Information regarding our 2022/23 admissions cycle

Our updated course listings for the 2022/23 postgraduate admissions cycle will be published at the beginning of October. Applications for 2022 entry will be available shortly after this. Check our how to apply pages for updates.

MSc Pure Mathematics

Year of entry: 2021

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Overview

Degree awarded
Master of Science
Duration
1 year
Entry requirements
The entry requirement to the programmes is normally a good honours degree in mathematics or a mathematically-related discipline or an equivalent overseas qualification in a mathematical subject.

Full entry requirements

How to apply

Apply online .

Course options

Full-time Part-time Full-time distance learning Part-time distance learning
MSc Y Y N N

Course description

This one year taught postgraduate programme leads to the degree of MSc in Pure Mathematics. The programme is suitable not only for students who wish to improve their background knowledge prior to applying to undertake a PhD by research, but also for students who wish to enhance their knowledge of postgraduate-level abstract mathematics.  The MSc comprises of the taught component, running from the start of the academic year in September until the end of the second semester in late Spring, followed by the dissertation component running from June until September.

During the taught component of the course, you will normally take six units together with a research skills and project unit.  You may choose exclusively pure topics, or a mixture of pure mathematics units and mathematical logic units. In the research skills and project unit you will first complete a mini-project to improve mathematical writing skills, and then undertake a project. The project is normally an expository account of a piece of mathematics and you will write this under the guidance of a supervisor. The taught component comprises of conventional lectures supported by examples classes, project work and independent learning via reading material.

After successfully completing the taught component, you will prepare a dissertation on an advanced topic in pure mathematics or mathematical logic, normally of current or recent research interest, chosen in consultation with your supervisor. 

You can also take the programme part-time, over a period of two years.  There is some flexibility in the precise arrangements for this programme, but you would normally attend two lecture courses each semester for three semesters before commencing work on your dissertation.

Within two weeks from the start of the academic year, students in this programme can opt to change to the Mathematical Logic Pathways leading to the degree of MSc in Pure Mathematics and Mathematical Logic.

Open days

For details of the next University Postgraduate open day, visit open days and visits

Fees

For entry in the academic year beginning September 2021, the tuition fees are as follows:

  • MSc (full-time)
    UK students (per annum): £12,000
    International, including EU, students (per annum): £21,000
  • MSc (part-time)
    UK students (per annum): £6,000
    International, including EU, students (per annum): £10,500

Further information for EU students can be found on our dedicated EU page.

Policy on additional costs

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

Scholarships/sponsorships

We offer a number of postgraduate taught scholarships and awards to outstanding UK and international students each year.

If you're a current or recent student at The University of Manchester and plan to start a master's course in the Faculty of Science and Engineering, you may be eligible for our  Manchester Alumni Scholarship Schemes .

The University of Manchester is committed to widening participation in master's study, and allocates £300,000 in funding each year. Our  Manchester Master¿s Bursaries  are aimed at widening access to master's courses by removing barriers to postgraduate education for students from underrepresented groups.

For more information, see the Department of Mathematics Fees and funding  page or visit the University of Manchester  funding for master¿s courses website for more information.

Contact details

Department
Department of Mathematics
Contact name
Postgraduate Admissions Team
Telephone
0161 543 4020
Email
Website
https://www.maths.manchester.ac.uk/
School/Faculty

Our internationally-renowned expertise across the School of Natural Sciences informs research led teaching with strong collaboration across disciplines, unlocking new and exciting fields and translating science into reality.  Our multidisciplinary learning and research activities advance the boundaries of science for the wider benefit of society, inspiring students to promote positive change through educating future leaders in the true fundamentals of science. Find out more about Science and Engineering at Manchester .

Courses in related subject areas

Use the links below to view lists of courses in related subject areas.

Entry requirements

Academic entry qualification overview

The entry requirement to the programmes is normally a good honours degree in mathematics or a mathematically-related discipline or an equivalent overseas qualification in a mathematical subject.

English language

All applicants will need to demonstrate competency in English language. Applicants who do not already possess an acceptable English Language qualification will need to take a recognised test and attain the required English Language score:

  • IELTS:  at least 6.5 overall with no sub-test below 6.0.
  • TOEFL iBT:  at least 90 overall with no sub-test below 20. We do not accept 'MyBestScore'.
  • Pearson PTE: at least 58 overall with no sub-test below 50.

Further information on language requirements can be found on our website .

If you require a student visa and choose to sit Pearson PTE, an overall score of 59 with no less than 59 in each component would be required.

Pre-sessional English

We will consider applicants who do not meet these scores but you may be required to complete a pre-sessional English language course at the University of Manchester prior to the start of the course.

To be considered for a pre-sessional English language course for this programme we require the following minimum IELTS (Academic) scores:

  • 6 Week Pre-Sessional Course:  Minimum 6.0 overall with no sub-test below 5.5.
  • 10 Week Pre-sessional Course: Minimum 5.5 overall with no sub-test below 5.5.

If you have not yet completed your current academic study and are interested in studying a pre-sessional course, you must hold an IELTS for UKVI (Academic) test certificate.

English language test validity

Some English Language test results are only valid for two years. Your English Language test report must be valid on the start date of the course.

Other international entry requirements

We accept a range of qualifications from different countries. For these and general requirements including English language see  entry requirements from your country .

Application and selection

How to apply

Advice to applicants

Apply online . Please note that only the MSc is available for application and the PG Cert and PG Dip are available as exit awards.

We require the following documents before we can consider your application.

  • Transcript of your studies to date, translated into English.
  • At least one academic reference on letter headed paper. These can be scanned and uploaded when you apply or emailed to pgt-maths@manchester.ac.uk . We do not request references on an applicant's behalf and it is your responsibility to ensure your referees know how to provide your reference to us.
  • Degree certificate if you have already graduated.
  • Curriculum vitae (CV) if you graduated more than three years ago.

If English is not your first language, we also require proof of your English language ability. If you have already taken an English language qualification, please include your certificate with your application. We may be willing to consider your application without this document, but if we choose to make you an offer, the conditions will include IELTS (or equivalent qualification).

How your application is considered

We consider your full academic history including which course units you have taken and the marks obtained. Even if you have met our minimum entry requirements, we will take into account your marks in relevant course units in our final decision making.

If you graduated more than three years ago, we will also consider the information contained on your CV and any relevant work experience you have to assess if you are still able to fulfil the entry criteria.

Interview requirements

No interview is required for this course.

Overseas (non-UK) applicants

CAS Information

Self-funded international applicants for this course will be required to pay a deposit of £1,000 towards their tuition fees before a confirmation of acceptance for studies (CAS) is issued. This deposit will only be refunded if immigration permission is refused. We will notify you about how and when to make this payment.

Please upload a copy of your current valid passport with your application showing the photograph page with your application. For CAS purposes, this must show your full name, date of birth, nationality, passport number and the date the passport is valid until, which must be later than the date of your planned arrival in the UK, and the start date of your course.

If you have previously studied in the UK on a Tier 4 visa as an undergraduate or postgraduate student, please send a copy of your previous CAS statement to us as it will assist with the issue of your new CAS statement. This includes study in the UK on study abroad programmes and any study that you did not complete.

You cannot use your CAS to apply for a visa more than three months before the start date of your course. The Admissions Team will contact you at the appropriate time.

Your CAS number is only valid for one Tier 4 application.

Deferrals

Applications for deferred entry are not accepted for this course. If you receive an offer for 2021 entry and decide not to accept it, should you subsequently wish to be considered for 2022 entry you would be required to reapply.

Re-applications

If you applied in the previous year and your application was not successful you may apply again. Your application will be considered against the standard course entry criteria for that year of entry. In your new application you should demonstrate how your application has improved. We may draw upon all information from your previous applications or any previous registrations at the University as a student when assessing your suitability for your chosen course.

Course details

Course description

This one year taught postgraduate programme leads to the degree of MSc in Pure Mathematics. The programme is suitable not only for students who wish to improve their background knowledge prior to applying to undertake a PhD by research, but also for students who wish to enhance their knowledge of postgraduate-level abstract mathematics.  The MSc comprises of the taught component, running from the start of the academic year in September until the end of the second semester in late Spring, followed by the dissertation component running from June until September.

During the taught component of the course, you will normally take six units together with a research skills and project unit.  You may choose exclusively pure topics, or a mixture of pure mathematics units and mathematical logic units. In the research skills and project unit you will first complete a mini-project to improve mathematical writing skills, and then undertake a project. The project is normally an expository account of a piece of mathematics and you will write this under the guidance of a supervisor. The taught component comprises of conventional lectures supported by examples classes, project work and independent learning via reading material.

After successfully completing the taught component, you will prepare a dissertation on an advanced topic in pure mathematics or mathematical logic, normally of current or recent research interest, chosen in consultation with your supervisor. 

You can also take the programme part-time, over a period of two years.  There is some flexibility in the precise arrangements for this programme, but you would normally attend two lecture courses each semester for three semesters before commencing work on your dissertation.

Within two weeks from the start of the academic year, students in this programme can opt to change to the Mathematical Logic Pathways leading to the degree of MSc in Pure Mathematics and Mathematical Logic.

Aims

The aims of the programme are to provide training in a range of topics related to pure mathematics, to encourage a sophisticated and critical approach to mathematics, and to prepare students who have the ability and desire to follow careers as professional mathematicians and logicians in industry or research.

Coursework and assessment

The taught component is assessed by coursework, project work and by written examination.  The written exams take place at the end of January (for the first semester course units) and the end of May (for the second semester course units).  The dissertation component is assessed by the quality and competence of the written dissertation.

The Postgraduate Diploma and Postgraduate Certificate exist as exit awards for students who do not pass at MSc level.

Course unit details

The taught courses cover material related to the research interests of the academic staff.

Course unit list

The course unit details given below are subject to change, and are the latest example of the curriculum available on this course of study.

TitleCodeCredit ratingMandatory/optional
MSc Pure Mathematics Research and Project Skills MATH61000 30 Mandatory
Fourier Analysis and Lebesgue Integration MATH61011 15 Optional
Differentiable Manifolds MATH61061 15 Optional
Noncommutative Algebra MATH62041 15 Optional
Representation and Characters of Groups MATH62062 15 Optional
Lie Algebras MATH62112 15 Optional
Galois Theory MATH62122 15 Optional
Algebraic Number Theory MATH62132 15 Optional
Computation and Complexity MATH63011 15 Optional
Set Theory MATH63022 15 Optional
Model theory MATH63051 15 Optional
Dynamical Systems MATH64041 15 Optional
Displaying 10 of 12 course units

Scholarships and bursaries

  Scholarships are available for this programme.

Facilities

The Department of Mathematics is the largest in the UK with an outstanding research reputation and  facilities .

Disability support

Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email: dass@manchester.ac.uk