# Mathematical Physics MMath

• Offers a Year in China

## Key information

• Course length: 4 years
• UCAS code: FGH1
• Year of entry: 2019
• Typical offer: A-level : AAB / IB : 35 / BTEC : Applications considered

### Programme Year One

#### Year One Compulsory Modules

• ##### Calculus I (MATH101)
Level 1 15 First Semester 80:20 1.       To introduce the basic ideas of differential and integral calculus, to develop the basic  skills required to work with them and to  apply these skills to a range of problems. 2.       To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity. 3.       To introduce the notions of sequences and series and of their convergence. differentiate and integrate a wide range of functions;​sketch graphs and solve problems involving optimisation and mensuration​understand the notions of sequence and series and apply a range of tests to determine if a series is convergent
• ##### Calculus II (MATH102)
Level 1 15 Second Semester 80:20 ·      To discuss local behaviour of functions using Taylor’s theorem. ·      To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals. use Taylor series to obtain local approximations to functions; ​obtain partial derivaties and use them in several applications such as, error analysis, stationary points change of variables​evaluate double integrals using Cartesian and Polar Co-ordinates​
• ##### Introduction to Linear Algebra (MATH103)
Level 1 15 First Semester 80:20 To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.      To develop geometrical intuition in 2 and 3 dimensions.      To introduce students to the concept of subspace in a concrete situation.    To provide a foundation for the study of linear problems both within mathematics and in other subjects. manipulate complex numbers and solve simple equations involving them    ​solve arbitrary systems of linear equations​understand and use matrix arithmetic, including the computation of matrix inverses​compute and use determinants​understand and use vector methods in the geometry of 2 and 3 dimensions​calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics
• ##### Newtonian Mechanics (MATH122)
Level 1 15 Second Semester 80:20 To provide a basic understanding of the principles of Classical Mechanics and their application to simple dynamical systems. Learning Outcomes:After completing the module students should be able to analyse real world problems involving: - the motions of bodies under simple force systems - conservation laws for momentum and energy - rigid body dynamics using centre of mass,   angular momentum and moments of inertia After completing the module students should be able to analyse real-world problems involving:​the motions of bodies under simple force systems​conservation laws for momentum and energy​rigid body dynamics using centre of mass, angular momentum and moments ​oscillation, vibration, resonance
• ##### Thermal Physics (PHYS102)
Level 1 15 First Semester 60:40 The module aims to make the student familiar with The concepts of Thermal Physics The zeroth, first and second laws of Thermodynamics Heat engines The kinetic theory of gasses Entropy The equation of state Van der Waals equation States of matter and state changes The basis of statistical mechanics Construct a temperature scale and understand how to calibrate a thermometer with that scale​Calculate the heat flow into and work done by a system and how that is constrained by the first law of Thermodynamics ​Analyse the expected performance of heat engines, heat pumps and refrigerators ​Relate the second law of thermodynamics to the operation of heat engines, particularly the Carnot engine​Understand the kinetic theory of gases and calculate properties of gases including the heat capacity and mean free path​Use the theory of equipartition to relate the structure of the molecules to the measured heat capacity ​Calculate the linear and volume thermal expansions of materials​Understand the basis of entropy and relate this to the second law of thermodynamics andcalculate entropy changes ​Relate the equation of state for a material to the macroscopic properties of the material​Understand the PV and PT diagrams for materials and the phase transitions that occur when changing the state variables for materials ​​​Be able to link the microscopic view of a system to its macroscopic state variables​Be able to demonstrate the equivalence of the Clausius and Kelvin-Planck statements of the second law of thermodynamics.​Be able to derive and use Maxwell''s equations
• ##### Wave Phenomena (PHYS103)
Level 1 15 Second Semester 60:40 To introduce the fundamental concepts and principles of wave phenomena. To highlight the many diverse areas of physics in which an understanding of waves is crucial. To introduce the concepts of interference and diffraction. Demonstrate an understanding of oscillators. ​Understand the fundamental principles underlying wave phenomena. ​Apply those principles to diverse phenomena. ​Understand wave reflection and transmission, superposition of waves. ​Solve problems on the behaviour of electromagnetic waves in vacuo and in dielectric materials. ​Understand linear and circular polarisation. ​Understand inteference and diffraction effects.  ​Understand lenses and optical instruments. ​Apply Fourier techniques and understand their link to diffraction patterns. ​Understand the basic principles of lasers
• ##### Foundations of Modern Physics (PHYS104)
Level 1 15 Second Semester 60:40 To introduce the theory of special relativity and its experimental proofs. To carry out calculations using relativity and visualise them. To introduce the concepts and the experimental foundations of quantum theory. To carry out simple calculations related to quantum mechanical problem tasks. To show the impact of relativity and quantum theory on contemporary science and society. An understanding why classical mechanics must have failed to describe the properties of light, the motion of objects with speeds close to the speed of light and the properties of microspopic systems.​A basic knowledge on the experimental and theoretical concepts which founded modern physics, i.e. that either relativity or quantum theory or both are needed to explain certain phenomena.​​A knowledge of the postulates of special relativity.​​An understanding of the concept of spacetime, of the relativity of length, time and velocity.​An ability to apply the Lorentz transformation and the concept of Lorentz invariance to simple cases​​An ability to apply the equations of relativistic energy, momentum and rest mass.​​An understanding of the Doppler effect for light and visualisation of relativistic effects.​​An ability to solve problems based on special relativity.​​An understanding why quantum theory is the conceptual framework to understand the microscopic properties of the universe.​​ ​An understanding of the quantum theory of light and the ability to apply the energy-momentum conservation for light, e.g. photo-electric effect, Compton effect.​​An understanding of the structure of atoms and its experimental foundations.​An understanding of Bohr''s theory of the atom and its application to the H-atom including the concept of principal quantum numbers.​​An understanding of de Broglie waves and their statistical interpretation.​​An ability to explain the experimental evidence of de Broglie waves with scattering experiments of electrons, X-rays and neutrons.​​An understanding of the principles of quantum mechanical measurements and Heisenberg''s uncertainty principle.​​ ​An understanding of the identity principle of microscopic particles and the basic idea of quantum (Fermi-Dirac and Bose-Einstein) statistics.​​A basic knowledge of contemporary applications of quantum theory and relativity, e.g. nuclear reactor and nuclear fissions, and the impact on our society.​
• ##### Introduction to Computational Physics (PHYS105)
Level 1 7.5 First Semester 0:100 To develop the ability to break down physical problems into steps amenable to solution using algorithms To develop skills in using computers to perform and run algorithms To introduce techniques for analysing and presenting dataTo introduce elemenatry Monte Carlo techniquesTo introduce basic computer algebraTo illustrate the insight into physics which can be obtained using computational methods Ability to produce algorithms to solve simple physical problems.Ability to program and use simple algorithms on a computerAbility to analyse and present physical dataAbility to produce simple Monte Carlo models​Ability to carry out basic symbolic manipulations using a computer
• ##### Practical Skills for Mathematical Physics (PHYS156)
Level 1 7.5 Second Semester 0:100 To improve science students'' skills in communicating scientific information in appropriate written and oral formats To provide a core of essential introductory laboratory methods which overlap and develop from A-level To introduce the basis of experimental techniques in physical measurement, the use of computer techniques in analysis and to provide experience doing experiments, keeping records and writing reports ​Appreciation of the practical nature of physics​ Awareness of the importance of accurate experimentation, particularly obervation and record keeping​ ​Ability to plan, execute and report on the results of an investigation using appropriate analysis of the data and associated uncertainties​ ​Practical and technical skill required for physics experimentation and an appreciation of the importance of a systematic approach to experimental measurement.​Problem solving skills of a practical nature​Analytical skills in the analysis of the data​ Investgative skills in performing the experiment and extracting information from various sources with which to compare the results​​​​ ​Ability to organise their time and meet deadlines​

### Programme Year Two

#### Year Two Compulsory Modules

• ##### Introduction to the Methods of Applied Mathematics (MATH224)
Level 2 15 Second Semester 90:10 To provide a grounding in elementary approaches to solution of some of the standard partial differential equations encountered in the applications of mathematics. To introduce some of the basic tools (Fourier Series) used in the solution of differential equations and other applications of mathematics. After completing the module students should: -               be fluent in the solution of basic ordinary differential equations, including systems of first order equations; -               be familiar with the concept of Fourier series and their potential application to the solution of both ordinary and partial differential equations; -               be familiar with the concept of Laplace transforms and their potential application to the solution of both ordinary and partial differential equations; -               be able to solve simple first order partial differential equations; -               be able to solve the basic boundary value problems for second order linear partial differential equations using the method of separation of variables.
• ##### Vector Calculus With Applications in Fluid Mechanics (MATH225)
Level 2 15 First Semester 85:15 To provide an understanding of the various vector integrals, the operators div, grad and curl and the relations between them. To give an appreciation of the many applications of vector calculus to physical situations. To provide an introduction to the subjects of fluid mechanics and electromagnetism. After completing the module students should be able to: -     Work confidently with different coordinate systems. -     Evaluate line, surface and volume integrals. -     Appreciate the need for the operators div, grad and curl together with the associated theorems of Gauss and Stokes. -     Recognise the many physical situations that involve the use of vector calculus. -     Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and inviscid fluid flow. All learning outcomes are assessed by both examination and course work.
• ##### Complex Functions (MATH243)
Level 2 15 First Semester 80:20 To introduce the student to a surprising, very beautiful theory which has intimate connections with other areas of mathematics and physical sciences, for instance ordinary and partial differential equations and potential theory. To understand the central role of complex numbers in mathematics;.​To develop the knowledge and understanding of all the classical holomorphic functions.​To be able to compute Taylor and Laurent series of standard holomorphic functions.​To understand various Cauchy formulae and theorems and their applications.​To be able to reduce a real definite integral to a contour integral.​To be competent at computing contour integrals.
• ##### Classical Mechanics (MATH228)
Level 2 15 Second Semester 90:10 To provide an understanding of the principles of Classical Mechanics and their application to dynamical systems. To understand the variational principles, Lagrangian mechanics, Hamiltonian mechanics. ​To be able to use Newtonian gravity and Kepler''s laws to perform the calculations of the orbits of satellites, comets and planetary motions.​To understand the motion relative to a rotating frame, Coriolis and centripetal forces, motion under gravity over the Earth''s surface.​To understand the connection between symmetry and conservation laws.​ To be able to work with inertial and non-inertial frames.
• ##### Electromagnetism (PHYS201)
Level 2 15 First Semester 70:30 To introduce the fundamental concepts and principles of electrostatics, magnetostatics, electromagnetism and Maxwell''s equations, and electromagnetic waves. To introduce differential vector analysis in the context of electromagnetism. To introduce circuit principles and analysis (EMF, Ohm''s law, Kirchhoff''s rules, RC and RLC circuits) To introduce the formulation fo Maxwell''s equations in the presence of dielectric and magnetic materials. To develop the ability of students to apply Maxwell''s equations to simple problems involving dielectric and magnetic materials. To develop the concepts of field theories in Physics using electromagnetism as an example. To introduce light as an electromagnetic wave. ​Demonstrate a good knowledge of the laws of electromagnetism and an understanding of the practical meaning of Maxwell''s equations in integral and differential forms. ​Apply differential vector analysis to electromagnetism. ​Demonstrate simple knowledge and understanding of how the presence of matter affects electrostatics and magnetostatics, and the ability to solve simple problems in these situations. ​Demonstrate knowledge and understanding of how the laws are altered in the case of non-static electric and magnetic fields and the ability to solve simple problems in these situations.
• ##### Condensed Matter Physics (PHYS202)
Level 2 15 First Semester 70:30 ​ The aims of Phys202 are to introduce the most important and basic concepts in condensed matter physics relating to the different materials we commonly see in the world around us. Condensed matter physics is one of the most active areas of research in modern physics, whose scope is extremely broad. The ultimate aim of this course is to introduce its central ideas and methodology to the students. Condensed matter refers to both liquids and solids and all kinds of other forms of matter in between those two extremes, generally known as “soft matter". While the course will touch on liquids, the emphasis will be on crystalline solids, including some nano-materials. The reason for focusing on crystals is that the periodicity of a crystal is what allows us to make progress in developing a theory for various phenomena in solids based on first principles. Two important concepts are: • the electronic states of electrons in a solid and • the vibrations of atoms in the solid. The description of these ideas basically refer to the theory of electronic band structure and the theory of phonons. These concepts form the basis for understanding a wide range of phenomena including how the atoms bond together to form the crystal, what are some basic statistical properties like specific heat, how electrons move in solids and electronic transport, why are some materials metals and others semiconductors and insulators, and how do solids interact with electromagnetic fields. The course will also introduce optical and magnetic properties in solids, scattering phenomena, thermal conductivity and effect of defects in solids, semiconductors, magnetism and go beyond the free electron model to touch on intriguing effects such as superconductivity. On satisfying the requirements of this course, students will have the knowledge and skills to understand the basic concepts of bonding in solids, establish an understanding of electron configuration in atoms and in the condensed matter in terms of bonding, and relating them to band structure description.​Students will be able to understand how solid structures are described mathematically and how material properties can be predicted​. ​Students will be able to establish a foundation in basic crystallography, using Bragg''s law, and understand the concept of the reciprocal lattice.​Students will understand basic transport properties, both electronic and thermal, in solids.​ Students will understand the concept of electron and hole carrier statistics, effective masses and transport in intrinsic and extrinsic semiconductors​Students will learn the basics of magnetism, the atomic origin and classical treatment of diamagnetism and paramagnetism, quantization of angular momentum and Hund''s rule, and introduced to weak magnetism in solids.​​Students will become familiar to the general language of condensed matter physics, key theories and concepts, ultimately enebling them to read and understand research papers.
• ##### Quantum and Atomic Physics (PHYS203)
Level 2 15 Second Semester 70:30 To introduce students to the concepts of quantum theory. To show how Schrodinger''s equation is applied to bound states (well potentials, harmonic oscillator, hydrogen atoms, multi-electron atoms) and particle flux (scattering). To show how quantum ideas provide an understanding of atomic structure. At the end of the module the student should have: An understanding of the reasons why microscopic systems require quantum description and statistical interpretation. Knowledge of the Schrodinger equation and how it is formulated to describe simple physical systems. Understanding of the basic technique of using Schrodinger''s equation and ability to determine solutions in simple cases. Understanding of how orbital angular momentum is described in quantum mechanics and why there is a need for spin. Understanding how the formalism of quantum mechanics describes the structure of atomic hydrogen and, schematically, how more complex atoms are described.
• ##### Nuclear and Particle Physics (PHYS204)
Level 2 15 Second Semester 70:30 To introduce Rutherford and related scattering. To introduce nuclear size, mass and decay modes To provide some applications and examples of nuclear physics To introduce particle physics, including interactions, reactions and decay To show some recent experimental discoveries To introduce relativistic 4-vectors for applications to collision problems basic understanding of Rutherford, electron on neutron scattering ​understanding of the basic principles that determine nuclear size, mass and decay modes ​knowledge of examples and applications of nuclear physics ​knowledge of elementary particles and their interactions ​basic understanding of relativistic 4-vectors

### Programme Year Three

• Choose one from;

MATH325      Quantum Mechanics

Or  PHYS361 Quantum Mechanics & Atomic Physics

Choose one from;

MATH432      Mathematical Physics Project

Or PHYS488 Modelling Physical Phenomena (Project)

MATH324      Cartesian Tensors and Mathematical Models of Solids and Viscous Fluids

MATH332      Population Dynamics

PHYS363        Condensed Matter Physics

PHYS375        Nuclear Physics

PHYS306        Practical Physics III

PHYS387        Materials Physics

PHYS389        Semiconductor Applications

PHYS391        Communicating Science

PHYS392        Statistics in Data Analysis

PHYS393        Statistical and Low Temperature Physics

MATH331      Mathematical Economics

MATH322      Chaos and Dynamical Systems

MATH340      Riemann Surfaces

MATH345      The Magic of Complex Numbers:Complex Dynamics, Chaos and the Madelbrot Set

MATH349      Differential Geometry

PHYS374        Relativity and Cosmology

PHYS377        Introduction to Particle Physics

PHYS381        Surface Physics

PHYS382        Physics of Life

PHYS388        Physics of Energy Sources

PHYS397        Technology Transfer and Commercialisation

And choose two modules from:

MATH421      Linear Differential Operators in Mathematical Physics

MATH425      Quantum Field Theory (only in Year 4)

MATH430      Variational Calculus & its Applications

PHYS470      Classical Mechanics

PHYS481      Accelerator Physics

PHYS491      Research Skills

PHYS499       Nanoscale Physics and Technology

PHYS497      Magnetic Structure and Function

MATH423      Introduction to String Theory

MATH424      Analytical and Computational Methods for Applied Mathematics

MATH426      Advanced Topics in Mathematical Biology

MATH427      Waves, Mathematical Modelling

MATH431      Introduction to Modern Particle Theory

MATH433      Asymptotic Methods for Differential Equations

#### Year Three Compulsory Modules

• ##### Further Methods of Applied Mathematics (MATH323)
Level 3 15 First Semester 100:0 To give an insight into some specific methods for solving important types of ordinary differential equations. To provide a basic understanding of the Calculus of Variations and to illustrate the techniques using simple examples in a variety of areas in mathematics and physics. To build on the students'' existing knowledge of partial differential equations of first and second order. After completing the module students should be able to: -     use the method of "Variation of Arbitrary Parameters" to find the solutions of some inhomogeneous ordinary differential equations. -     solve simple integral extremal problems including cases with constraints; -     classify a system of simultaneous 1st-order linear partial differential equations, and to find the Riemann invariants and general or specific solutions in appropriate cases; -     classify 2nd-order linear partial differential equations and, in appropriate cases, find general or specific solutions.   [This might involve a practical understanding of a variety of mathematics tools; e.g. conformal mapping and Fourier transforms.]
• ##### Relativity (MATH326)
Level 3 15 First Semester 100:0 1. To introduce the physical principles behind Special and General Relativity and their main consequences.2. To develop the competence in the mathematical framework of the subjects: Lorentz transformations and Minkowski space-time, semi-Riemannian geometry and curved space-time, symmetries and conservation laws, variational principles.3. To develop the understanding of the dynamcis of particles and of the Maxwell field in Minkowski space-time, and of particles in a curved space-time.4. To develop the knowledge of tests of General Relativity, including the classical tests (perihelion shift, gravitational deflection of light).5. To understand the basic concepts of black holes, and, time permitting, of relativistic cosmology and gravitational waves.​ ​ ​To be be proficient in calculations involving Lorentz transformations, the kinematical and dynamical quantities associated to particles in Minkowski space-times, and the application of the conservation law for the four-momentum to scattering processes.​To know the relativistically covariant form of the Maxwell equations​.​To know the action principles for relativistic particles, the Maxwell field and the gravitational field​.​ ​To be be proficient at calculations in semi-Riemannian geometry as far as needed for General Relativity, including calculations involving general coordinate transformations, tensor fields, covariant derivatives, parallel transport, geodesics and curvature​​ ​To understand the arguments leading to Einstein''s field equations and how Newton''s law of gravity arises as a limit​.To ​be able to calculate the trajectories of bodies in a Schwarzschild space-time​.
• ##### Quantum Mechanics (MATH325)
Level 3 15 First Semester 100:0 The aim of the module is to lead the student to an understanding of the way that relatively simple mathemactics (in modern terms) led Bohr, Einstein, Heisenberg and others to a radical change and improvement in our understanding of the microscopic world. ​ To be able to solve Schrodinger''s equation for simple systems.​To have an understanding of the significance of quantum mechanics for both elementary systems and the behaviour of matter.
• ##### Theory of Statistical Inference (MATH361)
Level 3 15 Second Semester 90:10 To introduce some of the concepts and principles which provide theoretical underpinning for the various statistical methods, and, thus, to consolidate the theory behind the other second year and third year statistics options. To acquire a good understanding of the classical approach to, and especially the likelihood methods for, statistical inference.  To acquire an understanding of the blossoming area of Bayesian approach to inference.
• ##### Mathematical Physics Project (MATH432)
Level M 15 Second Semester 0:100 To learn research and presentation skills by studying and reporting on an area of theoretical physics. After completing the essay with suitable guidance, the student should have ·      understood an area of advanced theoretical physics ·      had experience in consulting relevant literature ·      gained expertise in using appropriate mathematics ·      made a critical appraisal of the current state of knowledge of the area ·      learnt how to construct an essay  ·      gained familiarity with a scientific word-processing package such as TeX ·      acquired skills of  oral presentation
• ##### Modelling Physical Phenomena (PHYS488)
Level M 15 Second Semester 0:100 To introduce students to concepts and methods of a high-level Object-oriented programming language (Java)To apply Java for the computational modelling of physical phenomena and solution of physics problems using Monte Carlo TechniquesTo give students experience of working independently and in small groups on an original problem.To give students an opportunity to display the high quality of their work, initiative and ingenuity.To give students experience of report writing displaying high standards of composition and production.To give an opportunity for students to display communication skills. Acquire a working knowledge of a high level programming language including object-oriented elements.Gain experience how to apply computational methods to the solution of physics problems, including the set up of a complex model of physical phenomena or experimental situationExperience in researching literature and other sources of relevant information​​Experience in testing model against data from experiment or literature​Improved ability to organise and manage time.​Improved skills in report writing. ​Improved skills in explaining project under questioning.

#### Year Three Optional Modules

• ##### Cartesian Tensors and Mathematical Models of Solids and VIscous Fluids (MATH324)
Level 3 15 First Semester 100:0 To provide an introduction to the mathematical theory of viscous fluid flows and solid elastic materials. Cartesian tensors are first introduced. This is followed by modelling of the mechanics of continuous media. The module includes particular examples of the flow of a viscous fluid as well as a variety of problems of linear elasticity. ​ To understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations.​To apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.​
• ##### Population Dynamics (MATH332)
Level 3 15 Second Semester 100:0 - To provide a theoretical basis for the understanding of population ecology - To explore the classical models of population dynamics - To learn basic techniques of qualitative analysis of mathematical models ​The ability to relate the predictions of the mathematical models to experimental results obtained in the field.The ability to recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems.The ability to use analytical and graphical methods to investigate population growth and the stability of equilibrium states for continuous-time and discrete-time models of ecological systems.​
• ##### Advanced Condensed Matter Physics (PHYS363)
Level 3 7.5 Second Semester 100:0 To develop concepts introduced in Year 1 and Year 2 modules which relate to solids. To consolidate concepts related to crystal structure. To introduce the concept of reciprocal space and diffraction. To enable the students to apply these concepts to the description of crystals,transport properties and the electronic structure of condensed matter. To illustrate the use of these concepts in scientific research in condensed matter. To introduce various other solids Familiarity with the crystalline nature of both perfect and real materials. ​An understanding of the fundamental principles of the properties of condensed matter​An appreciation of the relationship between the real space and the reciprocal space view of the properties of crystalline matter​An ability to describe the crystal structure and electronic structure of matter​An awareness of current physics research in condensed matter.
• ##### Nuclear Physics (PHYS375)
Level 3 7.5 First Semester 100:0 To build on the second year module involving Nuclear Physics To develop an understanding of the modern view of nuclei, how they are modelled and of nuclear decay processes At the end of the module the student should have: Knowledge of evidence for the shell model of nuclei, its development and the successes and failures of the model in explaining nuclear properties ​Knowledge of the collective vibrational and rotational models of nuclei ​Basic knowledge of nuclear decay processes, alpha decay and fission, of gamma-ray transitions and internal conversion ​Knowledge of electromagnetic transitions in nuclei
• ##### Practical Physics III (PHYS306)
Level 3 15 First Semester 0:100 ​The Aims of the module are: To give further training in laboratory techniques, in the use of computer packages for modelling and analysis, and in the use of modern instruments.To develop independent judgement in performing physics experiments.To encourage students to research aspects of physics complementary to material met in lectures and tutorials.To consolidate the students ability to produce good quality work against realistic deadlines ​Experience of taking physics data with modern equipment​Knowledge of experimental techniques not met in previous laboratory practice​Improved skills in researching published papers and articles as source materials​Developed a personal responsibility for assuring that data taken are of a high quality​Increased skills in data taking and error analysis​Increased skills in reporting experiments and an appreciation of the factors needed to produce clear and complete reports​Improved skills in the time management and organisation of their experimental procedures to meet deadlines
• ##### Materials Physics (PHYS387)
Level 3 7.5 First Semester 100:0 To teach the properties and methods of preparation of a range of materials of scientific and technological importance To develop an understanding of the experimental techniques of materials characterisation To introduce materials such as amorphous solids, liquid crystals and polymers and to develop an understanding of the relationship between structure and physical properties for such materials To illustrate the concepts and principles by reference to examples At the end of the module the student should have: An understanding of the atomic structure in cyrstalline and amorphous materials Knowledge of the methods used for preparing single crystals and amorphous materials Knowledge of the experimental techniques used in materials characterisation Knowledge of the physical properties of superconducting materials An appreciation of the factors involved in the design of biomaterials The ability to interpret simple phase diagrams of binary systems
• ##### Semiconductor Applications (PHYS389)
Level 3 7.5 First Semester 100:0 To develop the physics concepts describing semiconductors in sufficient details for the purpose of understanding the construction and operation of common semiconductor devices At the end of the module the student should have: Knowledge of the basic theory of p-n junctions Knowledge of the structure and function of a variety of semiconductor devices An overview of semiconductor device manufacturing processes Knowledge of the basic processes involved in the interaction of radiation with matter Understanding the application of semiconductors in Nuclear and Particle physics
• ##### Communicating Science (PHYS391)
Level 3 7.5 First Semester 0:100 To improve science students'' skills in communicating scientific information in a wide range of contexts To develop students'' understanding of some concepts of: Science in general Their particular area of science Other areas of science ​ An ability to communicate more confidently​​ An understanding of some of the key factors in successfulcommunication​An appreciation of the needs of different audiences​​Experience of a variety of written and oral media​​A broader appreciation of science and particular areas ofscience​
• ##### Statistics for Physics Analysis (PHYS392)
Level 3 15 First Semester 50:50 To give a theoretical and practical understanding of the statistical principles involved in the analysis and interpretation of data.To give practice in analysing data by computer program.To show how to write code to solve problems in data analysis. Knowledge of experimental errors and probability distributions​The ability to use statistical methods in data analysis​The ability to apply statistical analysis to data from a range of sourcesUsing statistical information to detemine the validity of a hypothesis or experimental measurement​​The ability to write code to analyse data sets
• ##### Statistical and Low Temperature Physics (PHYS393)
Level 3 15 First Semester 100:0 To build on material presented in earlier Thermal Physics and Quantum Mechanics courses To develop the statistical treatment of quantum systems To use theoretical techniques to predict experimental observables To introduce the basic principles governing the behaviour of liquid helium and superconductors in cooling techniques Understanding of the statistical basis of entropy and temperature ​Ability to devise expressions for observables, (heat capacity, magnetisation) from statistical treatment of quantum systems ​Understanding of Maxwell Boltzmann, Fermi-Dirac and Bose Einstein gases ​Knowledge of cooling techniques ​Knowledge and understanding of basic theories of liquid helium behaviour and superconductivity in cooling techniques
• ##### Mathematical Economics (MATH331)
Level 3 15 Second Semester 100:0 ·      To explore, from a game-theoretic point of view, models which have been used to understand phenomena in which conflict and cooperation occur. ·      To see the relevance of the theory not only to parlour games but also to situations involving human relationships, economic bargaining (between trade union and employer, etc), threats, formation of coalitions, war, etc.. ·      To treat fully a number of specific games including the famous examples of "The Prisoners'' Dilemma" and "The Battle of the Sexes". ·      To treat in detail two-person zero-sum and non-zero-sum games. ·      To give a brief review of n-person games. ·      In microeconomics, to look at exchanges in the absence of money, i.e. bartering, in which two individuals or two groups are involved.   To see how the Prisoner''s Dilemma arises in the context of public goods. After completing the module students should: ·      Have further extended their appreciation of the role of mathematics in modelling in Economics and the Social Sciences. ·      Be able to formulate, in game-theoretic terms, situations of conflict and cooperation. ·      Be able to solve mathematically a variety of standard problems in the theory of games. ·      To understand the relevance of such solutions in real situations.
• ##### Chaos and Dynamical Systems (MATH322)
Level 3 15 First Semester 100:0 To develop expertise in dynamical systems in general and study particular systems in detail. After completing the module students will be able to understand the possible behaviour of dynamical systems with particular attention to chaotic motion; After completing the module students will ​be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points;​After completing the module students will understand how fractal sets arise and how to characterise them.
• ##### Riemann Surfaces (MATH340)
Level 3 15 Second Semester 100:0 To introduce to a beautiful theory at the core of modern mathematics. Students will learn how to handle some abstract geometric notions from an elementary point of view that relies on the theory of holomorphic functions. This will provide those who aim to continue their studies in mathematics with an invaluable source of examples, and those who plan to leave the subject with the example of a modern axiomatic mathematical theory. Students should be familiar with themost basic examples of Riemann surfaces: the Riemann sphere, hyperelliptic Riemann surfaces, and smooth plane algebraic curves.Students should understand and be able to use the abstract notions used to build the theory: holomorphic maps, meromorphic differentials, residues and integrals, Euler characteristic and genus.
• ##### The Magic of Complex Numbers: Complex Dynamics, Chaos and the Mandelbrot Set (MATH345)
Level 3 15 Second Semester 90:10 1. To introduce students to the theory of the iteration of functions of one complex variable, and its fundamental objects;2. To introduce students to some topics of current and recent research in the field;3. To study various advanced results from complex analysis, and show how to apply these in a dynamical setting;4. To illustrate that many results in complex analysis are "magic", in that there is no reason to expect them in a real-variable context, and the implications of this in complex dynamics;5. To explain how complex-variable methods have been instrumental in questions purely about real-valued one-dimensional dynamical systems, such as the logistic family.6. To deepen students'' understanding of formal reasoning and proof.​ To ​understand the compactification of the complex plane to the Riemann sphere, and be able to use spherical distances and derivatives.​To be able to use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems.​To be able to state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties.To be able to ​determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set.To know how to ​apply advanced results from complex analysis in a dynamical setting.To be able to ​determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not.
• ##### Differential Geometry (MATH349)
Level 3 15 Second Semester 85:15 This module is designed to provide an introduction to the methods of differential geometry, applied in concrete situations to the study of curves and surfaces in euclidean 3-space.  While forming a self-contained whole, it will also provide a basis for further study of differential geometry, including Riemannian geometry and applications to science and engineering.​ ​​​1a. Knowledge and understanding: Students will have a reasonable understanding of invariants used to describe the shape of explicitly given curves and surfaces. ​1b. Knowledge and understanding: Students will have a reasonable understanding of special curves on surfaces.​1c. Knowledge and understanding: Students will have a reasonable understanding of the difference between extrinsically defined properties and those which depend only on the surface metric.​1d. Knowledge and understanding: Students will have a reasonable understanding of the passage from local to global properties exemplified by the Gauss-Bonnet Theorem.​2a. Intellectual abilities: Students will be able to use differential calculus to discover geometric properties of explicitly given curves and surfaces.​2b. Intellectual abilities: Students will be able to understand the role played by special curves on surfaces.​3a. Subject-based practical skills: Students will learn to compute invariants of curves and surfaces.​3b. Subject-based practical skills: Students will learn to interpret the invariants of curves and surfaces as indicators of their geometrical properties.​​4a. General transferable skills: Students will improve their ability to think logically about abstract concepts,​4b. General transferable skills: Students will improve their ability to combine theory with examples in a meaningful way.​​
Level 3 15 Second Semester 100:0 To build on first and second year modules on electricity, magnetism and waves by understanding a range of electromagnetic phenomena in terms of Maxwell''s equations. To understand the properties of solutions to the wave equation for electromagnetic fields in free space, in matter (non-dispersive and dispersive dielectrics, and conductors). To understand the behaviour of electromagnetic waves at boundaries.To understand the behaviour of electromagnetic waves in cavities, waveguides and transmission lines. To understand the properties of electric dipole radiation. To introduce an explicity covariant formulation of electromagnetism in special relativity. To further develop students'' problem-solving and analytic skills. ​Students should have an understanding of the properties of solutions to the wave equation for electromagnetic fields in free space and in matter (non-dispersive and dispersive dielectrics, and conductors).​Students should have an understanding of the behaviour of electromagnetic waves at boundaries.​Students should have an understanding of the behaviour of electromagnetic waves in cavities, waveguides and transmission lines.​Students should have an understanding of the properties of electric dipole radiation.​Students should have the ability to explain an explicity covariant formulation of electromagnetism in special relativity.
• ##### Relativity and Cosmology (PHYS374)
Level 3 15 Second Semester 80:20 To introduce the ideas of general relativity and demonstrate its relevance to modern astrophysics To provide students with a full and rounded introduction to modern observational cosmology To develop the basic theoretical background required to understand and appreciate the significance of recent results from facilities such as the Hubble Space Telescope and the Wilkinson Microwave Anisotropy Probe ​The ability to explain the relationship between Newtonian gravity and Einstein''s General Relativity (GR) ​Understanding of the concept of curved space time and knowledge of metrics​.​ A broad and up-to-date knowledge of the basic ideas, most important discoveries and outstanding problems in modern cosmology​.​Knowledge of how simple cosmological models of the universe are constructed​.The ability to calculate physical parameters and make observational predictions for a range of such models.
• ##### Introduction to Particle Physics (PHYS377)
Level 3 7.5 Second Semester 100:0 To build on the second year module involving Nuclear and Particle Physics To develop an understanding of the modern view of particles, of their interactions and the Standard Model At the end of the module the student should have: Basic understanding of relativistic kinematics (as applied to collisions, decay processes and cross sections) ​Descriptive knowledge of the Standard Model using a non rigorous Feynman diagram approach​Knowledge of the fundamental particles of the Standard Model and the experimental evidence for the Standard Model ​Knowledge of conservation laws and discrete symmetries
• ##### Surface Physics (PHYS381)
Level 3 7.5 Second Semester 100:0 Develop a syllabus to describe the properties of surfacesConvey an understanding of the physical properties of SurfacesProvide knowledge  of a raneg of surface characterisation techniquesIllustrate surface processes and their relevance to technologies explain how the presence of the surface alters physical properties such as atomic an electronic structure​ choose the right characterisation technique to assess different surface properties have gained an  appreciation of surface processes and their relevance to the modification of surface properties​be able to describe surface alterations and processes using the right terminology
• ##### Physics of Life (PHYS382)
Level 3 7.5 Second Semester 100:0 To introduce students to the physical principles needed to address important problems such as climate change, the loss of biodiversity, the understanding of ecological systems, the growth of resistance to antibiotics, the challenge of sustainable development and the study of disease. These problems offer excellent opportunities for rewarding careers.​ ​ ​An understanding of the conditions necessary for life to evolve in a universe.​​An understanding of the thermodynamics and organization of living things.​​​​​Familiarity with physical techniques used in the study of biological systems. ​
• ##### Physics of Energy Sources (PHYS388)
Level 3 15 Second Semester 100:0 To develop an ability which allows educated and well informed opinions to be formed by the next generation of physicists on a wide range of issues in the context of the future energy needs of man To describe and understand methods of utilising renewable energy sources such as hydropower, tidal power, wave power, wind power and solar power. To give knowledge and understanding of the design and operation of nuclear reactors To give knowledge and understanding of nuclear fusion as a source of power To give knowledge and understanding relevant to overall safety in the nuclear power industry To describe the origin of environmental radioactivity and understand the effects of radiation on humans At the end of the module the student should have: Learned the fundamental physical principles underlying energy production using conventional and renewable energy sources Learned the fundamental physical principles underlying nuclear fission and fusion reactors Studied the applications of these principles in the design issues power generation An appreciation of the role of mathematics in modelling power generation Learned the fundamental physical principles concerning the origin and consequences of environmental radioactivity Developed an awareness of the safety issues involved in exposure to radiation Developed problem solving skills based on the material presented Developed an appreciation of the problems of supplying the required future energy needs and the scope and issues associated with the different possible methods
Level 3 15 Second Semester 0:100 To provide undergraduates with key transferable skills. To provide students with opportunity to learn to communicate physics at different levels. To provide students with work-place experience. To provide students with the opportunity to work with staff in a different environment with different priorities to the University. To provide teaching experience that encourages undergraduates to consider a career in teaching. To supply role models for secondary school students. To provide support and teaching assistance to secondary school teachers. To encourage a new generation of physicists. Communicate physicseffectively to others​​Plan a lessonDesign a worksheet​​Evaluate their planning​Assess the effectiveness of a session or worksheet that they have designed​Manage small groups ofpupils (e.g. to complete an experiment)​​Prioritise their work​
• ##### Technology Transfer and Commercialisation (PHYS397)
Level 3 7.5 Second Semester 0:100 ​This module aims to To  be able to develop skills in assessing thecommercial routes available to introduce a product or service into the market. To be adept in market information gathering andanalysis.To develop presentation and communicationskills and reporting skills beyond the classic essay format. To distinguish clearly between thedifferent business models available and to contrast merits and drawbacks ofeach solution. ​All students will be able to gather and analyse business data information​All students will be able to understand technology transfer dynamicsstudents will be able to communicate their ideas and work in a clear and concise manner​Students will be able to present data and project proposals in a professional manner, easily recognised by industry and companies.
• ##### Linear Differential Operators in Mathematical Physics (MATH421)
Level M 15 First Semester 90:10 This module provides a comprehensive introduction to the theory of partial differential equations, and it provides illustrative applications and practical examples in the theory of elliptic boundary value problems, wave propagation and diffusion problems. To understand and actively use the basic concepts of mathematical physics, such as generalised functions, fundamental solutions and Green''s functions.​ ​To apply powerful mathematical methods to problems of electromagnetism, elasticity, heat conduction and wave propagation.​
• ##### Quantum Field Theory (MATH425)
Level M 15 First Semester 100:0 To provide a broad understanding of the essentials of quantum field theory. After the course the students should understand the important features of the mathematical tools necessary for particle physics. In particular they should ·      be able to compute simple Feynman diagrams, ·      understand the basic principles of regularisation and renormalisation ·      be able to calculate elementary scattering cross-sections.
• ##### Variational Calculus and Its Applications (MATH430)
Level M 15 First Semester 90:10 ​This module provides a comprehensive introduction to the theory of the calculus of variations, providing illuminating applications and examples along the way. ​Students will posses a solid understanding of the fundamentals of variational calculus​​Students will be confident in their ability to apply the calculus of variations to range of physical problems​Students will also have the ability to solve a wide class of non-physical problems using variational methods​Students will develop an understanding of Hamiltonian formalism and have the ability to apply this framework to solve physical and non-physical problems​Students will be confident in their ability to analyse variational symmetries and generate the associated conservation laws
• ##### Classical Mechanics (PHYS470)
Level M 15 First Semester 100:0 ​To provide students with an awareness of the physical principles that can be applied to understand important features of classical (i.e. non-quantum) mechanical systems.To provide students with techniques that can be applied to derive and solve the equations of motion for various types of classical mechanical systems, including systems of particles and fields.To develop students'' understanding of the fundamental relationship between symmetries and conserved quantities in physics.To reinforce students’ knowledge of quantum mechanics, by developing and exploring the application of closely-related concepts in classical mechanics. ​Students should know the physical principles underlying the Lagrangian and Hamiltonian formulations of classical mechanics, in particular D’Alembert’s principle and Hamilton’s principle, and should be able to explain the significance of these advanced principles in classical and modern physics.​Students should be able to apply the Euler-Lagrange equations and Hamilton’s equations (as appropriate) to derive the equations of motion for specific dynamical systems, including complex nonlinear systems.Students should be able to use advanced concepts in classical mechanics to describe the connection between symmetries and conservation laws.​Students should be able to apply advanced techniques, including conservation laws, canonical transformations, generating functions, perturbation theory etc. to describe important features of various dynamical systems (including systems of particles and fields) and to solve the equations of motion in specific cases.
• ##### Accelerator Physics (PHYS481)
Level M 7.5 First Semester 70:30 To build on modules on electricity, magnetism and waves; To study the functional principle of different types of particle accelerators; To study the generation of ion and electron beams; To study the layout and the design of simple ion and electron optics; To study basic concepts in radio frequency engineering and technology. At the end of the module the student should have: An understanding of the description of the motion of charged particles in complex electromagnetic fields; An understanding of different types of accelerators, in which energy range and for which purposes they are utilised; An understanding of the generation and technical exploitation of synchrotron radiation; An understanding of the concept and the necessity of beam cooling.
• ##### Research Skils (PHYS491)
Level M 7.5 First Semester 0:100 This module will help students develop the ability to:Perform literature searches.Plan research projects.Explain research projects to both expert and non-expert audiences.Organise a team of people and work as a group.Assess the broader impact of research projects.Present a proposal as a written document ans orally. Experience in carrying out search of scientific literature.  Communicating research to non-expert audience.​Evaluating the possible broader impact of research.Writing a scientific case for an assessment panel.​  First experience with some project management tools.
• ##### Nanoscale Physics and Technology (PHYS499)
Level M 15 Second Semester 70:30 Tointroduce the emerging fields of nanoscale physics and nanotechnology To describe experimental techniques for probing physical properties of nanostructured materials ​Todescribe the novel size-dependent electronic, optical, magnetic and chemicalproperties of nanoscale materials​Todescribe several ‘hot topics'' in nanoscience research​Todevelop students'' problem-solving, investigative, communication and analyticskills through appropriate assignments for tutorials and a literature project. ​ After the module the students should have the ability to explain how and why nanoscalesystems form.After the module the students should have the ability to describe how nanoscale systems may be probed experimentally and compare different techniques in terms of strengths and weaknesses.After the module the students should have the ability to explain and apply the fundamental principles that govern nanoscale systems.​​After the module the students should have the ability to describe potential applications and to discuss their wider applications.​After the module the students should have enhanced problem-solving, investigative, communication, and analytic skills.
• ##### Magnetic Structure and Function (PHYS497)
Level M 7.5 First Semester 100:0 To build on the third year module Condensed Matter Physics To develop an understanding of the phenomena and fundamental mechanisms of magnetism in condensed matter ​ Have a basic understanding of the quantum origin of magnetism and magnetic moments.​Understand the concept of magnetic order and the role of exchange interactions.​Be able to identify the properties associated with various types of magnetism.​Be able to explain the cause of magnetic phenomena such as hysteresis and domain formation.​
• ##### Introduction to String Theory (MATH423)
Level M 15 Second Semester 100:0 To provide a broad understanding of string theory, and its utilization as a theory that unifies all of the known fundamental matter and interactions. After completing the module the students should: - be familiar with the properties of the classical string.​be familiar with the basic structure of modern particle physics and how it may arise from string theory.​ be familiar with the basic properties of first quantized string and the implications for space-time dimensions.  ​be familiar with string toroidal compactifications and T-duality.
• ##### Analytical & Computational Methods for Applied Mathematics (MATH424)
Level M 15 Second Semester 100:0 To provide an introduction to a range of analytical and numerical methods for partial differential equations arising in many areas of applied mathematics.   To provide a focus on advanced analytical techniques for solution of both elliptic and parabolic partial differential equations, and then on numerical discretisation methods of finite differences and finite elements.  To provide the algorithms for solving the linear equations arising from the above discretisation techniques. Apply a range of standard numerical methods for solution of PDEs and should have an understanding of relevant practical issues. ​Obtain solutions to certain important PDEs using a variety of analytical techniques and should be familiar with important properties of the solution. ​Understand and be able to apply standard approaches for the numerical solution of linear equations   ​Have a basic understanding of the variation approach to inverse problems.
• ##### Advanced Topics in Mathematical Biology (MATH426)
Level M 15 Second Semester 100:0 To introduce some hot problems of contemporary mathematical biology, including analysis of developmental processes, networks and biological mechanics. ​To further develop mathematical skills in the areas of difference equations and ordinary and partial differential equations. ​To explore biological applications of fluid dynamics in the limit of lowand high Reynolds number. To familiarise with mathematical modelling methodology used in contemporary mathematical biology.​Be able to use techniques from difference equations and ordinary and partial differential equations in tackling problems in biology.
• ##### Waves, Mathematical Modelling (MATH427)
Level M 15 Second Semester 100:0 This module gives an introduction to the mathematical theory of linear and non-linear waves. Illustrative applications involve problems of acoustics, gas dynamics and examples of solitary waves. To understand essential modelling techniques in problems of wave propagation.   To understand that mathematical models of the same type can be successfully used to describe different physical phenomena.To understand background mathematical theory in models of acoustics, gas dynamics and water  waves.​
• ##### Introduction to Modern Particle Theory (MATH431)
Level M 15 Second Semester 100:0 To provide a broad understanding of the current status of elementary particle theory. To describe the structure of the Standard Model of particle physics and its embedding in Grand Unified Theories. To understand the Lorentz and Poincare groups and their role in classification of elementary particles.​To understand the basics of Langrangian and Hamiltonian dynamics and the differential equations of bosonic and fermionic wave functions.​To understand the basic elements of field quantisation. ​ ​To understand the Feynman diagram pictorial representation of particle interactions.​To understand the role of symmetries and conservation laws in distinguishing the strong, weak and electromagnetic interactions.​To be able to describe the spectrum and interactions of elementary particles and their embedding into Grand Unified Theories (GUTs)To understand the flavour structure of the standard particle model and generation of mass through symmetry breaking​.​To understand the phenomenological aspects of Grand Unified Theories.
• ##### Asymptotic Methods for Differential Equations (MATH433)
Level M 15 Second Semester 100:0 This module provides an introduction into the perturbation theory for  partial differential equations. We consider singularly and regularly perturbed problems and applications in electro-magnetism, elasticity, heat conduction and propagation of waves. The ability to make appropriate use of asymptotic approximations.​The ability to analyse boundary layer effects.​The ability to use the method of compound asymptotic expansions in the analysis of singularly perturbed problems.
• ##### Advanced Nuclear Physics (PHYS490)
Level M 15 Second Semester 100:0 To build on the year 3 modules on Nuclear Physics To offer an insight into current ideas about the description of atomic nuclei and nuclear matter Knowledge of the basic properties of nuclear forces and the experimental evidence upon which these are based  Knowledge of the factors governing nuclear shapes​Understanding of the origin of pairing forces and the effect of these and rotational forces on nuclear behaviour ​An overview of phenomena observed for exotic nuclei far from the line of nuclear stability​Knowledge of astrophysical nucleosynthesis processes ​Knowledge of phases of nuclear matter
• ##### Advanced Particle Physics (PHYS493)
Level M 15 Second Semester 100:0 To build on the Year 3 module PHYS377 Particle Physics To give the student a deeper understanding of the Standard Model of Particle Physics and the basic extensions To review the detectors and accelerator technology available to investigate the questions posed by the Standard Model and its extensions An understanding of the Standard Model and its extensions. This will be placed in context of the understanding of the origin of the universe, its properties and its physical laws​An understanding of how present and future detector and accelerator technology will be applied to investigate the development of the Standard Model ​An understanding of the effects of symmetries on particle properties​Ablity to caclulate decay rates for particles

### Programme Year Four

There is a large set of modules available, some of which are taught in alternate years. MMath/MPhys students will take at least seven of these during Years three and four. There is also a compulsory project.

Choose three modules from:

MATH324      Cartesian Tensors and Mathematical Models of Solids and Viscous Fluids

MATH332      Population Dynamics

PHYS363      Condensed Matter Physics

PHYS375      Nuclear Physics

PHYS306      Practical Physics III

PHYS387       Materials Physics

PHYS389      Semiconductor Applications

PHYS391      Communicating Science

PHYS392      Statistics in Data Analysis

PHYS393      Statistical and Low Temperature Physics

MATH331      Mathematical Economics

MATH322      Chaos and Dynamical Systems

MATH340      Riemann Surfaces

MATH345      The Magic of Complex Numbers:Complex Dynamics, Chaos and the Madelbrot Set

MATH349       Differential Geometry

PHYS374        Relativity and Cosmology

PHYS377        Introduction to Particle Physics

PHYS381        Surface Physics

PHYS382        Physics of Life

PHYS388        Physics of Energy Sources

PHYS397        Technology Transfer and Commercialisation

Choose two modules from:

MATH421      Linear Differential Operators in Mathematical Physics

MATH425      Quantum Field Theory (only in Year 4)

MATH430      Variational Calculus & its Applications

PHYS470      Classical Mechanics

PHYS481      Accelerator Physics

PHYS491      Research Skills

PHYS499      Nanoscale Physics and Technology

PHYS497      Magnetic Structure and Function

MATH423      Introduction to String Theory

MATH424      Analytical and Computational Methods for Applied Mathematics

MATH426      Advanced Topics in Mathematical Biology

MATH427      Waves, Mathematical Modelling

MATH431      Introduction to Modern Particle Theory

MATH433      Asymptotic Methods for Differential Equations

#### Year Four Compulsory Modules

• ##### Advanced Quantum Physics (PHYS480)
Level M 15 First Semester 100:0 To build on Y3 module on Quantum Mechanics and Atomic Physics with the intention of providing breadth and depth in the understanding of the commonly used aspects of Quantum mechanics. To develop an understanding of the ideas of perturbation theory for complex quantum systems and of Fermi''s Golden Rule. To develop an understanding of the techniques used to describe the scattering of particles. To demonstrate creation and annihilation operators using the harmonic oscillator as an example. To develop skills which enable numerical calculation of real physical quantum problem. To encourage enquiry into the philosophy of quantum theory including its explanation of classical mechanics. At the end of the module the student should have: Understanding of variational techniques. Understanding of perturbation techniques. Understanding of transition and other matrix elements. Understanding of phase space factors. Understanding of partial wave techniques. Understanding of basic cross section calculations​ ​Understanding of examples of state-of-the art quantum physics experiments.​ ​Understanding of the implications of quantum physics in our daily lifes.
• ##### Mathematical Physics Project (MATH420)
Level M 30 Whole Session 0:100 To investigate and report on a topic at the boundary of current knowledge in theoretical physics. After completing the essay with suitable guidance, the student should have ·         understood an area of current research in theoretical physics ·         had experience in locating and consulting relevant research material, particularly through use of journals and the Internet ·         learnt and deployed appropriate mathematical techniques ·         learnt how to produce a dissertation ·         acquired and practised skills of oral presentation

#### Year Four Optional Modules

• ##### Cartesian Tensors and Mathematical Models of Solids and VIscous Fluids (MATH324)
Level 3 15 First Semester 100:0 To provide an introduction to the mathematical theory of viscous fluid flows and solid elastic materials. Cartesian tensors are first introduced. This is followed by modelling of the mechanics of continuous media. The module includes particular examples of the flow of a viscous fluid as well as a variety of problems of linear elasticity. ​ To understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations.​To apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.​
• ##### Population Dynamics (MATH332)
Level 3 15 Second Semester 100:0 - To provide a theoretical basis for the understanding of population ecology - To explore the classical models of population dynamics - To learn basic techniques of qualitative analysis of mathematical models ​The ability to relate the predictions of the mathematical models to experimental results obtained in the field.The ability to recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems.The ability to use analytical and graphical methods to investigate population growth and the stability of equilibrium states for continuous-time and discrete-time models of ecological systems.​
• ##### Advanced Condensed Matter Physics (PHYS363)
Level 3 7.5 Second Semester 100:0 To develop concepts introduced in Year 1 and Year 2 modules which relate to solids. To consolidate concepts related to crystal structure. To introduce the concept of reciprocal space and diffraction. To enable the students to apply these concepts to the description of crystals,transport properties and the electronic structure of condensed matter. To illustrate the use of these concepts in scientific research in condensed matter. To introduce various other solids Familiarity with the crystalline nature of both perfect and real materials. ​An understanding of the fundamental principles of the properties of condensed matter​An appreciation of the relationship between the real space and the reciprocal space view of the properties of crystalline matter​An ability to describe the crystal structure and electronic structure of matter​An awareness of current physics research in condensed matter.
• ##### Nuclear Physics (PHYS375)
Level 3 7.5 First Semester 100:0 To build on the second year module involving Nuclear Physics To develop an understanding of the modern view of nuclei, how they are modelled and of nuclear decay processes At the end of the module the student should have: Knowledge of evidence for the shell model of nuclei, its development and the successes and failures of the model in explaining nuclear properties ​Knowledge of the collective vibrational and rotational models of nuclei ​Basic knowledge of nuclear decay processes, alpha decay and fission, of gamma-ray transitions and internal conversion ​Knowledge of electromagnetic transitions in nuclei
• ##### Practical Physics III (PHYS306)
Level 3 15 First Semester 0:100 ​The Aims of the module are: To give further training in laboratory techniques, in the use of computer packages for modelling and analysis, and in the use of modern instruments.To develop independent judgement in performing physics experiments.To encourage students to research aspects of physics complementary to material met in lectures and tutorials.To consolidate the students ability to produce good quality work against realistic deadlines ​Experience of taking physics data with modern equipment​Knowledge of experimental techniques not met in previous laboratory practice​Improved skills in researching published papers and articles as source materials​Developed a personal responsibility for assuring that data taken are of a high quality​Increased skills in data taking and error analysis​Increased skills in reporting experiments and an appreciation of the factors needed to produce clear and complete reports​Improved skills in the time management and organisation of their experimental procedures to meet deadlines
• ##### Materials Physics (PHYS387)
Level 3 7.5 First Semester 100:0 To teach the properties and methods of preparation of a range of materials of scientific and technological importance To develop an understanding of the experimental techniques of materials characterisation To introduce materials such as amorphous solids, liquid crystals and polymers and to develop an understanding of the relationship between structure and physical properties for such materials To illustrate the concepts and principles by reference to examples At the end of the module the student should have: An understanding of the atomic structure in cyrstalline and amorphous materials Knowledge of the methods used for preparing single crystals and amorphous materials Knowledge of the experimental techniques used in materials characterisation Knowledge of the physical properties of superconducting materials An appreciation of the factors involved in the design of biomaterials The ability to interpret simple phase diagrams of binary systems
• ##### Semiconductor Applications (PHYS389)
Level 3 7.5 First Semester 100:0 To develop the physics concepts describing semiconductors in sufficient details for the purpose of understanding the construction and operation of common semiconductor devices At the end of the module the student should have: Knowledge of the basic theory of p-n junctions Knowledge of the structure and function of a variety of semiconductor devices An overview of semiconductor device manufacturing processes Knowledge of the basic processes involved in the interaction of radiation with matter Understanding the application of semiconductors in Nuclear and Particle physics
• ##### Communicating Science (PHYS391)
Level 3 7.5 First Semester 0:100 To improve science students'' skills in communicating scientific information in a wide range of contexts To develop students'' understanding of some concepts of: Science in general Their particular area of science Other areas of science ​ An ability to communicate more confidently​​ An understanding of some of the key factors in successfulcommunication​An appreciation of the needs of different audiences​​Experience of a variety of written and oral media​​A broader appreciation of science and particular areas ofscience​
• ##### Statistics for Physics Analysis (PHYS392)
Level 3 15 First Semester 50:50 To give a theoretical and practical understanding of the statistical principles involved in the analysis and interpretation of data.To give practice in analysing data by computer program.To show how to write code to solve problems in data analysis. Knowledge of experimental errors and probability distributions​The ability to use statistical methods in data analysis​The ability to apply statistical analysis to data from a range of sourcesUsing statistical information to detemine the validity of a hypothesis or experimental measurement​​The ability to write code to analyse data sets
• ##### Statistical and Low Temperature Physics (PHYS393)
Level 3 15 First Semester 100:0 To build on material presented in earlier Thermal Physics and Quantum Mechanics courses To develop the statistical treatment of quantum systems To use theoretical techniques to predict experimental observables To introduce the basic principles governing the behaviour of liquid helium and superconductors in cooling techniques Understanding of the statistical basis of entropy and temperature ​Ability to devise expressions for observables, (heat capacity, magnetisation) from statistical treatment of quantum systems ​Understanding of Maxwell Boltzmann, Fermi-Dirac and Bose Einstein gases ​Knowledge of cooling techniques ​Knowledge and understanding of basic theories of liquid helium behaviour and superconductivity in cooling techniques
• ##### Mathematical Economics (MATH331)
Level 3 15 Second Semester 100:0 ·      To explore, from a game-theoretic point of view, models which have been used to understand phenomena in which conflict and cooperation occur. ·      To see the relevance of the theory not only to parlour games but also to situations involving human relationships, economic bargaining (between trade union and employer, etc), threats, formation of coalitions, war, etc.. ·      To treat fully a number of specific games including the famous examples of "The Prisoners'' Dilemma" and "The Battle of the Sexes". ·      To treat in detail two-person zero-sum and non-zero-sum games. ·      To give a brief review of n-person games. ·      In microeconomics, to look at exchanges in the absence of money, i.e. bartering, in which two individuals or two groups are involved.   To see how the Prisoner''s Dilemma arises in the context of public goods. After completing the module students should: ·      Have further extended their appreciation of the role of mathematics in modelling in Economics and the Social Sciences. ·      Be able to formulate, in game-theoretic terms, situations of conflict and cooperation. ·      Be able to solve mathematically a variety of standard problems in the theory of games. ·      To understand the relevance of such solutions in real situations.
• ##### Chaos and Dynamical Systems (MATH322)
Level 3 15 First Semester 100:0 To develop expertise in dynamical systems in general and study particular systems in detail. After completing the module students will be able to understand the possible behaviour of dynamical systems with particular attention to chaotic motion; After completing the module students will ​be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points;​After completing the module students will understand how fractal sets arise and how to characterise them.
• ##### Riemann Surfaces (MATH340)
Level 3 15 Second Semester 100:0 To introduce to a beautiful theory at the core of modern mathematics. Students will learn how to handle some abstract geometric notions from an elementary point of view that relies on the theory of holomorphic functions. This will provide those who aim to continue their studies in mathematics with an invaluable source of examples, and those who plan to leave the subject with the example of a modern axiomatic mathematical theory. Students should be familiar with themost basic examples of Riemann surfaces: the Riemann sphere, hyperelliptic Riemann surfaces, and smooth plane algebraic curves.Students should understand and be able to use the abstract notions used to build the theory: holomorphic maps, meromorphic differentials, residues and integrals, Euler characteristic and genus.
• ##### The Magic of Complex Numbers: Complex Dynamics, Chaos and the Mandelbrot Set (MATH345)
Level 3 15 Second Semester 90:10 1. To introduce students to the theory of the iteration of functions of one complex variable, and its fundamental objects;2. To introduce students to some topics of current and recent research in the field;3. To study various advanced results from complex analysis, and show how to apply these in a dynamical setting;4. To illustrate that many results in complex analysis are "magic", in that there is no reason to expect them in a real-variable context, and the implications of this in complex dynamics;5. To explain how complex-variable methods have been instrumental in questions purely about real-valued one-dimensional dynamical systems, such as the logistic family.6. To deepen students'' understanding of formal reasoning and proof.​ To ​understand the compactification of the complex plane to the Riemann sphere, and be able to use spherical distances and derivatives.​To be able to use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems.​To be able to state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties.To be able to ​determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set.To know how to ​apply advanced results from complex analysis in a dynamical setting.To be able to ​determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not.
• ##### Differential Geometry (MATH349)
Level 3 15 Second Semester 85:15 This module is designed to provide an introduction to the methods of differential geometry, applied in concrete situations to the study of curves and surfaces in euclidean 3-space.  While forming a self-contained whole, it will also provide a basis for further study of differential geometry, including Riemannian geometry and applications to science and engineering.​ ​​​1a. Knowledge and understanding: Students will have a reasonable understanding of invariants used to describe the shape of explicitly given curves and surfaces. ​1b. Knowledge and understanding: Students will have a reasonable understanding of special curves on surfaces.​1c. Knowledge and understanding: Students will have a reasonable understanding of the difference between extrinsically defined properties and those which depend only on the surface metric.​1d. Knowledge and understanding: Students will have a reasonable understanding of the passage from local to global properties exemplified by the Gauss-Bonnet Theorem.​2a. Intellectual abilities: Students will be able to use differential calculus to discover geometric properties of explicitly given curves and surfaces.​2b. Intellectual abilities: Students will be able to understand the role played by special curves on surfaces.​3a. Subject-based practical skills: Students will learn to compute invariants of curves and surfaces.​3b. Subject-based practical skills: Students will learn to interpret the invariants of curves and surfaces as indicators of their geometrical properties.​​4a. General transferable skills: Students will improve their ability to think logically about abstract concepts,​4b. General transferable skills: Students will improve their ability to combine theory with examples in a meaningful way.​​
Level 3 15 Second Semester 100:0 To build on first and second year modules on electricity, magnetism and waves by understanding a range of electromagnetic phenomena in terms of Maxwell''s equations. To understand the properties of solutions to the wave equation for electromagnetic fields in free space, in matter (non-dispersive and dispersive dielectrics, and conductors). To understand the behaviour of electromagnetic waves at boundaries.To understand the behaviour of electromagnetic waves in cavities, waveguides and transmission lines. To understand the properties of electric dipole radiation. To introduce an explicity covariant formulation of electromagnetism in special relativity. To further develop students'' problem-solving and analytic skills. ​Students should have an understanding of the properties of solutions to the wave equation for electromagnetic fields in free space and in matter (non-dispersive and dispersive dielectrics, and conductors).​Students should have an understanding of the behaviour of electromagnetic waves at boundaries.​Students should have an understanding of the behaviour of electromagnetic waves in cavities, waveguides and transmission lines.​Students should have an understanding of the properties of electric dipole radiation.​Students should have the ability to explain an explicity covariant formulation of electromagnetism in special relativity.
• ##### Relativity and Cosmology (PHYS374)
Level 3 15 Second Semester 80:20 To introduce the ideas of general relativity and demonstrate its relevance to modern astrophysics To provide students with a full and rounded introduction to modern observational cosmology To develop the basic theoretical background required to understand and appreciate the significance of recent results from facilities such as the Hubble Space Telescope and the Wilkinson Microwave Anisotropy Probe ​The ability to explain the relationship between Newtonian gravity and Einstein''s General Relativity (GR) ​Understanding of the concept of curved space time and knowledge of metrics​.​ A broad and up-to-date knowledge of the basic ideas, most important discoveries and outstanding problems in modern cosmology​.​Knowledge of how simple cosmological models of the universe are constructed​.The ability to calculate physical parameters and make observational predictions for a range of such models.
• ##### Introduction to Particle Physics (PHYS377)
Level 3 7.5 Second Semester 100:0 To build on the second year module involving Nuclear and Particle Physics To develop an understanding of the modern view of particles, of their interactions and the Standard Model At the end of the module the student should have: Basic understanding of relativistic kinematics (as applied to collisions, decay processes and cross sections) ​Descriptive knowledge of the Standard Model using a non rigorous Feynman diagram approach​Knowledge of the fundamental particles of the Standard Model and the experimental evidence for the Standard Model ​Knowledge of conservation laws and discrete symmetries
• ##### Surface Physics (PHYS381)
Level 3 7.5 Second Semester 100:0 Develop a syllabus to describe the properties of surfacesConvey an understanding of the physical properties of SurfacesProvide knowledge  of a raneg of surface characterisation techniquesIllustrate surface processes and their relevance to technologies explain how the presence of the surface alters physical properties such as atomic an electronic structure​ choose the right characterisation technique to assess different surface properties have gained an  appreciation of surface processes and their relevance to the modification of surface properties​be able to describe surface alterations and processes using the right terminology
• ##### Physics of Life (PHYS382)
Level 3 7.5 Second Semester 100:0 To introduce students to the physical principles needed to address important problems such as climate change, the loss of biodiversity, the understanding of ecological systems, the growth of resistance to antibiotics, the challenge of sustainable development and the study of disease. These problems offer excellent opportunities for rewarding careers.​ ​ ​An understanding of the conditions necessary for life to evolve in a universe.​​An understanding of the thermodynamics and organization of living things.​​​​​Familiarity with physical techniques used in the study of biological systems. ​
• ##### Physics of Energy Sources (PHYS388)
Level 3 15 Second Semester 100:0 To develop an ability which allows educated and well informed opinions to be formed by the next generation of physicists on a wide range of issues in the context of the future energy needs of man To describe and understand methods of utilising renewable energy sources such as hydropower, tidal power, wave power, wind power and solar power. To give knowledge and understanding of the design and operation of nuclear reactors To give knowledge and understanding of nuclear fusion as a source of power To give knowledge and understanding relevant to overall safety in the nuclear power industry To describe the origin of environmental radioactivity and understand the effects of radiation on humans At the end of the module the student should have: Learned the fundamental physical principles underlying energy production using conventional and renewable energy sources Learned the fundamental physical principles underlying nuclear fission and fusion reactors Studied the applications of these principles in the design issues power generation An appreciation of the role of mathematics in modelling power generation Learned the fundamental physical principles concerning the origin and consequences of environmental radioactivity Developed an awareness of the safety issues involved in exposure to radiation Developed problem solving skills based on the material presented Developed an appreciation of the problems of supplying the required future energy needs and the scope and issues associated with the different possible methods
Level 3 15 Second Semester 0:100 To provide undergraduates with key transferable skills. To provide students with opportunity to learn to communicate physics at different levels. To provide students with work-place experience. To provide students with the opportunity to work with staff in a different environment with different priorities to the University. To provide teaching experience that encourages undergraduates to consider a career in teaching. To supply role models for secondary school students. To provide support and teaching assistance to secondary school teachers. To encourage a new generation of physicists. Communicate physicseffectively to others​​Plan a lessonDesign a worksheet​​Evaluate their planning​Assess the effectiveness of a session or worksheet that they have designed​Manage small groups ofpupils (e.g. to complete an experiment)​​Prioritise their work​
• ##### Technology Transfer and Commercialisation (PHYS397)
Level 3 7.5 Second Semester 0:100 ​This module aims to To  be able to develop skills in assessing thecommercial routes available to introduce a product or service into the market. To be adept in market information gathering andanalysis.To develop presentation and communicationskills and reporting skills beyond the classic essay format. To distinguish clearly between thedifferent business models available and to contrast merits and drawbacks ofeach solution. ​All students will be able to gather and analyse business data information​All students will be able to understand technology transfer dynamicsstudents will be able to communicate their ideas and work in a clear and concise manner​Students will be able to present data and project proposals in a professional manner, easily recognised by industry and companies.
• ##### Linear Differential Operators in Mathematical Physics (MATH421)
Level M 15 First Semester 90:10 This module provides a comprehensive introduction to the theory of partial differential equations, and it provides illustrative applications and practical examples in the theory of elliptic boundary value problems, wave propagation and diffusion problems. To understand and actively use the basic concepts of mathematical physics, such as generalised functions, fundamental solutions and Green''s functions.​ ​To apply powerful mathematical methods to problems of electromagnetism, elasticity, heat conduction and wave propagation.​
• ##### Quantum Field Theory (MATH425)
Level M 15 First Semester 100:0 To provide a broad understanding of the essentials of quantum field theory. After the course the students should understand the important features of the mathematical tools necessary for particle physics. In particular they should ·      be able to compute simple Feynman diagrams, ·      understand the basic principles of regularisation and renormalisation ·      be able to calculate elementary scattering cross-sections.
• ##### Variational Calculus and Its Applications (MATH430)
Level M 15 First Semester 90:10 ​This module provides a comprehensive introduction to the theory of the calculus of variations, providing illuminating applications and examples along the way. ​Students will posses a solid understanding of the fundamentals of variational calculus​​Students will be confident in their ability to apply the calculus of variations to range of physical problems​Students will also have the ability to solve a wide class of non-physical problems using variational methods​Students will develop an understanding of Hamiltonian formalism and have the ability to apply this framework to solve physical and non-physical problems​Students will be confident in their ability to analyse variational symmetries and generate the associated conservation laws
• ##### Classical Mechanics (PHYS470)
Level M 15 First Semester 100:0 ​To provide students with an awareness of the physical principles that can be applied to understand important features of classical (i.e. non-quantum) mechanical systems.To provide students with techniques that can be applied to derive and solve the equations of motion for various types of classical mechanical systems, including systems of particles and fields.To develop students'' understanding of the fundamental relationship between symmetries and conserved quantities in physics.To reinforce students’ knowledge of quantum mechanics, by developing and exploring the application of closely-related concepts in classical mechanics. ​Students should know the physical principles underlying the Lagrangian and Hamiltonian formulations of classical mechanics, in particular D’Alembert’s principle and Hamilton’s principle, and should be able to explain the significance of these advanced principles in classical and modern physics.​Students should be able to apply the Euler-Lagrange equations and Hamilton’s equations (as appropriate) to derive the equations of motion for specific dynamical systems, including complex nonlinear systems.Students should be able to use advanced concepts in classical mechanics to describe the connection between symmetries and conservation laws.​Students should be able to apply advanced techniques, including conservation laws, canonical transformations, generating functions, perturbation theory etc. to describe important features of various dynamical systems (including systems of particles and fields) and to solve the equations of motion in specific cases.
• ##### Accelerator Physics (PHYS481)
Level M 7.5 First Semester 70:30 To build on modules on electricity, magnetism and waves; To study the functional principle of different types of particle accelerators; To study the generation of ion and electron beams; To study the layout and the design of simple ion and electron optics; To study basic concepts in radio frequency engineering and technology. At the end of the module the student should have: An understanding of the description of the motion of charged particles in complex electromagnetic fields; An understanding of different types of accelerators, in which energy range and for which purposes they are utilised; An understanding of the generation and technical exploitation of synchrotron radiation; An understanding of the concept and the necessity of beam cooling.
• ##### Research Skils (PHYS491)
Level M 7.5 First Semester 0:100 This module will help students develop the ability to:Perform literature searches.Plan research projects.Explain research projects to both expert and non-expert audiences.Organise a team of people and work as a group.Assess the broader impact of research projects.Present a proposal as a written document ans orally. Experience in carrying out search of scientific literature.  Communicating research to non-expert audience.​Evaluating the possible broader impact of research.Writing a scientific case for an assessment panel.​  First experience with some project management tools.
• ##### Nanoscale Physics and Technology (PHYS499)
Level M 15 Second Semester 70:30 Tointroduce the emerging fields of nanoscale physics and nanotechnology To describe experimental techniques for probing physical properties of nanostructured materials ​Todescribe the novel size-dependent electronic, optical, magnetic and chemicalproperties of nanoscale materials​Todescribe several ‘hot topics'' in nanoscience research​Todevelop students'' problem-solving, investigative, communication and analyticskills through appropriate assignments for tutorials and a literature project. ​ After the module the students should have the ability to explain how and why nanoscalesystems form.After the module the students should have the ability to describe how nanoscale systems may be probed experimentally and compare different techniques in terms of strengths and weaknesses.After the module the students should have the ability to explain and apply the fundamental principles that govern nanoscale systems.​​After the module the students should have the ability to describe potential applications and to discuss their wider applications.​After the module the students should have enhanced problem-solving, investigative, communication, and analytic skills.
• ##### Magnetic Structure and Function (PHYS497)
Level M 7.5 First Semester 100:0 To build on the third year module Condensed Matter Physics To develop an understanding of the phenomena and fundamental mechanisms of magnetism in condensed matter ​ Have a basic understanding of the quantum origin of magnetism and magnetic moments.​Understand the concept of magnetic order and the role of exchange interactions.​Be able to identify the properties associated with various types of magnetism.​Be able to explain the cause of magnetic phenomena such as hysteresis and domain formation.​
• ##### Introduction to String Theory (MATH423)
Level M 15 Second Semester 100:0 To provide a broad understanding of string theory, and its utilization as a theory that unifies all of the known fundamental matter and interactions. After completing the module the students should: - be familiar with the properties of the classical string.​be familiar with the basic structure of modern particle physics and how it may arise from string theory.​ be familiar with the basic properties of first quantized string and the implications for space-time dimensions.  ​be familiar with string toroidal compactifications and T-duality.
• ##### Analytical & Computational Methods for Applied Mathematics (MATH424)
Level M 15 Second Semester 100:0 To provide an introduction to a range of analytical and numerical methods for partial differential equations arising in many areas of applied mathematics.   To provide a focus on advanced analytical techniques for solution of both elliptic and parabolic partial differential equations, and then on numerical discretisation methods of finite differences and finite elements.  To provide the algorithms for solving the linear equations arising from the above discretisation techniques. Apply a range of standard numerical methods for solution of PDEs and should have an understanding of relevant practical issues. ​Obtain solutions to certain important PDEs using a variety of analytical techniques and should be familiar with important properties of the solution. ​Understand and be able to apply standard approaches for the numerical solution of linear equations   ​Have a basic understanding of the variation approach to inverse problems.
• ##### Advanced Topics in Mathematical Biology (MATH426)
Level M 15 Second Semester 100:0 To introduce some hot problems of contemporary mathematical biology, including analysis of developmental processes, networks and biological mechanics. ​To further develop mathematical skills in the areas of difference equations and ordinary and partial differential equations. ​To explore biological applications of fluid dynamics in the limit of lowand high Reynolds number. To familiarise with mathematical modelling methodology used in contemporary mathematical biology.​Be able to use techniques from difference equations and ordinary and partial differential equations in tackling problems in biology.
• ##### Waves, Mathematical Modelling (MATH427)
Level M 15 Second Semester 100:0 This module gives an introduction to the mathematical theory of linear and non-linear waves. Illustrative applications involve problems of acoustics, gas dynamics and examples of solitary waves. To understand essential modelling techniques in problems of wave propagation.   To understand that mathematical models of the same type can be successfully used to describe different physical phenomena.To understand background mathematical theory in models of acoustics, gas dynamics and water  waves.​
• ##### Introduction to Modern Particle Theory (MATH431)
Level M 15 Second Semester 100:0 To provide a broad understanding of the current status of elementary particle theory. To describe the structure of the Standard Model of particle physics and its embedding in Grand Unified Theories. To understand the Lorentz and Poincare groups and their role in classification of elementary particles.​To understand the basics of Langrangian and Hamiltonian dynamics and the differential equations of bosonic and fermionic wave functions.​To understand the basic elements of field quantisation. ​ ​To understand the Feynman diagram pictorial representation of particle interactions.​To understand the role of symmetries and conservation laws in distinguishing the strong, weak and electromagnetic interactions.​To be able to describe the spectrum and interactions of elementary particles and their embedding into Grand Unified Theories (GUTs)To understand the flavour structure of the standard particle model and generation of mass through symmetry breaking​.​To understand the phenomenological aspects of Grand Unified Theories.
• ##### Asymptotic Methods for Differential Equations (MATH433)
Level M 15 Second Semester 100:0 This module provides an introduction into the perturbation theory for  partial differential equations. We consider singularly and regularly perturbed problems and applications in electro-magnetism, elasticity, heat conduction and propagation of waves. The ability to make appropriate use of asymptotic approximations.​The ability to analyse boundary layer effects.​The ability to use the method of compound asymptotic expansions in the analysis of singularly perturbed problems.
• ##### Advanced Nuclear Physics (PHYS490)
Level M 15 Second Semester 100:0 To build on the year 3 modules on Nuclear Physics To offer an insight into current ideas about the description of atomic nuclei and nuclear matter Knowledge of the basic properties of nuclear forces and the experimental evidence upon which these are based  Knowledge of the factors governing nuclear shapes​Understanding of the origin of pairing forces and the effect of these and rotational forces on nuclear behaviour ​An overview of phenomena observed for exotic nuclei far from the line of nuclear stability​Knowledge of astrophysical nucleosynthesis processes ​Knowledge of phases of nuclear matter
• ##### Advanced Particle Physics (PHYS493)
Level M 15 Second Semester 100:0 To build on the Year 3 module PHYS377 Particle Physics To give the student a deeper understanding of the Standard Model of Particle Physics and the basic extensions To review the detectors and accelerator technology available to investigate the questions posed by the Standard Model and its extensions An understanding of the Standard Model and its extensions. This will be placed in context of the understanding of the origin of the universe, its properties and its physical laws​An understanding of how present and future detector and accelerator technology will be applied to investigate the development of the Standard Model ​An understanding of the effects of symmetries on particle properties​Ablity to caclulate decay rates for particles

The programme detail and modules listed are illustrative only and subject to change.

#### Teaching and Learning

Your learning activities will consist of lectures, tutorials, practical classes, problem classes, private study and supervised project work. In Year One, lectures are supplemented by a thorough system of group tutorials and computing work is carried out in supervised practical classes. Key study skills, presentation skills and group work start in first-year tutorials and are developed later in the programme. The emphasis in most modules is on the development of problem solving skills, which are regarded very highly by employers. Project supervision is on a one-to-one basis, apart from group projects in Year Two.

#### Assessment

Most modules are assessed by a two and a half hour examination in January or May, but many have an element of coursework assessment. This might be through homework, class tests, mini-project work or key skills exercises.