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 and the early universe

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.

Research Excellence Framework 2021

  • 97% of our research outputs are rated as 'world-leading' or 'internationally excellent'
  • The school was placed in the top 3 for quality of research environment across all mathematical sciences units in the UK
  • 100% of the impact from the school is rated as either ‘world-leading’ or ‘internationally excellent’

This is highlighted in our commitment to attracting bright minds and inspiring academics to conduct mathematical research throughout the department.

Why choose this course?

Top 3 in UK

for research environment

Research Excellence Framework 2021

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

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 fundamental laws of physics have a profound geometric character. This fact can only be appreciated by familiarising oneself with modern differential geometry, to which this module gives an introduction. The topics covered include manifolds, in particular geometric objects that can be placed on manifolds, such as vector fields, differential forms and more generally tensors. The module also discusses symmetries, including the notion of infinitesimal symmetries as captured by Killing vector fields. Integration of differential forms, including the Stokes’ theorem is covered as well. The final part of the module gives an introduction to Lie Groups and Lie algebras, building up to the description of Lie algebras in terms of left-invariant vector fields on the group manifold.  


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, in an area covered by the taught modules but on a topic linked to a contemporary research forefront. The study will be largely self-directed, with oversight and support provided by a supervisor from the School of Mathematical Sciences or the School of Physics and Astronomy.

The topic could be based on a research investigation, a review of research literature, or a combination of these. You can choose among a range of topics proposed by supervisors or propose an original topic yourself. The dissertation offers an excellent introduction to exciting research topics, insights into how research is conducted, and a solid basis for pursuing a PhD.

Introduction to Quantum Information Science

The paradigm of quantum information science is that quantum systems such as atoms and photons are carriers of a new type of information featuring entanglement and coherence properties that are not shared by classical information. The rapidly developing area of quantum technology aims to harness these features in practical applications ranging from new modes of computation to secure communication and precision metrology.

This module provides an introduction to the mathematical theory of quantum information science and its applications. The first part sets out the operational framework involving fundamental concepts of states, measurements, and entanglement and then reviews some of the influential results in the field such as quantum teleportation, Bell's Theorem, and quantum key distribution. The second part introduces the circuit model of quantum computation and discusses simple quantum algorithms. This is followed by the theory of quantum channels and quantum error correction.

Modern Cosmology

This module facilitates an understanding of Friedmann models and hot big bang. It encompasses 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

This module provides an introduction to the theoretical and conceptual foundations of quantum field theory, which is a highly versatile and important subject in modern theoretical and mathematical physics. After a short review of some elementary aspects of classical field theory, the first part of this module introduces the crucial concept of field quantisation and develops perturbative methods leading to the famous Feynman diagrams. The more advanced component of this module includes the study of renormalisation techniques for quantum field theories and a discussion of physical applications to quantum electrodynamics 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 Monday 31 July 2023.

Due to timetabling availability, there may be restrictions on some module combinations.

Learning and assessment

How you will learn

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

You will broaden and deepen your knowledge of mathematical physics using a wide variety of different methods of study.

Alongside face to face lectures and problem classes, you will use our online learning platform to access lecture notes, exercise sheets and sample exam papers. Your personal tutor will be there to support you throughout the MSc.


How you will be assessed

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

Each module has its own specially tailored assessment method.

  • Differential Geomety, Quantum Information, and Black Holes are 100% examination.
  • Quantum Field Theory is assessed by a combination of courseworks and a presentation.
  • Gravity, Advanced Gravity and Modern Cosmology have specific combinations of coursework, presentations and small projects.

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 2024 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


Qualification MSc
Home / UK £11,850
International £22,600

Additional information for international students

If you are a student from the EU, EEA or Switzerland, you may be asked to complete a fee status questionnaire and your answers will be assessed using guidance issued by the UK Council for International Student Affairs (UKCISA) .

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

All students will need at least one device to approve security access requests via Multi-Factor Authentication (MFA). We also recommend students have a suitable laptop to work both on and off-campus. For more information, please check the equipment advice.

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

We invite our alumni to continue with us for masters study within The School of Mathematical Sciences. For 2024/25 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 destinations have included:

Career progression

84.8% of postgraduate taught students 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 £30,374.*

*HESA Graduate Outcomes 2019/20 data published in 2022. The Graduate Outcomes % is derived using The Guardian University Guide methodology. The average annual salary is based on graduates working full-time, postgraduate, home graduates within the UK.

Two masters graduates proudly holding their certificates
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Dr Madalin Guta

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This content was last updated on Monday 31 July 2023. 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.