core modules
Abstract Algebra
This topic, also known as algebra or algebraic structures, broadens the mind to mathematics beyond the common number systems and is crucial for a deeper understanding of many other branches of mathematics such as topology, differential equations, geometry, analysis and number theory. You extend your base of techniques beyond linear algebra to solve a variety of algebraic problems.
Analysis III
This module will extend the mathematical knowledge in Analysis by treating the case of vector-valued functions of several variables and their differentiation and integration. Accordingly, important applications, such as determining local extrema, approximation via Tayler expansion will be discussed, for functions of several variables, and, if appropriate, the vector valued case. The integration theory in several variables will follow the measure-theoretic approach of Lebesgue. Applications of integration theory will include surface integrals, volume integrals, line integrals and sketch their relevance in, e.g., mechanics and electrodynamics.
Artificial Intelligence
This module provides a general introduction to artificial intelligence (AI) with real-world applications around us. This includes the fundamental concepts of AI, common frameworks used in the analysis and design of intelligent systems, generic algorithms used for implementation and major techniques used in problem solving. This module also introduces popular applications of AI (for example, game design, virtual agents, robotics) and benefits of using AI (for example, how to enhance efficiency, productivity and reduce costs).
Differential Equations and Numerical Methods
This module focuses on applying your mathematical knowledge of differential equations to real-world problems. You are introduced to Numerical Methods and extend your base of techniques to solve a variety of problems. The emphasis is on developing competence in the identification of the most appropriate method to solve a given problem and its subsequent application.
Lectures are used to introduce techniques and underlying principles. Problem-solving seminars provide the opportunity for you to demonstrate understanding and develop competence in the application of these. You are shown how to implement numerical methods using appropriate software tools.
Mathematical Modelling
You use mathematics as a tool to solve problems using a range of real-world problems to motivate the use of various techniques. Additionally, varying tools are used to implement and calculate solutions. You gain a range of mathematical modelling skills to solve problems.
Lectures are used to introduce principles and concepts. Tutorials involve pen-and-paper as well as computer-based exercises to consolidate and develop your understanding and skills.
Statistical Analysis
This module provides a practical understanding of the useful modelling techniques of regression analysis and analysis of variance. The module instils an understanding and relevance of linear regression models facilitated through the use of a statistical computer package.
Lectures are used to introduce techniques and underlying principles. Problem-solving seminars in IT laboratories provide the opportunity for you to demonstrate understanding and develop competence in the application of these. You are shown how to implement numerical methods using appropriate software tools.
Optional work placement year
Work placement
You have the option to spend one year in industry learning and developing your skills. We encourage and support you with applying for a placement, job hunting and networking.
You gain experience favoured by graduate recruiters and develop your technical skillset. You also obtain the transferable skills required in any professional environment, including communication, negotiation, teamwork, leadership, organisation, confidence, self-reliance, problem-solving, being able to work under pressure, and commercial awareness.
Many employers view a placement as a year-long interview, therefore placements are increasingly becoming an essential part of an organisation's pre-selection strategy in their graduate recruitment process. Benefits include:
· improved job prospects
· enhanced employment skills and improved career progression opportunities
· a higher starting salary than your full-time counterparts
· a better degree classification
· a richer CV
· a year's salary before completing your degree
· experience of workplace culture
· the opportunity to design and base your final-year project within a working environment.
If you are unable to secure a work placement with an employer, then you simply continue on a course without the work placement.
Final-year core modules
Graph Theory
The module develops knowledge and understanding of topics in Graph Theory such as graphs, paths and cycles, Euler tours, connectivity, trees, spanning trees, planar graphs, graph colouring and random graphs. This knowledge will be applied to obtain and analyse models of real-world networks, for example in Transport Systems and Computer Networks.
Mathematical Data Science
The module introduces mathematical techniques for the processing and analysing massive datasets. In particular, the module discusses how to pre-process and store massive datasets and to design efficient algorithms.
Operational Research and Optimisation
This group project module is designed to develop awareness and understanding of operational research methods applicable to analysis of financial and economic data. You are introduced to numerical optimisation theories and processes and have the opportunity to develop theoretical and applied knowledge in optimisation problems within the financial domain.
Philosophy of Mathematics: History and Methodology
Project
This module extends the development of independent learning skills by allowing you to investigate an area of engineering or technology for an extended period.
You receive training in writing technical reports for knowledgeable readers and you produce a report or dissertation of the work covered. In addition, you give an oral presentation, a poster presentation or both. The topic can be in the form of a research project or a design project.
You develop key skills in research, knowledge application and creation through keynote lectures where appropriate and self-managed independent study. Support is provided through regular tutorial sessions.
