Mathematics (with a year abroad) BSc
AAA at A level, A in Mathematics; graduates earn a median £28,500 three years on.
Typical A level offer
AAA
A in Mathematics · 100% of entrants came with A levels · 95% stay on after year 1 · York course page, Discover Uni
Year 13 · applying
What do you need to get in?
AAAtypical A level offer; aab including a in mathematics and a in further mathematics; aab including a in mathematics and a in further mathematics at as level
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 | 36 points36 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 | A in Mathematics plus | — |
Years 1–4
What do you study?
6compulsory modules in year 1
Compulsory modules this year: mathematics & statistics 73% · digital & ict skills 19% · transversal skills 7% · language & communication 1%.
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
- Introduction to Applied Mathematics
What you learn (10)
- apply Newton's laws of motion to solve one-dimensional problems
- apply Newton's laws of motion to solve two-dimensional problems
- solve motion problems expressed in polar coordinates
- apply equations of motion to analyse planetary orbits
- derive scaling laws using dimensional analysis
- identify dimensionless numbers governing a physical system
- analyse first-order ordinary differential equations in applied problems
- analyse coupled pairs of first-order differential equations
- solve the wave equation using standard analytical methods
- solve the heat equation using standard analytical methods
- Introduction to Probability and Statistics
What you learn (7)
- represent simple random experiments using probability models
- compute standard probability values using core formulae
- analyse relationships between independent and correlated random variables
- apply basic statistical techniques to data
- interpret results obtained from statistical techniques
- perform introductory data analysis using statistical software
- run simple simulations using a statistical computing package
- 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
- Mathematical Programming and Skills
What you learn (12)
- write programs using variables, expressions and assignments
- construct loops and conditional structures in code
- build functions and arrays to perform mathematical operations
- create classes and objects for mathematical applications
- apply inheritance and dynamic methods in program design
- search scientific literature relevant to a mathematical topic
- synthesise findings from scientific sources into a coherent summary
- typeset mathematical documents using LaTeX
- collaborate with peers to produce a shared report
- compile a professional-standard integrated report
- reflect on personal development of programming and research skills
- articulate acquired skills for professional career applications
Year 2 · 2 core, 6 optional · 40 credits ≈ 400 hours
- Vector and Complex Calculus
What you learn (11)
- calculate gradient, divergence, curl and laplacian of scalar or vector fields
- perform dot and cross product operations on vectors
- apply algebraic and differential identities involving vector operators
- evaluate integrals of scalar fields over curves, surfaces and solids
- transform triple integrals using substitution or cylindrical and spherical coordinates
- apply the fundamental theorem of line integrals to evaluate vector field integrals
- apply Green's, Gauss' and Stokes' theorems to evaluate integrals
- apply the Cauchy-Riemann equations to test differentiability of complex functions
- determine whether a complex function is analytic
- compute the Laurent series expansion of a complex function
- apply the residue theorem to evaluate definite integrals
- 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
6 optional modules
- Probability and Markov Chains
What you learn (12)
- calculate joint and conditional probability distributions
- compute expectations derived from joint and conditional distributions
- derive generating functions for standard probability distributions
- use generating functions to find expectation and variance
- apply the weak law of large numbers to analyse random variable sequences
- apply the central limit theorem to deduce asymptotic behaviour of estimators
- assess unbiasedness and consistency of a sequence of estimators
- estimate distribution parameters using maximum likelihood methods
- estimate distribution parameters using the method of moments
- evaluate the quality of parameter estimators
- calculate absorption probabilities in discrete Markov chains
- interpret the meaning of a stationary distribution in context
- 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
- Classical Dynamics
What you learn (11)
- perform vector operations relevant to mechanics problems
- formulate many-body dynamics problems using vector methods
- apply different reference frames to dynamics problems
- explain the relationship between conservation laws and equations of motion
- investigate orbital properties arising from gravitational motion
- apply Lagrangian formulation to mechanical systems
- apply Hamiltonian formulation to mechanical systems
- relate Lagrangian and Hamiltonian frameworks to broader physical theories
- classify equilibrium points in one-dimensional dynamical systems
- analyse bifurcations in one-dimensional dynamical systems
- construct and interpret phase portraits for two-dimensional systems
- Quantum and Continuum Dynamics
What you learn (6)
- solve the wave equation in one and two dimensions
- describe properties of harmonic travelling waves and wave packets
- describe different types of ideal fluid flow
- solve the Schroedinger equation for simple quantum systems
- compute the energy spectrum of the harmonic oscillator
- compute the energy spectrum of the hydrogen atom
- 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
- Statistical Inference and Linear Models
What you learn (11)
- calculate confidence intervals for population parameters
- perform hypothesis tests using frequentist methods
- interpret results of confidence intervals and hypothesis tests
- adapt statistical procedures to new scenarios using underlying theory
- derive new statistical tools from first principles
- describe methods for fitting linear regression models
- explain techniques for assessing linear model adequacy
- explain procedures used for selecting variables in regression models
- justify the rationale behind variable selection approaches
- apply statistical methodology to analyse real datasets
- communicate statistical findings in a written report
Year 4 · 0 core, 27 optional
27 optional modules
- Communicating Mathematics in Education
What you learn (11)
- describe the main responsibilities of a class teacher in preparing and delivering lessons
- explain approaches to managing pupil behaviour in a classroom
- describe effective ways of liaising with teaching colleagues
- design lesson plans that meet defined criteria for teaching effectiveness
- create teaching materials suited to specific learning objectives
- explain mathematical concepts clearly to an individual pupil
- present mathematical ideas to a group of pupils in an accessible way
- demonstrate practical mathematical skills to pupils
- apply educational theory to practical mathematics teaching situations
- evaluate own classroom performance based on personal experience
- use feedback from pupils and teachers to improve teaching practice
- 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
- Time Series
What you learn (12)
- define key concepts underlying time series analysis
- apply stationarity concepts and transformations to real data
- fit arima and state space models to produce forecasts
- compute a correlogram and sample spectrum from data
- interpret correlogram and spectrum results
- derive mathematical properties of arima models
- select a suitable arima model for given data
- fit a chosen arima model using statistical software
- compute forecasts for various linear time series models
- fit state space models to time series data
- apply the kalman filter to estimate model states
- conduct spectral analysis of stationary time series
- 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
- Advanced Regression and Multivariate Analysis
What you learn (8)
- describe models used for multivariate data analysis
- describe models used for multilevel data analysis
- describe nonparametric statistical models
- apply key techniques for analysing multivariate and multilevel data
- apply nonparametric estimation methods to data sets
- select appropriate statistical techniques for different data types
- use R software to analyse multivariate data sets
- use R software to analyse multilevel data sets
- 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
- Mathematical Finance in Discrete Time
What you learn (11)
- describe the concepts underlying Markowitz portfolio theory
- analyse portfolio risk and return using Markowitz theory
- apply Markowitz theory to construct an efficient portfolio
- describe the structure and assumptions of the Capital Asset Pricing Model
- analyse asset pricing relationships derived from the Capital Asset Pricing Model
- apply the Capital Asset Pricing Model to estimate expected returns
- describe basic methods of compounding interest
- analyse the effects of different compounding methods on growth
- apply compounding calculations to financial problems
- analyse pricing outcomes under no-arbitrage conditions
- apply arbitrage pricing theory to value financial instruments
- Quantum Theory and Quantum Information
What you learn (7)
- describe the axiomatic structure of finite-dimensional quantum theory
- explain the concept of a quantum state and its measurement
- describe the role of probability in quantum mechanics
- use bra-ket notation to represent quantum states
- compare the informational power of quantum and classical systems
- construct simple quantum circuits
- describe the concept of a universal quantum computer
- Mathematical Ecology, Epidemiology and Evolution
What you learn (8)
- formulate dynamic mathematical models of ecological processes
- formulate mathematical models of disease transmission
- formulate mathematical models of evolutionary processes
- incorporate spatial effects into ecological and epidemiological models
- analyse mathematical models to predict dynamical behaviour
- explain interactions between ecological and evolutionary dynamics
- describe effects of randomness on eco-evolutionary and epidemiological models
- interpret mathematical results as biologically meaningful conclusions
- Mathematical Modelling: Nonlinearity, Uncertainty and Computational Methods
What you learn (9)
- analyse qualitative behaviour of low-dimensional ODE systems
- identify bifurcations and transitions such as Hopf bifurcations and tipping points
- use computational tools to simulate and visualise dynamical systems
- relate computational outputs to analytical findings
- apply computational methods to model high-dimensional nonlinear systems
- simulate stochastic and discrete models of reaction dynamics
- apply stochastic differential equations to real-world modelling problems
- explain complex model behaviour using insights from simpler analogues
- critically evaluate contemporary research studies related to module topics
- Fluids
What you learn (8)
- identify key characteristics of a given fluid flow
- derive governing equations for a fluid flow problem
- specify appropriate boundary conditions for fluid flow problems
- solve simple fluid flow equations using analytical methods
- distinguish between different fluid flow regimes
- explain theoretical principles underlying fluid flow dynamics
- perform exact calculations for standard fluid flow problems
- apply approximation methods to calculate fluid flow properties
- 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
- Relativity
What you learn (7)
- apply maxwell's equations to electrostatics problems
- apply maxwell's equations to electrodynamics problems
- solve problems involving static charges and steady currents
- solve problems involving electromagnetic waves
- describe the lorentz transformation
- apply the lorentz transformation to relativistic motion problems
- describe the relativistic formulation of electromagnetism
- Quantum Mechanics
What you learn (6)
- apply operator formalism to represent quantum states and observables
- explain wave function descriptions of quantum mechanics in position representation
- explain wave function descriptions of quantum mechanics in momentum representation
- describe the quantum harmonic oscillator model
- describe angular momentum theory in quantum mechanics
- identify quantum phenomena that differ from classical mechanics
- Mathematical Finance in Continuous Time
What you learn (2)
- explain the Black-Scholes formula for pricing options
- apply basic interest rate models to financial problems
- Partial Differential Equations
What you learn (8)
- solve basic first-order partial differential equations
- classify a second-order partial differential equation by type
- apply analytical methods to solve the wave equation
- apply analytical methods to solve the heat equation
- apply analytical methods to solve laplace and poisson equations
- analyse the error behaviour of finite-difference schemes for pdes
- evaluate the stability of finite-difference schemes for pdes
- compute numerical solutions of simple pdes using matlab
- 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
- Statistical Data Science
What you learn (6)
- explain the theoretical basis of key statistical models and tools
- discuss the strengths and limitations of different statistical approaches
- apply statistical techniques to analyse real datasets using R software
- select suitable machine learning or statistical methods for a given problem
- conduct independent statistical analysis to answer a research question
- present statistical findings clearly using tables and graphs
- Semigroup Theory
What you learn (7)
- describe fundamental concepts of semigroup theory
- apply Green's relations to analyse semigroups
- explain the significance of standard semigroup examples
- explain the function of structure theorems in semigroup theory
- apply Rees' theorem to completely 0-simple semigroups
- compare semigroup, inverse semigroup and group theories
- evaluate the significance of semigroup theory within mathematics
- Decision Theory and Bayesian Statistics
What you learn (6)
- describe fundamental concepts underlying Bayesian inference
- explain how Bayesian reasoning differs from classical inference
- apply Bayesian methods to standard statistical inference models
- use numerical techniques to compute Bayesian estimates
- apply credibility theory to estimate insurance risk
- apply Bayesian decision theory using loss functions
- Differential Geometry
What you learn (7)
- classify curves geometrically using curvature and torsion
- define the concept of a smooth surface
- differentiate smooth functions defined on a surface
- identify the tangent space of a smooth surface
- compute fundamental forms using local coordinates
- define different measures of surface curvature
- classify surface points by their curvature type
- Survival Analysis and Generalised Linear Models
What you learn (10)
- explain how exponential families unify models for differently scaled variables
- apply maximum likelihood methods to estimate generalised linear models
- apply logistic regression to analyse binary outcome data
- apply Poisson regression to analyse count data
- produce descriptive statistics summarising survival study data
- create graphical summaries representing survival data from various study designs
- estimate survival model parameters from censored data
- apply hypothesis testing techniques to draw conclusions about survival data
- use R software to carry out generalised linear model analysis
- use R software to carry out survival data analysis
- Lie Theory
What you learn (7)
- explain the correspondence between a Lie group and its Lie algebra
- state general structural properties of Lie algebras
- apply the concepts of solvable and semisimple Lie algebras to examples
- identify classical Lie groups from their defining properties
- define key properties of classical Lie groups
- identify linear representations of groups
- apply techniques for working with linear representations of groups
- Riemann Surfaces & Algebraic Curves
What you learn (5)
- apply the implicit function theorem to build complex charts for a curve
- construct algebraic curve examples of riemann surfaces
- calculate the genus of a given riemann surface
- compute the integral of a differential form over a riemann surface
- describe meromorphic functions constrained by a given divisor
- Prime Numbers & their Distribution
What you learn (5)
- apply diverse proof techniques used in number theory
- apply complex analysis methods to derive number theory results
- relate zeta function zeros to the distribution of primes
- explain the role of zeta zeros in the prime number theorem proof
- construct rigorous and logically precise mathematical arguments
“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, 24, 23
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 13% left | 95% | 200 |
| 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 £40,200 in fees over 4 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 2025-26
What do students say?
82%agreed the course was good overall (question 26)
NSS — a yearly survey of final-year students at every UK university; 60% of this course’s final year answered. Small groups can swing a lot year to year.
National Student Survey, via Discover Uni · 125 students answered
Highest: 92% agreed on question 3; lowest: 54% on question 24.
All questions26
| Question | Agree |
|---|---|
| Question 1 | 83% |
| Question 2 | 68% |
| Question 3 | 92% |
| Question 4 | 91% |
| Question 5 | 86% |
| Question 6 | 78% |
| Question 7 | 79% |
| Question 8 | 80% |
| Question 9 | 77% |
| Question 10 | 75% |
| Question 11 | 85% |
| Question 12 | 69% |
| Question 13 | 90% |
| Question 14 | 63% |
| Question 15 | 92% |
| Question 16 | 81% |
| Question 17 | 74% |
| Question 18 | 75% |
| Question 19 | 88% |
| Question 20 | 91% |
| Question 21 | 92% |
| Question 22 | 90% |
| Question 23 | 71% |
| Question 24 | 54% |
| Question 25 | 67% |
| Question 26 | 82% |
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.