# Mathematics and Business Studies BSc (Joint Hons)

- Course length: 3 years
- UCAS code: GN11
- Year of entry: 2018
- Typical offer: A-level : ABB / IB : 33 / BTEC : D*DD

## 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

#### Year One Compulsory Modules

##### The European Economic Environment (ECON159)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**75:25 **Aims**The aim of this module is to introduce students to:

- the theoretical basis of economic integration
- the main economic features of the European Union
- the workings of the main institutions
- the major current policy issues.

**Learning Outcomes**describe the main economic aspects and working of the EU in recent years

identify major economic problems experienced by the EU

use appropriate economic analysis to examine such problems

followdebates on current developments within the EU

cognitive skills of analysis and synthesisability to identify major issues relating to the EUability to conduct individual study by drawing onprimary sources especially access to the Europawebsite of the European Commissionabilityto discuss current policy issues, particularly as they affect the UK.

##### Calculus I (MATH101)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**80:20 **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**differentiate and integrate a wide range of functions;

sketch graphs and solve problems involving optimisation and mensuration

understand the notions of sequence and series and apply a range of tests to determine if a series is convergent

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

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**80:20 **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**manipulate complex numbers and solve simple equations involving them

solve arbitrary systems of linear equations

understand and use matrix arithmetic, including the computation of matrix inverses

compute and use determinants

understand and use vector methods in the geometry of 2 and 3 dimensions

calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics

##### Functions of Business I (ULMS101)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**50:50 **Aims**To provide an overview of three key business functions: accounting and finance; human resource management and marketing

- To enhance knowledge of basic financial instruments utilised by organisations
- To outline key elements of the marketing mix and their use within organisations
To develop awareness of segmentation, targeting and position

To identify and explore the main roles performed by the people management function

To develop knowledge and understanding of the principle actors in the employment relationship

**Learning Outcomes**Create and interpret basic financial statements Differentiate between models of employee relations

Analyse common techniques used by organisations to shape employee behaviour

Understand the marketing function, common marketing models and their role between business.

##### Economic Principles for Business and Markets (ECON127)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**80:20 **Aims**To enable students to demonstrate an understanding of the core principles of microeconomics including:

- The dynamic nature of supply and demand
- The efficient opperation of markets and when they fail
- How firms reach output decisions, interact and attain levels of profit under different market conditions

To enable students to demonstrate an understanding of the core principles of macroeconomics including:

- The aggregation of demand and supply in the economy to measure an economy''s output;
- The business cycle and behaviour and interaction of the big macroeconomic indicators: Growth; Unemployment; Inflation; Balance of payments & Exchange rates;

- To enable students to demonstrate an understanding of the global economic environment

To enable students to understand the impact of modern economics on day-to-day business operations

**Learning Outcomes**An understanding of the central economic problem (scarcity) and the nature of economics; An understanding of how the market price of goods and services is determined by supply and demand and how markets respond to changes in circumstances, measures of responsiveness and price control;

An understanding of how firms’ costs of production and revenue are considered to find points of profit maximisation;

An understanding of different Market environments – Specified by degree of competition in industries (perfect competition, monopoly, monopolistic competition, oligopoly); as well as strategic interactions arising such as game theory and price discrimination;

An understanding of why markets fail to achieve social efficiency;

An understanding of the theory of the whole economy 1 (macroeconomic objectives; the national income);

An understanding of the theory of the whole economy 2 (aggregate supply and demand, short-term fluctuations, economic growth); An understanding of the global economy, the gains from international trade as well as the arguments for restricting trade.##### 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**use Taylor series to obtain local approximations to functions;

obtain partial derivaties and use them in several applications such as, error analysis, stationary points change of variables

evaluate double integrals using Cartesian and Polar Co-ordinates

##### 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**to describe statistical data;

to use the Binomial, Poisson, Exponential and Normal distributions;

to perform simple goodness-of-fit tests

to use the package Minitab to present data, and to make statistical analysis

##### Functions of Business II (ULMS102)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**0:100 **Aims**This module builds on the knowledge gained in ULMS101 Functions of Business I. The focus moves from technical to operational aspects of finance, marketing and HR such that students will be introduced to the customer, financial and human implications of organisational decisions. The first part examines how the three key functions coalesce in organisations, informing decision making processes. The second is given over to integrative case studies requiring students to

i. analyse issues from different functional perspectives and

ii. demonstrate an understanding of the inter-related nature of the functions

A simple example of this would be the financial and HR impact of a store opening for longer hours to provide better customer service.

**Learning Outcomes**Apply enhanced knowledge of each functional area to analyse contemporary organisations Describe and evaluate how each function impacts on organisational decision making processes; and

Evaluate and explain the inter-relationships between each functional area

##### International Business Environment (MKIB152)

**Level**1 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **Aims**Students will be both introduced to relevant theoretical and conceptual frameworks and given a firm empirical understanding of the international business environment. The module will enable students to understand the challenges of international business and develop their knowledge and skills in the strategic issues multinational firms face. The module will also help students become aware of key political, socio-economic, and cultural dynamics and trends that characterize the globalized business environment. Finally, the module will cover the ethical and social responsibility consideration when doing business in a global scale.

These aims will be achieved via a combination of lectures and seminars.

**Learning Outcomes**Students will be able to develop an understanding of the principles underlying the internationalization of businesses

Students will be able to develop an awareness of the current trends in international business environment

Students will be able to developn understanding of the social, economic, political and cultural factors that influence international business.

Students will be able to develop the ability to critically evaluate the internationalization strategies of firms and apply them in a practical context.

Students will be able to develop an understanding of how diversity of moral and ethical norms in foreign locations affects key issues in corporate governance and corporate social responsibility.

#### Year Two Compulsory Modules

##### Introduction to People Management (ULMS206)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**

1. This module seeks to introduce students to the theoretical perspectives, roles, and practical activities associated with people management in contemporary organisations. 2. It aims to introduce current issues concerning people management and its application within contemporary business and organisational environments, preparing students for the workplace. 3. It will seek to:-- Support the development of subject specific and transferable skills necessary for future employment in careers that ultimately have a people managerial component.
- Support the enhancement of skills in written and spoken communication.
- To create independent team learners.
- Demonstrate progression from fundamental learning skills through to critical analysis, reflection and problem-solving.

**Learning Outcomes**Students will be able to explain the historical development of the roles and functions of People Management

Students will be able to describe the activities, functions and roles related to People Management in a variety of organisational contexts, and explain both the rationale for this and the implications for managers and staff

Students will be able to outline and explain the implication of ethics in the People Management process and its links to organisational strategies and people policies

Students will be able to explain the factors affecting the employment relationship, and the options available to manage and support this relationship

Students will be able to outline the main objectivesof the employmentrelationship in contemporary organisations, and the factors that impact upon it.

##### Business Ethics S2 (PHIL270)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**0:100 **Aims**- To introduce and explain major contemporary perspectives on corporate behaviours.
- To introduce moral perspectives as they relate to managerial decision making and corporate structures.
- To make students familiar with a range of recurrent ethical problems arising in business.
- To improve students'' skills in identifying and analyzing ethical issues that managers and employees face.
- To give students practice in formulating, defending, and planning the implementation of action plans managing ethical dilemmas.

**Learning Outcomes**Students will be able to discuss the main theories concerning the place of ethics in business.

Students will be able to state the broad principles of, and discuss the strengths and weaknesses of,basic moral theories, such as consequentialismStudents will be able to state and discuss the broad ethical principles concerning costs and benefits, the challenge posed by uncertainty, professional roles, profits and the right of shareholder interests, and affirmative action.

Students will be able to state and discuss the broad ethical principles concerning the obligations of complex organizations with respect to loyalty and whistle-blowing, insider information, customer responsibility, and corporate responsibility.Students will be able to state and discuss the broad ethical principles concerning social justice and executive compensation.

Students will be able to consider an ethical approach as a basis for sustainable marketing.##### International Business (MKIB225)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**50:50 **Aims**- The aims of the module are the productionof basic knowledge of both mainstream and alternative theories of whybusinesses internationalise and how they operate as transnational corporations. An understanding of transnational production in a holistic sense is key

- key concepts explaining how international businessoperate
- the (current) international economic order
- therelationship between transnational corporations and inter states, labour,social movements, etc

**Learning Outcomes**The ability to think analytically in the production of knowledge of the core debates relating to questions of why businesses internationalise and how transnational corporations operate. The ability to think analytically about the core debates on the current global economic and financial crisis and its impact on the international economic order and international business.

The ability to read analytically a wide range of texts originating from numerous “disciplines”, assessing the strengths and weaknesses of different arguments. This is to enable the development of an analytical understanding of key approaches, both mainstream and critical, on these issues.

Theability to undertake independent scholarly work, albeit in an assisted manner.

The ability to communicateknowledge, ideas and analysis clearly and concisely in both written and oralform.

Theability to work autonomously and demonstrateinitiative, self-organisation and time management, to plan and evaluate independentlearning and performance, and to apply learning strategies to improveperformance.

Theability to function effectively and cooperatively in group work

##### Functions of Business I (ULMS101)

**Level**1 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**50:50 **Aims**To provide an overview of three key business functions: accounting and finance; human resource management and marketing

- To enhance knowledge of basic financial instruments utilised by organisations
- To outline key elements of the marketing mix and their use within organisations
To develop awareness of segmentation, targeting and position

To identify and explore the main roles performed by the people management function

To develop knowledge and understanding of the principle actors in the employment relationship

**Learning Outcomes**Create and interpret basic financial statements Differentiate between models of employee relations

Analyse common techniques used by organisations to shape employee behaviour

Understand the marketing function, common marketing models and their role between business.

##### Ordinary Differential Equations (MATH201)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **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**After completing the module students should be:

- familiar with elementary techniques for the solution of ODE''s, and the idea of reducing a complex ODE to a simpler one;

- familiar with basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions;

- well versed in the solution of linear ODE systems (homogeneous and non-homogeneous) with constant coefficients matrix;

- aware of a range of applications of ODE.

##### 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**The ability to understand and describe mathematically real-life optimization problems.

Understanding the basic methods of dynamical decision making.

Understanding the basics of forecasting and simulation.

The ability to analyse elementary queueing systems.

#### Year Two Optional Modules

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

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**85:15 **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**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**90:10 **Aims**1. To provide an understanding of the techniques used in constructing, analysing, evaluating and interpreting mathematical models.

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

3. To use and develop mathematical skills introduced in Year 1 - particularly the calculus of functions of several variables and elementary differential equations.

**Learning Outcomes**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**90:10 **Aims**To introduce the basic elements of the theories of metric spaces and calculus of several variables.

**Learning Outcomes**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.

##### Complex Functions (MATH243)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**80:20 **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**After completing this module students should:

- appreciate the central role of complex numbers in mathematics;

- be familiar with all the classical holomorphic functions;

- be able to compute Taylor and Laurent series of such functions;

- understand the content and relevance of the various Cauchy formulae and theorems;

- be familiar with the reduction of real definite integrals to contour integrals;

- be competent at computing contour integrals.

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

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**To introduce general concepts of linear algebra and its applications in geometry and other areas of mathematics.

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

• appreciate the geometric meaning of linear algebraic ideas,

• appreciate the concept of an abstract vector space and how it is used in different mathematical

situations,

• apply a change of coordinates to simplify a linear map,

• manipulate matrix groups (in particular Gln, On and Son),

• understand bilinear forms from a geometric point of view.

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

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**- Appreciate the operational research approach.
- Be able to apply standard methods to a wide range of real-world problems as well as applications in other areas of mathematics.
- Appreciate the advantages and disadvantages of particular methods.
- Be able to derive methods and modify them to model real-world problems.
- Understand and be able to derive and apply the methods of sensitivity analysis.

**Learning Outcomes**Appreciate the operational research approach.Be able to apply standard methods to a wide range of real-world problems as well asapplications in other areas of mathematics.

Appreciate the advantages and disadvantages of particular methods.

Be able to derive methods and modify them to model real-world problems.Understand and be able to derive and apply the methods of sensitivity analysis. Appreciate the importance of sensitivity analysis.

##### Financial Mathematics I (MATH267)

**Level**2 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**This module is to provide an understanding of the fundamental concepts of financial mathematics, and how these concepts are applied in calculating present and accumulated values for various streams of cash flows. Students will also be given an introduction to financial instruments, such as derivatives, the concept of no-arbitrage.

**Learning Outcomes**1. Understand and calculate all kind of rates of interest, find the future value and present value of a cash flow, and write the equation of value given a set of cash flows and an interest rate.

2. Derive formulae for all kinds of annuities

3. Given an annuity with level payments, immediate (or due) , payable m-thly, (or payable continuously), and any three of present value, future value, interest rate, payment, and term of annuity, calculate the remaining two items.

4. Given an annuity with non-level payments, immediate (or due) , payable m-thly, (or payable continuously), the pattern of payment amounts, and any three of present value, future value, interest rate, payment, and term of annuity, calculate the remaining two items.

5. Calculate the outstanding balance at any point in time.

6. Calculate a schedule of repayments under a loan and identify the interest and capital components in a given payment.

7. Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.

8. Calculate the present value of payments from a fixed interest security, bounds for the present value of a redeemable fixed interest security.

9. Given the price, calculate the running yield and redemption yield from a fixed interest security.

10. Calculate the present value or real yield from an index-linked bond.

11. Calculate the price of, or yield from, a fixed interest security where the income tax and capital gains tax are implemented.

12. Calculate yield rate, the dollar-weighted and time weighted rate of return, the duration and convexity of a set of cash flows.

13. Describe the concept of a stochastic interest rate model and the fundamental distinction between this and a deterministic model.

##### Group Project Module (MATH206)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**0:100 **Aims**· To give students experience of working effectively in small groups.

· To train students to write about mathematics.

· To give students practice in delivering presentations.

· To develop students’ ability to study independently.

· To prepare students for later individual project work.

· To enhance students’ appreciation of the connections between different areas of mathematics.

· To encourage students to discuss mathematics with each other.

**Learning Outcomes**Work effectively in groups, and delegate common tasks.

Write substantial mathematical documents in an accessible form.Give coherent verbal presentations of more advanced mathematical topics.

Appreciate how mathematical techniques can be applied in a variety of different contexts##### 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**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 a basic understanding of the principles of Classical Mechanics and their application to simple dynamical systems.

**Learning Outcomes**the motions of bodies under simple force systems, including calculations of the orbits of satellites, comets and planetary motions

motion relative to a rotating frame, Coriolis and centripetal forces, motion under gravitry over the Earth''s surface

rigid body dynamics using centre of mass, angular momentum and moments of inertia

##### 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**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**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.

-determine and work with tangents, inflexions, curvature, cusps, nodes, length and other features.

-calculate envelopes and evolutes.

- solve the position and shape of some algebraic curves including conics.

The first learning outcome is assessed by coursework, the others by both coursework and examination.

##### Financial Mathematics II (MATH262)

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**90:10 **Aims** to provide an understanding of the basic financial mathematics theory used in the study process of actuarial/financial interest,

to provide an introduction to financial methods and derivative pricing financial instruments ,

to understand some financial models with applications to financial/insurance industry,

to prepare the students adequately and to develop their skills in order to be ready to sit for the CT1 & CT8 subject of the Institute of Actuaries (covers 20% of CT1 and material of CT8).

**Learning Outcomes**After completing the module students should:

(a) Understand the assumptions of CAMP, explain the no riskless lending or borrowing and other lending and borrowing assumptions, be able to use the formulas of CAMP, be able to derive the capital market line and security market line,

(b) Describe the Arbitrage Theory Model (APT) and explain its assumptions, perform estimating and testing in APT,

(c) Be able to explain the terms long/short position, spot/delivery/forward price, understand the use of future contracts, describe what a call/put option (European/American) is and be able to makes graphs and explain their payouts, describe the hedging for reducing the exposure to risk, be able to explain arbitrage, understand the mechanism of short sales,

(d) Explain/describe what arbitrage is, and also the risk neutral probability measure, explain/describe and be able to use (perform calculation) the binomial tree for European and American style options,

(e) Understand the probabilistic interpretation and the basic concept of the random walk of asset pricing,

(f) Understand the concepts of replication, hedging, and delta hedging in continuous time,

(g) Be able to use Ito''s formula, derive/use the the Black‐Scholes formula, price contingent claims (in particular European/American style options and forward contracts), be able to explain the properties of the Black‐Scholes formula, be able to use the Normal distribution function in numerical examples of pricing,

(h) Understand the role of Greeks , describe intuitively what Delta, Theta, Gamma is, and be able to calculate them in numerical examples.

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

**Level**2 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**85:15 **Aims**To introduce statistical methods with a strong emphasis on applying standard statistical techniques appropriately and with clear interpretation. The emphasis is on applications.

**Learning Outcomes**After completing the module students should have a conceptual and practical understanding of a range of commonly applied statistical procedures. They should have also developed some familiarity with the statistical package MINITAB.

##### 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**After completing the module students should understand basic probability calculus. They should be familiar with a range of techniques for solving real life problems of the probabilistic nature.

##### Numerical Methods (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**After completing the module students should be able to:

• write simple mathematical computer programs in Maple,

• understand the consequences of using fixed-precision arithmetic,

• analyse the efficiency and convergence rate of simple numerical methods,

• develop and implement algorithms for solving nonlinear equations,

• develop quadrature methods for numerical integration,

• apply numerical methods to solve systems of linear equations and to calculate eigenvalues and eigenvectors,

• solve boundary and initial value problems using finite difference methods.

### Programme Year Three

Choose four Business modules and four Mathematics modules

#### Year Three Optional Modules

##### International Economic Relations (ECON354)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**70:30 **Aims**The aim of this module is to provide a detailed coverage of the nature and determinants of the pattern of world trade and financial, capital and labour flows. The module also aims to provide students with a critical appreciation of why conflicts arise between nations due to international economic activity and what policy options are most appropriate for countries both individually and cooperatively to adopt. Throughout the module emphasis will be placed upon the role of theory in enhancing understanding of the patterns and nature of trade flows (in the context of both goods and services) in the context of the key issues in international economic relations.

**Learning Outcomes**Students will be able to explain why countries gain from trade and what pattern of trade flows exist using classic trade theories.Students will be able to explain why countries engage in trade protection, as well as predict and analyze the consequences that arise in case such protection is applied Students will be able to explain how key flows of goods, services, money and physical capital are valued. They will be able to use real and nominal exchange rates, understand, explain and apply the concept of PPP.

Students will be able to explain the reasons why trade blocs are formed and analyze and explain their costs and benefits. They will also be able to distinguish between trade blocs among countries of similar as well as different development levels.

Students will be able to explain why conflicts arise in the areas of labour migration and environmental pollution and suggest policy responses which may be used to correct such problems

Students will be able to explain the causes and consequences of financial crises and how financial contagion can spread from one country to another

Students will be able to explain the links between trade and capital flows and economic development using examples of the Latin American and East Asian countries

##### Tourism (MKIB337)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**70:30 **Aims**The aim of this module is to provide a coherent framework through which the structure, management and organisation of the Tourism Industry can be understood and the nature of tourism demand explained. The study of tourism depends on and draws from a wide range of disciplines. Consideration of tourism consumer behaviour involves elements of sociology and psychology, whilst concerns for the impacts of tourism cannot be fully understood without reference to economics, geography and planning. Consequently a multi-disciplinary approach will be adopted and the inter-relationships explored.

**Learning Outcomes**Understand factors influencing the tourist experience

Understand the structure, management and organisation of the Tourism Industry

Understand the role of tourism in the economic development of a country

Appraise the practical implications of the wider impacts of tourism including, environmental, social and cultural impacts

Identify a range of issues, current and future, facing the Tourism Industry

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

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**75:25 **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 competetive behaviour in general.

**Learning Outcomes**Explain game theoretical concepts

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

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

Explain the importance of game theoretic approaches in economic analysis

##### Corporate Communications (MKIB372)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**- to increase awareness of the importance of language and communication in the business and management contexts;

- to develop an in-depth understanding of internal communication systems (interpersonal and cross-cultural communications) and of external communication systems (public relations, marketing, political communication and the media)

- to explore the importance of integrated communications

- to broaden the understanding of communications within the theory of stakeholder management

- to apply core comunication and sociolinguistic theory to the business environment

**Learning Outcomes**understand the function of corporate communications

demonstrate an appreciation of the key issues and problems associated with corporate communications

explore methods of evaluating corporate communications, including corporate image

apply core communication, marketing and sociolinguistic theory to the business environment

demonstrate an ability to analyse critically and undertake independent research

develop an ability to write concise reports and opinions, and to communicate ideas effectively

demonstrate an ability to reflect on the learning process

##### E-business Models and Strategy (EBUS301)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**0:100 **Aims**To provide an introduction to the appraisal and formulation of e-business strategy and contemporary e-business models.

**Learning Outcomes**to understand the basics of business strategy to understand the capabilities and therefore business capabilities and therefore business strategies enabled by the Internet;

to be able to analyse, understand and constructively criticise an existing e-business strategy;

to be able to formulate an e-business strategy to help in addressing the strengths, weaknesses, opportunities and threats faced by a business;

to have well founded views on the future development of e-business models.

##### Supply Chain Operations Management (EBUS306)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**60:40 **Aims**The management of supply chains is key to the operations of modern organisations. The need to be competitive, reach new markets, source new goods and raw materials as well as globalisation have all been key contributors to the development of supply chains as a function. It has become clear that competitive advantage and customer satisfaction can be gained if all organisations in the chain work together to improve service and reduce cost. The module provides the student with comprehensive understanding of key principles and techniques of supply chain management (SCM) including topics such as inventory management, demand and capacity management, supply chain partnerships and IT

The aim of this module is to provide a study of the key principles, systems and techniques used to assure effective supply chain management. The module covers an extensive range of subjects including logistics, information management, inventory management, partnerships and information technology. The aims are to enable the student to:

A1. Understand the principles and role of SCM in organisations.

A2. Understand the nature and importance of inter-relationshipswithin the supply chain.

A3. Understand and apply a range of tools and techniquesrelevant to the optimisation of supply chains.

**Learning Outcomes**Students will be able to define and document a supply chain operation

Students will be able to analyse and evaluate the performance of the supply chain.

Students will be able to apply supply chain optimisation tools and techniques in a range of situations.

##### Corporate Governance (ACFI320)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**50:50 **Aims**The module aims to provide students with an understanding of the history and development of corporate governance and the key principles and systems that underpin corporate governance today.

It also provides the opportunity to assess the practical application of corporate governance systems across major international organisations.

**Learning Outcomes**understand the key principles within corporate governance frameworks, with specific reference to the UK Corporate Governance Code;

be able to critically analyse and discuss the corporate governance arrangements for several types of organisation.

##### Business in the Asia-pacific Region (MKIB338)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**60:40 **Aims**This module aims to familiarise students with the unique and contrasting business environment in the Asia Pacific region and to use concepts and theories from the international business/management literature to evaluate and explain this environment

**Learning Outcomes**Appreciate and identify the consequences of national differences in the business and management systems of the Asia Pacific region. Analyse and synthesise critical debates in the development of the Asia Pacific economies.

Evaluate the principal economic, political and social trends in the region and their consequence for the conduct of business.

Appraise the strategic issues involved in entering Asia Pacific markets.

Conduct a comparative analysis of different countries and businesses within the Asia Pacific region.

##### Business in Latin America (MKIB359)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**75:25 **Aims**This module is designed to enable students to undertake an empirical study of the activities and organisation of domestic and foreign business in a significant area of the developing world. Students are expected to build upon the knowledge and techniques developed in earlier modules to understand and analyse critically the behaviour of companies, investors, regulators, employees and consumers in the Latin American economies.

**Learning Outcomes**To develop students'' knowledge and understanding of contemporary Latin American businesses. To develop students'' appreciation of the problems and opportunities facing companies in the Latin American environment and their responses.

To develop students'' ability to synthesise quantitative and qualitative information and opinion from a range of sources.

To develop students'' abilities of critical analysis.

To develop report writing skills.

To develop the student''s capacity to join groups and engage in group work.

##### Advanced Entrepreneurship (ULMS360)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**0:100 **Aims**This module is aims to develop an ability to develop entrepreneurial ideas and to turn them into a concrete business plan. It aims to support those students who are considering a career in business support and consultancy and at developing entrepreneurship and small firms.

**Learning Outcomes**Effectively use a computer-based simulation (Simventure) in order to actively run a "virtual" start-up firm and experience the different elements as well as challenges involved in trying to grow a small business.

Work independently and within a small group in order to effectively organise and cooperate to complete the range of tasks required to transform an entrepreneurial idea into a business plan

Carry out in-depth research and analysis on the different elements required to draft a detailed business plan (including sales and marketing; organisation; operations; finance; and overall strategy) which is realistic and comprehensive

Synthesise the main elements of the business plan into a professional presentation with the aim of attracting financial support for the start up idea from a range of potential investors

Recognise and reflect on the key skills and attributes required in order to develop a coherent business plan as well as the challenges involved in trying to develop a real start up

##### The Football Business (ULMS370)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**75:25 **Aims**- to enhance students’ understanding and knowledge of the key issues surrounding the contemporary football business and associated industries;
to encourage students to apply their knowledge of economics, business and management to the football industry.

**Learning Outcomes**Students will develop their knowledge and understanding of the key issues surrounding the contemporary football business and associated industries;

Students will demonstrate an ability to apply business and management concepts to the football industry;

Students will develop their abilities to analyse critically, synthesise ideas and write reports and opinions.

- to enhance students’ understanding and knowledge of the key issues surrounding the contemporary football business and associated industries;
##### Business in Emerging Markets (MKIB369)

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**0:100 **Aims**This is an optional module focusing on the business environment in emerging markets and specifically in the BRIC countries, Brazil, Russia, India and China. In 2001, Jim O''Neill of Goldman-Sachs predicted that globalization would help Brazil, Russia, India and China (the BRICs), large countries endowed with raw materials but with difficult macro-contexts to develop rapidly and overtake the largest Western economies.

The aims of this module are to evaluate the extent to which the above prediction has come to pass and to explore the business and political uncertainty which has come with this period of rapid economic development.

The module aims to provide an insight into whether or not the BRICs can sustain their growth, what the implications of this growth are, and which nations might follow. MNEs based in the BRIC countries will also be discussed.

**Learning Outcomes**Tounderstand the reasons for rapid emergence of BRIC countries Tobe able to identify criteria which determine for rapid growth of emergingmarkets

Tounderstand who are the key stakeholders in emerging markets and how theyinteract with each others

Toexplore potential tradeoffs between rapid economic growth and social and otherdimensions of the markets

Toexamine other potential emerging markets to identify those which are mostlikely to grow rapidly

Tounderstand in detail the dynamics in specific markets such as China, India,Brazil and Russia

Tounderstand the importance of development of brands by BRIC countries

To understand the BRIC thesis and arrive atconclusions about whether this has been met and will continue in future

##### 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**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**After completing the module, students should be able to understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, and apply mathematical methods for analysis of problems involving the flow of viscous fluid or behaviour of solid elastic materials.

##### Group Theory (MATH343)

**Level**3 **Credit level**15 **Semester**First Semester **Exam:Coursework weighting**90:10 **Aims**To introduce the basic techniques of finite group theory with the objective of explaining the ideas needed to solve classification results.

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

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

The understanding of connections of the subject with other areas of Mathematics.

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

##### 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**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 occuring over time. To familiarise students with an important area of probability modelling.

**Learning Outcomes**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**100:0 **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 familiarity with the computer package SPSS.

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

understand the rationale and assumptions of linear regression and analysis of variance.

· understand the rationale and assumptions of generalized linear models.

· recognise the correct analysis for a given experiment.

· carry out and interpret linear regressions and analyses of variance, and derive appropriate theoretical results.

· carry out and interpret analyses involving generalised linear models and derive appropriate theoretical results.

· perform linear regression, analysis of variance and generalised linear model analysis using the SPSS computer 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**After completing the module students should be ableto:

master the basic results about measures and measurable functions;

master the basic results about Lebesgue integrals and their properties;to understand deeply the rigorous foundations ofprobability theory;

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

##### 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**After completing the module students should

. be able to model problems in terms of networks.

· be able to apply effectively a range of exact and heuristic optimisation techniques.

##### 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**After completing this module students should be able to understand and solve a wide range of problems about the integers, and have a better understanding of the properties of prime numbers.

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

**Level**3 **Credit level**15 **Semester**Second Semester **Exam:Coursework weighting**100:0 **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**will understand the compactification of the complex plane to the Riemann sphere, and be able to use spherical distances and derivatives

will be able to use Möbius transformations to transform the Riemann sphere and to normalise complex dynamical systems

will be able to state and apply the definitions of Julia and Fatou sets of polynomials, and understand their basic properties

will be able to determine whether points with simple orbits, such as certain periodic points, belong to the Julia set or the Fatou set

will know how to apply advanced results from complex analysis in a dynamical setting

will be able to determine whether certain types of quadratic polynomials belong to the Mandelbrot set or not

##### 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**1. Knowledge and understanding

After the module, students should have a basic understanding of

a) invariants used to describe the shape of explicitly given curves and surfaces,

b) special curves on surfaces,

c) the difference between extrinsically defined properties and those which depend only on the surface metric,

d) understanding the passage from local to global properties exemplified by the Gauss-Bonnet Theorem.

2. Intellectual abilities

After the module, students should be able to

a) use differential calculus to discover geometric properties of explicitly given curves and surface,

b) understand the role played by special curves on surfaces.

3. Subject-based practical skills

Students should learn to

a) compute invariants of curves and surfaces,

b) interpret the invariants of curves and surfaces as indicators of their geometrical properties.

4. General transferable skills

Students will improve their ability to

a) think logically about abstract concepts,

b) combine theory with examples in a meaningful way.

##### 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**After completing the module students should have a good understanding of the classical approach to, and especially the likelihood methods for, statistical inference.

The students should also gain an appreciation of the blossoming area of Bayesian approach to inference

##### 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**identify the types of problems encountered in medical statistics

demonstrate the advantages and disadvantages of different epidemiological study designs

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

explain and apply statistical techniques used in survival analysis

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

discuss statistical issues related to systematic review and apply appropriate methods of meta-analysisapply Bayesian methods to simple medical problems.

##### 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**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 the

R(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).

##### 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; or

c) 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**a) (Pure Maths option) - 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.

e) Mathematics in Society Projects. Only available to G1X3 students

Students interested in doing such a project should see Dr A Pratoussevitch and Dr T Eckl initially.

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.