Mathematics, Operational Research, Statistics and Economics (MORSE) MMorse
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 · 90% of entrants came with A levels · 85% 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: 90% with A levels, 10% with the IB. 55% arrived with 208 or more UCAS tariff points — roughly A*A*A or better. Based on 50 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?
10compulsory modules in year 1
Compulsory modules this year: mathematics & statistics 73% · green & sustainability 19% · transversal skills 4% · business & administration 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 · 10 core · 120 credits ≈ 1,200 hours
- 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
- 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
- Calculus 1
What you learn (6)
- describe the structure and properties of the real number system
- explain the concept of infinity as a mathematical symbol
- calculate limits of sequences and series
- distinguish between conditional and absolute convergence of series
- identify properties of continuous functions
- explain the concept of absolute continuity of functions
- Calculus 2
What you learn (6)
- define differentiability and higher-order derivatives of functions
- describe key properties of differentiable functions
- apply Taylor's theorem to approximate functions using series
- explain when a function can be represented by a power series
- apply fundamental properties of integrals to solve problems
- apply the fundamental theorem of calculus to evaluate integrals
- Vectors and Matrices
What you learn (10)
- explain the concept of a vector space
- 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
- perform row and column operations to reduce a matrix
- apply matrix reduction techniques to solve systems of linear equations
- calculate the determinant of an n by n matrix
- calculate eigenvalues and eigenvectors of a matrix
- interpret the geometric meaning of eigenvalues and eigenvectors
- describe linear transformations between euclidean spaces
- 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
Year 2 · 10 core, 8 optional · 135 credits ≈ 1,350 hours
- Economics 2
What you learn (17)
- describe macroeconomic policy instruments and objectives
- evaluate how economic theory informs policy effectiveness
- simplify complex economic problems using theoretical models
- communicate economic ideas in written and spoken form
- represent economic arguments graphically and mathematically
- apply theoretical models to underpin economic analysis
- explain the applications and limitations of economic models
- describe microeconomic policy measures
- critically analyse competing economic models and hypotheses
- present economic work to an audience
- conduct individual and collaborative research on economic topics
- use online and library resources to gather economic information
- formulate models to solve economic problems
- select appropriate economic models for policy problems
- produce concise analytical reports on economic issues
- explain key concepts in intermediate microeconomics
- explain key concepts in intermediate macroeconomics
- Mathematical Economics 1A
What you learn (2)
- explain the core tools and concepts of game theory
- apply game theory tools to solve varied economic problems
- Economics 2: Microeconomics
What you learn (15)
- explain core concepts of intermediate microeconomic theory
- apply theoretical models used in economic analysis
- communicate economic ideas in written and spoken form
- represent economic ideas using graphs and mathematical notation
- research an economic topic individually and in a group
- use online and library sources to gather economic information
- describe the design and impact of microeconomic policies
- simplify complex economic problems using theoretical models
- present findings from independent work to an audience
- analyse economic problems using formal models
- construct models to solve economic problems
- evaluate the applications and limitations of theoretical economic models
- critically compare competing economic models and hypotheses
- select suitable economic models for analysing policy problems
- produce concise analytical reports on economic issues
- Economics 2: Macroeconomics
What you learn (15)
- produce concise analytical reports on economic issues
- explain key concepts in intermediate macroeconomics
- communicate economic ideas in written and spoken form
- communicate economic ideas using graphs and equations
- apply theoretical models to economic analysis
- research an economic topic using online and library sources
- collaborate with peers on an economics research task
- simplify complex economic problems using theoretical models
- present own economic work to an audience
- formulate models to solve economic problems
- critique competing economic models and hypotheses
- select appropriate economic models for policy problems
- apply economic techniques to policy-related problems
- describe macroeconomic policies and their objectives
- evaluate theory-based analysis of policy effectiveness
- Mathematical Programming 2
What you learn (8)
- identify business problems suitable for optimisation modelling
- formulate business problems as mathematical optimisation models
- solve optimisation problems using spreadsheet software
- explain optimal solutions in business terms
- list the assumptions underlying key optimisation models
- critique the assumptions underlying key optimisation models
- evaluate the limitations of studied optimisation models
- evaluate the limitations of studied optimisation models
- 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
8 optional modules
- Mathematical Economics 1B
What you learn (4)
- explain the role of competitive markets in achieving pareto optimal allocations
- apply simple formal assumptions to analyse core economic problems
- identify limitations of established economic models
- describe recent developments in frontier economic research
- Simulation
What you learn (5)
- describe the nature and purpose of discrete-event simulation
- build a discrete-event simulation model for a given problem
- conduct experiments using a discrete-event simulation model
- analyse simulation data to identify patterns and results
- present analysed data clearly in reports or visual form
- 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
- 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
- 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 · 0 core, 47 optional
47 optional modules
- Mathematical Economics 2: Dynamics, Uncertainty & Asymmetrical Information
What you learn (8)
- evaluate strengths and weaknesses of mathematical methods in economic analysis
- explain key findings and unresolved issues within selected economic topics
- apply abstract reasoning to solve economic problems
- develop strategic and critical arguments to address economic questions
- present economic arguments clearly to an informed audience
- interpret feedback and questions from a critical audience
- analyse economic scenarios using logical reasoning
- analyse peer-reviewed economic research articles
- Econometrics 2: Time Series
What you learn (4)
- apply time series techniques to economic and financial data
- evaluate the validity of inferences drawn from time series results
- explain how data and economic theory interact in empirical inference
- critique empirical research papers in economics
- Industrial Economics 2: Strategy & Planning
What you learn (10)
- formulate models to analyse industrial organisation issues
- explain advanced theories of industrial organisation
- describe core concepts and methods in microeconomics and macroeconomics
- summarise current empirical debates in industrial economics research
- frame an economic problem using a researcher's perspective
- apply analytical reasoning to solve economic problems
- evaluate economic issues using critical and strategic thinking
- apply abstraction techniques to solve economic problems
- critically analyse module topics to formulate economic hypotheses
- evaluate how economic hypotheses are tested in published literature
- Topics in Financial Economics: Corporate Finance and Markets
What you learn (11)
- explain key concepts in corporate finance and markets
- describe characteristics of debt and equity instruments
- describe features of incomplete markets
- explain dividend policy and corporate governance practices
- simplify economic problems using basic theoretical methods
- present economic analysis in written and mathematical form
- research a finance topic individually and in groups using online and library sources
- formulate models to analyse and solve economic problems
- evaluate competing economic models and hypotheses critically
- select appropriate models to address policy-related financial problems
- produce concise analytical reports on financial issues
- Econometrics 2: Microeconometrics
What you learn (10)
- define a causal estimate in econometric analysis
- identify the conditions required to establish causal identification
- compare the theoretical strengths and weaknesses of causal estimation methods
- explain the empirical conditions needed to apply causal estimation methods
- analyse microeconomic datasets using suitable empirical techniques
- interpret the results generated by microeconometric analyses
- describe the characteristics of a robust policy evaluation
- design a robust evaluation strategy for a given scenario
- critique empirical research papers in microeconometrics
- prepare foundational skills for postgraduate microeconometric study
- Research in Policy Evaluation
What you learn (4)
- interpret published empirical studies on policy evaluation
- apply suitable techniques to carry out empirical research
- design an empirical research study on policy evaluation
- present findings of empirical research clearly
- Simulation
What you learn (5)
- describe the nature and purpose of discrete-event simulation
- build a discrete-event simulation model for a given problem
- conduct experiments using a discrete-event simulation model
- analyse simulation data to identify patterns and results
- present analysed data clearly in reports or visual form
- Operational Research for Strategic Planning
What you learn (8)
- identify methods and models used to support strategic decision making
- explain how different models support the development of strategy
- describe techniques for gathering and structuring data for strategy work
- apply methods that support divergent and convergent thinking in strategy formulation
- evaluate qualitative data inputs used within the strategy development process
- analyse complex information relevant to a strategic problem
- present analysed information in a clear and accessible format
- reflect on the use of operational research methods in practice
- Applied Optimization Methods
What you learn (4)
- apply numerical algorithms to solve unconstrained convex optimization problems
- apply numerical algorithms to solve constrained convex optimization problems
- apply heuristic methods to solve discrete optimization problems
- describe methods used for global optimization
- Problem Structuring: Facilitating Purposeful Analysis
What you learn (8)
- describe practical challenges encountered in real-world OR projects
- outline the sequential stages of an operational research project
- apply soft operational research tools to analyse real-world problems
- apply hard operational research tools to analyse real-world problems
- evaluate the real-world impact of operational research projects
- justify a chosen approach to an organisational problem
- solve quantitative organisational problems using spreadsheet models
- generate creative solutions to organisational problems using problem structuring methods
- Mathematical Game Theory: Combinatorial and Search Games
What you learn (6)
- describe game theoretic models used for combinatorial and search games
- explain methods used to analyse game theoretic models
- evaluate the relevance of game theoretic methods to given problems
- critique the limitations of game theoretic analysis methods
- identify real world problems that can be modelled as games
- distinguish problems suited to game theoretic analysis from those that are not
- Financial Optimisation
What you learn (9)
- define key concepts used in financial optimisation
- describe common optimisation methods applied in finance
- apply quantitative techniques to solve financial optimisation problems
- analyse difficulties in formulating financial optimisation models
- analyse difficulties in solving financial optimisation models
- select suitable methods for specific financial optimisation problems
- evaluate strengths and weaknesses of different optimisation approaches
- analyse financial case studies to identify underlying problems
- construct appropriate models representing case study problems
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Actuarial Models
What you learn (16)
- describe core principles underlying actuarial models
- describe general properties of stochastic processes
- classify stochastic processes into different types
- define a Markov chain
- apply a Markov chain to model transitions
- define a Markov jump process
- apply a Markov jump process to model transitions
- describe methods for estimating lifetime distributions
- describe the two-state single decrement model
- compare assumptions of two-state and random lifetime models
- derive maximum likelihood estimators for single decrement transition intensities
- describe methods to estimate age-dependent transition intensities
- describe tests for consistency of crude estimates with standard tables
- describe the process of graduating estimates
- explain heterogeneity in populations
- describe simple methods to address heterogeneity
- 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
- Actuarial Methods and Life Contingencies
What you learn (15)
- identify basic financial terminology
- interpret articles from the financial press
- define actuarial notation for assurance and annuity contracts
- explain relationships between actuarial symbols
- calculate values using actuarial notation
- apply life tables to calculate expected values of contracts
- calculate variances for simple assurance contracts using life tables
- calculate net premiums for assurance and annuity contracts
- calculate gross premiums for assurance and annuity contracts
- calculate premium reserves for assurance and annuity contracts
- estimate cash flows for contracts covering two lives
- apply multiple state models to multi-state contracts
- apply multiple decrement models to estimate contract cash flows
- evaluate the profitability of insurance contracts
- apply pricing methods to insurance contracts
- 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
- 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
Year 4 · 0 core, 28 optional
28 optional modules
- Quantitative Methods: Econometrics B
What you learn (8)
- explain core mathematical and statistical concepts used in economics modules
- apply quantitative concepts to economic problems
- explain advanced material required for empirical quantitative analysis
- describe theoretical foundations of modern econometrics
- apply applied econometric techniques to practical problems
- produce a rigorous empirical econometric analysis
- evaluate diagnostic and test statistics from empirical results
- judge the overall strength of empirical evidence presented
- Game Theory
What you learn (11)
- explain the concept of nash equilibrium
- explain the concept of rationalizability
- describe fundamental concepts of pure and applied game theory
- explain the concept of mixed strategy equilibrium
- explain the concept of correlated equilibrium
- apply bayesian nash equilibrium to industrial organisation problems
- apply bayesian nash equilibrium to political economy problems
- describe axiomatic approaches to bargaining theory
- describe strategic approaches to bargaining theory
- explain the structure of extensive form games
- analyse dynamic aspects of repeated games
- Applications of Data Science
What you learn (6)
- describe key statistical learning methods such as Lasso and SVM
- describe dimensionality reduction techniques including clustering and bagging
- explain the structure and function of neural networks for data analysis
- explain how statistical learning methods apply across varied practical contexts
- evaluate the suitability of different statistical methods for a given problem
- apply data science techniques to solve practical real-world problems
- Microeconomics B
What you learn (5)
- explain the mathematical techniques underlying microeconomic analysis
- apply microeconomic theory to practical economic situations
- explain key concepts of game theory
- explain principles of information economics
- analyse decision-making under uncertainty
- Macroeconomics B
What you learn (5)
- explain the theoretical foundations underlying macroeconomic analysis
- relate modern macroeconomic models to policy applications
- evaluate macroeconomic models against empirical evidence
- analyse theories of economic growth within modern macroeconomics
- critically assess modern macroeconomic concepts and arguments
- Information Theory and Coding
What you learn (9)
- explain the concept of entropy as a measure of information
- apply information theory concepts to analyse communication systems
- design a data compression technique using compression principles
- evaluate the efficiency of a data compression technique
- design an error correcting code for a given application
- evaluate the error performance of a coding scheme
- calculate the capacity of a communication channel using noisy channel analysis
- design a lossy compression implementation based on information theoretic principles
- analyse the performance of a lossy compression implementation
- Forecasting
What you learn (4)
- research a topic using appropriate literature sources
- present findings clearly at postgraduate standard
- explain the concepts underpinning common forecasting models
- evaluate criteria used to select appropriate forecasting models
- Supply Chain Analytics
What you learn (8)
- identify key challenges affecting supply chain design and operation
- explain various optimisation techniques used in supply chain problems
- apply optimisation methods to solve supply chain operation problems
- analyse an organisation's supply chain structure and processes
- assess risks present within a supply chain
- evaluate methods for mitigating supply chain risk
- analyse business case studies to identify underlying issues
- propose practical solutions to business problems identified in case studies
- Analytics in Practice
What you learn (5)
- structure a data mining project using a systematic methodology
- identify common challenges encountered in predictive modelling
- apply techniques to address predictive modelling challenges
- evaluate the quality of data visualisations
- detect potential data quality issues in a dataset
- Pricing Analytics
What you learn (5)
- explain how constrained capacity affects pricing decisions
- explain the role of opportunity cost in pricing decisions
- describe how customer response and demand uncertainty influence pricing
- compare different pricing opportunities and their distinguishing features
- evaluate appropriate strategies for addressing different pricing opportunities
- Data Management
What you learn (5)
- apply big data technologies to process large datasets
- explain core concepts and syntax of SQL
- write SQL queries to retrieve and manipulate data
- use software tools to manipulate and transform datasets
- apply normalization techniques to structure data
- Fourier Analysis
What you learn (2)
- derive fundamental properties of Fourier series and transforms
- apply convolution results with good kernels to solve partial differential equations
- 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
- Population Dynamics: Ecology & Epidemiology
What you learn (3)
- describe classical ecological and epidemiological models and their parameters
- apply classical models to address real-world ecological and epidemiological questions
- perform phase-plane analysis to assess steady states and their stability
- 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
- Brownian Motion
What you learn (6)
- apply the martingale property to derive wald's lemmas
- construct brownian motion from its defining properties
- explain the key properties of brownian motion
- apply brownian motion as a continuous-time continuous-state markov process
- derive convergence results using the random walk embedding
- translate one-dimensional brownian motion properties to higher dimensions
- 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
- Dynamic Stochastic Control
What you learn (7)
- formulate solution approaches for stochastic control and optimal stopping problems
- derive explicit solutions to simple Hamilton-Jacobi-Bellman equations
- compute numerical solutions to Hamilton-Jacobi-Bellman equations
- apply stochastic control methods to mathematical finance problems
- apply stochastic control methods to reinforcement learning problems
- select appropriate reinforcement learning algorithms for a given problem
- apply basic reinforcement learning algorithms to solve 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
- Applications of Stochastic Calculus in Finance
What you learn (8)
- explain the main stochastic models used for different asset classes
- discuss calibration and implementation issues of financial models
- apply stochastic calculus tools to understand new modelling developments
- describe practical challenges of implementing financial models commercially
- implement key stochastic finance models using appropriate techniques
- evaluate the appropriateness of a model for a specific financial product
- investigate recent developments in financial modelling techniques
- perform stochastic calculus calculations to implement unfamiliar models
- Advanced Trading Strategies
What you learn (5)
- calculate key variables used in trading strategy models
- explain the meaning of key variables in trading models
- apply mathematical techniques to solve trading strategy problems
- compare different modelling approaches used in trading strategies
- analyse strengths and weaknesses of alternative trading models
- Introduction to Advanced Probability
What you learn (6)
- evaluate measure-theoretic techniques for probability problems
- apply measure-theoretic methods to calculate event probabilities
- formulate formal definitions of probability concepts
- compute probabilities, independence and expectation for given scenarios
- apply probability concepts across varied situations
- evaluate data to construct probability models for random experiments
- Time Series
What you learn (9)
- apply techniques for analysing time series data
- evaluate different time series analysis techniques
- conduct exploratory analysis of time series data
- produce a descriptive analysis of time series data for applications such as finance
- derive statistical properties of linear time series models
- derive statistical properties of nonlinear time series models
- apply nonlinear modelling approaches to diverse time series situations
- design a time series modelling study including model selection and fitting
- apply forecasting and simulation methods to validate time series models
“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 24, 14, 13, 23
Half of graduates earned between £29,000 and £51,000. Five years on, the median is £53,000. 80% were in work or further study 15 months after finishing; 90% of those in work were in professional or managerial jobs.
All outcome figures7
| Measure | Value | Based on |
|---|---|---|
| Continue after year 110% left | 85% | 25 |
| In work or study, 15 months on5% studying | 80% | 15 |
| Professional or managerial job | 90% | 10 |
| 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?
97%agreed the course was good overall (question 26)
NSS — a yearly survey of final-year students at every UK university; 83% of this course’s final year answered. Small groups can swing a lot year to year.
National Student Survey, via Discover Uni · 30 students answered
Highest: 100% agreed on question 3; lowest: 77% on question 10.
All questions26
| Question | Agree |
|---|---|
| Question 1 | 97% |
| Question 2 | 90% |
| Question 3 | 100% |
| Question 4 | 100% |
| Question 5 | 93% |
| Question 6 | 100% |
| Question 7 | 90% |
| Question 8 | 90% |
| Question 9 | 90% |
| Question 10 | 77% |
| Question 11 | 90% |
| Question 12 | 90% |
| Question 13 | 80% |
| Question 14 | 80% |
| Question 15 | 97% |
| Question 16 | 100% |
| Question 17 | 100% |
| Question 18 | 97% |
| Question 19 | 93% |
| Question 20 | 93% |
| Question 21 | 93% |
| Question 22 | 100% |
| Question 23 | 90% |
| Question 24 | 83% |
| Question 25 | 79% |
| Question 26 | 97% |
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.