. "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" . . "Algebra"@en . . . . . . . . . . . . . . . . . . . . . "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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .