Theoretical Physics MPhys
 Course length: 4 years
 UCAS code: F344
 Year of entry: 2019
 Typical offer: Alevel : AAB / IB : 35 / BTEC : Applications considered
Honours Select
×This programme offers Honours Select combinations.
Honours Select 100
×This programme is available through Honours Select as a Single Honours (100%).
Honours Select 75
×This programme is available through Honours Select as a Major (75%).
Honours Select 50
×This programme is available through Honours Select as a Joint Honours (50%).
Honours Select 25
×This programme is available through Honours Select as a Minor (25%).
Study abroad
×This programme offers study abroad opportunities.
Year in China
×This programme offers the opportunity to spend a Year in China.
Accredited
×This programme is accredited.
Module details
Year One Compulsory Modules
Calculus I (MATH101)
Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims 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.
Learning Outcomes 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
Introduction to Linear Algebra (MATH103)
Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims  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.
Learning Outcomes 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
Thermal Physics (PHYS102)
Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 60:40 Aims 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
Learning Outcomes 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 changesRelate 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 variablesBe able to demonstrate the equivalence of the Clausius and KelvinPlanck statements of the second law of thermodynamics.
Be able to derive and use Maxwell''s equations
Introduction to Computational Physics (PHYS105)
Level 1 Credit level 7.5 Semester First Semester Exam:Coursework weighting 0:100 Aims  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 data
 To introduce elemenatry Monte Carlo techniques
 To introduce basic computer algebra
 To illustrate the insight into physics which can be obtained using computational methods
Learning Outcomes Ability to produce algorithms to solve simple physical problems.
Ability to program and use simple algorithms on a computer
Ability to analyse and present physical data
Ability to produce simple Monte Carlo models
Ability to carry out basic symbolic manipulations using a computer
Calculus II (MATH102)
Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims · To discuss local behaviour of functions using Taylor’s theorem.
· To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.
Learning Outcomes 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 Coordinates
Newtonian Mechanics (MATH122)
Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims 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 inertiaLearning Outcomes
After completing the module students should be able to analyse
realworld 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
Wave Phenomena (PHYS103)
Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 60:40 Aims  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.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 60:40 Aims  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.
Learning Outcomes 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 energymomentum conservation for light, e.g. photoelectric 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 Hatom 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, Xrays 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 (FermiDirac and BoseEinstein) 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.
Practical Skills for Mathematical Physics (PHYS156)
Level 1 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 0:100 Aims  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 Alevel
 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
Learning Outcomes 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
In the second and subsequent years of all programmes, there is a wide range of modules. For the programme that you choose there may be no compulsory modules (although you may have to choose a few from a subset such as Pure Mathematics). If you make a different choice, you will find that one or more modules have to be taken. Each year you will choose the equivalent of eight modules. Please note that we regularly review our teaching so the choice of modules may change.
Year Two Compulsory Modules
Vector Calculus With Applications in Fluid Mechanics (MATH225)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 85:15 Aims 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.
Learning Outcomes 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 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims 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.
Learning Outcomes After completing this module students should:
 appreciate the central role of complex numbers in mathematics;
 be familiar with all the classical holomorphic functions;
 be able to compute Taylor and Laurent series of such functions;
 understand the content and relevance of the various Cauchy formulae and theorems;
 be familiar with the reduction of real definite integrals to contour integrals;
 be competent at computing contour integrals.
Electromagnetism (PHYS201)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 70:30 Aims  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.
Learning Outcomes 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 nonstatic electric and magnetic fields and the ability to solve simple problems in these situations.
Condensed Matter Physics (PHYS202)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 70:30 Aims 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 nanomaterials. 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.
Learning Outcomes 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 semiconductorsStudents 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.
Introduction to the Methods of Applied Mathematics (MATH224)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims 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.
Learning Outcomes 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.
Classical Mechanics (MATH228)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims To provide an understanding of the principles of Classical Mechanics and their application to dynamical systems.
Learning Outcomes Understanding of variational principles, Lagrangian mechanics, Hamiltonian mechanics.
Newtonian gravity and Kepler''s laws, including calculations of the orbits of satellites, comets and planetary motions
Motion relative to a rotating frame, Coriolis and centripetal forces, motion under gravity over the Earth''s surface
Connection between symmetry and conservation laws
Inertial and noninertial frames.
Quantum and Atomic Physics (PHYS203)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 70:30 Aims  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, multielectron atoms) and particle flux (scattering).
 To show how quantum ideas provide an understanding of atomic structure.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 70:30 Aims  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 4vectors for applications to collision problems
Learning Outcomes 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 interactionsbasic understanding of relativistic 4vectors
Programme Year Three
Choose three modules from:
 Quantum Mechanics (MATH325) OR PHYS361 Quantum Mechanics & Atomic Physics
 Relativity (MATH326)
 Mathematical Physics Project (MATH432) or Modelling Physical Phenomena (Project) (PHYS488)
Choose at least three modules from:
 Further Methods of Applied Mathematics (MATH323)
 Cartesian Tensors and Mathematical Models of Solids and Viscous Fluids (MATH324)
 Population Dynamics (MATH332)
 Condensed Matter Physics (PHYS363)
 Nuclear Physics (PHYS375)
 Practical Physics III (PHYS306)
 Materials Physics (PHYS387)
 Semiconductor Applications (PHYS389)
 Communicating Science (PHYS391)
 Statistics in Data Analysis (PHYS392)
 Statistical and Low Temperature Physics (PHYS393)
 Mathematical Economics (MATH331)
 Chaos and Dynamical Systems (MATH322)
 Riemann Surfaces (MATH340)
 The Magic of Complex Numbers: Complex Dynamics, Chaos and the Madelbrot Set (MATH345)
 Differential Geometry (MATH349)
 Advanced Electromagnetism (PHYS370)
 Relativity and Cosmology (PHYS374)
 Introduction to Particle Physics (PHYS377)
 Surface Physics (PHYS381)
 Physics of Life (PHYS382)
 Physics of Energy Sources (PHYS388)
 Undergraduate Ambassadors Project (PHYS 396)
 Technology Transfer and Commercialisation (PHYS 397)
Choose at least two from;
 Linear Differential Operators in Mathematical Physics (MATH421)
 Quantum Field Theory (only in Year 4) (MATH425)
 Variational Calculus and its Applications (MATH430)
 Classical Mechanics (PHYS470)
 Accelerator Physics (PHYS481)
 Research Skills (PHYS491)
 Nanoscale Physics and Technology (PHYS499)
 Magnetic Structure and Function (PHYS497)
 Introduction to String Theory (MATH423)
 Analytical and Computational Methods for Applied Mathematics (MATH424)
 Advanced Topics in Mathematical Biology (MATH426)
 Waves, Mathematical Modelling (MATH427)
 Introduction to Modern Particle Theory (MATH431)
 Asymptotic Methods for Differential Equations (MATH433)
 Advanced Nuclear Physics (PHYS490)
Advanced Particle Physics (PHYS493)
Year Three Optional Modules
Statistical and Low Temperature Physics (PHYS393)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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, FermiDirac 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims · To explore, from a gametheoretic 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 twoperson zerosum and nonzerosum games.
· To give a brief review of nperson 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.
Learning Outcomes 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 gametheoretic 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 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims To develop expertise in dynamical systems in general and study particular systems in detail.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims 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.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims 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 realvariable context, and the implications of this in complex dynamics;
5. To explain how complexvariable methods have been instrumental in questions purely about realvalued onedimensional dynamical systems, such as the logistic family.
6. To deepen students'' appreciations for formal reasoning and proof.
After completing the module, students should be able to:
1. understand the compactification of the complex plane to the Riemann sphere, and use spherical distances and derivatives.2. use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems.
3. state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties.
4. determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set.
5. apply advanced results from complex analysis in the setting of complex dynamics.
6. determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not.Learning Outcomes will understand the compactification of the complex plane to the Riemann sphere, and be able to use spherical distances and derivatives
will be able to use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems
will be able to state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties
will be able to determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set
will know how to apply advanced results from complex analysis in a dynamical setting
will be able to determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not
Differential Geometry (MATH349)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 85:15 Aims 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 3space. While forming a selfcontained whole, it will also provide a basis for further study of differential geometry, including Riemannian geometry and applications to science and engineering.
Learning Outcomes 1. Knowledge and understanding
After the module, students should have a basic understanding of
a) invariants used to describe the shape of explicitly given curves and surfaces,
b) special curves on surfaces,
c) the difference between extrinsically defined properties and those which depend only on the surface metric,
d) understanding the passage from local to global properties exemplified by the GaussBonnet Theorem.
2. Intellectual abilities
After the module, students should be able to
a) use differential calculus to discover geometric properties of explicitly given curves and surface,
b) understand the role played by special curves on surfaces.
3. Subjectbased practical skills
Students should learn to
a) compute invariants of curves and surfaces,
b) interpret the invariants of curves and surfaces as indicators of their geometrical properties.
4. General transferable skills
Students will improve their ability to
a) think logically about abstract concepts,
b) combine theory with examples in a meaningful way.
Advanced Electromagnetism (PHYS370)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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 (nondispersive 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'' problemsolving and analytic skills.
Learning Outcomes Students should have an understanding of the properties of solutions to the wave equation for electromagnetic fields in free space and in matter (nondispersive 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims  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
Learning Outcomes 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 uptodate 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 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 100:0 Aims  Develop a syllabus to describe the properties of surfaces
 Convey an understanding of the physical properties of Surfaces
 Provide knowledge of a raneg of surface characterisation techniques
 Illustrate surface processes and their relevance to technologies
Learning Outcomes 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 propertiesbe able to describe surface alterations and processes using the right terminology
Physics of Life (PHYS382)
Level 3 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 100:0 Aims 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.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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
Undergraduate Ambassadors Project (PHYS396)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 0:100 Aims  To provide undergraduates with key transferable skills.
 To provide students with opportunity to learn to communicate physics at different levels.
 To provide students with workplace 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.
Learning Outcomes Communicate physicseffectively to others
Plan a lesson
Design 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 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 0:100 Aims 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.
Learning Outcomes All students will be able to gather and analyse business data information
All students will be able to understand technology transfer dynamics
students will be able to communicate their ideas and work in a clear and concise mannerStudents 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 Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 Aims 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.
Learning Outcomes This module will enable students to understand and actively use the basic concepts of mathematical physics, such as generalised functions, fundamental solutions and Green''s functions, and apply powerful mathematical methods to problems of electromagnetism, elasticity, heat conduction and wave propagation.
Quantum Field Theory (MATH425)
Level M Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims To provide a broad understanding of the essentials of quantum field theory.
Learning Outcomes 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 crosssections.
Variational Calculus and Its Applications (MATH430)
Level M Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 Aims This module provides a comprehensive introduction to the theory of the calculus of variations, providing illuminating applications and examples along the way.
Learning Outcomes 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 nonphysical problems using variational methods
Students will develop an understanding of Hamiltonian formalism and have the ability to apply this framework to solve physical and nonphysical problems
Students will be confident in their ability to analyse variational symmetries and generate the associated conservation laws
Classical Mechanics (PHYS470)
Level M Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims  To provide students with an awareness of the physical principles that can be applied to understand important features of classical (i.e. nonquantum) 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 closelyrelated concepts in classical mechanics.
Learning Outcomes 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 EulerLagrange 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 Credit level 7.5 Semester First Semester Exam:Coursework weighting 70:30 Aims  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.
Learning Outcomes 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 Credit level 7.5 Semester First Semester Exam:Coursework weighting 0:100 Aims  Perform literature searches.
 Plan research projects.
 Explain research projects to both expert and nonexpert 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.
Learning Outcomes Experience in carrying out search of scientific literature. Communicating research to nonexpert 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 70:30 Aims  Tointroduce the emerging fields of nanoscale physics and nanotechnology
To describe experimental techniques for probing physical properties of nanostructured materials
Todescribe the novel sizedependent electronic, optical, magnetic and chemicalproperties of nanoscale materials
Todescribe several ‘hot topics'' in nanoscience research
Todevelop students'' problemsolving, investigative, communication and analyticskills through appropriate assignments for tutorials and a literature project.
Learning Outcomes 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 problemsolving, investigative, communication, and analytic skills.
 Tointroduce the emerging fields of nanoscale physics and nanotechnology
Magnetic Structure and Function (PHYS497)
Level M Credit level 7.5 Semester First Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims To provide a broad understanding of string theory, and its utilization as a theory that unifies all of the known fundamental matter and interactions.
Learning Outcomes 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 spacetime dimensions.
be familiar with string toroidal compactifications and Tduality.Analytical & Computational Methods for Applied Mathematics (MATH424)
Level M Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims 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.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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 low
and high Reynolds number.Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims This module gives an introduction to the mathematical theory of linear and nonlinear waves. Illustrative applications involve problems of acoustics, gas dynamics and examples of solitary waves.
Learning Outcomes Students will learn essential modelling techniques in problems of wave propagation. They will also understand that mathematical models of the same type can be successfully used to describe different physical phenomena. Students will also study background mathematical theory in models of acoustics, gas dynamics and water waves.
Introduction to Modern Particle Theory (MATH431)
Level M Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims 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.
Learning Outcomes be familiar with the Lorentz and Poincare groups and their role in classification of elementary particles.

be familiar with the basics of Langrangian and Hamiltonian dynamics and the differential equations of bosonic and fermionic wave functions. 
be familiar with basic elements of field quantisation.

be familiar with the Feynman diagram pictorial representation of particle interactions. appreciate the role of symmetries and conservation laws in distinguishing the strong, weak and electromagnetic interactions. 
be able to describe the spectrum and interactions of elementary particles and their embedding into Grand Unified Theories (GUTs) 
be familiar with the flavour structure of the standard particle model and generation of mass through symmetry breaking
be aware of phenomenological aspects of Grand Unified TheoriesAsymptotic Methods for Differential Equations (MATH433)
Level M Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims This module provides an introduction into the perturbation theory for partial differential equations. We consider singularly and regularly perturbed problems and applications in electromagnetism, elasticity, heat conduction and propagation of waves.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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.
In addition to compuilsory modules, choose at least three modules from:
 Further Methods of Applied Mathematics (MATH323)
 Cartesian Tensors and Mathematical Models of Solids and Viscous Fluids (MATH324)
 Population Dynamics (MATH332)
 Condensed Matter Physics (PHYS363)
 Nuclear Physics (PHYS375)
 Practical Physics III (PHYS306)
 Materials Physics (PHYS387)
 Semiconductor Applications (PHYS389)
 Communicating Science (PHYS391)
 Statistics in Data Analysis (PHYS392)
 Statistical and Low Temperature Physics (PHYS393)
 Mathematical Economics (MATH331)
 Chaos and Dynamical Systems (MATH322)
 Riemann Surfaces (MATH340)
 The Magic of Complex Numbers: Complex Dynamics, Chaos and the Madelbrot Set (MATH345)
 Differential Geometry (MATH349)
 Advanced Electromagnetism (PHYS370)
 Relativity and Cosmology (PHYS374)
 Introduction to Particle Physics (PHYS377)
 Surface Physics (PHYS381)
 Physics of Life (PHYS382)
 Physics of Energy Sources (PHYS388)
 Undergraduate Ambassadors Project (PHYS396)
 Technology Transfer and Commercialisation (PHYS397)
Choose at least two from:
 Linear Differential Operators in Mathematical Physics (MATH421)
 Quantum Field Theory (only in Year 4) (MATH425)
 Variational Calculus and its Applications (MATH430)
 Classical Mechanics (PHYS470)
 Accelerator Physics (PHYS481)
 Research Skills (PHYS491)
 Nanoscale Physics and Technology (PHYS499)
 Magnetic Structure and Function (PHYS497)
 Introduction to String Theory (MATH423)
 Analytical and Computational Methods for Applied Mathematics (MATH424)
 Advanced Topics in Mathematical Biology (MATH426)
 Waves, Mathematical Modelling (MATH427)
 Introduction to Modern Particle Theory (MATH431)
 Asymptotic Methods for Differential Equations (MATH433)
 Advanced Nuclear Physics (PHYS490)
 Advanced Particle Physics (PHYS493)
Year Four Compulsory Modules
Advanced Quantum Physics (PHYS480)
Level M Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims  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.
Learning Outcomes 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 stateofthe art quantum physics experiments.
Understanding of the implications of quantum physics in our daily lifes.
Mathematical Physics Project (MATH420)
Level M Credit level 30 Semester Whole Session Exam:Coursework weighting 0:100 Aims To investigate and report on a topic at the boundary of current knowledge in theoretical physics.
Learning Outcomes 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
Statistical and Low Temperature Physics (PHYS393)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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, FermiDirac 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims · To explore, from a gametheoretic 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 twoperson zerosum and nonzerosum games.
· To give a brief review of nperson 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.
Learning Outcomes 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 gametheoretic 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 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims To develop expertise in dynamical systems in general and study particular systems in detail.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims 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.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims 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 realvariable context, and the implications of this in complex dynamics;
5. To explain how complexvariable methods have been instrumental in questions purely about realvalued onedimensional dynamical systems, such as the logistic family.
6. To deepen students'' appreciations for formal reasoning and proof.
After completing the module, students should be able to:
1. understand the compactification of the complex plane to the Riemann sphere, and use spherical distances and derivatives.2. use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems.
3. state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties.
4. determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set.
5. apply advanced results from complex analysis in the setting of complex dynamics.
6. determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not.Learning Outcomes will understand the compactification of the complex plane to the Riemann sphere, and be able to use spherical distances and derivatives
will be able to use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems
will be able to state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties
will be able to determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set
will know how to apply advanced results from complex analysis in a dynamical setting
will be able to determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not
Differential Geometry (MATH349)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 85:15 Aims 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 3space. While forming a selfcontained whole, it will also provide a basis for further study of differential geometry, including Riemannian geometry and applications to science and engineering.
Learning Outcomes 1. Knowledge and understanding
After the module, students should have a basic understanding of
a) invariants used to describe the shape of explicitly given curves and surfaces,
b) special curves on surfaces,
c) the difference between extrinsically defined properties and those which depend only on the surface metric,
d) understanding the passage from local to global properties exemplified by the GaussBonnet Theorem.
2. Intellectual abilities
After the module, students should be able to
a) use differential calculus to discover geometric properties of explicitly given curves and surface,
b) understand the role played by special curves on surfaces.
3. Subjectbased practical skills
Students should learn to
a) compute invariants of curves and surfaces,
b) interpret the invariants of curves and surfaces as indicators of their geometrical properties.
4. General transferable skills
Students will improve their ability to
a) think logically about abstract concepts,
b) combine theory with examples in a meaningful way.
Advanced Electromagnetism (PHYS370)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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 (nondispersive 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'' problemsolving and analytic skills.
Learning Outcomes Students should have an understanding of the properties of solutions to the wave equation for electromagnetic fields in free space and in matter (nondispersive 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims  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
Learning Outcomes 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 uptodate 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 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 100:0 Aims  Develop a syllabus to describe the properties of surfaces
 Convey an understanding of the physical properties of Surfaces
 Provide knowledge of a raneg of surface characterisation techniques
 Illustrate surface processes and their relevance to technologies
Learning Outcomes 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 propertiesbe able to describe surface alterations and processes using the right terminology
Physics of Life (PHYS382)
Level 3 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 100:0 Aims 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.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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
Undergraduate Ambassadors Project (PHYS396)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 0:100 Aims  To provide undergraduates with key transferable skills.
 To provide students with opportunity to learn to communicate physics at different levels.
 To provide students with workplace 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.
Learning Outcomes Communicate physicseffectively to others
Plan a lesson
Design 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 Credit level 7.5 Semester Second Semester Exam:Coursework weighting 0:100 Aims 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.
Learning Outcomes All students will be able to gather and analyse business data information
All students will be able to understand technology transfer dynamics
students will be able to communicate their ideas and work in a clear and concise mannerStudents 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 Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 Aims 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.
Learning Outcomes This module will enable students to understand and actively use the basic concepts of mathematical physics, such as generalised functions, fundamental solutions and Green''s functions, and apply powerful mathematical methods to problems of electromagnetism, elasticity, heat conduction and wave propagation.
Quantum Field Theory (MATH425)
Level M Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims To provide a broad understanding of the essentials of quantum field theory.
Learning Outcomes 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 crosssections.
Variational Calculus and Its Applications (MATH430)
Level M Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 Aims This module provides a comprehensive introduction to the theory of the calculus of variations, providing illuminating applications and examples along the way.
Learning Outcomes 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 nonphysical problems using variational methods
Students will develop an understanding of Hamiltonian formalism and have the ability to apply this framework to solve physical and nonphysical problems
Students will be confident in their ability to analyse variational symmetries and generate the associated conservation laws
Classical Mechanics (PHYS470)
Level M Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims  To provide students with an awareness of the physical principles that can be applied to understand important features of classical (i.e. nonquantum) 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 closelyrelated concepts in classical mechanics.
Learning Outcomes 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 EulerLagrange 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 Credit level 7.5 Semester First Semester Exam:Coursework weighting 70:30 Aims  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.
Learning Outcomes 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 Credit level 7.5 Semester First Semester Exam:Coursework weighting 0:100 Aims  Perform literature searches.
 Plan research projects.
 Explain research projects to both expert and nonexpert 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.
Learning Outcomes Experience in carrying out search of scientific literature. Communicating research to nonexpert 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 70:30 Aims  Tointroduce the emerging fields of nanoscale physics and nanotechnology
To describe experimental techniques for probing physical properties of nanostructured materials
Todescribe the novel sizedependent electronic, optical, magnetic and chemicalproperties of nanoscale materials
Todescribe several ‘hot topics'' in nanoscience research
Todevelop students'' problemsolving, investigative, communication and analyticskills through appropriate assignments for tutorials and a literature project.
Learning Outcomes 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 problemsolving, investigative, communication, and analytic skills.
 Tointroduce the emerging fields of nanoscale physics and nanotechnology
Magnetic Structure and Function (PHYS497)
Level M Credit level 7.5 Semester First Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims To provide a broad understanding of string theory, and its utilization as a theory that unifies all of the known fundamental matter and interactions.
Learning Outcomes 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 spacetime dimensions.
be familiar with string toroidal compactifications and Tduality.Analytical & Computational Methods for Applied Mathematics (MATH424)
Level M Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims 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.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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 low
and high Reynolds number.Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims This module gives an introduction to the mathematical theory of linear and nonlinear waves. Illustrative applications involve problems of acoustics, gas dynamics and examples of solitary waves.
Learning Outcomes Students will learn essential modelling techniques in problems of wave propagation. They will also understand that mathematical models of the same type can be successfully used to describe different physical phenomena. Students will also study background mathematical theory in models of acoustics, gas dynamics and water waves.
Introduction to Modern Particle Theory (MATH431)
Level M Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims 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.
Learning Outcomes be familiar with the Lorentz and Poincare groups and their role in classification of elementary particles.

be familiar with the basics of Langrangian and Hamiltonian dynamics and the differential equations of bosonic and fermionic wave functions. 
be familiar with basic elements of field quantisation.

be familiar with the Feynman diagram pictorial representation of particle interactions. appreciate the role of symmetries and conservation laws in distinguishing the strong, weak and electromagnetic interactions. 
be able to describe the spectrum and interactions of elementary particles and their embedding into Grand Unified Theories (GUTs) 
be familiar with the flavour structure of the standard particle model and generation of mass through symmetry breaking
be aware of phenomenological aspects of Grand Unified TheoriesAsymptotic Methods for Differential Equations (MATH433)
Level M Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims This module provides an introduction into the perturbation theory for partial differential equations. We consider singularly and regularly perturbed problems and applications in electromagnetism, elasticity, heat conduction and propagation of waves.
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  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
Learning Outcomes 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 firstyear 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 onetoone 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, miniproject work or key skills exercises.