Mathematics

This module will build upon and extend your A-Level (or equivalent) mathematical probability knowledge and develop the subject of probability with applications.

You will be introduced to the concept of proofs and construct simple proofs. It will give you an understanding of fundamental concepts of limit, continuity, differentiability, integration and function in mathematical analysis. On completion of the module you will be able to apply the notion of limit to prove fundamental theorems and to perform integration.

Linear algebra is a fundamental topic which has applications in many branches of mathematics. You will look at the methods and theory behind the solution of simultaneous equations, and you will develop skills in solving linear problems using matrix methods and the concept of abstract vectors.

You will build on your A-Level (or equivalent) mathematical techniques and knowledge in preparation for subsequent mathematics modules. Specifically, you will cover the subject of differential equations with applications.

This module will build upon and extend your A-Level (or equivalent) mathematical techniques providing a mathematical foundation in support of subsequent mathematics modules. You will also cover differential equations with applications and be introduced to problem solving using a symbolic computing environment.

You will be introduced to the principles of classical mechanics and vector calculus. You will develop skills in solving numerical problems in mechanics and vector calculus.

This module will give you experience in business and industrial working practices and how to solve practical mathematical problems.

At the start of the module, a series of seminars will be given by speakers on a variety of mathematical applications in business in industry including: probability and statistics, operational research, fluids, structural and solid mechanics, (intelligent) computer algorithms, business and economic models, and how these impact on their work.

You will deliver written reports and oral presentations, which are assessed on a group basis, both during and at the end of the semester.

You will extend your methods in differential and integral calculus, first and second order partial differential equations and methods in differential and integral calculus for the complex variable.

You will learn how to present key solutions in optimisation of numerical algorithms using the computer. The topics of root finding, interpolation techniques, numerical calculus and linear algebra enable you to optimise physical problems.

You will develop a sound knowledge in probability models and distribution theory, skills in statistics and data analysis and provide an awareness of the principles and scope of data analysis models often implemented in statistical software packages.

This module introduces you to tensors and tensor algebra. You will learn how these powerful tools can be applied to problems in fluid and structural dynamics.

An understanding of nonlinear dynamics is fundamental in modern applied mathematics, with physical applications ranging from population modelling and weather prediction to stock market datasets and anharmonic vibrations. This module will introduce some of the concepts and phenomena of dynamical systems by merging mathematical analysis and numerical computation.

You will investigate more advanced techniques of solving differential equations using for methods such as Fourier and Laplace transforms, series methods and more.

The project will give you the opportunity to develop a mathematical model within a challenging research theme, including those areas prioritised by EPSRC and the EU Research Council and of benefit and importance to society. These are: climate, nanotechnology, renewable energy and sustainable economics. The aim is for you to demonstrate your understanding of the application of mathematics to one of these areas and give you an opportunity to demonstrate your knowledge, understanding and skills.

Using probability theory as well as other branches of mathematics such as linear algebra and analysis, you will revisit the foundations of statistics from a more mathematical standpoint. You will gain theoretical and practical skills in mathematical statistics, study some of the most widely used probability distributions and recognise and employ them in practical applications.

In this module, you will learn to apply mathematics to a variety of problems in physics, economics and life sciences.

You will learn the skills to construct mathematically based models to find better solutions to real-life and complex decision-making problems. These models draw upon mathematical knowledge, such as mathematical modelling, statistical analysis, mathematical optimization and artificial intelligence to find an optimal or near-optimal solution to problems from a variety of industries and government areas.

In this module, you will learn to apply mathematics to problems in fluid and structural dynamics.