. "Physics"@en . . "Astronomy"@en . . "English"@en . . "Foundations of physics 1"@en . . "40.0" . "**Prerequisites** \nA-Level Physics and A-Level Mathematics.\n\n**Corequisites**\n(Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) or (Linear Algebra I (MATH1071) and Calculus I (MATH1061)).\n\n**Aims**\n* This module is designed primarily for students studying Department of Physics or Natural Science degree programmes.\n* It provides the minimum core physics required for progression to Level 2 physics modules and should be taken by all students intending to study physics beyond Level 1.\n* It provides courses in classical aspects of wave phenomena and electromagnetism, and introduces basic concepts in Newtonian mechanics, quantum mechanics, special relativity and optical physics.\n* The module provides students with practice in the informal discussion of scientific ideas within a small group.\n* It also provides students with opportunitites to develop their study skills. Such skills include being able to understand the difference between University and A-level physics; understanding how to engage with the course material efficiently and developing problem-solving strategies.\n* It provides students with practice at synthesising and proposing new problems based on their understanding of the knowledge base.\n* It will enable students to analyse a physical system and to formulate a piece of computer code that substantially solves a problem or models the behaviour.\n\n**Content**\nThe course will contain the following fundamental topics.\n* Mechanics: Motion in a straight line. Motion in 2 or 3 dimensions. Newton's Laws. Work and Kinetic Energy. Potential Energy and Energy Conservation. Momentum, impulse, and collisions. Angular velocity and angular acceleration. Rotational kinetic energy, moment of inertia. Torque. Angular momentum. Combined linear and angular motion. Equilibrium, centre of mass. Gravitation: force and energy. Kepler’s laws. Periodic motion and harmonic oscillators.\n* Waves and optics: Mechanical waves and the wave equation. Wave velocity and energy transport. Interference of waves and normal modes. Sounds waves and the Doppler effect. The nature and propagation of light. Refraction, polarization, Snell and Malus law. Geometrical optics and ray tracing. Lenses and mirrors. Interference of light. Young's slits. Diffraction.\n* Electricity and magnetism: Coulomb's law. Electric fields due to point charges. Charge distributions. Electric flux and non-uniform electric fields Gauss' law. Work done by and against electrostatic forces. Electric potential and potential energy. Capacitance. Potential energy stored in charged capacitors. Magnetic field and magnetic forces. Magnetic forces on current. Sources of magnetism: the Biot Savart Law. Ampere's law. Magnetic materials. Electromagnetic induction. Inductance. Potential energy stored in inductors. EM waves. Maxwell's equations.\n* Circuits: DC and AC Electrical currents. Electromotive Force. Electrical resistance. Electrical power. Kirchoff's rules. Resistors in series and parallel. RL, LC and LCR circuits.\n* Special relativity: Invariance of Physical Laws. Relativity of Simultaneity. Relativity of time intervals. Relativity of length intervals. The Lorentz transformations. Relativistic momentum. Relativistic work and energy.\n* Quantum mechanics: Photoelectric Effect. X-ray production. Electron Waves. Wave-particle duality. Probability and Uncertainty. Atomic spectra and the Bohr model of the Atom. Wavefunctions and the 1-dimensional Schrödinger equation. Wave packets, stationary states and time dependence. Interpretation of wavefunction. Particle in a one-dimensional box. Potential wells. Potential barriers and tunnelling. Harmonic oscillator.\n* Oscillations: Simple harmonic motion. Damped harmonic motion. Driven harmonic motion. Resonance (width, Q-factor, phase). Applications in mechanics, LCR circuits, atomic transitions; nuclear reactions; elementary particle reactions. Collisions, conservation and fields: Centre of momentum frame; rocket motion; relativistic collisions; conservation in fluid flow (continuity, Bernoulli's equation). Continuity in electromagnetism. Gauss' law in electromagnetism and gravity. Conservative force fields.\n* Collisions, conservation and fields: Centre of momentum frame; rocket motion; relativistic collisions; conservation in fluid flow (continuity, Bernoulli's equation). Continuity in electromagnetism. Gauss' law in electromagnetism and gravity. Conservative force fields.\n\n**Learning Outcomes**\nSubject-specific Knowledge:\n* Students will be able to apply knowledge of the concepts and principles of the following foundational areas of physics to unfamiliar problems: Mechanics; Waves and optics; Circuits; Oscillations; Electromagnetism; Quantum mechanics; Special Relativity.\n* Students will be able to formulate and solve equations of motion for particles to describe and predict their dynamics. Students will be able to apply conservation laws in applicable circumstances as an alternative method.\n* Students will be able to describe and predict the behaviour of light using both (i) the ray picture of geometrical optics and (ii) simple physical optics.\n* Students will be able to analyse a simple circuit driven by DC or AC using circuit theory.\n* Students will be able to analyse physical systems in terms of charges and electromagnetic fields and predict the behaviour of charges and fields using the relevant concepts.\n* Students will be able to describe the quantum-mechanical behaviour of particles in simple potentials. They will be able to predict departures from classical behaviour.\n* Students will be able to apply the Lorentz transformations in simple situations and describe the behaviour of dynamic systems at relativistic energies. They will be able to predict departures from non-relativistic behaviour.\n* Students will be able to outline areas of physics where harmonic oscillations govern the behaviour. They will be able to analyse and predict the behaviour of general oscillating systems including in unfamiliar contexts.\n* Students will be able to identify and apply conservation laws in analysing and describing physical systems. This includes applications of conservation laws to collision problems and the concept of a conservative field.\n\nSubject-specific Skills:\n* Students will become adept at problem solving and be able to analyse a simple physical problem and formulate a mathematical description of it. In some cases students will be required to manipulate or solve the resulting set of equations in order to explain or predict the system's behaviour.\n* Students will be able to sketch and graph the response of a physical system to a given set of initial and boundary conditions.\n* Students will be able to recognise a key piece of fundamental physics (such as resonance or conservation of momentum) in a variety of contexts and apply a similar detailed analysis irrespective of an unfamiliar context.\n\nKey Skills:\nModes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n* Teaching will be lectures, supported by tutorials.\n* The lectures will provide the means to give a concise, focused presentation of the subject matter of the module.\n* The lecture material will be explicitly linked to the contents of a single recommended textbook for the module, thus making clear where students can begin their private study.\n* When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times (the Department has a policy of encouraging such enquiries).\n* Regular problem exercises will give students the chance to develop their theoretical understanding and problem-solving abilities.\nThese problem exercises will form the basis for discussions in tutorial groups of typically six students.\n* The tutorials will also provide an informal environment for students to raise issues of interest or difficulty.\n* Student performance will be summatively assessed through written examinations, an open-book examination and an online test, and formatively assessed through problem exercises, progress tests and a Collection examination.\n* The written examinations, open-book examination and online test will provide the means for students to demonstrate their acquisition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises, progress tests and Collection examination will provide opportunities for feedback, for students to gauge their progress, and for staff to monitor progress throughout the duration of the module.\n\nMore details at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS1122" . . "Presential"@en . "TRUE" . . "Discovery skills in physics"@en . . "20.0" . "# Prerequisites\n- A-Level Physics\n- A-Level Mathematics\n\n# Corequisites\n- Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) or (Linear Algebra I (MATH1071) and Calculus I (MATH1061)))\n\n# Excluded Combination of Modules\nNone\n\n# Aims\nThis module is designed primarily for students studying Department of Physics or Natural Science degree programmes.\nIt provides basic experimental and key skills required by physicists, and should be taken by all students intending to study practical physics beyond Level 1.\nUsing experiments in physics as the vehicle, the module provides a structured introduction to laboratory skills development, with particular emphasis on measurement uncertainty, data analysis and written and oral communication skills.\nTo teach a scientific computing language.\nTo introduce the idea of scientific enterprise.\nTo provide students with experience in scientific communication.\nTo provide students with opportunities to know more about what the University Library offers and to learn about the career opportunities open to them after graduation.\n\n# Content\nThe syllabus contains:\n* Errors in practical work: systematic and random errors, combination of errors, common sense in errors.\n* Electronic document preparation.\n* Use of spreadsheets in data analysis\n* Developing a scientific style of writing, and writing for a non-specialist audience.\n* Good practice in maintaining laboratory notebooks.\n* Information literacy, including introduction to sources of reference material.\n* Experimental laboratory: safety in the laboratory, skills through practice, introduction to instrumentation.\n* Introductory experiments in physics.\n* Extended experiments in physics.\n* Introduction to programming in a scientific computer language and application to simple computational tasks.\n* Presentation of data.\n* An enterprise seminar.\n\n# Learning Outcomes\n## Subject-specific Knowledge\nStudents will have gained a working knowledge of the treatment of errors in laboratory work.\n\n## Subject-specific Skills\n* Students will know the constituents of a scientific style of writing and will be able to apply this to produce a clear scientific report including: theoretical background, experimental description, presentation and analysis of results, interpretation and evaluation, and lay summary.\n* They will be aware of a variety of reference sources and know how to use them effectively.\n* They will have acquired practical competence and accuracy in carrying out experimental procedures including measurement, use of apparatus and recording of results.\n* They will have a working knowledge of a scientific computing language.\n\n## Key Skills\n* They will be able to use computer software to write reports and to analyse data.\n\n# Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n* Teaching will be by lectures, practicals, exercises, workshops, computing exercises and an information literacy session.\n* The lectures will provide the means to give a concise, focused presentation of the theoretical material on error analysis and on data analysis.\n* The lectures will also provide essential information on good practice in laboratory notebook keeping, report writing, the use of spreadsheets and giving oral presentations.\n* The computing lectures give an introduction to the basic principles of scientific computing and the computing workshops and exercises give practice in applying these principles.\n* When appropriate the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times (the Department has a policy of encouraging such enquires).\n* The information literacy session will introduce students to a variety of reference sources and how to use them effectively.\n* The practicals will consist of experimental projects, data analysis exercises, an enterprise seminar, feedback on data analysis and report writing, and one individual oral presentation.\n* These sessions will provide the means for students to acquire practical competence and accuracy in carrying out experimental procedures including measurement, use of apparatus and the recording of results.\n* During the sessions students will be able to obtain help and guidance from the laboratory scripts and through discussions with laboratory demonstrators.\n* Student performance in the laboratories will be summatively assessed through the assessment of laboratory notebooks and a written report.\n* The written reports will provide the means for students to demonstrate their achievement of the stated learning outcomes.\n* Work in the early stages of the experimental laboratories will be formatively assessed. This will enable students to gauge their progress and will inform their subsequent work. Work in the later stages will be summatively assessed.\n* Student performance in computing is summatively assessed through computing exercises.\n* An information session will outline the services offered by the University Library and will give practical advice on careers and employability.\n\nMore information: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS1101" . . "Presential"@en . "TRUE" . . "Single mathematics a"@en . . "20.0" . "## Prerequisites\n* Normally, A level Mathematics at Grade A or better, or equivalent.\n\n## Corequisites\n* None.\n\n## Excluded Combination of Modules\n* Calculus I (Maths Hons) (MATH1081), Calculus (MATH1061), Linear Algebra I (Maths Hons) (MATH1091), Linear Algebra I\n (MATH1071), Mathematics for Engineers and Scientists (MATH1551)\nmay not be taken with or after this\nmodule.\n\n## Aims\n* This module has been designed to supply mathematics relevant to\nstudents of the physical sciences.\n\n## Content\n* Basic functions and elementary calculus: including\nstandard functions and their inverses, the Binomial Theorem, basic\nmethods for differentiation and integration.\n* Complex numbers: including addition, subtraction,\nmultiplication, division, complex conjugate, modulus, argument, Argand\ndiagram, de Moivre's theorem, circular and hyperbolic\nfunctions.\n* Single variable calculus: including discussion of real\nnumbers, rationals and irrationals, limits, continuity,\ndifferentiability, mean value theorem, L'Hopital's rule, summation of series,\nconvergence, Taylor's theorem.\n* Matrices and determinants: including determinants, rules\nfor manipulation, transpose, adjoint and inverse matrices,\nGaussian elimination, eigenvalues and eigenvectors,\n \n* Groups, axioms, non-abelian groups\n\n## Learning Outcomes\n* Subject-specific Knowledge: \n * By the end of the module students will: be able to solve a\nrange of predictable or less predictable problems in\nMathematics.\n * have an awareness of the basic concepts of theoretical\nmathematics in these areas.\n * have a broad knowledge and basic understanding of these\nsubjects demonstrated through one or more of the following topic\nareas: Elementary algebra.\n * Calculus.\n * Complex numbers.\n * Taylor's Theorem.\n * Linear equations and matrices.\n * Groups\n\n* Subject-specific Skills: \n\n* Key Skills: \n\n## Modes of Teaching, Learning and Assessment and how these contribute to\nthe learning outcomes of the module\n* Lectures demonstrate what is required to be learned and the\napplication of the theory to practical examples.\n* Initial diagnostic testing fills in gaps related to the wide\nvariety of syllabuses available at Mathematics A-level.\n* Tutorials provide the practice and support in applying the\nmethods to relevant situations as well as active engagement and feedback\nto the learning process.\n* Weekly coursework provides an opportunity for students\nto consolidate the learning of material as the module progresses (there\nare no higher level modules in the department of Mathematical Sciences which build on this module). It serves as a guide in the correct\ndevelopment of students' knowledge and skills, as well as an aid in developing their awareness of standards required.\n* The end-of-year written examination provides a substantial\ncomplementary assessment of the achievement of the student.\n\n## Teaching Methods and Learning Hours\n* Lectures: 63\n* Tutorials: 19\n* Support classes: 18\n* Preparation and Reading: 100\n* Total: 200\n\n## Summative Assessment\n* Examination: 90%\n * Written examination: 3 hours\n* Continuous Assessment: 10%\n * Fortnightly electronic assessments during the first 2 terms. Normally, each will consist of solving problems and will typically be one to two pages long. Students will have about one week to complete each assignment.\n\n## Formative Assessment: \n* 45 minute collection paper in the beginning of Epiphany term. Fortnightly formative assessment.\n\n## Attendance\n* Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University\n\nMore details in: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/MATH1561" . . "Presential"@en . "FALSE" . . "Single mathematics b"@en . . "20.0" . "#### Prerequisites\n\n* A level Mathematics at Grade A or better, or equivalent.\n\n#### Corequisites\n\n* Single Mathematics A (MATH1561).\n\n#### Excluded Combination of Modules\n\n* Mathematics for Engineers and Scientists (MATH1551) may not be taken with or after this module.\n\n#### Aims\n\n* This module has been designed to supply mathematics relevant to students of the physical sciences.\n\n#### Content\n\n* Vectors: including scalar and vector products, derivatives with respect to scalars, two-dimensional polar coordinates.\n* Ordinary differential equations: including first order, second order linear equations, complementary functions and particular integrals, simultaneous linear equations, applications.\n* Fourier analysis: including periodic functions, odd and even functions, complex form.\n* Functions of several variables: including elementary vector algebra (bases, components, scalar and vector products, lines and planes), partial differentiation, composite functions, change of variables, chain rule, Taylor expansions. Introductory complex analysis and vector calculus\n* Multiple integration: including double and triple integrals.\n* Introduction to probability: including sample space, events, conditional probability, Bayes' theorem, independent events, random variables, probability distributions, expectation and variance.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* By the end of the module students will: be able to solve a range of predictable or less predictable problems in Mathematics.\n* have an awareness of the basic concepts of theoretical mathematics in these areas.\n* have a broad knowledge and basic understanding of these subjects demonstrated through one or more of the following topic areas: Vectors.\n* Ordinary differential equations.\n* Fourier analysis.\n* Partial differentiation, multiple integrals.\n* Vector calculus.\n* Probability.\n\nSubject-specific Skills:\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Lectures demonstrate what is required to be learned and the application of the theory to practical examples.\n* Initial diagnostic testing fills in gaps related to the wide variety of syllabuses available at Mathematics A-level.\n* Tutorials provide the practice and support in applying the methods to relevant situations as well as active engagement and feedback to the learning process.\n* Weekly coursework provides an opportunity for students to consolidate the learning of material as the module progresses (there are no higher level modules in the department of Mathematical Sciences which build on this module). It serves as a guide in the correct development of students' knowledge and skills, as well as an aid in developing their awareness of standards required.\n* The end-of-year written examination provides a substantial complementary assessment of the achievement of the student." . . "Presential"@en . "FALSE" . . "Linear algebra"@en . . "20.0" . "#### Prerequisites\n\n* Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.\n\n#### Corequisites\n\n* Calculus I (MATH1061)\n\n#### Excluded Combination of Modules\n\n* Calculus I (Maths Hons) (MATH1081), Linear Algebra I (Maths Hons) (MATH1091), Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.\n\n#### Aims\n\n* This module is designed to follow on from, and reinforce, A level mathematics.\n* It will present students with a wide range of mathematics ideas in preparation for more demanding material later.\n* Aim: to give a utilitarian treatment of some important mathematical techniques in linear algebra.\n* Aim: to develop geometric awareness and familiarity with vector methods.\n\n#### Content\n\n* A range of topics are treated each at an elementary level to give a foundation of basic definitions, theorems and computational techniques.\n* A rigorous approach is expected.\n* Linear Algebra in n dimensions with concrete illustrations in 2 and 3 dimensions.\n* Vectors, matrices and determinants.\n* Vector spaces and linear mappings.\n* Diagonalisation, inner-product spaces and special polynomials.\n* Introduction to group theory.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* By the end of the module students will: be able to solve a range of predictable or less predictable problems in Linear Algebra.\n* have an awareness of the basic concepts of theoretical mathematics in Linear Algebra.\n* have a broad knowledge and basic understanding of these subjects demonstrated through one of the following topic areas:\n* Vectors in Rn, matrices and determinants.\n* Vector spaces over R and linear mappings.\n* Diagonalisation and Jordan normal form.\n* Inner product spaces.\n* Introduction to groups.\n* Special polynomials.\n\nSubject-specific Skills:\n\n* Students will have basic mathematical skills in the following areas: Modelling, Spatial awareness, Abstract reasoning, Numeracy.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Lectures demonstrate what is required to be learned and the application of the theory to practical examples.\n* Tutorials provide active engagement and feedback to the learning process.\n* Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills. They are also an aid in developing students' awareness of standards required.\n* Initial diagnostic testing and associated supplementary support classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level.\n* The examination provides a final assessment of the achievement of the student.\n\nMore details at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/MATH1071" . . "Presential"@en . "FALSE" . . "Calculus"@en . . "20.0" . "#### Prerequisites\n\n* Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.\n\n#### Corequisites\n\n* Linear Algebra I (MATH1071)\n\n#### Excluded Combination of Modules\n\n* Calculus I (Maths Hons) (MATH1081), Linear Algebra I (Maths Hons) (MATH1091), Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.\n\n#### Aims\n\n* This module is designed to follow on from, and reinforce, A level mathematics.\n* It will present students with a wide range of mathematics ideas in preparation for more demanding material later.\n* Aim: to introduce crucial basic concepts and important mathematical techniques.\n\n#### Content\n\n* A range of topics are treated each at an elementary level to give a foundation of basic definitions, theorems and computational techniques.\n* A rigorous approach is expected.\n* Elementary functions of a real variable.\n* Limits, continuity, differentiation and integration.\n* Ordinary Differential Equations.\n* Taylor series and Fourier series.\n* Calculus of functions of many variables\n* Partial differential equations and method of separation of variables\n* Fourier transforms\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* By the end of the module students will: be able to solve a range of predictable or less predictable problems in Calculus,\n* have an awareness of the basic concepts of theoretical mathematics in Calculus,\n* have a broad knowledge, and a basic understanding and working knowledge of each of the subtopics,\n* have gained confidence in approaching and applying calculus to novel problems.\n\nSubject-specific Skills:\n\n* Students will have enhanced skills in the following areas: modelling, spatial awareness, abstract reasoning and numeracy.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Lectures demonstrate what is required to be learned and the application of the theory to practical examples.\n* Tutorials provide active engagement and feedback to the learning process.\n* Weekly homework problems provide formative assessment to guide students in the development of their knowledge and skills. They also aid the development of students' awareness of the required standards of rigour.\n* Initial diagnostic testing and associated supplementary support classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level, and provide extra support to the course.\n* The examination provides a final assessment of the achievement of the student.\n\nMore details at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/MATH1061" . . "Presential"@en . "FALSE" . . "Foundations of physics 2a"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).\n\n#### Corequisites\n\n* Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables II (MATH2031) which covers similar material\n\n#### Excluded Combination of Modules\n\n* None\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes\n* It builds on the Level 1 module Foundations of Physics 1 (PHYS1122) by providing courses on Quantum Mechanics and Electromagnetism.\n\n#### Content\n\n* The syllabus contains:\n* Quantum Mechanics: Review of Level 1 quantum mechanics, wavefunction normalisation and expectation values, operators and non-commutative algebra \\[x,p\\]=-i hbar, time independent Schroedinger equation and general solution, properties of eigenfunctions (span the space, orthonormal), review of simple central potentials, generalized statistical interpretation, commuting operators, common eigenfunctions, 3D potentials in cartesian and spherical coordinates, angular momentum operators, spherical harmonics and vector model for L^2 and L\\_z, hydrogen wavefunctions and energies - transitions, generalised angular momentum and electron spin, nondegenerate perturbation theory, degenerate perturbation theory, application to hydrogen I - spin orbit coupling, adding angular momentum, application to hydrogen II - relativistic corrections and total fine structure, application to hydrogen III - lamb and hyperfine corrections, meaning of quantum mechanics “ Schroedinger's cat.\n* Electromagnetism: Divergence and Curl of Electrostatic Fields, Conductors. Electrostatic Fields in Matter: Polarization, The Electric Displacement, Linear Dielectrics. Magnetostatics: The Lorentz Force Law, The Biot-Savart Law, The Divergence and Curl of B, Magnetic Vector Potential. Magnetic Fields in Matter: Magnetization, The Auxiliary Field H, Linear Media. Electromotive Force, Electromagnetic Induction, Maxwell's Equations. Conservation Laws: Charge and Energy. Electromagnetic Waves: Waves in One Dimension, Electromagnetic Waves in Vacuum, Electromagnetic Waves in Matter, Absorption and Dispersion, Guided Waves.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied the module students will be familiar with the formal theory of quantum mechanics and have an ability to use the theory to solve standard problems for model systems\n* They will have a quantum mechanical understanding of the basic properties of the hydrogen atom and be able to use quantum theory to calculate various aspects of physical behaviour\n* They will be able to carry out simple quantum mechanical calculations using the variational method and time-independent perturbation theory\n* They will be familiar with and able to manipulate and solve Maxwell's equations in a variety of standard situations\n* They will have an understanding of how the electrical and magnetic properties of simple media can be represented, and an appreciation of the key concepts relating to the propagation and radiation of electromagnetic waves in free space and simple media.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and tutorial-style workshops\n* The lectures provide the means to give concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times\n* Student performance will be summatively assessed through a written examination and an online test and formatively assessed through problem exercises and a progress test. The written examination and online test will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress test and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2581" . . "Presential"@en . "TRUE" . . "Foundations of physics 2b"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).\n\n#### Corequisites\n\n* Foundations of Physics 2A (PHYS2581) AND (Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables II (MATH2031) which covers similar material).\n\n#### Excluded Combination of Modules\n\n* None\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 1 module Foundations of Physics 1 (PHYS1122) by providing courses on Thermodynamics, Condensed Matter Physics and Optics.\n\n#### Content\n\n* The syllabus contains:\n* Thermodynamics: Basic ideas, zeroth law and temperature; Definitions of state variables; the first law of thermodynamics; Heat engines and the second law of thermodynamics; Clausius inequality, Entropy and entropy change in reversible and non-reversible processes; Availability of Energy; Heat and refrigeration cycles; Thermodynamic Potentials and Maxwell's relations; Equilibrium, equations of state and phase transitions; Low temperatures and third law of thermodynamics; thermodynamics of other systems; Basic postulates of statistical mechanics; kinetic theory; Boltzmann formulation of entropy; Stirling's approximation; Boltzmann distribution function; Relationship between entropy and number of microstates in a macrostate; Bose-Einstein and Fermi-Dirac distribution functions.\n* Condensed Matter Physics: Review of crystal structures and their description; Wave Diffraction and the Reciprocal Lattice; Crystal binding and Elastic Constants; Bose and Fermi distributions; Phonons; The Drude model; Free Electron Fermi Gas Model; Energy Bands; Bending of energy bands close to the Brillouin zone boundary; Metals, Semimetals and Insulators.\n* Optics: Light as a wave: Superposition principle, spatial frequency; Intensity; Scalar approximation; Plane waves, spherical/cylindrical waves, and phasors; Interference – Young’s double slit, Michelson interferometer; Polarisation, Linear/circular basis, Malus’ law, Birefringence, Optical activity and the Faraday effect; Many waves: Multiple slits and the Fresnel diffraction integral; Fresnel and Fraunhofer diffraction; Laser beams.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will have an understanding of the thermodynamics of matter, the four laws of thermodynamics and their application.\n* They will have appreciation of distributions of classical and quantum particles leading to a discussion of entropy and temperature.\n* They will have the ability to describe the arrangement of atoms in a crystal structure and the diffraction pattern that results in both direct and reciprocal space.\n* They will have an understanding of elastic vibrations of atoms in crystals and how these vibrations are quantised into phonons.\n* They will have knowledge of the concept of phonons and how these explain the thermal properties of solids.\n* They will have knowledge of the breakdown in classical physics and how to apply quantum mechanics to the study of electrons in crystalline solids, the nature of electron states and how metallic, semiconducting and insulating materials arise.\n* They will have an appreciation of X-ray and neutron scattering as a probe of crystal structure, vibrational, and electronic properties of solids in 2 and 3 dimensions.\n* They will be able to use analytical methods to describe a range of wave phenomena, including interference, diffraction and polarisation, and will be familiar with their applications in optics.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and tutorial-style workshops.\n* The lectures provide the means to give concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through a written examination and an online test and formatively assessed through problem exercises and a progress test. The written examination and online test will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress test and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2591" . . "Presential"@en . "TRUE" . . "Stars and galaxies"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).\n\n#### Corequisites\n\n* None\n\n#### Excluded Combination of Modules\n\n* None\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It provides an introduction to Astronomy and the foundations for Astrophysics courses in later years.\n\n#### Content\n\n* The syllabus contains:\n* Telescopes; Binary stars and Stellar Parameters; The Classification of Stellar Spectra; Stellar Atmospheres; The Interior of Stars; The Sun; The Process of Star Formation; Post-Main-Sequence Stellar Evolution; Stellar Pulsation; The Degenerate Remnants of Stars; Black Holes; Close Binary Systems; The Milky Way Galaxy; The Nature of Galaxies; Galactic Evolution.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will be aware of the basic techniques of observational astronomy.\n* They will understand the basic physics of stellar interiors.\n* They will appreciate why we see stars of widely differing colours and brightnesses.\n* They will have had their understanding of stellar properties and physics extended to pulsating and binary stars.\n* They will have an introductory knowledge of galactic and extragalactic astronomy.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and tutorial-style workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of the written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress test and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2621" . . "Presential"@en . "TRUE" . . "Mathematical methods in physics"@en . . "20.0" . "#### Prerequisites\n\n* (Foundations of Physics 1 (PHYS1122) OR Physics for Geoscientists (GEOL1121)) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).\n\n#### Corequisites\n\n* None\n\n#### Excluded Combination of Modules\n\n* Analysis in Many Variables II (MATH2031).\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It supports the Level 2 modules Foundations of Physics 2A (PHYS2611) and Foundations of Physics 2B (PHYS2621) by supplying the necessary mathematical tools.\n\n#### Content\n\n* The syllabus contains:\n* Vector algebra.\n* Matrices and vector spaces.\n* Vector calculus.\n* Line and surface integrals.\n* Fourier series.\n* Fourier transforms.\n* Laplace transforms.\n* Higher order ODEs.\n* Series solution of ODEs.\n* PDEs: general and particular solutions.\n* PDEs: separation of variables.\n* Special functions.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will be familiar with some of the key results of vectors, vector integral and vector differential calculus, multivariable calculus and orthogonal curvilinear coordinates, Fourier analysis, orthogonal functions, the use of matrices, and with important mathematical tools for solving ordinary and partial differential equations occurring in a variety of physical problems.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and tutorial-style workshops.\n* The lectures provide the means to give concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of recommended textbooks for the module, making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress test and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2611" . . "Presential"@en . "TRUE" . . "Laboratory skills and electronics"@en . . "20.0" . "#### Prerequisites\n\n* Discovery Skills in Physics (PHYS1101) AND Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).\n\n#### Corequisites\n\n* None\n\n#### Excluded Combination of Modules\n\n* None\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on laboratory skills, such as experiment planning, data analysis, scientific communication and specific practical skills, encountered in the module PHYS1101 Discovery Skills in Physics.\n* It aims to teach electronics as a theoretical and a practical subject, to teach the techniques of computational physics and numerical methods and to provide experience of a research-led investigation in Physics.\n* To encourage students to think about their post-university careers, to provide them with a range of employability information and to introduce them to applications of physics in enterprises.\n\n#### Content\n\n* A team-based project, undertaken in June of the previous academic year, providing a transition from Level 1 to Level 2 laboratory work.\n* Activities to develop skills in data interpretation, experiment design, specific practical techniques, report writing, error analysis, team working and critical thinking.\n* Electronics lectures: Analogue Electronics: Components: Introduction to electrical circuit theory, networks, AC theory, passive filters; systems: noise. Digital Electronics: interfacing with microcontrollers, signal acquisition.\n* Electronics practical activities.\n* Performance of an extended practical project.\n* Computational physics: numerical differentiation and integration, numerical solutions of ordinary differential equations in one and multiple dimensions, numerical optimisation, simulation of random processes.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will know how to plan experiments and to interpret data quantitatively and systematically.\n* They will understand the theoretical principles of basic electronics.\n* They will have formed a detailed appreciation of the physics underlying a particular project and be prepared to undertake and report on similar projects.\n* They will know how to structure physics problems and their computational solutions.\n\nSubject-specific Skills:\n\n* Students will have specific practical skills generally useful in practical physics.\n* They will have developed practical skills in electronics and signal acquisition.\n* They will be able to apply their programming skills to solve problems using numerical methods.\n\nKey Skills:\n\n* Students will have developed their written presentation skills sufficiently to be able to write fluent and well-structured reports, including lay summaries.\n* They will be able to work successfully as part of a team to solve an open-ended problem.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures, practical sessions, workshops and project work.\n* The open-ended \"bridge project\" is undertaken in June of the previous academic year, providing a transition from Level 1 to Level 2 practical work. Students will work in teams on an extended project lasting the equivalent of one week, which will develop their problem-solving and teamwork skills. (Students who are unable, for good reason, to undertake the bridge project in June will undertake an equivalent project in the following Easter Term.)\n* The practical sessions are small group activities designed to develop skills in data interpretation, experiment design, team working, specific practical techniques and reporting, and critical reading of relevant scientific papers. The skills covered form the foundation needed for the research-led investigation in the second term and for later practical work. Students will be able to obtain help and guidance from discussions with laboratory demonstrators.\n* The electronics course aims to give a theoretical grounding in the elements of electronics “analogue circuits, interfacing using microcontrollers“ with practical activities to provide a working knowledge of the subject.\n* The computational physics lectures aim to give a theoretical grounding in the elements of computational physics and numerical methods, while the workshops provide opportunities for practice and discussion of the algorithms.\n* Regular exercises in coding algorithms, to be submitted and checked electronically, will give students practice in applying these principles and will form the basis for discussion in the workshops.\n* Student performance is summatively assessed through an online report on the \"bridge project\", through a formal report for the skills sessions, through an electronics practical assessment exercise, through a formal report for the research-led investigation and through exercises.\n* The practical classes, workshops and exercises provide opportunity for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n* Invited speakers give presentations on employability and the applications of physics in enterprises.\n\nMore details at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2641" . . "Presential"@en . "TRUE" . . "Theoretical physics 2"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).\n\n#### Corequisites\n\n* Foundations of Physics 2A (PHYS2581).\n\n#### Excluded Combination of Modules\n\n* Mathematical Physics II (MATH2071).\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It provides a working knowledge of classical mechanics and complements the quantum mechanics content of the module Foundations of Physics 2A by providing theoretical rigour.\n\n#### Content\n\n* The syllabus contains:\n* Classical Mechanics: Lagrangian mechanics; Variational calculus and its application; Linear oscillators; One-dimensional systems and central forces; Noether's theorem and Hamiltonian mechanics; Theoretical mechanics; Rotating coordinate systems; Dynamics of rigid bodies; Theory of small vibrations.\n* Quantum Theory: State of a system and Dirac notation; Linear operators, eigenvalues, Hermitean operators; Expansion of eigenfunctions; Commutation relations, Heisenberg uncertainty; Unitary transforms; Matrix representations; Schrodinger equation and time evolution; Schrodinger, Heisenberg and Interaction pictures; Symmetry principles and conservation; Angular momentum (operator form); Orbital angular momentum (operator form); General angular momentum (operator form); Matrix representation of angular momentum operators; Spin angular momentum; Spin ½; Pauli spin matrices; Total angular momentum; Addition of angular momentum.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will have developed an appreciation of the Lagrangian and Hamiltonian formulations of classical mechanics and be able to describe the rotational motion of a rigid body.\n* They will be able to describe elements of quantum mechanics in a rigorous mathematical way and to manipulate them at the operator level.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and tutorial-style workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of the written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress test and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore details at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2631" . . "Presential"@en . "FALSE" . . "Physics in society"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 1 (PHYS1122) AND Discovery Skills in Physics (PHYS1101).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* To give students an insight into the history, philosophy, communication and ethics of physics.\n* To provide experience of a research-led project in physics.\n* To give students experience in communicating physics using modern digital media.\n\n#### Content\n\n* History of Physics: Physics and mathematics in the ancient world; Mediaeval European and Arabic science; Copernicus to Newton and the rise of cosmology; classical fields, fluids, electromagnetism and the birth of relativity; the quantum revolution.\n* Philosophy of Physics: Introduction to the philosophy of science; induction and falsification; paradigms; research programmes; Feyerabend's case against method; the Bayesian approach; why physics is special; case studies in the philosophy of physics.\n* Communicating Physics: Physics in the media; citizen science; presenting complex physical concepts; the use and misuse of statistics; communication, science and policymaking.\n* Ethics: Ethical review of experiment design; institutional ethics; personal behaviour; pathological science: deliberate fraud or unfortunate mistakes?\n* Case Studies: Topics taken from the following: climate and ocean physics; geophysics; physics at the movies and physics of sport; energy; musical physics; physics of finance.\n* In the Epiphany Term students will work in teams to create a digital media output (such as a website or app) which communicates a concept in physics. Students will choose from a wide list of broad possible topics, and will devise their own approach to communicating the topic in the light of the topics covered in the lectures. Students will be expected to work independently and to manage the direction of their work. Each team will be assigned a member of staff as supervisor. Students will be expected to decide on a suitable method or framework to use to produce their work, including self-directed learning.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied the module students will be familiar with some of the key milestones in the history of physics and some of the key topics in the philosophy of physics, in science communication and in ethics in academia.\n* They will have formed an appreciation of the physics underlying a particular topic.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to communicate a concept in physics, using modern digital media, to a non-specialist audience.\n* They will be able to demonstrate technical competence in modern digital media.\n\nKey Skills:\n\n* They will be able to work successfully as part of a team.\n* They will be able to manage their time effectively.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures, supervisor meetings, group work and self-directed learning.\n* The lectures provide the means to give concise, focused presentation of the subject matter of the module. The lecture material will be explicitly linked to the contents of the recommended textbooks or other resources for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online. Some of the lectures will incorporate interactive discussions.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* The supervisor meetings relate to the digital media project. Each team will have an initial meeting with the supervisor towards the end of the Michaelmas Term, followed by three further meetings in Epiphany Term.\n* Students will be expected to work on their project, both as a group and individually, between the supervisor meetings. This work is to be organised by the students themselves, thereby enabling them to demonstrate their time management skills.\n* Students will undertake independent research to further their knowledge of the topic and self-directed learning to further their technical skills.\n* Student performance will be summatively assessed through an online test and a digital media project. The test will provide the means for students to demonstrate the acquisition of subject knowledge relating to the lectures. The project will provide the means for students to demonstrate their ability to communicate a concept in physics using modern digital media; it will include a group assessment of the project output plus an assessment of each student's personal contribution via a short individual interview, guided by peer assessment.\n* The supervisor meetings provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the project. The final meeting will take the form of individual interviews.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2651" . . "Presential"@en . "FALSE" . . "Foundations of physics 3a"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 2A (PHYS2581) AND (Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables (MATH2031)).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 2 modules Foundations of Physics 2A (PHYS2581) and Mathematical Methods in Physics (PHYS2611) by providing courses on Quantum Mechanics and Nuclear and Particle Physics appropriate to Level 3 students.\n\n#### Content\n\n* The syllabus contains:\n* Quantum Mechanics: Introduction to many-particle systems (wave function for systems of several particles, identical particles, bosons and fermions, Slater determinant); the variational method (ground state, excited states, trial functions with linear variational parameters); the ground state of two-electron atoms; the excited states of two-electron atoms (singlet and triplet states, exchange splitting, exchange interaction written in terms of spin operators); complex atoms (electronic shells, the central-field approximation); time-dependent perturbation theory; Fermi’s Golden Rule; periodic perturbations; the Schrödinger equation for a charged particle in an electromagnetic field; the dipole approximation; transition rates for harmonic perturbations; absorption and stimulated emission; Einstein coefficients; spontaneous emission; selection rules for electric dipole transitions; lifetimes; the interaction of particles with a static magnetic field (spin and magnetic moment, particle of spin one-half in a uniform magnetic field, charged particles with uniform magnetic fields; Larmor frequency; Landau levels); one-electron atoms in magnetic fields.\n* Nuclear and Particle Physics: Fundamental Interactions, symmetries and conservation Laws, global properties of nuclei (nuclides, binding energies, semi-empirical mass formula, the liquid drop model, charge independence and isospin), nuclear stability and decay (beta-decay, alpha-decay, nuclear fission, decay of excited states), scattering (relativistic kinematics, elastic and inelastic scattering, cross sections, Fermi’s golden rule, Feynman diagrams), geometric shapes of nuclei (kinematics, Rutherford cross section, Mott cross section, nuclear form factors), elastic scattering off nucleons (nucleon form factors), deep inelastic scattering (nucleon excited states, structure functions, the parton model), quarks, gluons, and the strong interaction (quark structure of nucleons, quarks in hadrons), particle production in electron–positron collisions (lepton pair production, resonances), phenomenology of the weak interaction (weak interactions, families of quarks and leptons, parity violation), exchange bosons of the weak interaction (real W and Z bosons), the Standard Model, quarkonia (analogy with Hydrogen atom and positronium, Charmonium, quark–antiquark potential), hadrons made from light quarks (mesonic multiplets, baryonic multiplets, masses and decays), the nuclear force (nucleon–nucleon scattering, the deuteron, the nuclear force), the structure of nuclei (Fermi gas model, shell Model, predictions of the shell model).\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will be familiar with some of the key results of quantum mechanics including perturbation theory and its application to atomic physics and the interaction of atoms with light.\n* They will be able to describe the properties of nuclei and how nucleons interact and have an appreciation of the key ingredients of the Standard Model of particle physics.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through a written examination and an online test and formatively assessed through problem exercises and a progress test. The written examination and online test will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises and progress test will provide opportunities for feedback, for students to gauge their progress, and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3621" . . "Presential"@en . "TRUE" . . "Foundations of physics 3b"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 2A (PHYS2581) AND Foundations of Physics 2B (PHYS2591) AND (Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables (MATH2031)).\n\n#### Corequisites\n\n* Foundations of Physics 3A (PHYS3621)\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 2 modules Foundations of Physics 2A (PHYS2581), Foundations of Physics 2B (PHYS2591) and Mathematical Methods in Physics (PHYS2611) by providing courses on Statistical Physics and Condensed Matter Physics appropriate to Level 3 students.\n\n#### Content\n\n* The syllabus contains:\n* Statistical Physics: Introduction and basic ideas:- macro and microstates, distributions; distinguishable particles, thermal equilibrium, temperature, the Boltzmann distribution, partition functions, examples of Boltzmann statistics: spin-1/2 solid and localized harmonic oscillators; Gases: the density of states: fitting waves into boxes, the distributions, fermions and bosons, counting particles, microstates and statistical weights; Maxwell-Boltzmann gases: distribution of speeds, connection to classical thermodynamics; diatomic gases: Energy contributions, heat capacity of a diatomic gas, hydrogen; Fermi-Dirac gases: properties, application to metals and helium-3; Bose-Einstein gases: properties, application to helium-4, phoney bosons; entropy and disorder, vacancies in solids; phase transitions: types, ferromagnetism of a spin-1/2 solid, real ferromagnetic materials, order-disorder transformations in alloys; statics or dynamics? ensembles, chemical thermodynamics: revisiting chemical potential, the grand canonical ensemble, ideal and mixed gases; dealing with interactions: electrons in metals, liquid helium 3 and 4, real imperfect gases; statistics under extreme conditions: superfluid states in Fermi-Dirac systems, statics in astrophysical systems.\n* Condensed Matter Physics: Review of the effect of a periodic potential, energy gap; reduced and periodic zone schemes; semiconductor crystals: crystal structures, band gaps, equations of motion, carrier concentrations of intrinsic and extrinsic semiconductors, law of mass action, transport properties, p-n junction; superconductivity: Meissner effect, London equation, type I and type II superconductors, thermodynamics of superconductors, Landau-Ginzburg theory, Josephson junctions; diamagnetism and paramagnetism: Langevin equation; quantum theory of paramagnetism, Hund’s rules, crystal field splitting, paramagnetism of conduction electrons; ferromagnetism and antiferromagnetism: Curie point, exchange integral, magnons, antiferromagnetism, magnetic susceptibility, dielectrics and ferroelectrics: macroscopic and local electric fields, dielectric constant and polarizilbility, structural phase transitions.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will understand the use of statistical concepts such as temperature and entropy and models to describe systems with a large number of weakly interacting particles.\n* They will build on their knowledge of nearly-free electron theory, and other concepts gained at Level 2, to explain the properties of semiconductors, superconductors, dielectric and magnetic materials.\n* They will understand the common theoretical treatment of quasiparticles and the experimental techniques used to understand the behaviour of materials.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through a written examination and an online test and formatively assessed through problem exercises and a progress test. The written examination and online test will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises and progress test will provide opportunities for feedback, for students to gauge their progress, and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3631" . . "Presential"@en . "TRUE" . . "Planets and cosmology 3"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 1 (PHYS1122).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It provides a knowledge appropriate to Level 3 students of the astrophysical origin of planetary systems and the cosmological origin of the Universe.\n\n#### Content\n\n* The syllabus contains:\n* Planetary Systems: Overview of the Solar System, orbital dynamics, planetary interiors, planetary atmospheres, formation of the Solar System, extrasolar planets.\n* Cosmology: Observational overview and the expansion of the Universe, the cosmological principle (homogeneity and isotropy), Newtonian gravity and the Friedmann equation, the geometry of the Universe, solutions of Friedmannʼs equations, the age of the Universe, weighing the Universe, the cosmological constant, general relativistic cosmology (the metric and Einstein equations), classic cosmology (distances and luminosities), type Ia SNe and galaxy number counts, the cosmic microwave background, the thermal history of the Universe, primordial nucleosynthesis, dark matter, problems with the hot big bang, inflation, current constraints on cosmological parameters.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will understand the formation and workings of our Solar System, its orbital dynamics, and the basic physics of planetary interiors and atmospheres.\n* They will be familiar with mathematical models for the expansion, thermal history, material and energy content of a homogeneous isotropic universe, and will understand the physical basis of the model and the observational evidence that constrains it.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises and progress test provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3651" . . "Presential"@en . "TRUE" . . "Computing project"@en . . "20.0" . "#### Prerequisites\n\n* Laboratory Skills and Electronics (PHYS2641) AND Foundations of Physics 1 (PHYS1122).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Science degree programmes.\n* To develop students’ problem-solving skills in advanced computational physics.\n* To develop computer skills.\n* To reproduce and then extend the results of a classic research paper.\n* To develop transferable skills in researching a topic and making oral and written presentations on the findings.\n\n#### Content\n\n* The syllabus contains:\n* Use of a computer to solve problems using a variety of modern computing techniques and the preparation of written and oral presentations.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will have formed an appreciation of the physics related to a chosen topic.\n\nSubject-specific Skills:\n\n* Students will have gained experience of solving physical problems using modern computing techniques.\n* They will have the skills to plan and carry out an extended project at an advanced level.\n* They will have demonstrated knowledge of scientific background and theoretical considerations.\n* They will have demonstrated the ability to produce a clear, detailed scientific report with appropriate presentation and lay summary.\n\nKey Skills:\n\n* Students will have the necessary skills to make written and oral presentations on their work.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures, computer classes and tutorials.\n* The lectures include training on general computing, testing and debugging.\n* The computer classes are designed to allow each student to obtain help and guidance through discussions with computing demonstrators.\n* The skills covered are transferable to a wide range of activities.\n* The tutorials provide support for research into an advanced topic of choice, develop skills in solving problems using modern computing techniques and provide a forum for developing oral and written presentation skills.\n* Students receive guidance and feedback on their presentation to the tutorial group and on their poster.\n* Student performance is formatively assessed through a milestone computer program and summatively assessed through the computing project.\n* The tutorials and computing classes provide opportunity for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3561" . . "Presential"@en . "TRUE" . . "Team project"@en . . "20.0" . "#### Prerequisites\n\n* Laboratory Skills Electronics (PHYS2641).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 2 module Laboratory Skills and Electronics (PHYS2641).\n* It allows students to experience the application of physical principles to the solution of a scientific question placed in an industrial/research context.\n\n#### Content\n\n* Team projects involve a group of up to six students working on a physics-related problem set by either members of staff from the Department or by local industry.\n* The problem will be 'real' in that there is no 'correct' solution and no script.\n* It might, for example, involve building a piece of equipment, testing a product, designing a control system, etc.\n* A presentation is made by the team at the end of the project.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\nSubject-specific Skills:\n\n* Having studied this module students will be able to solve an advanced scientific problem using physical principles.\n\nKey Skills:\n\n* Students will be able to respond to a briefing on a problem by a client.\n* They will be able to work successfully as part of a team to address the problem.\n* They will be able to make a final presentation on the outcome of the work.\n* They will be able to produce a clear and well-structured report, including lay summary.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Team projects involve a group of up to six students on a physics related problem in either the Michaelmas or Epiphany terms.\n* Experimental work will be based in the department and the problem to be tackled will be set either by members of staff from the Department or by local industry.\n* Students will be expected to evolve their own approach to the problem, organise themselves and work effectively as a team.\n* Student performance is summatively assessed through a short written report on the project and an oral presentation.\n* The practical classes provide opportunity to obtain advice from staff members, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3581" . . "Presential"@en . "FALSE" . . "Advanced laboratory"@en . . "20.0" . "#### Prerequisites\n\n* Laboratory Skills and Electronics (PHYS2641).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 2 module Laboratory Skills and Electronics (PHYS2641) and allows students to undergo an extended experiment-based project at an advanced level.\n\n#### Content\n\n* During the module, students will plan and execute an extended experiment-based project at an advanced level in either astrophysics, modern optics, high energy physics or condensed matter physics.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\nSubject-specific Skills:\n\n* Having studied this module students will have the skills to plan and carry out an extended experiment-based project at an advanced level.\n* They will have demonstrated knowledge of scientific background and theoretical considerations.\n* They will have demonstrated the ability to describe experimental details and procedures and to apply appropriate data analysis techniques.\n* They will have demonstrated the ability to produce a clear, detailed scientific report with appropriate presentation and lay summary.\n* They will have shown an understanding of good experimental practice.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by a mixture of independent project work and formal supervision.\n* The format is individual or small group extended experiment-based projects.\n* Students will be able to obtain help and guidance from the laboratory scripts and through discussions with laboratory demonstrators and leaders.\n* Students are expected to keep an electronic laboratory notebook, including a formal project plan.\n* Student performance is summatively assessed through technical performance during the project and through a formal report on the project.\n* The supervisory arrangements, formative assessment and electronic notebooks provide opportunity for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3601" . . "Presential"@en . "FALSE" . . "Mathematics workshop"@en . . "20.0" . "#### Prerequisites\n\n* Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables II (MATH2031).\n\n#### Corequisites\n\n* Foundations of Physics 3A (PHYS3621).\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 2 module Mathematical Methods in Physics (PHYS2611).\n* It provides the mathematical tools appropriate to Level 3 physics students necessary to tackle a variety of physical problems.\n\n#### Content\n\n* The syllabus contains:\n* Vectors and matrices, Hilbert spaces, linear operators, matrices, eigenvalue problem, diagonalisation of matrices, co-ordinate transformations, tensor calculus.\n* Complex Analysis: functions of complex variables, differentiable functions, Cauchy-Riemann conditions, Harmonic functions, multiple valued functions and Riemann surfaces, branch points and cuts, complex integration, Cauchy's theorem, Taylor and Laurent series, poles and residues, residue theorem and definite integrals, residue theorem and series summation.\n* Calculus of Variations: Euler–Lagrange equations, classic variational problems, Lagrange multipliers.\n* Infinite series and convergence, asymptotic series. Integration, Gaussian and related integrals, gamma function.\n* Integral Transforms: Fourier series and transforms, convolution theorem, Parseval's relation, Wiener-Khinchin theorem. Momentum representation in quantum mechanics, Hilbert transform, sampling theorem, Laplace transform, inverse Laplace transform and Bromwich integral.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will have knowledge of and an ability to use a range of mathematical methods needed to solve a wide array of physical problems.\n\nSubject-specific Skills:\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by two-hour workshops which are a mix of lectures and examples classes.\n* The lectures provide the means to give a concise, focussed presentation of the subject matter of the module. The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.\n* When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* New material is immediately backed up by example classes which give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, during the workshop sessions or at other mutually convenient times.\n* Student performance will be summatively assessed through two open-book examinations.\n* The example classes provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3591" . . "Presential"@en . "FALSE" . . "Physics into schools"@en . . "20.0" . "#### Prerequisites\n\n* At least two Level 2 modules in Physics; DBS check; successful completion of interview (by module co-ordinator; experienced, qualified science teacher; academic in the Department of Physics; member of the Science Outreach and Engagement Team).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* BIOL3431 Biology Into Schools, CHEM3081 Chemistry Into Schools, COMP3421 Computer Science into Schools, ENGI4321 L4 Engineering Into Schools, GEOL3251 Earth Sciences into Schools, and MATH3481 Mathematics into Schools.\n\n#### Aims\n\n* To develop a range of key skills in the student and to offer an early taste of teaching Physics to those interested in pursuing it as a career or for other career pathways where public understanding of science is required.\n* To help students gain confidence in communicating Physics, develop strong organisational and interpersonal skills, and understand how to address the needs of individuals.\n* To learn to devise and develop Physics projects and teaching methods appropriate to engage the relevant age group they are working with.\n* To help inspire a new generation of Physicists as prospective undergraduates by providing role models for school pupils.\n* To help teachers convey the excitement of their subject to pupils by showing them the long-term applications of school studies, especially the cross disciplinary relationships of Physics.\n* To help teachers by providing an assistant who can work with and support pupils at any point on the ability spectrum.\n\n#### Content\n\n* A competitive interview system will be used to match students with appropriate schools and a specific teacher in the local area, and each student selected will be given a chance to visit the school they will be working in before commencement of the placement.\n* One day training course on working in schools and with pupils.\n* Series of lectures on key transferable skills.\n* The student will be required to spend half a day (approx 4hrs) a week in the school every week for at least 10 weeks.\n* Tutorials which will provide an opportunity for students to share their experiences.\n* The students will be involved in the following activities in support of their learning and teaching:\n* Classroom observation and assistance: Initial contact with the teacher and pupils will be as a classroom assistant, watching how the teacher handles the class, observing the level being taught and the structure of the lesson, and offering practical support to the teacher.\n* Teaching assistance: The teacher will assign the student with actual teaching tasks, which will vary dependent on specific needs and the student's own ability as it develops over the term. This could include for example offering problem-solving coaching to a smaller group of higher ability pupils, or taking the last ten minutes of the lesson for the whole class. The student will have to demonstrate an understanding of how the level of the knowledge of the pupils they are teaching fits in to their overall learning context in other subjects.\n* Whole class teaching: Students will typically be offered, in collaboration with their teachers, at least one opportunity to undertake whole class teaching, albeit that it may be only for a small part of the lesson.\n* University awareness: Students will represent and promote their academic discipline as a potential university choice to pupils across the social and academic range represented at their partner schools.\n* Special projects: The student will devise a special Physics project on the basis of discussion with the teacher and module co-ordinator and their own assessment of what will interest the particular pupils they are working with. The student will implement the special project and evaluate it. The student will be required to show that they can analyse a specific teaching problem and devise and prepare appropriately targeted teaching materials, practical demonstrations and basis 'tests' where appropriate.\n* Extra-curricular projects: The student may be supervised by the teacher in helping to run an out-of-timetable activity, such as a lunchtime club or special coaching periods for higher ability pupils. The student will have to demonstrate an ability to think laterally in order to formulate interesting ways to illustrate more difficult scientific concepts.\n* Written reports: The student will keep a journal of their own progress in working in the classroom environment, and they will be asked to prepare a written report on the special project.\n* The teachers will act as the main source of guidance in the schools but, in addition, the students will also be able to discuss progress with the module co-ordinator or a member of the Science Outreach and Engagement Team whenever necessary.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* On successful completion of this module students:\n* Will be able to assess and devise appropriate ways to communicate a difficult principle or concept.\n* Will have gained a broad understanding of many of the key aspects of teaching in schools.\n* Will have an advanced understanding of Physics through having to explain to others.\n* Will have an advanced understanding of the problems of public perception of science.\n\nSubject-specific Skills:\n\n* On successful completion of this module students:\n* Will know the responsibilites and appropriate conduct for a teacher.\n* Will know how to give (and take) feedback on Physics issues.\n* Will be able to undertake public speaking on Physics generally.\n* Will know how to prepare lesson plans and teaching materials for Physics.\n\nKey Skills:\n\n* On successful completion of this module students:\n* Will be able to communicate effectively, both one to one and with small groups.\n* Will be able to understand the needs of individuals.\n* Will be able to use interpersonal skills when dealing with colleagues.\n* Will be able to improvise when necessary.\n* Will be able to organise, prioritise and negotiate.\n* Will know how to work with others in teams.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* This module includes an initial training course, lectures, tutorials and a school placement.\n* The initial training course provides an introduction to working in schools and with pupils. The lectures provide the means to give a concise, focused presentation on generic aspects of key transferable skils (e.g. teaching and learning skills and presentation skills). The lecture material will be explicitly linked to scenarios that are likely to arise in the school placement. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* The tutorials will provide opportunity for students to share their experiences and to discuss specific issues in Physics education and the public perception of science, giving them the chance to develop their theoretical understanding and communication skills. Students will be able to obtain further help in their studies by approaching the course leaders, either after lectures or tutorials or at other mutually convenient times.\n* The school placement allows the student to develop a range of interpersonal skills and the professional competencies expected of an effective teacher (or a facilitator to others), thus ensuring that the learning outcomes are met. Student performance will be summatively assessed through a Journal of Teaching Activity, an End of Module Report, an End of Module Presentation and a Teacher's Assessment.\n* The Journal of Teaching Activity and End of Module Report will provide the means for students to reflect on their experience of the school placement and on their own personal development, and to demonstrate written communication skills.\n* The End of Module Presentation will enable students to give a practical demonstration of teaching competencies including oral communication skills.\n* The Teacher's Assessment is an independent corroboration of progress, including the student's approach and attitude, appreciation of key educational issues, aptitude and potential as a science communicator and performance in the Special Project.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3611" . . "Presential"@en . "FALSE" . . "Theoretical physics 3"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 2A (PHYS2581) AND Theoretical Physics 2 (PHYS2631) AND (Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables (MATH2031)).\n\n#### Corequisites\n\n* Foundations of Physics 3A (PHYS3621).\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 2 modules Foundations of Physics 2A (PHYS2581) and Theoretical Physics 2 (PHYS2631) by introducing more advanced methods in electromagnetism that can be used to investigate more realistic problems and concepts, and by introducing more advanced topics in quantum mechanics as well as addressing further applications and conceptual issues of measurement and interpretation.\n\n#### Content\n\n* The syllabus contains:\n* Relativistic Electrodynamics: Einstein’s postulates, the geometry of relativity, Lorentz transformations, structure of space-time, proper time and proper velocity, relativistic energy and momentum, relativistic kinematics, relativistic dynamics, magnetism as a relativistic phenomenon, how the fields transform, the field tensor, electrodynamics in tensor notation, relativistic potentials, scalar and vector potentials, gauge transformations, Coulomb gauge, retarded potentials, fields of a moving point charge, dipole radiation, radiation from point charges.\n* Quantum Theory: Scattering experiments and cross sections; potential scattering (general features); spherical Bessel functions (application: the bound states of a spherical square well); the method of partial waves (scattering phase shift, scattering length, resonances, applications); the integral equation of potential scattering; the Born approximation; collisions between identical particles, introduction to multichannel scattering; the density matrix (ensemble averages, the density matrix for a spin-1/2 system and spin-polarization); quantum mechanical ensembles and applications to single-particle systems; systems of non-interacting particles (Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics, ideal Fermi-Dirac and Bose-Einstein gases); the Klein-Gordon equation; the Dirac equation; covariant formulation of Dirac theory; plane wave solutions of the Dirac equation; solutions of the Dirac equation for a central potential; negative energy states and hole theory; non-relativistic limit of the Dirac equation; measurements and interpretation (hidden variables, the EPR paradox, Bell’s theorem, the problem of measurement).\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will have developed a working knowledge of tensor calculus, and be able to apply their understanding to relativistic electromagnetism.\n* They will have a systematic understanding of quantum theory, including collision theory and relativistic quantum mechanics.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises and progress test provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3661" . . "Presential"@en . "FALSE" . . "Condensed matter physics 3"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 2A (PHYS2581) AND Foundations of Physics 2B (PHYS2591) AND (Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables (MATH2031))\n\n#### Corequisites\n\n* Foundations of Physics 3A (PHYS3621) AND Foundations of Physics 3B (PHYS3631)\n\n#### Excluded Combination of Modules\n\n* None\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It illustrates the relevant physics utilised in modern condensed matter physics based on scale, symmetry and the structure of matter and contains both material on \"hard\" condensed matter and an introduction to topics in soft matter physics.\n\n#### Content\n\n* Symmetry structure and excitations: Overview of energy, length and time scales in different areas of CMP. Comparison of hard CMP and soft CMP. Cohesion in solids. Introduction to symmetry and its influence on physical properties. The symmetry of crystals. Measuring structure using diffraction. Elementary excitations from a ground state: single particles and collective excitations in solids. Phonons in a system with a two atom basis: acoustic and optic branches. Anharmonic effects, soft modes. Measuring excitations using scattering and spectroscopy.\n* Introduction to soft matter physics: Introduction to soft matter physics and its basic phenomenology. Polymer physics and scaling. Liquid crystals. Free energies. Diffusion (Einstein diffusion coefficients, Peclet number and Fick’s laws). Elasticity of solids.\n* Broken symmetry: Symmetry breaking at phase transitions as a method of classifying the phenomena studied in CMP. Phase transitions and critical exponents. Excitations in a broken symmetry system. Generalised rigidity and order. Topological defects. How other systems fit into this framework: superconductors and superfluids; classical examples (binary fluids, polymers, liquid crystals etc.); weak interactions in the standard model, cosmological examples. Other topological objects: vortices, monopoles, skyrmions (in outline). Applications of broken symmetry systems.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will have an understanding of the themes of modern condensed matter research, and an appreciation of role of scales, symmetry and the structure of matter. They will have become familiar with the physics of a number of examples taken from across the subject.\n* They will understand the elements of soft matter structure, its dynamics, elasticity and phase transitions.\n* They will understand the notion of broken symmetry and its consequences and an appreciation of the classification of phenomena in solids that this allows.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises and progress test provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3711" . . "Presential"@en . "FALSE" . . "Modern atomic and optical physics 3"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 2A (PHYS2581) AND Foundations of Physics 2B (PHYS2591) AND (Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables (MATH2031))\n\n#### Corequisites\n\n* Foundations of Physics 3A (PHYS3621)\n\n#### Excluded Combination of Modules\n\n* None\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on Level 2 courses in geometric optics and quantum mechanics by providing courses on modern optics and atomic physics.\n\n#### Content\n\n* Fourier Optics: Fourier toolkit, angular spectrum, Gaussian beams, lasers and cavities, Fresnel and Fraunhofer, 2D diffraction – letters, circles, Babinet and apodization, lenses, imaging, spatial filtering.\n* Atomic Clocks: History of precision measurement of time. Principle of atomic clocks, revision of atomic structure, electric and magnetic dipole interactions with electromagnetic fields, selection rules. Visualising electron distributions in atoms during transitions. Spontaneous emission, Einstein A coefficient and relationship with atomic clocks, lifetimes, line widths, line intensities and line shapes. Fine-structure and hyperfine splitting, using degenerate perturbation theory to calculate the ground-state hyperfine splitting of the H atom. Lifetimes of electric dipole forbidden transitions, selection rules and relationship with atomic clocks. Zeeman effect, using degenerate perturbation theory to calculate Zeeman shifts of the hyperfine states of the ground-state of the H atom, relationship with atomic clocks. Derivation of Rabi equation for two-level system, transit-time broadening, relationship with atomic clocks. Light forces, the scattering force. Laser cooling of atoms, optical molasses, Doppler limit. Zeeman slowing and Sisyphus cooling of atoms. Magneto-optical trapping of atoms. Moving molasses, caesium fountain clock, Ramsay Interferometry. Optical frequency standards, laser locking. Optical frequency combs, ion trapping, Lamb-Dicke regime. Aluminium quantum logic clock, Ytterbium ion clock. Strontium optical lattice clock, AC Stark effect, dipole force, optical dipole traps and optical lattices, magic wavelength optical lattice. Systematic effects in optical frequency standards, comparisons between clocks. Applications of atomic clocks, time-variation of fundamental constants, electric-dipole moment of the electron and relativistic geodesy.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will be able to use Fourier methods to describe interference and diffraction and their applications in modern optics.\n* They will be familiar with some of the applications of quantum mechanics to atomic physics and the interaction of atoms with light.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises and progress test provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS3721" . . "Presential"@en . "FALSE" . . "Project"@en . . "60.0" . "#### Prerequisites\n\n* Foundations of Physics 3A (PHYS3621) AND (Discovery Skills in Physics (PHYS1101) or Laboratory Skills and Electronics (PHYS2641) or Laboratory Skills and Electronics 3 (PHYS3681)).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It provides experience of work in a research environment on a topic at the forefront of developments in a branch of either physics, applied physics, theoretical physics or astronomy, and develops transferable skills for the oral and written presentation of research.\n\n#### Content\n\n* The syllabus contains:\n* A research-based project carried out within one of the Department's research groups.\n* In the case of industrially linked projects, some time may be spent at the industrial site.\n* Projects may involve small groups of students working in a team.\n* Presentation and communication skills.\n* Research methods and techniques, scientific writing and presentation, interviews.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will have an understanding of the techniques used in either theoretical or experimental physics together with an appreciation of their applicability to a research project.\n\nSubject-specific Skills:\n\nKey Skills:\n\n* Students will be able to work independently and develop an effective work plan.\n* They will be able to solve problems with originality and be able to complete tasks efficiently.\n* They will be able to resolve complex problems by identifying creative solutions.\n* They will have the facility to express problems and communicate their solution via oral and written means.\n* They will have the confidence to advance and extend knowledge through the development of an independent learning ability and personal responsibility.\n* They will have further developed communication and oral presentation skills, including written communication of scientific concepts to a general audience.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* The project is based in a research group and may involve extensive private study, work on one or more computers or practical work in one of the research laboratories.\n* In the case of industrially linked projects, some time may be spent at the industrial site.\n* Supervisors monitor progress and provide guidance on the development of the project during weekly meetings.\n* Students will be able to obtain further help in their project by approaching their supervisors and/or other members of the appropriate research group.\n* The seminars provide formal instruction on communication skills, both written and oral, that are then reinforced by the project supervisors during the weekly meetings.\n* The seminars include training sessions on general computing, testing and debugging. The drop-in sessions are designed to allow each student to obtain programming help and guidance through discussions with computing demonstrators.\n* Progress is further monitored by a formatively assessed interim project progress report written over the Christmas vacation.\n* Together with the project seminar, this provides opportunities for feedback and for the students to gauge their progress.\n* Student performance is summatively assessed through technical performance during the project, through a formal final report on the project, through the project seminar and via an oral examination on the project report.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4213" . . "Presential"@en . "TRUE" . . "Advanced astrophysics"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 2B (PHYS2591) and Stars and Galaxies (PHYS2621) and Foundations of Physics 3A (PHYS3621).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the modules Stars and Galaxies (PHYS2621) and Foundations of Physics 3A (PHYS3621) and provides a working knowledge of advanced optical techniques used in modern astronomy and of the radiative processes that generate the emission that is studied in a wide range of astronomical observations at an advanced level appropriate to Level 4 physics students.\n\n#### Content\n\n* The syllabus contains:\n* Astronomical Techniques and Advanced Imaging: Introduction to astronomical techniques, review of optical theory, propagation of light through the atmosphere, adaptive Optics, interferometry, sectroscopy, non-optical techniques.\n* Radiative Processes in Astrophysics: Review of radiative transfer, accelerated charges, Compton processes, synchrotron and Bremsstrahlung, photoionisation/recombination, line formation, abundances, dust, plasma effect, RM and group velocity.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will be aware of advanced optical techniques used in modern astronomy, in particular of high angular resolution imaging techniques and their astrophysical applications.\n* They will understand the radiative processes that generate the emission that is studied in a wide range of astronomical observations and will know the observational context of the main theoretical aspects.\n\nSubject-specific Skills:\n\n* In addition to the acqusition of subject knowledge, students will be able to apply knowledge of specialist topics in physics to the solution of advanced problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module.\n* The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.\n* When appropriate, lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises.\n* The open-book examination will provide the means for students to demonstrate the acqusition of subject knowledge and the development of their problem- solving skills.\n* The problem exercises provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4161" . . "Presential"@en . "TRUE" . . "Theoretical astrophysics"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 3A (PHYS3621) and Planets and Cosmology 3 (PHYS3651).\n\n#### Corequisites\n\n* Planets and Cosmology 4 (PHYS4231) if Planets and Cosmology 3 (PHYS3651) has not been taken in Year 3.\n\n#### Excluded Combination of Modules\n\n* General Relativity IV (MATH4051).\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 3 module Foundations of Physics 3A (PHYS3621) and provides an overview of our current understanding of the formation and evolution of cosmic structure and an introduction to Einstein’s general theory of relativity at an advanced level appropriate to Level 4 physics students.\n\n#### Content\n\n* The syllabus contains:\n* Cosmic Structure Formation: Cosmological perturbations, fluid equations, Jeans theory, non-baryonic dark matter, temperature fluctuations in the cosmic microwave background radiation, spherical collapse model, N-body simulations, statistics of galaxy clustering.\n* General Relativity: Gravity as curvature, tensor algebra, mathematics of curved spacetime, the Einstein equations, the Schwarzschild metric, weak field tests of general relativity, black holes.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will be able to describe mechanisms that seed small perturbations in the early Universe and will be able to describe mathematically how these perturbations evolve throughout cosmic history. They will understand the physical processes that have shaped our universe.\n* They will be aware of the principles of general relativity, including the interpretation of gravity as spacetime curvature, and be able to apply them to the simplest gravitational systems.\n\nSubject-specific Skills:\n\n* In addition to the acqusition of subject knowledge, students will be able to apply knowledge of specialist topics in physics to the solution of advanced problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module.\n* The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.\n* When appropriate, lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises.\n* The open-book examination will provide the means for students to demonstrate the acqusition of subject knowledge and the development of their problem- solving skills.\n* The problem exercises provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4201" . . "Presential"@en . "TRUE" . . "Atoms, lasers and qubits"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 3A (PHYS3621).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 3 module Foundations of Physics 3A (PHYS3621) and provides a working knowledge of lasers and the physics of quantum computation at an advanced level appropriate to Level 4 physics students.\n\n#### Content\n\n* The syllabus contains:\n* Laser Physics: Definition of a laser. Atom-light interactions. Absorption, spontaneous and stimulated emission. Line broadening mechanisms and emission linewidth. Population inversion and gain. Laser oscillator: cavity basics and threshold; gain saturation and output power. Population inversion in 3 and 4-level systems. Laser pumping with case studies of specific laser systems. Cavity modes and cavity stability. Gaussian beams. Cavity effects: single frequency operation. Cavity effects: Q switching and mode locking. Laser spectroscopy and optical frequency combs. Case studies of laser applications.\n* Quantum Information and Computing: Manipulation of qubits: Limits of classical computing. Feynman’s insight. Quantum mechanics revision. Projection operators. Pauli matrices. Single-qubit operations: Resonant field, the Rabi solution. The Bloch sphere. The Ramsey technique. Two-qubit states. Tensor products. Correlations. Entanglement. Bell states. Two-qubit gates. The CNOT gate. Physical Realizations: The DiVincenzo criteria. Controlling the centre-of mass motion of atoms – laser cooling. Controlling the internal states of atoms. Trapping and manipulating single atoms. Rydberg states. Decoherence. Case studies of contemporary Quantum Information Processing.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will be aware of the principles of lasers and be able to describe the operation, design features and uses of various laser systems.\n* They will be familiar with the concept of the qubit and with the manipulation of qubits with electromagnetic fields, with many-qubit states, their correlation properties and the concept of entanglement, with quantum gates, quantum computing and the physical realization of these ideas.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply knowledge of specialist topics in physics to the solution of advanced problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module.\n* The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.\n* When appropriate, lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises.\n* The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4121" . . "Presential"@en . "FALSE" . . "Advanced theoretical physics"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 3A (PHYS3621) AND (Theoretical Physics 3 (PHYS3661) OR (Mathematical Physics II (MATH2071) AND Special Relativity and Electromagnetism II (MATH2657))).\n\n#### Corequisites\n\n* Advanced Quantum Theory IV (MATH4061) if Theoretical Physics 3 (PHYS3661) has not been taken.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 3 modules Foundations of Physics 3A (PHYS3621) and Theoretical Physics 3 (PHYS3661) and provides a working knowledge of non-relativistic quantum mechanical problems at an advanced level appropriate to Level 4 physics students.\n\n#### Content\n\n* The syllabus contains:\n* Revision of electronic structure and Bloch's theorem, many-body Schrodinger equation, Hartree and Hartree-Fock theories, density functional theory, electron exchange and correlation, modern methods of electronic structure calculation. Phonons in three dimensions, beyond the harmonic approximation. Elementary excitations in solids. Superconductivity: historical overview, Meissner effect, Cooper pairs, the superconducting phase transition, supercurrents, the London and Ginzburg-Landau theories, Josephson effects, BCS theory of superconductivity.\n* Quantization of light, creation and annihilation operators, Hamiltonian of the field, number states, coherent states, squeezed states, photon bunching and anti-bunching, density operator, pure states, mixed states, entangled states, decoherence, EPR experiments, applications (quantum cryptography, quantum computing, other applications).\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will understand some of the modern theories of electronic structure and vibrational properties of materials including superconductivity.\n* They will understand the quantum nature of light.\n* They will understand the concepts of entangled states and mixed states and their relevance in experiments.\n\nSubject-specific Skills:\n\n* In addition to the acqusition of subject knowledge, students will be able to apply knowledge of specialist topics in physics to the solution of advanced problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module.\n* The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.\n* When appropriate, lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises.\n* The open-book examination will provide the means for students to demonstrate the acqusition of subject knowledge and the development of their problem- solving skills.\n* The problem exercises provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4141" . . "Presential"@en . "FALSE" . . "Advanced condensed matter physics"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 2A (PHYS2581) and Foundations of Physics 3B (PHYS3631) and Condensed Matter Physics 3 (PHYS3711).\n\n#### Corequisites\n\n* Condensed Matter Physics 4 (PHYS4271) if Condensed Matter Physics 3 (PHYS3711) has not been taken in Year 3.\n\n#### Excluded Combination of Modules\n\n* None.\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 3 modules Foundations of Physics 3B (PHYS3631) and Condensed Matter Physics 3 (PHYS3711) and introduces students to some of the key topics in the area of soft matter and biological physics, provides a knowledge of the physical properties of zero, one and two dimensional materials and of the properties of metals and superconductors at an advanced level appropriate to Level 4 physics students.\n\n#### Content\n\n* The syllabus contains:\n* Standard models of condensed matter physics: Metals: The Fermi-gas and its predictions. Interactions in metals: adiabatic continuity in outline. Single particle band structure and tight binding. Quantum oscillations and fermiology. Examples of the behaviour of normal and exotic metals; Superfluidity and superconductivity: Superfluids and superconductors as broken symmetry states. Macroscopic quantum coherence. Microscopic description: BCS theory. Superconducting materials. Applications of superconductivity; superconducting devices.\n* Low-dimensional physics: Systems in 1D and 2D. Mermin-Wagner theorem. The Ising model in 1D. Polymers. Quantum Hall effect (magnetoresistance in 2D, conductivity and Hall effect; edge states). Topological objects in low dimensional solids. walls, kinks and solitons; vortices, monopoles and skyrmions. Semiconductor (p-n) junctions. Devices using the semiconductor p-n junction. Heterostructures and quantum wells.\n* Order and dynamics in soft matter and biophysics: Dynamics and susceptibilities. The kinetics of phase transitions including liquid-liquid demixing phase separation. Glasses. Self-assembly of micelles and membranes. Soft and biological systems out of equilibrium. Nucleation: crystal growth and self-assembly of molecular systems. Susceptibility, response and the fluctuation-dissipation theorem (in outline).\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will have an understanding of the themes of modern condensed matter research, and an appreciation of role of scales, symmetry and the structure of matter in advanced examples. They will have become familiar with the physics of a number of examples taken from across the subject.\n* Students will be able to demonstrate knowledge of the nature of order and dynamics in soft matter and biological systems.\n* They will be able to predict physical behaviour based on fundamental models of metals and superconductors.\n* They will be able to identify examples of where reduced dimensionality is relevant and to formulate descriptions of the underlying physics.\n* They will be able to apply their understanding of these topics in unfamiliar contexts in order to solve advanced problems.\n\nSubject-specific Skills:\n\n* In addition to the acqusition of subject knowledge, students will be able to apply knowledge of specialist topics in physics to the solution of advanced problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module.\n* The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.\n* When appropriate, lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises.\n* The open-book examination will provide the means for students to demonstrate the acqusition of subject knowledge and the development of their problem-solving skills.\n* The problem exercises provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4151" . . "Presential"@en . "FALSE" . . "Particle theory"@en . . "20.0" . "#### Prerequisites\n\n* Theoretical Physics 3 (PHYS3661).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* Advanced Quantum Theory IV (MATH4061)\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the Level 3 modules Foundations of Physics 3A (PHYS3621) and Theoretical Physics 3 (PHYS3661) and provide a working knowledge of relativistic quantum mechanics, quantum field theory and gauge theory at a level appropriate to Level 4 physics students.\n\n#### Content\n\n* The syllabus contains:\n* Klein–Gordon equation. Dirac equation. Spin. Free particle and antiparticle solutions of the Dirac equation. Massless fermions. Lagrangian form of classical electromagnetism. Lagrangian form of the Dirac equation. Global gauge invariance. Noether's theorem and conserved current for the Dirac equation. Second quantisation of classical Klein–Gordon field. Local gauge invariance. Lagrangian of Quantum Electrodynamics (QED).\n* Amplitudes, kinematics, phase space, cross sections and decay widths. Simple processes in quantum electrodynamics. Abelian and non-abelian gauge theories. Spontaneous symmetry breaking. Goldstone phenomenon and Higgs mechanism.\n* Standard Model of particle physics. Phenomenology of the weak and strong interactions: electron-positron annihilation, Z resonance, parity violation, muon decay, electroweak precision tests, properties of the Higgs boson, deep inelastic scattering, proton–proton scattering. The Large Hadron Collider. Beyond the Standard Model. Supersymmetry.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will be familiar with some of the key results of relativistic quantum mechanics and its application to simple systems including particle physics.\n* They will be familiar with the principles of quantum field theory and the role of symmetry in modern particle physics.\n* They will be familiar with the standard model of particle physics and its experimental foundations.\n\nSubject-specific Skills:\n\n* In addition to the acqusition of subject knowledge, students will be able to apply knowledge of specialist topics in physics to the solution of advanced problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module.\n* The lecture material will be explicitly linked to the contents of recommended textbooks for the module, thus making clear where students can begin private study.\n* When appropriate, lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises.\n* The open-book examination will provide the means for students to demonstrate the acqusition of subject knowledge and the development of their problem- solving skills.\n* The problem exercises provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4181" . . "Presential"@en . "FALSE" . . "Theoretical physics 4"@en . . "20.0" . "#### Prerequisites\n\n* Theoretical Physics 2 (PHYS2631) AND Foundations of Physics 3A (PHYS3621).\n\n#### Corequisites\n\n* Foundations of Physics 4A (PHYS4251) if Foundations of Physics 3A (PHYS3621) was not taken in Year 3\n\n#### Excluded Combination of Modules\n\n* Theoretical Physics 3 (PHYS3661).\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on the modules Theoretical Physics 2 (PHYS2631) and Foundations of Physics 3A (PHYS3621) by introducing more advanced methods in electromagnetism that can be used to investigate more realistic problems and concepts, and by introducing more advanced topics in quantum mechanics as well as addressing further applications and conceptual issues of measurement and interpretation.\n* It develops transferable skills in researching a topic at an advanced level and making a written presentation on the findings.\n\n#### Content\n\n* The syllabus contains:\n* Relativistic Electrodynamics: Einstein’s postulates, the geometry of relativity, Lorentz transformations, structure of space-time, proper time and proper velocity, relativistic energy and momentum, relativistic kinematics, relativistic dynamics, magnetism as a relativistic phenomenon, how the fields transform, the field tensor, electrodynamics in tensor notation, relativistic potentials, scalar and vector potentials, gauge transformations, Coulomb gauge, retarded potentials, fields of a moving point charge, dipole radiation, radiation from point charges.\n* Quantum Theory: Scattering experiments and cross sections; potential scattering (general features); spherical Bessel functions (application: the bound states of a spherical square well); the method of partial waves (scattering phase shift, scattering length, resonances, applications); the integral equation of potential scattering; the Born approximation; collisions between identical particles, introduction to multichannel scattering; the density matrix (ensemble averages, the density matrix for a spin-1/2 system and spin-polarization); quantum mechanical ensembles and applications to single-particle systems; systems of non-interacting particles (Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics, ideal Fermi-Dirac and Bose-Einstein gases); the Klein-Gordon equation; the Dirac equation; covariant formulation of Dirac theory; plane wave solutions of the Dirac equation; solutions of the Dirac equation for a central potential; negative energy states and hole theory; non-relativistic limit of the Dirac equation; measurements and interpretation (hidden variables, the EPR paradox, Bell’s theorem, the problem of measurement).\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will have developed a working knowledge of tensor calculus, and be able to apply their understanding to relativistic electromagnetism.\n* They will have a systematic understanding of quantum theory, including collision theory and relativistic quantum mechanics.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n* Students will have developed skills in researching a topic at an advanced level and making a written presentation.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Lecturers will provide a list of advanced topics related to the module content. Students will be required to research one of these topics in depth and write a dissertation on it. Some guidance on the research and feedback on the dissertation will be provided by the lecturer.\n* Student performance will be summatively assessed through an open-book examination and a dissertation and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The dissertation will provide the means for students to demonstrate skills in researching a topic at an advanced level and making a written presentation.\n* The problem exercises and progress test will provide opportunities for feedback, for students to gauge their progress, and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4241" . . "Presential"@en . "FALSE" . . "Condensed matter physics 4"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 3A (PHYS3621) AND Foundations of Physics 3B (PHYS3631)\n\n#### Corequisites\n\n* Foundations of Physics 4B (PHYS4261) if Foundations of Physics 3B (PHYS3631) was not taken in Year 3\n\n#### Excluded Combination of Modules\n\n* PHYS3??1 Condensed Matter Physics 3\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It illustrates the relevant physics utilised in modern condensed matter physics based on scale, symmetry and the structure of matter and contains both material on \"hard\" condensed matter and an introduction to topics in soft matter physics.\n* It develops transferable skills in researching a topic at an advanced level and making a written presentation on the findings.\n\n#### Content\n\n* Symmetry structure and excitations: Overview of energy, length and time scales in different areas of CMP. Comparison of hard CMP and soft CMP. Cohesion in solids. Introduction to symmetry and its influence on physical properties. The symmetry of crystals. Measuring structure using diffraction. Elementary excitations from a ground state: single particles and collective excitations in solids. Phonons in a system with a two atom basis: acoustic and optic branches. Anharmonic effects, soft modes. Measuring excitations using scattering and spectroscopy.\n* Introduction to soft matter physics: Introduction to soft matter physics and its basic phenomenology. Polymer physics and scaling. Liquid crystals. Free energies. Diffusion (Einstein diffusion coefficients, Peclet number and Fick’s laws). Elasticity of solids.\n* Broken symmetry: Symmetry breaking at phase transitions as a method of classifying the phenomena studied in CMP. Phase transitions and critical exponents. Excitations in a broken symmetry system. Generalised rigidity and order. Topological defects. How other systems fit into this framework: superconductors and superfluids; classical examples (binary fluids, polymers, liquid crystals etc.); weak interactions in the standard model, cosmological examples. Other topological objects: vortices, monopoles, skyrmions (in outline). Applications of broken symmetry systems.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will have an understanding of the themes of modern condensed matter research, and an appreciation of role of scales, symmetry and the structure of matter. They will have become familiar with the physics of a number of examples taken from across the subject.\n* They will understand the elements of soft matter structure, its dynamics, elasticity and phase transitions.\n* They will understand the notion of broken symmetry and its consequences and an appreciation of the classification of phenomena in solids that this allows.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n* Students will have developed skills in researching a topic at an advanced level and making a written presentation.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Lecturers will provide a list of advanced topics related to the module content. Students will be required to research one of these topics in depth and write a dissertation on it. Some guidance on the research and feedback on the dissertation will be provided by the lecturer.\n* Student performance will be summatively assessed through an open-book examination and a dissertation and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The dissertation will provide the means for students to demonstrate skills in researching a topic at an advanced level and making a written presentation.\n* The problem exercises and progress test provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4271" . . "Presential"@en . "FALSE" . . "Modern atomic and optical physics 4"@en . . "20.0" . "#### Prerequisites\n\n* Foundations of Physics 3A (PHYS3621) AND (Foundations of Physics 2B (PHYS2591) OR Foundations of Physics 3C (PHYS3671)).\n\n#### Corequisites\n\n* None.\n\n#### Excluded Combination of Modules\n\n* Modern Atomic and Optical Physics 3 (PHYS3721).\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It builds on Level 2 courses in geometric optics and quantum mechanics by providing courses on modern optics and atomic physics.\n* It develops transferable skills in researching a topic at an advanced level and making a written presentation on the findings.\n\n#### Content\n\n* Fourier Optics: Fourier toolkit, angular spectrum, Gaussian beams, lasers and cavities, Fresnel and Fraunhofer, 2D diffraction – letters, circles, Babinet and apodization, lenses, imaging, spatial filtering.\n* Atomic Clocks: History of precision measurement of time. Principle of atomic clocks, revision of atomic structure, electric and magnetic dipole interactions with electromagnetic fields, selection rules. Visualising electron distributions in atoms during transitions. Spontaneous emission, Einstein A coefficient and relationship with atomic clocks, lifetimes, line widths, line intensities and line shapes. Fine-structure and hyperfine splitting, using degenerate perturbation theory to calculate the ground-state hyperfine splitting of the H atom. Lifetimes of electric dipole forbidden transitions, selection rules and relationship with atomic clocks. Zeeman effect, using degenerate perturbation theory to calculate Zeeman shifts of the hyperfine states of the ground-state of the H atom, relationship with atomic clocks. Derivation of Rabi equation for two-level system, transit-time broadening, relationship with atomic clocks. Light forces, the scattering force. Laser cooling of atoms, optical molasses, Doppler limit. Zeeman slowing and Sisyphus cooling of atoms. Magneto-optical trapping of atoms. Moving molasses, caesium fountain clock, Ramsay Interferometry. Optical frequency standards, laser locking. Optical frequency combs, ion trapping, Lamb-Dicke regime. Aluminium quantum logic clock, Ytterbium ion clock. Strontium optical lattice clock, AC Stark effect, dipole force, optical dipole traps and optical lattices, magic wavelength optical lattice. Systematic effects in optical frequency standards, comparisons between clocks. Applications of atomic clocks, time-variation of fundamental constants, electric-dipole moment of the electron and relativistic geodesy.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module, students will be able to use Fourier methods to describe interference and diffraction and their applications in modern optics.\n* They will be familiar with some of the applications of quantum mechanics to atomic physics and the interaction of atoms with light.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of complex problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n* Students will have developed skills in researching a topic at an advanced level and making a written presentation.\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and workshops.\n* The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Lecturers will provide a list of advanced topics related to the module content. Students will be required to research one of these topics in depth and write a dissertation on it. Some guidance on the research and feedback on the dissertation will be provided by the lecturer.\n* Student performance will be summatively assessed through an open-book examination and a dissertation and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The dissertation will provide the means for students to demonstrate skills in researching a topic at an advanced level and making a written presentation.\n* The problem exercises and progress test provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS4281" . . "Presential"@en . "FALSE" . . "Master in Physics and Astronomy"@en . . "https://www.durham.ac.uk/study/courses/physics-and-astronomy-ff3n/" . "120"^^ . "Presential"@en . "**Course details**\nIf you are fascinated by the relationship between mathematics, the cosmos and the scientific world this MPhys could be for you. This integrated Master's degree is the first step towards Chartered Physicist status. It will suit those looking for an accredited course that leads to higher level education or a research role in physics, while also providing the knowledge, analytical and problem-solving skills for a career in the sciences, engineering, finance or IT.\n\nPhysics degrees at Durham offer a high level of flexibility. We offer four Institute of Physics accredited courses - MPhys qualifications in Physics, Physics and Astronomy, and Theoretical Physics and the three-year BSc in Physics - which follow the same core curriculum in Year 1.\n\nSubject to the optional modules chosen, it is possible to switch to one of the other courses until the end of the second year. You can also apply for a one-year work placement or study abroad opportunity with one of our partner organisations, increasing the course from four years to five or substituting the existing Year 3.\n\nThe first year lays the foundation in physics theory, mathematical skills and laboratory skills that you will need to tackle more complex content later in the course. From Year 2 the focus on astronomy and astrophysics increases.\n\nAs you progress through the course, learning is more closely aligned to real-world issues through project work and optional modules that are tailored to your interests and aspirations. Your knowledge is further extended with a project based on a live research topic, and higher-level modules which take your study of physics and astronomy to a greater depth.\n\n**Course structure**\n*Year 1*\nCore modules:\nFoundations of Physics introduces classical aspects of wave phenomena and electromagnetism, as well as basic concepts in Newtonian mechanics, quantum mechanics, special relativity and optical physics.\n\nDiscovery Skills in Physics provides a practical introduction to laboratory skills development with particular emphasis on measurement uncertainty, data analysis and written and oral communication skills. It also includes an introduction to programming.\n\nExamples of optional modules:\nSingle Mathematics\nLinear Algebra\nCalculus.\n\n*Year 2*\nCore modules:\nFoundations of Physics A develops your knowledge of quantum mechanics and electromagnetism. You will learn to apply the principles of physics to predictable and unpredictable problems and produce a well-structured solution, with clear reasoning and appropriate presentation.\n\nFoundations of Physics B extends your knowledge of thermodynamics, condensed matter physics and optics.\n\nStars and Galaxies introduces astronomy and astrophysics. You will develop an understanding of the basic physics of stellar interiors and learn why we see stars of differing colours and brightness. The module extends your knowledge of pulsating and binary stars and introduces galactic and extragalactic astronomy.\n\nMathematical Methods in Physics provides the necessary mathematical knowledge to successfully tackle the Foundations of Physics modules. It covers vectors, vector integral and vector differential calculus, multivariable calculus and orthogonal curvilinear coordinates, Fourier analysis, orthogonal functions, the use of matrices, and the mathematical tools for solving ordinary and partial differential equations occurring in a variety of physical problems.\n\nLaboratory Skills and Electronics builds lab-based skills, such as experiment planning, data analysis, scientific communication and specific practical skills. It aims to teach electronics as a theoretical and a practical subject, to teach the techniques of computational physics and numerical methods and to provide experience of a research-led investigation in physics in preparation for post-university life.\n\nExamples of optional modules:\nTheoretical Physics\nPhysics in Society.\n\n*Year 3*\nCore modules:\nFoundations of Physics A further develops your knowledge to include quantum mechanics and nuclear and particle physics. You will learn to apply the principles of physics to complex problems and produce a well-structured solution, with clear reasoning and appropriate presentation.\n\nFoundations of Physics B extends your knowledge to include statistical physics and condensed matter physics.\n\nPlanets and Cosmology explains the astrophysical origin of planetary systems and the cosmological origin of the Universe. You will learn about the formation and workings of our Solar System, its orbital dynamics and the basic physics of planetary interiors and atmospheres.\n\nThe Computing Project is designed to develop your computational and problem-solving skills. You work on advanced computational physics problems using a variety of modern computing techniques and present your findings in a project report, poster and oral presentation.\n\nExamples of optional modules:\nTeam Project\nAdvanced Laboratory\nMathematics Workshop\nPhysics into Schools\nTheoretical Physics\nCondensed Matter Physics\nModern Atomic and Optical Physics.\n\n*Year 4*\nCore modules:\nThe research-based MPhys Project provides experience of work in a research environment on a topic at the forefront of developments in a branch of either physics, applied physics, theoretical physics or astronomy, and develops transferable skills for the oral and written presentation of research. The project can be carried out individually or as part of a small group in one of the Department's research groups or in collaboration with an external organisation.\n\nAdvanced Astrophysics covers astronomical techniques and radiative processes in astrophysics. This module provides a working knowledge of the advanced optical techniques used in modern astronomy and of the radiative processes that generate the emission that is studied in a wide range of astronomical observations.\n\nTheoretical Astrophysics examines cosmic structure formation and general relativity. This module provides an overview of our current understanding of the formation and evolution of cosmic structure and an introduction to Einstein's general theory of relativity.\n\nExamples of optional modules:\nAtoms, Lasers and Qubits\nAdvanced Theoretical Physics\nAdvanced Condensed Matter Physics\nParticle Theory\nTheoretical Physics\nCondensed Matter Physics\nModern Atomic and Optical Physics.\nAdditional pathways\nStudents on the MPhys in Physics and Astronomy can apply to be transferred onto either the 'with Year Abroad' or 'with Placement' pathway during the second year. Places on these pathways are in high demand and if you are chosen you can choose to extend your course from four years to five, or substitute the existing Year 3.\n\n**Placement**\nYou may be able to take a work placement. Find out more in https://www.durham.ac.uk/study/undergraduate/how-to-apply/study-options/placements/.\n\nModules details: https://apps.dur.ac.uk/faculty.handbook/2023/UG/programme/FF3N"@en . . . "4"@en . "FALSE" . . "Master"@en . "Both" . "9250.00" . "British Pound"@en . "30500.00" . "Recommended" . "**Career opportunities**\n*Physics*\nWe seek to develop the practical and intellectual skills sought by employers and we are regularly ranked among the country's top performers for graduate employment. Our graduates have progressed to careers in business, industry, commerce, research, management and education, and typically more than fifth of our graduates go on to study for higher degrees.\n\nThe Department also has an impressive track record of spin-out technology companies that commercialise our knowledge in areas of semiconductors, composites and advanced instrumentation. Examples of high-profile employers include BT, Procter & Gamble, Rolls Royce and BAE Systems.\n\nOf those students who graduated in 2019:\n83% are in paid employment or further study 15 months after graduation across all our programmes\n\nOf those in employment:\n81% are in high skilled employment\nWith an average salary of £34,000.\n\n(Source: HESA Graduate Outcomes Survey. The survey asks leavers from higher education what they are doing 15 months after graduation. Further information about the Graduate Outcomes survey can be found here www.graduateoutcomes.ac.uk)"@en . "2"^^ . "TRUE" . "Downstream"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Institute of Physics"@en . .