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.
Please note: not all mathematics modules are listed and you will be required to take mathematics modules in each year.
| Compulsory modules | Credits |
|---|---|
| CALCULUS I (MATH101) | 15 |
| CALCULUS II (MATH102) | 15 |
| INTRODUCTION TO LINEAR ALGEBRA (MATH103) | 15 |
| INTRODUCTION TO LOGIC (PHIL127) | 15 |
| MIND, KNOWLEDGE AND REALITY (PHIL103) | 15 |
| PHILOSOPHICAL INSIGHTS (PHIL106) | 15 |
| PHILOSOPHY TOOLKIT (PHIL105) | 15 |
| Optional modules | Credits |
|---|---|
| NUMBERS, GROUPS AND CODES (MATH142) | 15 |
Programme details and modules listed are illustrative only and subject to change.
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.
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.
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.
We have a distinctive approach to education, the Liverpool Curriculum Framework, which focuses on research-connected teaching, active learning, and authentic assessment to ensure our students graduate as digitally fluent and confident global citizens.
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:
Our curriculum is characterised by the three Liverpool Hallmarks:
All this is underpinned by our core value of inclusivity and commitment to providing a curriculum that is accessible to all students.
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 the School of the Arts, although teaching will take place across the campus, including Mathematics. Our staff and students have created an environment where critical, independent thinking flourishes, in a city that has a long tradition of welcoming radical thinkers and philosophers. Our friendly, down-to-earth atmosphere makes the exchange of ideas enjoyable, as well as intellectually stimulating.
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 - £9,535
Year abroad fee - £1,430 (applies to year in China)
Full-time place, per year - £26,600
Year abroad fee - £13,300 (applies to year in China)
The tuition fees shown are correct for 2025/26 entry. 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.
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. This could include buying a laptop, books, or stationery.
Find out more about the additional study costs that may apply to this course.
We offer a range of scholarships and bursaries that could help pay your tuition and living expenses.
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.
Joining a School of Biosciences degree and have a household income of less than £25,000? If you’re a UK student, you could apply to receive £4,500 per year for three years of your undergraduate course.
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 £25,000 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.
Joining a degree in the School of Electrical Engineering, Electronics and Computer Science? If you’re a UK student with household income below £25,000, you could be eligible to apply for £5,000 a year for three years of study. Two awards will be available per academic year.
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 with A in the 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 | 33 including 6 in HL Mathematics with no score less than 4 |
| 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 | Accepted at grade B including A Level Mathematics at grade A and another A Level at grade B |
| Access | Access to HE Diploma in a relevant subject including Distinctions in units in Mathematics |
| 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 | 88 overall, with minimum scores of listening 17, writing 17, reading 17 and speaking 19. TOEFL Home Edition not accepted. |
| Duolingo English Test | 115 overall, with speaking, reading and writing not less than 105, and listening not below 100. For academic year 2025/26 only, we will also accept the production, literacy, comprehension and conversation score set: 105 overall, with no component below 95. |
| 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 |
| 5.5 overall, with no component below 5.5 | 10 weeks | On campus and online options available |
| 5.5 overall, with no more than one component below 5.5, and no component below 5.0 | 12 weeks | On campus and online options available |
| 5.5 overall, with no component below 4.5 | 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 below 4.5, and 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 6.5 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 8 May 2025 / / Programme terms and conditions