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Course overview

Are you are curious about how black holes behave? Are you are motivated to discover more about gravitation and quantum theory? This MSc will prepare you for a variety of research-intensive careers in mathematical physics.

This MSc provides an introduction to the physical principles and mathematical techniques of current research in:

  • general relativity
  • quantum gravity
  • particle physics
  • quantum field theory
  • quantum information
  • cosmology

There is particular focus on gravity, reflecting one of Nottingham's research strengths.

You'll be taught by dedicated researchers from the School of Mathematical Sciences and the School of Physics and Astronomy. They are working in classical and quantum gravity, geometry and relativity, quantum information theory, cosmology and particle physics.

You will learn how to apply a number of tools of differential geometry to real scientific problems. This will help you build vital skills, enhancing your employability in a growing area. You'll benefit from a year-long introduction to quantum field theory. This will enable you to gather your own data and insights and learn to analyse and evaluate the results.

Develop transferable skills, such as:

  • logical reasoning and analysis
  • communicating with clarity
  • presenting your work

A highlight of the masters is the research dissertation which allows you to develop your interests and expertise in a specific topic.

The course will help you prepare if you are considering to study for PhD. Alternatively, many graduates take up roles in engineering, industry and technology. For those currently in employment, the course provides a route back to academic study.

Why choose this course?

Top 10 in the UK

for research power and quality

Research Excellence Framework 2014

Combined expertise

taught jointly by Schools of Mathematical Sciences and Physics and Astronomy.


modules are influenced by current research taking place within the schools.

Dissertation support

receive one-to-one supervision for your dissertation project from a member of staff.

Gain scientific skills

for applying modern mathematical physics techniques to real world issues

Scholarships available

To help fund your postgraduate course

Top 20

UK university

QS World Rankings and the THE World University Rankings, 2022

Course content

The course will begin with introductory material on general relativity and its mathematical language of differential geometry. You will then continue with more advanced modules with applications to the study of black holes, cosmology and aspects of general relativity related to string theory.

There is a year-long introduction to quantum field theory which introduces the famous Feynman diagrams of particle physics in a systematic way, and studies aspects of modern particle physics. There is also an introduction to the concepts of quantum information theory.

The course assumes you have a familiarity with quantum mechanics and special relativity at an introductory level.

No prior knowledge of general relativity is required.

You will study a total of 180 credits, split across 120 credits worth of taught modules and a 60-credit research dissertation.


Core modules

Advanced Gravity

This module will develop the ideas behind General Relativity (GR) to an advanced level. You will explore solutions to these equations including black holes and cosmological solutions.

You will also have the opportunity to study more advanced topics including modified gravity models (eg models with extra dimensions) that are at the forefront of current research.

Black Holes

General relativity predicts the existence of black holes which are regions of space-time into which objects can be sent but from which no classical objects can escape. This module develops techniques to systematically study black holes and their properties, including horizons and singularities. Astrophysical processes involving black holes are discussed, and there is a brief introduction to black hole radiation discovered by Hawking.

Differential Geometry

The modern study of general relativity requires familiarity with a number of tools of differential geometry, including manifolds, symmetries, Lie Groups, differentiation and integration on manifolds. These are introduced in this module using examples of curved space-times.


This module provides an introduction to the modern theory of gravitation: Einstein's general theory of relativity.

Topics to be covered include:

  • Specifying geometry
  • Special Relativity
  • Equivalence principle
  • General relativity
  • Schwarzschild solution
  • Schwarzschild black hole:
Gravity, Particles and Fields Dissertation

The dissertation is an extended piece of research related to a taught element of the course. The study will be largely self-directed, with oversight and input provided where necessary by a supervisor from the School of Mathematical Sciences or the School of Physics and Astronomy.

The topic could be based on a theoretical investigation, a review of research literature, or a combination of the two.

Introduction to Quantum Information Science

The paradigm of Quantum Information Science (QIS) is that quantum devices, made of systems such as atoms and photons, can out-perform the present-day technology in key applications ranging from computing power and communication security to precision measurements. Quantum information processing and the measurement and control of individual quantum systems are central topics in QIS, lying at the intersection of quantum mechanics with 'classical' disciplines such as information theory, probability, and statistics, computer science and control engineering.

The aim of this module is to provide an introduction to QIS, emphasising the differences and similarities between the classical and the quantum theories. After a short review of the necessary probabilistic notions, the first part introduces the operational framework of quantum theory involving the fundamental concepts of states, measurements, quantum channels, instruments. This includes some of the influential results in the field such as entanglement and quantum teleportation, Bell's theorem and the quantum no-cloning theorem. The second part covers at least two topics from quantum Markovian evolutions, quantum statistics, continuous variable systems.

Modern Cosmology

This module facilitates an understanding of Friedmann models and hot big bang – encompassing the study of thermal history, freezout, relics, recombination, last scattering; dark matter candidates.

Other topics will include inflation, fluctuations from inflation, structure formation, gravitational lensing CMB anisotropies, and dark energy.

Quantum Field Theory

The aim of this module is to provide the quantum description of electrons, photons and other elementary particles, including a discussion of spin, bosons, and fermions.

Lectures will provide an introduction to functional integrals, Feynman diagrams, and the standard model of particle physics.

The above is a sample of the typical modules we offer 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. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on Tuesday 22 June 2021.

Learning and assessment

How you will learn

  • Lectures
  • Problem classes
  • Independent study
  • Supervision
  • Guided reading


How you will be assessed

  • Examinations
  • Coursework
  • In-class test
  • Oral exam
  • Dissertation
  • Reports

Contact time and study hours

The number of formal contact hours varies depending on the optional modules you are studying. As a guide, in the Autumn semester you will typically spend around 11 hours per week in lectures. Each module has around two additional hours of independent study as a minimum.

Class sizes are typically about 30 students and teaching takes place between Monday and Friday during term-time.

You will work on your research project between June and September. You will be based at the University and receive one-to one supervision from a member of staff within the School of Mathematical Sciences or the School of Physics and Astronomy.

Teaching is provided by academic staff within the School of Mathematical Sciences and that of Physics and Astronomy. All modules are typically delivered by Professors, Associate and Assistant Professors. Additional support in small group and practical classes may involve PhD students and post-doctoral researchers.

The majority of your lecturers and tutors will be based within the mathematics building or nearby physics building. This means if you need to get in touch with them during office hours, they can be contacted easily as they are close by.

MSc students are invited to attend the regular seminars series held on campus. Sessions are hosted by physics and mathematical physics academic staff.

Entry requirements

All candidates are considered on an individual basis and we accept a broad range of qualifications. The entrance requirements below apply to 2022 entry.

Undergraduate degree2:1 in physics, mathematical physics or mathematics

Joint degrees containing substantial elements of physics or mathematics will also be considered.

Previous knowledge of mechanics, quantum mechanics, special relativity and methods of mathematical physics (all as taught typically at BSc level) is required.


Our step-by-step guide covers everything you need to know about applying.

How to apply


UK fees are set in line with the national UKRI maximum fee limit. We expect fees for 2022 entry to be confirmed in August 2021.

Additional information for international students

If you are a student from the EU, EEA or Switzerland, you will pay international tuition fees in most cases. If you are resident in the UK and have 'settled' or 'pre-settled' status under the EU Settlement Scheme, you will be entitled to 'home' fee status.

Irish students will be charged tuition fees at the same rate as UK students. UK nationals living in the EU, EEA and Switzerland will also continue to be eligible for ‘home’ fee status at UK universities until 31 December 2027.

For further guidance, check our information for applicants from the EU.

These fees are for full-time study. If you are studying part-time, you will be charged a proportion of this fee each year (subject to inflation).

Additional costs

As a student on this course, we do not anticipate any extra significant costs, alongside your tuition fees and living expenses.


Due to our commitment to sustainability, we don’t print lecture notes but these are available digitally. You are welcome to buy print credits if you need them. 


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 which you would need to factor into your budget.


Personal laptops are not compulsory as we have computer labs that are open 24 hours a day but you may want to consider one if you wish to work at home.


School scholarships for UoN international alumni

For 2022/23 entry, 10% alumni scholarships may be offered to former University of Nottingham international graduates who have studied at the UK campus. 

There are many ways to fund your postgraduate course, from scholarships to government loans.

We also offer a range of international masters scholarships for high-achieving international scholars who can put their Nottingham degree to great use in their careers.

Check our guide to find out more about funding your postgraduate degree.

Postgraduate funding


We offer individual careers support for all postgraduate students.

Expert staff can help you research career options and job vacancies, build your CV or résumé, develop your interview skills and meet employers.

Each year 1,100 employers advertise graduate jobs and internships through our online vacancy service. We host regular careers fairs, including specialist fairs for different sectors.

International students who complete an eligible degree programme in the UK on a student visa can apply to stay and work in the UK after their course under the Graduate immigration route. Eligible courses at the University of Nottingham include bachelors, masters and research degrees, and PGCE courses.

Graduate destinations

Many graduates continue studying for a PhD whereas others will enter teaching and scientific roles.

Previous graduate destination roles have included jobs in the following organisations:

Career progression

97.5% of postgraduates from the School of Mathematical Sciences secured graduate level employment or further study within 15 months of graduation. The average annual salary for these graduates was £28,131.*

* HESA Graduate Outcomes 2020. The Graduate Outcomes % is derived using The Guardian University Guide methodology. The average annual salary is based on graduates working full-time within the UK.

Two masters graduates proudly holding their certificates
" My research lies at the interface between quantum physics and mathematics. I teach the Quantum Information module which offers a popular introduction to a rapidly developing field of science and technology. As Course Director I ensure the smooth running of the MSc activities, coordinate with lecturers and tutors, and act as contact point and career advisor for MSc students. "
Madalin Guta is an Associate Professor at the School of Mathematical Sciences.

Related courses

The University has been awarded Gold for outstanding teaching and learning (2017/18). Our teaching is of the highest quality found in the UK.

The Teaching Excellence Framework (TEF) is a national grading system, introduced by the government in England. It assesses the quality of undergraduate teaching at universities and how well they ensure excellent outcomes for their students in terms of graduate-level employment or further study.

This content was last updated on Tuesday 22 June 2021. Every effort has been made to ensure that this information is accurate, but changes are likely to occur given the interval between the date of publishing and course start date. It is therefore very important to check this website for any updates before you apply.