BSc (Hons)
Mathematics with Philosophy

Key Information


3-4 years

Typical Offer

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Brayford Pool



Academic Year

Course Overview

This joint programme combines a foundation of pure and applied mathematics with the study of Philosophy, reflecting the complementary nature of these two disciplines to help explain our world and our place in it.

Mathematics with Philosophy at Lincoln combines two of the most fundamental and widely applicable intellectual skills. The course aims to provide students with the knowledge and ability to tackle quantifiable problems and to analyse issues and question assumptions. This enables them to develop their understanding of logic and reasoning.

Students have the opportunity to learn from, and work alongside, our team of academics who can support and encourage them to apply imagination, creativity, and rigour to the solution of real-world problems. Individual and group projects during the course are designed to develop transferable skills.

Why Choose Lincoln

Subject ranked in the top 10 in the UK for student satisfaction*

Institute of Mathematics and its Applications (IMA) accreditation

Informed by cutting-edge research

Guest speakers from around the world

Additional problem-solving tutorials

Placement Year available

*Guardian University Guide 2023 (out of 65 ranking institutions).

YouTube video for Why Choose Lincoln

How You Study

Students can focus on numerical and analytical methods of mathematics, while developing a range of transferable skills, including logical reasoning, critical thinking, communication, and teamwork. This combination is intended to help students to develop the skills to tackle a variety of topics from different angles. It seeks to help students find answers and to evaluate the questions and reasoning behind them.

In the first year topics include algebra, calculus, ideas of mathematical proof, and an introduction to philosophical logic. In the second year students progress to differential equations, scientific computing, and the philosophy of science. The third year provides the opportunity for students to select from a range of optional modules to tailor the degree to their own interests.

The course is taught via lectures, problem solving classes, computer-based classes, and seminars.


† Some courses may offer optional modules. The availability of optional modules may vary from year to year and will be subject to minimum student numbers being achieved. This means that the availability of specific optional modules cannot be guaranteed. Optional module selection may also be affected by staff availability.

Algebra 2024-25MTH1001MLevel 42024-25This module begins with refreshing and expanding some of the material from the A-levels Maths, such as the binomial theorem, division of polynomials, polynomial root-finding, and factorisations. Then the Euclidean algorithm is introduced with some of its many applications, both for integers and for polynomials. This naturally leads to a discussion of divisibility and congruences, for integers and for polynomials, with emphasis on similarities and as a step towards abstraction.CoreCalculus 2024-25MTH1002MLevel 42024-25This module focuses on the concepts of the derivative and the Riemann integral, which are indispensable in modern sciences. Two approaches are used: both intuitive-geometric, and mathematically rigorous, based on the definition of continuous limits. Important results are the Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration. Further calculus tools are explored, such as the general properties of the derivative and the Riemann integral, as well as the techniques of integration. In this module, students may deal with many "popular" functions used throughout mathematics.CoreGeometrical Optics, Waves and Mechanics 2024-25PHY1002MLevel 42024-25This module introduces established theories describing optical, acoustic, and mechanical phenomena. The optics part includes Fermat’s principle of light propagation, Snell’s laws of reflection and refraction, thin lenses, and Huygens’s principle. The mechanics part includes the basic mathematical tools to describe the motion of objects (kinematics) and the laws of Newton (dynamics) underpinning these observed motions. The wave part of the module includes a discussion of propagating waves, the Doppler effect, phase and group velocities, and standing waves.CoreIdeas of Mathematical Proof 2024-25MTH1003MLevel 42024-25The purpose of this module is to introduce students to basic mathematical reasoning such as rigorous definitions and proofs, logical structure of mathematical statements. Students will have the opportunity to learn the set-theoretic notation, get acquainted with various strategies of mathematical proofs such as proof by mathematical induction or proof by contradiction. Rigorous definitions of limits of sequences and functions will form a foundation for other courses on calculus and differential equations. The importance of definitions and proofs will be illustrated by examples of "theorems" which may seem obvious but are actually false, as well as certain mathematical "paradoxes".CoreIntroduction to Moral Philosophy 2024-25PHL1004MLevel 42024-25This module is designed to introduce students to the three areas of discussion in contemporary moral philosophy. Metaethics is concerned with the nature of morality itself and questions such as ‘Are there moral facts?’, ‘If there are moral facts, what is their origin?’. Normative ethics is the attempt to provide a general theory that tells us how to live and enables us to determine what is morally right and wrong. Applied ethics involves the application of ethical principles to specific moral issues (e.g., abortion, euthanasia, animal rights) and the evaluation of the answers arrived at through this application. This module aims to introduce students to all three of these branches of ethics.CoreIntroduction to Philosophical Logic 2024-25PHL1002MLevel 42024-25This module introduces some of the basic ideas and concepts of philosophical logic and the technical vocabulary that is required for understanding contemporary philosophical writing. Students are introduced to logical concepts such as validity, soundness, consistency, possibility, necessity, contingency, inductive and deductive forms of argument, necessary and sufficient conditions, the rudiments of formalisation, and a range of logical fallacies. The emphasis will be on using logic to construct and evaluate arguments.CoreLinear Algebra 2024-25MTH1004MLevel 42024-25This module describes vector spaces and matrices. Matrices are regarded as representations of linear mappings between vector spaces. Eigenvalues and eigenvectors are introduced, which lead to diagonalisation and reduction to other canonical forms. Special types of mappings and matrices (orthogonal, symmetric) are also introduced.CoreProbability and Statistics 2024-25MTH1005MLevel 42024-25This module begins with an introduction of a probability space, which models the possible outcomes of a random experiment. Basic concepts such as statistical independence and conditional probability are introduced, with various practical examples used as illustrations. Random variables are introduced, and certain well-known probability distributions are explored. Further study includes discrete distributions, independence of random variables, mathematical expectation, random vectors, covariance and correlation, conditional distributions and the law of total expectation. The ideas developed for discrete distributions are applied to continuous distributions. Probability theory is a basis of mathematical statistics, which has so many important applications in science, industry, government and commerce. Students will have the opportunity to gain a basic understanding of statistics and its tools. It is important that these tools are used correctly when, for example, the full picture of a problem (population) must be inferred from collected data (random sample).CoreAlgebraic Structures 2025-26MTH2001MLevel 52025-26The concepts of groups, rings and fields are introduced, as examples of arbitrary algebraic systems. The basic theory of subgroups of a given group and the construction of factor groups is introduced, and then similar constructions are introduced for rings. Examples of rings are considered, including the integers modulo n, the complex numbers and n-by-n matrices. The ring of polynomials over a given field is studied in more detail.CoreCoding Theory 2025-26MTH2002MLevel 52025-26Transmission of data may mean sending pictures from the Mars rover, streaming live music or videos, speaking on the phone, answering someone's question “do you love me?”. Problems arise if there are chances of errors creeping in, which may be catastrophic (say, receiving “N” instead of “Y”). Coding theory provides error-correcting codes, which are designed in such a way that errors that occur can be detected and corrected (within certain limits) based on the remaining symbols. The problem is balancing reliability with cost and/or slowing the transmission. Students will have the opportunity to study various types of error-correcting codes, such as linear codes, hamming codes, perfect codes, etc., some of which are algebraic and some correspond to geometrical patterns.CoreComplex Analysis 2025-26MTH2003MLevel 52025-26Ideas of calculus of derivatives and integrals are extended to complex functions of a complex variable. Students will learn that complex differentiability is a very strong condition and differentiable functions behave very well. Integration along paths in the complex plane is introduced. One of the main results of this beautiful part of mathematics is Cauchy's Theorem that states that certain integrals along closed paths are equal to zero. This gives rise to useful techniques for evaluating real integrals based on the 'calculus of residues'.CoreDifferential Equations 2025-26MTH2004MLevel 52025-26Calculus techniques already provide solutions of simple first-order differential equations. Solution of second-order differential equations can sometimes be achieved by certain manipulations. Students may learn about existence and geometric interpretations of solutions, even when calculus techniques do not yield solutions in a simple form. This is a part of the existence theory of ordinary differential equations and leads to fundamental techniques of the asymptotic and qualitative study of their solutions, including the important question of stability. Fourier series and Fourier transform are introduced. This module provides an introduction to the classical second-order linear partial differential equations and techniques for their solution. The basic concepts and methods are introduced for typical partial differential equations representing the three classes: parabolic, elliptic, and hyperbolic.CoreExistentialism and Phenomenology 2025-26PHL2006MLevel 52025-26The aim of this module is to give students a thorough understanding of two intimately related philosophical traditions that came to prominence in the 19th and 20th centuries: existentialism and phenomenology. Each attempts to address the nature and meaning of human existence from the perspective of individual, first-person experience, focusing in particular on fundamental questions of being, meaning, death, nihilism, freedom, responsibility, value, human relations, and religious faith. The module will examine selected existential themes through the writings of thinkers such as Kierkegaard, Nietzsche, Heidegger, Sartre, De Beauvoir, and Camus. Since existentialism is as much a artistic phenomenon as a philosophical one, students will also be given the opportunity to explore existentialist ideas in the works of various literary figures, such as Shakespeare, Dostoyevsky, Kafka, and Milan Kundera.CoreIndustrial and Financial Mathematics 2025-26MTH2006MLevel 52025-26Students have the opportunity to learn how mathematics is applied to modern industrial problems, and how the mathematical apparatus finds applications in the financial sector.CorePhilosophy of Science 2025-26PHL2007MLevel 52025-26This module explores a range of philosophical questions relating to the nature of science. How are scientific theories developed? Are scientific theories discovered through a ‘flash of genius’ or is something more methodical involved? How much of scientific discovery is down to careful observation? Do scientific theories tell us how the world really is? Do the entities scientific theories postulate – atoms, electromagnetic waves, and so on – really exist? Or are scientific theories merely useful models of reality? Is science independent of its social context? To what extent is scientific inquiry affected by gender, race or politics? Is there such a thing as truth that is not relative to a particular culture, social class or historical era? Drawing on accessible examples from a variety of scientific fields and by answering these and related questions, we shall try to reach an understanding of how science works.CoreScientific Computing 2025-26MTH2008MLevel 52025-26Students will have the opportunity to utilise computers for the numerical solution and simulation of models of physical and mathematical systems, including the use of computer procedural programming languages to solve computational problems. Numerical algorithms will be introduced to exemplify key concepts in computational programming, with the emphasis on understanding the nature of the algorithm and the features and limitations of its computational implementation. In creating programs, the emphasis will be on using effective programming techniques and on efficient debugging, testing and validation methods. Students may also develop skills at using a logbook as a factual record and as reflective self-assessment to support their learning.CoreGroup Theory 2026-27MTH3003MLevel 62026-27Symmetry, understood in most broad sense as invariants under transformations, permeates all parts of mathematics, as well as natural sciences. Groups are measures of such symmetry and therefore are used throughout mathematics. Abstract group theory studies the intrinsic structure of groups. The course begins with definitions of subgroups, normal subgroups, and group actions in various guises. Group homomorphisms are introduced and the related isomorphism theorems are proved. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout, symmetry groups are used as examples.CoreMathematics Project 2026-27MTH3005MLevel 62026-27This is a double module in which a student undertakes a project under supervision of a research-active member of staff. The project can be undertaken at an external collaborating establishment. Projects will be offered to students in a wide range of subjects, assigned with consideration of a students' individual preferences and programme of their studies. Some projects will be more focused on a detailed study of mathematical theories or techniques in an area of current interest. Other projects may require solving specific problems that require the formulation of a mathematical model, its development and solution. Student meet regularly with their supervisor in order to receive guidance and review progress.CoreTensor Analysis 2026-27MTH3008MLevel 62026-27This module introduces tensors, which are abstract objects describing linear relations between vectors, scalars, and other tensors. The module aims to equip students with the knowledge of tensor manipulation, and introduces their applications in modern science.CoreApplied Ethics 2026-27PHL3014Level 62026-27This module gives students the opportunity to build and demonstrate problem-solving skills in the context of applied philosophy. Students will be introduced to the interdisciplinary methods of applied ethics and examine together a series of selected applied ethics case studies, drawn from a variety of different areas including health care, climate justice, AI, beginning and end of life. Students will then work on an individual project which they will present in poster form at the end of the module. The module will give students a thorough grounding in applied ethics and enable them to evidence the key employability skill of problem-solving in the context of applied philosophy.OptionalClassical Indian Philosophy 2026-27PHL3016Level 62026-27This module provides an introduction to Indian philosophy and gives students the opportunity to study some of the classic texts of Indian philosophy in detail. While texts will be studied in English translation students will also gain a familiarity with the elements of classical Indian (principally Sanskrit) philosophical vocabulary. Topics will be drawn from both the astika (orthodox Hindu) schools such as Naya-Vaisheshika and Samkhya-Yoga and nastika schools such as Jainism and Buddhism, and will cover areas such as logic, epistemology, metaphysics, and linguistics.OptionalContemporary Problems in Philosophy 2026-27PHL3018Level 62026-27This module gives students the opportunity to engage with some key issues and contemporary debates in key areas of philosophy, such as epistemological relativism, the nature of consciousness, the nature of causation in science, the nature of the self. The precise topics addressed will vary from year to year and students will have input into the choice of topics. The aim of the module is to explore in-depth some significant contemporary philosophical issues and to enable students to develop and enhance their key philosophical and debating skills.OptionalFluid Dynamics 2026-27MTH3002MLevel 62026-27This module gives a mathematical foundation of ideal and viscous fluid dynamics and their application to describing various flows in nature and technology. Students are taught methods of analysing and solving equations of fluid dynamics using analytic and most modern computational tools.OptionalLegal and Political Philosophy 2026-27PHL3015Level 62026-27This module gives students an opportunity to apply what they have learned in terms of philosophical methodology and analysis to issues involving political and legal institutions. For example, most people use concepts such as rights or justice in their everyday life, but few could articulate what those concepts mean. This makes discourse about political and legal matters difficult because there is no clarity, let alone agreement, about the concepts being used.OptionalMathematics Pedagogy 2026-27MTH3004MLevel 62026-27This module is designed to provide students with an insight into the teaching of Mathematics at secondary school level and does this by combining university lectures with an experience of a placement in a secondary school Mathematics department. The module aims to provide students with an opportunity to engage with cutting-edge maths education research and will examine how this research impacts directly on classroom practice. Students will have the opportunity to gain an insight into some of the key ideas in Mathematics pedagogy and how these are implemented in the school Mathematics lessons and will develop an understanding about the barriers to learning Mathematics that many students experience.OptionalMethods of Mathematical Physics 2026-27MTH3006MLevel 62026-27The module aims to equip students with methods to analyse and solve various mathematical equations found in physics and technology.OptionalNewton's Revolution 2026-27PHL3004MLevel 62026-27This module examines some of the philosophical issues raised by the Newtonian revolution in the natural sciences, such as: What is the nature of Newton’s distinction between ‘absolute’ and ‘relative’ space? In what sense can forces be said to exist? What is the ontology of force? Is it sufficient to provide a mathematical definition of force (e.g., f=ma)? Is gravity a special kind of force with its own unique set of properties? What is the nature of ‘action at a distance’? Is Newton’s view of space metaphysical? This is an interdisciplinary module that situates Newtonian science in its sociocultural context.OptionalNumerical Methods 2026-27MTH3007MLevel 62026-27The module aims to equip students with knowledge of various numerical methods for solving applied mathematics problems, their algorithms and implementation in programming languages.OptionalPhilosophy of Psychiatry and Mental Illness 2026-27PHL3017Level 62026-27This module focuses on a range of philosophical questions relating to mental illness and its treatment. What makes a person mentally healthy or mentally unhealthy? What makes a conscious state psychotic or delusional? How might mental disorders be distinguished from non-disordered mental states and conditions? Would certain putative mental illnesses be better characterized as “problems with living” rather than as medical conditions? We will also consider questions raised by particular psychopathologies. Questions will be explored through the lens of recent literature in the analytic tradition, as well as seminal texts in the history of the philosophy of mental illness (e.g., Freud, Foucault, R.D. Laing).Optional

What You Need to Know

We want you to have all the information you need to make an informed decision on where and what you want to study. In addition to the information provided on this course page, our What You Need to Know page offers explanations on key topics including programme validation/revalidation, additional costs, contact hours, and our return to face-to-face teaching.

How you are assessed

The course is assessed through a variety of means, including coursework, examinations, written reports, and oral presentations.


Our BSc programme currently meets the educational requirements of the Chartered Mathematician designation. This is awarded by the Institute of Mathematics and its Applications (IMA), when it is followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency for taught Master’s degrees.

Institute of Mathematics and its Applications Logo

Research-informed Teaching

Teaching on this course is conducted by academic members of staff who are active researchers in their fields. This research informs teaching at all levels of the programme. Staff conduct cutting-edge research in fundamental and applied mathematics and physics, ranging from pure mathematics to applied nano-science at the interface between biology, chemistry, physics, and mathematics. The School of Mathematics and Physics collaborates with top research institutions in Germany, Japan, Norway, the Netherlands, Singapore, Spain, and the USA.

Visiting Speakers

The School of Mathematics and Physics regularly welcomes guest speakers from around the world. Recent visitors to the University of Lincoln have included former vice president of the Royal Astronomical Society Professor Don Kurtz, mathematician and author Professor Marcus du Sautoy OBE, and operations research specialist Ruth Kaufman OBE.


Students on this course are encouraged to obtain and undertake work placements independently in the UK or overseas during their studies, providing hands-on experience in industry. These can range from a few weeks to a full year if students choose the sandwich year option. Placements may be conducted with external research institutions (which can be overseas). The option is subject to availability and selection criteria set by the industry or external institution. When undertaking optional placements, students will be required to cover their transport, accommodation, and general living costs.

What Can I Do with a Mathematics with Philosophy Degree?

Graduates may pursue careers in the fields of science, education, finance, business, consultancy, and research and development. This degree promotes skills in creative, critical, and independent thinking. It may prove beneficial in careers requiring flexibility and the ability to formulate a persuasive case. This could include careers in politics and the media, as well as the civil service, among other areas. Some graduates may choose to continue their studies at postgraduate level.

Entry Requirements 2024-25

United Kingdom

104 UCAS Tariff points from a minimum of 2 A Levels or equivalent qualifications to include 40 points in Maths.

International Baccalaureate: Pass Diploma from a minimum of 2 Higher Level subjects to include a Higher Level grade 5 in Mathematics.

Access to Higher Education Diploma: 45 Level 3 credits with a minimum of 104 UCAS Tariff points, including 40 points from 15 credits in Maths.

BTEC qualifications may be considered. Please contact our Admissions team for further information (

Applicants will also need at least three GCSEs at grade 4 or above, which must include English, Maths and Science. Equivalent Level 2 qualifications may also be considered.

The University accepts a wide range of qualifications as the basis for entry and do accept a combination of qualifications which may include A Levels, BTECs, EPQ etc.

We will also consider applicants with extensive and relevant work experience and will give special individual consideration to those who do not meet the standard entry qualifications.


Non UK Qualifications:

If you have studied outside of the UK, and are unsure whether your qualification meets the above requirements, please visit our country pages for information on equivalent qualifications.

EU and Overseas students will be required to demonstrate English language proficiency equivalent to IELTS 6.0 overall, with a minimum of 5.5 in each element. For information regarding other English language qualifications we accept, please visit the English Requirements page

If you do not meet the above IELTS requirements, you may be able to take part in one of our Pre-sessional English and Academic Study Skills courses.

For applicants who do not meet our standard entry requirements, our Science Foundation Year can provide an alternative route of entry onto our full degree programmes:

If you would like further information about entry requirements, or would like to discuss whether the qualifications you are currently studying are acceptable, please contact the Admissions team on 01522 886097, or email

Contextual Offers

At Lincoln, we recognise that not everybody has had the same advice and support to help them get to higher education. Contextual offers are one of the ways we remove the barriers to higher education, ensuring that we have fair access for all students regardless of background and personal experiences. For more information, including eligibility criteria, visit our Offer Guide pages.

Fees and Scholarships

Going to university is a life-changing step and it's important to understand the costs involved and the funding options available before you start. A full breakdown of the fees associated with this programme can be found on our course fees pages.

Course Fees

For eligible undergraduate students going to university for the first time, scholarships and bursaries are available to help cover costs. To help support students from outside of the UK, we are also delighted to offer a number of international scholarships which range from £1,000 up to the value of 50 per cent of tuition fees. For full details and information about eligibility, visit our scholarships and bursaries pages.

Find out More by Visiting Us

The best way to find out what it is really like to live and learn at Lincoln is to visit us in person. We offer a range of opportunities across the year to help you to get a real feel for what it might be like to study here.

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The University intends to provide its courses as outlined in these pages, although the University may make changes in accordance with the Student Admissions Terms and Conditions.