Mathematics and Philosophy BSc
AAB at A level, A in Mathematics; graduates earn a median £28,500 three years on.
Typical A level offer
AAB
A in Mathematics · 100% of entrants came with A levels · 100% stay on after year 1 · York course page, Discover Uni
Year 13 · applying
What do you need to get in?
AABtypical A level offer; aab including a in mathematics
Typical offer — the grades most applicants are asked for. Contextual offer: ABB, for applicants from under-represented backgrounds.
York course page, read 19 September 2026 · Discover Uni entry profile
- 1A in Mathematics
Who actually got in: 100% with A levels. Based on 10 entrants.
Other qualifications4
| Qualification | Typical offer | Required subjects |
|---|---|---|
| BTEC | DDDDDD plus grade A in A level Mathematics (or equivalent qualification) We consider a range of BTEC qualifications equivalent to 3 A Levels, or in combination with A Levels or other qualifications. For | Mathematics Distinction, Distinction in 2 BTEC Level 3 National Extended Certificates plus A in A Level Mathematics |
| IB | 35 points35 points overall, including 6 in Mathematics at Higher Level (either Analysis and Approaches or Applications and Interpretations) | 6 in Mathematics at Higher Level |
| Scottish Highers | BBBB | — |
| Advanced Highers | B in Mathematics plus | — |
Years 1–3
What do you study?
6compulsory modules in year 1
Compulsory modules this year: mathematics & statistics 44% · arts & humanities 25% · language & communication 21% · digital & ict skills 6%.
Module — one course unit, usually a term or a year long; “core” means everyone takes it. One UK credit is about ten hours of study; a full year is 120 credits.
York course page · optional modules vary by year
Year 1 · 6 core · 120 credits ≈ 1,200 hours
- Foundations and Calculus
What you learn (8)
- prove elementary results concerning sets and their properties
- prove elementary results concerning functions and their properties
- apply differentiation techniques to solve calculus problems
- apply integration techniques to solve calculus problems
- perform calculations with vectors and complex numbers to solve problems
- prove rigorous statements about the behaviour of limits
- solve problems relating limits to derivatives and integrals
- use a computer algebra system to solve module-related mathematical problems
- Introduction to Pure Mathematics
What you learn (5)
- apply foundational pure mathematics concepts to solve problems
- use a range of mathematical proof techniques
- formulate precise mathematical statements
- construct rigorous mathematical proofs
- evaluate mathematical arguments for correctness and rigour
- Multivariable Calculus and Matrices
What you learn (9)
- solve second-order differential equations using standard techniques
- construct a Fourier series expansion of a function
- construct a Taylor series expansion of a function
- differentiate functions of several variables
- integrate functions of several variables
- perform algebraic operations on matrices
- apply matrix methods to solve systems of linear equations
- use computer algebra software to solve multivariable calculus problems
- use computer algebra software to solve matrix algebra problems
- Logic
What you learn (6)
- explain core logical concepts including validity, consistency and necessity
- translate simple arguments into truth-functional logic notation
- apply truth-tables to assess tautological validity of arguments
- translate complex arguments into first-order logic notation
- construct a counter-interpretation to refute validity of a first-order logic argument
- construct a formal proof demonstrating validity of a first-order logic argument
- Knowledge and Perception
What you learn (2)
- explain differing theories of the nature of knowledge
- explain differing accounts of how knowledge is acquired
- Metaphysics and Humans or Ethics
What you learn (8)
- communicate metaphysical ideas in clear accessible language
- generate alternative solutions to metaphysical problems using course content
- present differing viewpoints on metaphysical issues open-mindedly
- construct arguments supporting alternative views on metaphysical problems
- critique weaknesses and potential improvements in philosophical arguments
- justify a personal position on a metaphysical problem with argument
- assess own work against departmental marking criteria
- apply feedback-based strategies to improve academic work
Year 2 · 4 core, 13 optional · 80 credits ≈ 800 hours
- Groups, Rings and Fields
What you learn (9)
- apply abstract algebraic concepts to specific groups, rings and fields
- explain the structure and purpose of mathematical proofs used in the module
- construct valid proofs for algebraic statements covered in the module
- apply the fundamental theorem of homomorphisms to familiar group examples
- apply the fundamental theorem of homomorphisms to unfamiliar group examples
- describe the construction of direct products of groups
- describe the construction of semidirect products of groups
- explain the division algorithm for polynomial rings
- apply the division algorithm to polynomials over a ring
- Linear Algebra
What you learn (13)
- identify whether a given subset forms a linear subspace
- apply subspace properties to solve algebraic problems
- determine a basis for a given vector space
- calculate the dimension of a vector space from a basis
- recognise whether a given map is linear
- determine the kernel and image of a linear map
- apply the rank-nullity theorem to solve problems
- calculate eigenvalues of a linear map or matrix
- calculate eigenvectors corresponding to given eigenvalues
- define real and Hermitian inner products
- apply inner products to determine orthogonality of vectors
- derive consequences of orthogonality in vector spaces
- perform matrix factorisation using computer algebra software
- Metric Spaces
What you learn (9)
- identify whether a given set with a distance function is a metric space
- perform calculations using the metric structure of a space
- determine whether a function between metric spaces is continuous
- apply continuity arguments to solve problems in metric spaces
- determine whether a sequence converges in an abstract metric space
- determine whether a metric space is complete
- apply the contraction mapping theorem to solve problems involving complete spaces
- demonstrate that a given space is compact
- prove results concerning compactness in abstract metric spaces
- Logic and Paradox
What you learn (6)
- describe a range of logical paradoxes
- evaluate proposed solutions to logical paradoxes
- apply non-classical logical systems to problems
- judge the relative merits of different non-classical logics
- discuss module topics constructively with peers
- defend a reasoned position on course topics in writing
13 optional modules
- Religious Ethics
What you learn (10)
- explain key problems and debates in religious ethics clearly
- formulate alternative solutions to religious ethics problems
- present alternative viewpoints with an open mind
- construct arguments supporting different ethical positions
- identify weaknesses and development points in ethical arguments
- judge the most defensible position on an ethical issue
- defend a chosen ethical position with reasoned argument
- appraise own work against assessment criteria
- apply feedback-based strategies to improve academic work
- evaluate contemporary ethical and cultural issues critically
- Philosophy of Language
What you learn (8)
- explain key problems and debates in philosophy of language clearly
- formulate alternative solutions to philosophical problems using module content
- construct arguments supporting alternative philosophical solutions
- identify weaknesses and development points in philosophical arguments
- judge the most convincing position on a philosophical problem
- defend a chosen philosophical position with reasoned argument
- evaluate own work against departmental marking criteria
- apply feedback-based strategies to improve academic work
- Metaphysics
What you learn (8)
- explain key problems and debates in metaphysics clearly
- formulate alternative solutions to metaphysical problems
- construct arguments supporting alternative metaphysical positions
- identify weaknesses and development points in a philosophical argument
- evaluate competing metaphysical views to form a reasoned judgement
- defend a chosen position on a metaphysical question
- assess own academic work against assessment criteria
- apply feedback-based strategies to improve academic work
- Philosophy of Mind
What you learn (8)
- explain key problems and debates in philosophy of mind clearly
- formulate alternative solutions to philosophy of mind problems
- construct arguments supporting alternative philosophical positions
- identify weaknesses and potential improvements in an argument
- evaluate competing views to determine the most defensible position
- defend a chosen philosophical position with reasoned argument
- assess own work against academic marking criteria
- apply feedback-based strategies to improve academic work
- Applied Ethics
What you learn (8)
- explain key problems and debates in applied ethics clearly
- formulate alternative solutions to applied ethics problems
- construct arguments supporting alternative ethical solutions
- identify weaknesses and development points in ethical arguments
- justify a personal judgement on an applied ethics problem
- evaluate own work against departmental marking criteria
- apply feedback-based strategies to improve written work
- analyse contemporary social and political issues using ethical reasoning
- Philosophy of Science
What you learn (10)
- explain key problems and debates in philosophy of science
- express philosophical understanding in clear accessible language
- generate alternative solutions to philosophy of science problems
- present alternative viewpoints in an open-minded manner
- construct arguments supporting alternative philosophical solutions
- identify weaknesses and development points in philosophical arguments
- judge the most convincing position on a philosophical problem
- defend a chosen philosophical position with argument
- evaluate own work against departmental marking criteria
- apply feedback-based strategies to improve own work
- Ethical Theory
What you learn (11)
- explain key problems and debates in ethical theory
- communicate ethical arguments clearly and accessibly
- generate alternative solutions to ethical problems using course materials
- present multiple viewpoints on ethical issues impartially
- construct arguments supporting alternative ethical positions
- identify weaknesses and development points in ethical arguments
- formulate a reasoned position on an ethical problem
- defend a chosen ethical position with supporting arguments
- evaluate own academic work against marking criteria
- apply feedback-based strategies to improve written work
- evaluate contemporary issues using social and ethical perspectives
- Aesthetics
What you learn (7)
- communicate philosophical ideas clearly and accessibly
- generate alternative solutions to problems in philosophy of art
- present varied perspectives on aesthetic issues with open-mindedness
- construct arguments supporting alternative views in philosophy of art
- identify weaknesses and potential improvements in philosophical arguments
- evaluate competing views to determine the strongest position on an aesthetic problem
- defend a chosen philosophical position with reasoned argument
- The Limits of Reason: Kant's Theoretical and Practical Philosophy
What you learn (10)
- explain Kant's theory of a priori knowledge and the phenomena/thing-in-itself distinction
- describe Kant's account of pure and practical reason, free will and determinism
- explain Kant's concepts of the good will and the categorical imperative
- interpret primary philosophical texts in translation
- reconstruct philosophical arguments from historical source texts
- evaluate Kant's claims and arguments using secondary literature
- formulate original critiques challenging Kant's philosophical arguments
- articulate personal philosophical ideas on the module's themes
- paraphrase Kant's ideas using one's own words
- describe the significance of Kant's work within the history of philosophy
- Politics and Freedom: Anarchism and Conservatism
What you learn (5)
- describe the core beliefs of various conservative and anarchist traditions
- explain the reasoning underlying different conservative and anarchist positions
- explain the philosophical arguments that motivate conservatism and anarchism
- identify value-theory issues underlying debates on conservatism and anarchism
- articulate the central questions in debates on political authority, tradition and liberty
- Knowledge and the Social Sciences
What you learn (5)
- evaluate the strengths and weaknesses of social research methods
- explain theories of how social reality is constructed
- justify a personal position on the extent and boundaries of social knowledge
- identify hidden conceptual and normative assumptions in social theories
- analyse the assumptions underlying social science methods and arguments
- Love, Law, and Solidarity: Recognition from Rousseau to Honneth
What you learn (4)
- describe major debates and arguments in the philosophy of recognition
- evaluate the strength of arguments supporting recognition theory positions
- formulate a personal philosophical position on recognition debates
- present a reasoned philosophical argument clearly in writing or discussion
- Being and Reason: Spinoza's Metaphysics
What you learn (11)
- explain key issues in Spinoza's philosophical system
- express philosophical understanding clearly and accessibly
- formulate alternative solutions to problems in Spinoza's philosophy
- present alternative philosophical solutions with open-mindedness
- construct arguments supporting alternative solutions to philosophical problems
- identify weaknesses and development points in philosophical arguments
- judge the most convincing view on a Spinozist problem
- defend a chosen philosophical position with argument
- appraise own work against departmental marking criteria
- apply feedback-based strategies to improve academic work
- interpret philosophical texts with sensitivity to cultural and historical context
Year 3 · 1 core, 26 optional · 20 credits ≈ 200 hours
- Foundations of Maths
What you learn (7)
- explain the historical crisis in mathematical foundations
- describe the emergence of logicism, intuitionism and formalism
- describe the core claims of logicism, intuitionism and formalism
- explain debates between Platonism and anti-Platonism in mathematics
- evaluate the indispensability argument against anti-Platonism
- critically analyse complex philosophical texts
- construct and defend a reasoned philosophical argument
26 optional modules
- Philosophy of Law
What you learn (17)
- explain established legal theories and concepts in philosophy of law
- apply legal principles and perspectives to philosophical problems
- critically evaluate competing legal theories and perspectives
- describe the historical development and purpose of law
- critique the relationship between law and society and other disciplines
- formulate independent arguments on legal issues in philosophy of law
- support legal arguments with critically appraised academic evidence
- apply problem-solving strategies to legal and academic problems
- evaluate proposed solutions to practical and academic legal problems
- design a research strategy appropriate to a legal question
- locate relevant and reliable legal sources and authorities
- evaluate the effectiveness of a chosen research methodology
- present legal analysis in written formats for varied audiences
- present legal analysis orally for specialist and non-specialist audiences
- describe standards of scholarly and professional legal practice
- reflect on personal learning and feedback received
- identify future learning needs based on reflection
- Cryptography
What you learn (8)
- identify weaknesses in classical cryptosystems
- exploit identified weaknesses to break classical ciphers
- apply public key cryptographic protocols to solve numerical problems
- exploit weaknesses of public key protocols in simple scenarios
- perform calculations involving the mathematical structure of AES
- apply quantum information postulates to solve calculations
- describe the sequence of steps in the BB84 protocol
- explain why the BB84 protocol is secure
- Topology
What you learn (6)
- describe key examples of topological spaces
- analyse the properties of standard topological spaces
- apply topological invariants to characterise spaces
- distinguish topological spaces using their invariants
- apply path homotopy concepts to compare spaces
- analyse the structure of spaces using the fundamental group
- Operations Research
What you learn (15)
- state key terminology used in linear programming
- describe fundamental results of linear programming theory
- describe the stages of the simplex algorithm
- apply the simplex method to solve a linear program
- state the fundamental theorem of linear programming
- prove the fundamental theorem of linear programming
- state the duality theorem of linear programming
- formulate transportation problems as mathematical models
- solve transportation problems using appropriate methods
- model and solve network optimisation problems
- describe key results from game theory
- apply game theory results to operations research problems
- translate real-world problems into mathematical formulations
- solve mathematical models using suitable operations research techniques
- interpret mathematical solutions in the context of original problems
- Number Theory
What you learn (7)
- apply diverse proof methods used in number theory
- evaluate the suitability of different proof strategies for a given problem
- apply taught algorithms to solve specific numerical problems
- apply techniques of diophantine approximation to solve problems
- apply algebraic methods to number-theoretic problems
- apply probabilistic reasoning to number-theoretic problems
- apply the concept of fractal dimension to number-theoretic problems
- Measure and Integration
What you learn (6)
- apply properties of measures and measurable sets to solve examples
- explain Caratheodory's construction of measures
- describe the construction of Lebesgue measure
- identify key properties of the Lebesgue integral
- evaluate Lebesgue integrals using Monotone and Dominated Convergence Theorems
- evaluate multiple integrals using Tonelli and Fubini Theorems
- Numerical Analysis
What you learn (5)
- select a suitable numerical method for a given mathematical problem
- apply a numerical technique to approximate a solution
- analyse the error behaviour of a numerical method
- determine the stability region of a numerical method
- implement numerical methods using Python
- Groups, Actions and Galois Theory
What you learn (5)
- apply group actions to solve problems in group theory
- construct Sylow subgroups of a given group
- apply the Sylow theorems to analyse group structure
- construct different types of field extensions
- use the Galois correspondence to examine intermediate fields
- Contemporary Issues in Bioethics
What you learn (5)
- describe recent advances in biomedicine
- apply philosophical theory to issues in biomedicine
- critically read philosophical texts
- present written philosophical arguments
- participate in philosophical discussion
- Philosophy of Physics
What you learn (6)
- explain key concepts of classical mechanics such as inertial frames
- explain relativistic concepts including space, time and simultaneity
- explain quantum phenomena such as wave-particle duality and entanglement
- analyse how key physical concepts interact within physical theories
- evaluate the influence of these concepts on the scientific world-view
- apply core philosophical reasoning skills to analyse arguments
- Consciousness
What you learn (7)
- describe the explanatory problem posed by consciousness
- explain major theories proposed to account for consciousness
- write clearly and coherently on a chosen consciousness topic
- identify key debates relevant to a chosen consciousness topic
- analyse how arguments support or undermine opposing positions
- formulate competing philosophical positions on consciousness
- evaluate the relative merits of these positions to reach a conclusion
- Action and Agency
What you learn (6)
- explain why action is a central concept in philosophy of mind
- articulate the implications of action's central role in philosophy of mind
- explain how reasons relate to actions
- evaluate competing philosophical theories of action
- interpret complex philosophical texts critically
- construct a sustained written argument defending a position on action theory
- Philosophy of Christianity
What you learn (6)
- explain core christian doctrines such as the trinity and incarnation
- describe differing interpretations of christian doctrines
- evaluate competing interpretations of christian doctrines against each other
- justify the most convincing interpretation of a given doctrine
- critique philosophical and theological texts from multiple perspectives
- formulate a personal reasoned position on theological debates
- German Idealism: Moral, Legal & Political Philosophy
What you learn (6)
- explain the moral, legal and political theories of key german idealist philosophers
- evaluate the arguments of german idealist philosophers on ethics and politics
- describe core concepts used in german idealist philosophy
- relate german idealist philosophy to current debates in moral and political thought
- critically analyse challenging philosophical texts
- construct and justify a personal position on complex philosophical issues
- Causation and Laws
What you learn (3)
- explain key theories of causation and natural laws
- analyse the relationship between causal laws and natural laws
- evaluate how theories of causation relate to moral responsibility
- Theories of Social Justice: Rawls and Beyond
What you learn (8)
- describe the key features of Rawls's theory of justice
- identify major scholarly responses to Rawls's theory
- compare areas of agreement and disagreement among theories of social justice
- explain what is at stake in theoretical disputes over social justice
- relate philosophical theories of social justice to real-world policy issues
- critically analyse complex texts in contemporary political philosophy
- formulate a reasoned personal position on questions of social justice
- defend a personal position on social justice using philosophical argument
- Cognitive Anomalies, Decision-Making and Democracy
What you learn (6)
- explain research on cognitive biases affecting rational decision-making
- describe philosophical perspectives on the implications of cognitive biases
- identify ethical implications arising from cognitive effects and biases
- evaluate views on how cognitive biases affect individual and group decisions
- relate cognitive bias research to broader debates in philosophy of mind and ethics
- present philosophical arguments in both collaborative and individual written formats
- Happiness, Utility and Wellbeing
What you learn (5)
- evaluate competing philosophical accounts of happiness and well-being
- articulate a personal position on the role of happiness in one's own life
- evaluate how happiness informs ethical theory and moral reasoning
- evaluate how considerations of happiness shape public policy decisions
- discuss how other academic disciplines contribute to philosophical theories of happiness
- Mind and Morality
What you learn (8)
- explain key problems and debates in moral psychology clearly
- formulate alternative solutions to moral psychology problems
- construct arguments supporting alternative solutions in moral psychology
- identify weaknesses and development points in proposed arguments
- judge the most convincing position on a moral psychology issue
- defend a chosen position with supporting argument
- appraise own work against departmental marking criteria
- apply feedback-based strategies to improve own work
- Property and Self-ownership
What you learn (5)
- explain major theories justifying property rights and self-ownership
- evaluate the strengths and weaknesses of theories of property and self-ownership
- critically appraise historical and contemporary philosophical texts
- integrate ideas drawn from diverse philosophical sources and topics
- construct a reasoned written argument evaluating a key module issue
- The Nature of Time
What you learn (7)
- construct arguments supporting particular theories of time
- construct arguments opposing particular theories of time
- evaluate competing theories of time to judge their plausibility
- justify a reasoned position on the most plausible theory of time
- critically appraise contemporary philosophical literature on time
- produce well-structured philosophical arguments in writing
- participate effectively in philosophical discussion
- Buddhism as Philosophy
What you learn (8)
- describe key teachings of the Buddha
- identify major schools of Buddhism
- identify philosophical problems arising from Buddhist teachings
- assess whether analytic philosophy can resolve Buddhist philosophical problems
- evaluate proposed solutions using scripture, tradition and reason
- argue for a preferred solution or for the absence of one
- explain key philosophical concepts and views in Buddhist philosophy
- critique philosophical arguments and defend a personal position
- World and Mind
What you learn (4)
- describe the Cartesian view of thought and knowledge
- explain major objections to the Cartesian account of mind
- evaluate the strength of these objections to Cartesianism
- justify a personal position on which Cartesian claims remain tenable
- Nine Art Works, Nine Philosophical Problems
What you learn (4)
- describe major topics in the philosophy of art
- explain how philosophical topics relate to specific artworks
- construct and justify a reasoned argument in an extended essay
- participate constructively in critical peer discussions on aesthetics
- Topics in Feminist Philosophy
What you learn (3)
- identify key arguments within a philosophical text
- critically analyse philosophical arguments for validity and assumptions
- present analysis of philosophical arguments in structured written or spoken form
“What you learn” restates each module’s published learning outcomes in our own words, as short skill statements in the same form as the GCSE and A level curriculum, with the help of an AI model; fields of knowledge follow the twelve fields of the knowledge sphere. The university’s module page, linked from each title, is the authoritative description.
After graduating
Where does it lead?
£28,500median pay three years after graduating
Lower quarter£22k
Median£29k
Upper quarter£37k
Median — the middle earner: half earned more, half less. Pay is for graduates of this subject at this university who finished in 2016-18, not adjusted for inflation; based on 190 graduates.
Discover Uni dataset (HESA and Office for Students, CC BY 4.0, contains HESA data); earnings from the Longitudinal Education Outcomes data (Department for Education) · aggregation level 13, 14, 23, 24
Half of graduates earned between £22,000 and £36,500. Five years on, the median is £36,000. 85% were in work or further study 15 months after finishing; 75% of those in work were in professional or managerial jobs.
All outcome figures7
| Measure | Value | Based on |
|---|---|---|
| Continue after year 10% left | 100% | 10 |
| In work or study, 15 months on13% studying | 85% | 65 |
| Professional or managerial job | 75% | 45 |
| Pay 15 months on, median | £31,500 | 30 |
| Pay 3 years on, median | £28,500 | 190 |
| Pay 5 years on, median | £36,000 | 215 |
Money
What does it cost?
£10,050a year for UK students, 2027/28 entry
Tuition fee loan — paid straight to the university; repayments start the April after you leave, at 9% of income above the threshold. UK fees are capped by government and rise with inflation; placement and study-abroad years are usually charged at a lower rate.
York fees page · source
About £30,150 in fees over 3 years, covered by a tuition fee loan you repay only when earning above the threshold. International students: £28,600 a year (2027/28).
National Student Survey 2024-26
What do students say?
80%agreed the course was good overall (question 26)
NSS — a yearly survey of final-year students at every UK university; 56% of this course’s final year answered. Small groups can swing a lot year to year.
National Student Survey, via Discover Uni · 10 students answered
Highest: 100% agreed on question 3; lowest: 50% on question 14.
All questions26
| Question | Agree |
|---|---|
| Question 1 | 90% |
| Question 2 | 90% |
| Question 3 | 100% |
| Question 4 | 80% |
| Question 5 | 90% |
| Question 6 | 90% |
| Question 7 | 70% |
| Question 8 | 80% |
| Question 9 | 80% |
| Question 10 | 100% |
| Question 11 | 100% |
| Question 12 | 80% |
| Question 13 | 90% |
| Question 14 | 50% |
| Question 15 | 90% |
| Question 16 | 70% |
| Question 17 | 90% |
| Question 18 | 89% |
| Question 19 | 75% |
| Question 20 | 90% |
| Question 21 | 90% |
| Question 22 | 100% |
| Question 23 | 90% |
| Question 24 | 60% |
| Question 25 | 57% |
| Question 26 | 80% |
Question texts are published by the Office for Students; the dataset carries only the question numbers.
Modules, entry requirements and fees are facts read from University of York’s course page on 2026-09-19 and may change; the university’s page is authoritative. Descriptions are not reproduced. Outcome figures are from the Discover Uni dataset. University of York is a trade mark of the university; sch.today is independent of it.