This module offers you the chance to learn about a range of statistical ideas and skills, along with concepts and techniques for modelling and practical data analysis. You will learn to write reports based on these topics which will help you in further studies.
This module provides an introduction to probability by developing a framework for the logic of uncertainty. Random variables and the topics surrounding them will also be introduced.
Analytical and Computational Foundations
This module will introduce you to three core concepts and techniques that underpin all maths modules in your degree. These are mathematical reasoning (the language of maths and providing concrete proof of mathematical theorems), an introduction to the computer package MATLAB (its use and application), and basic analysis methods.
You will begin by practising the basic concepts and methods of calculus including limits, functions, and continuity. In the second semester you will move onto more advanced usage of calculus. Topics will be based around the calculus of functions of several variables and include partial derivatives, chain rules, the vector operator grad, Lagrange multipliers and multiple integrals.
This module introduces you to the methods and practices of linear mathematics that you will need in subsequent modules on your course, such as complex numbers, vector algebra and matrix algebra. You will then expand your knowledge to include vector spaces, linear transformations and inner product spaces.
You will receive an introduction to classical mechanics and modelling in applied mathematics. This will provide you with a foundation in applied mathematics and you will begin to apply your knowledge to real world problems.
Statistical Models and Methods
The first part of this module provides an introduction to statistical concepts and methods and the second part introduces a wide range of techniques used in a variety of quantitative subjects. The key concepts of inference including estimation and hypothesis testing will be described as well as practical data analysis and assessment of model adequacy.
Probability Models and Methods
This module will give you an introduction to the theory of probability and random variables, with particular attention paid to continuous random variables. Fundamental concepts relating to probability will be discussed in detail, including well-known limit theorems and the multivariate normal distribution. You will then progress onto complex topics such as transition matrices, one-dimensional random walks and absorption probabilities.
Introduction to Scientific Computation
In this module you’ll be introduced to basic techniques in numerical methods and numerical analysis. You’ll build upon your core year one modules to generate approximate solutions to problems that may not be easy to analyse. There’ll be a wide range of topics such as iterative methods for nonlinear equations, rounding and truncation errors, polynomial interpolation and orthogonal polynomials.
This module provides a grounding in vector calculus methods that are widely used in applied mathematics, covering material fundamental to many modules in later levels. The module introduces the vector differentiation operations of gradient, divergence and curl, develops integration methods of scalar and vector quantities over paths, surfaces and volumes, and relates these operations to each other via the integral theorems of Green, Stokes and Gauss. The methods are then used in the application of curvilinear coordinate transformations.
In this module you will build on the foundation of knowledge gained from your core year one modules in Analytical and Computational Foundations and Calculus. You will learn to follow a rigorous approach needed to produce concrete proof of your workings.
Modelling with Differential Equations
In this module you will further explore mathematical modelling based on your knowledge from your core year one modules. You will learn techniques for studying linear and nonlinear systems of ordinary differential equations, using linearisation and phase planes. Models based on partial differential equations and how to analyse them will also be explored, along with continuum models to analyse the flow of fluids.
Professional Skills for Mathematicians
This module will equip you with the skills needed for graduate employment. You will work on two group projects based on open-ended mathematical topics agreed by your group. You will also work independently to improve your communication skills and learn how to summarise technical mathematical data for a general audience. You will be provided with some commercial and business awareness and explore how to use your mathematical sciences degree for your future career.
Typical year three modules
Applied Statistical Modelling
In this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will move on to enhance your understanding of statistical methodology including the analysis of discrete and survival data. You will also be trained in the use of a high-level statistical computer program.
In this module the concepts of discrete time Markov chains are explored and used to provide an introduction to probabilistic and stochastic modelling for investment strategies, and for the pricing of financial derivatives in risky markets. You will gain well-rounded knowledge of contemporary issues which are of importance in research and applications.
In this module you will explore two main concepts of statistical inference; classical (frequentist) and Bayesian. Topics such as sufficiency, estimating equations, likelihood ratio tests and best-unbiased estimators will be discussed in detail. You will gain knowledge of the theory and concepts underpinning contemporary research in statistical inference and methodology.
In this module you will develop your knowledge of discrete-time Markov chains by applying them to a range of stochastic models. You will be introduced to Poisson and birth-and-death processes and then you will move onto more extensive studies of epidemic models and queuing models with introductions to component and system reliability.
Time Series Analysis
This module will provide a general introduction to the analysis of data that arise sequentially in time. Several commonly-occurring models will be discussed and their properties derived, along with methods for model identification for real-time series data. You will develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values. You will also gain experience of using a statistical package and interpreting its output.
Coding and Cyrptography
In this module you will be introduced to two main topics of coding theory; error-correction codes and cryptography. Within these topics you will learn the main concepts, theorems and techniques and practise applying these with specific example.
The modules we offer are inspired by the research interests of our staff and as a result may change for reasons of, for example, research developments or legislation changes. The above list is a sample of typical modules we offer, not a definitive list.