Mathematics (International Study) BSc

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.

In this module you will apply the quantum mechanics that you learned in Year 2 to more general problems. New topics will be introduced such as the quantum theory of the hydrogen atom and aspects of angular momentum such as spin.

This course provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. It also provides an introduction to to cryptography, including classical mono and polyalphabetic ciphers as well as modern public key cryptography and digital signatures, their uses and applications.

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.

This is an excellent opportunity to gain first-hand experience of being involved with providing mathematical education. You will work in a local school alongside practising mathematics teachers in a classroom environment and improve your skills at communicating maths.

Typically, you will work within a class (or classes) for half a day a week for about sixteen weeks. You will be given a range of responsibilities, from classroom assistant to leading a self-originated mathematical activity or project.

The assessment is carried out in a variety of ways: an on-going reflective log, contribution to reflective seminar, oral presentation and a final written report.

The aim of Discrete Mathematics is the study of discrete and finite rather than continuous quantities. This includes counting problems, graphs and other quantities parametrised by integers.

As such Discrete Mathematics is of great importance for various branches of Pure Mathematics, Mathematical Physics, Statistics and Computer Sciences.

The course will cover a range of Discrete Mathematics topics, including:

• an introduction to advanced aspects of combinations and permutations
• ordinary and exponential generating functions
• recurrence relations and applications to counting problems
• graphs
• digraphs
• Eulerian and Hamiltonian trails
• planar graphs
• graph colouring
• trees
• minimum spanning tree algorithms

Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoner’s Dilemma. We look at tree-searching, including alpha-beta pruning, the ‘killer’ heuristic and its relatives. It then turns to mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.

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.

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.

Mathematics can be usefully applied to a wide range of applications in medicine and biology.

Without assuming any prior biological knowledge, this module describes how mathematics helps us understand topics such as:

• population dynamics
• biological oscillations
• pattern formation
• nonlinear growth phenomena

There is considerable emphasis on model building and development.

You will extend your understanding of fluid flow by introducing the concept of viscosity and studying the fundamental governing equations for the motion of liquids and gases.

Methods for solution of these equations are introduced, including exact solutions and approximate solutions valid for thin layers. A further aim is to apply the theory to model fluid dynamical problems of physical relevance.

The module provides an introduction to electromagnetism and the electrodynamics of charged particles. You will meet Maxwell’s equations and learn how they describe a wide variety of phenomena, including electrostatic fields and electromagnetic waves.

You will be introduced to Einstein’s theory of general and special relativity. The relativistic laws of mechanics will be described within a unified framework of space and time. You’ll learn how to compare other theories against this work and you’ll be able to explain exciting new phenomena that occur in relativity.

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.

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 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