Mathematics and Statistics MMathStat
A*A*A at A level, A* A* in Mathematics and Further Mathematics Or A*AA to include A* A; graduates earn a median £39,500 three years on.
Typical A level offer
A*A*A
A* A* in Mathematics and Further Mathematics Or A*AA to include A* A · 100% of entrants came with A levels · 90% stay on after year 1 · Warwick course page, Discover Uni
Year 13 · applying
What do you need to get in?
A*A*Atypical A level offer; the typical offer can be met by achieving any one of the following: a*a*a to include a* a* in mathematics and further mathematics or a*aa to include a* a (in any order) in mathematics and further math
Typical offer — the grades most applicants are asked for. Contextual offer: A*AB, for applicants from under-represented backgrounds.
Warwick course page, read 19 September 2026 · Discover Uni entry profile
- 1A* A* in Mathematics and Further Mathematics Or A*AA to include A* A
- 2A* A
- 3Useful subjects: A* in Mathematics and a in AS Further Mathematics Or A*AA to include A* in Mathematics and one of the following: STEP
Who actually got in: 100% with A levels. 55% arrived with 208 or more UCAS tariff points — roughly A*A*A or better. Based on 15 entrants.
UCAS tariff points — a points scale for grades: A* = 56, A = 48, so A*A*A = 160. Entrants’ totals include extra subjects.
Other qualifications4
| Qualification | Typical offer | Required subjects |
|---|---|---|
| IB | 39 pointsThe typical offer can be met by achieving any ONE of the following: 39 overall to include 7 in Higher Level Mathematics 'Analysis and Approaches' Or 38 overall to include 6 in Higher Level Mathematics | 6 in Higher Level Mathematics 'Analysis and Approaches' and one of the following: STEP; 6 in Higher Level Mathematics 'Applications and Interpretations' and one of the following: STEP |
| BTEC | —Level 3 BTECs will be considered alongside two A Levels including A Level Mathematics. | — |
| Advanced Highers | A1 in Advanced Higher Mathematics, A in one additional subject at Advanced HigheA1 in Advanced Higher Mathematics, A in one additional subject at Advanced Higher, and AAA in three additional Highers subjects. | — |
| Access | 45 Credits at Level 3, including Distinction in 33 Level 3 credits and Merit in We will consider applicants returning to study who are presenting a QAA-recognised Access to Higher Education Diploma on a case-by-case basis. Typically, we require 45 Credits at Level 3, including Di | — |
Years 1–4
What do you study?
8compulsory modules in year 1, 8 optional
Compulsory modules this year: mathematics & statistics 93% · transversal skills 5% · digital & ict skills 2%.
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.
Warwick course page · optional modules vary by year
Year 1 · 8 core, 8 optional · 90 credits ≈ 900 hours
- Sets and Numbers
What you learn (4)
- apply properties of standard number systems
- use set notation and quantifiers accurately
- describe functions and relations using formal notation
- apply different proof techniques to mathematical statements
- Mathematical Analysis 1
What you learn (7)
- describe the structure and properties of the real number system
- explain the concept of infinity and its use in mathematical analysis
- identify limits of sequences and series
- distinguish between conditional and absolute convergence of series
- apply convergence tests to determine series behaviour
- describe the properties of continuous functions
- explain the characteristics of absolutely continuous functions
- Linear Algebra
What you learn (13)
- define vector spaces and their properties
- determine whether a set of vectors is linearly independent
- identify a basis and calculate the dimension of a vector space
- explain the concept of a linear transformation
- apply linear transformations to vectors and spaces
- perform matrix manipulations using row and column operations
- apply matrix reduction techniques to solve systems of linear equations
- calculate determinants of n by n matrices
- compute cofactors and adjoint matrices
- explain how determinants and adjoints relate to solving linear systems
- compute eigenvalues and eigenvectors of a matrix
- interpret the geometric meaning of eigenvalues and eigenvectors
- describe linear transformations between euclidean spaces
- Mathematical Analysis 2
What you learn (10)
- determine whether a function is differentiable at a point
- compute higher-order derivatives of a function
- explain key properties of differentiable functions
- construct the Taylor series of a given function
- apply Taylor's theorem to estimate approximation error
- determine when a function can be represented by a power series
- construct the Riemann integral from first principles
- explain the theoretical basis of the Riemann integral's construction
- explain conditions guaranteeing integrability of continuous functions
- apply the Fundamental Theorem of Calculus to evaluate integrals
- Refresher Mathematics
What you learn (4)
- apply core A-level mathematical techniques to solve problems
- apply selected further mathematics concepts in problem solving
- explain the structure of mathematical definitions, theorems and proofs
- construct logical mathematical proofs using standard methods
- Introduction to Statistical Modelling
What you learn (14)
- formulate a probabilistic model for a given dataset
- derive a likelihood function corresponding to a simple model
- compute parameter estimates from observed data using a model
- quantify the uncertainty associated with estimated parameters
- compare predicted and observed data using graphical methods
- explain the assumptions underlying a statistical model
- interpret statistical model output to guide decisions
- write scripts in R to perform data analysis tasks
- produce data visualisations using the r environment
- discuss ethical issues in data collection and analysis
- evaluate ethical implications of communicating statistical results
- collaborate with peers to integrate diverse ideas into a shared task
- divide a complex task into manageable components for a team
- critique contributions from team members constructively
- Probability 1
What you learn (8)
- interpret standard mathematical notation
- apply problem solving techniques to mathematical tasks
- use visualisation methods to support mathematical reasoning
- construct concise and rigorous mathematical arguments
- calculate probabilities using appropriate methods
- interpret results of probability calculations
- explain key concepts of random variables
- interpret properties of probability distributions
- Probability 2
What you learn (5)
- calculate probabilities for random variables
- compute expectations of random variables
- explain fundamental concepts of probability theory
- explain theoretical concepts underlying probability distributions
- describe how randomness is incorporated into mathematical models
8 optional modules
- Design of Information Structures
What you learn (9)
- identify standard abstract data types used in programming
- describe how standard ADTs support common programming tasks
- assess the time and space complexity of simple algorithms
- evaluate the correctness of simple algorithms
- select appropriate algorithms to solve simple problems
- design user-defined abstract data types for a specific application
- develop algorithms associated with custom data structures
- apply software engineering principles within a larger software project
- use data structures as the foundation for software project design
- Introduction to Economics
What you learn (7)
- describe key economic behaviours and outcomes
- identify economic institutions and policies
- apply theoretical models to simplify economic problems
- explain core economic concepts and theories
- interpret economic data to identify trends and patterns
- select appropriate analytical tools based on data interpretation
- propose recommendations to support economic policy formulation
- Mathematical Programming 1
What you learn (8)
- identify business problems suited to optimisation modelling
- formulate a mathematical model representing a business optimisation problem
- solve mathematical optimisation problems using appropriate techniques
- list the underlying assumptions of key optimisation models
- critique the validity of assumptions made in optimisation models
- evaluate the limitations of different optimisation models
- explain the business implications of an optimal solution
- communicate quantitative results clearly to a business audience
- Programming for Scientists
What you learn (5)
- describe stages of software development from problem definition to tested code
- write programs in a high-level language using imperative constructs
- organise complex programs using encapsulation and abstraction techniques
- justify correctness of algorithms using informal reasoning arguments
- justify termination properties of a given program
- Differential Equations
What you learn (5)
- solve first order differential equations using standard methods
- solve linear second order differential equations
- solve coupled systems of first order differential equations
- solve simple difference equations using standard techniques
- interpret the qualitative behaviour of solutions to difference equations
- Mathematical Methods and Modelling 2
What you learn (7)
- describe scalar-valued and vector-valued functions of several variables
- apply coordinate transformations to mathematical problems
- explain the relationships between line, surface and volume integrals
- evaluate line, surface and volume integrals using integral theorems
- describe the Riemann integral of a multivariable function and its geometric meaning
- calculate integrals of functions over simple regions
- justify changes to area and volume elements under coordinate conversion
- Mathematical Methods and Modelling 1
What you learn (11)
- describe the stages of the modelling cycle
- formulate a simple mathematical model from a given problem
- analyse a simple mathematical model to assess its behaviour
- apply scaling and non-dimensionalisation to simplify a model
- apply linear stability analysis to identify dominant dynamics
- explain how underlying factors drive a system's dynamics
- solve first and second order ordinary differential equations
- interpret the qualitative behaviour of ode solutions
- solve simple difference equations
- relate difference equations to their continuous ode counterparts
- describe basic methods of numerical approximation
- Logic 1: Introduction to Symbolic Logic
What you learn (6)
- define what makes an argument logically valid
- distinguish methods for determining argument validity or invalidity
- formulate and assess sentences in propositional and first-order logic
- apply truth tables to evaluate argument validity
- construct formal proofs to establish argument validity
- devise counterexamples to disprove invalid arguments
Year 2 · 6 core, 18 optional · 60 credits ≈ 600 hours
- Mathematical Analysis 3
What you learn (7)
- compute contour integrals using cauchy's integral formulas
- apply cauchy's integral formulas to solve related problems
- distinguish uniform convergence from pointwise convergence of functions
- describe properties of the limit function of a convergent sequence
- apply the cauchy-riemann equations to test complex differentiability
- manipulate complex power series to represent analytic functions
- represent derivatives of multivariable functions as linear maps
- Stochastic Processes
What you learn (7)
- describe the concept of a markov chain
- apply conditional probability and matrix methods to discrete-time markov chains
- analyse long-run behaviour of markov chains including transience and recurrence
- determine equilibrium distributions of markov chains
- apply markov chain concepts to solve basic applied problems
- evaluate the suitability of markov chains as models for given situations
- present mathematical solutions using clear and logical argumentation
- Mathematical Methods for Statistics and Probability
What you learn (7)
- evaluate multiple integrals using suitable mathematical techniques
- solve optimisation problems by selecting appropriate methods
- examine properties of matrices and vector spaces
- apply spectral theory to identify structural features of matrices
- compare strategies for solving mathematical and probabilistic problems
- assess the effectiveness of methods used in multidimensional problems
- present mathematical solutions using clear and logical reasoning
- Probability for Mathematical Statistics
What you learn (7)
- derive properties of averages of random variables
- explain the significance of the central limit theorem in statistics
- describe joint and conditional probability distributions
- calculate conditional expectation and conditional variance
- derive properties of the multivariate normal distribution
- apply properties of distributions related to the normal distribution
- present mathematical solutions using clear and logical arguments
- Mathematical Statistics
What you learn (9)
- describe core concepts of statistical inference such as models, estimators and tests
- explain the uses and limitations of statistical inference techniques
- calculate maximum likelihood estimators for given statistical models
- apply likelihood ratios to compare competing statistical models
- construct hypothesis tests using likelihood ratio methods
- derive properties of sampling distributions for various estimators
- evaluate models using frequentist model selection criteria
- evaluate models using Bayesian model selection criteria
- present mathematical solutions using clear and logically structured arguments
- Linear Statistical Modelling with R
What you learn (11)
- define a normal linear model
- describe the assumptions underlying linear models
- derive statistical properties of estimators in linear models
- calculate confidence intervals for linear model parameters
- conduct hypothesis tests on linear model parameters
- fit regression models using R software
- check diagnostic adequacy of a fitted regression model
- improve and compare alternative regression models
- interpret the output and parameters of linear models
- evaluate the appropriateness of different linear models
- present statistical solutions using clear structured arguments
18 optional modules
- Metric Spaces
What you learn (11)
- define key properties of normed, metric and topological spaces
- apply theorems about metric and topological spaces to solve problems
- perform calculations involving distances and norms in metric spaces
- compare the open-set definition of continuity with other definitions
- apply continuity concepts to analyse open and closed sets
- describe fundamental concepts of compactness, connectedness and completeness
- apply theorems relating to compactness, connectedness and completeness
- perform calculations involving compactness, connectedness and completeness
- analyse relationships between compactness, connectedness and completeness
- evaluate how continuous maps preserve compactness, connectedness and completeness
- apply compactness, connectedness and completeness concepts to simple problems
- Modelling Nature's Nonlinearity
What you learn (4)
- demonstrate sensitivity of solutions to small changes in initial conditions or parameters
- explain how nonlinearity accounts for natural phenomena using mathematical models
- analyse nonlinear systems using analytical methods
- analyse nonlinear systems using numerical methods
- Combinatorics
What you learn (7)
- solve novel combinatorial problems using learned methods
- describe core definitions of enumerative combinatorics
- describe core definitions and theorems of graph theory
- describe core definitions and theorems of ramsey theory
- construct bijective proofs for numerical identities
- apply module concepts to analyse unfamiliar combinatorial structures
- adapt proof techniques from the module to new mathematical contexts
- Geometry
What you learn (8)
- perform analytic and algebraic calculations in euclidean geometry
- describe the geometric structure of the sphere
- describe the geometric structure of the hyperbolic plane
- compare metric properties of different geometric systems
- compare trigonometric relations across different geometries
- compare the behaviour of parallel lines across different geometries
- analyse abstract properties of lines and their incidence relations
- relate incidence properties to affine and projective geometry concepts
- Combinatorial Optimisation
What you learn (4)
- apply combinatorial structures to solve optimisation problems
- apply algorithmic techniques to solve specific combinatorial problems
- prove key results from combinatorial optimisation theory
- adapt optimisation methods to new combinatorial contexts
- Theory of ODEs
What you learn (7)
- identify conditions for existence and uniqueness of ODE solutions
- draw phase portraits for two-dimensional ODE systems
- classify critical points and trajectories of planar systems
- categorise orbit types and qualitative behaviours of non-linear odes
- describe solution behaviour near a critical point
- apply linearization techniques to non-linear differential equations
- apply ode methods to model physical or biological systems
- Introduction to Mathematical Biology
What you learn (5)
- construct simple models of biological phenomena from first principles
- analyse simple biological models using mathematical techniques
- derive biologically meaningful conclusions from mathematical analysis
- reconstruct standard models and key results for various biological systems
- describe the biological background of the systems studied
- Introduction to Number Theory
What you learn (5)
- decompose an integer into its prime factors
- use prime factorisations to deduce properties of integers
- solve linear and simultaneous congruence equations
- assess whether a number is a quadratic residue modulo another integer
- apply geometry of numbers techniques to solve Diophantine equations
- Multivariable Calculus
What you learn (10)
- define key concepts of functions of several variables
- explain core theorems of multivariable analysis
- perform calculations involving multivariable functions
- explain the Implicit Function Theorem and its conditions
- explain the Inverse Function Theorem and its conditions
- apply these theorems to solve multivariable problems
- describe properties and operations of vector fields
- apply the integral theorems of vector calculus to solve problems
- construct Taylor expansions for multivariable functions
- classify critical points using second order analysis
- Multilinear Algebra
What you learn (7)
- compute the jordan canonical form of a matrix
- explain the theoretical basis of jordan canonical form
- define functions of matrices
- calculate functions of matrices
- apply properties of bilinear forms to solve problems
- explain the concept of a tensor
- manipulate tensors using standard operations
- Groups and Rings
What you learn (4)
- describe core constructions in group theory
- describe core constructions in ring theory
- classify groups and rings according to given properties
- identify different types of ring from their defining properties
- Asymptotics and Integral Transforms
What you learn (13)
- describe the formal definition of an asymptotic series
- explain typical applications of asymptotic series
- identify regular and singular perturbation problems
- construct asymptotic series for algebraic equations using standard methods
- construct asymptotic approximations for integrals using standard methods
- construct asymptotic series for differential equations using standard methods
- apply matched asymptotic expansions to complex perturbation problems
- apply contour deformation to evaluate asymptotic integrals
- describe properties of fourier transforms
- apply fourier transform properties to solve differential and integral equations
- describe properties of laplace transforms
- apply laplace transform properties to solve differential and integral equations
- compare laplace and fourier transforms
- Numerical Methods and Computing
What you learn (6)
- derive fundamental numerical methods from mathematical principles
- analyse the accuracy and stability of numerical methods
- implement numerical algorithms using a scripting language
- test numerical implementations for correctness and performance
- design problem solving strategies for practical numerical problems
- evaluate the effectiveness of chosen solution strategies
- Games and Decisions
What you learn (7)
- compare mathematical foundations of alternative probability theories
- analyse philosophical basis of different probability approaches
- describe key characteristics of normative decision theory
- analyse decision-making models applied to real-world examples
- apply game theory to solve simplified mathematical games
- evaluate limitations of game theory in real-world scenarios
- present problem solutions using clear structured arguments
- Finance & Financial Reporting
What you learn (14)
- describe key principles underlying corporate governance
- explain the role of governance in corporate finance decisions
- prepare a statement of profit or loss for an organisation
- prepare a statement of financial position for an organisation
- prepare a cashflow statement incorporating basic tax principles
- analyse financial statements to identify key trends and issues
- draw conclusions from financial data for different stakeholder groups
- evaluate capital investment projects using appraisal techniques
- recommend an investment decision based on appraisal results
- describe the organisational structure of a company
- identify financial instruments used to raise finance and manage risk
- analyse how cost of capital relates to investment project characteristics
- analyse factors influencing a company's capital structure choices
- analyse factors influencing a company's dividend policy decisions
- Python for data-analytic tasks
What you learn (11)
- design a python program to solve a given problem
- write readable and valid python code
- build modular code structures for reuse
- verify code produces reliable results
- use python tools to manage and store data
- create data visualisations using python libraries
- apply python techniques to analyse datasets
- apply python techniques to solve optimisation problems
- document python code clearly for others to use
- produce reproducible outputs as python modules or packages
- collaborate with others to share coding work
- Visualisation and Communication of Data
What you learn (4)
- evaluate the quality and effectiveness of existing data visualisations
- produce improved versions of poorly designed visualisations using R
- select suitable visualisation types for specific data and tasks
- design original visualisations in R based on a dataset and specification
Year 3 · 1 core, 50 optional · 15 credits ≈ 150 hours
- Applied Statistical Modelling
What you learn (6)
- construct a statistical model for a real-world dataset
- interpret the output and parameters of a statistical model
- evaluate the adequacy and limitations of a statistical model
- collaborate with others on a shared statistical investigation
- deliver findings through an oral presentation
- produce a written report communicating statistical findings
50 optional modules
- Measure Theory
What you learn (4)
- explain the foundational concepts of abstract measure theory
- construct Lebesgue measure on the real line
- construct Lebesgue measure in n-dimensional Euclidean space
- outline advanced topics within measure theory
- Probability Theory
What you learn (8)
- identify different modes of convergence for sequences of random variables
- explain the relationships between different modes of stochastic convergence
- prove the Central Limit Theorem using characteristic functions
- apply the Central Limit Theorem to analyse practical problems
- describe basic properties of discrete-time martingales
- derive characteristics of simple random walks using martingale results
- explain concepts of independence and zero-one laws in probability
- apply zero-one laws to solve simple probability problems
- Applied Stochastic Processes
What you learn (5)
- formulate continuous-time Markov chain models for real-world problems
- apply fundamental theory to derive key properties of Markov chains
- calculate transition probabilities for finite-state Markov chains
- apply Markov chain methods to model queueing systems
- apply Markov chain methods to model epidemic spread
- Measure Theory for Probability
What you learn (7)
- construct probabilistic models for random experiments using probability space properties
- evaluate measure-theoretic techniques for analysing probability problems
- calculate probabilities of events using measure-theoretic methods
- formulate formal definitions of probability using rigorous mathematical reasoning
- compute probabilities, independence and expectation in varied problems
- apply modes of convergence of random variable sequences to probability problems
- justify the use of convergence results when computing integrals and expectations
- Applied Stochastic Processes with Advanced Topics
What you learn (5)
- formulate continuous-time Markov chain models for real-world problems
- apply basic theory to quickly determine equilibrium distributions of reversible chains
- calculate transition probabilities for Markov chains on finite state spaces
- apply Markov chain methods to model and analyse queueing systems
- apply Markov chain methods to model and analyse epidemic spread
- Mathematics of Cryptography
What you learn (13)
- explain the main algorithms used in public key cryptography
- apply public key cryptography methods to encrypt and decrypt messages
- describe common private key cryptography techniques
- explain the mathematical structure underlying elliptic curve cryptography
- compute elliptic curve cryptographic operations numerically
- explain how digital signature algorithms verify authenticity
- apply digital signature algorithms to sign and verify data
- explain the mathematical foundations of cryptocurrencies and blockchains
- describe the role of hash functions in securing blockchain data
- use python to implement cryptographic algorithms
- compose a structured mathematical project report
- collaborate effectively with peers to complete shared tasks
- deliver a clear oral presentation of technical material
- Waves and Metamaterials
What you learn (6)
- use transfer matrix methods to model wave behaviour in one-dimensional structures
- compute effective material properties for waves using asymptotic homogenisation techniques
- compute spectra of periodic operators using floquet-bloch theory
- explain how laplacian eigenvalues on a domain relate to wave behaviour
- describe basic properties of laplacian eigenvalues
- describe how mathematical methods inform the design of wave control devices
- Electromagnetism
What you learn (4)
- state Maxwell's equations in their standard forms
- derive Maxwell's equations from underlying physical laws
- apply Maxwell's equations to solve basic electromagnetic field problems
- interpret electromagnetic equations in terms of physical behaviour
- Rings and Modules
What you learn (12)
- explain why rings serve as a core structure in algebra
- describe a module as a generalisation of vector spaces and abelian groups
- construct direct sums, direct products and tensor products of modules
- identify simple modules using their defining properties
- apply Schur's lemma to analyse homomorphisms between simple modules
- describe semisimple and artinian modules with illustrative examples
- analyse endomorphism rings of semisimple and artinian modules
- explain the radical of a ring and its role in ring structure
- classify simple and semisimple artinian rings using examples
- apply the Artin-Wedderburn theorem to decompose semisimple rings
- describe the concept of a central simple algebra
- apply Wedderburn's and Frobenius' theorems to central simple algebras
- Topics in Mathematical Biology
What you learn (5)
- construct mathematical models of biological systems
- analyse dynamic behaviour of biological models
- apply ordinary and partial differential equations to biological problems
- apply probability theory to model biological phenomena
- apply branching processes and markov chains to biological models
- Matrix Analysis & Algorithms
What you learn (7)
- explain the theoretical foundations of matrix factorisation methods
- evaluate the computational cost of numerical algorithms
- assess the conditioning of numerical problems
- assess the stability of numerical algorithms
- implement matrix theory concepts using numerical software
- compare competing numerical methods for solving problems
- critique algorithmic design limitations in practical applications
- Algebraic Number Theory
What you learn (6)
- calculate norms of elements in algebraic number fields
- calculate discriminants of algebraic number fields
- determine the ring of integers of a number field using norms and discriminants
- factorize ideals into prime ideals in simple number field examples
- explain the proof of Minkowski's lattice theorem
- apply Minkowski's theorem to prove the four square theorem
- Fluid Dynamics
What you learn (3)
- explain how the governing equations of fluid motion are derived
- apply mathematical methods to find approximate solutions to fluid flow equations
- interpret mathematical solutions in terms of practical fluid flow problems
- Fractal Geometry
What you learn (5)
- describe explicit constructions of fractal sets
- identify different notions of dimension for fractal sets
- calculate estimates of fractal dimension values
- quantify the degree of fractal irregularity of a set
- relate fractal sets and dimension to other mathematical fields
- Galois Theory
What you learn (14)
- derive the formula for solving cubic equations by radicals
- outline the method for solving quartic equations by radicals
- identify the characteristic of a given field and its prime subfield
- represent a field extension as a vector space over its base field
- factorise polynomials over a field using ideal theory in k[x]
- prove that trisecting an arbitrary angle with straight-edge and compass is impossible
- prove the existence and uniqueness of splitting fields for a polynomial
- identify groups of field automorphisms associated with an extension
- apply the Galois correspondence to relate subgroups and subfields
- construct radical field extensions for given equations
- determine whether a group is soluble
- evaluate whether an equation is solvable by radicals using group solubility
- describe the structure of finite fields
- construct finite fields of given order
- Groups & Representations
What you learn (5)
- describe matrix representations of groups
- construct representations of a given group
- calculate character tables of groups
- state key theorems on groups and representations
- explain proofs of theorems on groups and representations
- Introduction to Topology
What you learn (4)
- identify topological invariants used to distinguish spaces
- apply topological invariants to differentiate between spaces
- describe methods for constructing spaces by gluing
- construct examples of spaces satisfying specified topological properties
- Theory of Partial Differential Equations
What you learn (3)
- classify different types of partial differential equations
- describe methods for proving existence and uniqueness for the Dirichlet problem
- describe key properties of harmonic functions
- Commutative Algebra
What you learn (14)
- explain the Hilbert basis theorem
- identify examples of Noetherian rings
- compute a Gröbner basis for a polynomial ideal
- determine the Spec of a given ring
- determine the zero locus of an ideal
- explain the proof of the Cayley-Hamilton theorem
- apply the Cayley-Hamilton theorem to prove Nakayama's lemma
- apply the Cayley-Hamilton theorem to prove the tower law and related module theorems
- determine algebraic integers using methods from finite extension theory
- compute the localisation of a ring
- compute the integral closure of a ring
- compute the dimension of a ring
- explain the proof of Hilbert's Nullstellensatz
- apply the Nullstellensatz to compute primary decomposition of polynomial ideals
- Functional Analysis II
What you learn (2)
- explain core concepts of functional analysis
- apply functional analysis techniques to problems in other mathematical fields
- Numerical Analysis & PDE's
What you learn (5)
- discretise elliptic partial differential equations using finite element methods
- discretise elliptic partial differential equations using finite difference methods
- evaluate error of discrete approximations to elliptic, parabolic and hyperbolic equations
- identify key issues in discretising different types of partial differential equations
- describe finite element and finite difference methods for discretising equations
- Markov Processes and Percolation Theory
What you learn (3)
- explain core concepts of markov processes and percolation theory
- apply standard techniques used in stochastic process analysis
- conduct independent research into a mathematical topic
- Set Theory
What you learn (8)
- construct injections and bijections to compare set sizes
- compare orderings of sets using explicit mappings
- interpret results using cardinal and ordinal arithmetic terminology
- outline the staged construction of the real numbers from first principles
- recognise the use of the Axiom of Choice within mathematical proofs
- justify when the Axiom of Choice can be avoided in arguments
- evaluate the strengths of Zermelo-Fraenkel set theory as a mathematical foundation
- evaluate the limitations of Zermelo-Fraenkel set theory as a mathematical foundation
- Manifolds
What you learn (8)
- explain key concepts underlying differentiable manifold theory
- manipulate differentiable objects using manifold techniques
- construct explicit charts to verify that a set forms a manifold
- apply the implicit function theorem to build manifolds
- describe the definition of the tangent space of a manifold
- perform constructions involving vector fields on manifolds
- manipulate differential forms on manifolds
- explain the statement and significance of stokes theorem
- Algebraic Topology
What you learn (7)
- define simplicial complexes
- define homology groups of simplicial complexes
- explain the geometric meaning of homology groups
- apply techniques to compute simplicial homology groups
- describe the extension of homology to singular homology
- evaluate the theoretical advantages of singular homology
- apply homology groups to analyse geometric problems
- Control Theory
What you learn (6)
- describe dynamical systems using mathematical equations
- apply methods to control system behaviour
- design feedback controllers using pole placement techniques
- analyse system stability using lyapunov's method
- design optimal controllers to minimise error or energy consumption
- identify practical problems suited to control theory applications
- Combinatorics II
What you learn (8)
- state key theorems of combinatorics covered in the module
- construct proofs of standard combinatorial results
- adapt established combinatorial methods to new problem contexts
- apply probabilistic reasoning to solve combinatorial problems
- apply algebraic reasoning to solve combinatorial problems
- use discrete analogues of geometric concepts in combinatorial analysis
- use discrete analogues of linear algebra concepts in combinatorial analysis
- derive approximate combinatorial results using the regularity method
- Mathematical Modelling with PDE
What you learn (5)
- distinguish microscopic from macroscopic modelling approaches
- rewrite model equations using dimensionless variables
- describe classical PDE models used in physics and continuum mechanics
- compute solutions to basic partial differential equation problems
- modify supplied Matlab code to solve modelling problems
- Approximation Theory and Applications
What you learn (6)
- explain key theorems of univariate approximation theory
- perform calculations related to univariate approximation methods
- describe fundamental concepts of multivariate approximation theory
- carry out calculations involving multivariate approximation techniques
- describe standard algorithms used in approximation theory
- apply approximation algorithms to worked examples
- Probability in Many Variables
What you learn (8)
- identify standard methods for bounding tail probabilities of random variables
- explain typical applications of tail-bounding techniques
- define Shannon entropy for discrete random variables
- apply entropy concepts to coding theorems
- apply Bernstein's and McDiarmid's inequalities to bound deviations
- derive the Poincare inequality for Gaussian random vectors
- apply exponential concentration bounds to Lipschitz functions of Gaussian vectors
- explain how Gaussian concentration supports slicing results for high-dimensional norms
- Mathematics of Machine Learning
What you learn (5)
- identify a suitable optimisation and modelling approach for a machine learning problem
- analyse optimisation algorithms by computational time and space complexity
- evaluate optimisation algorithms in terms of statistical accuracy
- implement a basic neural network architecture
- apply a neural network to a pattern recognition task
- Introduction to Group Theory
What you learn (10)
- explain the concept of a group acting on a set
- state the statement of Sylow's theorem
- construct multiple distinct proofs of Sylow's theorem
- apply Sylow's theorems and their corollaries to prove simplicity of alternating groups
- use Sylow's theorems to show that a given finite group is not simple
- describe the construction of direct and semidirect products of groups
- identify the isomorphism class of a given finite group
- explain the concept of a soluble group
- state the Jordan-Holder theorem
- construct a proof of the Jordan-Holder theorem
- Boolean Functions
What you learn (6)
- define the concept of a boolean function
- describe different representations of boolean functions
- state the statement of Post's theorem
- calculate the post class generated by a set of functions
- identify special classes of boolean functions such as quadratic or horn type
- explain the role of pseudo-boolean functions in optimisation problems
- Optimisation
What you learn (9)
- identify critical points of functions with several variables
- distinguish convex from nonconvex optimisation problems
- explain difficulties arising when solving nonconvex problems
- apply techniques to solve nonlinear optimisation problems
- apply techniques to solve nonconvex optimisation problems
- derive convergence rates for optimisation algorithms
- derive convergence guarantees for optimisation algorithms
- compare optimisation techniques based on their characteristics
- select an appropriate optimisation method for a given problem
- Knot Theory
What you learn (11)
- define the concept of a mathematical knot
- draw diagrams representing knots
- explain the theory underlying knot colourings
- calculate the colouring number of a given knot
- determine the colouring group associated with a knot
- explain the theoretical basis of knot polynomials
- calculate the Alexander polynomial of a knot
- calculate the Jones polynomial of a knot
- describe how bridges represent knot structures
- describe how plats represent knot structures
- describe how braids represent knot structures
- Bayesian Statistics and Decision Theory
What you learn (11)
- describe the construction and evaluation process for Bayesian models
- explain naive Bayes model assumptions and calibration issues
- perform prior to posterior updating for basic statistical models
- apply discrete prior to posterior inference to simple problems
- carry out beta and Dirichlet conjugate analysis
- explain the theoretical basis of utility theory
- apply utility theory to multi-attribute decision problems
- elicit a utility function from decision-maker preferences
- model complex systems using conditional independence structures
- explain how directed acyclic graphs structure probabilistic models
- estimate probabilities in DAGs using product Dirichlet conjugate distributions
- Designed Experiments
What you learn (8)
- differentiate between types of experimental design
- judge the efficiency and usefulness of a given design
- explain the fundamental concepts underlying designed experiments
- construct a design matrix for a simple experiment
- calculate parameter estimates from an experimental design matrix
- carry out an analysis of variance for standard experimental designs
- apply diagnostic checks to results of a designed experiment
- formulate an optimal or robust solution to a practical design problem
- Multivariate Statistics
What you learn (12)
- construct graphical displays of multivariate datasets
- interpret graphical displays to describe multivariate data patterns
- apply principal component analysis to reduce data dimensionality
- summarise high-dimensional datasets using derived components
- perform cluster analysis on multivariate data
- characterise identified subgroups within a population
- apply classification methods to assign individuals to groups
- evaluate discrimination techniques for group assignment accuracy
- conduct statistical inference for multivariate mean vectors
- construct confidence regions for multivariate parameters
- explain the use of confidence regions in comparing groups
- describe advanced multivariate statistical techniques covered in lectures
- Medical Statistics
What you learn (5)
- describe the contribution of statistical methods to medical research
- identify principles of good statistical practice in clinical studies
- apply generalised linear models to analyse medical data
- apply survival analysis techniques to medical data
- interpret results from generalised linear models and survival analysis
- Bayesian Forecasting and Intervention
What you learn (7)
- explain recurrence relations used in forecasting models
- calculate forecasting recurrences for specific special cases
- select a suitable forecasting model for a given simple scenario
- describe key dynamic linear models used for business forecasting
- apply intervention techniques to adjust forecasts using external information
- describe diagnostic methods for assessing dynamic linear models
- explain estimation techniques used within this model class
- Introduction to Mathematical Finance
What you learn (8)
- solve mean-variance portfolio optimisation problems
- describe the capital market line concept
- describe preference orders used by financial investors
- solve simple utility maximisation problems
- explain monetary measures of financial risk
- calculate value at risk for a given distribution
- calculate expected shortfall for a given distribution
- describe self-financing strategies and no-arbitrage conditions
- Topics in Data Science
What you learn (4)
- explain key concepts of the selected data science topics
- identify computational challenges arising in data analysis
- apply techniques designed to address data analysis challenges
- evaluate the application of selected data science topics
- Professional Practice of Data Analysis
What you learn (9)
- describe the stages of a statistical investigative cycle
- carry out a statistical investigation on a straightforward problem
- generate numerical summaries in R to support data analysis
- create graphical visualisations in R to support data analysis
- write a report presenting the findings of a statistical analysis
- present analysis results through an online format
- explain key approaches to teamwork and leadership
- identify common issues arising in team communication
- collaborate productively within a team on a shared task
- Generalised Linear Models for Regression and Classification
What you learn (9)
- identify a suitable regression model for a given response variable type
- select and fit a statistical model following a systematic procedure
- check whether a fitted model's assumptions hold
- quantify uncertainty in estimated model parameters
- quantify uncertainty in model predictions
- explain the core assumptions underlying generalised linear models
- extend a standard GLM to handle overdispersion
- explain the theoretical foundations of generalised linear models
- apply computational methods to fit generalised linear models
- Risk Theory
What you learn (7)
- describe how probability models represent general insurance risk
- explain methods of reinsurance used to hedge risk
- apply mathematical and statistical techniques to financial and insurance problems
- calculate claim distributions adjusted for policy limits and risk sharing
- calculate insurance premiums and reserves
- derive Bayesian estimators for insurance claim parameters
- derive credibility premiums for insurance pricing
- Machine Learning frameworks
What you learn (7)
- select appropriate statistical learning approach for a given problem
- design data-analytic pipelines for statistical learning tasks
- build machine learning and deep learning models using python frameworks
- write well-documented and reproducible python code
- share code and results collaboratively with others
- interpret results from a statistical analysis
- communicate analytical findings to diverse audiences
Year 4 · 1 core, 12 optional · 30 credits ≈ 300 hours
- Statistics Masters Dissertation
What you learn (7)
- produce an extended academic report with properly cited sources
- review and synthesise published literature on a chosen topic
- plan a structured research project in mathematics or statistics
- develop an advanced mathematical or statistical project to completion
- apply relevant theoretical methods drawn from the literature
- evaluate the suitability and interpretation of chosen methods
- present advanced research findings to a specialist audience
12 optional modules
- High Performance Computing
What you learn (6)
- explain the contribution of high performance computing to scientific and engineering work
- identify common paradigms used for parallel programming
- describe commonly used HPC platforms including cluster systems
- apply methods to measure the performance of HPC applications
- analyse the performance results of HPC applications
- describe how HPC management software handles administration, workload and resources
- Computational Biology
What you learn (12)
- describe high-throughput imaging methods for tissue slides
- identify key molecular biology concepts relevant to computational biology
- explain common algorithms used in bioinformatics
- describe algorithms for computing sequence alignments
- relate sequence alignment algorithms to current research applications
- identify common challenges in processing tissue images
- describe standard solutions to tissue image analysis problems
- apply image analysis techniques to computational pathology problems
- apply machine learning methods to computational pathology problems
- explain principles of fluorescence microscopy
- describe image-based modelling approaches for single cell dynamics
- apply mathematical techniques to model cellular dynamics
- Stochastic Analysis
What you learn (5)
- construct diffusion processes from Brownian motion
- apply Ito's stochastic integral to build diffusion models
- derive diffusions from stochastic differential equations
- apply Ito's formula to derive statistical properties of diffusions
- describe diffusion models used in mathematics, physics and finance
- Graph Theory
What you learn (5)
- state fundamental theorems and results in graph theory
- explain key mathematical concepts underlying graph theory
- differentiate between types of partial orders on graphs
- identify distinct structural properties of graphs
- apply basic techniques to decompose graphs
- Analytic Number Theory
What you learn (6)
- explain key properties of the Riemann zeta function
- derive the prime number theorem from zeta function theory
- relate zeros of the zeta function to exponential sums
- state the riemann hypothesis
- apply advanced analytic number theory concepts to novel problems
- integrate real and complex analysis techniques within number theory problems
- Epidemiology by Example
What you learn (14)
- adapt existing infection models using R
- create new infection models using R
- run simulations of infection models in R
- fit epidemiological models to data using frequentist methods
- fit epidemiological models to data using bayesian methods
- implement deterministic and stochastic epidemic models
- explain when deterministic or stochastic approaches are appropriate
- generate predictions from epidemiological models
- compare intervention strategies including adaptive approaches
- apply basic health economic concepts such as disability-adjusted life years
- apply health economic evaluation methods to modelling outputs
- communicate modelling results clearly to an audience
- assess the suitability of different models for real-world decisions
- evaluate how model assumptions affect outcomes
- Stochastic Methods in Finance
What you learn (3)
- describe how probability models represent financial market behaviour
- apply probability models to analyse financial problems
- explain the mathematical properties of Brownian motion
- Monte Carlo Methods
What you learn (7)
- describe a range of simulation methods including Markov chain Monte Carlo
- explain the procedures underlying Monte Carlo simulation
- design an MCMC algorithm tailored to a specified probability distribution
- implement an MCMC algorithm using computational tools
- assess the computational efficiency of a stochastic simulation algorithm
- judge the validity of inference results produced by a simulation algorithm
- apply Monte Carlo methods to solve scientific problems
- Advanced Topics in Data Science
What you learn (6)
- explain core concepts of the selected advanced data science topics
- identify computational challenges arising in data analysis
- apply techniques designed to address data analysis challenges
- evaluate the application of selected data science topics
- describe current research developments in selected data science topics
- critique recent research developments in selected data science topics
- Statistical Learning and Big Data
What you learn (9)
- explain core concepts of statistical learning
- critically discuss statistical learning methods and their limitations
- apply statistical learning tools to analyse data sets
- analyse key challenges in handling large-scale data sets
- discuss fundamental tools used for modelling big data
- implement prediction methods using data partitioning techniques
- evaluate the performance of partition-based predictive models
- apply sparsity and regularisation techniques to large data sets
- apply error rate control methods in high-dimensional data analysis
- Statistical Consulting
What you learn (11)
- select suitable statistical methods for a given dataset
- apply chosen statistical techniques to analyse data
- interpret the results of statistical analysis
- explain statistical concepts to non-specialist audiences
- present statistical findings clearly in written or spoken form
- use statistical software to perform data analysis
- evaluate the suitability of different software packages for analysis
- identify stages of team development
- define roles and responsibilities within a team
- apply critical thinking to solve practical statistical problems
- formulate evidence-based recommendations from analysis
“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?
£39,500median pay three years after graduating
Lower quarter£29k
Median£40k
Upper quarter£51k
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 325 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, 24, 23
Half of graduates earned between £29,000 and £51,000. Five years on, the median is £53,000. 70% were in work or further study 15 months after finishing; 87% of those in work were in professional or managerial jobs.
All outcome figures7
| Measure | Value | Based on |
|---|---|---|
| Continue after year 15% left | 90% | 20 |
| In work or study, 15 months on10% studying | 70% | 10 |
| Professional or managerial job | 87% | 160 |
| Pay 15 months on, median | £35,500 | 120 |
| Pay 3 years on, median | £39,500 | 325 |
| Pay 5 years on, median | £53,000 | 365 |
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.
Warwick 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.
National Student Survey 2025-26
What do students say?
92%agreed the course was good overall (question 26)
NSS — a yearly survey of final-year students at every UK university; 92% 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 1; lowest: 58% on question 25.
All questions26
| Question | Agree |
|---|---|
| Question 1 | 100% |
| Question 2 | 100% |
| Question 3 | 100% |
| Question 4 | 100% |
| Question 5 | 100% |
| Question 6 | 100% |
| Question 7 | 100% |
| Question 8 | 83% |
| Question 9 | 92% |
| Question 10 | 83% |
| Question 11 | 92% |
| Question 12 | 100% |
| Question 13 | 58% |
| Question 14 | 100% |
| Question 15 | 100% |
| Question 16 | 100% |
| Question 17 | 92% |
| Question 18 | 100% |
| Question 19 | 100% |
| Question 20 | 100% |
| Question 21 | 100% |
| Question 22 | 92% |
| Question 23 | 100% |
| Question 24 | 100% |
| Question 25 | 58% |
| Question 26 | 92% |
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 Warwick’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 Warwick is a trade mark of the university; sch.today is independent of it.