Mathematics and Philosophy
UCAS code GV15
- Study mode
- Full-time
- Duration
- 3 years
- Start date and application deadlines
-
- Start date
About this course
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.
Introduction
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.
Year in Industry
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.
What you'll learn
- A broad knowledge of Mathematics and of Philosophy
- Advanced numerical, logical, and quantitative skills
- Techniques for solving problems in several areas, and the ability to apply those techniques with confidence
- Competence in using a variety of educational resources
- Confidence in presenting technical material and previously unfamiliar ideas to small audiences
- Analytical, argumentative, communication and problem-solving skills
- Understanding of complex and demanding texts
- The ability to reason intelligently and imaginatively about ethical, metaphysical, and epistemological issues
Course content
Discover what you'll learn, what you'll study, and how you'll be taught and assessed.
Year one
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.
Modules
| 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.
Year two
In each semester, you will take 30 credits from Mathematics and 30 credits from Philosophy (SOTA260 counts towards Philosophy credits).
- SOTA260 is compulsory if you choose to study this programme with a Year in Industry.
- MATH142 may be taken in year two only by students that did not take it in year one.
- You may take up to one of PHIL271 and PHIL272.
Modules
| Compulsory modules | Credits |
|---|---|
| DIFFERENTIAL EQUATIONS (MATH221) | 15 |
| LOGIC (PHIL207) | 15 |
Programme details and modules listed are illustrative only and subject to change.
Final year
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.
- You must take at least one of PHIL306, SOTA300, PHIL311, PHIL365, but may not take both PHIL306 and PHIL311.
- You must consult with you academic advisor before taking both PHIL306 and SOTA300.
- Students who have taken SOTA600 (Year in Industry) are not allowed to take SOTA300.
- PHIL306 normally requires a minimum average of 60% in Year 2.
Modules
Programme details and modules listed are illustrative only and subject to change.
Teaching and assessment
How you'll learn
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.
How you're assessed
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.
Liverpool Hallmarks
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:
- 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.
Entry requirements
The qualifications and exam results you'll need to apply for this course.
| Qualification | Details |
|---|---|
| A levels |
BBC (including Mathematics: B) |
| BTEC Level 3 national extended diploma |
DDM and grade B in A level Mathematics. |
| BTEC combinations |
BTEC National Diploma DM plus grade B at Mathematics A level; BTEC National Extended Certificate M plus grade B in Mathematics at A level and grade B in another A level. |
| Welsh Baccalaureate Advanced |
C in the Welsh Baccalaureate, plus BB at A level to include Mathematics. |
| Access |
May be considered; please submit an application. |
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.
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
Year abroad
Broaden your world by spending an additional year of study at a partner university abroad following your second year of study.
- Choose from up-to 26 countries
- Experience another way of life
- Inspire your future career or studies
- Improved prospects of earning a 2:1 or First
- More likely to earn higher salary
- More likely to be employed after graduating
Where can I spend a year abroad on this course?
- Australia
- Canada
- Hong Kong
- Malaysia
- Singapore
- South Korea
- USA
Semester abroad
Take a semester of your second year of study at one of our worldwide partner institutions.
- Inspire your future career or studies
- Improved prospects of earning a 2:1 or First
- More likely to earn higher salary
- More likely to be employed after graduating
Summer abroad
Spend a summer abroad on a study placement or research project at one of our worldwide partner institutions.
- Spend a summer abroad in addition to your degree programme
- Study abroad without adding an extra year
- Choose any summer between your first and final year of study
- Get the chance to study subjects outside your discipline
Where can I spend a summer abroad on this course?
- Hong Kong
- Japan
- South Korea
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
Your experience
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.
Explore where you'll study
A day in the life of Philosophy student Alfie
Virtual tour
Supporting your learning
From arrival to alumni, we’re with you all the way:
- Careers and employability support, including help with career planning, understanding the job market and strengthening your networking skills
- A dedicated student services team can help you get assistance with your studies, help with health and wellbeing, and access to financial advice
- Confidential counselling and support to help students with personal problems affecting their studies and general wellbeing
- Support for students with differing needs from the Disability advice and guidance team. They can identify and recommend appropriate support provisions for you.
Why study Philosophy at Liverpool?
- Our students’ study some of the most profound questions facing humankind, in a city renowned for its rich history of culture, protest and philosophical debate
- Our friendly, down-to earth atmosphere makes the exchange of ideas enjoyable as well as intellectually stimulating
- We have a long history of combining research excellence in core areas of philosophy with innovative work at the frontiers of the discipline: from literature to spirituality, Chinese philosophy to animal ethics, neo-Platonism to feminism
- Ranked 4th in the sector for outstanding (4*) research impact (REF 2021)
- We work as part of our amazing city; working with partners in the Bluecoat Gallery, Tate Liverpool, National Museums Liverpool, NHS and more to inspire our thinking and the practices of our communities
The academic staff in the Department are fantastic and their doors are all open if you want to go and talk to them.
Chat with our students
Want to find out more about student life?
Chat with our student ambassadors and ask any questions you have.
Careers and employability
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:
- Barclays Bank plc
- Deloitte
- Forrest Recruitment
- Marks and Spencer
- Mercer Human Resource Consulting Ltd.
- Venture Marketing Group.
- BAE Systems
- BT
- Guardian Media Group
- Royal Bank of Scotland
- Siemens
- Unilever.
Meet our alumni
Hear what graduates say about their career progression and life after university.
The Honorable Wendy Beetlestone, BA (Hons) Philosophy 1984
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.
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 - £9,535
Year abroad fee - £1,430 (applies to year in China)
International fees
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.
Additional costs
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.
Scholarships and bursaries
We offer a range of scholarships and bursaries that could help pay your tuition and living expenses.
The Liverpool Bursary
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.
Asylum Seekers Scholarship
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.
Care Leavers’ Opportunity Bursary
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.
Cowrie Foundation Scholarship
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.
Estranged Students Bursary
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.
Nolan Scholarships
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.
Rigby Enterprise Award
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.
ROLABOTIC Scholarship
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.
Sport Liverpool Performance Programme
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.
Young Adult Carer’s (YAC) Bursary
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.
Last updated 7 July 2025 / / Programme terms and conditions