This page lists all modules in alphabetical order that are available as electives to students from other departments. The module names link to a full module description which include pre-requisites.  You must make sure you read these descriptions if you wish to take the particular module as an elective. Please check prerequisites carefully before asking to take particular modules as an elective.  In choosing an elective it will be assumed that you are familiar with all the material taught in the first year courses Calculus and Core Algebra or are willing to learn the material if necessary to complete the module you have chosen.

These modules are available to second, third and fourth year students. 

• Advanced Quantum Mechanics (10 credits, autumn term) Formalism of quantum mechanics. Angular momentum, spin, identical particles.  
• Applied Probability (10 credits, autumn term) This module is an introduction to stochastic processes. 
• Bayesian Statistics (10 credits, autumn term) A course on Bayesian statistics showing how to make inferences by combining prior beliefs with information obtained from experimental data.
• Calculus of Variations (10 credits, autumn term) The variational calculus of Euler, Lagrange, and Hamilton.
• Classical Mechanics (20 credits, spring term/summer term) Please check prerequisites carefully before asking to take this module as an elective.
• Complex Analysis and Integral Transforsm (20 credits, spring term/summer term) Complex Functions; Cauchy's theorem; contour integration and calculus of residues.  
• Differential Equations (10 credits, autumn term) Advanced aspects of the theory of differential equations.
• Differential Geometry (10 credits, autumn term) the geometry of curves in space; smooth surfaces in space; the geometry of smooth surfaces.
• Electromagnetism (10 credits, spring term) to understand Maxwell's equations; to solve simple problems involving static charges, steady currents and electromagnetic waves; understand the relativistic formulation of electromagnetism.
• Formal Languages and Automata (10 credits, autumn term) Please check prerequisites carefully before asking to take this module as an elective.
• Generalised Linear Models (10 credits, autumn term) Please check prerequisites carefully before asking to take this module as an elective.
• Groups Rings and Fields (20 credits, spring term/summer term) A second course on abstact algebra, assuming a basic knowledge of group thoery.  
• Introduction to Applied Mathematics (20 credits, spring term/summer term) This module is an introduction to applied mathematics, mathematical modelling, and Newtonian mechanics, aimed at students with prior exposure to calculus, basic differential equations, probability, vectors, and complex numbers.
• Introduction to General Relativity (10 credits, autumn term) An introductory course on General Relativity.
• Introduction to Group Theory (10 credits, autumn term) A second course on abstract algebra, assuming a basic knowledge of group theory.
• Introduction to Number Theory (10 credits, autumn term) Please check prerequisites carefully before asking to take this module as an elective.
• Introduction to Probability and Statistics (20 credits, autumn term) This module is an introduction to probability theory and data analysis. The approach is heuristic and non-rigorous.
• Introduction to Quantum Field Theory (10 credits, spring term) An elementary introduction to relativistic quantum field theory, which is the theoretical tool for describing the elementary particles. 
• Multivariate Analysis (10 credits, spring term) An introduction to multivariate statistical techniques, including
  principal components, factor analysis, cluster analysis,Hotelling's T2 and multivariate analysis of variance.
• Numerical Methods of Partial Differential Equations (10 credits, spring term) The aim of this module is to give an introduction to basic numerical methods for solving partial differential equations (PDEs) and to show how numerical algorithms can be implemented in practice.
• Quantum Information (10 credits, autumn term) This module introduces the theory of quantum information. After  a self-contained presentation of non-relativistic quantum mechanics in finite spaces, basic paradigms of the theory of quantum information proper will be discussed.
• Quantum Mechanics (10 credits, autumn term) A first module on quantum mechanics. Experimental findings are discussed which are difficult to reconcile using concepts of Classical Physics. An axiomatic formulation of quantum mechanics introduces to both the relevant mathematical structures and to their physical interpretation. Some properties of quantum systems will be illustrated by investigating the behaviour of a particle in various one-dimensional potentials is studied.
• Real Analysis (20 credits, spring term/summer term) A first course in Mathematical Analysis, covering real numbers, limits of sequences, series, convergence, absolute convergence, power series, continuity, differentiability and the Riemann integral.
• Riemannian Geometry (10 credits, spring term) a second module in differential geometry.
• Semigroup Theory (10 credits, spring term) Please check prerequisites carefully before asking to take this module as an elective.
• Special Functions (10 credits, spring term) This module aims to explore the realm beyond the elementary functions domain. We shall study functions defined by integrals which can not be expressed in terms of elementary functions, such as the celebrated Gamma function. We shall study their properties by means of the complex analysis and differential equations.
• Special Relativity (10 credits, autumn term) A first module on relativity covering the concept of spacetime and Lorentz transformations, and including an explanation of "E = mc²" etc.
• Statistics I (10 credits, autumn term) Introduction to distributions arising in inference from normally distributed samples (and some others).  Central limit theorem.  Sample mean and variance. 
• Statistics II (20 credits, spring term/summer term) Please check prerequisites carefully before asking to take this module as an elective.  
• Vector Calculus (20 credits, spring term/summer term) a mature study of fundamental ideas in advanced calculus.