General entry requirements

A level:

• A*AA to include A* in Mathematics, A in Further Mathematics and A in Physics
• For students not taking A level Further Mathematics, the typical offer is A* (Mathematics), A* (Physics) and A in a third subject at A level

IB:

• 38 to include 7 in Higher Level Mathematics (‘Analysis and Approaches’ only) and 6 in Higher Level Physics

BTEC:

• We will consider applications from students taking a BTEC in a relevant Science/Engineering alongside A level Maths and Further Maths on an individual basis

Additional requirements:

You will also need to meet our English Language requirements.

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International Students

We welcome applications from students with other internationally recognised qualifications.

Find out more about international entry requirements.

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Contextual data and differential offers

Warwick may make differential offers to students in a number of circumstances. These include students participating in the Realising Opportunities programme, or who meet two of the contextual data criteria. Differential offers will be one or two grades below Warwick’s standard offer (to a minimum of BBB).

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Warwick International Foundation Programme (IFP)

All students who successfully complete the Warwick IFP and apply to Warwick through UCAS will receive a guaranteed conditional offer for a related undergraduate programme (selected courses only).

Find out more about standard offers and conditions for the IFP.

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Taking a gap year

Applications for deferred entry welcomed.

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Interviews

We do not typically interview applicants. Offers are made based on your UCAS form which includes predicted and actual grades, your personal statement and school reference.

Year One

Calculus

Calculus is the mathematical study of continuous change. In this module there will be considerable emphasis throughout on the need to argue with much greater precision and care than you had to at school. With the support of your fellow students, lecturers and other helpers, you will be encouraged to move on from the situation where the teacher shows you how to solve each kind of problem, to the point where you can develop your own methods for solving problems. By the end of the year you will be able to answer interesting questions like, what do we mean by `infinity'?

Sets and Numbers

It is in its proofs that the strength and richness of mathematics is to be found. University mathematics introduces progressively more abstract ideas and structures, and demands more in the way of proof, until most of your time is occupied with understanding proofs and creating your own. Learning to deal with abstraction and with proofs takes time. This module will bridge the gap between school and university mathematics, taking you from concrete techniques where the emphasis is on calculation, and gradually moving towards abstraction and proof.

Linear Algebra

Linear algebra addresses simultaneous linear equations. You will learn about the properties of vector space, linear mapping and its representation by a matrix. Applications include solving simultaneous linear equations, properties of vectors and matrices, properties of determinants and ways of calculating them. You will learn to define and calculate eigenvalues and eigenvectors of a linear map or matrix. You will have an understanding of matrices and vector spaces for later modules to build on.

Differential Equations

Can you predict the trajectory of a tennis ball? In this module you cover the basic theory of ordinary differential equations (ODEs), the cornerstone of all applied mathematics. ODE theory proves invaluable in branches of pure mathematics, such as geometry and topology. You will be introduced to simple differential and difference equations and methods for their solution. You will cover first-order equations, linear second-order equations and coupled first-order linear systems with constant coefficients, and solutions to differential equations with one-and two-dimensional systems. We will discuss why in three dimensions we see new phenomena, and have a first glimpse of chaotic solutions.

Physics Foundations

You will look at dimensional analysis, matter and waves. Often the qualitative features of systems can be understood (at least partially) by thinking about which quantities in a problem are allowed to depend on each other on dimensional grounds. Thermodynamics is the study of heat transfers and how they can lead to useful work. Even though the results are universal, the simplest way to introduce this topic to you is via the ideal gas, whose properties are discussed and derived in some detail. You will also cover waves. Waves are time-dependent variations about some time-independent (often equilibrium) state. You will revise the relation between the wavelength, frequency and velocity and the definition of the amplitude and phase of a wave.

Electricity and Magnetism

You will largely be concerned with the great developments in electricity and magnetism, which took place during the nineteenth century. The origins and properties of electric and magnetic fields in free space, and in materials, are tested in some detail and all the basic levels up to, but not including, Maxwell's equations are considered. In addition, the module deals with both dc and ac circuit theory including the use of complex impedance. You will be introduced to the properties of electrostatic and magnetic fields, and their interaction with dielectrics, conductors and magnetic materials.

Classical Mechanics and Special Relativity

You will study Newtonian mechanics emphasizing the conservation laws inherent in the theory. These have a wider domain of applicability than classical mechanics (for example they also apply in quantum mechanics). You will also look at the classical mechanics of oscillations and of rotating bodies. It then explains why the failure to find the ether was such an important experimental result and how Einstein constructed his theory of special relativity. You will cover some of the consequences of the theory for classical mechanics and some of the predictions it makes, including: the relation between mass and energy, length-contraction, time-dilation and the twin paradox.

Quantum Phenomena

This module explains how classical physics is unable to explain the properties of light, electrons and atoms. (Theories in physics, which make no reference to quantum theory, are usually called classical theories.) It covers the most important contributions to the development of quantum physics including: wave-particle 'duality', de Broglie's relation and the Schrodinger equation. It also looks at applications of quantum theory to describe elementary particles: their classification by symmetry, how this allows us to interpret simple reactions between particles and how elementary particles interact with matter.

Physics Programming Workshop

You will be introduced to the Python programming language in this module. It is quick to learn and encourages good programming style. Python is an interpreted language, which makes it flexible and easy to share. It allows easy interfacing with modules, which have been compiled from C or Fortran sources. It is widely used throughout physics and there are many downloadable free-to-user codes available. You will also look at the visualisation of data. You will be introduced to scientific programming with the help of the Python programming language, a language widely used by physicists.

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Year Two

Analysis III

In the first half of this module, you will investigate some applications of year one analysis: integrals of limits and series; differentiation under an integral sign; a first look at Fourier series. In the second half you will study analysis of complex functions of a complex variable: contour integration and Cauchy’s theorem, and its application to Taylor and Laurent series and the evaluation of real integrals.

Methods of Mathematical Physics

On this module, you will learn the mathematical techniques required by second-, third- and fourth-year physics students. Starting with the theory of Fourier transforms and the Dirac delta function, you will learn why diffraction patterns in the far-field limit are the Fourier transforms of the ‘diffracting’ object before moving to diffraction more generally, including in the light of the convolution theorem. You will also be introduced to Lagrange multipliers, co-ordinate transformations and Cartesian tensors, which will be illustrated with examples of their use in physics.

Multivariable Calculus

There are many situations in pure and applied mathematics where the continuity and differentiability of a function f: R n. → R m has to be considered. Yet, partial derivatives, while easy to calculate, are not robust enough to yield a satisfactory differentiation theory. In this module you will establish the basic properties of this derivative, which will generalise those of single-variable calculus. The module will review line and surface integrals, introduce div, grad and curl and establish the divergence theorem.

Partial Differential Equations

The theory of partial differential equations (PDE) is important in both pure and applied mathematics. Since the pioneering work on surfaces and manifolds by Gauss and Riemann, PDEs have been at the centre of much of mathematics. PDEs are also used to describe many phenomena from the natural sciences (such as fluid flow and electromagnetism) and social sciences (such as financial markets). In this module you will learn how to classify the most important partial differential equations into three types: elliptic, parabolic, and hyperbolic. You will study the role of boundary conditions and look at various methods for solving PDEs.

Variational Principles

This course will introduce you to the calculus of variations and to appreciate its centrality to the formulation and understanding of physical laws and problems in geometry. At its conclusion, you should be able to set up and solve minimisation problems with and without constraints, derive Euler-Lagrange equations and appreciate how the laws of mechanics and geometrical problems involving least length and least area fit into this framework.

Physics of Fluids

The field of fluids is one of the richest and most easily appreciated in physics. Tidal waves, cloud formation and the weather generally are some of the more spectacular phenomena encountered in fluids. In this module you will establish the basic equations of motion for a fluid - the Navier-Stokes equations - and show that in many cases they can yield simple and intuitively appealing explanations of fluid flows. You will be concentrating on incompressible fluids.

Quantum Mechanics and its Applications

In the first part of this module you will use ideas, introduced in the first year module, to explore atomic structure. You will discuss the time-independent and the time-dependent Schrödinger equations for spherically symmetric and harmonic potentials, angular momentum and hydrogenic atoms. The second half of the module looks at many-particle systems and aspects of the Standard Model of particle physics. It introduces the quantum mechanics of free fermions and discusses how it accounts for the conductivity and heat capacity of metals and the state of electrons in white dwarf stars.

Thermal Physics II

Any macroscopic object we meet contains a large number of particles, each of which moves according to the laws of mechanics (which can be classical or quantum). Yet, we can often ignore the details of this microscopic motion and use a few average quantities such as temperature and pressure to describe and predict the behaviour of the object. Why we can do this, when we can do this and how to do it are the subject of this module. The most important idea in the field is due to Boltzmann, who identified the connection between entropy and disorder. The module shows you how the structure of equilibrium thermodynamics follows from Boltzmann's definition of the entropy and shows you how, in principle, any observable equilibrium quantity can be computed.

Electromagnetic Theory and Optics

You will develop the ideas of first year electricity and magnetism into Maxwell's theory of electromagnetism. Maxwell's equations pulled the various laws of electricity and magnetism (Faraday's law, Ampere's law, Lenz's law, Gauss's law) into one unified and elegant theory. The module shows you that Maxwell's equations in free space have time-dependent solutions, which turn out to be the familiar electromagnetic waves (light, radio waves, X-rays, etc.), and studies their behaviour at material boundaries (Fresnel Equations). You will also cover the basics of optical instruments and light sources.

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Year Three

Fluid Dynamics

Starting with a solid understanding of the underlying mathematical description of fluid in different fluid flows, you will find qualitative and quantitative solutions for particular fluid dynamics problems, ranging from simple laminar flows to fully developed turbulence, and use the concepts and techniques you have learned to analyse other partial differential equations, for example in plasma physics or nonlinear optics. An important aim of the module is to provide you with an appreciation of the complexities and beauty of fluid motion, which will be brought out in computer demonstrations and visualisations.

Quantum Physics of Atoms

The basic principles of quantum mechanics are applied to a range of problems in atomic physics. The intrinsic property of spin is introduced and its relation to the indistinguishability of identical particles in quantum mechanics discussed. Perturbation theory and variational methods are described and applied to several problems. The hydrogen and helium atoms are analysed and the ideas that come out from this work are used to obtain a good qualitative understanding of the periodic table. In this module, you will develop the ideas of quantum theory and apply these to atomic physics.

Electrodynamics

You will revise the magnetic vector potential, A, which is defined so that the magnetic field B=curl A. We will see that this is the natural quantity to consider when exploring how electric and magnetic fields transform under Lorentz transformations (special relativity). The radiation (EM-waves) emitted by accelerating charges will be described using retarded potentials and have the wave-like nature of light built in. The scattering of light by free electrons (Thompson scattering) and by bound electrons (Rayleigh scattering) will also be described. Understanding the bound electron problem led Rayleigh to his celebrated explanation of why the sky is blue and why sunlight appears redder at sunrise and sunset.

Kinetic Theory

Kinetic Theory' is the theory of how distributions change and is therefore essentially about non-equilibrium phenomena. The description of such phenomena is statistical and is based on Boltzmann's equation, and on the related Fokker-Planck equation. These study the evolution in time of a distribution function, which gives the density of particles in the system's phase space. In this module you will establish the relations between conductivity, diffusion constants and viscosity in gases. You will look also at molecular simulation and applications to financial modelling.

Laboratory for Mathematics and Physics Students

You will be introduced to collaborative, experimental and computational work and some advanced research techniques. It will give you the opportunity to plan and direct an experiment and to work within a team. It should acquaint you with issues associated with experimental work, including data acquisition and the analysis of errors and the health and safety regulatory environment within which all experimental work must be undertaken. It will also provide you experience of report writing and making an oral presentation to a group.

Mathematical Methods for Physicists III

Requiring functions of complex variables to be analytic (differentiable with respect to their complex argument in some domain) turns out to constrain such functions very strongly. As the module shows: only the constant function is differentiable everywhere, analytic functions are actually equal to their Taylor series and not just approximated by them, a function that is once differentiable is differentiable infinitely many times. Complex differentiable functions are clean, they are fun and they are important in physics. For example, response functions like the dielectric response function are analytic functions with the domain, in which the function is analytic, being related to causality.

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Year Four

Physics Project

You will work, normally in pairs, on an extended project which may be experimental, computational or theoretical (or indeed a combination of these). Through discussions with your supervisor and partner you will establish a plan of work which you will frequently review as you progress. In general, the project will not be closely prescribed and will contain an investigative element. The project will provide you an experience of working on an extended 'research-like' project in collaboration with a supervisor and partner.

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Examples of optional modules/options for current students:

• Probability
• Programming for Scientists
• Geometry
• Metric Spaces
• Functional Analysis
• Galaxies
• Astrophysics
• Physics in Medicine
• The Solar System
• Hamiltonian Mechanics
• Electrodynamics

Tuition fees

Find out more about Tuition fees fees and funding

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Additional course costs

There may be costs associated with other items or services such as academic texts, course notes, and trips associated with your course. Students who choose to complete a work placement or study abroad will pay reduced tuition fees for their third year.

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Warwick Undergraduate Global Excellence Scholarship 2021

We believe there should be no barrier to talent. That's why we are committed to offering a scholarship that makes it easier for gifted, ambitious international learners to pursue their academic interests at one of the UK's most prestigious universities. This new scheme will offer international fee-paying students 250 tuition fee discounts ranging from full fees to awards of £13,000 to £2,000 for the full duration of your Undergraduate degree course.

Find out more about the Warwick Undergraduate Global Excellence Scholarship 2021

Your career

Graduates from this course have gone on to work for employers including:

• Deloitte Digital
• Brunei Shell Petroleum
• British Red Cross
• EDF Energy
• Civil Service
• Deutsche Bank

They have pursued roles such as:

• physical scientists
• finance and investment analysts
• programmers and software development professionals
• graphic designers
• researchers

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Helping you find the right career

Our department has a dedicated professionally qualified Senior Careers Consultant to support you. They offer impartial advice and guidance, together with workshops and events throughout the year. Previous examples of workshops and events include:

• Career options with a Physics Degree
• Careers in Science
• Warwick careers fairs throughout the year
• Physics Alumni Evening
• Careers and Employer networking event for Physics students

Find out more about careers support at Warwick.