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Mathematics and Philosophy

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Ready to apply? You can apply for this course online now using the UCAS website. The deadline for UK students to apply for this course is 25 January 2023.

The deadline for international students is 30 June 2023.

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Use these details to apply for this course through UCAS:

  • University name: University of Liverpool
  • Course: Mathematics and Philosophy GV15
  • Location: Main site
  • Start date: 25 September 2023

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Bachelor of Arts

A Bachelor of Arts (BA Hons) is a bachelor’s degree awarded for an undergraduate programme in the arts.

Course overview

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 ethical 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, communications 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.

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 LOGIC (PHIL127)

Credits: 15 / Semester: semester 2

This module teaches students how to assess arguments using the formal methods of modern symbolic logic. Taking this module will enhance your ability to work with abstract material and your problem solving skills. It will help you understand logical notation where you encounter it in your reading, and prepare you, where appropriate, for more advanced logical study. The module is taught by lecture (1hr/week) and workshop (2hrs/week from week 2 onwards). There are three assessment components; an online multiple choice test (30%), an in-class test administered in the 9th workshop (40%), and a final exam (1hr, 30%).

MIND, KNOWLEDGE AND REALITY (PHIL103)

Credits: 15 / Semester: semester 1

This module introduces students to modern metaphysics, with an emphasis on a coherent historical narrative that explains the role that early modern philosophers, especially Rene Descartes and John Locke, have played in the development of our contemporary intellectual culture. The module covers Descartes’ and Locke’s philosophical systems in the early modern period, then goes on to outline the ‘scientific turn’ in philosophy in the late 19th and early 20th century. Taking this module will give students a grasp of why philosophers ask big questions about the nature of reality, and how those questions bear on their everyday lives and political experiences. The module is taught by lecture (2 x 1 hour per week) and seminar (1 hour per week). Assessment has two components, a set of 5 short pieces of writing (5 x 150 words) worth 25% of the module mark and spread through the teaching term, and a final essay worth the remaining 75%.

Philosophical Insights (PHIL106)

Credits: 15 / Semester: semester 2

This module brings the history of philosophy to life by unpacking the meaning behind well-known philosophical quotations (e.g. ‘The unexamined life is not worth living’; ‘One is not born, but rather becomes, a woman’). The quotations will be selected from key thinkers in the history of philosophy, and will be presented in chronological order. They will also be selected so that the material covered complements, but does not overlap with, readings on other philosophy modules. Students are introduced to well-known philosophical quotations in lectures. The lectures provide background context required to understand the quotations. Students then carry out independent research into the meanings of these quotations after the lecture. In workshops they write short summaries of what is meant by these quotations. In seminars they present and discuss these summaries, and have a debate about the plausibility of the philosophical views underlying the quotations they are working on. At the end of the course they combine three of their five summaries into a wiki, and they write a blogpost on one of the quotations that explains its meaning and evaluates the philosophical views and ideas expressed in it.

Students taking this module will improve their skills in reading and writing philosophy. Students will gain skill in explaining complex information in a concise manner to an audience, in practising the intellectual virtues associated with philosophy, in conducting their own independent research and in critically discussing important ideas in the history of philosophy. They will also gain familiarity with modes of writing other than essays (wikis, blogposts). In addition, there is a two-hour information skills workshop provided by the Library.

PHILOSOPHY TOOLKIT (PHIL105)

Credits: 15 / Semester: semester 1

Students taking this module will develop key skills which are essential for studying philosophy. Students will learn how to approach philosophical texts written in a variety of styles – how to identify arguments, how to distinguish arguments from rhetoric, and how to evaluate arguments. They will also learn how to summarise views accurately, clearly and concisely, and how to write persuasively when presenting their own analysis of the philosophical topics covered. This module also includes lectures on successful presenting, and how to conduct fruitful philosophical discussions. Students will also be advised on understanding and learning from feedback. Students will gain skills in conducting their own independent, enquiry-led research, which is facilitated by a two-hour information and research skills workshop provided by the Library.
The seminar readings cover three particularly engaging philosophical topics: animal ethics, lying and bullshit (epistemology) and aesthetics. Since the lecture content is devoted to developing the skills involved with philosophical practice, this module also features three podcasts which serve as introductions to the three seminar topics.

The module is assessed as follows: seminar participation counts for 10% of the overall grade, a 1,000-word executive summary of any two of the seminar readings counts for 30% of the module result, and a 2000-word essay counts for the remaining 60%. Feedback on the executive summary and the essay is provided online using VITAL. It specifically relates the assessed work to the marking descriptors (which are published online in advance). Feedback on seminar participation is provided informally by the seminar leader (and by the students’ peers). Students will also have the opportunity to discuss their participation by making use of their seminar leader’s feedback and advice hours.

Optional modules

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.

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. MATH122 provides the foundations for more advanced modules like MATH228, 322, 325, 326, 423, 425 and 431.

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

Year in industry

Year in industry placements give you an in-depth workplace experience where you can develop your skills and apply your learning.

  • Develop key employability skills that graduate employers are looking for
  • Experience and understand workplace culture and disciple
  • Understand the relationship between academic theory and real world application
  • Begin your professional network
  • Gain industry insight and insight into potential career options.

You don't need to decide now - you can choose to add a year in industry after you've begun your degree.

Learn more about year in industry

To spend a year in industry, you'll need to secure a placement with an organisation. If you're unable to find a placement, you'll continue with the standard version of the course without a year in industry.

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

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.

Virtual tour

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

Kate Johnson, MMath Mathematics

Careers and employability

As a student in the School of the Arts, you will be supported to maximise your employability from day one. The School has its own placements and employability officer, and you will have the opportunity to undertake a work placement or a year in industry as part of your programme.

3 in 4 philosophy students find their main activity after graduation meaningful.

Graduate Outcomes, 2018-19.

Employers value the general and widely applicable analytical, argumentative, communications and problem-solving skills developed by studying Mathematics and Philosophy. Graduates in philosophy obtain work in such fields as advertising, the arts, broadcasting, the charitable sector, commerce, the Civil Service, computing, journalism, marketing, politics, law, management, the media and teaching.

Preparing you for future success

At Liverpool, our goal is to support you to build your intellectual, social, and cultural capital so that you graduate as a socially-conscious global citizen who is prepared for future success. We achieve this by:

  • Embedding employability within your , through the modules you take and the opportunities to gain real-world experience offered by many of our courses.
  • Providing you with opportunities to gain experience and develop connections with people and organisations, including student and graduate employers as well as our global alumni.
  • Providing you with the latest tools and skills to thrive in a competitive world, including access to Handshake, a platform which allows you to create your personalised job shortlist and apply with ease.
  • Supporting you through our peer-to-peer led Careers Studio, where our career coaches provide you with tailored advice and support.

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

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 tuition fees, funding and student finance.

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.

Additional study 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 additional study costs.

Scholarships and bursaries

We offer a range of scholarships and bursaries to help cover tuition fees and help with living expenses while at university.

Scholarships and bursaries you can apply for from the United Kingdom

Entry requirements

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

My qualifications are from: United Kingdom.

Your qualification Requirements

About our typical entry requirements

A levels

ABB

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.

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:

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

A level Mathematics at grade A or equivalent

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

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.

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 and Philosophy BA (Hons)

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.