Mathematics and Physics | BSc (Hons)

An Introduction to Your Modules

† Some courses may offer optional modules. The availability of optional modules may vary from year to year and will be subject to minimum student numbers being achieved. This means that the availability of specific optional modules cannot be guaranteed. Optional module selection may also be affected by staff availability.

Algebra 2023-24MTH1001MLevel 42023-24This module begins with refreshing and expanding some of the material from the A-levels Maths, such as the binomial theorem, division of polynomials, polynomial root-finding, and factorisations. Then the Euclidean algorithm is introduced with some of its many applications, both for integers and for polynomials. This naturally leads to a discussion of divisibility and congruences, for integers and for polynomials, with emphasis on similarities and as a step towards abstraction.CoreCalculus 2023-24MTH1002MLevel 42023-24This module focuses on the concepts of the derivative and the Riemann integral, which are indispensable in modern sciences. Two approaches are used: both intuitive-geometric, and mathematically rigorous, based on the definition of continuous limits. Important results are the Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration. Further calculus tools are explored, such as the general properties of the derivative and the Riemann integral, as well as the techniques of integration. In this module, students may deal with many "popular" functions used throughout mathematics.CoreComputer Algebra and Technical Computing 2023-24MTH1006MLevel 42023-24This module presents an introduction to computer packages for analytic formulas manipulation (computer algebra) and technical computing. Students will also have the opportunity to develop skills including; utilising a logbook as a factual record and as reflective self-assessment to support their learning.CoreElectricity, Magnetism, Thermal and Quantum Physics 2023-24PHY1003MLevel 42023-24This module covers basic notions of modern physics. In electricity and magnetism these include Coulombs law, electrostatic vector and potential fields, magnetic fields, motion of charges and currents in electromagnetic fields, and the basics of electric circuits. In thermal physics these include the zeroth, and first and second laws of thermodynamics applied to different model situations. The quantum physics part introduces notions such as wave-particle duality, the concept of a wavefunction, energy quantization, and simple models of the atom.CoreGeometrical Optics, Waves and Mechanics 2023-24PHY1002MLevel 42023-24 This module introduces established theories describing optical, acoustic, and mechanical phenomena. The optics part includes Fermats principle of light propagation, Snells laws of reflection and refraction, thin lenses and Huygenss principle. The mechanics part includes the basic mathematical tools used to describe the motion of objects (kinematics) and the laws of Newton (dynamics) underpinning these observed motions. The wave part of the module includes a discussion of propagating waves, the Doppler effect, phase and group velocities and standing waves.CoreLinear Algebra 2023-24MTH1004MLevel 42023-24This module describes vector spaces and matrices. Matrices are regarded as representations of linear mappings between vector spaces. Eigenvalues and eigenvectors are introduced, which lead to diagonalisation and reduction to other canonical forms. Special types of mappings and matrices (orthogonal, symmetric) are also introduced.CoreProbability and Statistics 2023-24MTH1005MLevel 42023-24This module begins with an introduction of a probability space, which models the possible outcomes of a random experiment. Basic concepts such as statistical independence and conditional probability are introduced, with various practical examples used as illustrations. Random variables are introduced, and certain well-known probability distributions are explored. Further study includes discrete distributions, independence of random variables, mathematical expectation, random vectors, covariance and correlation, conditional distributions and the law of total expectation. The ideas developed for discrete distributions are applied to continuous distributions. Probability theory is a basis of mathematical statistics, which has so many important applications in science, industry, government and commerce. Students will have the opportunity to gain a basic understanding of statistics and its tools. It is important that these tools are used correctly when, for example, the full picture of a problem (population) must be inferred from collected data (random sample).CoreProfessional Skills and Group Study 2023-24MTH1007MLevel 42023-24This module provides students the opportunity to learn a variety of transferable skills: to communicate scientific ideas via a variety of media, to work in groups, to manage and plan projects, to keep record of work. Students have the opportunity to develop an understanding of general and specialized databases, their uses and searches. Group study can develop Students' skills in team-working around investigating a topic from literature. Students have the opportunity to take on administrative roles within the team and work towards common aims and objectives.CoreAlgebraic Structures 2024-25MTH2001MLevel 52024-25The concepts of groups, rings and fields are introduced, as examples of arbitrary algebraic systems. The basic theory of subgroups of a given group and the construction of factor groups is introduced, and then similar constructions are introduced for rings. Examples of rings are considered, including the integers modulo n, the complex numbers and n-by-n matrices. The ring of polynomials over a given field is studied in more detail.CoreCondensed Matter Physics 2024-25PHY2001MLevel 52024-25In contemporary research, condensed matter physics pertains to the physics of condensed phases of matter such as solid and liquids. Depending on the properties of interest, condensed matter physics is traditionally split into two different sub-fields: solid state physics dealing primarily with the behavior of electrons in periodic solids, and soft-matter physics dealing with the properties of assemblies of atoms in a somewhat confined space. This module introduces the basic ideas of these two worlds from Drudes model and the band theory of electrical conductivity in solids to the physics of colloidal and polymeric systems.CoreDifferential Equations 2024-25MTH2004MLevel 52024-25Calculus techniques already provide solutions of simple first-order differential equations. Solution of second-order differential equations can sometimes be achieved by certain manipulations. Students may learn about existence and geometric interpretations of solutions, even when calculus techniques do not yield solutions in a simple form. This is a part of the existence theory of ordinary differential equations and leads to fundamental techniques of the asymptotic and qualitative study of their solutions, including the important question of stability. Fourier series and Fourier transform are introduced. This module provides an introduction to the classical second-order linear partial differential equations and techniques for their solution. The basic concepts and methods are introduced for typical partial differential equations representing the three classes: parabolic, elliptic, and hyperbolic.CoreElectrodynamics 2024-25PHY2002MLevel 52024-25This module covers the first established classical theory of fields, namely the theory of electromagnetic fields. After introducing the necessary mathematical tools such as curl, divergence, and gradient, the module discusses the macroscopic and microscopic Maxwells equations of electromagnetism as well as their solutions for some model problems in vacuum and in some materials. Topics covered include Gausss law, Maxwells law of induction, Faradays law, time-dependent electromagnetic fields, electromagnetic waves, and dielectric and magnetic materials.CoreGroup Project 2024-25MTH2005MLevel 52024-25This module aims to provide students with the experience of working as part of a team on a project. Students will have the opportunity to produce a set of deliverables relevant to their programme of study. Final deliverables will be negotiated between the group and their supervisor, the module coordinator will be responsible for ensuring that each project covers the learning outcomes of the module. Groups are expected to manage their own processes, and to hold regular meetings both with and without their supervisor. Groups will be allocated by the module coordinator and other members of staff. The process of development of the topic under study and the interaction and management of group members underpins the assessment of skills in the module.CoreIndustrial and Financial Mathematics 2024-25MTH2006MLevel 52024-25Students have the opportunity to learn how mathematics is applied to modern industrial problems, and how the mathematical apparatus finds applications in the financial sector.CoreLagrangian and Hamiltonian Mechanics 2024-25MTH2007MLevel 52024-25This module is concerned with a modern formulation of mechanics called Lagrangian mechanics in which the actually observed motion of an object is viewed as one among many potentially conceivable motions. The selection process of the actual motion satisfies the so-called Principle of Minimum Action. The corresponding formalism allows us to tackle very intricate mechanical problems and has many technical advantages with regards to changes of variables. A dual theory called Hamiltonian mechanics is also introduced and has its own advantages for addressing problems in mechanics. These two theories constitute the foundation on which quantum mechanics, statistical, and quantum field theories are based. The module delivery includes the Minimum Action Principle, Euler-Lagrange equations, Noethers theorem, Hamiltons equations, and Poisson brackets.CoreScientific Computing 2024-25MTH2008MLevel 52024-25Students will have the opportunity to utilise computers for the numerical solution and simulation of models of physical and mathematical systems, including the use of computer procedural programming languages to solve computational problems. Numerical algorithms will be introduced to exemplify key concepts in computational programming, with the emphasis on understanding the nature of the algorithm and the features and limitations of its computational implementation. In creating programs, the emphasis will be on using effective programming techniques and on efficient debugging, testing and validation methods. Students may also develop skills at using a logbook as a factual record and as reflective self-assessment to support their learning.CoreNumerical Methods 2025-26MTH3007MLevel 62025-26The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.CoreProject 2025-26PHY3003MLevel 62025-26In this module, students conduct research relating to the interface between mathematics and physics. This research can take place in a research group of the school, the university or in an external collaborating establishment.CoreQuantum Mechanics 2025-26PHY3004MLevel 62025-26This module covers the formalism of quantum mechanics, which underpins a substantial part of our current understanding of the microscopic world. Topics covered include commutators, operators and observables, Shrodingers equation, Born rule, spin, Hydrogen atom, time-independent perturbation theory, time-dependent perturbation theory, and identical particles.CoreStatistical Mechanics 2025-26PHY3005MLevel 62025-26This module is concerned with bridging a microscopic description of the world (via classical or quantum Hamiltonian mechanics) with a macroscopic description of the world (via thermodynamics). This is done by considering a probability measure on the space of possible mechanical (micro)states of a system. Topics covered include basics of probability theory, notions of statistical equilibrium, statistical ensembles (canonical and microcanonical) applied to model systems, thermodynamic potentials and partition functions, and the statistical mechanics of identical particles.CoreAdvanced Topics of Mathematics and Mathematics Seminar 2025-26MTH3001MLevel 62025-26The module will cover several advanced topics of modern mathematics. The choice of the topics will be governed by the current research interests of academic staff and/or visiting scientists. Students will also have the opportunity to participate in mathematics research seminars.OptionalAdvanced Topics of Physics and Physics Seminar 2025-26PHY3001MLevel 62025-26The module will cover several advanced topics of modern physics. The choice of the topics will be governed by the current research interests of academic staff and/or visiting scientists. Students may also participate in physics research seminars.OptionalFluid Dynamics 2025-26MTH3002MLevel 62025-26This module gives a mathematical foundation of ideal and viscous fluid dynamics and their application to describing various flows in nature and technology. Students are taught methods of analysing and solving equations of fluid dynamics using analytic and most modern computational tools.OptionalGroup Theory 2025-26MTH3003MLevel 62025-26Symmetry, understood in most broad sense as invariants under transformations, permeates all parts of mathematics, as well as natural sciences. Groups are measures of such symmetry and therefore are used throughout mathematics. Abstract group theory studies the intrinsic structure of groups. The course begins with definitions of subgroups, normal subgroups, and group actions in various guises. Group homomorphisms are introduced and the related isomorphism theorems are proved. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout, symmetry groups are used as examples.OptionalMathematics Pedagogy 2025-26MTH3004MLevel 62025-26This module is designed to provide students with an insight into the teaching of Mathematics at secondary school level and does this by combining university lectures with an experience of a placement in a secondary school Mathematics department. The module aims to provide students with an opportunity to engage with cutting-edge maths education research and will examine how this research impacts directly on classroom practice. Students will have the opportunity to gain an insight into some of the key ideas in Mathematics pedagogy and how these are implemented in the school Mathematics lessons and will develop an understanding about the barriers to learning Mathematics that many students experience.OptionalMethods of Mathematical Physics 2025-26MTH3006MLevel 62025-26The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.OptionalPhysics of the Universe 2025-26PHY3006MLevel 62025-26This module covers the physics of astronomical, astrophysical, and cosmological phenomena. Topics covered include distance measures in the universe, planetary formation, stellar physics, and some elements of cosmology.OptionalPhysics Pedagogy 2025-26PHY3002MLevel 62025-26This module is designed to provide students with an insight into the teaching of science at secondary school level and does this by combining university lectures with an experience of a placement in a secondary school science department. The module is particularly aimed at those considering a career in science teaching and provides students with an opportunity to engage with cutting edge science education research and will examine how this research impacts directly on classroom practice. Students will have the opportunity to gain an insight into some of the key ideas in science pedagogy and how these are implemented in the school science lessons and will develop an understanding about the barriers to learning science that many students experience.OptionalTensor Analysis 2025-26MTH3008MLevel 62025-26This module introduces tensors, which are abstract objects describing linear relations between vectors, scalars, and other tensors. The module aims to equip students with the knowledge of tensor manipulation, and introduces their applications in modern science.Optional

An Introduction to Your Modules

Algebra 2022-23MTH1001MLevel 42022-23This module begins with refreshing and expanding some of the material from the A-levels Maths, such as the binomial theorem, division of polynomials, polynomial root-finding, and factorisations. Then the Euclidean algorithm is introduced with some of its many applications, both for integers and for polynomials. This naturally leads to a discussion of divisibility and congruences, for integers and for polynomials, with emphasis on similarities and as a step towards abstraction.CoreCalculus 2022-23MTH1002MLevel 42022-23This module focuses on the concepts of the derivative and the Riemann integral, which are indispensable in modern sciences. Two approaches are used: both intuitive-geometric, and mathematically rigorous, based on the definition of continuous limits. Important results are the Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration. Further calculus tools are explored, such as the general properties of the derivative and the Riemann integral, as well as the techniques of integration. In this module, students may deal with many "popular" functions used throughout mathematics.CoreComputer Algebra and Technical Computing 2022-23MTH1006MLevel 42022-23This module presents an introduction to computer packages for analytic formulas manipulation (computer algebra) and technical computing. Students will also have the opportunity to develop skills including; utilising a logbook as a factual record and as reflective self-assessment to support their learning.CoreElectricity, Magnetism, Thermal and Quantum Physics 2022-23PHY1003MLevel 42022-23This module covers basic notions of modern physics. In electricity and magnetism these include Coulombs law, electrostatic vector and potential fields, magnetic fields, motion of charges and currents in electromagnetic fields, and the basics of electric circuits. In thermal these include the zeroth, and first and second laws of thermodynamics applied to different model situations. The quantum physics part introduces notions such as the wave-particle duality, the concept of wavefunction, energy quantization, and simple models of the atom.CoreGeometrical Optics, Waves and Mechanics 2022-23PHY1002MLevel 42022-23This module introduces established theories describing optical, acoustic, and mechanical phenomena. The optics part includes Fermats principle of light propagation, Snells laws of reflection and refraction, thin lenses, and Huygenss principle. The mechanics part includes the basic mathematical tools to describe the motion of objects (kinematics) and the laws of Newton (dynamics) underpinning these observed motions. The wave part of the module includes a discussion of propagating waves, the Doppler effect, phase and group velocities, and standing waves.CoreLinear Algebra 2022-23MTH1004MLevel 42022-23This module describes vector spaces and matrices. Matrices are regarded as representations of linear mappings between vector spaces. Eigenvalues and eigenvectors are introduced, which lead to diagonalisation and reduction to other canonical forms. Special types of mappings and matrices (orthogonal, symmetric) are also introduced.CoreProbability and Statistics 2022-23MTH1005MLevel 42022-23This module begins with an introduction of a probability space, which models the possible outcomes of a random experiment. Basic concepts such as statistical independence and conditional probability are introduced, with various practical examples used as illustrations. Random variables are introduced, and certain well-known probability distributions are explored. Further study includes discrete distributions, independence of random variables, mathematical expectation, random vectors, covariance and correlation, conditional distributions and the law of total expectation. The ideas developed for discrete distributions are applied to continuous distributions. Probability theory is a basis of mathematical statistics, which has so many important applications in science, industry, government and commerce. Students will have the opportunity to gain a basic understanding of statistics and its tools. It is important that these tools are used correctly when, for example, the full picture of a problem (population) must be inferred from collected data (random sample).CoreProfessional Skills and Group Study 2022-23MTH1007MLevel 42022-23This module provides students the opportunity to learn a variety of transferable skills: to communicate scientific ideas via a variety of media, to work in groups, to manage and plan projects, to keep record of work. Students have the opportunity to develop an understanding of general and specialized databases, their uses and searches. Group study can develop Students' skills in team-working around investigating a topic from literature. Students have the opportunity to take on administrative roles within the team and work towards common aims and objectives.CoreAlgebraic Structures 2023-24MTH2001MLevel 52023-24The concepts of groups, rings and fields are introduced, as examples of arbitrary algebraic systems. The basic theory of subgroups of a given group and the construction of factor groups is introduced, and then similar constructions are introduced for rings. Examples of rings are considered, including the integers modulo n, the complex numbers and n-by-n matrices. The ring of polynomials over a given field is studied in more detail.CoreCondensed Matter Physics 2023-24PHY2001MLevel 52023-24In contemporary research condensed matter physics pertains to the physics of condensed phases of matter such as solid and liquids. Depending on the properties of interest, condensed matter physics is traditionally split in two different sub-fields: solid state physics dealing primarily with the behavior of electrons in periodic solids, and soft-matter physics dealing with the properties of assemblies of atoms in a somewhat confined space. This module introduces the basic ideas of these two worlds from Drudes model and the band theory of conductivity in solids to the physics of colloidal and polymeric systems.CoreDifferential Equations 2023-24MTH2004MLevel 52023-24Calculus techniques already provide solutions of simple first-order differential equations. Solution of second-order differential equations can sometimes be achieved by certain manipulations. Students may learn about existence and geometric interpretations of solutions, even when calculus techniques do not yield solutions in a simple form. This is a part of the existence theory of ordinary differential equations and leads to fundamental techniques of the asymptotic and qualitative study of their solutions, including the important question of stability. Fourier series and Fourier transform are introduced. This module provides an introduction to the classical second-order linear partial differential equations and techniques for their solution. The basic concepts and methods are introduced for typical partial differential equations representing the three classes: parabolic, elliptic, and hyperbolic.CoreElectrodynamics 2023-24PHY2002MLevel 52023-24This modules covers the first established classical theory of fields, namely the theory of electromagnetic fields. After introducing the necessary mathematical tools such as curl, divergence, and gradient, the module discusses the macroscopic and microscopic Maxwells equations of electromagnetism as well as their solutions for some model problems in vacuum and in some materials. Topics covered include Gausss law, Maxwells law of induction, Faradays law, time-dependent electromagnetic fields, electromagnetic waves, and dielectric and magnetic materials.CoreGroup Project 2023-24MTH2005MLevel 52023-24This module aims to provide students with the experience of working as part of a team on a project. Students will have the opportunity to produce a set of deliverables relevant to their programme of study. Final deliverables will be negotiated between the group and their supervisor, the module coordinator will be responsible for ensuring that each project covers the learning outcomes of the module. Groups are expected to manage their own processes, and to hold regular meetings both with and without their supervisor. Groups will be allocated by the module coordinator and other members of staff. The process of development of the topic under study and the interaction and management of group members underpins the assessment of skills in the module.CoreIndustrial and Financial Mathematics 2023-24MTH2006MLevel 52023-24Students have the opportunity to learn how mathematics is applied to modern industrial problems, and how the mathematical apparatus finds applications in the financial sector.CoreLagrangian and Hamiltonian Mechanics 2023-24MTH2007MLevel 52023-24This module is concerned with a modern formulation of mechanics called Lagranian mechanics whereby the actually observed motion of an object is viewed as one among many potentially conceivable motions. The selection process of the actual motion satisfies the so-called Principle of Minimum Action. The corresponding formalism allows to tackle very intricate mechanical problems and has many technical advantages with regards to changes of variables. A dual theory called Hamiltonian mechanics can also be formalized with its own advantages to address problems in mechanics. These two theories constitute the foundation on which quantum mechanics, statistical and quantum field theories are based. The module delivery includes the Minimum Action Principle, Euler-Lagrange equations, Noethers theorem, Hamiltons equations, and Poisson bracketsCoreScientific Computing 2023-24MTH2008MLevel 52023-24Students will have the opportunity to utilise computers for the numerical solution and simulation of models of physical and mathematical systems, including the use of computer procedural programming languages to solve computational problems. Numerical algorithms will be introduced to exemplify key concepts in computational programming, with the emphasis on understanding the nature of the algorithm and the features and limitations of its computational implementation. In creating programs, the emphasis will be on using effective programming techniques and on efficient debugging, testing and validation methods. Students may also develop skills at using a logbook as a factual record and as reflective self-assessment to support their learning.CoreNumerical Methods 2024-25MTH3007MLevel 62024-25The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.CoreProject 2024-25PHY3003MLevel 62024-25In this module, students conduct research relating to the interface between mathematics and physics. This research can take place in a research group of the school, the university or in an external collaborating establishment.CoreQuantum Mechanics 2024-25PHY3004MLevel 62024-25This module covers the formalism of quantum mechanics underpinning a substantial part of our current understanding of the microscopic world. Topics covered include commutators, operators and observables, Shrodingers equation, Born rule, spin, Hydrogen atom, time-independent perturbation theory, time-dependent perturbation theory, and identical particles.CoreStatistical Mechanics 2024-25PHY3005MLevel 62024-25This module is concerned with bridging a microscopic description of the world (via classical or quantum Hamiltonian mechanics) with a macroscopic description world (via thermodynamics). This is done by considering a probability measure on the space of possible mechanical (micro)states of a system. Topics covered include the basics of probability theory, notions of statistical equilibrium, statistical ensembles (canonical and microcanonical) applied to model systems, thermodynamic potentials and partition functions, and the statistical mechanics of identical particles.CoreAdvanced Topics of Mathematics and Mathematics Seminar 2024-25MTH3001MLevel 62024-25The module will cover several advanced topics of modern mathematics. The choice of the topics will be governed by the current research interests of academic staff and/or visiting scientists. Students will also have the opportunity to participate in mathematics research seminars.OptionalAdvanced Topics of Physics and Physics Seminar 2024-25PHY3001MLevel 62024-25The module will cover several advanced topics of modern physics. The choice of the topics will be governed by the current research interests of academic staff and/or visiting scientists. Students may also participate in physics research seminars.OptionalFluid Dynamics 2024-25MTH3002MLevel 62024-25This module gives a mathematical foundation of ideal and viscous fluid dynamics and their application to describing various flows in nature and technology. Students are taught methods of analysing and solving equations of fluid dynamics using analytic and most modern computational tools.OptionalGroup Theory 2024-25MTH3003MLevel 62024-25Symmetry, understood in most broad sense as invariants under transformations, permeates all parts of mathematics, as well as natural sciences. Groups are measures of such symmetry and therefore are used throughout mathematics. Abstract group theory studies the intrinsic structure of groups. The course begins with definitions of subgroups, normal subgroups, and group actions in various guises. Group homomorphisms are introduced and the related isomorphism theorems are proved. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout, symmetry groups are used as examples.OptionalMathematics Pedagogy 2024-25MTH3004MLevel 62024-25This module is designed to provide students with an insight into the teaching of Mathematics at secondary school level and does this by combining university lectures with an experience of a placement in a secondary school Mathematics department. The module aims to provide students with an opportunity to engage with cutting-edge maths education research and will examine how this research impacts directly on classroom practice. Students will have the opportunity to gain an insight into some of the key ideas in Mathematics pedagogy and how these are implemented in the school Mathematics lessons and will develop an understanding about the barriers to learning Mathematics that many students experience.OptionalMethods of Mathematical Physics 2024-25MTH3006MLevel 62024-25The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.OptionalPhysics of the Universe 2024-25PHY3006MLevel 62024-25This module covers the physics of astronomical, astrophysical, and cosmological phenomena. Topics covered include distance measures in the universe, planetary formation, stellar physics, and some elements of cosmology.OptionalPhysics Pedagogy 2024-25PHY3002MLevel 62024-25This module is designed to provide students with an insight into the teaching of science at secondary school level and does this by combining university lectures with an experience of a placement in a secondary school science department. The module is particularly aimed at those considering a career in science teaching and provides students with an opportunity to engage with cutting edge science education research and will examine how this research impacts directly on classroom practice. Students will have the opportunity to gain an insight into some of the key ideas in science pedagogy and how these are implemented in the school science lessons and will develop an understanding about the barriers to learning science that many students experience.OptionalTensor Analysis 2024-25MTH3008MLevel 62024-25This module introduces tensors, which are abstract objects describing linear relations between vectors, scalars, and other tensors. The module aims to equip students with the knowledge of tensor manipulation, and introduces their applications in modern science.Optional

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