Statistics BSc

Calculus provides the basic, underpinning mathematics for much of modern technology, from the design of chemical reactors and high-speed trains, to models for gene networks and space missions.

The basic ideas that underpin calculus are functions and limits. To study these rigorously you need to learn about the tools of mathematical analysis. In addition to differential equations and the calculus of functions of one or more variables and their differentiation, integration and analysis, you will learn the basics of logic and how to construct rigorous proofs.

You’ll learn how to construct and analyse differential equations that model real-world systems. Applications that you’ll learn about include systems governed by Newton’s laws of motion, such as sets of interacting particles and the orbits of planets, as well as models of population dynamics. You will also be introduced to the mathematical basis of concepts such as work and energy.

Linear algebra underpins many areas of modern mathematics. The basic objects that you will study in this module are vectors, matrices and linear transformations. Topics covered include:

• vector geometry
• matrix algebra
• vector spaces
• linear systems of equations
• eigenvalues and eigenvectors
• inner product spaces.

The mathematical tools that you study in this module are fundamental to many mathematical, statistical, and computational models of the real world.

Probability theory allows us to assess risk when calculating insurance premiums. It can help when making investment decisions. It can be used to estimate the impact that government policy will have on climate change or the spread of disease. 

You will study the theory and practice of discrete and continuous probability, including topics such as:

• Bayes’ theorem
• multivariate random variables
• probability distributions
• the central limit theorem

There is no area of modern mathematics that does not use computational methods to make progress on problems with which the human brain is unable to cope due to the volume of calculations required.

Scientific computation underpins many technological developments in all sectors of the economy. You'll learn how to write code for mathematical applications using Python.

Python is a freely available, widely-used computer language. No previous computing knowledge will be assumed. It will be used throughout your degree programme.

Statistics is concerned with methods for collecting, organising, summarising, presenting and analysing data. It enables us to draw valid conclusions and make reasonable decisions based on statistical analysis. It can be used to answer a diverse range of questions in areas such as the pharmaceuticals industry, economic planning and finance. 

The module covers statistical inference, you'll learn how to analyse, interpret and report data. Topics that you’ll learn about include:

• point estimators and confidence intervals
• hypothesis testing
• linear regression
• goodness-of-fit tests

Pure mathematics at university is typically very different to the pure mathematics you've learnt at school or college.

In this module, you'll use the language of sets, functions and relations to study abstract mathematical ideas. You will also learn how to construct mathematical proofs. Topics that you will learn about include:

• set theory
• prime numbers
• symmetry and groups
• rings, fields and integer
• polynomial arithmetic

This module introduces various analytical methods for the solution of ordinary and partial differential equations.

You will begin by studying asymptotic techniques, which can be used when the equations involve a small parameter, which is often the case. We will also study some aspects of dynamical systems theory, which has wide applicability to models of real world problems.

This module will develop your understanding of probability theory and random variables from Probability 1. There's particular attention paid to continuous random variables.

Fundamental concepts relating to probability will be discussed in detail, including limit theorems and the multivariate normal distribution. You will then progress onto more advanced topics such as transition matrices, one-dimensional random walks and absorption probabilities.

Most mathematical problems cannot be solved analytically or would take too long to solve by hand. Instead, computational algorithms must be used. 

Scientific Computation teaches you about algorithms for approximating functions, derivatives, and integrals, and for solving many types of equation.

The first part of this module provides you with an introduction to statistical concepts and methods. 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.

This module teaches you the mathematical foundations of multidimensional differential and integral calculus of scalar and vector functions. This provides essential background for later study involving mathematical modelling with differential equations, such as fluid dynamics and mathematical physics. You will learn about vector differential operators, the divergence theorem and Stokes’ theorem, as well as meeting various curvilinear coordinate systems.

This module teaches you how Newtonian mechanics can be developed into the more powerful formulations due to Lagrange and Hamilton. You will also be introduced to the basic structure of quantum mechanics.

The module provides the foundation for a wide range of more advanced modules in mathematical physics.

This module will provide you with tools to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. You will also meet the fundamental mathematical concepts required to model the flow of liquids and gases. This will enable you to apply the resulting theory to model physical situations.

This module will develop your understanding of probability theory and random variables from Probability 1. There's particular attention paid to continuous random variables.

Fundamental concepts relating to probability will be discussed in detail, including limit theorems and the multivariate normal distribution. You will then progress onto more advanced topics such as transition matrices, one-dimensional random walks and absorption probabilities.

This module will further develop your understanding of the tools of real and complex analysis. This provides you with a solid foundation for subsequent modules in metric and topological spaces, relativity, and numerical analysis.

You’ll study topics such as:

• the Bolzano-Weierstrass Theorem
• norms, sequences and series of functions
• differentiability
• the Riemann integral

You will also learn about functions of complex variables and study topics including, analyticity, Laurent series, contour integrals and residue calculus and its applications.

This module involves the application of mathematics to a variety of practical, open-ended problems - typical of those that mathematicians encounter in industry and commerce.

Specific projects are tackled through workshops and student-led group activities. The real-life nature of the problems requires you to develop skills in model development and refinement, report writing and teamwork. There are various streams within the module, for example:

• Pure Mathematics
• Applied Mathematics
• Data Analysis
• Mathematical Physics

This ensures that you can work in the area that you find most interesting.

During this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will progress 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.

This module provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. You’ll learn cryptography, including classical mono- and polyalphabetic ciphers.  There will also be a focus on modern public key cryptography and digital signatures, their uses and applications.

You will be introduced to various analytical methods for the solution of ordinary and partial differential equations. We will begin by studying asymptotic techniques, which can be used when the equations involve a small parameter, which is often the case.

We will also study some aspects of dynamical systems theory, which has wide applicability to models in real world problems.

You will explore the concepts of discrete time Markov chains to understand how they used. We will also provide an introduction to probabilistic and stochastic modelling of 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 workplace applications.

This module is concerned with the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction.

Key topics to be covered include:

• principal components analysis
• modelling and inference for multivariate data
• classification of observation vectors into sub-populations using a training sample
• canonical correlation analysis
• factor analysis
• methods of clustering
• multidimensional scaling

In this module a variety of techniques of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming.

These techniques have a wide range of applications to real world problems, in which a process or system needs to be made to perform optimally.

You'll learn how to use numerical techniques for determining the approximate solution of ordinary and partial differential equations where a solution cannot be found through analytical methods alone. You will also cover topics in numerical linear algebra, discovering how to solve very large systems of equations and find their eigenvalues and eigenvectors using a computer.

This module is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference.

You will explore the following topics in detail:

• sufficiency
• estimating equations
• likelihood ratio tests
• best-unbiased estimators

There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

This module 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. You will then move onto more extensive studies of epidemic models and queuing models, with introductions to component and system reliability.