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Mathematics MPhil, PhD

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PhD/DPhil - Doctor of Philosophy

Newcastle University

22-APR-24, 16-SEP-24, 06-JAN-25, 28-APR-25

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In Pure Mathematics our two main fields are functional analysis and geometric algebra. In Applied Mathematics our research is predominantly in fluid mechanics, astrophysics and cosmology.

We invite MPhil and PhD proposals in any of our research areas.

As a research postgraduate in the School of Mathematics, Statistics and Physics you'll work under the supervision of an expert in your chosen field.

Within each field of Pure Mathematics there are multiple subgroups. In analysis, one subgroup concentrates on operator theory and function theory, the other on Banach algebras, cohomology and modules. In algebra there are subgroups devoted to the study of infinite groups, and finite classical groups and their geometries.

Our Applied Mathematics staff have research interests in:

  • astrophysical and geophysical fluid dynamics
  • quantum matter
  • mathematical biology and archaeology
  • cosmology and quantum gravity

Our Careers Service

Our award-winning Careers Service is one of the largest and best in the country, and we have strong links with employers. We provide an extensive range of opportunities to all students through our ncl+ initiative.

What students say

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A 2:1 honours degree, or international equivalent in: computing science; mathematics; physics; statistics; another strongly quantitative discipline.

Students living in

£4,712 per year

Students from Domestic

The mentioned fees is for 2023/24 entry. There may be slight increase in 2024/25 year.

£22,900 per year

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Mathematics MPhil, PhD Newcastle University

Newcastle University

Course options

Qualification.

PhD/DPhil - Doctor of Philosophy

Newcastle University

22-APR-24, 16-SEP-24, 06-JAN-25, 28-APR-25

  • TUITION FEES
  • ENTRY REQUIREMENT
  • UNIVERSITY INFO

Course summary

In Pure Mathematics our two main fields are functional analysis and geometric algebra. In Applied Mathematics our research is predominantly in fluid mechanics, astrophysics and cosmology.

We invite MPhil and PhD proposals in any of our research areas.

As a research postgraduate in the School of Mathematics, Statistics and Physics you'll work under the supervision of an expert in your chosen field.

Within each field of Pure Mathematics there are multiple subgroups. In analysis, one subgroup concentrates on operator theory and function theory, the other on Banach algebras, cohomology and modules. In algebra there are subgroups devoted to the study of infinite groups, and finite classical groups and their geometries.

Our Applied Mathematics staff have research interests in:

  • astrophysical and geophysical fluid dynamics
  • quantum matter
  • mathematical biology and archaeology
  • cosmology and quantum gravity

Our Careers Service

Our award-winning Careers Service is one of the largest and best in the country, and we have strong links with employers. We provide an extensive range of opportunities to all students through our ncl+ initiative.

Tuition fees

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£ 22,900 per year

Tuition fees shown are for indicative purposes and may vary. Please check with the institution for most up to date details.

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Newcastle University, King’s Gate, Newcastle upon Tyne, Northumberland, NE1 7RU, England

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41st out of 70 7

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Physics MPhil, PhD

Newcastle university.

  • 36 months Full time degree: £4,712 per year (UK)
  • 72 months Part time degree: £2,356 per year (UK)

Chemistry MPhil, PhD

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Nanoscale Science and Technology PhD

Civil engineering (water resources) mphil, phd, mathematics mphil, phd, neuroscience phd, english literature mphil, phd.

  • 36 months Full time degree
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Mathematics PhD Newcastle University

  • On campus - h Main Site (Newcastle)
  • Sep 1, 2023 Part-time - 72 Months
  • Sep 1, 2023 Part-time - 24 Months
  • Sep 1, 2023 Full-time - 12 Months
  • Sep 1, 2023 Full-time - 36 Months

Key Course Facts

Course description.

We invite MPhil and PhD proposals in any of our research areas. In Pure Mathematics our two main fields are functional analysis and geometric algebra. In Applied Mathematics our research is predominantly in fluid mechanics, astrophysics and cosmology.

As a research postgraduate in the School of Mathematics and Statistics you will be working under the supervision of an expert in your chosen field. To help you identify a topic and potential supervisor, we encourage you to find out more about our staff specialisms.

Research areas:

Within each field of Pure Mathematics there are multiple subgroups. In analysis, one subgroup concentrates on operator theory and function theory, the other on Banach algebras, cohomology and modules. In algebra there are subgroups devoted to the study of infinite groups, and finite classical groups and their geometries.

Our Applied Mathematics staff have research interests in: •fluid dynamics, including numerical modelling of quantum fluids (superfluid liquid Helium and Bose-Einstein condensates) •classical and astrophysical fluids (the Earth's core, planetary dynamos, accretion discs and galaxies) •cosmology, including the very early universe and quantum gravity.

Research seminars and events:

We run weekly research seminars in algebra and geometries, analysis, and applied mathematics, as well as postgraduate seminars led by students.

Specialist courses are offered through the MAGIC distance learning consortium, sponsored in part by the Engineering and Physical Sciences Research Council (EPSRC).

Partnerships and networks:

We are part of: •the North British Functional Analysis Seminar •the North British Geometric Group Theory Seminar •Algebra and Representation Theory in the North, funded by the London Mathematical Society and the Edinburgh Mathematical Society.

With Durham University, we are part of the Joint Quantum Centre broadly dedicated to various aspects of quantum science.

Facilities:

You will have access to online research facilities via your own desktop PC in a shared postgraduate work space. There is also a teaching cluster (of about 150 PCs) within the School.

As well as the library resources provided by the main Peter Robinson Library, you will have access to the School's mathematics and statistics library and reading room.

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PhD and research masters

The School of Information and Physical Sciences offers the following research Doctor of Philosophy (PhD) and Master of Philosophy degrees.

  • PhD and Master of Philosophy (Mathematics)
  • PhD and Master of Philosophy (Physics)
  • PhD and Master of Philosophy (Statistics)
  • PhD and Master of Philosophy (Computer Science)
  • PhD and Master of Philosophy (Information Systems)
  • PhD and Master of Philosophy (Information Technology)
  • PhD and Master of Philosophy (Software Engineering)
  • Master of Philosophy (Medical Physics)

Student success story: Riya Aggarwal

Phd in computational and applied mathematics.

Riya Aggarwal started her PhD in 2017 and completed her thesis on Neutron Strain Tomography. During her studies, Riya was always searching for additional ways to get involved in the opportunities that came with being a PhD student. In particular, she was lucky enough to gain an Australian Postgraduate Research internship with Veris and to secure ongoing employment with them.

PhD Pathway Stories: Riya Aggarwal

Graduate research.

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Mathematics MMath Honours

  • UCAS code: G103

Our professionally accredited four-year Mathematics MMath Honours degree covers pure mathematics, applied mathematics, and statistics and includes an integrated year of master's-level study.

You are currently viewing course information for entry year: 2024-25

Next start date:

  • September 2024

Fees (per year)

  • Home: £9250
  • International: £22800

Entry requirements and offers

  • A-Level: AAB-A*BB
  • IB: 34 points

View contextual offers

UCAS Institution name and code:

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  • Sign up for an Open Day

Course overview

We focus on three core areas – pure mathematics, applied mathematics, and statistics – and you have the flexibility to tailor the combination of these to suit your interests.

On this degree, you will select mostly mathematics modules in the later stages. These include:

  • introduction to vector calculus
  • methods for solving differential equations
  • algebra and linear algebra

In Stage 4 you explore more advanced topics in detail, drawing on the research expertise of our staff.

You also complete a substantial research project on a topic that interests you.

BSc or MMath?

We offer our degrees at two levels:

  • three-year Bachelor of Science (BSc) degrees
  • four-year Master of Mathematics (MMath) or Master of Mathematics and Statistics (MMathStat) degrees

Our four-year degrees are more in-depth and include:

  • advanced topics and a wider choice of modules
  • a specialist study, tailored to your own interests, that develops your skills in research and communication
  • more technical skills, for those who wish to enhance their employability or proceed to postgraduate study

Transfer between the two levels is possible up until the middle of Stage 3.

To qualify for Stages 3 and 4 of the MMath/MMathStat degree, you must normally have obtained at least an upper-second-class average mark in Stages 2 and 3.

Download information about this course as a PDF

Your course and study experience - disclaimers and terms and conditions   Please rest assured we make all reasonable efforts to provide you with the programmes, services and facilities described. However, it may be necessary to make changes due to significant disruption, for example in response to Covid-19. View our  Academic experience page , which gives information about your Newcastle University study experience for the academic year 2023-24. See our  terms and conditions and student complaints information , which gives details of circumstances that may lead to changes to programmes, modules or University services.

Additional information

Flexible degree structure.

All of our mathematics and statistics degrees follow a common core set of modules for the first two years, this means transfer between degree specialisms is possible. 

There is also flexibility (mainly at Stage 1) to choose topics from other areas of the University, for example:

  • a foreign language
  • another science

Quality and ranking

Professional accreditation and recognition.

All professional accreditations are reviewed regularly by their professional body.

Modules and learning

The information below is intended to provide an example of what you will study.

Most degrees are divided into stages. Each stage lasts for one academic year, and you'll complete modules totalling 120 credits by the end of each stage. 

Our teaching is informed by research. Course content may change periodically to reflect developments in the discipline, the requirements of external bodies and partners, and student feedback.

Featured module

Develop an understanding of ordinary differential equations and introduce the calculus of functions of several variables.

Multivariable calculus.

Optional module availability Student demand for optional modules may affect availability. Full details of the modules on offer will be published through the  Programme Regulations and Specifications ahead of each academic year. This usually happens in May. To find out more please see our terms and conditions.

You'll take a set of core modules. These equip you with the key skills and knowledge that all mathematicians and statisticians need and the main areas of pure mathematics, applied mathematics, algebra, probability and statistics.

There is also flexibility to choose topics from other areas of the University, for example, accounting, music, a foreign language or another science.

You'll take a common set of core modules. These equip you with the key skills and knowledge that all mathematicians and statisticians need and the main areas of pure mathematics, applied mathematics, algebra, probability and statistics.

Compulsory Modules

Linear Algebra  (10 credits)

Complex Analysis  (10 credits)

Algebra  (10 credits)

Groups and Discrete Mathematics  (10 credits)

Vector Calculus  (10 credits)

Fluid Dynamics  (10 credits)

Scientific Computation with Python  (10 credits)

Introduction to Statistical Inference  (10 credits)

Introduction to Bayesian Methods  (10 credits)

Computational Probability and Statistics with R  (10 credits)

Differential Equations, Transforms and Waves  (10 credits)

Introduction to Regression and Stochastic Modelling  (10 credits)

You'll select from a wide range of optional modules, which are closely linked to the research expertise of our staff. This gives you freedom to specialise in areas of particular interest.

This year of advanced study draws heavily on our research expertise. A substantial research project accounts for a third of your time.

We base these figures and graphs on the most up-to-date information available to us. They are based on the modules chosen by our students in 2022-23.

Teaching time is made up of:

  • scheduled learning and teaching activities. These are timetabled activities with a member of staff present.
  • structured guided learning. These are activities developed by staff to support engagement with module learning. Students or groups of students undertake these activities without direct staff participation or supervision

Teaching and assessment

Teaching methods.

You'll be taught through:

  • problem classes
  • tutorials and drop-in sessions
  • practical computer classes and computer-based assessments
  • data collection and analysis

Assessment methods

You'll be assessed through a combination of:

Assignments – written or fieldwork

Examinations – practical or online

Skills and experience

Business skills.

Throughout your degree, you'll develop a whole range of transferable skills, for example analytical, report writing and presentation skills.

You'll have the opportunity to take part in optional industrial and business projects and placements. These opportunities are very flexible. They are arranged throughout the academic year, during the summer period or through students taking a break from academic studies.

Projects with industry prepare you well for a career both outside and within academia, learning vital new skills and gaining new experiences.

Research skills

In Stage 4 you'll work on an extended research project, developing and enhancing your research skills.

Chat to a student

We have a range of different sessions from lectures and problems classes to group meetings and computer labs, this stops uni work getting monotonous and boring. Andrew, Mathematics student
  • Opportunities

Study abroad

Experience life in another country by choosing to study abroad as part of your degree. You’ll be encouraged to embrace fun and challenging experiences, make connections with new communities and graduate as a globally aware professional, ready for your future.

You can choose to spend up to a year studying at a partner institution overseas. Our overseas partner institutions include:

  • Universiteit Leiden, in The Netherlands
  • L-Universta ta' Malta, in Malta
  • Universitat Politècnica de Catalunya, in Barcelona
  • Technisches Universitat Munchen, Munich

There are also lots of options in North America, Australia and Asia, including:

  • Buffalo (New York State)
  • McGill (Montreal)
  • University of New South Wales (Sydney)

During your time studying abroad, you will select from a range of modules offered by your host university. Alongside taking some subject-relevant modules, you will be given greater flexibility to choose modules from different disciplines (eg Languages, Business)

If you choose to study abroad, it will extend your degree by a year.

A full year not for you? No problem - there are usually lots of short-term student mobility experiences to take part in. This includes field trips and student conferences.

Find out more about study abroad

Work placement

Get career-ready with a work placement and leave as a confident professional in your field. You can choose to spend 9 to 12 months working in any organisation in the world, and receive University support from our dedicated team to secure your dream placement. Work placements take place between stages 3 and 4.

You'll gain first-hand experience of working in the sector, putting your learning into practice and developing your professional expertise.

If you choose to take a work placement, it will extend your degree by a year. Work placement is not available if you're spending a year abroad. Placements are subject to availability.

Find out more about work placements

Facilities and environment

You'll join the  School of Mathematics, Statistics and Physics based in the Herschel Building.

A state-of-the-art learning environment will support your studies and you'll have access to extensive IT facilities for teaching and self-study, including:

  • computer-based exercises with instant review of model solutions
  • problem-solving video tutorials
  • recording system for video capture of lectures, which you can download and watch again to help with your revision

We also have a dedicated mathematics and statistics library and reading room.

The Herschel Building in Newcastle's city-centre campus

To support you in your studies, all new students entering year 1 or year 2 will receive a tablet. You can download the online learning resources you'll need for your course (helping us to make our campus more sustainable).

You'll have the support of an academic member of staff as a personal tutor throughout your degree to help with academic and personal issues. There is a transition officer specifically to help your transition from school/college to university life.

Peer mentors will help you in your first year. They are fellow students who can help you settle in and answer any questions you have when starting university.

You'll also benefit from our:

  • induction programme, including social events, to help you settle in quickly
  • activities and events run by our student-run society, MathSoc
  • homework classes to help with assignments

Your future

Join a network of successful graduates.

88% of our Mathematics BSc Honours graduates were employed or in further study within 6 months of graduating, with an average salary of £21,150*.

Recent graduates have secured roles such as:

  • information analyst
  • actuarial analyst

*Destinations of (undergraduate, UK and EU) Leavers from Higher Education Survey 2016/17

Careers for mathematicians and statisticians

Mathematicians and statisticians have always been highly valued by employers for their analytical and problem-solving skills, and their ability to think logically and quantitatively.

You'll also develop key skills which are essential for the employment market such as communication, teamwork, planning, and organisation.

There are some careers for which a degree in mathematics is usually required, for example, teaching mathematics, statistical work, actuarial work, some research and development, and some areas of computing.

Mathematics graduates are also strong candidates in areas such as:

  • management consultancy
  • accountancy
  • information technology
  • transportation

Industry too is always looking out for specialists with an interest in the applications of mathematics to engineering.

A degree in mathematics and statistics can also lead on to further study including PhD, MSc and PGCE courses.

Benefit from strong industry links

You'll also benefit from our well-established links with organisations within the industry. Through research or placements we work with companies such as:

  • Northern Gas networks
  • Office for National Statistics
  • Centre for Life
  • Department for Environment, Food and Rural Affairs
  • Drager Safety
  • Enzen Global

Nissan logo.

Make a difference

newcastle university math phd

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Follow in their footsteps

newcastle university math phd

  • Graduated: 2016
  • Now working as: Hiscox Insurance

"It is great to be able to take the skills and knowledge I learnt at university and apply it to real-world applications."

We asked Emma to take a look back at her time at Newcastle and tell us how it has impacted her career as a catastrophe modeller.

Find out about Emma's journey

Careers support

Our award-winning Careers Service is one of the largest and best in the country, and we have strong links with employers. We provide an extensive range of opportunities to all students through our ncl+ initiative.

Visit our Careers Service website

Recognition of professional qualifications outside of the UK

From 1 January 2021 there is an update to the way professional qualifications are recognised by countries outside of the UK

Check the government’s website for more information .

Entry requirements

All candidates are considered on an individual basis and we accept a broad range of qualifications. The entrance requirements and offers below apply to  2024 entry.

Other UK and the Republic of Ireland qualifications

Contextual offers.

Through one of our contextual routes, you could receive an offer of up to three grades lower than the typical requirements.

What is a contextual offer? Find out more and if you’re eligible for this or our PARTNERS Programme supported entry route.

Qualifications from outside the UK

English language requirements, entrance courses (into).

International Pathway Courses are specialist programmes designed for international students who want to study in the UK. We provide a range of study options for international students in partnership with INTO. 

Find out more about International Pathway Courses

Admissions policy

This policy applies to all undergraduate and postgraduate admissions at Newcastle University. It is intended to provide information about our admissions policies and procedures to applicants and potential applicants, to their advisors and family members, and to staff of the University.

  • Download our admissions policy  (PDF: 201KB)
  • Other policies related to admissions

Credit transfer and Recognition of Prior Learning

Recognition of Prior Learning (RPL) can allow you to convert existing relevant university-level knowledge, skills and experience into credits towards a qualification.  Find out more about the RPL policy which may apply to this course.

Tuition fees and scholarships

Tuition fees for 2024 entry (per year).

The maximum fee that we are permitted to charge for home fee-paying students is set by the UK government.

As a general principle, you should expect the tuition fee to increase in each subsequent academic year of your course, subject to government regulations on fee increases and in line with inflation.

Read more about fees and funding

Depending on your residency history, if you’re a student from the EU, other EEA or a Swiss national, with settled or pre-settled status under the EU Settlement Scheme, you’ll normally pay the ‘Home’ tuition fee rate and may be eligible for Student Finance England support.

EU students without settled or pre-settled status will normally be charged fees at the ‘International’ rate and will not be eligible for Student Finance England support.

If you are unsure of your fee status, check out the latest guidance here .

Scholarships

We support our EU and international students by providing a generous range of Vice-Chancellor's automatic and merit-based scholarships. See our  undergraduate scholarship page for more information.

Year abroad and additional costs

For programmes where you can spend   a year on a work placement or studying abroad,   you will receive a significant fee reduction for that year. 

Some of our degrees involve additional costs which are not covered by your tuition fees.

Find out more about:

  • different tuition fees
  • additional costs
  • scholarships for UK, EU and international students
  • Student Loans and Government financial support for UK and EU students

Open days and events

You'll have a number of opportunities to meet us throughout the year at our on-campus and virtual open days.

You'll be able to:

• explore our beautiful campus

• find out about our vibrant city

• discover what students think about studying at Newcastle

You'll also have the opportunity to speak to academic staff and find out more about the subjects you're interested in.

Find out about how you can visit Newcastle in person and virtually.

We regularly travel overseas to meet with students interested in studying at Newcastle University. Visit our  events calendar to find out when we're visiting your region.

Visit our events calendar for the latest virtual events

Apply through UCAS

To apply for undergraduate study at Newcastle University, you must use the online application system managed by the Universities and Colleges Admissions Service (UCAS). All UK schools and colleges, and a small number of EU and international establishments, are registered with UCAS. You will need:

  • the UCAS name and institution codes for Newcastle University (NEWC/N21)
  • the UCAS code for the course you want to apply for
  • the UCAS 'buzzword' for your school or college

If you are applying independently, or are applying from a school or college which is not registered to manage applications, you will still use the Apply system. You will not need a buzzword.

Apply through an agent

International students often apply to us through an agent. Have a look at our recommended agents and get in touch with them.

Visit our International pages

Get in touch

Call us on  +44 (0) 191 208 3333 and press option 1. Our opening hours are Monday to Friday 10am until 4pm.

Our NCL chatbot might be able to give you an answer straight away. If not, it’ll direct you to someone who can help.

You'll find our NCL chatbot in the bottom right of this page.

Fill in our enquiry form

Keep updated

We regularly send email updates and extra information about the University.

Social Media

You may be interested in.

  • Course Overview
  • Quality & Ranking
  • Modules & Learning
  • Facilities & Environment
  • Your Future
  • Entry Requirements
  • Tuition Fees & Scholarships

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