# Mathematics and Economics BSc (Hons)

- Course length: 3 years
- UCAS code: GL11
- Year of entry: 2021
- A-level requirements: ABB

## Honours Select

×This programme offers Honours Select combinations.

## Honours Select 100

×This programme is available through Honours Select as a Single Honours (100%).

## Honours Select 75

×This programme is available through Honours Select as a Major (75%).

## Honours Select 50

×This programme is available through Honours Select as a Joint Honours (50%).

## Honours Select 25

×This programme is available through Honours Select as a Minor (25%).

## Study abroad

×This programme offers study abroad opportunities.

## Year in China

×This programme offers the opportunity to spend a Year in China.

## Accredited

×This programme is accredited.

### Module details

### Programme Year One

After passing the first year, you have the flexibility of transfer to Economics if you wish, subject to approval.

#### Year One Compulsory Modules

##### Calculus I (MATH101)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**50:50 **Aims**1. To introduce the basic ideas of differential and integral calculus, to develop the basic skills required to work with them and to apply these skills to a range of problems.

2. To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.3. To introduce the notions of sequences and series and of their convergence.

**Learning Outcomes**(LO1) Understand the key definitions that underpin real analysis and interpret these in terms of straightforward examples.

(LO2) Apply the methods of calculus and real analysis to solve previously unseen problems (of a similar style to those covered in the course).

(LO3) Understand in interpret proofs in the context of real analysis and apply the theorems developed in the course to straightforward examples.

(LO4) Independently construct proofs of previously unseen mathematical results in real analysis (of a similar style to those demonstrated in the course).

(LO5) Differentiate and integrate a wide range of functions;

(LO6) Sketch graphs and solve problems involving optimisation and mensuration

(LO7) Understand the notions of sequence and series and apply a range of tests to determine if a series is convergent

(S1) Numeracy

##### Calculus II (MATH102)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**To discuss local behaviour of functions using Taylor’s theorem.

To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.**Learning Outcomes**(LO1) Use Taylor series to obtain local approximations to functions

(LO2) Obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables.

(LO3) Evaluate double integrals using Cartesian and Polar Co-ordinates.

(LO5)

##### Introduction to Linear Algebra (MATH103)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**• To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.

• To develop geometrical intuition in 2 and 3 dimensions.

• To introduce students to the concept of subspace in a concrete situation.

• To provide a foundation for the study of linear problems both within mathematics and in other subjects**Learning Outcomes**(LO1) Manipulate complex numbers and solve simple equations involving them, solve arbitrary systems of linear equations.

(LO2) Understand and use matrix arithmetic, including the computation of matrix inverses.

(LO3) Compute and use determinants.

(LO4) Understand and use vector methods in the geometry of 2 and 3 dimensions.

(LO5) Calculate eigenvalues and eigenvectors.

(S1) Numeracy

##### Introduction to Statistics (MATH162)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**•To introduce topics in Statistics and to describe and discuss basic statistical methods.

•To describe the scope of the application of these methods.**Learning Outcomes**(LO1) To know how to describe statistical data.

(LO2) To be able to use the Binomial, Poisson, Exponential and Normal distributions.

(LO3) To be able to perform simple goodness-of-fit tests.

(LO4) To be able to use an appropriate statistical software package to present data and to make statistical analysis.

(S1) Numeracy

(S2) Problem solving skills

(S3) IT skills

(S4) Communication skills

##### Principles of Microeconomics (ECON121)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**80:20 **Aims**This module aims to provide students with a clear foundation of the purpose, scope and topics of microeconomic analysis. Students will develop their ability to think critically and analytically, and understand how to frame real world problems in an economic model. This module forms the starting point for all future courses in Microeconomics.

This module also emphasizes the role of mathematics in economics.**Learning Outcomes**(LO1) Students will have the ability to understand, explain, analyse and solve core problems in microeconomics.

(LO2) Students will be able to practice and develop their mathematical techniques and understand the role of mathematical analysis in microeconomics.

(LO3) Students will be able to familiarise themselves with the principles of using an 'economic model' and how to model individual decision-making for both consumers and producers.

(LO4) Students will be able to apply their understanding of economic decision-making, optimisation and equilibrium to real world situations.

(S1) Problem solving skills

(S2) Numeracy

(S3) Communication skills

(S4) IT skills

##### Mathematical It Skills (MATH111)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**•To acquire key mathematics-specific computer skills.

•To reinforce mathematics as a practical discipline by active experience and experimentation, using the computer as a tool.

•To illustrate and amplify mathematical concepts and techniques.

•To initiate and develop problem solving, group work and report writing skills.

•To initiate and develop modelling skills.

•To develop team work skills.**Learning Outcomes**(LO1) After completing the module, students should be able to tackle project work, including writing up of reports detailing their solutions to problems.

(LO2) After completing the module, students should be able to use computers to create documents containing formulae, tables, plots and references.

(LO3) After completing the module, students should be able to use mathematical software packages such as Maple and Matlab to manipulate mathematical expressions and to solve simple problems.

(LO4) After completing the module, students should be able to better understand the mathematical topics covered, through direct experimentation with the computer.

(S1) Problem solving skills

(S2) Numeracy

(S3) Communication skills

(S4) IT skills

(S5) Teamwork

(S6) Adaptability

(S7) Leadership

(S8) Mathematical modelling skills

##### Principles of Macroeconomics (ECON123)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**40:60 **Aims**The aims of this module are:

To complement and build on Principles of Microeconomics and to provide a foundation for further studies in macroeconomics.

To introduce concepts and theories of economics which help understand changes in the macroeconomic environment.

To explain and analyse the formulation of government macroeconomic policy.**Learning Outcomes**(LO1) Explain the relationship between expenditures and national income and demonstrate how monetary and fiscal policies may be used to influence them

(LO2) Explain the behaviour of economic aggregates such as national income, inflation and unemployment over time

(LO3) Explain and assess government policy in a range of policy situations

(LO4) Explain the framework of national income accounting

(LO5) Use graphical and algebraic modelling to analyse the economy and economic policy

(LO6) Explain the interconnections between the markets for goods, money and labour

(LO7) Explain the principal influences on long-term growth and the short-run fluctuation in output around the long-run growth trend

(LO8) Locate, select and analyse information relevant to assessing the state of the economy and economic policy

(S1) Problem solving skills

(S2) Numeracy

(S3) Commercial awareness

(S4) Teamwork

(S5) Organisational skills

(S6) Communication skills

(S7) International awareness

(S8) Lifelong learning skills

(S9) Ethical awareness

##### Introduction to Finance (ACFI103)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**This module aims:

to introduce the students to finance.

to provide a firm foundation for the students to build on later on in the second and third years of their programmes, by covering basic logical and rational analytical tools that underpin financial decisions**Learning Outcomes**(LO1) Understand the goals and governance of the firm, how financial markets work and appreciate the importance of finance.

(LO2) Understand the time value of money.

(LO3) Understand the determinants of bond yields.

(LO4) Recognize how stock prices depend on future dividends and value stock prices.

(LO5) Understand net present value rule and other criteria used to make investment decisions.

(LO6) Understand risk, return and the opportunity cost of capital.

(LO7) Understand the risk-return tradeoff, and know the various ways in which capital can be raised and determine a firm's overall cost of capital.

(LO8) Know different types of options, and understand how options are priced.

(S1) Problem solving skills

(S2) Numeracy

(S3) Commercial awareness

(S4) Teamwork

(S5) Organisational skills

(S6) Communication skills

(S7) IT skills

(S8) International awareness

(S9) Lifelong learning skills

(S10) Ethical awareness

### Programme Year Two

Year two optional moduels: Choose one module from: ECON241, ECON211, ECON224

Choose three additional modules (one on semester 1 and two in semester 2) from: MATH201, MATH225, MATH227, MATH241, MATH243, MATH244, MATH261, MATH268, MATH224, MATH228, MATH247, MATH248, MATH260, MATH263, MATH264, MATH266.

#### Year Two Compulsory Modules

##### Econometrics 1 (ECON212)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**Econometrics is concerned with the testing of economic theory using real world data. This module introduces the subject by focusing on the principles of Ordinary Least Squares regression analysis. The module will provide practical experience via regular laboratory session. This module also aims to equip students with the necessary foundations in econometrics to successfully study more advanced modules such as ECON213 Econometrics II, ECON311 Methods of Economic Investigation: Time Series Econometrics and ECON312 Methods of Economic Investigation 2: Microeconometrics.

**Learning Outcomes**(LO1) Reinforce the understanding of fundamental principles of statistics, probability and mathematics to be used in the context of econometric analysis

(LO2) Estimate simple regression models with pen and paper using formulae and with the econometric software EViews8

(LO3) Understand the assumptions underpinning valid estimation and inference in regression models

(LO4) Formulate and conduct intervals of confidence and tests of hypotheses

(LO5) Evaluate the impact that changes in the unit of accounts of variables and changes in the functional form of equations may have upon the results of OLS and their interpretation

(LO6) Assess the goodness of results by means of appropriate tests and indicators

(LO7) Assess predictions

(LO8) Extend analysis to the context of multiple linear regression

(LO9) Use EViews7 to estimate simple linear regression models and multiple linear regression models

(S1) Problem solving skills

(S2) Numeracy

(S3) IT skills

##### Microeconomics 1 (ECON221)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**This module, in accordance with Microeconomics 2, aims to provide a solid foundation of intermediate level microeconomic theory. It develops and extends three of the topics introduced in Principles of Microeconomics, namely, Consumer Theory, Producer Theory and General Equilibrium. It prepares the students for the more advanced modules in the second and third year like Microeconomics 2 and Game Theory.

**Learning Outcomes**(LO1) Students will be able to demonstrate a thorough understanding of the core concepts and models used in consumer theory, producer theory and general equilibrium and an ability to apply these to arange of markets and settings.

(LO2) Students will be able to think and apply themselves analytically to problems in the above-mentioned topics.

(LO3) Students will be able to gain problem solving skills using verbal, diagrammatic and mathematical methods to problems in the above topics.

(LO4) Students will be able to have a critical perspective regarding the assumptions underlying microeconomics models.

(S1) Adaptability

(S2) Problem solving skills

(S3) Numeracy

(S4) Organisational skills

(S5) communication skills

(S6) IT skills

(S7) Lifelong learning skills

##### Microeconomics 2 (ECON222)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**70:30 **Aims**This module, following on from with Microeconomics 1, aims to provide a solid foundation of intermediate level microeconomic theory.

The module uses the theoretical foundations developed in the first semester and aims to extend the application of the skills acquired to more advanced topics such as welfare economics.

This module also aims to prepare students for the more advanced modules in the third year by introducing topics such as asymmetric information and game theory.**Learning Outcomes**(LO1) Have a thorough understanding of the core concepts and models used in Welfare Economics, Asymmetric Information, and Game Theory.

(LO2) To prepare students to think and apply themselves to analyse a range of problems in the three areas mentioned above.

(LO3) To develop problem solving skills using verbal, diagrammatic and mathematical methods to problems in the above topics.

(LO4) To deepen a critical perspective regarding the assumptions underlying microeconomics models.

(S1) Adaptability

(S2) Problem solving skills

(S3) Numeracy

(S4) Organisational skills

(S5) Communication skills

(S6) Lifelong learning skills

##### Macroeconomics I (ECON223)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**To extend the study of macroeconomic theory to the intermediate level.

To analyse the classical and Keynesian macroeconomic models, and their policy implications, in order to provide a context for subsequent developments in modern macroeconomics associated with monetarism, new classical and new Keynesian economics.**Learning Outcomes**(LO1) Students will be able to understand how employment, output, interest rate and the price level are determined in the classical model

(LO2) Students will be able to understand the origin of economic growth in the short runand in the long run

(LO3) Students will be able to understand the effects of fiscal and monetary policies in the IS-LM model

(LO4) Students will be able to understand the effects of fiscal and monetary policies under different exchange-rate regimes

(S1) Problem-solving skills

(S2) Numeracy

(S3) Organisational skills

(S4) Communication skills

(S5) International awareness

(S6) Lifelong learning skills

#### Year Two Optional Modules

##### Math201 - Ordinary Differential Equations (MATH201)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**•To familiarize students with basic ideas and fundamental techniques to solve ordinary differential equations.

•To illustrate the breadth of applications of ODEs and fundamental importance of related concepts.

**Learning Outcomes**(LO1) To understand the basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions.

(LO2) To know the elementary techniques for the solution of ODEs.

(LO3) To understand the idea of reducing a complex ODE to a simpler one.

(LO4) To be able to solve linear ODE systems (homogeneous and non-homogeneous) with constant coefficients matrix.

(LO5) To understand a range of applications of ODE.

(S1) Problem solving skills

(S2) Numeracy

##### Vector Calculus With Applications in Fluid Mechanics (MATH225)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**50:50 **Aims**To provide an understanding of the various vector integrals, the operators div, grad and curl and the relations between them. To give an appreciation of the many applications of vector calculus to physical situations. To provide an introduction to the subjects of fluid mechanics and electromagnetism.

**Learning Outcomes**(LO1) After completing the module students should be able to: - Work confidently with different coordinate systems. - Evaluate line, surface and volume integrals. - Appreciate the need for the operators div, grad and curl together with the associated theorems of Gauss and Stokes. - Recognise the many physical situations that involve the use of vector calculus. - Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and inviscid fluid flow. All learning outcomes are assessed by both examination and course work.

##### Mathematical Models: Microeconomics and Population Dynamics (MATH227)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**50:40 **Aims**•To provide an understanding of the techniques used in constructing, analysing, evaluating and interpreting mathematical models.

•To do this in the context of two non-physical applications, namely microeconomics and population dynamics.

•To use and develop mathematical skills introduced in Year 1 - particularly the calculus of functions of several variables and elementary differential equations.**Learning Outcomes**(LO1) After completing the module students should be able to: - Use techniques from several variable calculus in tackling problems in microeconomics. - Use techniques from elementary differential equations in tackling problems in population dynamics. - Apply mathematical modelling methodology in these subject areas. All learning outcomes are assessed by both examination and course work.

##### Metric Spaces and Calculus (MATH241)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**50:50 **Aims**To introduce the basic elements of the theory of metric spaces and calculus of several variables.

**Learning Outcomes**(LO1) After completing the module students should: Be familiar with a range of examples of metric spaces. Have developed their understanding of the notions of convergence and continuity. Understand the contraction mapping theorem and appreciate some of its applications. Be familiar with the concept of the derivative of a vector valued function of several variables as a linear map. Understand the inverse function and implicit function theorems and appreciate their importance. Have developed their appreciation of the role of proof and rigour in mathematics.

(S1) Problem solving skills

##### Complex Functions (MATH243)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**To introduce the student to a surprising, very beautiful theory having intimate connections with other areas of mathematics and physical sciences, for instance ordinary and partial differential equations and potential theory.

**Learning Outcomes**(LO1) To understand the central role of complex numbers in mathematics;.

(LO2) To develop the knowledge and understanding of all the classical holomorphic functions.

(LO3) To be able to compute Taylor and Laurent series of standard holomorphic functions.

(LO4) To understand various Cauchy formulae and theorems and their applications.

(LO5) To be able to reduce a real definite integral to a contour integral.

(LO6) To be competent at computing contour integrals.

(S1) Problem solving skills

(S2) Numeracy

(S3) Adaptability

##### Linear Algebra and Geometry (MATH244)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**50:48 **Aims**To introduce general concepts of linear algebra and its applications in geometry and other areas of mathematics.

**Learning Outcomes**(LO1) To understand the geometric meaning of linear algebraic ideas.

(LO2) To know the concept of an abstract vector space and how it is used in different mathematical situations.

(LO3) To be able to apply a change of coordinates to simplify a linear map.

(LO4) To be able to work with matrix groups, in particular GL(n), O(n) and SO(n),.

(LO5) To understand bilinear forms from a geometric point of view.

(S1) Problem solving skills

(S2) Numeracy

(S3) Adaptability

##### Introduction to Methods of Operational Research (MATH261)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**50:50 **Aims**The aims of the module are to develop an understanding of how mathematical modelling and operational research techniques are applied to real-world problems and to gain an understanding of linear and convex programming, multi-objective problems, inventory control and sensitivity analysis.

**Learning Outcomes**(LO1) To understand the operational research approach.

(LO2) To be able to apply standard methods of operational research to a wide range of real-world problems as well as to problems in other areas of mathematics.

(LO3) To understand the advantages and disadvantages of particular operational research methods.

(LO4) To be able to derive methods and modify them to model real-world problems.

(LO5) To understand and be able to derive and apply the methods of sensitivity analysis.

(LO6) To understand the importance of sensitivity analysis.

(S1) Adaptability

(S2) Problem solving skills

(S3) Numeracy

(S4) Self-management readiness to accept responsibility (i.e. leadership), flexibility, resilience, self-starting, initiative, integrity, willingness to take risks, appropriate assertiveness, time management, readiness to improve own performance based on feedback/reflective learning

##### Operational Research: Probabilistic Models (MATH268)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To introduce a range of models and techniques for solving under uncertainty in Business, Industry, and Finance.

**Learning Outcomes**(LO1) The ability to understand and describe mathematically real-life optimization problems.

(LO2) Understanding the basic methods of dynamical decision making.

(LO3) Understanding the basics of forecasting and simulation.

(LO4) The ability to analyse elementary queueing systems.

(S1) Problem solving skills

(S2) Numeracy

##### Introduction to the Methods of Applied Mathematics (MATH224)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**•To provide a grounding in elementary approaches to solution of some of the standard partial differential equations encountered in the applications of mathematics.

•To introduce some of the basic tools (Fourier Series) used in the solution of differential equations and other applications of mathematics.

**Learning Outcomes**(LO1) After completing the module students should: - be fluent in the solution of basic ordinary differential equations, including systems of first order equations:- be familiar with the concept of Fourier series and their potential application to the solution of both ordinary and partial differential equations:- be familiar with the concept of Laplace transforms and their potential application to the solution of both ordinary and partial differential equations: - be able to solve simple first order partial differential equations: - be able to solve the basic boundary value problems for second order linear partial differential equations using the method of separation of variables.

##### Classical Mechanics (MATH228)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To provide an understanding of the principles of Classical Mechanics and their application to dynamical systems.

**Learning Outcomes**(LO1) To understand the variational principles, Lagrangian mechanics, Hamiltonian mechanics.

(LO2) To be able to use Newtonian gravity and Kepler's laws to perform the calculations of the orbits of satellites, comets and planetary motions.

(LO3) To understand the motion relative to a rotating frame, Coriolis and centripetal forces, motion under gravity over the Earth's surface.

(LO4) To understand the connection between symmetry and conservation laws.

(LO5) To be able to work with inertial and non-inertial frames.

(S1) Applying mathematics to physical problems

(S2) Problem solving skills

##### Commutative Algebra (MATH247)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To give an introduction to abstract commutative algebra and show how it both arises naturally, and is a useful tool, in number theory.

**Learning Outcomes**(LO1) After completing the module students should be able to: • Work confidently with the basic tools of algebra (sets, maps, binary operations and equivalence relations). • Recognise abelian groups, different kinds of rings (integral, Euclidean, principal ideal and unique factorisation domains) and fields. • Find greatest common divisors using the Euclidean algorithm in Euclidean domains. • Apply commutative algebra to solve simple number-theoretic problems.

##### Geometry of Curves (MATH248)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To introduce geometric ideas and develop the basic skills in handling them.

To study the line, circle, ellipse, hyperbola, parabola, cubics and many other curves.

To study theoretical aspects of parametric, algebraic and projective curves.

To study and sketch curves using an appropriate computer package.

**Learning Outcomes**(LO1) After completing this module students should be able to use a computer package to study curves and their evolution in both parametric and algebraic forms.

(LO2) After completing this module students should be able to determine and work with tangents, inflexions, curvature, cusps, nodes, length and other features.

(LO3) After completing this module students should be able to determine the position and shape of some algebraic curves including conics.

(S1) Problem solving skills

(S2) Numeracy

(S3) IT skills

(S4) Adaptability

##### Financial Mathematics (MATH260)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**To provide an understanding of basic theories in Financial Mathematics used in the study process of actuarial/financial interest.

To provide an introduction to financial methods and derivative pricing financial instruments in discrete time set up.

**Learning Outcomes**(LO1) Know how to optimise portfolios and calculating risks associated with investment.

(LO2) Demonstrate principles of markets.

(LO3) Assess risks and rewards of financial products.

(LO4) Understand mathematical principles used for describing financial markets.

##### Statistical Theory and Methods I (MATH263)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**75:25 **Aims**To introduce statistical methods with a strong emphasis on applying standard statistical techniques appropriately and with clear interpretation.

To introduce students to an appropriate statistical software package.

**Learning Outcomes**(LO1) To have a conceptual and practical understanding of a range of commonly applied statistical procedures.

(LO2) To have developed some familiarity with an appropriate statistical software package.

(S1) Problem solving skills

(S2) Numeracy

(S3) IT skills

(S4) Communication skills

##### Statistical Theory and Methods II (MATH264)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To introduce statistical distribution theory which forms the basis for all applications of statistics, and for further statistical theory.

**Learning Outcomes**(LO1) To have an understanding of basic probability calculus.

(LO2) To have an understanding of a range of techniques for solving real life problems of probabilistic nature.

(S1) Problem solving skills

(S2) Numeracy

##### Numerical Methods for Applied Mathematics (MATH266)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To provide an introduction to the main topics in Numerical Analysis and their relation to other branches of Mathematics

**Learning Outcomes**(LO1) To strengthen students’ knowledge of scientific programming, building on the ideas introduced in MATH111.

(LO2) To provide an introduction to the foundations of numerical analysis and its relation to other branches of Mathematics.

(LO3) To introduce students to theoretical concepts that underpin numerical methods, including fixed point iteration, interpolation, orthogonal polynomials and error estimates based on Taylor series.

(LO4) To demonstrate how analysis can be combined with sound programming techniques to produce accurate, efficient programs for solving practical mathematical problems.

(S1) Numeracy

(S2) Problem solving skills

##### Securities Markets (ECON241)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**75:25 **Aims**This module seeks to provide an understanding of:

the role of securities markets in the economy;

their basic mechanics and technical features;

the valuation of financial assets;

the operational and allocative efficiency of the market.**Learning Outcomes**(LO1) Appreciate the central role of securities markets in the economy

(LO2) Understand and apply appropriate economic theory to market organisation

(LO3) Display an understanding of the usefulness of portfolio theory and the approaches to the valuation of financial assets

(LO4) Read the financial press and appreciate issues relating to the study of the securities markets

(S1) Adaptability

(S2) Problem solving skills

(S3) Numeracy

(S4) Commercial awareness

(S5) Teamwork

(S6) Organisational skills

(S7) Communication skills

(S8) IT skills

(S9) International awareness

(S10) Lifelong Learning Skills

(S11) Ethical Awareness

##### Mathematical Economics 2 (ECON211)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**The aim of this module is to introduce students to the use of mathematical models in the study of Economics

To build on the material of Year 1 Mathematics and Economics and deepen students' knowledge of mathematical techniques involved in Microeconomics and game theory

To develop more advanced mathematical skills

To develop an ability to use models to solve economic problems**Learning Outcomes**(LO1) Students will be able to revise univariate calculus.

(LO2) Students will be able to introduce matrix algebra.

(LO3) Students will be able to acquire skills with multivariate calculus.

(LO4) Students will be able to develop study optimisation.

(LO5) Students will be able to apply these skills to microeconomic problems

(LO6) Students will be able to apply these skills to macroeconomic problems

(S1) Problem-solving skills

(S2) Numeracy

##### Macroeconomics II (ECON224)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**To further extend the study of macroeconomic theory at the intermediate level by analysing business-cycle fluctuations in closed and open economies using the real business cycle model and also the new Keynesian model that are based on solid microfoundation

**Learning Outcomes**(LO1) Understand the microfoundation of modern macroeconomic models

(LO2) Explain the implications of macroeconomic disturbances and fiscalpolicies using the real business cycle model

(LO3) Contrast the different implications of monetary policies in thereal business cycle model and in the new Keynesian model.

(LO4) Analyse business cycles in the open economy.

(S1) Problem solving skills

(S2) Numeracy

(S3) Commercial awareness

(S4) Communication skills

(S5) IT skills

(S6) International awareness

(S7) Lifelong learning skills

(S8) Ethical awareness

(S9) Teamwork

(S10) Organised and able to work under pressure

### Programme Year Three

Year three optional modules: Choose 2 modules from each semester. ECON322 cannot be taken with MATH331. Choose from: ECON308, ECON322, ECON335, ECON342, ECON333, ECON360, ECON306, ECON311, ECON343.

Choose 2 modules from each semester. MATH331 cannot be taken with ECON222. Choose from: MATH323, MATH324, MATH325, MATH343, MATH344, MATH362, MATH363, MATH365, MATH367, MATH322, MATH326, MATH390 (math390 cannot be taken with MATH399), MATH327, MATH331, MATH332, MATH342, MATH345, MATH346, MATH349, MATH360, MATH361, MATH364, MATH366, MATH371, MATH399.

#### Year Three Optional Modules

##### Further Methods of Applied Mathematics (MATH323)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**•To give an insight into some specific methods for solving important types of ordinary differential equations.

•To provide a basic understanding of the Calculus of Variations and to illustrate the techniques using simple examples in a variety of areas in mathematics and physics.

•To build on the students'' existing knowledge of partial differential equations of first and second order.

**Learning Outcomes**(LO1) After completing the module students should be able to:

- use the method of "Variation of Arbitrary Parameters" to find the solutions of some inhomogeneous ordinary differential equations.- solve simple integral extremal problems including cases with constraints;

- classify a system of simultaneous 1st-order linear partial differential equations, and to find the Riemann invariants and general or specific solutions in appropriate cases;

- classify 2nd-order linear partial differential equations and, in appropriate cases, find general or specific solutions.

[This might involve a practical understanding of a variety of mathematics tools; e.g. conformal mapping and Fourier transforms.]##### Cartesian Tensors and Mathematical Models of Solids and VIscous Fluids (MATH324)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To provide an introduction to the mathematical theory of viscous fluid flows and solid elastic materials. Cartesian tensors are first introduced. This is followed by modelling of the mechanics of continuous media. The module includes particular examples of the flow of a viscous fluid as well as a variety of problems of linear elasticity.

**Learning Outcomes**(LO1) To understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations.

(LO2) To apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.

(S1) Problem solving skills

(S2) Numeracy

(S3) Adaptability

##### Quantum Mechanics (MATH325)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**The aim of the module is to lead the student to an understanding of the way that relatively simple mathematics (in modern terms) led Bohr, Einstein, Heisenberg and others to a radical change and improvement in our understanding of the microscopic world.

**Learning Outcomes**(LO1) To be able to solve Schrodinger's equation for simple systems.

(LO2) To have an understanding of the significance of quantum mechanics for both elementary systems and the behaviour of matter.

(S1) Problem solving skills

(S2) Numeracy

##### Group Theory (MATH343)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To introduce the basic techniques of finite group theory with the objective of explaining the ideas needed to solve classification results.

**Learning Outcomes**(LO1) Understanding of abstract algebraic systems (groups) by concrete, explicit realisations (permutations, matrices, Mobius transformations).

(LO2) The ability to understand and explain classification results to users of group theory.

(LO3) The understanding of connections of the subject with other areas of Mathematics.

(LO4) To have a general understanding of the origins and history of the subject.

(S1) Problem solving skills

(S2) Logical reasoning

##### Combinatorics (MATH344)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**To provide an introduction to the problems and methods of Combinatorics, particularly to those areas of the subject with the widest applications such as pairings problems, the inclusion-exclusion principle, recurrence relations, partitions and the elementary theory of symmetric functions.

**Learning Outcomes**(LO1) After completing the module students should be able to: understand of the type of problem to which the methods of Combinatorics apply, and model these problems; solve counting and arrangement problems; solve general recurrence relations using the generating function method; appreciate the elementary theory of partitions and its application to the study of symmetric functions.

##### Applied Probability (MATH362)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To give examples of empirical phenomena for which stochastic processes provide suitable mathematical models. To provide an introduction to the methods of probabilistic model building for ‘‘dynamic" events occurring over time. To familiarise students with an important area of probability modelling.

**Learning Outcomes**(LO1) 1. Knowledge and Understanding After the module, students should have a basic understanding of:

(a) some basic models in discrete and continuous time Markov chains such as random walk and Poisson processes

(b) important subjects like transition matrix, equilibrium distribution, limiting behaviour etc. of Markov chain

(c) special properties of the simple finite state discrete time Markov chain and Poisson processes, and perform calculations using these.

2. Intellectual Abilities After the module, students should be able to:

(a) formulate appropriate situations as probability models: random processes

(b) demonstrate knowledge of standard models (c) demonstrate understanding of the theory underpinning simple dynamical systems

3. General Transferable Skills

(a) numeracy through manipulation and interpretation of datasets

(b) communication through presentation of written work and preparation of diagrams

(c) problem solving through tasks set in tutorials

(d) time management in the completion of practicals and the submission of assessed work

(e) choosing, applying and interpreting results of probability techniques for a range of different problems.##### Linear Statistical Models (MATH363)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**70:30 **Aims**- To understand how regression methods for continuous data extend to include multiple continuous and categorical predictors, and categorical response variables.

- To provide an understanding of how this class of models forms the basis for the analysis of experimental and also observational studies.

- To understand generalized linear models.

- To develop skills in using an appropriate statistical software package.

**Learning Outcomes**(LO1) Be able to understand the rationale and assumptions of linear regression and analysis of variance.

(LO2) Be able to understand the rationale and assumptions of generalized linear models.

(LO3) Be able to recognise the correct analysis for a given experiment.

(LO4) Be able to carry out and interpret linear regressions and analyses of variance, and derive appropriate theoretical results.

(LO5) Be able to carry out and interpret analyses involving generalised linear models and derive appropriate theoretical results.

(LO6) Be able to perform linear regression, analysis of variance and generalised linear model analysis using an appropriate statistical software package.

##### Measure Theory and Probability (MATH365)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**The main aim is to provide a sufficiently deepintroduction to measure theory and to the Lebesgue theory of integration. Inparticular, this module aims to provide a solid background for the modernprobability theory, which is essential for Financial Mathematics.

**Learning Outcomes**(LO1) After completing the module students should be ableto:

(LO2) master the basic results about measures and measurable functions;

(LO3) master the basic results about Lebesgue integrals and their properties;

(LO4) to understand deeply the rigorous foundations ofprobability theory;

(LO5) to know certain applications of measure theoryto probability, random processes, and financial mathematics.

(S1) Problem solving skills

(S2) Logical reasoning

##### Networks in Theory and Practice (MATH367)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**•To develop an appreciation of network models for real world problems.

•To describe optimisation methods to solve them.

•To study a range of classical problems and techniques related to network models.

**Learning Outcomes**(LO1) After completing the module students should be able to model problems in terms of networks and be able to apply effectively a range of exact and heuristic optimisation techniques.

##### Chaos and Dynamical Systems (MATH322)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To develop expertise in dynamical systems in general and study particular systems in detail.

**Learning Outcomes**(LO1) After completing the module students will be able to understand the possible behaviour of dynamical systems with particular attention to chaotic motion;

(LO2) After completing the module students will be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed points;

(LO3) After completing the module students will understand how fractal sets arise and how to characterise them.

(S1) Problem solving skills

(S2) Numeracy

##### Relativity (MATH326)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**To impart

(i) a firm grasp of the physical principles behind Special and General Relativity and their main consequences;

(ii) technical competence in the mathematical framework of the subjects - Lorentz transformation, coordinate transformations and geodesics in Riemann space;

(iii) knowledge of some of the classical tests of General Relativity - perihelion shift, gravitational deflection of light;

(iv)basic concepts of black holes and (if time) relativistic cosmology.

**Learning Outcomes**(LO1) After completing this module students should understand why space-time forms a non-Euclidean four-dimensional manifold.

(LO2) After completing this module students should be proficient at calculations involving Lorentz transformations, energy-momentum conservation, and the Christoffel symbols.

(LO3) After completing this module students should understand the arguments leading to the Einstein's field equations and how Newton's law of gravity arises as a limiting case.

(LO4) After completing this module students should be able to calculate the trajectories of bodies in a Schwarzschild space-time.

##### Professional Projects and Employability in Mathematics (MATH390)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**The first aim of the module is to further develop students' problem solving abilities and ability to select techniques and apply mathematical knowledge to authentic work-style situations. Specifically, within this aim, the module aims to:

1) develop students' ability to solve a problem in depth over an extended period and produce reports;

2) develop students' ability to communicate mathematical results to audiences of differing technical ability, including other mathematicians, business clients and the general public;

3) develop an appreciation of how groups operate, different roles in group work, and the different skills required to successfully operate as a team.

The second aim of the module is to develop students' employability skills in key areas such as public speaking, task management and professionalism.

**Learning Outcomes**(LO1) Select appropriate techniques and apply mathematical knowledge to solve problems related to real-world phenomena.

(LO2) Communicate mathematical results to audiences of differing technical ability via different methods.

(LO3) Reflect on skills development and identify areas for further development.

(LO4) Articulate employability skills.

(LO5) Produce reports based on the development of a piece of work, in depth over an extended period of time.

(S1) Problem solving skills

(S2) Commercial awareness

(S3) Adaptability

(S4) Teamwork

(S5) Organisational skills

(S6) Communication skills

##### Statistical Physics (MATH327)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**1. To develop an understanding of the foundations of Statistical Physics normally including statistical ensembles and related extensive and intrinsic quantities.

2. To develop an understanding of the properties of classical and quantum gases and an appreciation of their applications to concepts such as the classical equation of state or the statistical

theory of photons.

3. To obtain a reasonable level of skill in using computer simulations for describing diffusion and transport in terms of stochastic processes.

4. To knowledge the laws of thermodynamics and thermodynamical cycles.

5. To obtain a reasonable understanding of interacting statistical systems and related phenomenons such as phase transitions.**Learning Outcomes**(LO1) Demonstrate understanding of the microcanonical, canonical and grand canonical ensembles, their relation and the derived concepts of entropy, temperature and particle number

density.(LO2) Understand the derivation of the equation-of-state for non-interacting classical or quantum gases.

(LO3) Demonstrate numerical skills to understand diffusion from an underlying stochastic process.

(LO4) Know the laws of thermodynamics and demonstrate their application to thermodynamic cycles.

(LO5) Be aware of the effect of interactions including an understanding of the origin of phase transitions.

(S1) Problem solving skills

(S2) Numeracy

(S3) Adaptability

(S4) Communication skills

(S5) IT skills

(S6) Organisational skills

(S7) Teamwork

##### Game Theory (MATH331)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**To explore, from a game-theoretic point of view, models which have been used to understand phenomena in which conflict and cooperation occur. To see the relevance of the theory not only to parlour games but also to situations involving human relationships, economic bargaining (between trade union and employer, etc), threats, formation of coalitions, war, etc. To treat fully a number of specific games including the famous examples of "The Prisoners' Dilemma" and "The Battle of the Sexes". To treat in detail two-person zero-sum and non-zero-sum games. To give a brief review of n-person games. In microeconomics, to look at exchanges in the absence of money, i.e. bartering, in which two individuals or two groups are involved.To see how the Prisoner's Dilemma arises in the context of public goods.

**Learning Outcomes**(LO1) To extend the appreciation of the role of mathematics in modelling in Economics and the Social Sciences.

(LO2) To be able to formulate, in game-theoretic terms, situations of conflict and cooperation.

(LO3) To be able to solve mathematically a variety of standard problems in the theory of games and to understand the relevance of such solutions in real situations.

##### Population Dynamics (MATH332)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**- To provide a theoretical basis for the understanding of population ecology - To explore the classical models of population dynamics - To learn basic techniques of qualitative analysis of mathematical models

**Learning Outcomes**(LO1) The ability to relate the predictions of the mathematical models to experimental results obtained in the field.

(LO2) The ability to recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems.

(LO3) The ability to use analytical and graphical methods to investigate population growth and the stability of equilibrium states for continuous-time and discrete-time models of ecological systems.

(S1) Problem solving skills

(S2) Numeracy

##### Number Theory (MATH342)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**To give an account of elementary number theory with use of certain algebraic methods and to apply the concepts to problem solving.

**Learning Outcomes**(LO1) To understand and solve a wide range of problems about integers numbers.

(LO2) To have a better understanding of the properties of prime numbers.

(S1) Problem solving skills

(S2) Numeracy

(S3) Communication skills

##### The Magic of Complex Numbers: Complex Dynamics, Chaos and the Mandelbrot Set (MATH345)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**1. To introduce students to the theory of the iteration of functions of one complex variable, and its fundamental objects;

2. To introduce students to some topics of current and recent research in the field;

3. To study various advanced results from complex analysis, and show how to apply these in a dynamical setting;

4. To illustrate that many results in complex analysis are "magic", in that there is no reason to expect them in a real-variable context, and the implications of this in complex dynamics;

5. To explain how complex-variable methods have been instrumental in questions purely about real-valued one-dimensional dynamical systems, such as the logistic family.

6. To deepen students' appreciations for formal reasoning and proof. After completing the module, students should be able to:

1. understand the compactification of the complex plane to the Riemann sphere, and use spherical distances and derivatives.

2. use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems.

3. state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties.

4. determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set.

5. apply advanced results from complex analysis in the setting of complex dynamics.

6. determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not.**Learning Outcomes**(LO1) To understand the compactification of the complex plane to the Riemann sphere, and be able to use spherical distances and derivatives.

(LO2) To be able to use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems.

(LO3) To be able to state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties.

(LO4) To be able to determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set.

(LO5) To know how to apply advanced results from complex analysis in a dynamical setting.

(LO6) To be able to determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not.

(S1) Problem solving/ critical thinking/ creativity analysing facts and situations and applying creative thinking to develop appropriate solutions.

(S2) Problem solving skills

##### Topology (MATH346)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**1. To introduce students to the mathematical notions of space and continuity.

2. To develop students’ ability to reason in an axiomatic framework.

3. To provide students with a foundation for further study in the area of topology and geometry, both within their degree and subsequently.

4. To introduce students to some basic constructions in topological data analysis.

5. To enhance students’ understanding of mathematics met elsewhere within their degree (in particular real and complex analysis, partial orders, groups) by placing it within a broader context.

6. To deepen students’ understanding of mathematical objects commonly discussed in popular and recreational mathematics (e.g. Cantor sets, space-filling curves, real surfaces).**Learning Outcomes**(IM1) An understanding of the ubiquity of topological spaces within mathematics.

(IM2) Knowledge of a wide range of examples of topological spaces, and of their basic properties.

(IM3) The ability to construct proofs of, or counter-examples to, simple statements about topological spaces and continuous maps.

(IM4) The ability to decide if a (simple) space is connected and/or compact.

(IM5) The ability to construct the Cech and Vietoris-Rips complexes of a point set in Euclidean spac. e

(IM6) The ability to compute the fundamental group of a (simple) space, and to use it to distinguish spaces.

##### Differential Geometry (MATH349)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**85:15 **Aims**This module is designed to provide an introduction to the methods of differential geometry, applied in concrete situations to the study of curves and surfaces in euclidean 3-space. While forming a self-contained whole, it will also provide a basis for further study of differential geometry, including Riemannian geometry and applications to science and engineering.

**Learning Outcomes**(LO1) 1a. Knowledge and understanding: Students will have a reasonable understanding of invariants used to describe the shape of explicitly given curves and surfaces.

(LO2) 1b. Knowledge and understanding: Students will have a reasonable understanding of special curves on surfaces.

(LO3) 1c. Knowledge and understanding: Students will have a reasonable understanding of the difference between extrinsically defined properties and those which depend only on the surface metric.

(LO4) 1d. Knowledge and understanding: Students will have a reasonable understanding of the passage from local to global properties exemplified by the Gauss-Bonnet Theorem.

(LO5) 2a. Intellectual abilities: Students will be able to use differential calculus to discover geometric properties of explicitly given curves and surfaces.

(LO6) 2b. Intellectual abilities: Students will be able to understand the role played by special curves on surfaces.

(LO7) 3a. Subject-based practical skills: Students will learn to compute invariants of curves and surfaces.

(LO8) 3b. Subject-based practical skills: Students will learn to interpret the invariants of curves and surfaces as indicators of their geometrical properties.

(LO9) 4a. General transferable skills: Students will improve their ability to think logically about abstract concepts,

(LO10) 4b. General transferable skills: Students will improve their ability to combine theory with examples in a meaningful way.

(S1) Problem solving skills

(S2) Numeracy

##### Applied Stochastic Models (MATH360)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**To give examples of empirical phenomena for which stochastic processes provide suitable mathematical models. To provide an introduction to the methods of stochastic model building for 'dynamic' events occurring over time or space. To enable further study of the theory of stochastic processes by using this course as a base.

**Learning Outcomes**(LO1) To understans the theory of continuous-time Markov chains.

(LO2) To understans the theory of diffusion processes.

(LO3) To be able to solve problems arising in epidemiology, mathematical biology, financial mathematics, etc. using the theory of continuous-time Markov chains and diffusion processes.

(LO4) To acquire an undertanding of the standard concepts and methods of stochastic modelling.

(S1) Problem solving skills

(S2) Numeracy

##### Theory of Statistical Inference (MATH361)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims**To introduce some of the concepts and principles which provide theoretical underpinning for the various statistical methods, and, thus, to consolidate the theory behind the other second year and third year statistics options.

**Learning Outcomes**(LO1) To acquire a good understanding of the classical approach to, and especially the likelihood methods for, statistical inference.

(LO2) To acquire an understanding of the blossoming area of Bayesian approach to inference.

(S1) Problem solving skills

(S2) Numeracy

##### Medical Statistics (MATH364)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**The aims of this module are to: demonstrate the purpose of medical statistics and the role it plays in the control of disease and promotion of health explore different epidemiological concepts and study designs apply statistical methods learnt in other programmes, and some new concepts, to medical problems and practical epidemiological research enable further study of the theory of medical statistics by using this module as a base.

**Learning Outcomes**(LO1) identify the types of problems encountered in medical statistics

(LO2) demonstrate the advantages and disadvantages of different epidemiological study designs

(LO3) apply appropriate statistical methods to problems arising in epidemiology and interpret results

(LO4) explain and apply statistical techniques used in survival analysis

(LO5) critically evaluate statistical issues in the design and analysis of clinical trials

(LO6) discuss statistical issues related to systematic review and apply appropriate methods of meta-analysis

(LO7) apply Bayesian methods to simple medical problems.

(S1) Problem solving skills

##### Mathematical Risk Theory (MATH366)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**•To provide an understanding of the mathematical risk theory used in the study process of actuarial interest

• To provide an introduction to mathematical methods for managing the risk in insurance and finance (calculation of risk measures/quantities)

• To develop skills of calculating the ruin probability and the total claim amount distribution in some non‐life actuarial risk models with applications to insurance industry

• To prepare the students adequately and to develop their skills in order to be ready to sit for the exams of CT6 subject of the Institute of Actuaries (MATH366 covers 50% of CT6 in much more depth).

**Learning Outcomes**(LO1) After completing the module students should be able to:

(a) Define the loss/risk function and explain intuitively the meaning of it, describe and determine optimal strategies of game theory, apply the decision criteria's, be able to decide a model due to certain model selection criterion, describe and perform calculations with Minimax and Bayes rules.

(b) Understand the concept (and the mathematical assumptions) of the sums of independent random variables, derive the distribution function and the moment generating function of finite sums of independent random variables.

(c) Define and explain the compound Poisson risk model, the compound binomial risk model, the compound geometric risk model and be able to derive the distribution function, the probability function, the mean, the variance, the moment generating function and the probability generating function for exponential/mixture of exponential severities and gamma (Erlang) severities, be able to calculate the distribution of sums of independent compound Poisson random variables.

(d) Understand the use of convolutions and compute the distribution function and the probability function of the compound risk model for aggregate claims using convolutions and recursion relationships.

(e) Define the stop‐loss reinsurance and calculate the (mean) stop‐loss premium for exponential and mixtures of exponential severities, be able to compare the original premium and the stoploss premium in numerical examples.

(f) Understand and be able to use Panjer's equation when the number of claims belongs to theR(a, b, 0) class of distributions, use the Panjer's recursion in order to derive/evaluate the probability function for the total aggregate claims.

(g) Explain intuitively the individual risk model, be able to calculate the expected losses (as well as the variance) of group life/non‐life insurance policies when the benefits of the each person of the group are assumed to have deterministic variables.

(h) Derive a compound Poisson approximations for a group of insurance policies (individual risk model as approximation),

(i) Understand/describe the classical surplus process ruin model and calculate probabilities of the number of the risks appearing in a specific time period, under the assumption of the Poisson process.

(j) Derive the moment generating function of the classical compound Poisson surplus process, calculate and explain the importance of the adjustment coefficient, also be able to make use of Lundberg's inequality for exponential and mixtures of exponential claim severities.

(k) Derive the analytic solutions for the probability of ruin, psi(u), by solving the corresponding integro‐differential equation for exponential and mixtures of exponential claim amount severities,

(l) Define the discrete time surplus process and be able to calculate the infinite ruin probability, psi(u,t) in numerical examples (using convolutions).

(m) Derive Lundberg's equation and explain the importance of the adjustment coefficient under the consideration of reinsurance schemes.

(n) Understand the concept of delayed claims and the need for reserving, present claim data as a triangle (most commonly used method), be able to fill in the lower triangle by comparing present data with past (experience) data.

(o) Explain the difference and adjust the chain ladder method, when inflation is considered.

(p) Describe the average cost per claim method and project ultimate claims, calculate the required reserve (by using the claims of the data table).

(q) Use loss ratios to estimate the eventual loss and hence outstanding claims.

(r) Describe the Bornjuetter‐Ferguson method (be able to understand the combination of the estimated loss ratios with a projection method). Use the aforementioned method to calculate the revised ultimate losses (by making use of the credibility factor).##### Numerical Analysis for Financial Mathematics (MATH371)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**80:20 **Aims**1. To provide basic background in solving mathematical problems numerically, including understanding of stability and convergence of approximations to exact solution.

2. To acquaint students with two standard methods of derivative pricing: recombining trees and Monte Carlo algorithms.

3. To familiarize students with implementation of numerical methods in a high level programming language.**Learning Outcomes**(LO2) Ability to analyse a simple numerical method for convergence and stability

(LO3) Ability to formulate approximations to derivative pricing problems numerically.

(LO4) Ability to program matlab for pricing options

(LO5) Awareness of the major issues when solving mathematical problems numerically.

(S1) Problem solving skills

(S2) Numeracy

##### Projects in Mathematics (MATH399)

**Level**3 **Credit level**15 **Semester**Whole Session **Exam:Coursework weighting**0:100 **Aims**a) To study in depth an area of pure mathematics and report on it; or

b) To construct and study mathematical models of a chosen problem;

orc) To demonstrate a critical understanding and historical appreciation of some branch of mathematics by means of directed reading and preparation of a report.; or d) To study in depth a particular problem in statistics, probability or operational research.

**Learning Outcomes**(LO1) a) (Pure Maths)After completing the report with suitable guidance the student should have · gained a greater understanding of the chosen mathematical topic · gained experience in applying his/her mathematical skills · had experience in consulting relevant literature · learned how to construct a written project report · had experience in making an oral presentation b) (Applied Mathematics)After completing the project with suitable guidance the students should have: - learned strategies for simple model building - gained experience in choosing and using appropriate mathematics - understood the nature of approximations used - made critical appraisal of results - had experience in consulting related relevant literature - learned how to construct a written project report - had experience in making an oral presentation. c) (Applied Maths/Theoretical Physics)After researching and preparing the mathematical essay the student should have: · gained a greater understanding of the chosen mathematical topic · gained an appreciation of the historical context · learned how to abstract mathematical concepts and explain them · had experience in consulting related relevant literature · learned how to construct a written project report · had experience in making an oral presentation. d) (Statistics, Probability and Operational Research) After completing the project the student should have: · gained an in-depth understanding of the chosen topic · had experience in consulting relevant literature · learned how to construct a written project report; · had experience in making an oral presentation.

(S1) Problem solving skills

(S2) Numeracy

(S3) Adaptability

(S4) Organisational skills

(S5) Communication skills

(S6) IT skills

##### Quantitative Financial Economics (ECON308)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**This module provides a thorough overview of financial economics, starting from the decision-making under uncertainty and applying these concepts to optimal portfolio choice by the consumer, optimal investment by the firm, pricing contingent claims, term structure of interest rates and real option analysis. In addition to standard asset pricing models, the efficient capital markets theory will be extensively covered.

**Learning Outcomes**(LO1) Students will be able to understand the role of capital markets

(LO2) Students will be able to use capital budgeting techniques

(LO3) Students will be able to understand and measure risk aversion

(LO4) Students will be able to calculate the optimal portfolio between two risky assets

(LO5) Students will be able to forecast asset return based on historical data

(LO6) Students will be able to forecast asset return volatility based on historical data

(LO7) Students will be able to understand and use futures and forward contracts

(LO8) Students will be able to understand and be able to use options

(S1) Problem-solving skills

(S2) Numeracy

##### Game Theoretical Approaches to Microeconomics (ECON322)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**100:0 **Aims**The objective of the module is to provide an introduction to game theory. This is the study of strategic interactions ie situations where outcomes depend not only on our own actions but also how others react to our actions. This module complements those in core macro and microeconomics and offers more insight into strategic decisions and competitive behaviour in general.

**Learning Outcomes**(LO1) Distinguish between types of games

(LO2) Explain game theoretical concepts

(LO3) Conduct advanced microeconomic analysis by formulating a game and its associated solution concepts and deriving solutions to games

(LO4) Apply games in a range of economic, business and social contexts

(LO5) Explain the importance of game theoretic approaches in economic analysis

(S1) Problem Solving Skills

(S2) Numeracy

(S3) Commercial Awareness

(S4) Teamwork

(S5) Organisational Skills

(S6) Communication skills

(S7) IT skills

(S8) International awareness

(S9) Lifelong learning skills

(S10) Ethical awareness

##### International Trade (ECON335)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**To develop an appreciation and understanding of basic principles determining the observed patterns of trade in the increasingly globalised world economy.

**Learning Outcomes**(LO1) Students will be able to understand the role of both absolute and comparative advantage in explaining observed patterns of trade in the global economy

(LO2) Students will be able to recognise both the strengths and limitations of the basic Ricardian approach and the Hecksher-Ohlin Theory of trade.

(LO3) Students will be able to critically evaluate the roles, achievements and failures of various international institutions in the context of international economic performance.

(LO4) Students will be able to critically understand and approach trade based on increasing returns to scale

(LO5) Students will be able to recognise the implications of different types of trade barriers and why countries protect.

(LO6) Students will develop a critical understanding of the importance and implications of different levels of economic integration in the context of NAFTA and the EU.

(LO7) Students will be able to critically evaluate trade-oriented growth strategies for less developed economies.

(S1) Problem solving skills

(S2) Teamwork

(S3) Organisational skills

(S4) Communication skills

(S5) IT skills

(S6) International awareness

##### Advanced Microeconomics (ECON342)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**This module aims to provide an understanding of the market failure resulting from asymmetric information. The course covers some of the canonical models of adverse selection and moral hazard focussing on the design of optimal contracts under informational asymmetries.

**Learning Outcomes**(LO1) Solve simple economic models

(LO2) Understand underlying assumptions

(LO3) Understand theorems and key proofs

(LO4) Predict the choices of economic agents

(S1) problem solving skills

(S2) numeracy

(S3) Communication skills

##### Industrial Organisation (ECON333)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**50:50 **Aims**To apply the tools of microeconomics to the analysis of firms, markets and industries in order to understand the nature and consequences of the process of competition. These tools will also be applied to the evaluation of relevant government policy. This will extend knowledge and skills of microeconomic analysis by covering recent advances in theory as well as empirical analysis of relevant microeconomic topics.

**Learning Outcomes**(LO1) Students will be able to use economic principles, concepts and techniques to discuss and analyse government policy and economic performance with reference to standard frameworks in Industrial Organisation.

(LO2) Students will be able to apply standard frameworks, including verbal, graphical, mathematical and statistical representations of economic concepts and models, to explain and evaluate the effects of a range of competitive behaviours by firms and how they are influenced by economic incentives and the ethical issues enveloped within this.

(LO3) Students will be able to analyse current issues and problems in business and industry from domestic, international and cross-border perspectives.

(LO4) Students will be able to compare, contrast and critically evaluate alternative schools of thought in Industrial Organisation with reference to empirical evidence.

(LO5) Students will be able to conduct competent applied economic research by locating, selecting and analysing information relevant to the study of Industrial Organisation from domestic and global perspectives.

(LO6) Students will be able to communicate effectively in writing and in accordance with a report specification

(S1) Problem solving skills

(S2) Numeracy

(S3) Commercial awareness

(S4) Communication skills

(S5) IT skills

(S6) Ethical awareness

##### Law and Economics (ECON360)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**This course does not require prior knowledge of the law, nor is its objective to teach students about the law. The main objective is to show students how they can apply the tools of economic analysis to understand the basic structure and function of the law. The course focuses on the core common law areas of torts, contracts, and property, along with a discussion of the litigation process, the economics of crime, and antitrust law.

**Learning Outcomes**(LO1) Students will be able to understand the use of economics to analyse the law

(LO2) Students will be able to understand the importance of the law in economics

(LO3) Students will be able to understand the use of model in law and economics

(LO4) Students will be able to develop the ability to do a positive analysis of liability rules

(S1) Problem solving skills

(S2) Numeracy

(S3) Communication skills

(S4) Lifelong learning skills

##### The Economics of Developing Countries (ECON306)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**This module aims to introduce students to the theoretical perspectives andempirical debates within development economics and impart an in-depthappreciation of the issues related to economic development and its determinantsin less developed countries.

**Learning Outcomes**(LO1) To understand the nature and determinants of economic development in the LDCs;

(LO2) To recognise both the strengths andlimitations of various alternative models of the development process

(LO3) To understand the determinants ofeconomic welfare in LDCs

(LO4) To recognise the implications fordeveloping countries of international exchange, trade liberalisation andglobalisation

(LO5) To appreciate the relationships betweenglobalisation and economic performance in low and middle income economies

(LO6) To critically evaluate the roles,achievements and failures of various international policy initiatives in thecontext of developing country measured economic performance and domesticeconomic welfare.

(S1) Problem solving skills

(S2) Teamwork

(S3) Organisational skills

(S4) Communication skills

(S5) International awareness

(S6) Lifelong learning skills

(S7) Ethical awareness

##### Methods of Economic Investigation 1: Time Series Econometrics (ECON311)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**The aim of this module is to give students an understanding of econometric time series methodology. The module will build upon the materials of ECON212 Basic Econometrics. Important extensions include volatility models of financial time series and multivariate (multiple equations) models such as vector error correction and related cointegrating error correction models.

**Learning Outcomes**(LO1) Specify and demonstratethe distributional characteristics of a range of time series models

(LO2) Estimate appropriate models for financial andeconomic time series for the purposes of forecasting andinference

(LO3) Understand a range ofunivariate and multivariate models of financial and economic time series processes.

(LO4) Applyunivariate and multivariate model selection and evaluation methods

(LO5) Understand theimplications of conditional heteroskedasticity, unit roots and cointegration in economic andfinancial time series analysis

(S1) Problem solving skills

(S2) Numeracy

##### Advanced Macroeconomics (ECON343)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**To further develop understanding of macroeconomic theory, where appropriate, to integrate the theory with issues of current policy interest.

To further develop students' analytical and problem solving abilities applied to economic principles**Learning Outcomes**(LO1) Acquire advanced knowledge and understanding of contemporary macroeconomic

(LO2) Be able to critically appraise the relevant theory and evidence

(LO3) Apply macroeconomic theory to analyse macroeconomic developments and evaluate their implications

(LO4) Apply macroeconomic theory to analyse policy implications

(LO5) Further develop their mathematical and analytical skills as applied in modern economics

(S1) Problem solving skills

(S2) Numeracy

(S3) Teamwork

(S4) Adaptability

(S5) Lifelong Learning Skills

The programme detail and modules listed are illustrative only and subject to change.

#### Teaching and Learning

Your learning activities will consist of lectures, tutorials, practical classes, problem classes, private study and supervised project work. In Year One, lectures are supplemented by a thorough system of group tutorials and computing work is carried out in supervised practical classes. Key study skills, presentation skills and group work start in first-year tutorials and are developed later in the programme. The emphasis in most modules is on the development of problem solving skills, which are regarded very highly by employers. Project supervision is on a one-to-one basis, apart from group projects in Year Two.

#### Assessment

Most modules are assessed by a two and a half hour examination in January or May, but many have an element of coursework assessment. This might be through homework, class tests, mini-project work or key skills exercises.