Mathematical Physics (MMath)

The notion of limit and convergence are two key ideas on which rest most of modern Analysis. This module aims to present these notions building on the experience gained by students in first year Calculus module. The context of our study is: limits and co...

Beginning with a review of Newton's Laws applied to systems of particles, the course moves on to rotational motion, dynamical gravity (Kepler's Laws) and motion in non-inertial reference frames. Systems of coupled oscillators are studied.

Differential equations occupy a central role in mathematics because they allow us to describe a wide variety of real-world systems. The module will aim to stress the importance of both theory and applications of differential equations. The module begin...

After studying this course students should be able to explain the concept of quantum mechanical wave function and its basic properties, the Schrödinger equation, the concepts of operator, eigenstates and the significance of measurements, and describe the ...

Statistical mechanics links the microscopic properties of physical systems to their macroscopic properties. Thermodynamics, which describes macroscopic properties, can then be derived from statistical mechanics with a few well motivated postulates. It lea...

In the first part of this module we build on multivariate calculus studied in the first year and extend it to the calculus of scalar and vector functions of several variables. Line, surface and volume integrals are considered and a number of theorems inv...

This course introduces the properties and mechanics of waves, from the derivation and solution of wave equations, through the origins of the classical processes of refraction, dispersion and interference, to the quantum mechanical phenomenon of the uncert...

Electromagnetism is one of the brilliant successes of nineteenth century physics and the equations formulated by Maxwell are believed to account exactly for all classical electromagnetic phenomena. The aim of this course is to present the laws of elect...

Over the last four hundred years progress in understanding the physical world (theoretical physics) has gone hand in hand with progress in the mathematical sciences, so much so that the terms applied mathematics and theoretical physics have come to be alm...

For all mathematics students, this project is compulsory. The module will consist of some discussion elements in semester 1 that will aid the development of The project typically entails a weekly visit to a supervisor who advises and assists the student i...

Modelling fluid flow requires us first to extend vector calculus to include volumes that change with time. This will allow us to rephrase Newton’s second law of motion, that the force is equal to the time derivative of the linear momentum, in a way that ...

Partial Differential Equations (PDEs) occur frequently in many areas of mathematics. This module extends earlier work on PDEs by presenting a variety of more advanced solution techniques together with some of the underlying theory.

The aim of this course is to apply quantum physics to the study of atoms.

Complex Analysis is the theory of functions in a complex variable. While the initial theory is very similar to Analysis (i.e, the theory of functions in one real variable as seen in the second year), the main theorems provide a surprisingly elegant, found...

This course builds upon the Second Year Quantum Physics of Matter Course (PHYS2024) to form a complete basic course on the fundamentals of the physics of solids. After the course the student should have developed the necessary theoretical knowledge to ena...

Many classes of problems are difficult to solve in their original domain. An integral transform maps the problem from its original domain into a new domain in which solution is easier. The solution is then mapped back to the original domain with the inver...

The course provides an introduction to modern optical physics to arm students with a basic knowledge of light-matter interactions, electro-optics and nonlinear optics. It aims to provide a fundamental base for understanding the techniques and technologies...

Biology is undergoing a quantitative revolution, generating vast quantities of data that are analysed using bioinformatics techniques and modelled using mathematics to give insight into the underlying biological processes. This module aims to give a flavo...

The module consists of three parts : 1. Introductory/revision lectures on the use of mathematical resources for original research, report writing, oral presentation skills and associated report and presentation software (1 week). 2. Group research pro...

Students will learn about Nuclear Scattering, various properties of Nuclei, the Liquid Drop Model and the Shell Model, radioactive decay, fission and fusion. By the end of the course, the students should be able to classify elementary particles into hadro...

Introduce the students to the practical application of a relatively wide spectrum of numerical techniques and familiarise the students with numerical coding. Often in mathematics, it is possible to prove the existence of a solution to a given problem, ...

This is a module principally on Einstein's general theory of relativity, a relativistic theory of gravitation which explains gravitational effects as coming from the curvature of space-time. It provides a comprehensive introduction to material which is cu...

This course is a showcase for how the various branches of physics come together to give rise to real life phenomena. Using the example of stars, we will revisit a wide range of different physics and see how the various ingredients interact and thus how al...

Variational methods in classical physics will be reviewed and the extension of these ideas in quantum mechanics will be introduced.

This module provides a compulsory two semester project in the fourth year of the MMath programme. The project entails a weekly meeting with a supervisor during term-time who advises and assists the student in the study of a particular topic. The dissertat...

General relativity is the theory of spacetime and gravity developed by Einstein. This module aims to develop a geometric understanding of general relativity and explore advanced applications of GR. In particular, we will study the physics of black holes (...

Partial Differential Equations (PDEs) occur frequently in many areas of mathematics. This module extends earlier work on PDEs by presenting a variety of more advanced solution techniques together with some of the underlying theory.

This course will cover advanced topics of quantum mechanics including postulates of quantum mechanics, tools of quantum mechanics, Dirac notation, Simple Harmonic oscillator (studied using raising and lowering operators), orbital and spin angular momentum...

While coherence phenomena have long been familiar in the context of light waves, their manifestation in the context of matter waves is an exciting development of much more recent origins. While this is true this course aims to introduce the basic concepts...

This Computational Physics course is designed for students with definite interest in tackling physics problems that are only tractable through the use of computers. It covers all types of application of computers by physicists, except the control of equip...

Modern cosmology is a fascinating and fast-developing field, with intense research activity fuelled by major discoveries made in the last decade. These have overturned our understanding of the Universe’s properties and established a new standard cosmologi...

This is a compulsory lecture module for MMath students in their fourth year. The module will begin by looking at differential manifolds and the differential calculus of maps between manifolds. Manifolds are an abstraction of the idea of a smooth surfa...

This module is designed for MMath and MPhys students in their fourth year, and builds directly upon MATH3006 Relativity, Blackholes and Cosmology. Gravitational waves are tiny ripples in space-time, first predicted by Einstein himself in 1916. These ...

Homotopy theory is the study of continuous deformations. A geometric object may be continuously deformed by pulling, stretching, pressing or compressing, but not by tearing or puncturing (which are discontinuous). Two objects can then be regarded as equiv...

The emphasis of this module is on the methods required to develop mathematical models using differential equations to understand physical problems. The module involves both conventional lectures as well as discussion lectures. The discussion lectures comp...

Relativistic wave equations with their predictions of anti-particles and fermion spin will be explored. The fundamental role of gauge symmetries in current theories of force will lead to the study of the standard model of particle physics including the sy...

Since the end of the 1990s, cosmology has experienced one of the most impressive advances among all scientific disciplines. This happened mainly because of astonishing progress in the precision and accuracy of astronomical and cosmological observations ...

Networks are ubiquitous in the modern world: from the biological networks that regulate cell behaviour, to technological networks such as the Internet and social networks such as Facebook. Typically real-world networks are large, complex, and exhibit both...