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UCAS code GV15
What are numbers? Do they exist? How can we know about them if they are not to be found in the familiar world of space and time that we inhabit? These are just some of the philosophical questions raised by the study of Mathematics.
The relationship between philosophy and mathematics runs both ways: mathematics has helped formalise the study of logical argument that lies at the base of all good philosophy. So, it is no surprise that some of the greatest philosophers (eg Descartes, Leibniz, Frege, and Russell) have been mathematicians too.
This programme allows you to study Mathematics and Philosophy in equal amounts over three years. The Philosophy component of the degree course includes modules in logic and the formal study of reasoning, in which you will learn how to assess arguments and construct proofs. You will learn how to understand complex and demanding texts, and to recognise good and bad arguments. In Mathematics, the core first-year modules introduce fundamental ideas, and are designed to bridge the gap between previous study and university. In subsequent years, you will generally take four modules in mathematics each year, choosing either to specialise or to continue to study a broad range of topics.
By the end of the programme, you will be able to understand complex and demanding texts, reason intelligently and imaginatively about ethical, metaphysical, and epistemological issues, and have a grasp of the advantages and problems of a wide range of metaphysical and philosophical views. In addition, you will have mastered a wide range of mathematical disciplines, and have extended your numerical, logical, and quantitative skills.
This programme is available with a Year in Industry. Year Three is spent on a paid placement within an organisation in industry, broadly defined. You will be supported by the School of the Arts and the Department of Philosophy throughout, and your reflective written account of the experience will contribute towards your final degree result. If you wish to study this programme with a Year in Industry, please put the option code ‘YI’ in the ‘Further Choices’ section of your UCAS application form.
Discover what you'll learn, what you'll study, and how you'll be taught and assessed.
You will take seven required modules: four from Philosophy, and three core foundation modules from Mathematics; and choose one optional module from Mathematics in semester two.
| Compulsory modules | Credits |
|---|---|
| MIND, KNOWLEDGE AND REALITY (PHIL103) | 15 |
| PHILOSOPHY TOOLKIT (PHIL105) | 15 |
| CALCULUS I (MATH101) | 15 |
| INTRODUCTION TO LINEAR ALGEBRA (MATH103) | 15 |
| CALCULUS II (MATH102) | 15 |
| INTRODUCTION TO LOGIC (PHIL127) | 15 |
| PHILOSOPHICAL INSIGHTS (PHIL106) | 15 |
| Optional modules | Credits |
|---|---|
| NEWTONIAN MECHANICS (MATH122) | 15 |
| NUMBERS, GROUPS AND CODES (MATH142) | 15 |
| INTRODUCTION TO STATISTICS USING R (MATH163) | 15 |
Programme details and modules listed are illustrative only and subject to change. The course content currently shown on this page reflects the programme as it is running in September 2026. The University is currently reviewing all of its programmes for 2027 entry. View the 2027 version of this course for more information.
In each semester, you will take 30 credits from Mathematics and 30 credits from Philosophy (SOTA260 counts towards Philosophy credits).
| Compulsory modules | Credits |
|---|---|
| DIFFERENTIAL EQUATIONS (MATH221) | 15 |
| LOGIC (PHIL207) | 15 |
Programme details and modules listed are illustrative only and subject to change. The course content currently shown on this page reflects the programme as it is running in September 2026. The University is currently reviewing all of its programmes for 2027 entry. View the 2027 version of this course for more information.
In each semester, you will take 30 credits of Mathematics and 30 credits of Philosophy. Modules weighted at 30 credits are whole-year modules and count as 15 credits per semester. SOTA300 counts as a Philosophy module.
Programme details and modules listed are illustrative only and subject to change. The course content currently shown on this page reflects the programme as it is running in September 2026. The University is currently reviewing all of its programmes for 2027 entry. View the 2027 version of this course for more information.
In studying Philosophy you will learn how to defend your views with reasoned arguments, and to assess the arguments of others. Argumentative skills are learned through attending lectures and reading philosophical texts, developed by group seminar discussions, and formally assessed through essays and exams. You will complete modules to the value of 120 credits per year, from a wide range of options available. Most modules employ a blend of lectures, seminars, and online support materials. You will learn by reading and studying outside class time, by attending and participating in classes, by doing coursework and, for dissertations, via one-to-one meetings with a supervisor. There is also scope, both formally in the placement module and informally, for you to develop practical skills by volunteering.
In Mathematics, your learning activities will consist of lectures, tutorials, practical classes, problem classes, private study, and supervised project work. In year one, lectures are supplemented by a thorough system of group tutorials, and computing work is carried out in supervised practical classes. Key study skills, presentation skills, and group work start in first-year tutorials, and are developed later in the programme. The emphasis in most modules is on the development of problem solving skills, which are regarded very highly by employers. Project supervision is on a one-to-one basis, apart from group projects in year two.
Philosophy employs a mixture of modes of assessment: exams and coursework in many different varieties including essays, oral presentations, dissertations, exercises, and supported independent work (eg in the placement module).
In Mathematics, most modules are assessed by an examination lasting two and a half hours in January or May, but many have an element of coursework assessment. This might be through homework, class tests, mini-project work, or exercises in developing key skills.
At Liverpool, we take a distinctive approach to education through the Liverpool Learning Framework. This means teaching that is engaging, inclusive and designed to help you succeed during your studies and beyond.
You’ll develop specialist subject knowledge alongside the skills employers value most, including:
Our curriculum is characterised by the three Liverpool Hallmarks:
We also embed key priorities across our curriculum, including AI literacy, employability, and sustainability, helping you prepare for the future and make a positive impact in the world.
We’re committed to creating a supportive and inclusive learning environment where every student can thrive.
Studying with us means you can tailor your degree to suit you. Here's what is available on this course.
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.
Immerse yourself in Chinese culture on an optional additional year at Xi'an Jiaotong Liverpool University in stunning Suzhou.
Broaden your world by spending an additional year of study at a partner university abroad following your second year of study.
Take a semester of your second year of study at one of our worldwide partner institutions.
Spend a summer abroad on a study placement or research project at one of our worldwide partner institutions.
Every student at The University of Liverpool can study a language as part of, or alongside their degree. You can choose:
The Department of Philosophy is based in Gillian Howie House, although teaching will take place across the campus. Gillian Howie House is an accessible and inclusive space. We have ramp and lift access to all floors, single sex, gender neutral and disabled toilets, and a Hearing Assist System in our seminar rooms. Students who require one can ask for a disability support plan and access to dedicated support.
From arrival to alumni, we’re with you all the way:
The academic staff in the Department are fantastic and their doors are all open if you want to go and talk to them.
Want to find out more about student life?
Chat with our student ambassadors and ask any questions you have.
A mathematically-based degree opens up a wide range of career opportunities, including some of the most lucrative professions.
Recent employers of our graduates are:
Hear what graduates say about their career progression and life after university.
US District Judge Wendy Beetlestone described her time at University of Liverpool as a “great start” that delivered the “thought discipline” that continues to influence her professional life.
Your tuition fees, funding your studies, and other costs to consider.
Full-time place, per year - £9,790
Year in industry fee - £1,955
Year abroad fee - £1,465 (applies to year in China)
Full-time place, per year - £29,500
Year in industry fee - £1,955
Year abroad fee - £13,300 (applies to year in China)
The fees shown are for the academic year 2026/27. Please be advised that tuition fees may increase each year for both UK and international students. For UK students, this will be subject to the government’s regulated fee limits.
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.
We understand that budgeting for your time at university is important, and we want to make sure you understand any course-related costs that are not covered by your tuition fee. You can find information on the general and subject-specific costs you could expect to incur on our study costs webpage.
We offer a range of scholarships and bursaries that could help pay your tuition and living expenses.
This scholarship will support undergraduate students from widening participation backgrounds in the Department of Languages, Cultures and Film with their year abroad.
This award offers £3,000 per year for a UK undergraduate student from an under-represented background who has successfully completed the Liverpool Scholars or Pathways to Medicine programme.
If you’re a UK student joining an undergraduate degree and have a household income below £35,000, you could be eligible for a Liverpool Bursary worth up to £2,000 for each year of undergraduate study.
Apply for an Asylum Seekers Scholarship and you could have your tuition fees paid in full and receive help with study costs. You’ll need to have applied for asylum in the UK, or be the dependant of an asylum seeker, and be joining an eligible undergraduate degree.
If you’ve spent 13 or more weeks in Local Authority care since age 14, you could be eligible for a bursary of £3,000 per year of study. You’ll need to be a UK student joining an eligible undergraduate degree and be aged 28 or above on 1 September in the year you start.
Are you a UK student with a Black African or Caribbean heritage and a household income of £25,000 or less? You could be eligible to apply for a Cowrie Foundation Scholarship worth up to £8,000 for each year of undergraduate study.
If you’re a UK student identified as estranged by Student Finance England (or the equivalent UK funding body), you could be eligible for a bursary of £1,000 for each year of undergraduate study.
Do you live in the Liverpool City Region with a household income of £25,000 or less? Did neither of your parents attend University? You could be eligible to apply for a Nolan Scholarship worth £5,000 per year for three years of undergraduate study.
Are you a UK student with a household income of £25,000 or less? If you’ve participated in an eligible outreach programme, you could be eligible to apply for a Rigby Enterprise Award worth £5,000 per year for three years of your undergraduate degree.
Are you a UK student with a household income of £26,500 or less? Did neither of your parents attend University? You could be eligible to apply for a ROLABOTIC Scholarship worth £4,500 for each year of your undergraduate degree.
Apply to receive tailored training support to enhance your sporting performance. Our athlete support package includes a range of benefits, from bespoke strength and conditioning training to physiotherapy sessions and one-to-one nutritional advice.
If you’re a young adult and a registered carer in the UK, you might be eligible for a £1,000 bursary for each year of study. You’ll need to be aged 18-25 on 1 September in the year you start your undergraduate degree.
The qualifications and exam results you'll need to apply for this course.
| Qualification | Details |
|---|---|
| A levels |
ABB including A level Mathematics at grade A.Applicants with the Extended Project Qualification (EPQ) are eligible for a reduction in grade requirements. For this course, the offer is ABC from A levels, with A in the EPQ including A in Maths and A in EPQ. You may automatically qualify for reduced entry requirements through our contextual offers scheme. 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. If you don't meet the entry requirements, you may be able to complete a foundation year which would allow you to progress to this course. Available foundation years: |
| 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. |
| BTEC Level 3 National Extended Diploma | Applications encouraged when combined with A Level Mathematics at grade A. BTEC applications are encouraged. We evaluate each BTEC application on its merits. |
| International Baccalaureate | 32 points overall with no score less than 4 and including 6 in Higher Level Mathematics or pass the IB Diploma plus 6,5,5 in 3 HL subjects with 6 in Higher Level Mathematics. |
| Irish Leaving Certificate | H1, H2, H2, H2, H3, H3 including H1 in Mathematics |
| Scottish Higher/Advanced Higher | Scottish Highers at AABBB plus Scottish Advanced Highers grade A in Maths or Scottish Advanced Highers at ABB including Maths at grade A, combinations are also welcome. |
| Welsh Baccalaureate Advanced | B in the Welsh Baccalaureate, plus AB at A level to include Mathematics at grade A. |
| Access | Pass relevant Access to HE Diploma with 45 Level 3 credits with 33 at Distinction including Distinctions in units in Mathematics and 12 at Merit. |
| International qualifications |
If you hold a bachelor’s degree or equivalent, but don’t meet our entry requirements, you could be eligible for a Pre-Master’s course. This is offered on campus at the University of Liverpool International College, in partnership with Kaplan International Pathways. It’s a specialist preparation course for postgraduate study, and when you pass the Pre-Master’s at the required level with good attendance, you’re guaranteed entry to a University of Liverpool master’s degree. |
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.
| Qualification | Details |
|---|---|
| IELTS | 6.5 overall, with no component below 5.5 |
| TOEFL iBT | If you took a TOEFL test on or before 20 January 2026, you’ll need 88 overall, with minimum scores of listening 17, writing 17, reading 17 and speaking 19. If you took a TOEFL test from 21 January 2026 onwards, when a new scoring system was introduced, you’ll need 4.5 overall, with 4 or above in all components. TOEFL Home Edition not accepted. |
| Duolingo English Test | 115 overall, with speaking, reading and writing not less than 105, and listening not below 100 |
| Pearson PTE Academic | 61 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 B overall, with a minimum of grade 2 in speaking. Speaking must be separately endorsed on the certificate. 0511: Grade B overall. |
| Cambridge IGCSE Second Language English 0993/0991 | 0993: Grade 6 overall, with a minimum of grade 2 in speaking. Speaking must be separately endorsed on the certificate. 0991: Grade 6 overall. |
| Cambridge ESOL Level 2/3 Advanced | 176 overall, with no paper below 162 |
| International Baccalaureate English A: Literature or Language & Literature | Grade 4 at Standard Level or grade 4 at Higher Level |
| International Baccalaureate English B | Grade 6 at Standard Level or grade 5 at Higher Level |
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.
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 |
|---|---|---|
| 6.0 overall, with no component below 5.5 | 6 weeks | On campus or online |
| 5.5 overall, with no more than one component at 5.0 | 10 weeks | On campus or online |
| 5.5 overall, with no component below 5.0 | 12 weeks | Online |
| 5.0 overall, with no component below 5.0 | 20 weeks | On campus |
| 5.0 overall, with no component below 4.5 | 30 weeks | On campus |
| 4.5 overall, with no more than one component at 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 6.5 overall, with no component below 5.5, for further details.
Have a question about this course or studying with us? Our dedicated enquiries team can help.
Last updated 21 April 2026 / / Programme terms and conditions