A Level Requirements
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Full time 3 Year(s)
Taught jointly with Lancaster’s Department of Mathematics and Statistics, our BSc degree in Theoretical Physics with Mathematics combines core physics and specialised theoretical physics subjects with classes in pure mathematics. This equips you with an understanding of the mathematical foundations of physics, for example, you will learn how quantum mechanics is underpinned by the powerful mathematical concept of a Hilbert space.
In your first year you will cover the core of physics in modules such as Quantum Physics and Electromagnetism, and the core of mathematics including geometry and calculus, numbers and relations, and probability.
In years two and three, the core physics modules are complemented by courses from the Theoretical Physics scheme and mathematical topics such as group theory and differential equations.
In your final year you also carry out an investigative group project, and have a choice of options such as Quantum Information and Advanced Gravity and Relativity.
A Level AAB
Required Subjects A level Mathematics grade A and A level Physics grade A
IELTS 6.0 overall with at least 5.5 in each component. For other English language qualifications we accept, please see our English language requirements webpages.
Interviews Applicants may be interviewed before being made an offer.
International Baccalaureate 35 points overall with 16 points from the best 3 Higher Level subjects including 6 in Mathematics HL and Physics HL
BTEC May be considered alongside A level Mathematics and A level Physics.
Access to HE Diploma May occasionally be accepted.
We welcome applications from students with a range of alternative UK and international qualifications, including combinations of qualification. Further guidance on admission to the University, including other qualifications that we accept, frequently asked questions and information on applying, can be found on our general admissions webpages.
Contact Admissions Team + 44 (0) 1524 592028 or via firstname.lastname@example.org
Many of Lancaster's degree programmes are flexible, offering students the opportunity to cover a wide selection of subject areas to complement their main specialism. You will be able to study a range of modules, some examples of which are listed below.
This module provides the student with an understanding of functions, limits, and series, and knowledge of the basic techniques of differentiation and integration. We introduce examples of functions and their graphs, and techniques for building new functions from old. We then consider the notion of a limit and introduce the main tools of calculus and Taylor Series. Students will also learn how to add, multiply and divide polynomials, and be introduced to rational functions and their partial fractions.
The exponential function is defined by means of a power series which is subsequently extended to the complex exponential function of an imaginary variable, so that students understand the connection between analysis, trigonometry and geometry. The trigonometric and hyperbolic functions are introduced in parallel with analogous power series so that students understand the role of functional identities. Such functional identities are later used to simplify integrals and to parametrise geometrical curves.
In Classical Mechanics you’ll apply the ideas of fundamental Newtonian mechanics to real large-scale systems such as rotating bodies, planetary systems and classical fluids.
Our focus is on gravitation, and its central importance in determining the large-scale behaviour of the Universe. You’ll look at concepts such as inertial and gravitational mass, Mach's principle, black holes and even dark matter.
We consider how to extend the principles of basic kinematics and dynamics to rotational situations, giving you an understanding of concepts of torque, moment of inertia, centre of mass, angular momentum and equilibrium.
Part of your time will also be spent looking at how to describe basic processes in the properties of materials including elasticity of solids and fluid dynamics.
This module provides a rigorous overview of real numbers, sequences and continuity. Covering bounds, monotonicity, subsequences, invertibility, and the intermediate value theorem, among other topics, students will become familiar with definitions, theorems and proofs.
Examining a range of examples, students will become accustomed to mathematical writing and will develop an understanding of mathematical notation. Through this module, students will also gain an appreciation of the importance of proof, generalisation and abstraction in the logical development of formal theories, and develop an ability to imagine and ‘see’ complicated mathematical objects.
In addition to learning and developing subject specific knowledge, students will enhance their ability to assimilate information from different presentations of material; learn to apply previously acquired knowledge to new situations; and develop their communication skills.
Students are introduced to the basic ideas and notations involved in describing sets and their functions. The module helps students to formalise the idea of the size of a set and what it means to be finite, countably infinite or uncountably finite. For finite sets, we can say that one is bigger than another if it contains more elements. What about infinite sets? Are some infinite sets bigger than others? We develop the tools to answer these questions and other counting problems, such as those involving recurrence relations, e.g. the Fibonacci numbers.
Rather than counting objects, we might be interested in connections between them, leading to the study of graphs and networks – collections of nodes joined by edges. There are many applications of this theory in designing or understanding properties of systems, such as the infrastructure powering the internet, social networks, the London Underground and the global ecosystem.
Covering the basic laws of electromagnetism, this module allows you to investigate the similarities and differences between electric and magnetic fields, and to explore the basic concepts of electromagnetic phenomena including charge, current, field, force and potential.
You’ll begin by studying electrostatics, describing forces and fields due to charge distributions using Coulomb's law and Gauss's law. You’ll also look at the concept of polarisation, and how this can be applied to capacitance and combinations of capacitors.
Later on you will be introduced to magnetostatics, and will learn how to describe it using the concepts of field, flux and force, and the motion of charged particles in a magnetic field. You’ll also look at the origins of magnetic fields and Ampere's law, and Faraday's law of electromagnetic induction.
This module extends the theory of calculus from functions of a single real variable to functions of two real variables. Students will learn more about the notions of differentiation and integration and how they extend from functions defined on a line to functions defined on the plane. We see how partial derivatives help us to understand surfaces, while repeated integrals enable us to calculate volumes. Students will also investigate complex polynomials and use De Moivre’s theorem to calculate complex roots.
In mathematical models, it is common to use functions of several variables. For example, the speed of an airliner can depend upon the air pressure, temperature and wind direction. To study functions of several variables, we introduce rates of change with respect to several quantities. We learn how to find maxima and minima. Applications include the method of least squares. Finally, we investigate various methods for solving differential equations of one variable.
Building on MATH113, this module explores the familiar topics of integration, series and differentiation, and develops them further. Taking a different approach, students will learn about the concept of integrability of continuous functions; improper integrals of continuous functions; the definition of differentiability for functions; and the algebra of differentiation.
Applying the skills and knowledge gained from this module, students will tackle questions such as: “Can you sum up infinitely many numbers and get a finite number?”. Students will also enhance their knowledge and understanding of the fundamental theorem of calculus.
Introducing the theory of matrices together with some basic applications, students will learn essential techniques such as arithmetic rules, row operations and computation of determinants by expansion about a row or a column.
The second part of the module covers a notable range of applications of matrices, such as solving systems of simultaneous linear equations, linear transformations, characteristic equation and eigenvectors and eigenvalues.
This module introduces the student to logic and mathematical proofs, with emphasis placed on proving general theorems than on performing calculations. This is because a result which can be applied to many different cases is clearly more powerful than a calculation that deals only with a single specific case.
We take a look at the language and structure of mathematical proofs in general, emphasising how logic can be used to express mathematical arguments in a concise and rigorous manner. These ideas are then applied to the study of number theory, establishing several fundamental results such as Bezout’s Theorem on highest common factors and the Fundamental Theorem of Arithmetic on prime factorisations.
The concept of congruence of integers is introduced to students and they study the idea that a highest common factor can be generalised from the integers to polynomials.
Probability theory is the study of chance phenomena, the concepts of which are fundamental to the study of statistics. This module will introduce students to some simple combinatorics, set theory and the axioms of probability.
Students will become aware of the different probability models used to characterise the outcomes of experiments that involve a chance or random component. The module covers ideas associated with the axioms of probability, conditional probability, independence, discrete random variables and their distributions, expectation and probability models.
The ultimate description of the universe requires quantum and not classical mechanics.
In this module, we begin by investigating how specific experiments led to the breakdown of classical physics, before moving into the quantum world.
You’ll look at the basic ideas of wave mechanics, particularly wave particle duality, as well as considering the probabilistic nature of phenomena and the uncertainty principle through the Schrodinger equation and its solution for simple situations.
To enable students to achieve a solid understanding of the broad role that statistical thinking plays in addressing scientific problems, the module begins with a brief overview of statistics in science and society and then moves on to the selection of appropriate probability models to describe systematic and random variations of discrete and continuous real data sets. Students will learn to implement statistical techniques and to draw clear and informative conclusions.
The module will be supported by the statistical software package ‘R’, which forms the basis of weekly lab sessions. Students will develop a strategic understanding of statistics and the use of associated software, and this underpins the skills needed for all subsequent statistical modules of the degree.
In this module you’ll have the opportunity to explore the nature and methods of physics by considering the different scales of the universe and the areas of physics which relate to them.
You’ll model real phenomena and situations, looking at the physical principles which are fundamental to mechanics, particularly Newton’s laws relating to forces and motion, and the principles of the conservation of energy and momentum.
Later on you’ll also focus on the Special Theory of Relativity, beginning with Einstein's postulates and moving on to inertial reference frames, the physics of simultaneity, length contraction and time dilation, and space-time diagrams.
This module allows you to study the thermal properties of matter, and to gain an understanding of how to relate them to the fundamental mechanical properties of systems.
We begin with an introduction to the concepts of temperature and heat, thermal equilibrium and temperature scales. We then look at how to describe mechanisms of heat transfer, particularly in phase changes and equations of state, and the kinetic model of an ideal gas.
As part of the module you’ll also have the opportunity to explore the first and second laws of thermodynamics, including concepts of internal energy, heat and work done, heat engines and refrigerators, and entropy. You’ll then learn about the role of thermodynamics in describing macroscopic physical situations, looking in particular at temperature, entropy, work, heat, and internal energy.
The main focus of this course is vectors in two and three-dimensional space. We start off with the definition of vectors and we see some applications to finding equations of lines and planes. We then consider some different ways of describing curves and surfaces via equations or parameters, and we use partial differentiation to determine tangent lines and planes, as well as using integration to calculate the length of a curve.
In the second half of the course, we study functions of several variables. When attempting to calculate an integral over one variable, we often substitute one variable for another more convenient one; here we will see the equivalent technique for a double integral, where we have to substitute two variables simultaneously. We also investigate some methods for finding maxima and minima of a function subject to certain conditions.
Finally, we discuss how to calculate the areas of various surfaces and the volumes of various solids.
This module is ideal for students looking to develop their understanding of vector algebra and coordinate geometry in a physical context, extending elementary ideas of functions and calculus to a three-dimensional description based on vector fields and potentials.
You’ll begin by exploring the real functions of many variables and their partial derivatives, followed by implicit differentiation of the functions of many variables and the chain rule. You’ll then go on to study the gradient vector in three dimensions in relation to directional derivatives, and will investigate the divergence and curl of a vector field as well as Stokes' theorem and the divergence theorem.
Vector Calculus places a focus on calculus in higher dimensional space, allowing you to develop your knowledge of parametric representations of curves, surfaces and volumes, calculation of areas and volumes including the use of changes of variables and Jacobians, and the calculation of line and surface integrals.
This module builds on the binary operations studies in previous modules, such as addition or multiplication of numbers and composition of functions. Here you’ll select a small number of properties which these and other examples have in common, and use them to define a group.
You’ll also consider the elementary properties of groups. It turns out that several surprisingly elegant results can be proved fairly simply! By looking at maps between groups which 'preserve structure' you’ll discover a way of formalizing (and extending) the natural concept of what it means for two groups to be 'the same'.
Ring theory provides a framework for studying sets with two binary operations: addition and multiplication. This gives us a way to abstractly model various number systems, proving results that can be applied in many different situations, such as number theory and geometry. Familiar examples of rings include the integers, the integers modulation, the rational numbers, matrices and polynomials, but you’ll meet several less familiar examples too.
Complex Analysis has its origins in differential calculus and the study of polynomial equations.
In this module you’ll consider the differential calculus of functions of a single complex variable and study power series and mappings by complex functions. You’ll use integral calculus of complex functions to find elegant and important results, including the fundamental theorem of algebra, and you’ll also use classical theorems to evaluate real integrals.
The module ends with basic discussion of harmonic functions, which play a significant role in physics.
This module provides students with a working knowledge of electromagnetion through Maxwell’s equations using the tools of vector calculus. Students will become familiar with the common connections between the many different phenomena in nature that share the mathematical model of a harmonic oscillator or of a wave. This module addresses the basic properties of wave propagation, diffraction and inference, and laser operation.
Students will develop an appreciation for the power of vector calculus and Maxwell’s equations for the description of electromagnetic phenomena, and will gain practical knowledge of Fresnel and Fraunhofer diffraction, as well as thin-film interference fringes and anti-reflection coatings. Additionally, the module aims to enhance students’ understanding of the origin of polarisation, and the relevance of dichroism, along with an understanding of the basic elements of a laser, laser operation and important features of laser light.
The module expands students’ knowledge on topics such as Newton's laws, solution of one-dimensional dynamical problems, and Lagrangian, its relation to Newton's equations and the least action principle. This module includes lectures on analytical methods used both in classical mechanics and in broader areas of theoretical and mathematical physics. Students are given the opportunity to perform experiments in optics, mechanics and electric circuits which illustrate and compliment the taught material, and are additionally required to write a scientific report on one of the experiments.
By the end of the module, students will understand methods of integration of equations of motion for dynamical problems in classical mechanics, be able to use variational calculus in application to functionals and exploit the generality of Lagrangian and Hamiltonian techniques by using appropriate generalised coordinates. They will also be acquainted with the concepts of phase space, stability of motion and chaos. Additionally, students will develop useful techniques for experimental data collection and analysis and understand how to assess the statistical validity of data and their interpretation.
This module will give you the opportunity to study vector spaces, together with their structure-preserving maps and their relationship to matrices.
You’ll consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of your study will also involve looking at the concepts of length and angle with regard to vector spaces.
Students will be introduced to various axioms for quantum mechanics, such as eigenvalues, diagonalisation, differential and matrix operators and commutation relations. They will also learn about rotations and angular momentum, the interaction of magnetic moment with static magnetic field and electron spin. Students can expect to investigate approximation methods, such as the time-dependent Rayleigh-Schrodinger perturbation theory, and time dependent interactions, including the Heisenberg picture and time dependent Hamiltonians.
Students will learn to apply quantum mechanics to problems in one and three dimensions, including the hydrogen atom, by solving the Schrödinger equation, and will develop the ability to find approximate solutions for not exactly solvable systems. The module will enhance students’ understanding of expectation values and probabilities in the context of experiments on quantum systems, along with an appreciation for the mathematical consistency of quantum mechanics.
In this module you’ll take a thorough look at the limits of sequences and convergence of series. You’ll learn to extend the notion of a limit to functions, leading to the analysis of differentiation, including proper proofs of techniques learned at A-level.
You’ll spend time studying the Intermediate Value Theorem and the Mean Value Theorem, and will discover that they have many applications of widely differing kinds. The next topic is new: sequences and series of functions (rather than just numbers), which again has many applications and is central to more advanced analysis.
Next we put the notion of integration under the microscope. Once it’s properly defined (via limits), you’ll learn how to get from this definition to the familiar technique of evaluating integrals by reverse differentiation. You’ll also explore some applications of integration that are quite different from the ones in A-level, such as estimations of discrete sums of series.
Further possible topics include Stirling's Formula, infinite products and Fourier series.
Students receive an introductory concepts-based approach to the module, giving a basic understanding of nuclei and fundamental particles. The module covers the general properties of nuclei, such as composition, the forces within the nucleus, mass and binding energy. Students are then introduced to the standard model of particle physics, including the three generations of fundamental particles.
By the end of the module, students will gain a working knowledge of Einstein’s theory of special relativity, both conceptually and mathematically, and will understand why the theory has replaced Newton’s concepts of absolute space and time. Additionally, students will develop a broad understanding of the equivalence principle and its relevance for general relativity.
This module introduces one-electron atoms and the spin-orbit magnetic interaction, along with identical particles and the Helium atom. Students will investigate the Fermi gas model and the single particle shell model, and will compare predictions of the shell model for nuclear spins, parities and magnetic moments with experimental results. The module explores the nuclear beta decay process and the Fermi and Gamow - Teller selection rules, and students are provided with a description of the beta decay rate and the electron energy spectrum in terms of a nuclear matrix element and a statistical factor.
Students will develop their knowledge in atomic and nuclear physics to an advanced level, and will be able to use the results of basic quantum mechanics to explain the basic characteristics of atomic and nuclear structure, in addition to gaining the ability to describe the processes of atomic transitions and nuclear decays. The module will provide an explanation of the concept and importance of the parity of an atomic or nuclear state, and will provide students with the opportunity to study the nuclear beta decay process and in particular the neutrino and parity non-conservation.
The module explores symmetries, the Quark model and gives an introduction to QCD. Students will explore leptons, as well as forces and their carrier particles and Feynman diagrams. The module aims to provide a general introduction to theoretical and experimental topics in elementary particle physics, essentially the Standard Model of particle physics.
Students will gain the ability to describe the main features of the Standard Model of particle physics and understand its place in physics as a whole, and will be able to identify major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used, such as accelerators and detectors. In addition, students will understand the role of symmetry and conservation laws in fundamental physics, and will develop the ability to perform calculations of physically observable quantities relevant to the subject, along with solving problems based on the application of the general principles of particle physics.
The module offers an introduction to reciprocal lattice and diffraction of waves, the electronic band structure in metals, and insulators and semiconductors. Students will explore electrons in semiconductors, effective mass and the heat capacity of solids. There will be a Summary of experimental phenomena, tunnelling, Josephson Junctions and an outline of BCS theory.
Students will be introduced to theoretical and experimental topics in solid state physics at an advanced level, and will develop an understanding of the main features of the physics of electrons in solids, along with knowledge of the main features of the optical properties of solids.
Students will gain an enhanced understanding of crystal lattices and phonons, along with the main features of the thermal properties of solids, and will be able to describe major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used.
This module explores the ideas, techniques and results of statistical physics. Students will examine gases and the density of states, along with the statistics of gases, fermions and bosons and the two distributions for gases. Maxwell-Boltzmann gases, velocity distribution and fermi-Dirac gases are investigated as the module provides an uncomplicated and direct approach to the subject, using frequent illustrations from low temperature physics.
Students will provide a unified survey of the statistical physics of gases, including a full treatment of quantum statistics, gaining a fuller insight into the meaning of entropy. Students will gain knowledge in applications of statistics to various types of gas. Ultimately, students will develop the ability to apply expressions and distributions in order to form accurate deductions, for example using the Boltzmann distribution for the probability of finding a system in a particular quantum state. Additionally, students will learn the role of statistical concepts in understanding macroscopic systems, and will be able to describe superfluidity in liquid helium, Bose-Einstein condensation and black body radiation.
In the Theoretical Physics Group Project, students will work as part of a team and will receive guidance on project management, planning and meetings. The module will culminate in a writing-up stage in which the groups will prepare a group report, and students will be presented an opportunity to give an individual talk at the physics mini-conference.
The module equips students with the ability to develop a theoretical physics research project with formulation, literature searches, data gathering, analysis and presentation.
This module requires independent study in various aspects of theoretical physics is guided by a series of workshops. Students will solve problems, partake in intense reading, and prepare and deliver presentations. Students will be provided with an opportunity to extend their preliminary studies by undertaking open-ended investigations into various aspects and problems of theoretical physics, writing up their findings in an individual report.
The module will teach analytical recipes of theoretical physics used in quantum mechanics, with the focus on the variational functions method, operator techniques with applications in perturbation theory methods and coherent states of a quantum harmonic oscillator, whilst students will train in the use of the operator algebra of 'creation' and 'annihilation' operators in the harmonic oscillator problem, which will develop a basis for the introduction of second quantisation in many-body systems. Students will develop an understanding in the algebra of creation and annihilation operators for Bose and Fermi systems, along with exploring the second-quantised representation of Hamiltonians of interacting many-body systems.
Additionally, students will analyse Bose-Einstein condensation in one-, two-, and three-dimensional systems and will develop the ability to describe the condensate using the method of coherent states, as well as covering the Ginzburg-Landau theory of a superfluid phase transition and to describe vortices in a superfluid. They will learn to relate Bose and Fermi statistics to the symmetry of many-body systems with respect to permutations of identical particles and will receive computer programming skills, as well as gaining experience in individual project work. The module’s main aim is to prepare students to enable them to undertake fourth year theoretical physics projects.
This module considers questions relating to linear ordinary differential equations. While explicit solutions can only be found for special types of equations, some of the ideas of real analysis allow us to answer questions about the existence and uniqueness of solutions to more general equations as well as allowing us to study certain properties of these solutions.
In this module you’ll develop the knowledge of groups that you’ve gained in second year. You’ll study ‘direct products’ which are used to construct new groups, while any finite group is shown to ‘factor’ into ‘simple’ pieces. You’ll also consider situations in which a group ‘acts’ on a set by permuting its elements; this powerful idea is used to identify the symmetries of the Platonic solids, and to help study the structure of groups themselves.
In this module you’ll examine the notion of a norm, which introduces a generalized notion of ‘distance’ to the purely algebraic setting of vector spaces. You’ll learn several quite natural ways to do this, both for vectors of any dimension and for functions. You’ll then focus on the more special notion of an inner product which generalizes angles at the same time as distances.
Once we’ve established these concepts, you’ll have the opportunity to study geometrical ideas like orthogonality, which can be seen to apply to much more general spaces than Euclidean spaces of three (or even n) dimensions, notably to infinite dimensional spaces of functions. For example, Hilbert space theory shows how Fourier series are really another case of expressing an element in terms of a basis, and how you can use orthogonality to find best approximations to a given function by functions of a prescribed type. Finally, you’ll look at some of the main results of linear algebra, which generalize very nicely to linear operators between Hilbert spaces.
This module covers the basics of ordinary representation theory. You’ll learn the concepts of R-module and of group representations, the main results pertaining to group representations, and will handle basic applications in the study of finite groups. You’ll also learn to perform computations with representations and morphisms in a selection of finite groups.
Lancaster University offers a range of programmes, some of which follow a structured study programme, and others which offer the chance for you to devise a more flexible programme. We divide academic study into two sections - Part 1 (Year 1) and Part 2 (Year 2, 3 and sometimes 4). For most programmes Part 1 requires you to study 120 credits spread over at least three modules which, depending upon your programme, will be drawn from one, two or three different academic subjects. A higher degree of specialisation then develops in subsequent years. For more information about our teaching methods at Lancaster visit our Teaching and Learning section.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research.
Physics is an exciting subject that is fundamental to the developments in modern society. Applications of the subject range from the very pure to the very practical, and a physics degree opens up a wide range of rewarding careers in scientific research and technological development, as well as in a variety of other professions. A substantial number of our graduates continue on to postgraduate education, or enter employment that directly relies on their specialist skills. Our students also find employment in careers where they are valued because of general skills gained during the course such as logical thinking, problem solving, numeracy and computer literacy. Examples include consulting, finance, computer programming, and accountancy, as well as managerial and administrative positions.
Lancaster University is dedicated to ensuring you not only gain a highly reputable degree, you also graduate with the relevant life and work based skills. We are unique in that every student is eligible to participate in The Lancaster Award which offers you the opportunity to complete key activities such as work experience, employability/career development, campus community and social development. Visit our Employability section for full details.
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Students taking Part I of the course are charged £10 for a bound copy of the lab manual. There are a number of optional one-day visits to places of interest and students pay travel costs.
Students also need to consider further costs which may include books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation it may be necessary to take out subscriptions to professional bodies and to buy business attire for job interviews.
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