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Home > Courses > Courses for 2017 > Undergraduate > Economics and Mathematics
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Economics and Mathematics BSc

UCAS code LG11
Year of entry 2017
View 2018 entry »
Course Length
3 years full time
Department Economics »
Mathematics »

 

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.

  • Excellent career prospects; both economics and mathematics have impressive employment record sand graduates’ starting salaries are amongst the highest in the country.
  • Flexibility to specialise in areas, including: economics in warfare, probability economics: financial econometrics, economic growth, rings and factorisation, complex variable and quantum theory II.
  • Quality research and teaching;one of only two Economics departments in the country placed in the top ten for both research and student satisfaction and the Mathematics department is 2nd in the UK for research impact (Research Assessment Exercise, 2014 and National Student Survey 2015).
  • Inspiring close community: Royal Holloway has a friendly and relaxing community environment where everyday interactions with student and staff from different departments and nationalities are a norm.

Core modules

Year 1

Economics: Principles of Economics

You will gain an understanding of the basic theories of microeconomics (the behaviour of individuals and firms) and macroeconomics (the behaviour of the economy as a whole and relations). In macroeconomics you will learn about circular flow; the goods market; money, bonds, income, and interest; fiscal policy; monetary policy; aggregate demand and supply; the Phillips curve; and long term growth. Discussions will take place on the current financial / debt crisis and the inflation-unemployment trade-off. In microeconomics you will learn about supply and demand; elasticity; theories of the consumer and the firm; and market structures. 

Economics: Post-Crisis Economics

This module covers economic institutions, economic history, post-crisis economics, and experimental and behavioural economics. You will be provided with an overview of each of these topics based on economic theory, followed by applications and relevant supporting data. You will discuss the topics and learn 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.

Mathematics: Principles of Statistics

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.

Mathematics: Calculus

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 first-order differential equations, and reduce other equations to these forms and solve them.

Mathematics: Functions of Several Variables

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.

Mathematics: Number Systems

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 comon 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.

Mathematics: Matrix Algebra

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 three-dimensional 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

Economics: Microeconomics

This module covers microeconomic analysis and policy. You will be introduced to analytical tools for studying the behaviour of individuals and firms across a range of economic settings. Topics include optimisation of consumer and firm problems; strategic interactions between firms in different non-competitive environments; choice under uncertainty; intertemporal decisions; and general equilibrium theory. For each topic, real world applications will show how models are used to examine complex issues, make predictions and prescribe policy. You will also study the features of economies that give rise to desirable market outcomes under different welfare criteria in conjunction with situations that result in market failures.

Economics: Macroeconomics

This module covers macroeconomic theory and policy. You will develop an understanding of macroeconomics at the intermediate level, considering the determinants of aggregate variables such as unemployment, investment, consumption, interest rates, inflation, exchange rates and the balance of trade (net exports). Topics include the goods and financial markets and the Hicks-Hansen (IS-LM) model in the short run; aggregate supply, the labour market and the Aggregate Demand – Aggregate Supply (AD-AS) model in the medium run; the Phillips curve, disinflation and Okun’s law; Economic growth and the Solow model; consumption and investment theory and the role of expectations in the IS-LM model; open economy, exchange rate regimes and Mundell-Fleming model; hyperinflation, financial crises and the euro zone; and fiscal policy, monetary policy, and the practice of policy making.

Mathematics: Statistical Methods

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 non-parameric methods, such as the Wilxocon and Kolmogorov-Smirnov goodness-of-fit tests, and learn to use the Minitab statistical software package.

Mathematics: Graphs and Optimisation

In this module you will develop an understanding of the basic concepts of graph theory and linear programming. You will consider how railroad networks, electrical networks, social networks, and the web can be modelled by graphs, and look at basic examples of graph classes such as paths, cycles and trees. You will examine the flows in networks and how these are related to linear programming, solving problems using the simplex algorithm and the strong duality theorem.

Year 3

All modules are optional

Optional modules

In addition to these mandatory course units there are a number of optional course units available during your degree studies. The following is a selection of optional course units that are likely to be available. Please note that although the College will keep changes to a minimum, new units may be offered or existing units 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

Only core modules are taken

Year 2

Economics: Financial Markets and Institutions

Economics: Insutrial Growth and Competition

Economics: Personnel Economics

Economics: Introduction to Economic Growth

Mathematics: Vector Analysis and Fluids

In this module you will develop an understanding of the concepts of scalar and vector fields. You examine how vector calculus is used to define general coordinate systems and in differential geometry. You will learn how to solve simple partial differential equations by separating variables, and become familiar with how these concepts can be appield in the field of dynamics of inviscid fluids.

Mathematics: Probability

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.

Mathematics: Ordinary Differential Equations and Fourier Analysis

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

Mathematics: Linear Algebra and Group Project

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 so-called 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. Working in small groups, you will put together different aspects of mathematics in a project on a topic of your choosing, disseminating your findings in writing and giving an oral presentation to your peers.

Mathematics: Rings and Factorisation

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.

Mathematics: Groups and Group Actions

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.

Mathematics: Further Linear Alegbra and Modules

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.

Mathematics: Complex Variable

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 Cauchy-Riemann 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.

Mathematics: Real Analysis

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

Economics: Industrial Economics

Economics: Financial Economics

Economics: Understanding Financial Crises

Economics: Environmental Economics

Economics: Economics of Warfare

Economics: Experimental Economics

Economics: Monetary Economics

Economics: Topics In Game Theory

Economics: Econometrics

Economics: Financial Econmetrics

Economics: Labour Economics

Economics: Philosophy of Economics

Economics: Public Economics

Economics: Topics in Economics History

Economics: Topics in Development Economics

Economics: Advanced Topics in Game Theory

Economics: Economics of Inequality

Mathematics: Number Theory

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.

Mathematics: Computational Number Theory

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 state-of-the art factorisation methods. You will also look at how to analyse the complexity of fundamental number-theoretic algorithms.

Mathematics: Complexity 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.

Mathematics: Priniciples of Algorithm Design

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, worst-case analysis, and basic data structures such as arrays, stacks, balanced search trees, and hashing.

Mathematics: Quantum Theory 2

In this module you will develop an understanding of how the Rayleigh-Ritz 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.

Mathematics: Non-Linear Dynamical Systems - Routes to Chaos

In this module, you will develop an understanding of non-linear dynamical systems. You will investigate whether the behaviour of a non-linear 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 non-linear world and the appearance of chaos, examining the significant developments achieved in this field during the final quarter of the 20th Century.

Mathematics: Inference

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 Neyman-Pearson framework, likelihood ratio tests, and decision theory.

Mathematics: Time Series Analysis

In this module you will develop an understanding of statistics by looking at the theory and methods used in time series analysis and forecasting. You will look at descriptive methods and theoretical techniques to analyse time series data from fields such as finance, economics, medicine, meteorology, and agriculture. You will learn to use the statistical computing package Minitab as a data analysis, calculation and graphical aid.

Mathematics: Applied Probability

In this module you will develop an understanding of the 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.

Mathematics: Channels

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.

Mathematics: Quantum Information and Coding

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 no-cloning 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.

Mathematics: Maths of Financial Markets

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 Black-Scholes formula for the pricing of options.

Mathematics: Advanced Financial Mathematics

In this module you will develop an understanding of the role of mathematics and statistics in securities markets. You will investigate the validity of various linear and non-linear time series occurring in finance, and apply stochastic calculus, including partial differential equations, for interest rate and credit analysis. You will also consider how spot rates and prices for Asian and barrier exotic options are modelled.

Mathematics: Combinatorics

In this module you will develop an understanding of some of the standard 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 includion an exclusion. You will examine the applications of number theory and consider the use of simple probabilistic tools for solving combinatorial problems.

Mathematics: Error Correcting Codes

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.

Mathematics: Cipher Systems

In this module you will develop an understanding of secure communication and how cryptography is used to achieve this. You will look at some of the historical cipher systems, considering what security means and the kinds of attacks an adversary might launch. You will examine the structure of stream ciphers and block ciphers, and the concept of public key cryptography, including details of the RSA and ElGamal cryptosystems. You will see how these techniques are used to achieve privacy and authentication, and assess the problems of key management and distribution.

Mathematics: Public Key Cryptography

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 cyptosystems, 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.

Mathematics: Application of Field Theory

"In this module you will develop an understanding of Field Theory. You will learn how to express equations such as X2017=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."

Mathematics: Groups and Group Actions

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.

Mathematics: Further Linear Alegbra and Modulus

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.

Mathematics: Topology

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.

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

Typical offers

Typical offers
A-levels ABB
Required/preferred subjects

Required: Grade A in Maths
At least five GCSE passes at grades A* to C.

Other UK Qualifications
International Baccalaureate 6,5,5 at Higher Level subjects including 6 in Higher Level Maths with 32 points overall
BTEC Extended Diploma Distinction, Distinction, Distinction in a relevant subject plus grade A in A-Level
BTEC National Extended Diploma Distinction, Distinction in a relevant subject plus grade A in A-Level Maths
BTEC National Extended Certificate Distinction in a relevant subject plus A-Level grades AB including grade A in Maths
Welsh Baccalaureate Requirements are as for A-levels where one non-subject-specified A-level can be replaced by the same grade in the Welsh Baccalaureate Advanced Level Core.
Scottish Advanced Highers AB incuding A in Maths plus Highers requirement
Scottish Highers AABBB plus Advanced Higher requirements
Irish Leaving Certificate H2,H2,H3,H3,H3 including H2 in Maths
Access to Higher Education Diploma Pass with at least 30 level 3 credits at Distinction and 15 level 3 credits at Merit PLUS A- level Maths grade A. 

Other UK qualifications

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International and EU entry requirements

Please select your country from the drop-down list below

English language
requirements

IELTS 6.5 overall with 6.0 in both Reading and Writing and no lower than 5.5 in every other subscore. For equivalencies please see here.

For more information about entry requirements for your country please visit our International pages. For international students who do not meet the direct entry requirements, we offer an International Foundation Year, run by Study Group at the Royal Holloway International Study Centre. Upon successful completion, students can progress on to selected undergraduate degree programmes at Royal Holloway, University of London.

A 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 students to recognise their own strengths, skills and abilities so that they can make strong applications for their chosen job or further study.  We also provide support through a dedicated careers programme which give you access to employability workshops, events and guest speakers.

  • Graduates are highly employable; 85% of economics graduates and 90% of mathematics graduates achieved full time employment or further study achieved within six months of graduation (Unistats 2015).
  • In recent years, graduates have launched careers in with a wide-range of organisations, including Royal Capital Management, Barclays Bank, and government departments such as the Department of Health. 
  • Graduates have entered roles as investment advisor, financial analyst, finance broker, government economist, chartered accountant, statistician, researcher and teacher.
  • Certain exemptions may be given by the Institute of Actuaries and other professional bodies to students who have taken appropriate course units as part of their Mathematics degree at Royal Holloway.

Home and EU students tuition fee per year 2017/18*: £9,250

International students tuition fee per year 2017/18**: £15,600

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.

*Tuition fees for UK and EU nationals starting a degree in the academic year 2017/18 will be £9,250 for that year. This amount is subject to the UK Parliament approving a change to fee and loan regulations that has been proposed by the UK Government. In the future, should the proposed changes to fee and loan regulations allow it, Royal Holloway reserves the right to increase tuition fees for UK and EU nationals annually. If relevant UK legislation continues to permit it, Royal Holloway will maintain parity between the tuition fees charged to UK and EU students for the duration of their degree studies.

**Royal Holloway reserves the right to increase tuition fees for international fee paying students annually. Tuition fees are unlikely to rise more than 5 per cent each year. For further information on tuition fees please see Royal Holloway’s Terms & Conditions.

***These estimated costs relate to studying this particular degree programme at Royal Holloway. Costs, such as accommodation, food, books and other learning materials and printing etc., have not been included.

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