Course options
Key information
Duration: 3 years full time
UCAS code: LG11
Institution code: R72
Campus: Egham
The course
Economics and Mathematics (BSc)
Studying Economics and Mathematics at Royal Holloway means that you will learn from internationally renowned experts at two of the UK’s top ten teaching and research centres. Economic analysis relies increasingly on mathematical foundations and this joint degree combines the core program of both subjects. Optimal individual behaviour is found through the use of calculus, the dynamic properties of economics are studied with difference and differential equations, and important results in welfare economics are established from topological properties. Advanced mathematics and computing are vital for businesses in determining the best strategy. This degree provides the knowledge and transferable skills for a career in business or finance.
In your studies you will consider the analysis of individual behaviour and markets, with options in financial and industrial economics and other fields; you will learn how to analyse data and understand the fundamental properties of the mathematics used, from calculus to probability and statistics, graphs and optimisation and financial mathematics.
Our balanced approach to research and teaching guarantees high quality teaching from subject leaders, cutting edge materials and intellectually challenging debates. The course follows a coherent and developmental structure which is combined with an effective and flexible approach to study.
 In depth understanding of most recent economic theories.
 Work across two friendly departments.
From time to time, we make changes to our courses to improve the student and learning experience. If we make a significant change to your chosen course, we’ll let you know as soon as possible.
Course structure
Core Modules
Year 1
You will take the following modules in Economics:

Principles of Economics is a firstyear undergraduate module in how the economy works. The module is suitable for students with or without ALevel economics or equivalent. We will cover the basic theories of macroeconomics (that of the economy as a whole) and microeconomics (the behaviour of individuals, firms and governments and the interactions between them).
The module adopts the stateoftheart CORE approach (Curriculum Openaccess Resources in Economics) to teaching Principles of Economics. The approach has three pillars which we rely on throughout the module:
 Formulate a problem that our society is facing now or has faced in the past;
 Build a theory to explain and solve the problem;
 Evaluate the usefulness of the theory by using data observations and more novel theories.

In this module you will develop an understanding of information surrounding economic institutions, economic history, applied economics and policy & experimental & behavioural economics. In the seminars, you will discuss each topic and learn among other things how to write an essay, how to present, how to collect economic data, how to find relevant economic research, and how to think like an economist.

This module will describe the key principles of academic integrity, focusing on university assignments. Plagiarism, collusion and commissioning will be described as activities that undermine academic integrity, and the possible consequences of engaging in such activities will be described. Activities, with feedback, will provide you with opportunities to reflect and develop your understanding of academic integrity principles.
You will take the following modules in Mathematics:

In this module you will develop an understanding of the notion of probability and the basic theory and methods of statistics. You will look at random variables and their distributions, calculate probabilities of events that arise from standard distributions, estimate means and variances, and carry out t tests for means and differences of means. You will also consider the notions of types of error, power and significance levels, gaining experience in sorting a variety of data sets in a scientific way.

In this module, you will develop an understanding of the key concepts in Calculus, including differentiation and integration. You will learn how to factorise polynomials and separate rational functions into partial fractions, differentiate commonly occurring functions, and find definite and indefinite integrals of a variety of functions using substitution or integration by parts. You will also examine how to recognise the standard forms of firstorder differential equations, and reduce other equations to these forms and solve them.

In this module you will develop an understanding of the calculus functions of more than one variable and how it may be used in areas such as geometry and optimisation. You learn how to manipulate partial derivatives, construct and manipulate line integrals, represent curves and surfaces in higher dimensions, calculate areas under a curve and volumes between surfaces, and evaluate double integrals, including the use of change of order of integration and change of coordinates.

In this module you will develop an understanding of the fundamental algebraic structures, including familiar integers and polynomial rings. You will learn how to apply Euclid's algorithm to find the greatest common divisor of two integers, and use mathematical induction to prove simple results. You will examine the use of arithmetic operations on complex numbers, extract roots of complex numbers, prove De Morgan's laws, and determine whether a given mapping is bijective.

In this module you will develop an understanding of basic linear algebra, in particular the use of matrices and vectors. You will look at the basic theoretical and computational techniques of matrix theory, examining the power of vector methods and how they may be used to describe threedimensional space. You will consider the notions of field, vector space and subspace, and learn how to calculate the determinant of an n x n matrix.
Year 2
You will take the following modules in Economics:

In this module you will develop an understanding of the models of individual optimisation and their applications. You will look at the key determinants of an individual’s behaviour in a variety of circumstances and the behaviour of firms in different market environments, such as perfect competition, monopoly and oligopoly. You will consider how changing circumstances and new information influences the actions of the economic agents concerned, and examine the properties of competitive markets and the need for government intervention to correct market failures.

In this module you will develop an understanding of macroeconomics and macroeconomic policymaking. You will look at a variety of contemporary and historical macroeconomic events, and the differences between the short, medium and long run. You will consider why some countries are rich and some are poor, why different economies grow at different rates, and what determines economic growth and prosperity. You will examine the role of monetary and fiscal policy, its impact on the economy and its limitations. You will also analyse how taxation, budget deficits, and public debt affect the economy.

In this module you will develop an understanding of the behaviour of individuals and firms in the economy. You will look at models of individual optimisation and their applications, considering the key determinants of an individual’s behaviour in a variety of circumstances. You will examine the behaviour of firms in different market environments such as perfect competition, monopoly and oligopoly, and the factors which are important in shaping the decisions that firms make in each market environment. You will learn to manipulate and solve diagrammatic and algebraic models of microeconomics, analysing the properties of competitive markets and assessing the role of government intervention in correcting market failures.
You will take the following modules in Mathematics:

In this module you will develop an understanding of statistical modelling, becoming familiar with the theory and the application of linear models. You will learn how to use the classic simple linear regression model and its generalisations for modelling dependence between variables. You will examine how to apply nonparametric methods, such as the Wilxocon and KolmogorovSmirnov goodnessoffit tests, and learn to use the R open source software package.

In this module you will develop an understanding of the basic principles of the mathematical theory of probability. You will use the fundamental laws of probability to solve a range of problems, and prove simple theorems involving discrete and continuous random variables. You will learn how to forumulate an explain fundamental limit theorems, such as the weak law of large numbers and the central limit theorem.
Year 3
 All modules are optional
Optional Modules
There are a number of optional course modules available during your degree studies. The following is a selection of optional course modules that are likely to be available. Please note that although the College will keep changes to a minimum, new modules may be offered or existing modules may be withdrawn, for example, in response to a change in staff. Applicants will be informed if any significant changes need to be made.
Year 1

All modules are core
Year 2
Optional modules in Economics may include:

In this module you will develop an understanding of the economic principles underlying the working of national and international financial institutions. You will look at what a financial system is and does, and the distinct functions of each component. You will consider the key financial instruments and the relationship between assets, agents, and institutions, and learn to solve simple problems using quantitative and graphical tools. You will critically evaluate country differences and analyse the interdependencies and rapid change of the modern financial world.

In this module you will develop an understanding of the principalagent problem, the Coase theorem, theories of the firm, the role of transaction costs, moral hazard, adverse selection, and issues surrounding organisation, investment, governance and expansion of corporations. You will look the role of incentivisation and how conflicts of interests shape economic interactions. You will consider the role of transaction costs in determining the existence, scale and scope of firms, and examine why government regulation may be inferior to market solutions when dealing with externalities. You will also analyse the developments of AngloAmerican industrial and Japanese capitalism.

In this module you will develop an understanding of the basic theoretical models of personnel economics and how these can be applied to policy issues. You will look at contracts between firms and their workers, focussing on hiring, training, pay, job assignments, promotion, quits and dismissals, and pensions. You will consider the nature of labour contracts, and use statistical analysis to examine the empirical relevance of different types of contract.

In this module you will develop an understanding of the process of economic growth at the world level, and the sources of income and growth differences across countries. You will look at Piketty's work on income distribution and economic growth, Malthus' work on population and economic growth, and Solow's standard economic growth model. You will examine why some countries are rich and some are poor, and consider the differences between countries that explain economic success and failures.
Year 2
Optional modules in Mathematics may include:

In this module the vector calculus methods are applied to a variety of problems in the physical sciences, with a focus on electromagnetism and optics. On completion of the module, the student should be able to calculate relevant physical quantities such as field strengths, forces, and energy distributions in static as well as dynamical electromagnetic systems and be able to treat mathematically the interactions between moving electrical charges, magnets and optical fields.

In this module you will develop an understanding of the basic principles of the mathematical theory of probability. You will use the fundamental laws of probability to solve a range of problems, and prove simple theorems involving discrete and continuous random variables. You will learn how to forumulate an explain fundamental limit theorems, such as the weak law of large numbers and the central limit theorem.

In this module you will develop an understanding of the concepts arising when the boundary conditions of a differential equation involves two points. You will look at eigenvalues and eigenfunctions in trigonometric differential equations, and determine the Fourier series for a periodic function. You will learn how to manipulate the Dirac deltafunction and apply the Fourier transform. You will also examine how to solve differential equations where the coefficients are variable.

In this module you will develop an understanding of vectors and matrices within the context of vector spaces, with a focus on deriving and using various decompositions of matrices, including eigenvalue decompositions and the socalled normal forms. You will learn how these abstract notions can be used to solve problems encountered in other fields of science and mathematics, such as optimisation theory.

In this module you will develop an understanding of ring theory and how this area of algebra can be used to address the problem of factorising integers into primes. You will look at how these ideas can be extended to develop notions of 'prime factorisation' for other mathematical objects, such as polynomials. You will investigate the structure of explicit rings and learn how to recognise and construct ring homomorphisms and quotients. You will examine the Gaussian integers as an example of a Euclidean ring, Kronecker's theorem on field extensions, and the Chinese Remainder Theorem.

In this module you will develop an understanding of the algebraic structures known as groups. You will look at how groups represent symmetries in the world around us, examining examples that arise from the theory of matrices and permutations. You will see how groups are ubiquitous and used in many different fields of human study, including mathematics, physics, the study of crystals and atoms, public key cryptography, and music theory. You also will also consider how various counting problems concerning discrete patterns can be solved by means of group actions.

In this module you will develop an understanding of the language and concepts of linear algebra that are used within Mathematics. You will look at topics in linear algebra and the theory of modules, which can be seen as generalisations of vector spaces. You will learn how to use alternative matrix representations, such as the Jordan canonical or the rational canonical form, and see why they are important in mathematics.

In this module you will develop an understanding of the basic complex variable theory. You will look at the definitions of continuity and differentiability of a complex valued function at a point, and how CauchyRiemann equations can be applied. You will examine how to use a power series to define the complex expontential function, and how to obtain Taylor series of rational and other functions of standard type, determining zeros and poles of given functions. You will also consider how to use Cauchy's Residue Theorem to evaulate real integrals.

In this module you will develop an understanding of the convergence of series. You will look at the Weierstrass definition of a limit and use standard tests to investigate the convergence of commonly occuring series. You will consider the power series of standard functions, and analyse the Intermediate Value and Mean Value Theorems. You will also examine the properties of the Riemann integral.
Year 3
Optional modules in Economics may include:

The module is designed to broaden the economist’s statistical toolkit beyond the standard regression analysis and introduces modern techniques in machine learning. Topics covered will include kNearest Neighbours, decision trees, Linear Regression, Logistic Regression, Neural Networks, comparing prediction algorithms and Model Selection, Ensemble Methods, Unsupervised Learning including Clustering and Density Estimation. Weekly lab sessions where weekly assignments are covered will complement the theoretical material presented in the lecture.

In this module you will develop an understanding of the methods and models applied by economists in the analysis of firms and industries. You will learn how to manipulate these models and analytically solve problems relating to industrial economics. You will consider the applications of the models to important policy areas, exploring topics such as collusion, mergers, product differentiation and asymmetric information. You will also also examine the limitations of the theory.

The module aims to introduce the student to what factors affect corporate financial decisions. Particular emphasis is given to the concepts of Net Present Value and Risk. The learning outcomes include: Understand what the goals of a firm are; Understand how investments are valued (Internal rate of returns) in order to help with good financial planning); Understand the concepts of risk, agency costs and how they feed into financial decision making; Understand the process of price formation in financial markets; Understand venture capital and different types of debt finance and debt valuation, including leverage.

In this module you will develop an understanding of the wide range of fixed income securities and derivatives available to investors in the financial markets. You will look at the basic institutional features of derivatives markets, as well as the pricing of bonds and of derivative instruments and using them for hedging purposes. You will consider investment and trading strategies that use bonds and derivatives, and evaluate the use of bonds in immunising portfolios based on the bond's duration. You will also explore the features and uses of the most popular types of derivatives available today, including options, futures, forwards, and swaps.

In this module you will develop an understanding of the theoretical properties of different econometric estimation and testing procedures under various modelling assumptions. You will learn to formulate, estimate, test and interpret suitable models for the empirical study of economic phenomena. You will consider how to apply regression techniques and evaluate the appropriateness of each econometric estimation method under different data limitations.

In this module you will develop an understanding of the theoretical properties of different econometric estimation and testing procedures under various modelling assumptions. You will look at regression techniquies and learn how to apply relevant econometric and statistical methods to your own research. You will also evaluate the appropriateness of each of the economic estimation methods and the impact of consider data limirations.

In this module you will develop an understanding of the fragility of the financial system and its relevance to the current financial crisis. You will learn the economic meaning of the terms liquidity and solvency in the context of financial intermediaries. You will look at the models of equilibrium bank runs and consider the implications of imposing capital structure controls and liquidity control on financial intermediaries. You will also critically evaluate the links between financial crises and the macroeconomy.

In this module you will develop an understanding of how economic methods can be applied to environmental issues facing society. You will consider the difficulties arising in using economic analysis in environmental policy design and learn how to solve and manipulate a variety of diagrammatic and algebraic models in environmental economics. You will evaluate a number of realworld environmental policy problems and see how economic analysis has been applied in their solution.

In this module you will develop an understanding of the use of experiments to test economic theories. You will look at how individuals make decisions in markets, how individuals decide to spend money today or save it for future spending, the assumption of selfregarding preferences commonly made in standard economic models, and the ability to act rationally in a strategic environment. You will consider the issues raised by experimental design and critically evaluate the advantages and disadvantages of experimental methods.

In this module you will develop an understanding of the role of money in the economy. You will look at models where inflation shows persistence, the theory of monetary policy, monetary policy operating procedures and the central banking mechanisms. You will consider why inflation is persistent in the data and how the political forces affecting monetary policymaking may affect inflation.

This module will analyse ways in which mathematics can be applied to situations that involve making strategic decisions, and will apply game theory to a wide variety of situations including to examples from business and economics.

In this module you will develop an understanding of the mathematics of optimisation and of equilibrium models. You will look at the linkage between markets and Pareto optimality and consider the social outcomes that can be implemented in gametheoretic equilibrium. You will also examine the basic types of auctions and when and why they implement identical outcomes.

In this module you will develop an understanding of the principal techniques used in financial econometrics. You will look at why deviations from standard models are required to handle the peculiarities of financial data and consider how to interpret the theoretical techniques used in finance. You will also learn how to apply the techniques using standard econometric software packages such as STATA.

This module will analyse the economic issues of behaviour and outcomes in labour markets. It will focus on topics relating to labour supply and demand, wage formation and earnings inequalities, e.g.: Labour Demand; Labour Supply; Human Capital and Compensating Wage Differentials; Inequality in Earnings; Labour Mobility; Discrimination; Unemployment.

In this module you will develop an understanding of the different approaches to national economic policy. You will consider the economic advantages and disadvantages of globalisation and look at the effects of taxcutting, deregulation, privatisation, mixed economy, efficiency and income distribution.

In this module you develop an understanding of the effects of government policy upon the economy and the design of policy. You will look at empirical methods for policy evaluation and discuss research carried out in public economics, on topics such as income taxation, welfare support, behavioural responses, and social security.

In this module you will develop your understanding of important topics from economic history, covering periods of economic growth and wellbeing, agricultural and urban development, globalisation and migration, banking and monetary systems, and the Great Depression and recovery.

Data visualization techniques are central to both for revealing structure and patterns in the data at hand and for conveying these patterns to relevant audiences  it forms an integral part of the "data journey" from data acquisition, through analysis to product. The aim of the module is to provide students with the tools to be able tackle data of various structures and natures and select and implement appropriate and efficient tools data visualization and presentation in current standard software, including R. The content will introduce the notion of the psychology of data visualisation, outline key development tools and methods, describe how to achieve analytics storytelling for impact, distinguish between univariate and multivariate analysis, and other forms of data  e.g geographical and timeseries data  and structures including groups, hierarchies, networks and highdimensional data. Students will have significant handson experience with material and will investigate problems on their own, under the continued guidance of module leaders. By the end of the module, students will have the tools to be able to conduct their own presentation and visualization choices, and create a portfolio of highquality presentations of complex data structures.

In this module you will develop an understanding of the mathematical models used to study and analyse strategic interactions between agents. You will look at the fundamental concepts in game theory as applied to economics in general and microeconomics in particular. You will become familiar with basic equilibrium concepts such as Nash equilibrium and subgame perfect equilibrium, and be able to find equilibrium outcomes of simple games including the use of backward induction.

In this module you will develop an understanding of economic inequality. You will look at the factors that determine wage differentials among workers from a theoretical and empirical point of view. You will consider why similar workers are paid differently and examine how labour mobility can improve the allocation of workers to firms, enhance aggregate productivity, and reduce inequality.

The Dissertation provides you with the opportunity to undertake an extended piece of individual research work. You will use the econometric and statistical techniques you have learned about in the quantitative method modules taken earlier in the course.
Optional modules in Mathematics may include:

You will carry out a detailed investigation on a topic of your choosing, guided by an academic supervisor. You will prepare a written report around 7,000 words in length, and give a tenminute presentation outlining your findings.

In this module you will develop an understanding of how prime numbers are the building blocks of the integers 0, ±1, ±2, … You will look at how simple equations using integers can be solved, and examine whether a number like 2017 should be written as a sum of two integer squares. You will also see how Number Theory can be used in other areas such as Cryptography, Computer Science and Field Theory.

In this module you will develop an understanding the different classes of computational complexity. You will look at computational hardness, learning how to deduce cryptographic properties of related algorithms and protocols. You will examine the concept of a Turing machine, and consider the millennium problems, including P vs NP, with a $1,000,000 prize on offer from the Clay Mathematics Institute if a correct solution can be found.

In this module you will develop an understanding of quantum theory, and the development of the field to explain the behaviour of particles at the atomic level. You will look at the mathematical foundations of the theory, including the Schrodinger equation. You will examine how the theory is applied to one and three dimensional systems, including the hydrogen atom, and see how a probabilistic theory is required to interpret what is measured.

In this module you will develop an understanding of nonlinear dynamical systems. You will investigate whether the behaviour of a nonlinear system can be predicted from the corresponding linear system and see how dynamical systems can be used to analyse mechanisms such as the spread of disease, the stability of the universe, and the evolution of economic systems. You will gain an insight into the 'secrets' of the nonlinear world and the appearance of chaos.

In this module you will develop an understanding of the main priciples and methods of statstics, in particular the theory of parametric estimation and hypotheses testing.You will learn how to formulate statistical problems in mathematical terms, looking at concepts such as Bayes estimators, the NeymanPearson framework, likelihood ratio tests, and decision theory.

In this module you will develop an understanding of some of the descriptive methods and theoretical techniques that are used to analyse time series. You will look at the standard theory around several prototype classes of time series models and learn how to apply appropriate methods of times series analysis and forecasting to a given set of data using Minitab, a statistical computing package. You will examine inferential and associated algorithmic aspects of timeseries modelling and simulate time series based on several prototype classes.

In this module you will develop an understanding of the mathematics of communication, focusing on digital communication as used across the internet and by mobile telephones. You looking at compression, considering how small a file, such as a photo or video, can be made, and therefore how the use of data can be minimised. You will examine error correction, seeing how communications may be correctly received even if something goes wrong during the transmission, such as intermittent wifi signal. You will also analyse the noiseless coding theorem, defining and using the concept of channel capacity.

In this module you will develop an understanding of how financial markets operate, with a focus on the ideas of risk and return and how they can be measured. You will look at the random behaviour of the stock market, Markowitz portfolio optimisation theory, the Capital Asset Pricing Model, the Binomial model, and the BlackScholes formula for the pricing of options.

In this module you will develop an understanding of some of the techniques and concepts of combinatorics, including methods of counting, generating functions, probabilistic methods, permutations, and Ramsey theory. You will see how algebra and probability can be used to count abstract mathematical objects, and how to calculate sets by inclusion and exclusion. You will examine the applications of number theory and consider the use of simple probabilistic tools for solving combinatorial problems.

In this module you will develop an understanding of how error correcting codes are used to store and transmit information in technologies such as DVDs, telecommunication networks and digital television. You will look at the methods of elementary enumeration, linear algebra and finite fields, and consider the main coding theory problem. You will see how error correcting codes can be used to reconstruct the original information even if it has been altered or degraded.

In this module you will develop an understanding of the elementary ideas of electromagnetism. You will learn how to calculate electric fields and electric potentials from given fixed charge distributions and how to calculate magnetic fields and vector potentials from given steady current distributions. You will examine the magnetic effects of currents, including electromagnetic induction and displacement currents, and analyse the BiotSavart law and Ampere's law. You will examine Maxwell's equations, and the properties of electromagnetic waves in free space, as well as electric and magnetic dipoles and the electromagnetism of matter.

In this module you will develop an understanding of Field Theory. You will learn how to express equations such as X^{2017}=1 in a formal algebraic setting, how to classify finite fields, and how to determine the number of irreducible polynomials over a finitie field. You will also consider some the applications of fields, including ruler and compass constructions and why it is impossible to generically trisect an angle using them.

In this module you will develop an understanding of a range of methods for teaching children up to Alevel standard. You will act act as a role model for pupils, devising appropriate ways to convey the principles and concepts of mathematics. You will spend one session a week in a local school, taking responsibility for preparing lesson plans, putting together relevant learning aids, and delivering some of the classes. You will work with a specific teacher, who will act as a trainer and mentor, gaining valuable transferable skills.

In this module you will develop an understanding of a range methods used for testing and proving primality, and for the factorisation of composite integers. You will look at the theory of binary quadratic forms, elliptic curves, and quadratic number fields, considering the principles behind stateofthe art factorisation methods. You will also look at how to analyse the complexity of fundamental numbertheoretic algorithms.

In this module you will develop an understanding of efficient algorithm design and its importance for handling large inputs. You will look at how computers have changed the world in the last few decades, and examine the mathematical concepts that have driven these changes. You will consider the theory of algorithm design, including dynamic programming, handling recurrences, worstcase analysis, and basic data structures such as arrays, stacks, balanced search trees, and hashing.

In this module you will develop an understanding of how the theory of ideal fluids can be used to explain everyday phenomena in the world around us, such as how sound travels, how waves travel over the surface of a lake, and why golden syrup (or volcanic lava) flows differently from water. You will look at the essential features of compressible flow and consider basic vector analysis techniques.

In this module you will develop an understanding of how the RayleighRitz variational principle and perturbation theory can be used to obtain approximate solutions of the Schrödinger equation. You will look at the mathematical basis of the Period Table of Elements, considering spin and the Pauli exclusion principle. You will also examine the quantum theory of the interaction of electromagnetic radiation with matter.

In this module you will develop an understanding of the probabilistic methods used to model systems with uncertain behaviour. You will look at the structure and concepts of discrete and continuous time Markov chains with countable stable space, and consider the methods of conditional expectation. You will learn how to generate functions, and construct a probability model for a variety of problems.

In this module you will develop an understanding of how the behaviour of quantum systems can be harnessed to perform information processing tasks that are otherwise difficult, or impossible, to carry out. You will look at basic phenomena such as quantum entanglement and the nocloning principle, seeing how these can be used to perform, for example, quantum key distribution. You will also examine a number of basic quantum computing algorithms, observing how they outperform their classical counterparts when run on a quantum computer.

This module shows how mathematics is used by those who work in securities markets. The topics in the module are chosen to demonstrate important applications, and may include the basic asset pricing models, the general behaviour of markets, the theory of derivative securities and elements of portfolio theory.

This module continues the study of financial mathematics begun in Financial Mathematics I. In this module, students will develop a further understanding of the role of mathematics in securities markets. The topics in the module may include models of interest rates, elements of portfolio theory and models for financial returns.

In this module you will develop an understanding of how error correcting codes are used to store and transmit information in technologies such as DVDs, telecommunication networks and digital television. You will look at the methods of elementary enumeration, linear algebra and finite fields, and consider the main coding theory problem. You will see how error correcting codes can be used to reconstruct the original information even if it has been altered or degraded.

In this module you will develop an understanding of public key cryptography and the mathematical ideas that underpin it, including discrete logarithms, lattices and elliptic curves. You will look at several important public key cryptosystems, including RSA, Rabin, ElGamal encryption and Schnorr signatures. You will consider notions of security and attack models relevant for modern theoretical cryptography, such as indistinguishability and adaptive chosen ciphertext attack.

In this module you will develop an understanding of the algebraic structures known as groups. You will look at how groups represent symmetries in the world around us, examining examples that arise from the theory of matrices and permutations. You will see how groups are ubiquitous and used in many different fields of human study, including mathematics, physics, the study of crystals and atoms, public key cryptography, and music theory. You also will also consider how various counting problems concerning discrete patterns can be solved by means of group actions.

In this module you will develop an understanding of the language and concepts of linear algebra that are used within Mathematics. You will look at topics in linear algebra and the theory of modules, which can be seen as generalisations of vector spaces. You will learn how to use alternative matrix representations, such as the Jordan canonical or the rational canonical form, and see why they are important in mathematics.

In this module you will develop an understanding of geometric objects and their properties. You will look at objects that are preserved under continuous deformation, such as through stretching or twisting, and will examine knots and surfaces. You will see how colouring a knot can be used to determine whether or not it can be transformed into the unknot without any threading. You will also consider why topologists do not distinguish between a cup and a donut.

In this module you will develop an understanding of the algebraic structures known as groups. You will look at how groups represent symmetries in the world around us, examining examples that arise from the theory of matrices and permutations. Groups are ubiquitous and used in many different fields of human study, including mathematics, physics, the study of crystals and atoms, public key cryptography, and music theory.

Optimisation problems usually seek to maximise or minimise some function subject to a number of constraints; for example, how products should be shipped from factories to shops so as to minimise cost, or finding the shortest route a delivery driver should take. Linear programming is concerned with solving optimisation problems whose requirements are represented by linear relationships. This module introduces different types of optimisation problems and the appropriate approaches for solving each type of problem.
Teaching & assessment
Teaching is mostly by means of lectures and seminars, the latter providing a forum for students to work through problem sets and applications in a smaller and more interactive setting. Outside of scheduled teaching sessions, students work independently, or collaboratively, researching, reading and preparing for seminars.
Assessment is usually carried out by end of year examinations as well as class tests and assignments. Final year students can choose to complete an extended essay, which offers students the chance to conduct an original piece of research.
Entry requirements
A Levels: ABBBBB
Required subjects:
 Alevel Mathematics at grade A
 At least five GCSEs at grade A*C or 94 including English and Mathematics.
Your future career
An Economics and Mathematic degree at Royal Holloway will provides you with an excellent background for a career in business or finance, focusing on developing your quantitative and analytical skills.
We will help you to recognise your own strengths, skills and abilities so that you can make strong applications for your chosen job or further study. We also provide support through short dedicated careers modules, which include employability workshops, events and guest speakers.
 Get equipped with transferable skills such as numeracy problemsolving, computing and analytics
 Develop your professional network by attending workshops, events and guest speaker talks
 Dedicated short employability modules to help you in your career
Fees, funding & scholarships
Home (UK) students tuition fee per year*: £9,250
EU and international students tuition fee per year**: £27,500
Other essential costs***: There are no single associated costs greater than £50 per item on this course.
How do I pay for it? Find out more about funding options, including loans, scholarships and bursaries. UK students who have already taken out a tuition fee loan for undergraduate study should check their eligibility for additional funding directly with the relevant awards body.
*The tuition fee for UK undergraduates is controlled by Government regulations. The fee for the academic year 2024/25 is £9,250 and is provided here as a guide. The fee for UK undergraduates starting in 2025/26 has not yet been set, but will be advertised here once confirmed.
**This figure is the fee for EU and international students starting a degree in the academic year 2025/26.
Royal Holloway reserves the right to increase tuition fees annually for overseas feepaying students. The increase for continuing students who start their degree in 2025/26 will be 5%. For further information see fees and funding and the terms and conditions.
*** These estimated costs relate to studying this particular degree at Royal Holloway during the 2025/26 academic year and are included as a guide. Costs, such as accommodation, food, books and other learning materials and printing, have not been included.