- Mathematics and Physics
BSc (Hons), MMath or MPhys — 2025 entry Mathematics and Physics
Study on our BSc, MPhys or MMath Mathematics and Physics degrees and you'll gain a comprehensive understanding of both disciplines, emphasising the fascinating interconnectedness of mathematics and physics. Graduates are well-prepared for careers in a variety of industries.
Why choose
this course?
If you have a passion for understanding the universe and a love of mathematics, our mathematics and physics courses could be perfect for you.
Our BSc, MMath and MPhys give you a deeper understanding of mathematics and explore how it’s applied to solve physics problems. Whether you think of it as applied mathematics or theoretical physics, this joint programme gives you the best of both worlds.
Two unique aspects of these courses are:
- Our award-winning Professional Training placements:
- As part of our BSc, you can take a paid placement in a research laboratory or company, gaining valuable industry-relevant experience. On our MPhys or MMath, you can take a research placement in Year 4 in one of our world-leading research groups.
- Our focus on undergraduate research and innovation:
- You can apply for paid summer research placements with our research groups and those of our South East Physics Network partners. We offer in-house grants that students can apply for to fund a research placement, attend a conference, or develop a new business idea.
Statistics
16th in the UK
For physics in the Guardian University Guide 2024
96%
of our mathematics and physics undergraduates go on to employment or further study (Graduate Outcomes 2024, HESA)
Accreditation
Video
What you will study
- Explore core topics across both subjects, including linear algebra, quantum physics, differential equations and particle physics.
- Choose from a range of fascinating optional modules – such as fluid dynamics, nuclear astrophysics, Galois theory and general relativity – and take an extended project, enabling you to tailor the course to suit your own interests.
- Your final research project will be carried out under the supervision of an academic who’s a leading researcher in the field. The outcomes of the project could even lead to a publication in a peer-reviewed scientific journal.
- Formal lectures are complemented with work in our specialist radiation laboratories, which have recently been refurbished and enlarged at a cost £2.7m. As an undergraduate student you’ll use these labs to undertake experiments related to the Nuclear and Particle Physics module.
- You can apply to study for either a BSc or an MMath or MPhys. The latter two are direct routes to a masters qualification, known as an integrated masters. If you study toward one of the integrated masters, you’ll spend part of your last year doing a research project in either physics or mathematics.
Professional recognition
BSc (Hons) - Institute of Physics (IOP)
Recognised by the Institute of Physics (IOP) for the purpose of eligibility for Associate Membership.
MPhys - Institute of Physics (IOP)
Recognised by the Institute of Physics (IOP) for the purpose of eligibility for Associate Membership.
MMath - Institute of Physics (IOP)
Recognised by the Institute of Physics (IOP) for the purpose of eligibility for Associate Membership.
Facilities
We have state-of-the-art laboratories and equipment to enhance student learning opportunities and research. These include:
- Characterisation laboratories
- Detector preparation laboratories
- Ellipsometry equipment
- High-performance computing clusters
- Magnetic resonance imaging facilities
- Microscopes and spectrometers
- Nuclear magnetic resonance facilities
- Radiation and medical physics facilities
- Soft matter laboratories.
We also share facilities with Surrey’s acclaimed Advanced Technology Institute, which conducts world-leading research in energy generation and storage, nanotechnology, healthcare, information technology and sustainable technology.
Our Experimental Nuclear Physics Group has access to facilities at prestigious institutions around the globe. These include:
- CERN/ISOLDE (Geneva)
- GSI/FAIR (Germany)
- RIKEN (Japan)
- TRIUMF (Canada).
The academic year is divided into two semesters of 15 weeks each. Each semester consists of a period of teaching, revision/directed learning and assessment.
The structure of our programmes follow clear educational aims that are tailored to each programme. These are all outlined in the programme specifications which include further details such as the learning outcomes.
- Mathematics and Physics BSc (Hons)
- Mathematics and Physics BSc (Hons) with placement
- Mathematics and Physics BSc (Hons) with foundation year
- Mathematics and Physics BSc (Hons) with foundation year and placement
- Mathematics and Physics MMath
- Mathematics and Physics MMath with placement
- Mathematics and Physics MPhys
- Mathematics and Physics MPhys with placement
Please note: The full module listing for the optional Professional Training placement part of your course is available in the relevant programme specification.
Modules
Modules listed are indicative, reflecting the information available at the time of publication. Modules are subject to teaching availability, student demand and/or class size caps.
The University operates a credit framework for all taught programmes based on a 15-credit tariff.
Course options
Year 1 - BSc (Hons)
Semester 1
Compulsory
This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied. Such equations have important applications for interpreting and understanding the world around us.
View full module detailsThis module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.
View full module detailsThis module covers some of the fundamental principles in classical physics including a discussion of units of measurement, the kinematics and dynamics of objects and conservation laws. This material revises and builds upon concepts that are first encountered in the A-level physics course and the study of mechanics as part of A-level mathematics.
View full module detailsThis module covers introductory concepts of simple harmonic motion and waves, drawing on and bringing together examples from different branches of physics including mechanics, optics, electronics, and electromagnetism. Some of these concepts will build upon examples that may have been encountered as part of the Physics A-level material but others are new. It combines the mathematical description, physical interpretation as well as experiments and their analysis of oscillations and wave phenomena to provide students with a well-balanced introduction to the important physical concepts that are required for further study in the subsequent modules of your physics course.
View full module detailsSemester 2
Compulsory
This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics. This module builds on MAT1031: Algebra and provides a foundation for a variety of subsequent modules, including MAT2009 Operations Research and Optimisation, MAT2047 Curves and Surfaces, MAT2048 Groups & Rings, MAT3004 Introduction to Function Spaces and MAT3039 Quantum Mechanics.
View full module detailsThis module will introduce the classical physics that is relevant to gases and condensed matter, making use of the thermodynamic equations of state. The emphasis will be on the structure of matter and its relationship to mechanical and thermal properties, such as elasticity and thermal expansivity. Laws of classical thermodynamics will be introduced. The module will prepare the student for the study of solid state physics and advanced thermodynamics at Level FHEQ 5.
View full module detailsThis module identifies the new theories necessary to describe physical processes when we go beyond the normal speeds and sizes experienced in everyday life. A review of new phenomena that led to the development of quantum theory follows naturally into an introduction to the theory of atomic structure. Along the way, the Schrödinger equation is introduced and elementary applications are considered. Several important aspects of the structure and spectroscopy of atoms are considered in detail. The basis is laid for the study of the properties of matter in more detail at higher levels.
View full module detailsThis module introduces basic mathematical programming in Python and professional skills. The module covers digital skills such as basic data handling, processing and least squares fitting to analyze real-world problems. The professional skills cover employability, teamworking, writing a technical report, and presentation skills. The goal of the module is to equip students with the skills to tackle real-world problems, communicate their results and prepare them for employment after their degree.
View full module detailsYear 2 - BSc (Hons)
Semester 1
Compulsory
This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.
View full module detailsThe Quantum Physics course focuses on the basic formalism of quantum mechanics, its physical interpretation and its application to simple problems. The emphasis is on elementary (one-dimensional) quantum physics, including the infinite-potential well, the parabolic well, one-dimensional step and barrier potentials.
View full module detailsThis module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics. This module builds on material on two-variable calculus introduced in MAT1043 Multivariable Calculus.
View full module detailsThe module will introduce the physical significance and the mathematical methods (and selected theorems) of the operators of vector calculus: div, grad and curl in different co-ordinate systems. The module will introduce the partial differential equations of mathematical physics and their solution for selected physical systems involving different co-ordinate systems and involving time. The module will introduce the foundations of electromagnetism, up to Gauss’ Law and Laplace’s equation, as a major application of the vector calculus and partial differential equations techniques.
View full module detailsSemester 2
Compulsory
When an analytical approach is not known or practical for solving a mathematical problem, which is the case for most real-world problems, a numerical approach can be useful in finding approximate solutions that are as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of systems of linear and nonlinear equations, for finding a function that interpolates or approximates a set of data points, for finding numerical values of derivatives and integrals, and for solving initial value problems. For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also analyse the complexity of numerical methods in order to estimate the computational resources required for achieving a given accuracy. Students will learn and practice implementing some of the methods in Python.
View full module detailsThe module reprises electrostatics (Gauss’ Law) and proceeds to introduce electromagnetic theory through a development of Maxwell’s Equations and concepts associated with the electric and magnetic polarisation of materials. The module introduces electromagnetic wave theory and its applications to a range of traditional applications and problems as well as the use of Fourier processing for wave signal analysis.
View full module detailsThe general properties of nuclei and radioactivity are studied, with an introduction to the deeper structure of elementary particles and the Standard Model. The nuclear physics includes alpha- and beta- and gamma-ray decay, nuclear fission and models of nuclear structure. The high energy physics includes the quark structure of hadrons, CPT conservation and CP violation and the impact of conservation rules on simple reactions of elementary particles.
View full module detailsOptional
This module presents a complete introduction to modern astronomy and astrophysics. We start by introducing astronomy as a unique science; measurement in astronomy (position on the sky, velocity and distance); and multi-messenger probes. We then discuss acceleration due to gravity (the dominant force in the Universe) and we show that timescales are typically so long that we must use models to calculate what happened in the past and what will happen in the future. Armed with an understanding of how to make measurements in astronomy and how to model gravity, we then move from the smallest scales to the largest, studying first the interstellar medium from which stars form; stellar structure and evolution; and stellar remnants (white dwarfs, neutron stars and black holes). We compare and contrast the latest models for how planets form and we discuss the prospects for detecting life and intelligent life beyond Earth. Finally, we discuss the formation and evolution of galaxies in the Universe and the Universe as a whole. We show that the Universe appears to be mostly dark: dark matter (~22%) and dark energy (~74%). Understanding what these mysterious components are is one of the key challenges for physics in the next decade. The module includes either a computer or telescope project. Students enrolled in physics with astronomy with undertake the telescope project where (weather willing) students will gain hands on experience of taking real observational data. They will develop software tools to analyse and interpret these data and write up a final report. Students not enrolled in physics with astronomy will undertake a computational project of similar scope and length, also culminating in a final report.
View full module detailsThe Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in detail. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.
View full module detailsThis module introduces students to inviscid fluid flows including surface waves. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.
View full module detailsThis module provides an introduction to abstract algebra, focusing on the theory of algebraic structures called groups and rings. The module builds on preliminary material on groups introduced in MAT1031 Algebra. This module forms the starting point for subsequent algebraic modules, such as MAT3032 Advanced Algebra, MATM035 Representation Theory and MATM011 Lie Algebras.
View full module detailsOptional modules for Year 2 - FHEQ Level 5
Semester 2: choose 1 optional module
Year 3 - BSc (Hons)
Semester 1
Optional
Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give an oral presentation on their work.
View full module detailsThis module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsIn this module, students will learn key methods adopted in astrophysics to carry out advanced research: scientific computing, statistics, data analysis, machine learning. Much of the course develops highly transferrable skills that apply to science research in general. The goal is to ensure that students are well-prepared for either their research year or their future careers.
View full module detailsThis module introduces six advanced topics in physics. Students will be assessed on only four of these topics, with individuals self-selecting the contact sessions, coursework options and exam questions that reflect their preference. An indicative list of these six topics include: biological physics, special relativity, physics of electronic & photonic materials, cosmology, nuclear astrophysics, and quantum computing.
View full module detailsThe first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives. The second half of the module then focusses on optimization problems with examples including logistics, aerospace, traffic control and finance (which includes pricing, risk managements and portfolio optimizations in financial markets). There is a particular focus on the role of quantum optimization and the use of quantum computer algorithms in finance.
View full module detailsQuantum computers are built around a central processing unit which is a physical device operating according to the rules of quantum mechanics. This module teaches the principles of how quantum processors are built and how they function. The module follows the superconducting architecture, which currently has a significant role in the industry and has been widely studied and implemented. The module will start with reviewing the basic physics required to understand superconducting qubits and the theory of superconducting circuits. It will then continue to the operation of such qubits to perform gates, storage, and readout. After studying the basic building blocks and operations, the module will discuss early demonstrations of important algorithms on superconducting processors. These will lead us naturally to the important topics of improving performance through protection of coherence, advanced control, and validation. The last part of the module will focus on state-of-the-art superconducting processors, focusing on the various challenges in scaling up and the strategies that the industry is pursuing to overcome them.
View full module detailsThe module will introduce students to research level equipment and techniques that are used within the research groups of Physics via extended projects. The four-week projects will cover astrophysics, experimental and theoretical nuclear physics, experimental and theoretical soft matter physics, and quantum technologies. Students will gain experience using state-of-the-art equipment and software, analysing and working with large data sets and in problem solving. The module builds upon experience gained during first- and second-year laboratory and computing classes with project-based work that is typically more open ended and less structured. Students are expected to take more responsibility for the planning and direction of work than in previous years. The goal is to help prepare students for independent research within a team and for future project work (e.g. Final Year Projects and MPhys research years). Numbers will be limited on certain projects.
View full module detailsThis module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.
View full module detailsThis module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies, and give an oral presentation on their work.
View full module detailsGraph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.
View full module detailsThis 30 credit project module is designed to give students the opportunity to explore an area of interest in physics in some depth, either through experimental, theoretical or computational means, or in the form of a literature survey. The module also develops generic professional skills such as teamwork, scientific writing and professional ethics. The module involves writing a dissertation and an oral assessment
View full module detailsThe course will follow the historical development of the main medical imaging techniques. The first part will consider, from a theoretical perspective, the fundamentals of X-ray image formation both in the planar modality and in the Computed Tomography modality. Elements of image processing and image reconstruction will be addressed. The second will look at the physical principles and methods of Nuclear Medicine. The third will look at the principles underlying the application of diagnostic ultrasound in medicine. The fourth will consider Magnetic Resonance Imaging (MRI), one of the most important techniques of medical imaging used in hospitals today. In parallel to the related theoretical classes, laboratory experiments will be carried out on X-ray imaging and ultrasound.
View full module detailsData science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda.
View full module detailsThe module will introduce students to key concepts in education as well as the tools and strategies for effective public engagement in their discipline areas and for different audiences. Students will gain practical experience by planning, implementing, and evaluating an education or public engagement-based activity. Opportunities will also exist for classroom (e.g. school; early-year University) teaching experience and / or involvement in external exhibitions. The projects will be related to current Faculty, department and / or outreach needs thus leading to informed student partnership activities.
View full module detailsThis module aims to provide an advanced level understanding of the physics of stars and nuclear astrophysics. In particular, the course will provide an understanding of advanced nucleosynthetic pathways, an analytical underpinning of resonant reaction rates, together with the experimental techniques involved in their determination.
View full module detailsThis module covers circuit-based quantum computers and some of the algorithms that can be implemented using them. The idea of a classical computational algorithm and its complexity is introduced, and used as a language to discuss quantum computational algorithms. Components of quantum circuits are discussed individually, and then built up to show how algorithms such as the quantum Fourier transform and Grover¿s search algorithm can be implemented, and how such algorithms can be used in applications such as factorizing integers using Shor's algorithm. The Python package qiskit is introduced and used as a tool to implement the algorithms on simulated quantum computers.
View full module detailsThis module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.
View full module detailsThis module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.
View full module detailsTime series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.
View full module detailsSemester 1 & 2
Optional
Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give oral presentations on their work.
View full module detailsOptional modules for Year 3 - FHEQ Level 6
Students must choose either MAT3019 or PHY3002.
Semester 1: Choose 45 credits if MAT3019 is selected. Choose 60 credits if PHY3002 is selected.
Semester 2: Choose 45 credits if MAT3019 is selected. Choose 30 credits if PHY3002 is selected.
MAT3036 cannot be chosen if MAT3019 taken.
At least one MAT3xxx and one PHY3xxx module must be taken each semester. Some combinations may not be possible due to timetabling constraints.
Year 1 - BSc (Hons) with placement
Semester 1
Compulsory
This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied. Such equations have important applications for interpreting and understanding the world around us.
View full module detailsThis module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.
View full module detailsThis module covers some of the fundamental principles in classical physics including a discussion of units of measurement, the kinematics and dynamics of objects and conservation laws. This material revises and builds upon concepts that are first encountered in the A-level physics course and the study of mechanics as part of A-level mathematics.
View full module detailsThis module covers introductory concepts of simple harmonic motion and waves, drawing on and bringing together examples from different branches of physics including mechanics, optics, electronics, and electromagnetism. Some of these concepts will build upon examples that may have been encountered as part of the Physics A-level material but others are new. It combines the mathematical description, physical interpretation as well as experiments and their analysis of oscillations and wave phenomena to provide students with a well-balanced introduction to the important physical concepts that are required for further study in the subsequent modules of your physics course.
View full module detailsSemester 2
Compulsory
This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics. This module builds on MAT1031: Algebra and provides a foundation for a variety of subsequent modules, including MAT2009 Operations Research and Optimisation, MAT2047 Curves and Surfaces, MAT2048 Groups & Rings, MAT3004 Introduction to Function Spaces and MAT3039 Quantum Mechanics.
View full module detailsThis module will introduce the classical physics that is relevant to gases and condensed matter, making use of the thermodynamic equations of state. The emphasis will be on the structure of matter and its relationship to mechanical and thermal properties, such as elasticity and thermal expansivity. Laws of classical thermodynamics will be introduced. The module will prepare the student for the study of solid state physics and advanced thermodynamics at Level FHEQ 5.
View full module detailsThis module identifies the new theories necessary to describe physical processes when we go beyond the normal speeds and sizes experienced in everyday life. A review of new phenomena that led to the development of quantum theory follows naturally into an introduction to the theory of atomic structure. Along the way, the Schrödinger equation is introduced and elementary applications are considered. Several important aspects of the structure and spectroscopy of atoms are considered in detail. The basis is laid for the study of the properties of matter in more detail at higher levels.
View full module detailsThis module introduces basic mathematical programming in Python and professional skills. The module covers digital skills such as basic data handling, processing and least squares fitting to analyze real-world problems. The professional skills cover employability, teamworking, writing a technical report, and presentation skills. The goal of the module is to equip students with the skills to tackle real-world problems, communicate their results and prepare them for employment after their degree.
View full module detailsYear 2 - BSc (Hons) with placement
Semester 1
Compulsory
This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.
View full module detailsThe Quantum Physics course focuses on the basic formalism of quantum mechanics, its physical interpretation and its application to simple problems. The emphasis is on elementary (one-dimensional) quantum physics, including the infinite-potential well, the parabolic well, one-dimensional step and barrier potentials.
View full module detailsThis module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics. This module builds on material on two-variable calculus introduced in MAT1043 Multivariable Calculus.
View full module detailsThe module will introduce the physical significance and the mathematical methods (and selected theorems) of the operators of vector calculus: div, grad and curl in different co-ordinate systems. The module will introduce the partial differential equations of mathematical physics and their solution for selected physical systems involving different co-ordinate systems and involving time. The module will introduce the foundations of electromagnetism, up to Gauss’ Law and Laplace’s equation, as a major application of the vector calculus and partial differential equations techniques.
View full module detailsSemester 2
Compulsory
When an analytical approach is not known or practical for solving a mathematical problem, which is the case for most real-world problems, a numerical approach can be useful in finding approximate solutions that are as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of systems of linear and nonlinear equations, for finding a function that interpolates or approximates a set of data points, for finding numerical values of derivatives and integrals, and for solving initial value problems. For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also analyse the complexity of numerical methods in order to estimate the computational resources required for achieving a given accuracy. Students will learn and practice implementing some of the methods in Python.
View full module detailsThe module reprises electrostatics (Gauss’ Law) and proceeds to introduce electromagnetic theory through a development of Maxwell’s Equations and concepts associated with the electric and magnetic polarisation of materials. The module introduces electromagnetic wave theory and its applications to a range of traditional applications and problems as well as the use of Fourier processing for wave signal analysis.
View full module detailsThe general properties of nuclei and radioactivity are studied, with an introduction to the deeper structure of elementary particles and the Standard Model. The nuclear physics includes alpha- and beta- and gamma-ray decay, nuclear fission and models of nuclear structure. The high energy physics includes the quark structure of hadrons, CPT conservation and CP violation and the impact of conservation rules on simple reactions of elementary particles.
View full module detailsOptional
This module presents a complete introduction to modern astronomy and astrophysics. We start by introducing astronomy as a unique science; measurement in astronomy (position on the sky, velocity and distance); and multi-messenger probes. We then discuss acceleration due to gravity (the dominant force in the Universe) and we show that timescales are typically so long that we must use models to calculate what happened in the past and what will happen in the future. Armed with an understanding of how to make measurements in astronomy and how to model gravity, we then move from the smallest scales to the largest, studying first the interstellar medium from which stars form; stellar structure and evolution; and stellar remnants (white dwarfs, neutron stars and black holes). We compare and contrast the latest models for how planets form and we discuss the prospects for detecting life and intelligent life beyond Earth. Finally, we discuss the formation and evolution of galaxies in the Universe and the Universe as a whole. We show that the Universe appears to be mostly dark: dark matter (~22%) and dark energy (~74%). Understanding what these mysterious components are is one of the key challenges for physics in the next decade. The module includes either a computer or telescope project. Students enrolled in physics with astronomy with undertake the telescope project where (weather willing) students will gain hands on experience of taking real observational data. They will develop software tools to analyse and interpret these data and write up a final report. Students not enrolled in physics with astronomy will undertake a computational project of similar scope and length, also culminating in a final report.
View full module detailsThe Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in detail. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.
View full module detailsThis module introduces students to inviscid fluid flows including surface waves. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.
View full module detailsThis module provides an introduction to abstract algebra, focusing on the theory of algebraic structures called groups and rings. The module builds on preliminary material on groups introduced in MAT1031 Algebra. This module forms the starting point for subsequent algebraic modules, such as MAT3032 Advanced Algebra, MATM035 Representation Theory and MATM011 Lie Algebras.
View full module detailsOptional modules for Year 2 (with PTY) - FHEQ Level 5
Semester 2: choose 1 optional module
Year 3 - BSc (Hons) with placement
Semester 1
Optional
Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give an oral presentation on their work.
View full module detailsThis module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsIn this module, students will learn key methods adopted in astrophysics to carry out advanced research: scientific computing, statistics, data analysis, machine learning. Much of the course develops highly transferrable skills that apply to science research in general. The goal is to ensure that students are well-prepared for either their research year or their future careers.
View full module detailsThis module introduces six advanced topics in physics. Students will be assessed on only four of these topics, with individuals self-selecting the contact sessions, coursework options and exam questions that reflect their preference. An indicative list of these six topics include: biological physics, special relativity, physics of electronic & photonic materials, cosmology, nuclear astrophysics, and quantum computing.
View full module detailsThe first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives. The second half of the module then focusses on optimization problems with examples including logistics, aerospace, traffic control and finance (which includes pricing, risk managements and portfolio optimizations in financial markets). There is a particular focus on the role of quantum optimization and the use of quantum computer algorithms in finance.
View full module detailsQuantum computers are built around a central processing unit which is a physical device operating according to the rules of quantum mechanics. This module teaches the principles of how quantum processors are built and how they function. The module follows the superconducting architecture, which currently has a significant role in the industry and has been widely studied and implemented. The module will start with reviewing the basic physics required to understand superconducting qubits and the theory of superconducting circuits. It will then continue to the operation of such qubits to perform gates, storage, and readout. After studying the basic building blocks and operations, the module will discuss early demonstrations of important algorithms on superconducting processors. These will lead us naturally to the important topics of improving performance through protection of coherence, advanced control, and validation. The last part of the module will focus on state-of-the-art superconducting processors, focusing on the various challenges in scaling up and the strategies that the industry is pursuing to overcome them.
View full module detailsThe module will introduce students to research level equipment and techniques that are used within the research groups of Physics via extended projects. The four-week projects will cover astrophysics, experimental and theoretical nuclear physics, experimental and theoretical soft matter physics, and quantum technologies. Students will gain experience using state-of-the-art equipment and software, analysing and working with large data sets and in problem solving. The module builds upon experience gained during first- and second-year laboratory and computing classes with project-based work that is typically more open ended and less structured. Students are expected to take more responsibility for the planning and direction of work than in previous years. The goal is to help prepare students for independent research within a team and for future project work (e.g. Final Year Projects and MPhys research years). Numbers will be limited on certain projects.
View full module detailsThis module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.
View full module detailsThis module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies, and give an oral presentation on their work.
View full module detailsGraph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.
View full module detailsThis 30 credit project module is designed to give students the opportunity to explore an area of interest in physics in some depth, either through experimental, theoretical or computational means, or in the form of a literature survey. The module also develops generic professional skills such as teamwork, scientific writing and professional ethics. The module involves writing a dissertation and an oral assessment
View full module detailsThe course will follow the historical development of the main medical imaging techniques. The first part will consider, from a theoretical perspective, the fundamentals of X-ray image formation both in the planar modality and in the Computed Tomography modality. Elements of image processing and image reconstruction will be addressed. The second will look at the physical principles and methods of Nuclear Medicine. The third will look at the principles underlying the application of diagnostic ultrasound in medicine. The fourth will consider Magnetic Resonance Imaging (MRI), one of the most important techniques of medical imaging used in hospitals today. In parallel to the related theoretical classes, laboratory experiments will be carried out on X-ray imaging and ultrasound.
View full module detailsData science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda.
View full module detailsThe module will introduce students to key concepts in education as well as the tools and strategies for effective public engagement in their discipline areas and for different audiences. Students will gain practical experience by planning, implementing, and evaluating an education or public engagement-based activity. Opportunities will also exist for classroom (e.g. school; early-year University) teaching experience and / or involvement in external exhibitions. The projects will be related to current Faculty, department and / or outreach needs thus leading to informed student partnership activities.
View full module detailsThis module aims to provide an advanced level understanding of the physics of stars and nuclear astrophysics. In particular, the course will provide an understanding of advanced nucleosynthetic pathways, an analytical underpinning of resonant reaction rates, together with the experimental techniques involved in their determination.
View full module detailsThis module covers circuit-based quantum computers and some of the algorithms that can be implemented using them. The idea of a classical computational algorithm and its complexity is introduced, and used as a language to discuss quantum computational algorithms. Components of quantum circuits are discussed individually, and then built up to show how algorithms such as the quantum Fourier transform and Grover¿s search algorithm can be implemented, and how such algorithms can be used in applications such as factorizing integers using Shor's algorithm. The Python package qiskit is introduced and used as a tool to implement the algorithms on simulated quantum computers.
View full module detailsThis module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.
View full module detailsThis module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.
View full module detailsTime series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.
View full module detailsSemester 1 & 2
Optional
Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give oral presentations on their work.
View full module detailsOptional modules for Year 3 (with PTY) - FHEQ Level 6
Students must choose either MAT3019 or PHY3002.
Semester 1: choose 45 credits if MAT3019 is selected. Choose 60 credits if PHY3002 is selected.
Semester 2: choose 45 credits if MAT3019 is selected. Choose 30 credits if PHY3002 is selected.
MAT3036 cannot be chosen if MAT3019 taken.
At least one MAT3xxx and one PHY3xxx module must be taken each semester. Some combinations may not be possible due to timetabling constraints.
Year 3 - BSc (Hons) with placement
Semester 1 & 2
Core
This module supports students’ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning, and is a process that involves self-reflection, documented via the creation of a personal record, planning and monitoring progress towards the achievement of personal objectives. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written and presentation skills.
View full module detailsThis module supports students¿ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning and is a process that involves self-reflection. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written skills.
View full module detailsThis module supports students¿ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning, and is a process that involves self-reflection, documented via the creation of a personal record, planning and monitoring progress towards the achievement of personal objectives. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written skills.
View full module detailsBSc (Hons) with foundation year
Semester 1
Compulsory
This mathematics module is designed to reinforce and broaden basic A-Level mathematics material, develop problem solving skills and prepare students for the more advanced mathematical concepts and problem-solving scenarios in the semester 2 modules.The priority is to develop the students’ ability to solve real- world problems in a confident manner. The concepts delivered on this module reflect the skills and knowledge required to understand the physical around us. This is vital as mathematics plays a critical role in the students’ future employability and achievement on their respective undergraduate choices.
View full module detailsThe emphasis of this module is on the development of digital capabilities, academic skills and problem-solving skills. The module will facilitate the development of competency in working with software commonly used to support calculations, analysis and presentation. Microsoft Excel will be used for spreadsheet-based calculations and experimental data analysis. MATLAB will be used as a platform for developing elementary programming skills and applying various processes to novel problem-solving scenarios. The breadth and depth of digital capabilities will be further enhanced by working with HTML, CSS and JavaScript within the GitHub environment to develop a webpage, presenting the student's research project narrative. The project provides students with an opportunity to carry out guided research and prepare an online article on one of many discipline-specific topic choices. Students will develop a wide range of writing, referencing and other important academic skills and learn how to use embedded and/or interactive online content to support the presentation of their online article.
View full module detailsThis module introduces several principles and processes which underpin most physical science and engineering disciplines, which you are likely to study beyond the Foundation Year. Specifically, you will study topics that include S.I. units and measurement theory, electric and magnetic fields and their interactions, the properties of ideal gases, heat transfer and thermodynamics, fluid statics and dynamics, and engineering instrumentation and measurement. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported by the use of the university’s virtual learning platform.
View full module detailsThe module is designed to develop and extend your critical thinking skills and problem solving skills beyond that which would normally be acquired in an A-level (or comparable level) course. From a theoretical perspective, you will study pure mathematics, probability & statistics together with some applied computational mathematics. The practical computing aspect of the module brings together a variety of techniques in data processing, analysis, modelling and probability and statistics so that you may further advance your problem solving skills and apply some of the theory within a variety of interesting and challenging contexts using Microsoft Excel.
View full module detailsSemester 2
Compulsory
A foundation level physics module designed to reinforce and broaden basic A-Level Physics material in electricity and electronics, nuclear physics, develop practical skills, and prepare students for the more advanced concepts and applications in the first year of their Engineering or Physical Sciences degree. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported using the university’s virtual learning platform.
View full module detailsThis module builds further on the mathematical and computing skills that you developed previously. As before, there is a strong emphasis on critical thinking, problem solving and becoming more independent as a learner. A number of advanced topic areas will be introduced in both the mathematics and computing components. These two module components are equally weighted at 50% each. There are a total of 11 advanced mathematics lectures with associated tutorials and 11 computer laboratory sessions with associated tutorials.The main topic areas covered by the mathematics component are; matrices & vectors, complex numbers and calculus. Associated geometrical concepts are introduced in all of these topic areas. In the computing component you will learn to use Python and associated packages as a language for implementing a variety of interesting and challenging processes. An emphasis will be placed on the process of abstraction and implementation, with process design considerations at holistic and atomic levels.Your progress on the module is assessed in 12 separate units of assessment (6 for mathematics and 6 for computing.)
View full module detailsThis module builds on ENG0011 Mathematics A and is designed to reinforce and broaden A-Level Calculus, Vectors, Matrices and Complex Numbers. The students will continue to develop their ability to solve real- world problems in a confident manner. The concepts delivered on this module reflect the skills and knowledge required to understand the physical world around us. This is vital, as mathematics plays a critical role in the students’ future employability and achievement on their respective undergraduate courses. On completion of the module students are prepared for the more advanced Mathematical concepts and problem solving scenarios in the first year of their Engineering or Physical Sciences degree.
View full module detailsThis module introduces several principles and processes which underpin most physical science and engineering disciplines, which you are likely to study beyond the Foundation Year. Specifically, you will study topics that include vectors and scalars, equations of motion under constant acceleration, momentum conservation, simple harmonic motion and wave theory. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported by the use of the university’s virtual learning platform.
View full module detailsOptional modules for Foundation - FHEQ Level 3
For further information on FHEQ levels 4, 5 and 6 please view the programme specification for the full-time BSc (Hons) Mathematics and Physics programme.
BSc (Hons) with foundation year and placement
Semester 1
Compulsory
This module introduces several principles and processes which underpin most physical science and engineering disciplines, which you are likely to study beyond the Foundation Year. Specifically, you will study topics that include S.I. units and measurement theory, electric and magnetic fields and their interactions, the properties of ideal gases, heat transfer and thermodynamics, fluid statics and dynamics, and engineering instrumentation and measurement. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported by the use of the university’s virtual learning platform.
View full module detailsThe module is designed to develop and extend your critical thinking skills and problem solving skills beyond that which would normally be acquired in an A-level (or comparable level) course. From a theoretical perspective, you will study pure mathematics, probability & statistics together with some applied computational mathematics. The practical computing aspect of the module brings together a variety of techniques in data processing, analysis, modelling and probability and statistics so that you may further advance your problem solving skills and apply some of the theory within a variety of interesting and challenging contexts using Microsoft Excel.
View full module detailsThis mathematics module is designed to reinforce and broaden basic A-Level mathematics material, develop problem solving skills and prepare students for the more advanced mathematical concepts and problem-solving scenarios in the semester 2 modules.The priority is to develop the students’ ability to solve real- world problems in a confident manner. The concepts delivered on this module reflect the skills and knowledge required to understand the physical around us. This is vital as mathematics plays a critical role in the students’ future employability and achievement on their respective undergraduate choices.
View full module detailsThe emphasis of this module is on the development of digital capabilities, academic skills and problem-solving skills. The module will facilitate the development of competency in working with software commonly used to support calculations, analysis and presentation. Microsoft Excel will be used for spreadsheet-based calculations and experimental data analysis. MATLAB will be used as a platform for developing elementary programming skills and applying various processes to novel problem-solving scenarios. The breadth and depth of digital capabilities will be further enhanced by working with HTML, CSS and JavaScript within the GitHub environment to develop a webpage, presenting the student's research project narrative. The project provides students with an opportunity to carry out guided research and prepare an online article on one of many discipline-specific topic choices. Students will develop a wide range of writing, referencing and other important academic skills and learn how to use embedded and/or interactive online content to support the presentation of their online article.
View full module detailsSemester 2
Compulsory
This module builds on ENG0011 Mathematics A and is designed to reinforce and broaden A-Level Calculus, Vectors, Matrices and Complex Numbers. The students will continue to develop their ability to solve real- world problems in a confident manner. The concepts delivered on this module reflect the skills and knowledge required to understand the physical world around us. This is vital, as mathematics plays a critical role in the students’ future employability and achievement on their respective undergraduate courses. On completion of the module students are prepared for the more advanced Mathematical concepts and problem solving scenarios in the first year of their Engineering or Physical Sciences degree.
View full module detailsThis module introduces several principles and processes which underpin most physical science and engineering disciplines, which you are likely to study beyond the Foundation Year. Specifically, you will study topics that include vectors and scalars, equations of motion under constant acceleration, momentum conservation, simple harmonic motion and wave theory. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported by the use of the university’s virtual learning platform.
View full module detailsA foundation level physics module designed to reinforce and broaden basic A-Level Physics material in electricity and electronics, nuclear physics, develop practical skills, and prepare students for the more advanced concepts and applications in the first year of their Engineering or Physical Sciences degree. You will attend several lectures and a tutorial each teaching week alongside guided independent study opportunities to develop your understanding of topics more deeply, supported using the university’s virtual learning platform.
View full module detailsThis module builds further on the mathematical and computing skills that you developed previously. As before, there is a strong emphasis on critical thinking, problem solving and becoming more independent as a learner. A number of advanced topic areas will be introduced in both the mathematics and computing components. These two module components are equally weighted at 50% each. There are a total of 11 advanced mathematics lectures with associated tutorials and 11 computer laboratory sessions with associated tutorials.The main topic areas covered by the mathematics component are; matrices & vectors, complex numbers and calculus. Associated geometrical concepts are introduced in all of these topic areas. In the computing component you will learn to use Python and associated packages as a language for implementing a variety of interesting and challenging processes. An emphasis will be placed on the process of abstraction and implementation, with process design considerations at holistic and atomic levels.Your progress on the module is assessed in 12 separate units of assessment (6 for mathematics and 6 for computing.)
View full module detailsOptional modules for Foundation (with PTY) - FHEQ Level 3
For further information on FHEQ levels 4, 5 and 6 and professional training year please view the programme specification for the full-time with PTY BSc (Hons) Mathematics and Physics programme.
Year 1 - MMath
Semester 1
Compulsory
This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied. Such equations have important applications for interpreting and understanding the world around us.
View full module detailsThis module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.
View full module detailsThis module covers some of the fundamental principles in classical physics including a discussion of units of measurement, the kinematics and dynamics of objects and conservation laws. This material revises and builds upon concepts that are first encountered in the A-level physics course and the study of mechanics as part of A-level mathematics.
View full module detailsThis module covers introductory concepts of simple harmonic motion and waves, drawing on and bringing together examples from different branches of physics including mechanics, optics, electronics, and electromagnetism. Some of these concepts will build upon examples that may have been encountered as part of the Physics A-level material but others are new. It combines the mathematical description, physical interpretation as well as experiments and their analysis of oscillations and wave phenomena to provide students with a well-balanced introduction to the important physical concepts that are required for further study in the subsequent modules of your physics course.
View full module detailsSemester 2
Compulsory
This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics. This module builds on MAT1031: Algebra and provides a foundation for a variety of subsequent modules, including MAT2009 Operations Research and Optimisation, MAT2047 Curves and Surfaces, MAT2048 Groups & Rings, MAT3004 Introduction to Function Spaces and MAT3039 Quantum Mechanics.
View full module detailsThis module will introduce the classical physics that is relevant to gases and condensed matter, making use of the thermodynamic equations of state. The emphasis will be on the structure of matter and its relationship to mechanical and thermal properties, such as elasticity and thermal expansivity. Laws of classical thermodynamics will be introduced. The module will prepare the student for the study of solid state physics and advanced thermodynamics at Level FHEQ 5.
View full module detailsThis module identifies the new theories necessary to describe physical processes when we go beyond the normal speeds and sizes experienced in everyday life. A review of new phenomena that led to the development of quantum theory follows naturally into an introduction to the theory of atomic structure. Along the way, the Schrödinger equation is introduced and elementary applications are considered. Several important aspects of the structure and spectroscopy of atoms are considered in detail. The basis is laid for the study of the properties of matter in more detail at higher levels.
View full module detailsThis module introduces basic mathematical programming in Python and professional skills. The module covers digital skills such as basic data handling, processing and least squares fitting to analyze real-world problems. The professional skills cover employability, teamworking, writing a technical report, and presentation skills. The goal of the module is to equip students with the skills to tackle real-world problems, communicate their results and prepare them for employment after their degree.
View full module detailsYear 2 - MMath
Semester 1
Compulsory
This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.
View full module detailsThe Quantum Physics course focuses on the basic formalism of quantum mechanics, its physical interpretation and its application to simple problems. The emphasis is on elementary (one-dimensional) quantum physics, including the infinite-potential well, the parabolic well, one-dimensional step and barrier potentials.
View full module detailsThis module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics. This module builds on material on two-variable calculus introduced in MAT1043 Multivariable Calculus.
View full module detailsThe module will introduce the physical significance and the mathematical methods (and selected theorems) of the operators of vector calculus: div, grad and curl in different co-ordinate systems. The module will introduce the partial differential equations of mathematical physics and their solution for selected physical systems involving different co-ordinate systems and involving time. The module will introduce the foundations of electromagnetism, up to Gauss’ Law and Laplace’s equation, as a major application of the vector calculus and partial differential equations techniques.
View full module detailsSemester 2
Compulsory
When an analytical approach is not known or practical for solving a mathematical problem, which is the case for most real-world problems, a numerical approach can be useful in finding approximate solutions that are as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of systems of linear and nonlinear equations, for finding a function that interpolates or approximates a set of data points, for finding numerical values of derivatives and integrals, and for solving initial value problems. For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also analyse the complexity of numerical methods in order to estimate the computational resources required for achieving a given accuracy. Students will learn and practice implementing some of the methods in Python.
View full module detailsThe module reprises electrostatics (Gauss’ Law) and proceeds to introduce electromagnetic theory through a development of Maxwell’s Equations and concepts associated with the electric and magnetic polarisation of materials. The module introduces electromagnetic wave theory and its applications to a range of traditional applications and problems as well as the use of Fourier processing for wave signal analysis.
View full module detailsThe general properties of nuclei and radioactivity are studied, with an introduction to the deeper structure of elementary particles and the Standard Model. The nuclear physics includes alpha- and beta- and gamma-ray decay, nuclear fission and models of nuclear structure. The high energy physics includes the quark structure of hadrons, CPT conservation and CP violation and the impact of conservation rules on simple reactions of elementary particles.
View full module detailsOptional
This module presents a complete introduction to modern astronomy and astrophysics. We start by introducing astronomy as a unique science; measurement in astronomy (position on the sky, velocity and distance); and multi-messenger probes. We then discuss acceleration due to gravity (the dominant force in the Universe) and we show that timescales are typically so long that we must use models to calculate what happened in the past and what will happen in the future. Armed with an understanding of how to make measurements in astronomy and how to model gravity, we then move from the smallest scales to the largest, studying first the interstellar medium from which stars form; stellar structure and evolution; and stellar remnants (white dwarfs, neutron stars and black holes). We compare and contrast the latest models for how planets form and we discuss the prospects for detecting life and intelligent life beyond Earth. Finally, we discuss the formation and evolution of galaxies in the Universe and the Universe as a whole. We show that the Universe appears to be mostly dark: dark matter (~22%) and dark energy (~74%). Understanding what these mysterious components are is one of the key challenges for physics in the next decade. The module includes either a computer or telescope project. Students enrolled in physics with astronomy with undertake the telescope project where (weather willing) students will gain hands on experience of taking real observational data. They will develop software tools to analyse and interpret these data and write up a final report. Students not enrolled in physics with astronomy will undertake a computational project of similar scope and length, also culminating in a final report.
View full module detailsThe Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in detail. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.
View full module detailsThis module introduces students to inviscid fluid flows including surface waves. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.
View full module detailsThis module provides an introduction to abstract algebra, focusing on the theory of algebraic structures called groups and rings. The module builds on preliminary material on groups introduced in MAT1031 Algebra. This module forms the starting point for subsequent algebraic modules, such as MAT3032 Advanced Algebra, MATM035 Representation Theory and MATM011 Lie Algebras.
View full module detailsOptional modules for Year 2 - FHEQ Level 5
Choose 1 optional module
Year 3 - MMath
Semester 1
Optional
This module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsIn this module, students will learn key methods adopted in astrophysics to carry out advanced research: scientific computing, statistics, data analysis, machine learning. Much of the course develops highly transferrable skills that apply to science research in general. The goal is to ensure that students are well-prepared for either their research year or their future careers.
View full module detailsThis module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.
View full module detailsThis module introduces six advanced topics in physics. Students will be assessed on only four of these topics, with individuals self-selecting the contact sessions, coursework options and exam questions that reflect their preference. An indicative list of these six topics include: biological physics, special relativity, physics of electronic & photonic materials, cosmology, nuclear astrophysics, and quantum computing.
View full module detailsThe first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives. The second half of the module then focusses on optimization problems with examples including logistics, aerospace, traffic control and finance (which includes pricing, risk managements and portfolio optimizations in financial markets). There is a particular focus on the role of quantum optimization and the use of quantum computer algorithms in finance.
View full module detailsQuantum computers are built around a central processing unit which is a physical device operating according to the rules of quantum mechanics. This module teaches the principles of how quantum processors are built and how they function. The module follows the superconducting architecture, which currently has a significant role in the industry and has been widely studied and implemented. The module will start with reviewing the basic physics required to understand superconducting qubits and the theory of superconducting circuits. It will then continue to the operation of such qubits to perform gates, storage, and readout. After studying the basic building blocks and operations, the module will discuss early demonstrations of important algorithms on superconducting processors. These will lead us naturally to the important topics of improving performance through protection of coherence, advanced control, and validation. The last part of the module will focus on state-of-the-art superconducting processors, focusing on the various challenges in scaling up and the strategies that the industry is pursuing to overcome them.
View full module detailsThis module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.
View full module detailsThe module will introduce students to research level equipment and techniques that are used within the research groups of Physics via extended projects. The four-week projects will cover astrophysics, experimental and theoretical nuclear physics, experimental and theoretical soft matter physics, and quantum technologies. Students will gain experience using state-of-the-art equipment and software, analysing and working with large data sets and in problem solving. The module builds upon experience gained during first- and second-year laboratory and computing classes with project-based work that is typically more open ended and less structured. Students are expected to take more responsibility for the planning and direction of work than in previous years. The goal is to help prepare students for independent research within a team and for future project work (e.g. Final Year Projects and MPhys research years). Numbers will be limited on certain projects.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.
View full module detailsThe course will follow the historical development of the main medical imaging techniques. The first part will consider, from a theoretical perspective, the fundamentals of X-ray image formation both in the planar modality and in the Computed Tomography modality. Elements of image processing and image reconstruction will be addressed. The second will look at the physical principles and methods of Nuclear Medicine. The third will look at the principles underlying the application of diagnostic ultrasound in medicine. The fourth will consider Magnetic Resonance Imaging (MRI), one of the most important techniques of medical imaging used in hospitals today. In parallel to the related theoretical classes, laboratory experiments will be carried out on X-ray imaging and ultrasound.
View full module detailsData science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda.
View full module detailsThe module will introduce students to key concepts in education as well as the tools and strategies for effective public engagement in their discipline areas and for different audiences. Students will gain practical experience by planning, implementing, and evaluating an education or public engagement-based activity. Opportunities will also exist for classroom (e.g. school; early-year University) teaching experience and / or involvement in external exhibitions. The projects will be related to current Faculty, department and / or outreach needs thus leading to informed student partnership activities.
View full module detailsThis module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.
View full module detailsThis module covers circuit-based quantum computers and some of the algorithms that can be implemented using them. The idea of a classical computational algorithm and its complexity is introduced, and used as a language to discuss quantum computational algorithms. Components of quantum circuits are discussed individually, and then built up to show how algorithms such as the quantum Fourier transform and Grover¿s search algorithm can be implemented, and how such algorithms can be used in applications such as factorizing integers using Shor's algorithm. The Python package qiskit is introduced and used as a tool to implement the algorithms on simulated quantum computers.
View full module detailsThis module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.
View full module detailsTime series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.
View full module detailsOptional modules for Year 3 - FHEQ Level 6
Students must choose 60 credits of options in each Semester.
Year 4 - MMath
Semester 1
Optional
Asset prices in financial markets go up and down in accordance with how markets digest the flow of information. To understand the causal relation between information flow and price movements, it is necessary to model market information and use this to infer the price dynamics. In this way, market dynamics can be replicated artificially on a computer. This module explains the powerful process of artificially generating realistic market models. The module begins with elements of probability theory. We will then learn the idea of conditional expectation and the Bayes formula, which gives the optimal inference under uncertainty. The meaning of the Bayes formula will be explained, leading to the understanding of what is meant by “intelligence”. The module then covers the basics of stochastic process (specifically, the Brownian motion) and calculus (specifically, the Ito calculus), sufficient to follow the contents of the module. Then simple models for flows of information in financial markets will be introduced, and by use of the Bayes formula the associated price dynamics will be derived. The module concludes with a brief application to the asset valuation problems in financial markets (such as options or other derivatives).
View full module detailsMathematics underpinning real-world uncertain events has become indispensable in many applications, including in particular financial markets. This module will begin with the introduction to probability theory and stochastic processes, with an emphasis on the Ito calculus for treating functions of Brownian motion. Such functions are commonly used in financial markets to model asset price dynamics, required for the valuation of financial contracts. The module then discusses structures of financial markets, with an emphasis on the equity market. Several of the standard and exotic contingent claims will be introduced, and the need for mathematical models for the valuation and risk management of these products will be explained. The pricing of a standard call option will then be worked out in a single-period binomial model, for which option price will be worked out in two ways: first using the portfolio replication and no arbitrage argument, and second using the risk-neutral expectation argument. The model is then extended into multi-period binomial tree model, leading to the Cox-Ross-Rubinstein option pricing formula. Finally, a continuous-time geometric Brownian motion model, originally introduced by Samuelson, will be considered, and used to deduce the famous Black-Scholes option pricing formula. This can be applied for the purpose of both pricing, as well as risk-management purposes, which will be demonstrated by working out the hedging strategy. The meaning of the pricing formula, and how it can be used in practical investment banking context, will be explained.
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
This 15-credit M-Level module introduces important topics and techniques in theoretical physics that have a wide range of applications in many areas physics and engineering and which the students will not have met before. Both the mathematical techniques and their applications are covered at a level appropriate for Masters level students coming to the end of their degree and who should be able to pull many different ideas in theoretical physics together.
View full module detailsThis module aims to provide an advanced level understanding of explosive nuclear astrophysics and the physics of stars. In particular, the course will provide an analytical underpinning of resonant reaction rates, together with the experimental techniques involved in their determination, as well as a theoretical treatment of nuclear reactions and celestial objects.
View full module detailsThis module will introduce the students to the principles and formalism of General Relativity and its applications to Black Holes and astrophysical phenomena.
View full module detailsGroup theory is a branch of mathematics developed to understand symmetries, which are powerful tools for understanding the properties of complex mathematical problems and physical systems. Group representations map abstract group elements to linear transformations on vector spaces. Representation theory allows us to better understand the properties of symmetry groups, and leads to powerful and compact solutions of otherwise difficult and intractable problems. This module builds on groups theory in MAT1031 Algebra and MAT2048 Groups & Rings.
View full module detailsQuantum Mechanics topics are essential building blocks for our understanding of many physical systems. The module assumes basic knowledge in quantum mechanics from modules in earlier years, but will provide a review at the beginning. Topics include a review of quantum mechanics, operator methods and applications to the harmonic oscillator, spin & angular momentum, symmetries in quantum mechanics. The second half of the module then moves beyond isolated quantum systems by addressing the topic of Quantum Entanglement and Quantum Coherence. Here the important concepts of entanglement and decoherence will be studied by developing an understanding of open quantum systems and the density matrix formalism.
View full module detailsThis module comprises two independent halves, on making qubit, and quantum communications. Quantum technologies, including quantum computing, rely on the quantum mechanical principles of superposition and entanglement. Furthermore, this superposition and entanglement needs to be controlled in useful ways. In this module you will learn about what physical systems allow quantum technology production, and their limitations. Quantum computers are only one type of device that uses these principles, and several other technologies are being created that are also enhanced by use of superpositions. Others include atomic clocks and Magnetic Resonance Imaging, MRI. We will also learn about the errors that inevitably build up in quantum computers when quantum superpositions are disturbed, and the strategies that might be built in to correct them. Quantum communications. This course provides a comprehensive introduction to the principles, protocols, and applications of quantum communications. Students will explore the fundamental concepts of quantum information transmission, quantum cryptography, and quantum communication protocols. They will also examine the challenges, advancements, and real-world applications of quantum communications including both theory and practical aspects.
View full module detailsThe module is an introduction to nonlinear partial differential equations (PDEs) with a focus on hyperbolic and dispersive PDEs. The module takes key classes of equations as the organising centre. Each class of PDEs is considered and the properties, analytical techniques, and analysis of each is taken in turn.
View full module detailsThis module introduces programming in Python for data science, with a focus on data pre-processing, data mining and analysis, machine learning and deep learning. Besides the practical hands-on experience with writing code, this course also covers the theoretical background on different data analysis techniques and machine learning approaches. The goal is to develop an understanding of how information can be extracted from data and how this information can be further used to make predictions, but importantly how this is done practically in terms of writing clear and transparent source code. Using real-world data sets and illustrative examples, this course will help to develop a theoretical understanding of data science as well as practical experience by developing useful software tools. Many of the techniques acquired through this module are likely to be of potential use in the dissertation project.
View full module detailsThe course provides an introduction to nuclear energy generation and applications of nuclear science. Nuclear reactors, their physics and operation are described. Nuclear reactor safety case work is also discussed. Future potential energy generation mechanisms such including nuclear fusion will be discussed. The module will also present a range of applications of radioactivity measurement including aspects of Environmental Science and Medical Diagnogstics and treatment therapy. The module will include some aspects of calculus and first order differential equations.
View full module detailsSemester 1 & 2
Compulsory
Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give oral presentations on their work.
View full module detailsOptional modules for Year 4 - FHEQ Level 7
Students on the MMath pathway must take the MATM050 MMath Project. Choose 6 options overall, to maintain a 60:60 credit balance between Semesters 1 and 2
Year 1 - MMath with placement
Semester 1
Compulsory
This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied. Such equations have important applications for interpreting and understanding the world around us.
View full module detailsThis module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.
View full module detailsThis module covers some of the fundamental principles in classical physics including a discussion of units of measurement, the kinematics and dynamics of objects and conservation laws. This material revises and builds upon concepts that are first encountered in the A-level physics course and the study of mechanics as part of A-level mathematics.
View full module detailsThis module covers introductory concepts of simple harmonic motion and waves, drawing on and bringing together examples from different branches of physics including mechanics, optics, electronics, and electromagnetism. Some of these concepts will build upon examples that may have been encountered as part of the Physics A-level material but others are new. It combines the mathematical description, physical interpretation as well as experiments and their analysis of oscillations and wave phenomena to provide students with a well-balanced introduction to the important physical concepts that are required for further study in the subsequent modules of your physics course.
View full module detailsSemester 2
Compulsory
This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics. This module builds on MAT1031: Algebra and provides a foundation for a variety of subsequent modules, including MAT2009 Operations Research and Optimisation, MAT2047 Curves and Surfaces, MAT2048 Groups & Rings, MAT3004 Introduction to Function Spaces and MAT3039 Quantum Mechanics.
View full module detailsThis module will introduce the classical physics that is relevant to gases and condensed matter, making use of the thermodynamic equations of state. The emphasis will be on the structure of matter and its relationship to mechanical and thermal properties, such as elasticity and thermal expansivity. Laws of classical thermodynamics will be introduced. The module will prepare the student for the study of solid state physics and advanced thermodynamics at Level FHEQ 5.
View full module detailsThis module identifies the new theories necessary to describe physical processes when we go beyond the normal speeds and sizes experienced in everyday life. A review of new phenomena that led to the development of quantum theory follows naturally into an introduction to the theory of atomic structure. Along the way, the Schrödinger equation is introduced and elementary applications are considered. Several important aspects of the structure and spectroscopy of atoms are considered in detail. The basis is laid for the study of the properties of matter in more detail at higher levels.
View full module detailsThis module introduces basic mathematical programming in Python and professional skills. The module covers digital skills such as basic data handling, processing and least squares fitting to analyze real-world problems. The professional skills cover employability, teamworking, writing a technical report, and presentation skills. The goal of the module is to equip students with the skills to tackle real-world problems, communicate their results and prepare them for employment after their degree.
View full module detailsYear 2 - MMath with placement
Semester 1
Compulsory
This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.
View full module detailsThe Quantum Physics course focuses on the basic formalism of quantum mechanics, its physical interpretation and its application to simple problems. The emphasis is on elementary (one-dimensional) quantum physics, including the infinite-potential well, the parabolic well, one-dimensional step and barrier potentials.
View full module detailsThis module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics. This module builds on material on two-variable calculus introduced in MAT1043 Multivariable Calculus.
View full module detailsThe module will introduce the physical significance and the mathematical methods (and selected theorems) of the operators of vector calculus: div, grad and curl in different co-ordinate systems. The module will introduce the partial differential equations of mathematical physics and their solution for selected physical systems involving different co-ordinate systems and involving time. The module will introduce the foundations of electromagnetism, up to Gauss’ Law and Laplace’s equation, as a major application of the vector calculus and partial differential equations techniques.
View full module detailsSemester 2
Compulsory
When an analytical approach is not known or practical for solving a mathematical problem, which is the case for most real-world problems, a numerical approach can be useful in finding approximate solutions that are as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of systems of linear and nonlinear equations, for finding a function that interpolates or approximates a set of data points, for finding numerical values of derivatives and integrals, and for solving initial value problems. For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also analyse the complexity of numerical methods in order to estimate the computational resources required for achieving a given accuracy. Students will learn and practice implementing some of the methods in Python.
View full module detailsThe module reprises electrostatics (Gauss’ Law) and proceeds to introduce electromagnetic theory through a development of Maxwell’s Equations and concepts associated with the electric and magnetic polarisation of materials. The module introduces electromagnetic wave theory and its applications to a range of traditional applications and problems as well as the use of Fourier processing for wave signal analysis.
View full module detailsThe general properties of nuclei and radioactivity are studied, with an introduction to the deeper structure of elementary particles and the Standard Model. The nuclear physics includes alpha- and beta- and gamma-ray decay, nuclear fission and models of nuclear structure. The high energy physics includes the quark structure of hadrons, CPT conservation and CP violation and the impact of conservation rules on simple reactions of elementary particles.
View full module detailsOptional
The Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in detail. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.
View full module detailsThis module presents a complete introduction to modern astronomy and astrophysics. We start by introducing astronomy as a unique science; measurement in astronomy (position on the sky, velocity and distance); and multi-messenger probes. We then discuss acceleration due to gravity (the dominant force in the Universe) and we show that timescales are typically so long that we must use models to calculate what happened in the past and what will happen in the future. Armed with an understanding of how to make measurements in astronomy and how to model gravity, we then move from the smallest scales to the largest, studying first the interstellar medium from which stars form; stellar structure and evolution; and stellar remnants (white dwarfs, neutron stars and black holes). We compare and contrast the latest models for how planets form and we discuss the prospects for detecting life and intelligent life beyond Earth. Finally, we discuss the formation and evolution of galaxies in the Universe and the Universe as a whole. We show that the Universe appears to be mostly dark: dark matter (~22%) and dark energy (~74%). Understanding what these mysterious components are is one of the key challenges for physics in the next decade. The module includes either a computer or telescope project. Students enrolled in physics with astronomy with undertake the telescope project where (weather willing) students will gain hands on experience of taking real observational data. They will develop software tools to analyse and interpret these data and write up a final report. Students not enrolled in physics with astronomy will undertake a computational project of similar scope and length, also culminating in a final report.
View full module detailsThis module introduces students to inviscid fluid flows including surface waves. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.
View full module detailsThis module provides an introduction to abstract algebra, focusing on the theory of algebraic structures called groups and rings. The module builds on preliminary material on groups introduced in MAT1031 Algebra. This module forms the starting point for subsequent algebraic modules, such as MAT3032 Advanced Algebra, MATM035 Representation Theory and MATM011 Lie Algebras.
View full module detailsOptional modules for Year 2 (with PTY) - FHEQ Level 5
Choose 1 optional module
Year 3 - MMath with placement
Semester 1
Optional
This module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras
View full module detailsIn this module, students will learn key methods adopted in astrophysics to carry out advanced research: scientific computing, statistics, data analysis, machine learning. Much of the course develops highly transferrable skills that apply to science research in general. The goal is to ensure that students are well-prepared for either their research year or their future careers.
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsThis module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.
View full module detailsThis module introduces six advanced topics in physics. Students will be assessed on only four of these topics, with individuals self-selecting the contact sessions, coursework options and exam questions that reflect their preference. An indicative list of these six topics include: biological physics, special relativity, physics of electronic & photonic materials, cosmology, nuclear astrophysics, and quantum computing.
View full module detailsThe first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives. The second half of the module then focusses on optimization problems with examples including logistics, aerospace, traffic control and finance (which includes pricing, risk managements and portfolio optimizations in financial markets). There is a particular focus on the role of quantum optimization and the use of quantum computer algorithms in finance.
View full module detailsQuantum computers are built around a central processing unit which is a physical device operating according to the rules of quantum mechanics. This module teaches the principles of how quantum processors are built and how they function. The module follows the superconducting architecture, which currently has a significant role in the industry and has been widely studied and implemented. The module will start with reviewing the basic physics required to understand superconducting qubits and the theory of superconducting circuits. It will then continue to the operation of such qubits to perform gates, storage, and readout. After studying the basic building blocks and operations, the module will discuss early demonstrations of important algorithms on superconducting processors. These will lead us naturally to the important topics of improving performance through protection of coherence, advanced control, and validation. The last part of the module will focus on state-of-the-art superconducting processors, focusing on the various challenges in scaling up and the strategies that the industry is pursuing to overcome them.
View full module detailsThis module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.
View full module detailsThe module will introduce students to research level equipment and techniques that are used within the research groups of Physics via extended projects. The four-week projects will cover astrophysics, experimental and theoretical nuclear physics, experimental and theoretical soft matter physics, and quantum technologies. Students will gain experience using state-of-the-art equipment and software, analysing and working with large data sets and in problem solving. The module builds upon experience gained during first- and second-year laboratory and computing classes with project-based work that is typically more open ended and less structured. Students are expected to take more responsibility for the planning and direction of work than in previous years. The goal is to help prepare students for independent research within a team and for future project work (e.g. Final Year Projects and MPhys research years). Numbers will be limited on certain projects.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.
View full module detailsThe course will follow the historical development of the main medical imaging techniques. The first part will consider, from a theoretical perspective, the fundamentals of X-ray image formation both in the planar modality and in the Computed Tomography modality. Elements of image processing and image reconstruction will be addressed. The second will look at the physical principles and methods of Nuclear Medicine. The third will look at the principles underlying the application of diagnostic ultrasound in medicine. The fourth will consider Magnetic Resonance Imaging (MRI), one of the most important techniques of medical imaging used in hospitals today. In parallel to the related theoretical classes, laboratory experiments will be carried out on X-ray imaging and ultrasound.
View full module detailsData science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda.
View full module detailsThe module will introduce students to key concepts in education as well as the tools and strategies for effective public engagement in their discipline areas and for different audiences. Students will gain practical experience by planning, implementing, and evaluating an education or public engagement-based activity. Opportunities will also exist for classroom (e.g. school; early-year University) teaching experience and / or involvement in external exhibitions. The projects will be related to current Faculty, department and / or outreach needs thus leading to informed student partnership activities.
View full module detailsThis module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.
View full module detailsThis module covers circuit-based quantum computers and some of the algorithms that can be implemented using them. The idea of a classical computational algorithm and its complexity is introduced, and used as a language to discuss quantum computational algorithms. Components of quantum circuits are discussed individually, and then built up to show how algorithms such as the quantum Fourier transform and Grover¿s search algorithm can be implemented, and how such algorithms can be used in applications such as factorizing integers using Shor's algorithm. The Python package qiskit is introduced and used as a tool to implement the algorithms on simulated quantum computers.
View full module detailsThis module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.
View full module detailsTime series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.
View full module detailsOptional modules for Year 3 (with PTY) - FHEQ Level 6
Students must choose 60 credits of options in each Semester.
Year 3 - MMath with placement
Semester 1 & 2
Core
This module supports students’ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning, and is a process that involves self-reflection, documented via the creation of a personal record, planning and monitoring progress towards the achievement of personal objectives. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written and presentation skills.
View full module detailsThis module supports students¿ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning and is a process that involves self-reflection. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written skills.
View full module detailsThis module supports students¿ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning, and is a process that involves self-reflection, documented via the creation of a personal record, planning and monitoring progress towards the achievement of personal objectives. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written skills.
View full module detailsOptional modules for Professional Training Year (PTY) -
NA
Year 4 - MMath with placement
Semester 1
Optional
Asset prices in financial markets go up and down in accordance with how markets digest the flow of information. To understand the causal relation between information flow and price movements, it is necessary to model market information and use this to infer the price dynamics. In this way, market dynamics can be replicated artificially on a computer. This module explains the powerful process of artificially generating realistic market models. The module begins with elements of probability theory. We will then learn the idea of conditional expectation and the Bayes formula, which gives the optimal inference under uncertainty. The meaning of the Bayes formula will be explained, leading to the understanding of what is meant by “intelligence”. The module then covers the basics of stochastic process (specifically, the Brownian motion) and calculus (specifically, the Ito calculus), sufficient to follow the contents of the module. Then simple models for flows of information in financial markets will be introduced, and by use of the Bayes formula the associated price dynamics will be derived. The module concludes with a brief application to the asset valuation problems in financial markets (such as options or other derivatives).
View full module detailsMathematics underpinning real-world uncertain events has become indispensable in many applications, including in particular financial markets. This module will begin with the introduction to probability theory and stochastic processes, with an emphasis on the Ito calculus for treating functions of Brownian motion. Such functions are commonly used in financial markets to model asset price dynamics, required for the valuation of financial contracts. The module then discusses structures of financial markets, with an emphasis on the equity market. Several of the standard and exotic contingent claims will be introduced, and the need for mathematical models for the valuation and risk management of these products will be explained. The pricing of a standard call option will then be worked out in a single-period binomial model, for which option price will be worked out in two ways: first using the portfolio replication and no arbitrage argument, and second using the risk-neutral expectation argument. The model is then extended into multi-period binomial tree model, leading to the Cox-Ross-Rubinstein option pricing formula. Finally, a continuous-time geometric Brownian motion model, originally introduced by Samuelson, will be considered, and used to deduce the famous Black-Scholes option pricing formula. This can be applied for the purpose of both pricing, as well as risk-management purposes, which will be demonstrated by working out the hedging strategy. The meaning of the pricing formula, and how it can be used in practical investment banking context, will be explained.
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
This 15-credit M-Level module introduces important topics and techniques in theoretical physics that have a wide range of applications in many areas physics and engineering and which the students will not have met before. Both the mathematical techniques and their applications are covered at a level appropriate for Masters level students coming to the end of their degree and who should be able to pull many different ideas in theoretical physics together.
View full module detailsThis module aims to provide an advanced level understanding of explosive nuclear astrophysics and the physics of stars. In particular, the course will provide an analytical underpinning of resonant reaction rates, together with the experimental techniques involved in their determination, as well as a theoretical treatment of nuclear reactions and celestial objects.
View full module detailsThis module will introduce the students to the principles and formalism of General Relativity and its applications to Black Holes and astrophysical phenomena.
View full module detailsGroup theory is a branch of mathematics developed to understand symmetries, which are powerful tools for understanding the properties of complex mathematical problems and physical systems. Group representations map abstract group elements to linear transformations on vector spaces. Representation theory allows us to better understand the properties of symmetry groups, and leads to powerful and compact solutions of otherwise difficult and intractable problems. This module builds on groups theory in MAT1031 Algebra and MAT2048 Groups & Rings.
View full module detailsQuantum Mechanics topics are essential building blocks for our understanding of many physical systems. The module assumes basic knowledge in quantum mechanics from modules in earlier years, but will provide a review at the beginning. Topics include a review of quantum mechanics, operator methods and applications to the harmonic oscillator, spin & angular momentum, symmetries in quantum mechanics. The second half of the module then moves beyond isolated quantum systems by addressing the topic of Quantum Entanglement and Quantum Coherence. Here the important concepts of entanglement and decoherence will be studied by developing an understanding of open quantum systems and the density matrix formalism.
View full module detailsThis module comprises two independent halves, on making qubit, and quantum communications. Quantum technologies, including quantum computing, rely on the quantum mechanical principles of superposition and entanglement. Furthermore, this superposition and entanglement needs to be controlled in useful ways. In this module you will learn about what physical systems allow quantum technology production, and their limitations. Quantum computers are only one type of device that uses these principles, and several other technologies are being created that are also enhanced by use of superpositions. Others include atomic clocks and Magnetic Resonance Imaging, MRI. We will also learn about the errors that inevitably build up in quantum computers when quantum superpositions are disturbed, and the strategies that might be built in to correct them. Quantum communications. This course provides a comprehensive introduction to the principles, protocols, and applications of quantum communications. Students will explore the fundamental concepts of quantum information transmission, quantum cryptography, and quantum communication protocols. They will also examine the challenges, advancements, and real-world applications of quantum communications including both theory and practical aspects.
View full module detailsThe module is an introduction to nonlinear partial differential equations (PDEs) with a focus on hyperbolic and dispersive PDEs. The module takes key classes of equations as the organising centre. Each class of PDEs is considered and the properties, analytical techniques, and analysis of each is taken in turn.
View full module detailsThis module introduces programming in Python for data science, with a focus on data pre-processing, data mining and analysis, machine learning and deep learning. Besides the practical hands-on experience with writing code, this course also covers the theoretical background on different data analysis techniques and machine learning approaches. The goal is to develop an understanding of how information can be extracted from data and how this information can be further used to make predictions, but importantly how this is done practically in terms of writing clear and transparent source code. Using real-world data sets and illustrative examples, this course will help to develop a theoretical understanding of data science as well as practical experience by developing useful software tools. Many of the techniques acquired through this module are likely to be of potential use in the dissertation project.
View full module detailsThe course provides an introduction to nuclear energy generation and applications of nuclear science. Nuclear reactors, their physics and operation are described. Nuclear reactor safety case work is also discussed. Future potential energy generation mechanisms such including nuclear fusion will be discussed. The module will also present a range of applications of radioactivity measurement including aspects of Environmental Science and Medical Diagnogstics and treatment therapy. The module will include some aspects of calculus and first order differential equations.
View full module detailsSemester 1 & 2
Compulsory
Under the guidance of an academic supervisor, the student will investigate a mathematical topic of interest to them in some depth. They will compose a written report on their studies and give oral presentations on their work.
View full module detailsOptional modules for Year 4 (with PTY) - FHEQ Level 7
Students on the MMath pathway must take the MATM050 MMath Project. Choose 6 options overall, to maintain a 60:60 credit balance between Semesters 1 and 2
Year 1 - MPhys
Semester 1
Compulsory
This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied. Such equations have important applications for interpreting and understanding the world around us.
View full module detailsThis module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.
View full module detailsThis module covers some of the fundamental principles in classical physics including a discussion of units of measurement, the kinematics and dynamics of objects and conservation laws. This material revises and builds upon concepts that are first encountered in the A-level physics course and the study of mechanics as part of A-level mathematics.
View full module detailsThis module covers introductory concepts of simple harmonic motion and waves, drawing on and bringing together examples from different branches of physics including mechanics, optics, electronics, and electromagnetism. Some of these concepts will build upon examples that may have been encountered as part of the Physics A-level material but others are new. It combines the mathematical description, physical interpretation as well as experiments and their analysis of oscillations and wave phenomena to provide students with a well-balanced introduction to the important physical concepts that are required for further study in the subsequent modules of your physics course.
View full module detailsSemester 2
Compulsory
This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics. This module builds on MAT1031: Algebra and provides a foundation for a variety of subsequent modules, including MAT2009 Operations Research and Optimisation, MAT2047 Curves and Surfaces, MAT2048 Groups & Rings, MAT3004 Introduction to Function Spaces and MAT3039 Quantum Mechanics.
View full module detailsThis module will introduce the classical physics that is relevant to gases and condensed matter, making use of the thermodynamic equations of state. The emphasis will be on the structure of matter and its relationship to mechanical and thermal properties, such as elasticity and thermal expansivity. Laws of classical thermodynamics will be introduced. The module will prepare the student for the study of solid state physics and advanced thermodynamics at Level FHEQ 5.
View full module detailsThis module identifies the new theories necessary to describe physical processes when we go beyond the normal speeds and sizes experienced in everyday life. A review of new phenomena that led to the development of quantum theory follows naturally into an introduction to the theory of atomic structure. Along the way, the Schrödinger equation is introduced and elementary applications are considered. Several important aspects of the structure and spectroscopy of atoms are considered in detail. The basis is laid for the study of the properties of matter in more detail at higher levels.
View full module detailsThis module introduces basic mathematical programming in Python and professional skills. The module covers digital skills such as basic data handling, processing and least squares fitting to analyze real-world problems. The professional skills cover employability, teamworking, writing a technical report, and presentation skills. The goal of the module is to equip students with the skills to tackle real-world problems, communicate their results and prepare them for employment after their degree.
View full module detailsOptional modules for Year 1 - FHEQ Level 4
NA
Year 2 - MPhys
Semester 1
Compulsory
This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.
View full module detailsThe Quantum Physics course focuses on the basic formalism of quantum mechanics, its physical interpretation and its application to simple problems. The emphasis is on elementary (one-dimensional) quantum physics, including the infinite-potential well, the parabolic well, one-dimensional step and barrier potentials.
View full module detailsThis module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics. This module builds on material on two-variable calculus introduced in MAT1043 Multivariable Calculus.
View full module detailsThe module will introduce the physical significance and the mathematical methods (and selected theorems) of the operators of vector calculus: div, grad and curl in different co-ordinate systems. The module will introduce the partial differential equations of mathematical physics and their solution for selected physical systems involving different co-ordinate systems and involving time. The module will introduce the foundations of electromagnetism, up to Gauss’ Law and Laplace’s equation, as a major application of the vector calculus and partial differential equations techniques.
View full module detailsSemester 2
Compulsory
When an analytical approach is not known or practical for solving a mathematical problem, which is the case for most real-world problems, a numerical approach can be useful in finding approximate solutions that are as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of systems of linear and nonlinear equations, for finding a function that interpolates or approximates a set of data points, for finding numerical values of derivatives and integrals, and for solving initial value problems. For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also analyse the complexity of numerical methods in order to estimate the computational resources required for achieving a given accuracy. Students will learn and practice implementing some of the methods in Python.
View full module detailsThe module reprises electrostatics (Gauss’ Law) and proceeds to introduce electromagnetic theory through a development of Maxwell’s Equations and concepts associated with the electric and magnetic polarisation of materials. The module introduces electromagnetic wave theory and its applications to a range of traditional applications and problems as well as the use of Fourier processing for wave signal analysis.
View full module detailsThe general properties of nuclei and radioactivity are studied, with an introduction to the deeper structure of elementary particles and the Standard Model. The nuclear physics includes alpha- and beta- and gamma-ray decay, nuclear fission and models of nuclear structure. The high energy physics includes the quark structure of hadrons, CPT conservation and CP violation and the impact of conservation rules on simple reactions of elementary particles.
View full module detailsOptional
The Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in detail. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.
View full module detailsThis module presents a complete introduction to modern astronomy and astrophysics. We start by introducing astronomy as a unique science; measurement in astronomy (position on the sky, velocity and distance); and multi-messenger probes. We then discuss acceleration due to gravity (the dominant force in the Universe) and we show that timescales are typically so long that we must use models to calculate what happened in the past and what will happen in the future. Armed with an understanding of how to make measurements in astronomy and how to model gravity, we then move from the smallest scales to the largest, studying first the interstellar medium from which stars form; stellar structure and evolution; and stellar remnants (white dwarfs, neutron stars and black holes). We compare and contrast the latest models for how planets form and we discuss the prospects for detecting life and intelligent life beyond Earth. Finally, we discuss the formation and evolution of galaxies in the Universe and the Universe as a whole. We show that the Universe appears to be mostly dark: dark matter (~22%) and dark energy (~74%). Understanding what these mysterious components are is one of the key challenges for physics in the next decade. The module includes either a computer or telescope project. Students enrolled in physics with astronomy with undertake the telescope project where (weather willing) students will gain hands on experience of taking real observational data. They will develop software tools to analyse and interpret these data and write up a final report. Students not enrolled in physics with astronomy will undertake a computational project of similar scope and length, also culminating in a final report.
View full module detailsThis module introduces students to inviscid fluid flows including surface waves. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.
View full module detailsThis module provides an introduction to abstract algebra, focusing on the theory of algebraic structures called groups and rings. The module builds on preliminary material on groups introduced in MAT1031 Algebra. This module forms the starting point for subsequent algebraic modules, such as MAT3032 Advanced Algebra, MATM035 Representation Theory and MATM011 Lie Algebras.
View full module detailsOptional modules for Year 2 - FHEQ Level 5
Choose 1 optional module
Year 3 - MPhys
Semester 1
Optional
This module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsIn this module, students will learn key methods adopted in astrophysics to carry out advanced research: scientific computing, statistics, data analysis, machine learning. Much of the course develops highly transferrable skills that apply to science research in general. The goal is to ensure that students are well-prepared for either their research year or their future careers.
View full module detailsThis module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.
View full module detailsThis module introduces six advanced topics in physics. Students will be assessed on only four of these topics, with individuals self-selecting the contact sessions, coursework options and exam questions that reflect their preference. An indicative list of these six topics include: biological physics, special relativity, physics of electronic & photonic materials, cosmology, nuclear astrophysics, and quantum computing.
View full module detailsThe first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives. The second half of the module then focusses on optimization problems with examples including logistics, aerospace, traffic control and finance (which includes pricing, risk managements and portfolio optimizations in financial markets). There is a particular focus on the role of quantum optimization and the use of quantum computer algorithms in finance.
View full module detailsQuantum computers are built around a central processing unit which is a physical device operating according to the rules of quantum mechanics. This module teaches the principles of how quantum processors are built and how they function. The module follows the superconducting architecture, which currently has a significant role in the industry and has been widely studied and implemented. The module will start with reviewing the basic physics required to understand superconducting qubits and the theory of superconducting circuits. It will then continue to the operation of such qubits to perform gates, storage, and readout. After studying the basic building blocks and operations, the module will discuss early demonstrations of important algorithms on superconducting processors. These will lead us naturally to the important topics of improving performance through protection of coherence, advanced control, and validation. The last part of the module will focus on state-of-the-art superconducting processors, focusing on the various challenges in scaling up and the strategies that the industry is pursuing to overcome them.
View full module detailsThis module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.
View full module detailsThe module will introduce students to research level equipment and techniques that are used within the research groups of Physics via extended projects. The four-week projects will cover astrophysics, experimental and theoretical nuclear physics, experimental and theoretical soft matter physics, and quantum technologies. Students will gain experience using state-of-the-art equipment and software, analysing and working with large data sets and in problem solving. The module builds upon experience gained during first- and second-year laboratory and computing classes with project-based work that is typically more open ended and less structured. Students are expected to take more responsibility for the planning and direction of work than in previous years. The goal is to help prepare students for independent research within a team and for future project work (e.g. Final Year Projects and MPhys research years). Numbers will be limited on certain projects.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.
View full module detailsThe course will follow the historical development of the main medical imaging techniques. The first part will consider, from a theoretical perspective, the fundamentals of X-ray image formation both in the planar modality and in the Computed Tomography modality. Elements of image processing and image reconstruction will be addressed. The second will look at the physical principles and methods of Nuclear Medicine. The third will look at the principles underlying the application of diagnostic ultrasound in medicine. The fourth will consider Magnetic Resonance Imaging (MRI), one of the most important techniques of medical imaging used in hospitals today. In parallel to the related theoretical classes, laboratory experiments will be carried out on X-ray imaging and ultrasound.
View full module detailsData science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda.
View full module detailsThe module will introduce students to key concepts in education as well as the tools and strategies for effective public engagement in their discipline areas and for different audiences. Students will gain practical experience by planning, implementing, and evaluating an education or public engagement-based activity. Opportunities will also exist for classroom (e.g. school; early-year University) teaching experience and / or involvement in external exhibitions. The projects will be related to current Faculty, department and / or outreach needs thus leading to informed student partnership activities.
View full module detailsThis module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.
View full module detailsThis module covers circuit-based quantum computers and some of the algorithms that can be implemented using them. The idea of a classical computational algorithm and its complexity is introduced, and used as a language to discuss quantum computational algorithms. Components of quantum circuits are discussed individually, and then built up to show how algorithms such as the quantum Fourier transform and Grover¿s search algorithm can be implemented, and how such algorithms can be used in applications such as factorizing integers using Shor's algorithm. The Python package qiskit is introduced and used as a tool to implement the algorithms on simulated quantum computers.
View full module detailsThis module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.
View full module detailsTime series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.
View full module detailsOptional modules for Year 3 - FHEQ Level 6
Students must choose 60 credits of options in each Semester.
Year 4 - MPhys
Semester 1
Optional
Asset prices in financial markets go up and down in accordance with how markets digest the flow of information. To understand the causal relation between information flow and price movements, it is necessary to model market information and use this to infer the price dynamics. In this way, market dynamics can be replicated artificially on a computer. This module explains the powerful process of artificially generating realistic market models. The module begins with elements of probability theory. We will then learn the idea of conditional expectation and the Bayes formula, which gives the optimal inference under uncertainty. The meaning of the Bayes formula will be explained, leading to the understanding of what is meant by “intelligence”. The module then covers the basics of stochastic process (specifically, the Brownian motion) and calculus (specifically, the Ito calculus), sufficient to follow the contents of the module. Then simple models for flows of information in financial markets will be introduced, and by use of the Bayes formula the associated price dynamics will be derived. The module concludes with a brief application to the asset valuation problems in financial markets (such as options or other derivatives).
View full module detailsMathematics underpinning real-world uncertain events has become indispensable in many applications, including in particular financial markets. This module will begin with the introduction to probability theory and stochastic processes, with an emphasis on the Ito calculus for treating functions of Brownian motion. Such functions are commonly used in financial markets to model asset price dynamics, required for the valuation of financial contracts. The module then discusses structures of financial markets, with an emphasis on the equity market. Several of the standard and exotic contingent claims will be introduced, and the need for mathematical models for the valuation and risk management of these products will be explained. The pricing of a standard call option will then be worked out in a single-period binomial model, for which option price will be worked out in two ways: first using the portfolio replication and no arbitrage argument, and second using the risk-neutral expectation argument. The model is then extended into multi-period binomial tree model, leading to the Cox-Ross-Rubinstein option pricing formula. Finally, a continuous-time geometric Brownian motion model, originally introduced by Samuelson, will be considered, and used to deduce the famous Black-Scholes option pricing formula. This can be applied for the purpose of both pricing, as well as risk-management purposes, which will be demonstrated by working out the hedging strategy. The meaning of the pricing formula, and how it can be used in practical investment banking context, will be explained.
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
This 15-credit M-Level module introduces important topics and techniques in theoretical physics that have a wide range of applications in many areas physics and engineering and which the students will not have met before. Both the mathematical techniques and their applications are covered at a level appropriate for Masters level students coming to the end of their degree and who should be able to pull many different ideas in theoretical physics together.
View full module detailsThis module aims to provide an advanced level understanding of explosive nuclear astrophysics and the physics of stars. In particular, the course will provide an analytical underpinning of resonant reaction rates, together with the experimental techniques involved in their determination, as well as a theoretical treatment of nuclear reactions and celestial objects.
View full module detailsThis module will introduce the students to the principles and formalism of General Relativity and its applications to Black Holes and astrophysical phenomena.
View full module detailsGroup theory is a branch of mathematics developed to understand symmetries, which are powerful tools for understanding the properties of complex mathematical problems and physical systems. Group representations map abstract group elements to linear transformations on vector spaces. Representation theory allows us to better understand the properties of symmetry groups, and leads to powerful and compact solutions of otherwise difficult and intractable problems. This module builds on groups theory in MAT1031 Algebra and MAT2048 Groups & Rings.
View full module detailsQuantum Mechanics topics are essential building blocks for our understanding of many physical systems. The module assumes basic knowledge in quantum mechanics from modules in earlier years, but will provide a review at the beginning. Topics include a review of quantum mechanics, operator methods and applications to the harmonic oscillator, spin & angular momentum, symmetries in quantum mechanics. The second half of the module then moves beyond isolated quantum systems by addressing the topic of Quantum Entanglement and Quantum Coherence. Here the important concepts of entanglement and decoherence will be studied by developing an understanding of open quantum systems and the density matrix formalism.
View full module detailsThis module comprises two independent halves, on making qubit, and quantum communications. Quantum technologies, including quantum computing, rely on the quantum mechanical principles of superposition and entanglement. Furthermore, this superposition and entanglement needs to be controlled in useful ways. In this module you will learn about what physical systems allow quantum technology production, and their limitations. Quantum computers are only one type of device that uses these principles, and several other technologies are being created that are also enhanced by use of superpositions. Others include atomic clocks and Magnetic Resonance Imaging, MRI. We will also learn about the errors that inevitably build up in quantum computers when quantum superpositions are disturbed, and the strategies that might be built in to correct them. Quantum communications. This course provides a comprehensive introduction to the principles, protocols, and applications of quantum communications. Students will explore the fundamental concepts of quantum information transmission, quantum cryptography, and quantum communication protocols. They will also examine the challenges, advancements, and real-world applications of quantum communications including both theory and practical aspects.
View full module detailsThe module is an introduction to nonlinear partial differential equations (PDEs) with a focus on hyperbolic and dispersive PDEs. The module takes key classes of equations as the organising centre. Each class of PDEs is considered and the properties, analytical techniques, and analysis of each is taken in turn.
View full module detailsThis module introduces programming in Python for data science, with a focus on data pre-processing, data mining and analysis, machine learning and deep learning. Besides the practical hands-on experience with writing code, this course also covers the theoretical background on different data analysis techniques and machine learning approaches. The goal is to develop an understanding of how information can be extracted from data and how this information can be further used to make predictions, but importantly how this is done practically in terms of writing clear and transparent source code. Using real-world data sets and illustrative examples, this course will help to develop a theoretical understanding of data science as well as practical experience by developing useful software tools. Many of the techniques acquired through this module are likely to be of potential use in the dissertation project.
View full module detailsThe course provides an introduction to nuclear energy generation and applications of nuclear science. Nuclear reactors, their physics and operation are described. Nuclear reactor safety case work is also discussed. Future potential energy generation mechanisms such including nuclear fusion will be discussed. The module will also present a range of applications of radioactivity measurement including aspects of Environmental Science and Medical Diagnogstics and treatment therapy. The module will include some aspects of calculus and first order differential equations.
View full module detailsSemester 1 & 2
Compulsory
Under the guidance of an academic supervisor, the student will investigate a Physics topic of interest to him in depth. He will compose a written report on his studies, and give oral presentations on the work.
View full module detailsOptional modules for Year 4 - FHEQ Level 7
Students on the MPhys pathway must take the PHYM060 MPhys MaP Project module.
Choose 5 options overall, to maintain a 60:60 credit balance between Semesters 1 and 2.
Year 1 - MPhys with placement
Semester 1
Compulsory
This module introduces students to the most important techniques in Calculus. In particular, the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide fundamental tools for quantitative descriptions of the real world across the entirety of applied mathematics. Tools and methods for differentiation and integration will be presented in detail. In addition, simple first and second order ordinary differential equations will be studied. Such equations have important applications for interpreting and understanding the world around us.
View full module detailsThis module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.
View full module detailsThis module covers some of the fundamental principles in classical physics including a discussion of units of measurement, the kinematics and dynamics of objects and conservation laws. This material revises and builds upon concepts that are first encountered in the A-level physics course and the study of mechanics as part of A-level mathematics.
View full module detailsThis module covers introductory concepts of simple harmonic motion and waves, drawing on and bringing together examples from different branches of physics including mechanics, optics, electronics, and electromagnetism. Some of these concepts will build upon examples that may have been encountered as part of the Physics A-level material but others are new. It combines the mathematical description, physical interpretation as well as experiments and their analysis of oscillations and wave phenomena to provide students with a well-balanced introduction to the important physical concepts that are required for further study in the subsequent modules of your physics course.
View full module detailsSemester 2
Compulsory
This module is an introduction to Linear Algebra, a fundamental mathematical discipline that revolves around the exploration of vector spaces as well as linear maps between these spaces. This often necessitates the solution of systems of linear equations, which are elegantly described by matrices and vectors. Techniques from Linear Algebra find application in numerous disciplines ranging from pure and applied mathematics to many fields of science, engineering, computing and economics. This module builds on MAT1031: Algebra and provides a foundation for a variety of subsequent modules, including MAT2009 Operations Research and Optimisation, MAT2047 Curves and Surfaces, MAT2048 Groups & Rings, MAT3004 Introduction to Function Spaces and MAT3039 Quantum Mechanics.
View full module detailsThis module will introduce the classical physics that is relevant to gases and condensed matter, making use of the thermodynamic equations of state. The emphasis will be on the structure of matter and its relationship to mechanical and thermal properties, such as elasticity and thermal expansivity. Laws of classical thermodynamics will be introduced. The module will prepare the student for the study of solid state physics and advanced thermodynamics at Level FHEQ 5.
View full module detailsThis module identifies the new theories necessary to describe physical processes when we go beyond the normal speeds and sizes experienced in everyday life. A review of new phenomena that led to the development of quantum theory follows naturally into an introduction to the theory of atomic structure. Along the way, the Schrödinger equation is introduced and elementary applications are considered. Several important aspects of the structure and spectroscopy of atoms are considered in detail. The basis is laid for the study of the properties of matter in more detail at higher levels.
View full module detailsThis module introduces basic mathematical programming in Python and professional skills. The module covers digital skills such as basic data handling, processing and least squares fitting to analyze real-world problems. The professional skills cover employability, teamworking, writing a technical report, and presentation skills. The goal of the module is to equip students with the skills to tackle real-world problems, communicate their results and prepare them for employment after their degree.
View full module detailsOptional modules for Year 1 (with PTY) - FHEQ Level 4
NA
Year 2 - MPhys with placement
Semester 1
Compulsory
This module builds on the differential equation aspects of the Level 4 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.
View full module detailsThe Quantum Physics course focuses on the basic formalism of quantum mechanics, its physical interpretation and its application to simple problems. The emphasis is on elementary (one-dimensional) quantum physics, including the infinite-potential well, the parabolic well, one-dimensional step and barrier potentials.
View full module detailsThis module is an introduction to the theory of complex functions of a complex variable, also known as complex analysis. We will study the continuity and differentiability of complex functions, integration along paths on the complex plane, Taylor and Laurent series expansions of complex functions with isolated singularities, and residue calculus and its applications. Complex analysis and residue calculus are widely used in many branches of Mathematics and Physics. This module builds on material on two-variable calculus introduced in MAT1043 Multivariable Calculus.
View full module detailsThe module will introduce the physical significance and the mathematical methods (and selected theorems) of the operators of vector calculus: div, grad and curl in different co-ordinate systems. The module will introduce the partial differential equations of mathematical physics and their solution for selected physical systems involving different co-ordinate systems and involving time. The module will introduce the foundations of electromagnetism, up to Gauss’ Law and Laplace’s equation, as a major application of the vector calculus and partial differential equations techniques.
View full module detailsSemester 2
Compulsory
When an analytical approach is not known or practical for solving a mathematical problem, which is the case for most real-world problems, a numerical approach can be useful in finding approximate solutions that are as close as possible to the exact one. This module introduces a selection of numerical methods for the solution of systems of linear and nonlinear equations, for finding a function that interpolates or approximates a set of data points, for finding numerical values of derivatives and integrals, and for solving initial value problems. For each numerical method, we will consider the error that results from using approximations and introduce some theories of quantifying the error, which then indicates the accuracy of a numerical solution. We also analyse the complexity of numerical methods in order to estimate the computational resources required for achieving a given accuracy. Students will learn and practice implementing some of the methods in Python.
View full module detailsThe module reprises electrostatics (Gauss’ Law) and proceeds to introduce electromagnetic theory through a development of Maxwell’s Equations and concepts associated with the electric and magnetic polarisation of materials. The module introduces electromagnetic wave theory and its applications to a range of traditional applications and problems as well as the use of Fourier processing for wave signal analysis.
View full module detailsThe general properties of nuclei and radioactivity are studied, with an introduction to the deeper structure of elementary particles and the Standard Model. The nuclear physics includes alpha- and beta- and gamma-ray decay, nuclear fission and models of nuclear structure. The high energy physics includes the quark structure of hadrons, CPT conservation and CP violation and the impact of conservation rules on simple reactions of elementary particles.
View full module detailsOptional
The Linear PDEs Module introduces students to linear partial differential equations, mainly in one and two space dimensions. The classical linear PDEs such as the heat, wave and Laplace equation will be analyzed in detail. Questions of existence and uniqueness of solutions will be addressed and their physical and mathematical meaning emphasized.
View full module detailsThis module presents a complete introduction to modern astronomy and astrophysics. We start by introducing astronomy as a unique science; measurement in astronomy (position on the sky, velocity and distance); and multi-messenger probes. We then discuss acceleration due to gravity (the dominant force in the Universe) and we show that timescales are typically so long that we must use models to calculate what happened in the past and what will happen in the future. Armed with an understanding of how to make measurements in astronomy and how to model gravity, we then move from the smallest scales to the largest, studying first the interstellar medium from which stars form; stellar structure and evolution; and stellar remnants (white dwarfs, neutron stars and black holes). We compare and contrast the latest models for how planets form and we discuss the prospects for detecting life and intelligent life beyond Earth. Finally, we discuss the formation and evolution of galaxies in the Universe and the Universe as a whole. We show that the Universe appears to be mostly dark: dark matter (~22%) and dark energy (~74%). Understanding what these mysterious components are is one of the key challenges for physics in the next decade. The module includes either a computer or telescope project. Students enrolled in physics with astronomy with undertake the telescope project where (weather willing) students will gain hands on experience of taking real observational data. They will develop software tools to analyse and interpret these data and write up a final report. Students not enrolled in physics with astronomy will undertake a computational project of similar scope and length, also culminating in a final report.
View full module detailsThis module introduces students to inviscid fluid flows including surface waves. By the end of the module, students should be able to recognise dominant features of fluid motion, and to derive some simple solutions of the equations of motion. Students should also have an appreciation of the force balances that produce various classes of flows.
View full module detailsThis module provides an introduction to abstract algebra, focusing on the theory of algebraic structures called groups and rings. The module builds on preliminary material on groups introduced in MAT1031 Algebra. This module forms the starting point for subsequent algebraic modules, such as MAT3032 Advanced Algebra, MATM035 Representation Theory and MATM011 Lie Algebras.
View full module detailsOptional modules for Year 2 (with PTY) - FHEQ Level 5
Choose 1 optional module
Year 3 - MPhys with placement
Semester 1
Optional
This module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced. This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsIn this module, students will learn key methods adopted in astrophysics to carry out advanced research: scientific computing, statistics, data analysis, machine learning. Much of the course develops highly transferrable skills that apply to science research in general. The goal is to ensure that students are well-prepared for either their research year or their future careers.
View full module detailsThis module introduces fundamental concepts in analytical dynamics and illustrates their application to real-world problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and symplectic manifolds. The module also leads to a deeper understanding of the role of symmetries and conservation laws in dynamical systems. This module builds on material from MAT1036 Classical Dynamics and lays the foundations for MAT3039 Quantum Mechanics.
View full module detailsThis module introduces six advanced topics in physics. Students will be assessed on only four of these topics, with individuals self-selecting the contact sessions, coursework options and exam questions that reflect their preference. An indicative list of these six topics include: biological physics, special relativity, physics of electronic & photonic materials, cosmology, nuclear astrophysics, and quantum computing.
View full module detailsThe first half of this module covers various applications of statistical physics to model share prices and financial markets. This mathematics is then applied to calculating prices for some examples of financial derivatives. The second half of the module then focusses on optimization problems with examples including logistics, aerospace, traffic control and finance (which includes pricing, risk managements and portfolio optimizations in financial markets). There is a particular focus on the role of quantum optimization and the use of quantum computer algorithms in finance.
View full module detailsQuantum computers are built around a central processing unit which is a physical device operating according to the rules of quantum mechanics. This module teaches the principles of how quantum processors are built and how they function. The module follows the superconducting architecture, which currently has a significant role in the industry and has been widely studied and implemented. The module will start with reviewing the basic physics required to understand superconducting qubits and the theory of superconducting circuits. It will then continue to the operation of such qubits to perform gates, storage, and readout. After studying the basic building blocks and operations, the module will discuss early demonstrations of important algorithms on superconducting processors. These will lead us naturally to the important topics of improving performance through protection of coherence, advanced control, and validation. The last part of the module will focus on state-of-the-art superconducting processors, focusing on the various challenges in scaling up and the strategies that the industry is pursuing to overcome them.
View full module detailsThis module introduces students to topological spaces and manifolds. Topology is the study of properties of spaces which are invariant under continuous transformations, and forms one of the cornerstones of pure mathematics. Study of topology leads to a deeper understanding of the concepts of continuity and connectedness. After introducing these key ideas, with appropriate examples, smooth manifolds are introduced. Differential forms and cohomology are developed, which enables the classification of manifolds using topologically invariant numbers. MAT2047 Curves and Surfaces is a recommended prior module, but is not pre-requisite. Students will also find the material in MAT3044 Riemannian Geometry complementary.
View full module detailsThe module will introduce students to research level equipment and techniques that are used within the research groups of Physics via extended projects. The four-week projects will cover astrophysics, experimental and theoretical nuclear physics, experimental and theoretical soft matter physics, and quantum technologies. Students will gain experience using state-of-the-art equipment and software, analysing and working with large data sets and in problem solving. The module builds upon experience gained during first- and second-year laboratory and computing classes with project-based work that is typically more open ended and less structured. Students are expected to take more responsibility for the planning and direction of work than in previous years. The goal is to help prepare students for independent research within a team and for future project work (e.g. Final Year Projects and MPhys research years). Numbers will be limited on certain projects.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
Graph theory is an aesthetically appealing branch of pure mathematics with strong links to other areas of mathematics (combinatorics, algebra, topology, probability, optimisation and numerics) and well-developed applications to a wide range of other disciplines (including operations research, data science, chemistry, systems biology, statistical mechanics and quantum field theory). This module provides an introduction to graph theory. There is an emphasis on theorems and proofs.
View full module detailsThe course will follow the historical development of the main medical imaging techniques. The first part will consider, from a theoretical perspective, the fundamentals of X-ray image formation both in the planar modality and in the Computed Tomography modality. Elements of image processing and image reconstruction will be addressed. The second will look at the physical principles and methods of Nuclear Medicine. The third will look at the principles underlying the application of diagnostic ultrasound in medicine. The fourth will consider Magnetic Resonance Imaging (MRI), one of the most important techniques of medical imaging used in hospitals today. In parallel to the related theoretical classes, laboratory experiments will be carried out on X-ray imaging and ultrasound.
View full module detailsData science is the study of data to extract meaningful and actionable insights at all levels of society such as dynamical systems and social media networks. This module introduces the role of data in society and provides students with the underpinning mathematics that drives data methodology and algorithms. This module then covers wide-ranging topics with a focus on the Surrey brand of data, as research into data is part of the department research agenda.
View full module detailsThe module will introduce students to key concepts in education as well as the tools and strategies for effective public engagement in their discipline areas and for different audiences. Students will gain practical experience by planning, implementing, and evaluating an education or public engagement-based activity. Opportunities will also exist for classroom (e.g. school; early-year University) teaching experience and / or involvement in external exhibitions. The projects will be related to current Faculty, department and / or outreach needs thus leading to informed student partnership activities.
View full module detailsThis module introduces fundamental concepts in Quantum Mechanics and its applications to real-world quantum problems. The module covers the mathematics of Hilbert spaces and Dirac notation, the postulates of Quantum Mechanics, the uncertainty principle, the Schroedinger equation with one-dimensional applications to a particle in a potential well and the quantum harmonic oscillator, and angular momentum and spin. This module utilises material from MAT1034 Linear Algebra and MAT2007 Ordinary Differential Equations. The module also builds on material from MAT1036 Classical Dynamics and MAT3008 Lagrangian & Hamiltonian Dynamics, although these modules are not pre-requisite.
View full module detailsThis module covers circuit-based quantum computers and some of the algorithms that can be implemented using them. The idea of a classical computational algorithm and its complexity is introduced, and used as a language to discuss quantum computational algorithms. Components of quantum circuits are discussed individually, and then built up to show how algorithms such as the quantum Fourier transform and Grover¿s search algorithm can be implemented, and how such algorithms can be used in applications such as factorizing integers using Shor's algorithm. The Python package qiskit is introduced and used as a tool to implement the algorithms on simulated quantum computers.
View full module detailsThis module introduces the ideas of viscous fluid flows which build on the ideas some students would have seen in MAT2050: Inviscid Fluid Dynamics. By the end of the module, students should be familiar with the Navier-Stokes equations, and should be able to solve these equations in various simplified situations as well as in a variety of geometries.
View full module detailsTime series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.
View full module detailsOptional modules for Year 3 (with PTY) - FHEQ Level 6
Students must choose 60 credits of options in each Semester.
Year 3 - MPhys with placement
Semester 1 & 2
Core
This module supports students’ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning, and is a process that involves self-reflection, documented via the creation of a personal record, planning and monitoring progress towards the achievement of personal objectives. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written and presentation skills.
View full module detailsThis module supports students¿ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning and is a process that involves self-reflection. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written skills.
View full module detailsThis module supports students¿ development of personal and professional attitudes and abilities appropriate to a Professional Training placement. It supports and facilitates self-reflection and transfer of learning from their Professional Training placement experiences to their final year of study and their future employment. The PTY module is concerned with Personal and Professional Development towards holistic academic and non-academic learning, and is a process that involves self-reflection, documented via the creation of a personal record, planning and monitoring progress towards the achievement of personal objectives. Development and learning may occur before and during the placement, and this is reflected in the assessment model as a progressive process. However, the graded assessment takes place primarily towards the end of the placement. Additionally, the module aims to enable students to evidence and evaluate their placement experiences and transfer that learning to other situations through written skills.
View full module detailsOptional modules for Professional Training Year (PTY) -
NA
Year 4 - MPhys with placement
Semester 1
Optional
Asset prices in financial markets go up and down in accordance with how markets digest the flow of information. To understand the causal relation between information flow and price movements, it is necessary to model market information and use this to infer the price dynamics. In this way, market dynamics can be replicated artificially on a computer. This module explains the powerful process of artificially generating realistic market models. The module begins with elements of probability theory. We will then learn the idea of conditional expectation and the Bayes formula, which gives the optimal inference under uncertainty. The meaning of the Bayes formula will be explained, leading to the understanding of what is meant by “intelligence”. The module then covers the basics of stochastic process (specifically, the Brownian motion) and calculus (specifically, the Ito calculus), sufficient to follow the contents of the module. Then simple models for flows of information in financial markets will be introduced, and by use of the Bayes formula the associated price dynamics will be derived. The module concludes with a brief application to the asset valuation problems in financial markets (such as options or other derivatives).
View full module detailsMathematics underpinning real-world uncertain events has become indispensable in many applications, including in particular financial markets. This module will begin with the introduction to probability theory and stochastic processes, with an emphasis on the Ito calculus for treating functions of Brownian motion. Such functions are commonly used in financial markets to model asset price dynamics, required for the valuation of financial contracts. The module then discusses structures of financial markets, with an emphasis on the equity market. Several of the standard and exotic contingent claims will be introduced, and the need for mathematical models for the valuation and risk management of these products will be explained. The pricing of a standard call option will then be worked out in a single-period binomial model, for which option price will be worked out in two ways: first using the portfolio replication and no arbitrage argument, and second using the risk-neutral expectation argument. The model is then extended into multi-period binomial tree model, leading to the Cox-Ross-Rubinstein option pricing formula. Finally, a continuous-time geometric Brownian motion model, originally introduced by Samuelson, will be considered, and used to deduce the famous Black-Scholes option pricing formula. This can be applied for the purpose of both pricing, as well as risk-management purposes, which will be demonstrated by working out the hedging strategy. The meaning of the pricing formula, and how it can be used in practical investment banking context, will be explained.
View full module detailsThis module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.
View full module detailsUnderstanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.
View full module detailsSemester 2
Optional
This 15-credit M-Level module introduces important topics and techniques in theoretical physics that have a wide range of applications in many areas physics and engineering and which the students will not have met before. Both the mathematical techniques and their applications are covered at a level appropriate for Masters level students coming to the end of their degree and who should be able to pull many different ideas in theoretical physics together.
View full module detailsThis module aims to provide an advanced level understanding of explosive nuclear astrophysics and the physics of stars. In particular, the course will provide an analytical underpinning of resonant reaction rates, together with the experimental techniques involved in their determination, as well as a theoretical treatment of nuclear reactions and celestial objects.
View full module detailsThis module will introduce the students to the principles and formalism of General Relativity and its applications to Black Holes and astrophysical phenomena.
View full module detailsGroup theory is a branch of mathematics developed to understand symmetries, which are powerful tools for understanding the properties of complex mathematical problems and physical systems. Group representations map abstract group elements to linear transformations on vector spaces. Representation theory allows us to better understand the properties of symmetry groups, and leads to powerful and compact solutions of otherwise difficult and intractable problems. This module builds on groups theory in MAT1031 Algebra and MAT2048 Groups & Rings.
View full module detailsQuantum Mechanics topics are essential building blocks for our understanding of many physical systems. The module assumes basic knowledge in quantum mechanics from modules in earlier years, but will provide a review at the beginning. Topics include a review of quantum mechanics, operator methods and applications to the harmonic oscillator, spin & angular momentum, symmetries in quantum mechanics. The second half of the module then moves beyond isolated quantum systems by addressing the topic of Quantum Entanglement and Quantum Coherence. Here the important concepts of entanglement and decoherence will be studied by developing an understanding of open quantum systems and the density matrix formalism.
View full module detailsThis module comprises two independent halves, on making qubit, and quantum communications. Quantum technologies, including quantum computing, rely on the quantum mechanical principles of superposition and entanglement. Furthermore, this superposition and entanglement needs to be controlled in useful ways. In this module you will learn about what physical systems allow quantum technology production, and their limitations. Quantum computers are only one type of device that uses these principles, and several other technologies are being created that are also enhanced by use of superpositions. Others include atomic clocks and Magnetic Resonance Imaging, MRI. We will also learn about the errors that inevitably build up in quantum computers when quantum superpositions are disturbed, and the strategies that might be built in to correct them. Quantum communications. This course provides a comprehensive introduction to the principles, protocols, and applications of quantum communications. Students will explore the fundamental concepts of quantum information transmission, quantum cryptography, and quantum communication protocols. They will also examine the challenges, advancements, and real-world applications of quantum communications including both theory and practical aspects.
View full module detailsThe module is an introduction to nonlinear partial differential equations (PDEs) with a focus on hyperbolic and dispersive PDEs. The module takes key classes of equations as the organising centre. Each class of PDEs is considered and the properties, analytical techniques, and analysis of each is taken in turn.
View full module detailsThis module introduces programming in Python for data science, with a focus on data pre-processing, data mining and analysis, machine learning and deep learning. Besides the practical hands-on experience with writing code, this course also covers the theoretical background on different data analysis techniques and machine learning approaches. The goal is to develop an understanding of how information can be extracted from data and how this information can be further used to make predictions, but importantly how this is done practically in terms of writing clear and transparent source code. Using real-world data sets and illustrative examples, this course will help to develop a theoretical understanding of data science as well as practical experience by developing useful software tools. Many of the techniques acquired through this module are likely to be of potential use in the dissertation project.
View full module detailsThe course provides an introduction to nuclear energy generation and applications of nuclear science. Nuclear reactors, their physics and operation are described. Nuclear reactor safety case work is also discussed. Future potential energy generation mechanisms such including nuclear fusion will be discussed. The module will also present a range of applications of radioactivity measurement including aspects of Environmental Science and Medical Diagnogstics and treatment therapy. The module will include some aspects of calculus and first order differential equations.
View full module detailsSemester 1 & 2
Compulsory
Under the guidance of an academic supervisor, the student will investigate a Physics topic of interest to him in depth. He will compose a written report on his studies, and give oral presentations on the work.
View full module detailsOptional modules for Year 4 (with PTY) - FHEQ Level 7
Students on the MPhys pathway must take the PHYM060 MPhys MaP Project module.
Choose 5 options overall, to maintain a 60:60 credit balance between Semesters 1 and 2.
Teaching and learning
Computers are used as teaching aids in the laboratory for experimental control and data analysis, in modelling of physical problems, and for effective communication.
You’ll be taught by research-led academics who specialise in both theoretical and mathematical physics. They lead research in many areas, including our understanding of the structure and dynamics of complex systems – from atomic nuclei, to galaxies and super-massive black holes. Research in mathematical physics includes ergodic theory, quantum field theory, general relativity, fluid dynamics and mathematical biology.
- Laboratory work
- Lectures
- Online learning
- Practical sessions
- Project work
- Tutorials
Assessment
We use a variety of methods to assess you, including:
- Coursework
- Essays
- Examinations
- Presentations
- Reports.
General course information
Contact hours
Contact hours can vary across our modules. Full details of the contact hours for each module are available from the University of Surrey's module catalogue. See the modules section for more information.
Timetable
New students will receive their personalised timetable in Welcome Week. In later semesters, two weeks before the start of semester.
Scheduled teaching can take place on any day of the week (Monday – Friday), with part-time classes normally scheduled on one or two days. Wednesday afternoons tend to be for sports and cultural activities.
View our code of practice for the scheduling of teaching and assessment (PDF) for more information.
Location
Stag Hill is the University's main campus and where the majority of our courses are taught.
We offer careers information, advice and guidance to all students whilst studying with us, which is extended to our alumni for three years after leaving the University.
Over the last decade, our employment figures have been among the best in the UK. The Graduate Outcomes 2024, HESA), results show that 96 per cent of Surrey's undergraduate mathematics and physics students go on to employment or further study.
Our physicists and mathematicians are highly sought after in industry, research, education, management, medicine, law and business because of their wide-ranging skills, their knowledge of fundamental theory and their ability to solve complex problems.
Our Mathematics and Physics courses provide you with the analytical, experimental and computational skills valued in a wide range of careers. You’ll also learn a range of skills during your studies that will help with your employability, including interview techniques, CV preparation and job applications. If you opt to take a Professional Training placement, you’ll gain invaluable employment experience.
Recent graduate roles
Recent graduates are now employed in a range of organisations, including:
- 3M
- BBC
- BT
- Defence Research Agency
- GEC Marconi Research
- National Physical Laboratory
- NHS
- Nokia
- Shell International Petroleum
- Surrey Medical Imaging Systems.
Pursue further education
Many graduates take masters courses in a range of subjects, such as geophysics, nanotechnology, meteorology, quantum field theory, education management and science communication.
Others, particularly those with an MMath or MPhys, choose to pursue PhDs in nonlinear dynamics, fluids, data science, theoretical physics, nuclear science, astrophysics, semiconductors or photonics.
Learn more about the qualifications we typically accept to study this course at Surrey.
Typical offer
- BSc (Hons)
- ABB
- Required subjects: Mathematics at Grade A and Physics at grade B
- MPhys (Hons)
- AAA-AAB
- Required subjects: Mathematics at Grade A and Physics at grade A
- MMath (Hons)
- AAA
- Required subjects: Mathematics and Physics.
- BSc (Hons) with foundation year
- CCC
- Required subjects: Mathematics C and either Physics or Chemistry, or equivalent
Please note: A-level General Studies and A-level Critical Thinking are not accepted. Applicants taking the Science Practical Endorsement are expected to pass.
GCSE or equivalent: English Language at Grade 4 (C).
- BSc (Hons):
- DDD BTEC Extended Diploma and A-Level Mathematics at grade A
- Required subjects: BTEC must be in a relevant subject.
- MPhys (Hons):
- D*DD BTEC Extended Diploma and A-level Mathematics grade A
- Required subjects: BTEC must be in a relevant subject.
- MMath (Hons):
- D*DD BTEC Extended Diploma and A-level Mathematics grade A.
- Required subjects: BTEC must be in a relevant subject.
- BSc (Hons) with foundation year:
- MMM BTEC Extended Diploma and A Level Mathematics at grade C
- Required subjects: BTEC must be in a relevant subject.
GCSE or equivalent: English Language at Grade 4 (C).
- BSc (Hons):
- 33
- Required subjects: HL5/SL6 in Physics and either HL6/SL7 in Maths (Analysis and Approaches) or HL6 in Maths (Applications and Interpretations
- MPhys (Hons):
- 35-34
- Required subjects: HL6/SL7 in Physics and either HL6/SL7 in Maths (Analysis and Approaches) or HL6 in Maths (Applications and Interpretations
- MMath (Hons):
- 35
- Required subjects: HL6/SL7 in Physics and either HL6/SL7 in Maths (Analysis and Approaches) or HL6 in Maths (Applications and Interpretations
- BSc Hons) with Foundation Year:
- 29
- Required subjects: HL4/SL6 in Physics and either HL4/SL6 in Maths (Analysis and Approaches) or HL4 in Maths (Applications and Interpretations
GCSE or equivalent: English A HL4/SL4 or English B HL5/SL6
- BSc (Hons):
- 78%
- Required subjects: Grade 8.5 in Mathematics (5 Period) and at least 7.5 in Physics.
- MPhys (Hons):
- 85%-82%
- Required subjects: Grade 8.5 and 7.5 in Maths and Physics.
- MMath (Hons):
- 85%
- Required subjects: Grade 8.5 and 7.5 in Maths and Physics
- BSc (Hons) with foundation year:
- For foundation year equivalencies please contact the Admissions team.
GCSE or equivalent: English Language (1/2) - 6 English Language (3) - 7.