## Overview

Ever since Newton invented calculus to develop his theories of motion and gravity, mathematics and physics have been linked. You will study modules taught by the School of Physics and Astronomy and the School of Mathematical Sciences that provide a thorough background in the mathematical techniques and concepts physicists and mathematicians use today.

- Study in a school ranked 3rd in the UK for research (Research Excellence Framework, 2014)
- Gain a thorough background in the mathematical techniques and concepts used today
- Choose from a range of optional modules in year four

In years one and two, the foundations of the two subjects are laid down. You then study topics chosen from a wide range for a further year. Year four offers you the chance to choose from a variety of optional modules including black holes, advanced gravity and theoretical particle physics. You will also undertake a substantial project in either applied mathematics or theoretical physics. There are no laboratory modules in our mathematical physics courses.

### What's an MSci?

MSci degrees are undergraduate-level courses which last for four years and have an integrated masters qualification. They are the equivalent to a bachelors degree plus** **a masters level qualification. These courses usually provide additional industry and/or research experience to enhance your future prospects. An MSci is excellent preparation for further study such as a PhD.

If you choose to study an MSci, your student loan will cover tuition fees and living costs for the additional year too (home/EU students only). If you are unsure on whether to choose an MSci or BSc, we recommend you choose the MSci to secure your funding. Transfer to the BSc is possible.

The entry requirements for our MSci degrees are the same as the BSc degrees.

## Entry requirements

**A levels:** A*AA-AAA, including A* in either maths or physics.

### English language requirements

IELTS 6.5 (no less than 6.0 in any element)

If you require additional support to take your language skills to the required level, you may be able to attend a presessional course at the Centre for English Language Education, which is accredited by the British Council for the teaching of English in the UK.

Students who successfully complete the presessional course to the required level can progress onto their chosen degree course without retaking IELTS or equivalent.

### Alternative qualifications

For details see the alternative qualifications page

### Flexible admissions policy

In recognition of our applicants’ varied experience and educational pathways, the University of Nottingham employs a flexible admissions policy. We may make some applicants an offer lower than advertised, depending on their personal and educational circumstances. Please see the University’s admissions policies and procedures for more.

## Additional information

### Teaching methods and assessment

### Lectures

Group teaching sizes are small enough for us to know all of our students as individuals and the total class size is large enough to allow us to offer a wide range of modules. This means that you will be able to tailor your degree to your scientific interests.

Typically there are 10 lectures per week including problem sheets and directed reading. You will learn a modern programming language so that you can solve equations and model physical situations. The course structure ensures there are formative assessments throughout the year to help you to guide your studies and gain regular feedback on how you're getting on. If there is something you do not understand, you are always welcome to discuss it with a member of staff.

### Tutorials

You will take part in weekly small group tutorials (typically five students), where your tutor will provide support and guidance. The practical modules involve working between three and six hours per week in laboratories, where, in addition to traditional experimental techniques, we emphasise the importance of computer control and simulation throughout the course.

### Examinations and assignments

For a typical core module the examination carries a weight of 80%, the remaining 20% usually being allocated for regular coursework and workshop assignments throughout the year. Experimental and other practical work is continually assessed through laboratory notebooks and formal reports.

### Accreditation

The Institute of Physics accredits bachelor and integrated masters degree programmes for the purposes of the professional award of Chartered Physicist. Chartered Physicist requires an IOP accredited degree followed by an appropriate period of experience during which professional skills are acquired.

An accredited bachelor degree partially fulfils the academic requirement for Chartered Physicist status. Further study to masters level, or equivalent work-based experience, is required to achieve Chartered Physicist.

## Year one

In this year, you will gain a basic grounding in physics and mathematics, including mechanics special relativity, electromagnetism and quantum theory, mathematical modelling, calculus, linear mathematics and mathematical reasoning, along with an introduction to scientific computing.

### Core modules

This module introduces students to a broad range of core mathematical concepts and techniques. It has three components.

- Mathematical reasoning (the language of mathematics, the need for rigour, and methods of proof).
- The computer package MATLAB and its applications.
- Elementary analysis.

You will begin by practising the basic concepts and methods of calculus including limits, functions, and continuity. In the second semester you will move onto more advanced usage of calculus. Topics will be based around the calculus of functions of several variables and include partial derivatives, chain rules, the vector operator grad, Lagrange multipliers and multiple integrals.

This module introduces you to the methods and practices of linear mathematics that you will need in subsequent modules on your course, such as complex numbers, vector algebra and matrix algebra. You will then expand your knowledge to include vector spaces, linear transformations and inner product spaces.

This year-long module will train you in the mathematical modelling of physical processes. You’ll cover topics such as basic statistics and errors, dimensional analysis, curve sketching, orders of magnitude and estimates, and integrating problems in physics among others.

You’ll receive training in basic computing techniques using MatLab, and will be introduced to their use in solving physical problems.

You’ll spend three to four hours in computer classes and a one hour lecture each week.

The above is a sample of the typical modules that we offer at the date of publication but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. This prospectus may be updated over the duration of the course, as modules may change due to developments in the curriculum or in the research interests of staff.

## Year two

In this year, you will learn the core elements of the classic theories of physics: electromagnetism, quantum mechanics, thermal and statistical mechanics, and optics.

In parallel, you will learn the mathematical language in which these theories are expressed, such as vector calculus amd Fourier analysis. You will also take one or two optional modules.

### Core modules

This course explores the classical and quantum mechanical description of motion. The laws of classical mechanics are investigated both in their original formulation due to Newton and in the mathematically equivalent but more powerful formulations due to Lagrange and Hamilton. Applications are made to problems such as planetary motion, rigid body motion and vibrating systems. Quantum mechanics is developed in terms of a wave function obeying Schroedinger's equation, and the appropriate mathematical notions of Hermitian operators and probability densities are introduced. Applications include problems such as the harmonic oscillator and a particle in a three-dimensional central force field.

This course aims to give students a sound grounding in the application of both differential and integral calculus to vectors, and to apply vector calculus methods and separation of variables to the solution of partial differential equations. The module is an important pre-requisite for a wide range of other courses in Applied Mathematics.

Macroscopic systems exhibit behaviour that is quite different from that of their microscopic constituents studied in isolation. New physics emerges from the interplay of many interacting degrees of freedom. In this module you will learn about the important physical properties of matter and the two main approaches to their description. One, thermodynamics, treats macroscopically relevant degrees of freedom (temperature, pressure and so on) and find relations between these and the fundamental laws which govern them, independent of their microscopic structure. The other approach, statistical mechanics, links the macroscopically relevant properties to the microphysics by replacing the detailed microscopic dynamics with a statistical description. The common feature of both of these methods is the introduction of two macroscopic quantities, temperature and entropy, that have no microscopic meaning.

### Optional

You will develop your knowledge of the various physical processes occurring in stars of different types. You’ll use this knowledge to build both mathematical models and your qualitative physical understanding of stellar structure and evolution will be enhanced. You’ll have two hours per week of lectures studying this module.

This module will develop your current understanding of the various physical processes that dictate the formation, evolution and structure of galaxies. You’ll explore a number of topics including The Milky Way, The Dynamics of Galaxies, Active Galaxies and Galaxy Evolution among others. You’ll spend two hours per week in lectures studying this module.

You’ll be given an overview of how forces at the nanoscale are different to those observed in macroscopic systems and will consider how they can be exploited in nanometre-scale processes and devices.

You’ll focus on the physical basis and measurement of forces operating on the nanoscale, considering van der Waals, electrostatic, hydrophobic and hydrophilic interactions.

You’ll spend around three hours per week in lectures and workshops studying this module.

In this module you will learn about the theory and applications of functions of a complex variable using a method and applications approach. You will develop an understanding of the theory of complex functions and evaluate certain real integrals using your new skills.

In this module you will build on the foundation of knowledge gained from your core year one modules in Analytical and Computational Foundations and Calculus. You will learn to follow a rigorous approach needed to produce concrete proof of your workings.

This course aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations.

The above is a sample of the typical modules that we offer at the date of publication but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. This prospectus may be updated over the duration of the course, as modules may change due to developments in the curriculum or in the research interests of staff.

## Year three

You will take core modules in advanced quantum theory, relativity, solid- state physics and elementary particles and carry out a project in the general area of mathematical physics.

You choose from a range of optional modules and will also be given training in communication skills in preparation for the more student-centred approaches taken in some of the fourth-year modules.

### Core modules

In this module you will apply the general theory you learnt in Introduction to Mathematical Physics to more general problems. New topics will be introduced such as the quantum theory of the hydrogen atom and aspects of angular momentum such as spin.

This module will introduce students to the physics of atoms, nuclei and the fundamental constituents of matter and their interactions. The module will also develop the quantum mechanical description of these.

Topics to be covered are:

- Approximation techniques first order perturbation theory, degeneracies, second order perturbation theory, transition rates, time-dependent perturbation theory, Fermi's golden rule
- Particle Physics protons and neutrons, antiparticles, particle accelerators and scattering experiments, conservation laws, neutrinos, leptons, baryons and hadrons, the quark model and the strong interaction, weak interactions, standard model
- Introduction to atomic physics review of simple model of hydrogen atom, Fermi statistics and Pauli principle, aufbau principle, hydrogenic atoms, exchange, fine structure and hyperfine interactions, dipole interaction, selection rules and transition rates
- Lasers optical polarization and photons, optical cavities, population inversions, Bose statistics and stimulated emission, Einstein A and B coefficients
- Nuclear Physics Radioactivity, decay processes, alpha, beta and gamma emission, detectors, stability curves and binding energies, nuclear fission, fusion, liquid drop and shell models.

- Bonding nature of chemical bonds, thermodynamics of solid formation
- Crystal structures description of crystal structures, k-space, reciprocal lattice, Bragg diffraction, Brillouin zones
- Nearly-free electron model - Bloch's theorem, band gaps from electron Bragg scattering, effective masses
- Band theory Fermi surfaces, qualitative picture of transport, metals, insulators and semiconductors
- Semiconductors - doping, inhomogeneous semiconductors, basic description of pn junction
- Phonons normal modes of ionic lattice, quantization, Debye theory of heat capacities, acoustic and optical phonons
- Optical properties of solids absorption and reflection of light by metals, Brewster angle, dielectric constants, plasma oscillations
- Magnetism- Landau diamagnetism, paramagnetism, exchange interactions, Ferromagnetism, antiferromagnetism, neutron scattering, dipolar interactions and domain formation, magnetic technology

In this module you’ll have an introduction to Einstein’s theory of general and special relativity. The relativistic laws of mechanics will be described within a unified framework of space and time. You’ll learn how to compare other theories against this work and you’ll be able to explain new phenomena which occur in relativity.

In this module you'll carry out a project drawn from an area of physics. The project will be theoretical or computational in nature. You'll work either singly or in pairs and have regular meetings with a staff supervisor to advise on the project and monitor your progress.

### Optional

In this module you’ll explore the theoretical aspect of atmospheric physics. Topics will include planetary atmosphere, troposphere, solar radiation and the Energy budget, radiation transfer and Photochemistry among others. You’ll have two hours of lectures per week studying this module.

To make models of extreme astrophysical sources and environments basedon physical theory.

To interpret observational data in the light of relevant physical theory.

In this module you will develop your knowledge of classical mechanics of simple linear behaviour to include the behaviour of complex nonlinear dynamics. You’ll learn about the way in which nonlinear deterministic systems can exhibit essentially random behaviour because of sensitivity relating to initial conditions. You’ll have two hours per week of lectures studying this module.

This module aims to provide you with the skills necessary to use computational methods in the solution of non-trivial problems in physics and astronomy. You’ll also sharpen your programming skills through a three hour computing class and one hour of lectures per week.

This course is structured in two main parts. The first part focuses on the foundation of quantum mechanics and solid state physics needed to describe a low dimensional system. The module then moves on describing the physical principles of semiconductor junction and devices.

This course aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations.

The course introduces and explores methods, concepts and paradigm models for classical and quantum mechanical dynamics exploring how classical concepts enter quantum mechanics, and how they can be used to find approximate semi-classical solutions.

In classical dynamics we discuss full integrability and basic notions of chaos in the framework of Hamiltonian systems, together with advanced methods like canonical transformations, generating functions and Hamiltonian-Jacobi theory. In quantum mechanics we recall Schrödinger's equation and introduce the semi-classical approximation. We derive the Bohr-Sommerfeld quantization conditions based on a WKB-approch to the eigenstates. We will discuss some quantum signatures of classical chaos and relate them to predictions of random-matrix theory. We will also introduce Gaussian states and coherent states and discuss their semi-classical dynamics and how it is related to the corresponding classical dynamics. An elementary introduction to complete descriptions of quantum mechanics in terms of functions on the classical phase space will be given.

This course introduces various analytical methods for the solution of ordinary and partial differential equations, focussing on asymptotic techniques and dynamical systems theory. Students taking this course will build on their understanding of differential equations covered in MATH2012.

The above is a sample of the typical modules that we offer at the date of publication but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. This prospectus may be updated over the duration of the course, as modules may change due to developments in the curriculum or in the research interests of staff.

## Year four

In this year, you will take a number of options which may include topics such as black holes, quantum field theory, cosmology and astrophysics (subject to sufficient student numbers), as well as carrying out a substantial project in mathematical physics.

### Core modules

The module consists of a project which aims to solve a theoretical problem. Problems are sponsored by theoreticians from either physics and astronomy or mathematical sciences. Day-to-day supervision of the project is carried out by the supervisor but the assessment will involve input from both the supervisor and the module convenors.

### Optional

In this module you’ll develop your understanding of the ideas of general relativity to an advanced level. You’ll use scientific models applied to current research, including modified gravity models with extra dimensions, to assist your learning. You’ll have three hours of lectures for seven weeks of the semester while studying this module.

In this module you will develop your knowledge of classical mechanics of simple linear behaviour to include the behaviour of complex nonlinear dynamics. You’ll learn about the way in which nonlinear deterministic systems can exhibit essentially random behaviour because of sensitivity relating to initial conditions. You’ll have two hours per week of lectures studying this module.

This module will explain how the intrinsic spin of nuclei and electrons is exploited in magnetic resonance experiments. It will describe the classical and quantum pictures of the phenomenon of nuclear magnetic resonance (NMR) and show why NMR forms such a powerful analytical tool, today. Basic electron paramagnetic resonance (EPR) will also be described, along with the equipment used for NMR and EPR, and some applications of these techniques.

In this module you'll gain an appreciation of the broad societal impact of physics (and science in general). You'll be introduced to the politics surrounding science policy (on, e.g., global warming/renewable energy R&D) and research funding. You'll also explorre some of the key ideas in the philosophy of physics and science, particularly as they relate to public perception of scientific research.

- Bose condensation review of Bose statistics, BEC, BEC in cold atomic gases.
- Superfluidity in Helium-4 quantum fluids, macroscopic wave functions, superfluidity, non-classical rotational inertia and vortices, phonon and roton excitations.
- Superconductivity conduction in metals, superconducting materials, zero-resistivity, Meissner effect, perfect diamagnetism, type I and type II behaviour, London theory.
- BCS theory of superconductivity.- electron-phonon interaction, Cooper pairs, BCS wave function, order parameter and microscopic origin of GL.
- Applications: squids, superconducting magnets etc.

In this module you’ll systematically study black holes and their properties, including astrophysical processes, horizons and singularities. You’ll have an introduction to black hole radiation to give you an insight into problems of research interest. You’ll gain knowledge to help you begin research into general relativity. You’ll have four hours of lectures per week studying this module.

In this module you’ll be equipped with the tools and knowledge to extend your understanding of general relativity. You’ll explore more abstract and powerful concepts using examples of curved space-times such as Lie groups and manifolds among others. You’ll have three hours of lecture per week studying this module, which may be used as example or problem classes when required.

In this year-long module you’ll be introduced to the study of the quantum dynamics of relativistic particles. You’ll learn about the quantum description of electrons, photons and other elementary particles leading to an understanding of the standard model of particle physics. You’ll have two hours per week of lectures studying this module.

Studying at Nottingham has given me the opportunity to pursue a career path I had never even considered before starting university. The staff and students are all friendly and supportive. It’s a home away from home.

## Careers

You will have a thorough grounding in the fundamental principles of physics and mathematics, and experience of the application of mathematical techniques to theoretical physics. A combination of intellectual rigour, numeracy and problem solving will prepare you for employment in areas ranging from research and development in industry to the financial sector.

Due to their training, physicists are adaptable and proficient at mathematics and problem solving. Employers see a physics graduate as someone who has demonstrated an ability to work through a demanding course of study and who has gained a wide variety of transferable technical skills.

### Average starting salary and career progression

In 2017, 96.5% of undergraduates in the school who were available for employment had secured work or further study within six months of graduation. The average starting salary was £25,000 with the highest being £46,800.*

** Known destinations of full-time home undergraduates 2016/17. Salaries are calculated based on the median of those in full-time paid employment within the UK.*

### Careers support and advice

Studying for a degree at the University of Nottingham will provide you with the type of skills and experiences that will prove invaluable in any career, whichever direction you decide to take.

Throughout your time with us, our Careers and Employability Service can work with you to improve your employability skills even further; assisting with job or course applications, searching for appropriate work experience placements and hosting events to bring you closer to a wide range of prospective employers.

Have a look at our careers page for an overview of all the employability support and opportunities that we provide to current students.

The University of Nottingham is consistently named as one of the most targeted universities by Britain’s leading graduate employers (Ranked in the top ten in The Graduate Market in 2013-2019, High Fliers Research).

## Fees and funding

### Additional costs

As a student on this course, you should factor some additional costs into your budget, alongside your tuition fees and living expenses. You should be able to access most of the books you’ll need through our libraries, though you may wish to purchase your own copies.

### Scholarships and bursaries

We offer a range of scholarships designed to assist you in settling in to your studies and meeting the financial requirements of your course. Some of these are means-tested but we also offer special scholarships that reward academic achievement.

One is offered on the basis of performance in the qualifying examinations for university entrance (eg A levels). A scholarship package is also offered to reward good performance in the qualifying (first) year examinations. This scheme includes special prizes that have been inaugurated in collaboration with our commercial partners. Full details of all scholarship prizes will be provided at the UCAS open days.

For more details about scholarships, please visit the School of Physics and Astronomy website.

### Home students*

Over one third of our UK students receive our means-tested core bursary, worth up to £2,000 a year. Full details can be found on our financial support pages.

* A 'home' student is one who meets certain UK residence criteria. These are the same criteria as apply to eligibility for home funding from Student Finance.

### International/EU students

Our International Baccalaureate Diploma Excellence Scholarship is available for select students paying overseas fees who achieve 38 points or above in the International Baccalaureate Diploma. We also offer a range of High Achiever Prizes for students from selected countries, schools and colleges to help with the cost of tuition fees. Find out more about scholarships, fees and finance for international students.

## Related courses

**Disclaimer**This online prospectus has been drafted in advance of the academic year to which it applies. Every effort has been made to ensure that the information is accurate at the time of publishing, but changes (for example to course content) are likely to occur given the interval between publishing and commencement of the course. It is therefore very important to check this website for any updates before you apply for the course where there has been an interval between you reading this website and applying.