Mathematical Physics MMath Add to your prospectus

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Key information


  • Course length: 4 years
  • UCAS code: FGH1
  • Year of entry: 2018
  • Typical offer: A-level : AAB / IB : 35 / BTEC : Applications considered
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Module details

Programme Year One

 

Year One Compulsory Modules

  • Calculus I (MATH101)
    Level1
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting80:20
    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

  • Calculus II (MATH102)
    Level1
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting80:20
    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 Co-ordinates

  • Introduction to Linear Algebra (MATH103)
    Level1
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting80:20
    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

  • Newtonian Mechanics (MATH122)
    Level1
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting80:20
    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 inertia

    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

    ​oscillation, vibration, resonance

  • Thermal Physics (PHYS102)
    Level1
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting60:40
    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 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
  • Wave Phenomena (PHYS103)
    Level1
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting60:40
    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

    At the end of the module the student should be able to:

    • 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)
    Level1
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting60:40
    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 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.​

  • Working With Physics I (PHYS105)
    Level1
    Credit level7.5
    SemesterFirst Semester
    Exam:Coursework weighting0:100
    Aims
    • To develop skills with spreadsheets
    • To develop skills in using computers to perform mathematical calculations
    • To illustrate the insight into physics which can be obtained by exploiting computational software packages
    • To improve science students'' skills in communicating scientific information in appropriate written and oral formats

     

    Learning Outcomes

    Ability to use spreadsheets and mathematical packages to calculate and graph mathematical equations.

    Ability to apply mathematical software packages to physics problems

    Ability to communicate more confidently

    Understanding of some of the key factors in successful communication

  • Practical Skills for Mathematical Physics (PHYS156)
    Level1
    Credit level7.5
    SemesterSecond Semester
    Exam:Coursework weighting0:100
    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 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
    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

 

Year Two Compulsory Modules

  • Introduction to the Methods of Applied Mathematics (MATH224)
    Level2
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting90:10
    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.

  • Vector Calculus With Applications in Fluid Mechanics (MATH225)
    Level2
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting85:15
    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)
    Level2
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting80:20
    Aims

    To introduce the student to a surprising, very beautiful theory having 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.

  • Classical Mechanics (MATH228)
    Level2
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting90:10
    Aims

    To provide a basic understanding of the principles of Classical Mechanics and their application to simple dynamical systems.

    Learning Outcomes

    ​the motions of bodies under simple force systems, including calculations of the orbits of satellites, comets and planetary motions

    ​ motion relative to a rotating frame, Coriolis and centripetal forces, motion under gravitry over the Earth''s surface 

    ​rigid body dynamics using centre of mass, angular momentum and moments of inertia

  • Electromagnetism (PHYS201)
    Level2
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting70:30
    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 non-static electric and magnetic fields and the ability to solve simple problems in these situations.

  • Condensed Matter Physics (PHYS202)
    Level2
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting70:30
    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 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.

    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 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)
    Level2
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting70:30
    Aims
    • To introduce students to the concepts of quantum theory.
    • To show how Schrodinger''s equation is applied to particle flux and to bound states.
    • 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)
    Level2
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting70:30
    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 4-vectors for applications to collision problems
    Learning Outcomes

    At the end of the module the student should have:

    • 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)

     

    Optional modules. Choose two 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

    PHYS370        Advanced Electromagnetism

    PHYS374        Relativity and Cosmology

    PHYS377        Introduction to Particle Physics

    PHYS381        Surface Physics

    PHYS382        Physics of Life

    PHYS388        Physics of Energy Sources

    PHYS396        Undergraduate Ambassadors Project

    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

    PHYS490        Advanced Nuclear Physics

    PHYS493        Advanced Particle Physics

Year Three Compulsory Modules

  • Further Methods of Applied Mathematics (MATH323)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims

    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.

    Learning Outcomes

    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)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims

    To impart

    (i)              a firm grasp of the physical principles behind Special and General Relativity and their main consequences;

    (ii)           technical competence in the mathematical framework of the subjects - Lorentz transformation, coordinate transformations and geodesics in Riemann space;

    (iii)          knowledge of some of the classical tests of General Relativity - perihelion shift, gravitational deflection of light;

    (iv)          basic concepts of black holes and (if time) relativistic cosmology.

    Learning Outcomes

    After  completing this module students should

    (i)              understand why space-time forms a non-Euclidean four-dimensional manifold;

    (ii)           be proficient at calculations involving Lorentz transformations, energy-momentum conservation, and the Christoffel symbols.

    (iii)          understand the arguments leading to the Einstein''s field equations and how Newton''s law of gravity arises as a limiting case.

    (iv) be able to calculate the trajectories of bodies in a Schwarzschild space-time.

  • Quantum Mechanics (MATH325)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims

    The development of Quantum Mechanics, requiring as it did revolutionary changes in our understanding of the nature of reality, was arguably the greatest conceptual achievement of all time.  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.

    Learning Outcomes

    After completing the module students should be able to solve Schrodinger''s equation for simple systems, and have some intuitive understanding of the significance of quantum mechanics for both elementary systems and the behaviour of matter.

  • Theory of Statistical Inference (MATH361)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting90:10
    Aims

    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.

    Learning Outcomes

    After completing the module students should have a good understanding of the classical approach to, and especially the likelihood methods for, statistical inference. 

    The students should also gain an appreciation of the blossoming area of Bayesian approach to inference

  • Mathematical Physics Project (MATH432)
    LevelM
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting0:100
    Aims

    To learn research and presentation skills by studying and reporting on an area of theoretical physics.

    Learning Outcomes

    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)
    LevelM
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting0:100
    Aims
    • To 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.
    • To give students an opportunity to display qualities such as initiative and ingenuity.
    • To introduce students to concepts, methods and applicability of computational modelling of physical phenomena using the Java language.
    • To give students experience of report writing displaying high standards of composition and production.
    • To give an opportunity for students to display communication skills.
    Learning Outcomes

    At the end of the module the student should have:

    Acquired working knowledge of a high level OO programming language.

    ​Experience in researching literature and other sources of relevant information.

    ​Set up model of physical phenomena or situation.

    ​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)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims

    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.

    Learning Outcomes

    After completing the module, students should be able to understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, and apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.

  • Population Dynamics (MATH332)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims

    - 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

    Learning Outcomes

    ​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)
    Level3
    Credit level7.5
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims
    • 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
    Learning Outcomes

    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)
    Level3
    Credit level7.5
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims
    • 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
    Learning Outcomes

    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)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting0:100
    Aims

    ​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

    Learning Outcomes

    ​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)
    Level3
    Credit level7.5
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims
    • 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
    Learning Outcomes

    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)
    Level3
    Credit level7.5
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims
    • To develop the physics concepts describing semiconductors in sufficient details for the purpose of understanding the construction and operation of common semiconductor devices
    Learning Outcomes

    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)
    Level3
    Credit level7.5
    SemesterFirst Semester
    Exam:Coursework weighting0:100
    Aims
    • 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
    Learning Outcomes

    ​ 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 in Data Analysis (PHYS392)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting50:50
    Aims

    To give a theoretical and practical understanding of the statistical principles involved in the analysis and interpretation of data.

    Learning Outcomes

    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 sources

     

    •  Using statistical information to detemine the validity of a hypothesis or experimental measurement
  • Statistical and Low Temperature Physics (PHYS393)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    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, 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)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims

    ·      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.

    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 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)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims

    To develop expertise in dynamical systems in general and study particular systems in detail.

    Learning Outcomes

    After completing the module students should be able to:

    understand the possible behaviour of dynamical systems with particular attention to chaotic motion;

      

    ​be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points;

    ​understand how fractal sets arise and how to characterise them.

  • Riemann Surfaces (MATH340)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims1. 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'' 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)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting85:15
    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 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.

    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 Gauss-Bonnet 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. Subject-based 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)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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 (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.
    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 (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)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting80:20
    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 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)
    Level3
    Credit level7.5
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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)
    Level3
    Credit level7.5
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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 properties

    ​be able to describe surface alterations and processes using the right terminology

  • Physics of Life (PHYS382)
    Level3
    Credit level7.5
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims
    • To explain the constraints on physical forces which are necessary for life to evolve in the Universe
    • To describe the characteristics of life on earth
    • To describe physical techniques used in the study of biological systems
    Learning Outcomes​​​

    At the end of the module the student should have:

    • An understanding of the framework of physical forces within which life is possible

    • An understanding of the nature of life on earth


    • Familiarity with physical techniques used in the study of biological systems​
  • Physics of Energy Sources (PHYS388)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting0:100
    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 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.
    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)
    Level3
    Credit level7.5
    SemesterSecond Semester
    Exam:Coursework weighting0:100
    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 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)
    LevelM
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting90:10
    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, weak solutions and Green''s functions, and apply powerful mathematical methods to problems of electromagnetism, elasticity, heat conduction and wave propagation.

  • Quantum Field Theory (MATH425)
    LevelM
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    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 cross-sections.

  • Variational Calculus and Its Applications (MATH430)
    LevelM
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    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 non-physical problems using variational methods​

    ​Students will develop an understanding of Hamiltonian mechanics and an appreciation of how symmetries relate to conservation laws​

  • Classical Mechanics (PHYS470)
    LevelM
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims
    1. ​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.
    2. 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.
    3. To develop students'' understanding of the fundamental relationship between symmetries and conserved quantities in physics.
    4. To reinforce students’ knowledge of quantum mechanics, by developing and exploring the application of closely-related 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 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)
    LevelM
    Credit level7.5
    SemesterFirst Semester
    Exam:Coursework weighting70:30
    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)
    LevelM
    Credit level7.5
    SemesterFirst Semester
    Exam:Coursework weighting0:100
    Aims
    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.
     
      Learning OutcomesExperience 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.

    1. Nanoscale Physics and Technology (PHYS499)
      LevelM
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting70:30
      Aims
    2. Tointroduce the emerging fields of nanoscale physics and nanotechnology
    3. To describe experimental techniques for probing physical properties of nanostructured materials

    4. Todescribe the novel size-dependent electronic, optical, magnetic and chemicalproperties of nanoscale materials​

    5. Todescribe several ‘hot topics'' in nanoscience research​

    6. Todevelop students'' problem-solving, investigative, communication and analyticskills through appropriate assignments for tutorials and a literature project. ​

    7. 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 problem-solving, investigative, communication, and analytic skills.

    8. Magnetic Structure and Function (PHYS497)
      LevelM
      Credit level7.5
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      Aims
      • To build on the third year modules Condensed Matter Physics
      • To develop an understanding of the phenomena and fundamental mechanisms of magnetism in condensed matter
      Learning Outcomes

      At the end of the module the student should have:

      • A basic understanding of the quantum origin of the magnetism and magnetic moments
      • An introduction to the Weiss molecular field theory of ferromagnetism
      • A basic understanding of spin waves in ordered magnets
      • An introduction to the techniques of neutron scattering and magnetic x-ray scattering
      • An appreciation of simple magnetic structures and magnetic excitations
      • An introduction to new magnetic materials
    9. Introduction to String Theory (MATH423)
      LevelM
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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 space-time dimensions.  

      be familiar with string toroidal compactifications and T-duality.
    10. Analytical & Computational Methods for Applied Mathematics (MATH424)
      LevelM
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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.

    11. Advanced Topics in Mathematical Biology (MATH426)
      LevelM
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      Aims
    12. To introduce some hot problems of contemporary mathematical biology, including analysis of developmental processes, networks and biological mechanics.
    13. ​To further develop mathematical skills in the areas of difference equations and ordinary and partial differential equations.

    14. ​To explore biological applications of fluid dynamics in the limit of low
      and high Reynolds number.

    15. Learning OutcomesTo 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.

    16. Waves, Mathematical Modelling (MATH427)
      LevelM
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      Aims

      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.

      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.

    17. Introduction to Modern Particle Theory (MATH431)
      LevelM
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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 Theories
    18. Asymptotic Methods for Differential Equations (MATH433)
      LevelM
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      Aims

      This module provides an introduction into the perturbation theory for  partial differential equations. We consider singularly and regularly perturbed problems and applications in electro-magnetism, 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.

    19. Advanced Nuclear Physics (PHYS490)
      LevelM
      Credit level7.5
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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

      At the end of the module the student should have:

      • Knowledge of the basic properties of nuclear forces and the experimental evidence upon which these are based
      • Basic 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
      • Basic knowledge of astrophysical nucleosynthesis processes
      • Basic knowledge of phases of nuclear matter
    20. Advanced Particle Physics (PHYS493)
      LevelM
      Credit level7.5
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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

      At the end of the module the student should have:

      • 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

    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.

     

    Year Four Compulsory Modules

    • Advanced Quantum Physics (PHYS480)
      LevelM
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      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 state-of-the art quantum physics experiments.

      ​Understanding of the implications of quantum physics in our daily lifes.

    • Mathematical Physics Project (MATH420)
      LevelM
      Credit level30
      SemesterWhole Session
      Exam:Coursework weighting0:100
      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

    • Cartesian Tensors and Mathematical Models of Solids and VIscous Fluids (MATH324)
      Level3
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      Aims

      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.

      Learning Outcomes

      After completing the module, students should be able to understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, and apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.

    • Population Dynamics (MATH332)
      Level3
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      Aims

      - 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

      Learning Outcomes

      ​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)
      Level3
      Credit level7.5
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      Aims
      • 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
      Learning Outcomes

      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)
      Level3
      Credit level7.5
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      Aims
      • 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
      Learning Outcomes

      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)
      Level3
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting0:100
      Aims

      ​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

      Learning Outcomes

      ​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)
      Level3
      Credit level7.5
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      Aims
      • 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
      Learning Outcomes

      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)
      Level3
      Credit level7.5
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      Aims
      • To develop the physics concepts describing semiconductors in sufficient details for the purpose of understanding the construction and operation of common semiconductor devices
      Learning Outcomes

      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)
      Level3
      Credit level7.5
      SemesterFirst Semester
      Exam:Coursework weighting0:100
      Aims
      • 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
      Learning Outcomes

      ​ 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 in Data Analysis (PHYS392)
      Level3
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting50:50
      Aims

      To give a theoretical and practical understanding of the statistical principles involved in the analysis and interpretation of data.

      Learning Outcomes

      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 sources

       

      •  Using statistical information to detemine the validity of a hypothesis or experimental measurement
    • Statistical and Low Temperature Physics (PHYS393)
      Level3
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      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, 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)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      Aims

      ·      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.

      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 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)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      Aims

      To develop expertise in dynamical systems in general and study particular systems in detail.

      Learning Outcomes

      After completing the module students should be able to:

      understand the possible behaviour of dynamical systems with particular attention to chaotic motion;

        

      ​be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points;

      ​understand how fractal sets arise and how to characterise them.

    • Riemann Surfaces (MATH340)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      Aims1. 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'' 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)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting85:15
      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 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.

      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 Gauss-Bonnet 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. Subject-based 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)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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 (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.
      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 (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)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting80:20
      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 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)
      Level3
      Credit level7.5
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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)
      Level3
      Credit level7.5
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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 properties

      ​be able to describe surface alterations and processes using the right terminology

    • Physics of Life (PHYS382)
      Level3
      Credit level7.5
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      Aims
      • To explain the constraints on physical forces which are necessary for life to evolve in the Universe
      • To describe the characteristics of life on earth
      • To describe physical techniques used in the study of biological systems
      Learning Outcomes​​​

      At the end of the module the student should have:

      • An understanding of the framework of physical forces within which life is possible

      • An understanding of the nature of life on earth


      • Familiarity with physical techniques used in the study of biological systems​
    • Physics of Energy Sources (PHYS388)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting100:0
      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)
      Level3
      Credit level15
      SemesterSecond Semester
      Exam:Coursework weighting0:100
      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 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.
      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)
      Level3
      Credit level7.5
      SemesterSecond Semester
      Exam:Coursework weighting0:100
      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 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)
      LevelM
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting90:10
      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, weak solutions and Green''s functions, and apply powerful mathematical methods to problems of electromagnetism, elasticity, heat conduction and wave propagation.

    • Quantum Field Theory (MATH425)
      LevelM
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      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 cross-sections.

    • Variational Calculus and Its Applications (MATH430)
      LevelM
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      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 non-physical problems using variational methods​

      ​Students will develop an understanding of Hamiltonian mechanics and an appreciation of how symmetries relate to conservation laws​

    • Classical Mechanics (PHYS470)
      LevelM
      Credit level15
      SemesterFirst Semester
      Exam:Coursework weighting100:0
      Aims
      1. ​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.
      2. 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.
      3. To develop students'' understanding of the fundamental relationship between symmetries and conserved quantities in physics.
      4. To reinforce students’ knowledge of quantum mechanics, by developing and exploring the application of closely-related 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 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)
      LevelM
      Credit level7.5
      SemesterFirst Semester
      Exam:Coursework weighting70:30
      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)
      LevelM
      Credit level7.5
      SemesterFirst Semester
      Exam:Coursework weighting0:100
      Aims
      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.
       
        Learning OutcomesExperience 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.

      1. Nanoscale Physics and Technology (PHYS499)
        LevelM
        Credit level15
        SemesterSecond Semester
        Exam:Coursework weighting70:30
        Aims
      2. Tointroduce the emerging fields of nanoscale physics and nanotechnology
      3. To describe experimental techniques for probing physical properties of nanostructured materials

      4. Todescribe the novel size-dependent electronic, optical, magnetic and chemicalproperties of nanoscale materials​

      5. Todescribe several ‘hot topics'' in nanoscience research​

      6. Todevelop students'' problem-solving, investigative, communication and analyticskills through appropriate assignments for tutorials and a literature project. ​

      7. 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 problem-solving, investigative, communication, and analytic skills.

      8. Magnetic Structure and Function (PHYS497)
        LevelM
        Credit level7.5
        SemesterFirst Semester
        Exam:Coursework weighting100:0
        Aims
        • To build on the third year modules Condensed Matter Physics
        • To develop an understanding of the phenomena and fundamental mechanisms of magnetism in condensed matter
        Learning Outcomes

        At the end of the module the student should have:

        • A basic understanding of the quantum origin of the magnetism and magnetic moments
        • An introduction to the Weiss molecular field theory of ferromagnetism
        • A basic understanding of spin waves in ordered magnets
        • An introduction to the techniques of neutron scattering and magnetic x-ray scattering
        • An appreciation of simple magnetic structures and magnetic excitations
        • An introduction to new magnetic materials
      9. Introduction to String Theory (MATH423)
        LevelM
        Credit level15
        SemesterSecond Semester
        Exam:Coursework weighting100:0
        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 space-time dimensions.  

        be familiar with string toroidal compactifications and T-duality.
      10. Analytical & Computational Methods for Applied Mathematics (MATH424)
        LevelM
        Credit level15
        SemesterSecond Semester
        Exam:Coursework weighting100:0
        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.

      11. Advanced Topics in Mathematical Biology (MATH426)
        LevelM
        Credit level15
        SemesterSecond Semester
        Exam:Coursework weighting100:0
        Aims
      12. To introduce some hot problems of contemporary mathematical biology, including analysis of developmental processes, networks and biological mechanics.
      13. ​To further develop mathematical skills in the areas of difference equations and ordinary and partial differential equations.

      14. ​To explore biological applications of fluid dynamics in the limit of low
        and high Reynolds number.

      15. Learning OutcomesTo 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.

      16. Waves, Mathematical Modelling (MATH427)
        LevelM
        Credit level15
        SemesterSecond Semester
        Exam:Coursework weighting100:0
        Aims

        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.

        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.

      17. Introduction to Modern Particle Theory (MATH431)
        LevelM
        Credit level15
        SemesterSecond Semester
        Exam:Coursework weighting100:0
        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 Theories
      18. Asymptotic Methods for Differential Equations (MATH433)
        LevelM
        Credit level15
        SemesterSecond Semester
        Exam:Coursework weighting100:0
        Aims

        This module provides an introduction into the perturbation theory for  partial differential equations. We consider singularly and regularly perturbed problems and applications in electro-magnetism, 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.

      19. Advanced Nuclear Physics (PHYS490)
        LevelM
        Credit level7.5
        SemesterSecond Semester
        Exam:Coursework weighting100:0
        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

        At the end of the module the student should have:

        • Knowledge of the basic properties of nuclear forces and the experimental evidence upon which these are based
        • Basic 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
        • Basic knowledge of astrophysical nucleosynthesis processes
        • Basic knowledge of phases of nuclear matter
      20. Advanced Particle Physics (PHYS493)
        LevelM
        Credit level7.5
        SemesterSecond Semester
        Exam:Coursework weighting100:0
        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

        At the end of the module the student should have:

        • 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

      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.