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Mathematics

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The deadline for international students is 30 June 2025.

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  • University name: University of Liverpool
  • Course: Mathematics G101
  • Location: Main site
  • Start date: 22 September 2025

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Master of Mathematics

Master of Mathematics, MMath, is an integrated master’s degree which combines undergraduate and postgraduate study into a single course.

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Course overview

This four-year programme is ideal for ambitious students who want to study mathematics in depth. Graduates gain a master's qualification, which provides a competitive edge in the employment market and opens the door to careers in research.

Introduction

Mathematics is a beautiful and diverse subject. It underpins a wide range of disciplines, from physical sciences to social science, from biology to business and finance. The further your study of mathematics progresses, the more fascinating it becomes.

The University of Liverpool has a large Mathematical Sciences department with highly qualified staff, a first class reputation in teaching and research, and a friendly, supportive environment. We use mixed approaches to teaching and assessment, taking the best from traditional lectures, tutorials and assignments, and modern methods such as interactive learning sessions, video content and online assessment. Our programmes are designed with the needs of employers in mind, to give you a solid foundation from which you may take your career in whatever direction you choose.

The first two years of the MMath programme are the same as the Mathematics BSc. You will have the opportunity to learn about a range of fundamental topics, building on the mathematics you already know and providing the background for the more advanced modules in years three and four. No assumptions are made about whether you have previously studied mechanics, statistics or computer programming. In years three and four, we offer a wide range of advanced modules in pure mathematics, applied mathematics and statistics, enabling you to specialise in the areas of mathematics that interest you most. In the final year, students on this programme complete a substantial project on a mathematical topic of their own choice, supervised by an expert in the relevant field. Graduates completing the programme have experience of mathematics research and independent working skills that are highly valued by employers.

This programme also has a year abroad option, an incredible opportunity to spend an academic year at one of our partner universities. On the four-year integrated master’s programme, you can go abroad either between years two and three (apply in year two), or between years three and four (apply in year three).

What you'll learn

  • Fundamentals of pure and applied mathematics, probability and statistics
  • Advanced material from the branches of mathematics that interest you most
  • Teamwork
  • Digital fluency
  • Sophisticated problem solving skills
  • How to communicate complex ideas

Accreditation

Liverpool’s MMath degree is accredited by the Institute of Mathematics and its Applications (IMA) and the Royal Statistical Society (RSS)

Accreditations in detail

Teaching Excellence Framework 2023

We’re proud to announce we’ve been awarded a Gold rating for educational excellence.

Accreditations

Liverpool’s MMath degree is accredited by the Institute of Mathematics and its Applications (IMA) and the Royal Statistical Society (RSS)

Course content

Discover what you'll learn, what you'll study, and how you'll be taught and assessed.

Year one

All students on the programme take the same modules in year one. These build on the mathematics you already know, and lay the foundations for the more advanced material introduced later.

Compulsory modules

Calculus I (MATH101)

Credits: 15 / Semester: semester 1

​At its heart, calculus is the study of limits. Many quantities can be expressed as the limiting value of a sequence of approximations, for example the slope of a tangent to a curve, the rate of change of a function, the area under a curve, and so on. Calculus provides us with tools for studying all of these, and more. Many of the ideas can be traced back to the ancient Greeks, but calculus as we now understand it was first developed in the 17th Century, independently by Newton and Leibniz. The modern form presented in this module was fully worked out in the late 19th Century. MATH101 lays the foundation for the use of calculus in more advanced modules on differential equations, differential geometry, theoretical physics, stochastic analysis, and many other topics. It begins from the very basics – the notions of real number, sequence, limit, real function, and continuity – and uses these to give a rigorous treatment of derivatives and integrals for real functions of one real variable.​ ​

CALCULUS II (MATH102)

Credits: 15 / Semester: semester 2

This module, the last one of the core modules in Year 1, is built upon the knowledge you gain from MATH101 (Calculus I) in the first semester. The syllabus is conceptually divided into three parts: Part I, relying on your knowledge of infinite series, presents a thorough study of power series (Taylor expansions, binomial theorem); part II begins with a discussion of functions of several variables and then establishes the idea of partial differentiation together with its various applications, including chain rule, total differential, directional derivative, tangent planes, extrema of functions and Taylor expansions; finally, part III is on double integrals and their applications, such as finding centres of mass of thin bodies. Undoubtedly, this module, together with the other two core modules from Semester 1 (MATH101 Calculus I and MATH103 Introduction to linear algebra), forms an integral part of your ability to better understand modules you will be taking in further years of your studies.

Introduction to Linear Algebra (MATH103)

Credits: 15 / Semester: semester 1

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It is the study of lines, planes, and subspaces and their intersections using algebra.

Linear algebra first emerged from the study of determinants, which were used to solve systems of linear equations. Determinants were used by Leibniz in 1693, and subsequently, Cramer’s Rule for solving linear systems was devised in 1750. Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination. All these classical themes, in their modern interpretation, are included in the module, which culminates in a detailed study of eigenproblems. A part of the module is devoted to complex numbers which are basically just planar vectors. Linear algebra is central to both pure and applied mathematics. This module is an essential pre-requisite for nearly all modules taught in the Department of Mathematical Sciences.

Introduction to Statistics using R (MATH163)

Credits: 15 / Semester: semester 2

Students will learn fundamental concepts from statistics and probability using the R programming language and will learn how to use R to some degree of proficiency in certain contexts. Students will become aware of possible career paths using statistics.

Mathematical IT skills (MATH111)

Credits: 15 / Semester: semester 1

This module introduces students to powerful mathematical software packages such as Maple and Matlab which can be used to carry out numerical computations or to produce a more complicated sequence of computations using their programming features. We can also do symbolic or algebraic computations in Maple. These software packages have built-in functions for solving many kinds of equations, for working with matrices and vectors, for differentiation and integration. They also contain functions which allow us to create visual representations of curves and surfaces from their mathematical descriptions, to work interactively, generate graphics and create mathematical documents. This module will teach students many of the above-mentioned features of mathematical software packages. This knowledge will be helpful in Years 2, 3 and 4 when working on different projects, for example in the modules MATH266 and MATH371.

Introduction to Study and Research in Mathematics (MATH107)

Credits: 15 / Semester: semester 1

This module looks at what it means to be a mathematician as an undergraduate and beyond. The module covers the discussion of mathematics at university, research mathematics and careers for mathematicians as well as core elements of mathematical language and writing such as logic, proofs, numbers, sets and functions. The activities include sessions delivered by staff on their research areas, sessions by alumni and other mathematicians working outside academia on careers for mathematicians and sessions by careers services. The module also provides key tools needed for studying mathematics at university level. You will explore the core mathematical concepts in more detail in groups and individually and practice communicating mathematics in speech and writing.

NEWTONIAN MECHANICS (MATH122)

Credits: 15 / Semester: semester 2

This module is an introduction to classical (Newtonian) mechanics. It introduces the basic principles like conservation of momentum and energy, and leads to the quantitative description of motions of bodies under simple force systems. It includes angular momentum, rigid body dynamics and moments of inertia.

Numbers, Groups and Codes (MATH142)

Credits: 15 / Semester: semester 2

A group is a formal mathematical structure that, on a conceptual level, encapsulates the symmetries present in many structures. Group homomorphisms allow us to recognise and manipulate complicated objects by identifying their core properties with a simpler object that is easier to work with. The abstract study of groups helps us to understand fundamental problems arising in many areas of mathematics. It is moreover an extremely elegant and interesting part of pure mathematics. Motivated by examples in number theory, combinatorics and geometry, as well as applications in data encryption and data retrieval, this module is an introduction to group theory. We also develop the idea of mathematical rigour, formulating our theorems and proofs precisely using formal logic.

Programme details and modules listed are illustrative only and subject to change.

Our curriculum

The Liverpool Curriculum framework sets out our distinctive approach to education. Our teaching staff support our students to develop academic knowledge, skills, and understanding alongside our graduate attributes:

  • Digital fluency
  • Confidence
  • Global citizenship

Our curriculum is characterised by the three Liverpool Hallmarks:

  • Research-connected teaching
  • Active learning
  • Authentic assessment

All this is underpinned by our core value of inclusivity and commitment to providing a curriculum that is accessible to all students.

Course options

Studying with us means you can tailor your degree to suit you. Here's what is available on this course.

Global Opportunities

University of Liverpool students can choose from an exciting range of study placements at partner universities worldwide. Choose to spend a year at XJTLU in China or a year or semester at an institution of your choice.

What's available on this course?

Year in China

Immerse yourself in Chinese culture on an optional additional year at Xi'an Jiaotong Liverpool University in stunning Suzhou.

  • Learn Chinese
  • Study in a bustling world heritage city
  • Improve employment prospects
  • Study Chinese culture
  • 30 minutes from Shanghai
  • Learn new skills

Read more about Year at XJTLU, China

Language study

Every student at The University of Liverpool can study a language as part of, or alongside their degree. You can choose:

  • A dedicated languages degree
  • A language as a joint or major/ minor degree
  • Language modules (selected degrees)
  • Language classes alongside your studies

Read more about studying a language

Study as a bachelor's degree

This course is also available as a three year BSc (Hons) programme.

View Mathematics BSc (Hons)

Your experience

Virtual tour

Supporting your learning

From arrival to alumni, we’re with you all the way:

What students say...

The academic staff in the Department are fantastic and their doors are all open if you want to go and talk to them

, MMath Mathematics

Careers and employability

A mathematically-based degree opens up a wide range of career opportunities, including some of the most lucrative professions as employers value mathematicians’ high level of numeracy and problem solving skills.

Typical types of work our graduates have gone onto include:

  • actuarial trainee analyst in the audit practice
  • graduate management trainee risk analyst
  • trainee chartered accountant on a graduate business programme.

Recent employers of our graduates include:

  • Aston University
  • Deloitte
  • EuroMoney Training
  • Norwich Union
  • Venture Marketing Group
  • Wolsley Group.

87.5% of mathematical sciences graduates go on to work or further study within 15 months of graduation.

Discover Uni, 2018-19.

Meet our alumni

Hear what graduates say about their career progression and life after university.

Fees and funding

Your tuition fees, funding your studies, and other costs to consider.

Tuition fees

UK fees (applies to Channel Islands, Isle of Man and Republic of Ireland)
Full-time place, per year £9,250
Year in industry fee £1,850
Year abroad fee £1,385
International fees
Full-time place, per year £24,800
Year abroad fee £12,400
Fees shown are for the academic year 2024/25. Please note that the Year Abroad fee also applies to the Year in China.

Tuition fees cover the cost of your teaching and assessment, operating facilities such as libraries, IT equipment, and access to academic and personal support. Learn more about paying for your studies..

Additional costs

Your tuition fee covers almost everything but you may have additional study costs to consider, such as books.

Find out more about the additional study costs that may apply to this course.

Additional study costs

Your tuition fee covers almost everything but you may have additional study costs to consider, such as books.

Find out more about additional study costs.

Scholarships and bursaries

We offer a range of scholarships and bursaries to provide tuition fee discounts and help with living expenses while at university.

Check out our Liverpool Bursary, worth up to £2,000 per year for eligible UK students. Or for international students, our Undergraduate Global Advancement Scholarship offers a tuition fee discount of up to £5,000 for eligible international students starting an undergraduate degree from September 2024.

Discover our full range of undergraduate scholarships and bursaries

Entry requirements

The qualifications and exam results you'll need to apply for this course.

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Your qualification Requirements

About our typical entry requirements

A levels

AAB including Mathematics A level grade A.

Applicants with the Extended Project Qualification (EPQ) are eligible for a reduction in grade requirements. For this course, the offer is ABB with A in the EPQ.

You may automatically qualify for reduced entry requirements through our contextual offers scheme.

T levels

T levels are not currently accepted.

GCSE 4/C in English and 4/C in Mathematics
Subject requirements

Applicants must have studied Mathematics at Level 3 within 2 years of the start date of their course.

For applicants from England: For science A levels that include the separately graded practical endorsement, a "Pass" is required.

BTEC Level 3 National Extended Diploma

Applications Considered. Relevant when combined with A level Mathematics grade A

International Baccalaureate

35 including 6 in Higher Mathematics

Irish Leaving Certificate H1, H1, H2, H2, H2, H3 including Mathematics at H1
Scottish Higher/Advanced Higher

Advanced Highers accepted at grades AAB including grade A in Mathematics.

Welsh Baccalaureate Advanced Acceptable at grade B or above alongside AA at A level including grade A in Mathematics.
Access Considered
International qualifications

Many countries have a different education system to that of the UK, meaning your qualifications may not meet our entry requirements. Completing your Foundation Certificate, such as that offered by the University of Liverpool International College, means you're guaranteed a place on your chosen course.

English language requirements

You'll need to demonstrate competence in the use of English language, unless you’re from a majority English speaking country.

We accept a variety of international language tests and country-specific qualifications.

International applicants who do not meet the minimum required standard of English language can complete one of our Pre-Sessional English courses to achieve the required level.

English language qualification Requirements
IELTS 6.0 overall, with no component below 5.5
TOEFL iBT 78 overall, with minimum scores of listening 17, writing 17, reading 17 and speaking 19
Duolingo English Test 105 overall, with no component below 95
Pearson PTE Academic 59 overall, with no component below 59
LanguageCert Academic 65 overall, with no skill below 60
Cambridge IGCSE First Language English 0500 Grade C overall, with a minimum of grade 2 in speaking and listening. Speaking and listening must be separately endorsed on the certificate.
Cambridge IGCSE First Language English 0990 Grade 4 overall, with Merit in speaking and listening
Cambridge IGCSE Second Language English 0510/0511 0510: Grade C overall, with a minimum of grade 2 in speaking. Speaking must be separately endorsed on the certificate. 0511: Grade C overall.
Cambridge IGCSE Second Language English 0993/0991 0993: Grade 5 overall, with a minimum of grade 2 in speaking. Speaking must be separately endorsed on the certificate. 0991: Grade 5 overall.
International Baccalaureate Grade 5 at Standard Level or grade 4 at Higher Level
Cambridge ESOL Level 2/3 Advanced 169 overall, with no paper below 162

PRE-SESSIONAL ENGLISH

Do you need to complete a Pre-Sessional English course to meet the English language requirements for this course?

The length of Pre-Sessional English course you’ll need to take depends on your current level of English language ability.

Find out the length of Pre-Sessional English course you may require for this degree.

Pre-sessional English

If you don’t meet our English language requirements, we can use your most recent IELTS score, or the equivalent score in selected other English language tests, to determine the length of Pre-Sessional English course you require.

Use the table below to check the course length you're likely to require for your current English language ability and see whether the course is available on campus or online.

Your most recent IELTS score Pre-Sessional English course length On campus or online
5.5 overall, with no component below 5.5 6 weeks On campus
5.5 overall, with no component below 5.0 10 weeks On campus and online options available
5.0 overall, with no component below 5.0 12 weeks On campus and online options available
5.0 overall, with no component below 4.5 20 weeks On campus
4.5 overall, with no component below 4.5 30 weeks On campus
4.0 overall, with no component below 4.0 40 weeks On campus

If you’ve completed an alternative English language test to IELTS, we may be able to use this to assess your English language ability and determine the Pre-Sessional English course length you require.

Please see our guide to Pre-Sessional English entry requirements for IELTS 6.0, with no component below 5.5, for further details.

Contextual offers: reduced grade requirements

Based on your personal circumstances, you may automatically qualify for up to a two-grade reduction in the entry requirements needed for this course. When you apply, we consider a range of factors – such as where you live – to assess if you’re eligible for a grade reduction. You don’t have to make an application for a grade reduction – we’ll do all the work.

Find out more about how we make reduced grade offers.

About our entry requirements

Our entry requirements may change from time to time both according to national application trends and the availability of places at Liverpool for particular courses. We review our requirements before the start of the new UCAS cycle each year and publish any changes on our website so that applicants are aware of our typical entry requirements before they submit their application.

Recent changes to government policy which determine the number of students individual institutions may admit under the student number control also have a bearing on our entry requirements and acceptance levels, as this policy may result in us having fewer places than in previous years.

We believe in treating applicants as individuals, and in making offers that are appropriate to their personal circumstances and background. For this reason, we consider a range of factors in addition to predicted grades, widening participation factors amongst other evidence provided. Therefore the offer any individual applicant receives may differ slightly from the typical offer quoted in the prospectus and on the website.

Alternative entry requirements

Changes to Mathematics MMath

See what updates we've made to this course since it was published. We document changes to information such as course content, entry requirements and how you'll be taught.

7 June 2022: New course pages

New course pages launched.

6 December 2022: Module changes

Year 3 optional module list updated – See course page

 

Year 4 optional module list updated – See course page

7 December 2022: Module changes

Year 3 optional module list updated – See course page

 

Year 4 optional module list updated – See course page

20 May 2024: Mathematics MMath – course overview update

In the ‘Course Overview’ section after ‘This programme also has a year abroad option, an incredible opportunity to spend an academic year at one of our partner universities.’ add ‘On the 4-year integrated masters programme, you can go abroad either between Year 2 and 3 (apply in Year 2) OR Year 3 and 4 (apply in Year 3).’