Materials Science Unit Catalogue

ECOI0006: Introductory microeconomics
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 1
Assessment: EX50 OT50
Requisites: Ex ECOI0001
Aims & learning objectives:
The course is designed to provide an introduction to the methods of microeconomic analysis, including the use of simple economic models and their application. Students should gain an ability to derive conclusions from simple economic models and evaluate their realism and usefulness.
Content:
An introduction to economic methodology; the concept of market equilibrium; the use of demand and supply curves, and the concept of elasticity; elementary consumer theory, indifference curves and their relationship to market demands; elementary theory of production, production possibilities and their relationship to cost curves; the supply behaviour of competitive firms and its relationship to supply curves; the idea of general competitive equilibrium; the efficiency properties of competitive markets; examples of market failure.

ECOI0007: Introductory macroeconomics
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 1
Assessment: EX50 OT50
Requisites: Ex ECOI0002
Aims & learning objectives:
The course is designed to provide an introduction to the methods of macroeconomic analysis, including the use of simple macroeconomic models and their application in a UK policy context.
Content:
The circular flow of income and expenditure; national income accounting; aggregate demand and supply; the components and determinants of private and public aggregate expenditure in closed and open economies; output and the price level in the short- and long -run; monetary institutions and policy. The analysis of inflation and unemployment policies, the balance of payments and exchange rates, savings and economic growth.

ECOI0010: Intermediate microeconomics
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 2
Assessment: EX50 OT50
Requisites: Pre ECOI0006
Aims & learning objectives:
The aim is to provide students specialising in economics with the analytical foundations for the study of resource allocation within the household, firm, government, or other institutions in a modern economy. It is essential for anyone wishing to undertake further study of the economics of industry, labour, environment and other sectoral economic issues.
Content:
The course will cover the theory of consumer behaviour, the theory of the firm in a competitive situation, industrial organisation and imperfect competition, the theory of factor markets, the economics of information, welfare economics and general equilibrium theory.

ECOI0018: Mathematical economics
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 2
Assessment: EX80 CW20
Requisites: Pre ECOI0006, Pre ECOI0007
Aims & learning objectives:
The aim of this course is to equip students with an understanding of, and an ability to use, mathematical methods in economics
Content:
The course covers constrained optimisation for the household and the firm using the Lagrangian method, including duality; linear programming; matrix algebra as applied to input-output analysis and macro-models; the use of first and second order difference and differential equations in economic dynamics; simple non-linear dynamics. Students who have completed the first year of a Mathematics degree programme or have A-level Mathematics may also take this unit.

ECOI0024: Economics of development 1
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX50 ES30 CW20
Requisites: Pre ECOI0001, Pre ECOI0002, Pre ECOI0006, Pre ECOI0007
Aims & learning objectives:
To relate economic theory to debates over the determinants of global poverty, and over the prospects for economic development and poverty reduction in low and middle income countries.
Content:
The status of development economics as a sub-discipline. Open and closed dual economy models of industrialization. Industrialization and trade strategies. Definition and measurement of poverty. Models of the farm-household, and theories of agrarian change. Demographic transition and the environment. As well as the stated pre-requisites students must also have taken at least 2 second year economics units.

ECOI0025: Economics of development 2
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX50 ES50
Requisites: Pre ECOI0024, Pre ECOI0028
Aims & learning objectives:
To apply general theories of economic development to contemporary issues in selected low and middle income countries, and to understand the relationship between economics and other social science disciplines relevant to the analysis of these issues.
Content:
Development economics is first located within the wider framework of development studies. Contemporary policy issues in selected low and middle income countries are then considered, with a current focus on the origins, components and effects of stabilisation and structural adjustment in Sub-Saharan Africa and South Asia.

ECOI0026: Economics of transition
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0010, Pre ECOI0011
Aims & learning objectives:
To use economic analysis to understand the changes which are taking place in Central and Eastern Europe and the former Soviet Union, relating them to the creation of market economies.
Content:
Topics covered will include the speed and sequencing of adjustment; privatisation; financial markets; foreign trade; growth and inflation; legal changes; the labour market; public finance issues.

ECOI0027: International monetary economics
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0010, Pre ECOI0011
Aims & learning objectives:
The aim is to present a fairly rigorous account of the material that relates to monetary aspects of an open economy. The emphasis is on theory and analysis rather than policy. Students should gain a critical appreciation of the theoretical tools used in this important area of economics alongside an understanding of the different "economic" worlds they can be used to create.
Content:
The course tries to emphasise debate by generally constrasting a Keynesian real side approach with a more classically inspired monetary approach. Specific topics include: the nature and significance of the balance of payments; parity concepts; the "efficient markets" hypothesis; devaluation; open economy macroeconomics; flexible versus fixed exchange rates; the foreign trade sector, "Europe" and international policy co-ordination.

ECOI0028: Economic growth & natural resources
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0010, Pre ECOI0011
Aims & learning objectives:
The aim is to provide a fairly sophisticated account of theories of economic growth and of natural resource use, leading on to a discussion of the concept of sustainable development. Though the course draws on some techniques of dynamic optimisation, the emphasis is on economic intuition and empirical relevance rather than rigorous mathematical proof.
Content:
The neo-classical model of growth; endogenous growth; optimal saving; depletion of exhaustible resources; management of renewable resources; intergenerational equity; sustainable development.

ECOI0029: Environmental economics
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0010
Aims & learning objectives:
The course provides the economic perspective on environmental regulation and on the management of natural resources. The emphasis is on the use of economic tools to value environmental impacts and the use of natural resources; and to design cost effective methods of controlling pollution and misuse of the natural environment.
Content:
The course will discuss the welfare economic basis of environmental economics and why market systems do not provide adequate environmental protection. It will go on to study different methods of valuing the environment and on regulating it in a national context. Finally it will deal with the theme of environment and development, and the idea of sustainable development.

ECOI0030: Advanced microeconomics
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0010, Pre ECOI0018
Aims & learning objectives:
The aim of this course is to build on second year microeconomics and introduce topics that are the subject of recent academic research. This will provide students with: (i) an understanding of the scope of modern microeconomics and its applications, (ii) an ability to read and understand current literature in microeconomics, (iii) an ability to use advanced microeconomic concepts in analysing specific issues.
Content:
The course covers topics that deal with three inter-related issues: the passage of time, uncertainty about the future, the use of information. These include: the principles of decision making under uncertainty, with applications to insurance, stock-markets and firm behaviour; investment behaviour of firms under certainty and uncertainty; problems of asymmetric information; screening and signalling; strategic behaviour.

ECOI0031: Advanced macroeconomics
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0011
Aims & learning objectives:
The aim of this course is to build on second year macroeconomics and introduce topics that are the subject of recent academic research, this will provide students with: (I) anunderstanding of the scope of modern macroeconomics and its applications, (ii) an ability to read and understand current literature in macroeconomics, (iii) an ability to use advanced macroeconomic concepts in analysing specific issues.
Content:
The course covers in depth two inter-related issues: the causes of business cycles and of unemployment. Topics covered include modern real business cycle theory; endogenous business cycles, simple non-linear models, wage and price rigidity, insider and outsider behaviour, efficiency wages and unemployment hysteresis.

ECOI0034: International trade
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0010
Aims & learning objectives:
The aim of the course is to provide an understanding of the way in which economic theory can be applied to issues such as why countries engage in international trade and why they adopt trade restraints. The emphasis of the course is on theory and analysis rather than description. Students will become more skilled in understanding and applying economic analysis and more aware of economic debates concerning current issues in international trade.
Content:
After an introduction to basic concepts, the topics discussed will include: comparative advantage; the gains from trade; adjustment costs; the Heckscher-Ohlin-Samuelson model; the Specific Factors Model; theories of intra-industry trade; the costs of protection, smuggling, trade taxes as a revenue source; the optimum tariff; export subsidies; international cartels, quotas and voluntary export restraint,; international integration; multinational enterprises and the welfare effects of the international movement of factors of production.

ECOI0035: Public expenditure & public choice
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0010
Aims & learning objectives:
The aim of the course is to examine alternative ways by which the allocation of resources within the public sector can be evaluated. Criteria for evaluation of public expenditure are discussed and techniques, such as cost benefit analysis, are appraised. An important learning objective is to develop an understanding of how different perspectives can be applied. In particular, the standard public finance approach is contrasted with the more recent public choice approach. The course is theoretical and analytical rather than descriptive.
Content:
The course begins with a review of welfare economics (- as public expenditure analysis is applied welfare economics). Market failure and the rationale for government intervention is assessed. The impact of alleged failings in the political process is also assessed. The behaviour of voters, political parties, bureaucrats and pressure groups is analysed using microeconomic theory. The growth of the public sector is considered in terms of both market and government failure. Techniques for public sector appraisal are discussed.

ECOI0036: Economics of taxation
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0010, Pre ECOI0011
Aims & learning objectives:
The aim is to provide criteria which can be used to assess different taxes. The student will learn how to appraise tax reform against a set of criteria which include efficiency, equity, etc. The learning objective is to develop skills associated with the application of economic theory. The course is theoretical and analytical rather than descriptive.
Content:
The course begins with an analysis of the welfare costs of taxation. Tax incidence is discussed. The effect of tax on work effort, saving and risk taking is explored (and, in particular, the claims of supply-side economists are assessed). Tax expenditures (e.g. tax relief for charitable giving) are appraised. Tax evasion and policy to deter tax evasion is discussed International taxation is considered. The choice between taxation and government borrowing is examined.

ECOI0037: Macroeconomic modelling
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
The aim is to provide a thorough grounding in the practice, techniques and limitations of macroeconomic modelling.
Content:
Building a macroeconomic model, optimisation subject to the constraints of a model, comparison of UK macroeconomic models and industry forecasting models.

ECOI0038: Advanced econometrics 1
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0021, Pre ECOI0020
Aims & learning objectives:
The aim is to extend the knowledge of econometrics to a very high and rigorous level. The language is a combination of matrix algebra and maximum likelihood. The emphasis is on both theory and applications in equal measure. The course concentrates on both time series analysis and cross section analysis.
Content:
The course builds on the econometrics course and includes 3sls, fiml, probit, logit and other limited dependent variable techniques and sure.

ECOI0039: Advanced econometrics 2
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 3
Assessment: EX100
Requisites: Pre ECOI0038
Aims & learning objectives:
The aim is to extend the knowledge of econometrics to a very high and rigorous level. The language is a combination of matrix algebra and maximum likelihood. The emphasis is on both theory and applications in equal measure. The course concentrates on both time series analysis.
Content:
The course builds on the Advanced Econometrics I course and includes splines, vars, Granger causality, Box and Cox methods and spectral analysis.

ECOI0045: Placement
Academic Year
Credits: 60
Contact:
Topic:
Level: Level 2
Assessment:
Requisites:
Aims & learning objectives:
The placement period enables the student to gain valuable practical experience.
Content:
Please see the Director or Studies or course tutor for details about individual placements.

ELEC0047: Design & realisation of integrated circuits
Semester 2
Credits: 6
Contact:
Topic:
Level: Undergraduate Masters
Assessment: EX100
Requisites:
Aims & learning objectives:
This course covers all aspects of the realisation of integrated circuits, including both digital, analogue and mixed-signal implementations. Consideration is given to the original specification for the circuit which dictates the optimum technology to be used also taking account of the financial implications. The various technologies available are described and the various applications, advantages and disadvantages of each are indicated. The design of the circuit building blocks for both digital and analogue circuits are covered. Computer aided design tools are described and illustrated and the important aspects of testing and design for testability are also covered. After completing this module the student should be able to take the specification for an IC and, based on all the circuit, technology and financial constraints, be able to determine the optimum design approach. The student should have a good knowledge of the circuit design approaches and to be able to make use of the computer aided design tools available and to understand their purposes and limitations. The student should also have an appreciation of the purposes of IC testing and the techniques for including testability into the overall circuit design.
Content:
Design of ICs: the design cycle, trade-offs, floorplanning, power considerations, economics. IC technologies: Bipolar, nMOS, CMOS, BiCMOS, analogue, high frequency. Transistor level design: digital gates, analogue components, sub-circuit design. IC realisation: ASICs, PLDs, gate arrays, standard cell, full custom. CAD: schematic capture, hardware description languages, device and circuit modelling, simulation, layout, circuit extraction. Testing: types of testing, fault modelling, design for testability, built in self test, scan-paths.

ESML0208: Chinese stage 3A (advanced beginners) (6 credits)
Semester 1
Credits: 6
Contact:
Topic: Chinese
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0209
Aims & learning objectives:
This course builds on the Chinese covered in Chinese Stage 2 A and B in order to enhance the student's abilities in the four skill areas.
Content:
This unit contains a variety of listening, reading, speaking and writing tasks covering appropriate grammatical structures and vocabulary relating to China, Singapore and Taiwan. There will be discussion in the target language of topics derived from teaching materials, leading to small-scale research projects based on the same range of topics and incorporating the use of press reports and articles as well as audio and visual material. Students are encouraged to devote time and energy to developing linguistic proficiency outside the timetabled classes, for instance by additional reading and/or participating in informally arranged conversation groups and in events at which Chinese is spoken.

ESML0209: Chinese stage 3B (6 credits)
Semester 2
Credits: 6
Contact:
Topic: Chinese
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0208
Aims & learning objectives:
A continuation of Chinese Stage 3A
Content:
A continuation of Chinese Stage 3A

ESML0214: French stage 9A (further advanced) (6 credits)
Semester 1
Credits: 6
Contact:
Topic: French
Level: Level 2
Assessment: EX45 CW40 OR15
Requisites: Co ESML0215
Aims & learning objectives:
A continuation of the work outlined in French 8A and 8B
Content:
This unit contains a variety of listening, reading, speaking and writing tasks covering appropriate grammatical structures and vocabulary. Teaching materials used cover a wide variety of sources and cover aspects of cultural political and social themes relating to France. Works of literature or extracts may be included, as well as additional subject-specific material, as justified by class size. This may encompass scientific and technological topics as well as materials relevant to business and industry. There will be discussion in the target language of topics relating to and generated by the teaching materials, with the potential for small-scale research projects and presentations. Audio and video materials form an integral part of this study, along with newspaper, magazine and journal articles. Students are actively encouraged to consolidate their linguistic proficiency outside the timetabled classes, by additional reading, links with native speakers and participating in events at which French is spoken. Audio and video laboratories are available to augment classroom work.

ESML0215: French stage 9B (6 credits)
Semester 2
Credits: 6
Contact:
Topic: French
Level: Level 2
Assessment: EX45 CW40 OR15
Requisites: Co ESML0214
Aims & learning objectives:
A continuation of French Stage 9A
Content:
A continuation of French Stage 9A

ESML0220: French stage 6A (advanced intermediate) (6 credits)
Semester 1
Credits: 6
Contact:
Topic: French
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0221
Aims & learning objectives:
This course concentrates on the more advanced aspects of French with continued emphasis on practical application of language skills in a relevant context, in order to refine further the student's abilities.
Content:
This unit contains a variety of listening, reading, speaking and writing tasks covering appropriate grammatical structures and vocabulary. There is continued further development of the pattern of work outlined in French Stage 5A and 5B

ESML0221: French stage 6B (6 credits)
Semester 2
Credits: 6
Contact:
Topic: French
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0220
Aims & learning objectives:
A continuation of course French Stage 6A
Content:
A continuation of course French Stage 6A

ESML0226: German stage 3A (advanced beginners) (6 credits)
Semester 1
Credits: 6
Contact:
Topic: German
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0227
Aims & learning objectives:
This course builds on the German covered in German Stage 2A and 2B in order to enhance the student's abilities in the four skill areas.
Content:
This unit contains a variety of listening, reading, speaking and writing tasks covering appropriate grammatical structures and vocabulary relating to a selection of topics. Teaching materials cover a wide range of cultural, political and social topics relating to German speaking countries and may include short works of literature. There will be discussion in the target language of topics derived from teaching materials, leading to small-scale research projects based on the same range of topics and incorporating the use of press reports and articles as well as audio and visual material. Students are encouraged to devote time and energy to developing linguistic proficiency outside the timetabled classes, for instance by additional reading and/or participating in informally arranged conversation groups and in events at which German is spoken. Audio and video laboratories are available to augment classroom work.

ESML0227: German stage 3B (6 credits)
Semester 2
Credits: 6
Contact:
Topic: German
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0226
Aims & learning objectives:
A continuation of German Stage 3A
Content:
A continuation of German Stage 3A

ESML0238: German stage 6A (advanced intermediate) (6 credits)
Semester 1
Credits: 6
Contact:
Topic: German
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0239
Aims & learning objectives:
This course concentrates on the more advanced aspects of German with continued emphasis on practical application of language skills in a relevant context, in order to refine further the student's abilities.
Content:
This unit contains a variety of listening, reading, speaking and writing tasks covering appropriate grammatical structures and vocabulary. There is continued further development of the pattern of work outlined in German Stage 5A and 5B

ESML0239: German stage 6B (6 credits)
Semester 2
Credits: 6
Contact:
Topic: German
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0238
Aims & learning objectives:
A continuation of German Stage 6A
Content:
A continuation of German Stage 6A

ESML0244: Italian stage 3A (advanced beginners) (6 credits)
Semester 1
Credits: 6
Contact:
Topic: Italian
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0245
Aims & learning objectives:
This course builds on the Italian covered in Italian Stage 2A and 2B in order to enhance the students abilities in the four skill areas.
Content:
This unit contains a variety of listening, reading, speaking and writing tasks covering appropriate grammatical structures and vocabulary relating to a selection of topics. Teaching materials cover a wide range of cultural, political and social topics relating to Italy and may include short works of literature. There will be discussion in the target language of topics derived from teaching materials, leading to small-scale research projects based on the same range of topics and incorporating the use of press reports and articles as well as audio and visual material. Students are encouraged to devote time and energy to developing linguistic proficiency outside the timetabled classes, for instance by additional reading and/or participating in informally arranged conversation groups and in events at which Italian is spoken. Audio and video laboratories are available to augment classwork

ESML0245: Italian stage 3B (6 credits)
Semester 2
Credits: 6
Contact:
Topic: Italian
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0244
Amis & Learning Objectives: A continuation of Italian Stage 3A.
Content:
A continuation of Italian Stage 3A.

ESML0262: Spanish stage 6A (advanced intermediate) (6 credits)
Semester 1
Credits: 6
Contact:
Topic: Spanish
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0263
Aims & learning objectives:
This course concentrates on the more advanced aspects of Spanish with continued emphasis on practical application of language skills in a relevant context, in order to refine further the student's abilities.
Content:
This unit contains a variety of listening, reading, speaking and writing tasks covering appropriate grammatical structures and vocabulary. There is continued further development of the pattern of work outlined in Spanish Stage 5A and 5B

ESML0263: Spanish stage 6B (6 credits)
Semester 2
Credits: 6
Contact:
Topic: Spanish
Level: Level 1
Assessment: EX45 CW40 OR15
Requisites: Co ESML0262
Aims & learning objectives:
A continuation of Spanish Stage 6A
Content:
A continuation of Spanish Stage 6A

MANG0069: Introduction to accounting & finance
Semester 1
Credits: 5
Contact:
Topic:
Level: Level 1
Assessment: EX50 CW50
Requisites:
Aims & learning objectives:
To provide students undertaking any type of degree study with an introductory knowledge of accounting and finance
Content:
The role of the accountant, corporate treasurer and financial controller Sources and uses of capital funds Understanding the construction and nature of the balance sheet and profit and loss account Principles underlying the requirements for the publication of company accounts Interpretation of accounts - published and internal, including financial ratio analysis Planning for profits, cash flow. Liquidity, capital expenditure and capital finance Developing the business plan and annual budgeting Estimating the cost of products, services and activities and their relationship to price. Analysis of costs and cost behaviour

MANG0069: Introduction to accounting & finance
Semester 2
Credits: 5
Contact:
Topic:
Level: Level 1
Assessment: EX50 CW50
Requisites:
Aims & learning objectives:
To provide students undertaking any type of degree study with an introductory knowledge of accounting and finance
Content:
The role of the accountant, corporate treasurer and financial controller Sources and uses of capital funds Understanding the construction and nature of the balance sheet and profit and loss account Principles underlying the requirements for the publication of company accounts Interpretation of accounts - published and internal, including financial ratio analysis Planning for profits, cash flow. Liquidity, capital expenditure and capital finance Developing the business plan and annual budgeting Estimating the cost of products, services and activities and their relationship to price. Analysis of costs and cost behaviour

MANG0072: Managing human resources
Semester 1
Credits: 5
Contact:
Topic:
Level: Level 1
Assessment: EX100
Requisites:
Aims & learning objectives:
The course aims to give a broad overview of major features of human resource management. It examines issues from the contrasting perspectives of management, employees and public policy.
Content:
Perspectives on managing human resources. Human resource planning, recruitment and selection. Performance, pay and rewards. Control, discipline and dismissal.

MANG0073: Marketing
Semester 2
Credits: 5
Contact:
Topic:
Level: Level 1
Assessment: EX100
Requisites: Ex MANG0016
Aims & learning objectives:
1. To provide an introduction to the concepts of Marketing. 2. To understand the principles and practice of marketing management. 3. To introduce students to a variety of environmental and other issues facing marketing today.
Content:
Marketing involves identifying and satisfying customer needs and wants. It is concerned with providing appropriate products, services, and sometimes ideas, at the right place and price, and promoted in ways which are motivating to current and future customers. Marketing activities take place in the context of the market, and of competition. The course is concerned with the above activities, and includes: consumer and buyer behaviour market segmentation, targetting and positioning market research product policy and new product development advertising and promotion marketing channels and pricing

MANG0074: Business information systems
Semester 1
Credits: 5
Contact:
Topic:
Level: Level 1
Assessment: EX60 CW25 OT15
Requisites:
Aims & learning objectives:
Information Technology (IT) is rapidly achieving ubiquity in the workplace. All areas of the business community are achieving expansion in IT and investing huge sums of money in this area. Within this changing environment, several key trends have defined a new role for computers: a) New forms and applications of IT are constantly emerging. One of the most important developments in recent years has been the fact that IT has become a strategic resource with the potential to affect competitive advantage: it transforms industries and products and it can be a key element in determining the success or failure of an organisation. b) Computers have become decentralised within the workplace: PCs sit on managers desks, not in the IT Department. The strategic nature of technology also means that managing IT has become a core competence for modern organisations and is therefore an important part of the task of general and functional managers. Organisations have created new roles for managers who can act as interfaces between IT and the business, combining a general technical knowledge with a knowledge of business. This course addresses the above issues, and, in particular, aims to equip students with IT management skills for the workplace. By this, we refer to those attributes that they will need to make appropriate use of IT as general or functional managers in an information-based age.
Content:
Following on from the learning aims and objectives, the course is divided into two main parts: Part I considers why IT is strategic and how it can affect the competitive environment, taking stock of the opportunities and problems it provides. It consists of lectures, discussion, case studies. The objective is to investigate the business impact of IS. For example: in what ways are IS strategic? what business benefits can IS bring? how does IS transform management processes and organisational relationships? how can organisations evaluate IS? how should IS, which transform organisations and extend across functions, levels and locations, be implemented? Part II examines a variety of technologies available to the manager and examines how they have been used in organisations. A number of problem-oriented case studies will be given to project groups to examine and discuss. The results may then be presented in class, and are open for debate. In summary, the aim of the course is to provide the knowledge from which students should be able to make appropriate use of computing and information technology in forthcoming careers. This necessitates some technical understanding of computing, but not at an advanced level. This is a management course: not a technical computing course.

MANG0076: Business policy
Semester 2
Credits: 5
Contact:
Topic:
Level: Level 1
Assessment: EX60 CW40
Requisites:
Aims & learning objectives:
To provide an appreciation of how organisations develop from their entrepreneurial beginnings through maturity and decline . To examine the interrelationship between concepts of policy and strategy formulation with the behavioural aspects of business To enable students to explore the theoretical notions behind corporate strategy Students are expected to develop skills of analysis and the ability to interpret complex business situations.
Content:
Business objectives , values and mission; industry and market analysis ; competitive strategy and advantage ; corporate life cycle; organisational structures and controls .

MATE0001: Introduction to materials science & engineering 1A
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: CW80 PR20
Requisites:
Aims & learning objectives:
Materials Science applies principles of physics and chemistry to materials of engineering interest. This course aims to be of general interest, and to show students its scope and philosophy.
Content:
(i) An introduction to the various categories of materials - polymers, metals, ceramics and natural materials. A comparative overview of their price, availability and mechanical properties followed by an introduction to the manufacturing processes that can be applied to them. (ii) Can strength and stiffness of materials be explained in terms of atomic structure? Concepts of strength and elastic modulus; the atomic and molecular constitution of different types of material. Primary and secondary bonding; potential energy curves for ionic, covalent and van der Waals bonds. Structure and 'bond density'; relation between potential energy curves and modulus; Hooke's law;. Relation between P.E. curves and strength; brittle strength; surface cracks; toughening; fibres & whiskers. Students must have A-level Physics or Chemistry to undertake this unit.

MATE0002: Crystal structure
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX60 CW20 PR20
Requisites:
Aims & learning objectives:
To introduce the techniques for concise representation of atomic arrangements in crystalline materials. To present the basic rules governing the crystal structures adopted by both elements and simple compounds. On completion, the student should be able to: describe simple crystal structures using standard crystallographic notation and terminology; represent crystal planes and directions using standard notation and perform simple calculations; identify the key features of a given material which are responsible for its observed crystal structure.
Content:
Crystallography: Lattices, unit cells and cell centring, crystal systems, Bravais lattices, symmetry. Lattice planes and directions, notation and calculation of interplanar spacing and angles. Crystal Chemistry: Structures of metals, CCP, HCP and BCC, interstitial sites in metal structures. Factors governing ionic structures, coordination numbers and polyhedra, radius ratio rules, polarisation effects, Pauling's rules. Factors governing covalent structures. Examples of structures, AX and AX2 compounds, carbon, Perovskite, SiO2 structures and phase transitions, silicates. Crystallinity in polymers: Evidence for crystallinity, structures of polymers, single crystals, spherulites, factors influencing crystallinity. Students must have A-level Physics or Chemistry in order to undertake this unit.

MATE0004: Materials chemistry 1A
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX60 PR20 CW20
Requisites:
Aims & learning objectives:
To revise and extend knowledge of the principles of physical chemistry, as applied to materials. On completion, the student should be able to: perform simple calculations on enthalpy, entropy and Gibbs Free Energy and their inter-relationships, phase equilibria, chemical kinetics, and electrochemistry.
Content:
Thermodynamics: thermodynamic functions, the first law, thermochemistry; the second law, classical and statistical definitions of entropy, reversible and irreversible processes, free energy and chemical equilibrium; phase equilibria in one-component systems, Clausius-Clapeyron equation. Introduction to equilibria in binary systems, introduction to Gibbs phase rule; introduction to the third law and standard entropies. Kinetics: rate of reaction, differential rate equations, order of reaction, integral rate equation for first and second order reactions; effect of temperature on reaction rates, the Arrhenius equation, introduction to transition state theory; evaluation of rate constant, determination of reaction mechanisms. Electrochemistry: Faraday's Laws, electrodes and electrochemical cells, cell notation, electrode and cell potentials, Nernst's equation, electrochemical and galvanic series, introduction to corrosion cells.

MATE0005: Introduction to materials science & engineering 1B
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: CW80 PR20
Requisites: Pre MATE0001
Aims & learning objectives:
Materials Science applies principles of physics and chemistry to materials of engineering interest. This course aims to be of general interest, and to show students its scope and philosophy.
Content:
(i) Why do metals corrode? The causes of corrosion; corrosion as an electrochemical process. Examples (with case studies): galvanic corrosion, differential aeration cell, crevice corrosion, pitting corrosion, selective de-alloying, sensitisation of stainless steel and weld decay. General case study: corrosion and corrosion control in motor vehicles. (ii) Collapse of the Alexander Kjelland oil rig. Need for engineering structures in extreme environments. Economics of North Sea oil, nature of North Sea environment. Load bearing capacity of materials, failure of materials. Need for rational analysis of elasticity, fracture and flow. Outline of elementary elastic analysis and Griffith fracture theory. Materials parameters (modulus, strength, toughness) and dependence on material (esp. quality of steels). Description of Alexander Kjelland rig. Report of sequence of events in disaster. Analysis of events and explanation of causes of collapse in terms of materials science and engineering. Consequences for design of systems to withstand failure, general approach for all major engineering projects (other examples:- Amsterdam 747 crash, Challenger space shuttle explosion).

MATE0006: Crystal imperfections
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX60 CW20 PR20
Requisites:
Aims & learning objectives:
To introduce the concept of crystal imperfections, in particular point defects and dislocations. To describe the principal characteristics of such defects and illustrate their behaviour. On completion the student should be able to: describe the principal types of point and line defects; understand how they move and interact; relate aspects of macroscopic materials properties to microscopic defect behaviour.
Content:
Imperfections in crystals: Point defects in elements and compounds, thermodynamics of point defects, diffusion mechanisms, origin of non-equilibrium point defect concentrations. Influences of point defects on materials properties. Theoretical shear stress. Geometry of dislocations, the Burgers vector and Burgers circuit, edge, screw and mixed dislocations. Dislocation glide, force acting on a dislocation, Peierls-Nabarro stress. Dislocation climb. Techniques for the observation of dislocations. Elastic properties of dislocations, strain energy, line tension. Dislocation intersections and jogs. Dislocations in FCC crystals, perfect and imperfect dislocations, Shockley and Frank partials, Thompson's tetrahedron, dislocation reactions. Origin of dislocations, point defect condensation, Frank-Read source, multiple cross-slip, misfit dislocations and growth-induced dislocations. Barriers to dislocation motion.

MATE0007: Mechanics of materials
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
To introduce the mathematical techniques used to describe the response of materials to applied loads. On completion, the student should be able to: perform calculations relating deformations and states of stress in solid materials to the loads applied, for a number of simple cases.
Content:
Forces on a structure and their distribution and measurement. Tension and compression stress and strain, Hooke's law, strain energy in a deformed solid. Two-dimensional stress and Mohr's circle of stress. Two- and three-dimensional stress/strain relationships, hydrostatic stress and bulk modulus. Plane stress and plane strain. Plastic yielding of isotropic solids: the von Mises and Tresca failure criteria. Stress distributions around a hole of circular or elliptical shape and qualitative treatment of the stress concentration at a sharp notch. Stress distribution in simple components, compatibility of strains and equilibrium of stress. Tension of elastic homogeneous and non-homogeneous rods. Tension of circular shafts. Symmetric bending of homogeneous and composite elastic beams. Thin-walled and thick-walled cylinders under pressure. Deflection curves of elastic beams. Twisting of shafts. Inelastic bending and residual stress. Elastic failure: the Euler theory of buckling.

MATE0008: Materials processing 1B
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX60 CW20 PR20
Requisites:
Aims & learning objectives:
To acquaint students with the physical principles involved in common manufacturing processes, to establish the link between processing route and internal structure of materials. On completion, the student should be able to: describe the main features of common manufacturing processes for metals; explain the variations in macro- and microstructure produced by the different processes; discuss the advantages and limitations of competing processes.
Content:
Processing from the Liquid State: structure and properties of castings, effect of process variables on casting quality. Residual stresses. Processing from the Solid State: Rolling, extrusion, drawing, pressing and forging. Deformation characteristics, the effect of temperature and deformation rate on micro and macrostructures. Superplasticity. Quality control during processing. Effect of processing on material properties and structure. Machining: brief survey of conventional and specialised methods. Quality of machined surfaces, 'machinability', advantages and disadvantages. Joining Processes: solidification in weld metal, residual stresses, chemical reactions, contaminants; fusion and solid state processes, brazing and soldering, adhesive bonding. Non-Destructive Testing: dye penetrant, x-ray, magnetic particles, ultrasonic, optical holography, acoustic emission.

MATE0009: Metals & alloys
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX60 CW20 PR20
Requisites: Pre MATE0002
Aims & learning objectives:
To introduce the principles of alloy constitution and show their application to the thermal and mechanical treatment of engineering alloys. On completion, the student should be able to: identify common types of alloy phase, their characteristics and their interactions; interpret simple binary phase diagrams; describe and explain the effects of commercial heat treatments on steels and light alloys.
Content:
Microstructure of metals, grain refinement, influence of grain size on mechanical properties, the Petch equation; microstructural and mechanical effects of cold-working and annealing; applications and limitations of pure metals. Alloys: Solid solutions, factors determining solubility, effect of composition on properties, intermediate phases and phase structure. Phase diagrams of binary systems, invariant reactions, precipitation from solution. Equilibrium microstructures in simple systems of commercial interest; Al-Si, Cu-Ni, Cu-Zn, Cu-Al, Fe-C, cast irons. Departures from equilibrium, coring and undercooling. Normalised and annealed steels. Non-equilibrium structures; age-hardening systems, steels, quenching and hardenability, tempering, selected alloy steels.

MATE0010: Electronic structure & materials properties
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX60 CW20 PR20
Requisites:
Aims & learning objectives:
To provide a coherent quantum-mechanical treatment of the behaviour and role of electrons in solids. To introduce the concepts of: wave-particle duality; quantum mechanical uncertainty and wave functions. To provide a quantum mechanical description of bonding and electrical conduction in solids.
Content:
Classical theory of electrical conduction in metals, Ohm's Law, thermal conductivity, electronic specific heat and the failure of classical theory. DeBroglie wave length, wave-particle duality, Heisenberg uncertainty principle, Schroedinger wave equation. Electrons in an infinite potential well, quantum states, quantum numbers, energy levels, density of states, the free electron model, Fermi energy, k-space, the Fermi surface. Electrical conduction in a free-electron metal, electron scattering, resistivity of pure and impure metals. Nearly free electron model, Bragg reflections, energy gaps, zone boundaries, Brillouin zones, band overlap, semi-conductors and insulators. Qualitative solution of the Schroedinger equation for hydrogen, wave functions and quantum numbers; atomic orbitals. Bonding between atoms; linear combination of atomic orbitals; hybridisation; s and p bonds; delocalisation; structure of molecules. Students must have A-level Mathematics and A-level Physics or Chemistry in order to undertake this unit.

MATE0011: Mechanical properties of materials
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX60 CW20 PR20
Requisites:
Aims & learning objectives:
To extend the mathematical description of the effects of loads upon materials, and to relate their mechanical behaviour to their internal structures. On completion, the student should be able to: convert between tensor and orthodox descriptions of elastic behaviour; characterise time-dependent effects in the deformation of materials; recognise the interaction of time and temperature effects.
Content:
Elasticity: cohesion and bonding, energy-distance curves and Hooke's Law, departures from linear elastic behaviour, elastic properties derived from bond energies. Elasticity theory of crystals, stress and strain tensors, elastic anisotropy, symmetry. Elastically isotropic solids, technical elastic moduli, measurement of moduli. Anelasticity: cyclic stressing and internal friction. thermoelastic effect, Snoek effect, other mechanisms. Specific damping capacity, logarithmic decrement, loss tangent. Viscoelasticity: viscous flow, linear viscoelasticity, spring and dashpot models. Creep and stress relaxation behaviour. Physical mechanisms of viscoelastic behaviour. The glass transition temperature. Time-temperature superposition, master curves for creep compliance and stress relaxation modulus. Effect of molecular architecture and chemical composition on viscoelastic properties. Dynamic viscoelasticity, the complex modulus, dynamic loading of Voigt and Maxwell models, standard linear solid and generalised models, master curves. Moduli and loss tangent as functions of frequency and temperature. Inter-relation of viscoelastic parameters. The effect of polymer structure and crystallinity on dynamic behaviour, mechanical spectroscopy. Non-linear viscoelastic behaviour.

MATE0012: Materials processing 2A
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX60 CW20 PR20
Requisites:
Aims & learning objectives:
To extend the student's knowledge of processing / structure / property relationships in materials, in particular to include polymer and ceramic processing. On completion, the student should be able to: assess materials processing routes using objective criteria such as production rate, dimensional accuracy, flexibility; be aware of techniques for the surface modification of materials.
Content:
Polymer Processing; Newtonian and power flow, Poiseuille equation, rheometry. Injection moulding and extrusion of thermoplastics, die design and quality control, blow moulding, calendering and pressure forming of polymer sheet. Transfer and pressure moulding of filled and unfilled thermosetting and thermoplastic polymers. Ceramic processing: production of powders: purity control, cold and hot compacting, sintering. Relative merits of powder methods for metals and ceramics.

MATE0013: Ceramics & glasses
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX60 CW20 PR20
Requisites: Pre MATE0009, Pre MATE0002
Aims & learning objectives:
To introduce the application of constitutional and kinetic principles to the manufacture and exploitation of ceramics and inorganic glasses. On completion, the student should be able to: distinguish between ceramics and glasses on a basis of their structures and properties; describe the relationship between various classes of ceramic and their applications.
Content:
Classification of Ceramics. What is a ceramic? Revision of crystal structures and forces with specific reference to the scientifically and technologically important ceramic materials. General properties of ceramics, mechanical, chemical, thermal, optical, magnetic and electrical. The nature of brittle ceramics and the use of statistics for mechanical design. Classification of ceramics, traditional, refractories, advanced ceramics, both structural and functional to include examples of technological importance. Strengthening and toughening of ceramics. Precursor materials, powder manufacture and powder processing. Ceramic forming methods, wet and dry. Drying of ceramic powder compacts. Densification and sintering, both solid and liquid phase. Hot pressing. Reaction bonding. Pyrolytic deposition. Use of phase diagrams. Structural chemistry of the common glasses. Networks and network modifiers. The glass transition temperature, viscosity, thermal optical and electrical properties. Special glasses, their technology and use. Electrical properties, ionic and electronic conduction, Switching glasses. Lenses, fibre optics, thermal and mechanical properties, glass to metal seals. Stress relief, toughened glass, surface effects, ion exchange and implantation. Composite applications. Glass ceramics.

MATE0014: Polymers
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX60 CW20 PR20
Requisites: Pre MATE0002
Aims & learning objectives:
To introduce the principles of polymer science with particular emphasis on those aspects relevant to polymers as practical engineering materials.
Content:
Introduction. Homopolymers, copolymers,linear, crosslinked, tacticity, plastics, rubbers, fibres, molecular weight. The versatility of polymers.
* The Length of Chains: Molecular Weight
* Molecular Weight - Definitions, determination
* Molecular Motion & the Glass Transition
* Glass transition temperature effect of structure.
* Molecular motion: nature of vitrification
* Viscoelasticity effect of temperature rate and structure
* Crystallinity. Morphology effect of molecular structure Where do polymers come from? - Polymerisation
* Polymerisation Classification. Examples and mechanisms of step and chain polymerisation. Kinetics of radical polymerisation
* Step polymerisation. Carothers equation. Molecular weight distribution, Copolymer equation. The dramatic properties of rubber
* Elastomers. Chemical nature, vulcanisation
* Stereospecific polymerisation, kinetic theory of rubber elasticity The environmental dimension
* Additives. Fillers, plasticisers, antistatic agents.
* Degradation: thermal, ultra-violet, stabilisers.

MATE0015: Physical methods of analysis
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX60 CW20 PR20
Requisites: Pre MATE0010
Aims & learning objectives:
To introduce the physical principles employed in a variety of instrumental techniques for materials analysis, particularly those based on diffraction and on spectroscopy. On completion, the student should be able to: describe methods of forming an image by electromagnetic waves; recognise the scope and limitations of optical microscopy n its various forms; discuss the scattering, diffraction and absorption of X-rays and electrons and their use in chemical and structural analysis.
Content:
Electromagnetic Waves: e-m spectrum, generation of e-m waves. Lasers. Polarization. Superposition of waves, interference. Huygens' wave construction, diffraction from a single aperture, diffraction grating. Optical Microscopy: resolving power, depth of field, lens aberrations. Spectroscopy: emission and absorption spectra. Optical, infrared and ultraviolet spectroscopy. X-ray techniques: generation of X-rays, characteristic and continuous radiation. X-ray scattering and absorption. Detection of X-rays. X-ray fluorescence analysis. X-ray diffraction, powder patterns, determination of lattice parameters, structure factor and diffraction intensities. Single crystal diffraction, Laue back reflection technique. Electron Microscopy and Analysis: Electron waves, interaction of electrons with matter. Transmission electron microscope. The Laue conditions, reciprocal lattice and the Ewald sphere. Electron diffraction, analysis of diffraction patterns. Methods of specimen preparation, applications. Scanning electron microscope, resolving power, image contrast. Applications. Electron probe microanalysis, X-ray spectrometers and solid state detectors, quantitative analysis, applications. Scanning transmission electron microscopy. Surface analysis techniques: auger analysis, electron spectroscopy, secondary ion mass spectrometry.

MATE0016: Dissertation 2B
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: ES80 OR20
Requisites:
Aims & learning objectives:
To provide a self-instruction exercise in the seeking, retrieval, organisation and presentation of information in a technological field. On completion, the student should be able to: write an extended critical discussion of a given subject area; make an oral presentation of the relevant material.
Content:
An introduction to an essential research technique - the retrieval and assessment of information from the scientific literature. Each student is assigned a specific subject area and with the help of a supervisor prepares an extended essay based on a critical review of the literature. An oral presentation is to be made at a conference within the School.

MATE0017: Physical properties of materials
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX60 CW20 PR20
Requisites:
Aims & learning objectives:
To introduce the methods of statistical mechanics. To provide a coherent explanation of the thermal properties of crystalline electrically insulating solids. To explain the magnetic and dielectric properties of materials and their optimization for particular engineering applications.
Content:
Thermal Properties: Elements of statistical mechanics, Maxwell-Boltzmann distribution: introduction to lattice vibrations, quantisation. Debye temperature, specific heat, thermal conductivity, phonons, thermal expansion. Magnetic Properties: Dipole moment of atomic orbitals, quantisation, dipole moment of atoms in solids, spin-orbit coupling, orbital quenching, crystalline field anisotropy, exchange, spontaneous magnetisation, ferromagnetism. Magnetocrystalline anisotropy, magnetisation energy, domains, Bloch walls, magnetisation process, hysteresis, domain wall pinning, soft and hard materials. Permanent magnets and transformer cores. Ferrimagnetism, ferrites magnetic recording. Dielectrics: Dielectric constant, dielectric breakdown. Capacitors, Ferroelectricity, properties of perovskite dielectrics, piezoelectricity, applications and materials. Pyro-electricity, infrared detection.

MATE0018: Deformation & fracture of materials
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
To present a detailed treatment of the micromechanisms of deformation in the main categories of materials, encompassing effects of temperature, load pattern and environment. On completion, the student should be able to: discuss theoretical "strengthening mechanisms" in metals and alloys, and their ability to account for mechanical behaviour over a wide range of conditions; describe mechanisms of large-scale deformation in amorphous and semicrystalline polymers; use concepts of fracture mechanics and probability to account for the strengths of brittle materials.
Content:
Plastic deformation of metals: revision of dislocation theory. High temperature deformation, creep mechanisms, structural changes. Effect of cyclic loading, structural changes and appearance of fracture surfaces, the fatigue limit, crack initiation and growth. Plastic deformation of polymers: large scale deformation and flow in amorphous and semi-crystalline polymers, cold drawing and molecular orientation, effect of temperature and strain rate. Mechanics and physics of fracture: theoretical cleavage strength, the real strength of brittle solids, the conditions for ductile/brittle transition; Griffith's treatment of thermodynamics of fracture, Orowan's extension to non-ideally-brittle solids. Work of fracture, stress distribution at the tip of cracks. Fracture mechanics, critical stress intensity and strain energy release rate. Plane strain and plane stress, KIc as an engineering design parameter, measurement of KIc. Statistical analysis of failure, flaw-size distributions, weakest link model. Environmental effects, slow crack growth in glasses and polymers, K/V diagrams, environmental stress cracking.

MATE0019: Electrical and magnetic properties of materials
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
To explain the magnetic and dielectric properties of materials and their optimization for particular engineering applications. To provide a coherent quantum-mechanical treatment of the behaviour and role of electrons in solids. To provide the theoretical background for the treatment of electrons in semiconductors that is employed in MATE0037, Semiconductor microtechnology.
Content:
Magnetic Properties: Dipole moment of atomic orbitals, quantisation, dipole moment of atoms in solids, spin-orbit coupling, orbital quenching, crystalline field anisotropy, exchange, spontaneous magnetisation, ferromagnetism. Magnetocrystalline anisotropy, magnetisation energy, domains, Bloch walls, magnetisation process, hysteresis, domain wall pinning, soft and hard materials. Permanent magnets and transformer cores. Ferrimagnetism, ferrites magnetic recording. Dielectrics: Dielectric constant, dielectric breakdown. Capacitors, Ferroelectricity, properties of perovskite dielectrics, piezoelectricity, applications and materials. Pyro-electricity, infrared detection. Classical theory of electrical conduction in metals, Ohm's Law, thermal conductivity, electronic specific heat and the failure of classical theory. DeBroglie wave length, wave-particle duality, Heisenberg uncertainty principle, Schroedinger wave equation. Electrons in an infinite potential well, quantum states, quantum numbers, energy levels, density of states, the free electron model, Fermi energy, k-space, the Fermi surface. Electrical conduction in a free-electron metal, electron scattering, resistivity of pure and impure metals. Nearly free electron model, Bragg reflections, energy gaps, zone boundaries, Brillouin zones, band overlap, semi-conductors and insulators.

MATE0020: Thermodynamics of materials
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
This unit, which builds on principles established in the Materials Chemistry 1A unit, aims to introduce the thermodynamic and kinetic basis for the understanding of structural changes in materials, and of material / environment interactions. On completion, the student should be able to: perform thermodynamic calculations relating to oxidation-reduction reactions, equilibria at solid / liquid interfaces, equilibria between binary phases; interpret binary phase diagrams; discuss the stability of phases in thermodynamic terms.
Content:
Brief revision of essential thermodynamic principles. Development of these to the chemical potential. Derivation of Gibbs' phase rule; application of this rule to phase diagrams. Ellingham diagrams for oxides and other systems, and their application to materials processing. Thermodynamics of liquid and solid surfaces: the equations of Young, Laplace and Kelvin; surface stress, orientation and grain-boundary effects; wetting of solids by liquids, equations of Young and DuPré. Solution thermodynamics: ideal and regular solutions, entropy of mixing, free energy curves, solid solubility, order, disorder and clustering. The uses of solution thermodynamics for understanding the behaviour of multicomponent materials. Phase Transformations: Homogeneous nucleation theory, transition state theory of growth, application to liquid-solid transformations. Solid state reactions, homogeneous and heterogeneous nucleation, influence of lattice strain on nucleus shape and coherency. Diffusion in Solids: The diffusion equation, solution of Fick's Second Law, effects of variables on diffusion constant, the Kirkendall effect, intrinsic and self-diffusion coefficients. Diffusion mechanisms; vacancy, pipe, and grain boundary diffusion. Thermodynamics of Phase Diagrams: Rationalisation of binary diagrams by relation to free energy/composition curves, metastable phases, driving force for transformations, spinodal region, ternary phase diagrams. Transformation Kinetics: Interplay of thermodynamics and kinetics in glass-forming systems. Precipitation of phase differing in composition from matrix, including intermediate transformation products, spinodal decomposition. Martensitic reactions.

MATE0021: Project dissertation
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: ES80 OR20
Requisites:
Aims & learning objectives:
To provide a thorough preparation for the final year experimental project. On completion, the student should be able to: write an extended literature review in the field of his project, and define its objectives; present a detailed experimental programme to achieve these objectives; make an oral presentation based on the above.
Content:
An introduction to the planning of a research programme. Each student is assigned a specific project, and with the help of a supervisor prepares an extended critical review of the literature, and plans an experimental programme in the relevant area.

MATE0022: Materials selection in engineering design
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
To co-ordinate previous studies of structural materials, first by a detailed consideration of composite materials, and afterwards by examining the selection of materials for real engineering applications. On completion, the student should be able to: describe the various types of fibre composite materials, their manufacture and characteristics; discuss theoretical models for strength and stiffness of composites; describe the overall process of engineering design, and the place in it of materials selection; deduce from standard test results the materials information required for design; analyse materials requirements and propose solutions to the selection problem in specified design situations.
Content:
Introduction to composites and their applications in engineering. Nature of fibre composite materials, manufacturing processes, elastic behaviour; elements of classical thin laminate theory, strength, toughness; the use of commercial software for designing with composites. The design process; the designer and materials selection. Design aspects of elastic properties, strength and fracture toughness. Design procedures for creep in metals and plastics, extrapolation methods. Fatigue, master diagrams for design purposes, damage accumulation laws, application of fracture mechanics, designing against fatigue. Non-destructive evaluation of materials and component quality. Selection of a manufacturing process. Formalised procedures for materials selection.

MATE0023: Surfaces & interfaces
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX75 CW25
Requisites:
Aims & learning objectives:
Students will be introduced to techniques for the observation, manipulation and control of solid surfaces on the nanometre scale and to some fundamental aspects of the science of adhesion. After participating in the course, students should be familiar with the physical principles and instrumentation associated with scanning probe microscopy, and be aware of a range of its application in science and nanotechnology. They should also understand the importance, and underlying scientific principles of crystal engineering through the control of crystallisation behaviour. They will be encouraged to integrate their knowledge and understanding of other units throughout the Materials Science and Engineering course, and will have had experience of reading original literature and of presenting their own views of it orally to their peers.
Content:
The structure and nature of crystalline surfaces. Basic surface crystallography, reconstruction and relaxation, overview of surface characterisation techniques.Nanoscale observation and manipulation of solid surfaces. Scanning probe microscopy, principles and methods, scanning tunnelling microscopy, force microscopy and variants. Applications: characterisation, atomic and molecular manipulation, nanoscale surface modification for data storage, nanoscale electronic devices. Crystal engineering through control of surface processes. Technological importance of crystallite properties, crystalline imperfections, impurity effects, tailor-made additives.Practical surfaces of engineering materials. Adhesion: strength of an adhesive bond, mechanical properties and interfacial forces. Study of some original literature in the area of interfaces, polymers and adhesion.

MATE0024: Corrosion engineering
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
To present a detailed consideration of the factors influencing the interaction of materials with their environments, with a view to improving durability in practical situations. On completion, the student should be able to: apply thermodynamic and kinetic principles to the operation of electrochemical processes of corrosion and anti-corrosion; assess the merits of various anti-corrosion measures; describe the mechanisms of attack upon metals by high-temperature gases.
Content:
Electrochemical corrosion: types of corrosion, thermodynamics of corrosion cells, electrode kinetics, exchange current density, activation polarisation, Butler-Volmer equation, Tafel equation, concentration and resistance polarisation. Common cathodic processes. Evans diagrams, applications. Pourbaix diagrams. Polarisation studies, pitting phenomena. Conjoint action, stress-corrosion, hydrogen embrittlement, corrosion fatigue, fretting corrosion, cavitation erosion and impingement attack. Corrosion prevention, surface preparation and coatings, cathodic and anodic protection, corrosion inhibitors, corrosion resistant alloys. Introduction to thermodynamics and kinetics of oxidation of metals. Adsorption of gases on solids, physical and chemical adsorption, Henry's Law, Langmuir and BET equations. High temperature corrosion: nucleation and growth of oxides; the oxidation rate laws. Wagner theory of parabolic oxidation. Defect nature of oxides; effects of partial pressure of oxygen, effect of foreign ion additions to base metal; stresses in oxides. Oxidation of alloys, internal oxidation and scale formation. Corrosion of alloys in combustion gases, oxidation, sulphidation, molten salt attack (hot corrosion).

MATE0025: Materials engineering
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
To make the student aware of issues of current scientific and professional interest across the field of materials engineering. On completion, the student should be able to: discuss critically, topics of current interest, identifying their underlying principles and commenting upon their significance, both technical and social.
Content:
Research Colloquia. This part of the course consists of talks by experts in their fields on advanced aspects of the science and engineering of materials which complement and extend the more formal curriculum of the lecture courses.

MATE0026: Project
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: PR80 OR20
Requisites:
Aims & learning objectives:
To provide experience in the performance of an extended research programme, involving assimilation of the relevant literature, planning and execution of experimental work, analysis of results, and the drawing and reporting of conclusions. On completion, the student should be able to: exploit information sources to familiarise himself with a new subject area; identify critical parameters in an experiment, measure and analyse them; recognise and account for factors limiting the precision of experimental measurements; write an extended report in acceptable style describing his findings; make a clear oral presentation of the project.
Content:
The student will carry out an experimental research project which is timetabled for one full day per week. This will be done under the guidance of a member of staff. In many cases the project will be part of a wider programme involving graduate students and research staff, so that the student will gain experience of research team work.

MATE0031: Study year abroad
Academic Year
Credits: 60
Contact:
Topic:
Level: Level 2
Assessment:
Requisites:
Aims & learning objectives:
Please see Director of Studies for further information about the Aims & Learning Objectives of the Study year abroad.

MATE0032: Industrial training
Academic Year
Credits: 60
Contact:
Topic:
Level: Level 2
Assessment:
Requisites:
Aims & Learning Objective: Please see the Director of Studies for more detailed information about the Aims & Learning Objectives of the Industrial training year.

MATE0033: Project dissertation (MEng)
Semester 2
Credits: 6
Contact:
Topic:
Level: Undergraduate Masters
Assessment: ES80 OR20
Requisites:
Aims & learning objectives:
Please see the Director of Studies for further information about this unit which is designed for MEng students and enables them to undertake an extended research project.

MATE0037: Semiconductor microtechnology
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
To provide detailed coverage of the science and technology exploited in semiconductor electronic devices. On completion, the student should be able to: treat quantitatively the electrical characteristics of semiconducting materials and simple devices; describe the manufacture and characteristics of semiconductor devices and have a quantitative appreciation of the limitations imposed and effects caused by impurities and materials imperfections.
Content:
Revision of nearly-free electron model, electron effective mass, electrons and holes, contact potentials. Intrinsic semiconductors; Fermi level, carrier concentration, mobility, conductivity, temperature dependence, recombination and trapping, carrier diffusion. Extrinsic semiconductors; P type and N type impurities, Fermi level, carrier concentration, conductivity, temperature dependence. The P-N junction; 'built-in potential', carrier diffusion, depletion layer, forward and reverse bias. The junction transistor, field effect transistor, semiconductor surface potentials, surface effect devices, other simple semiconductor devices. Crystal purification and growth, epitaxy. Doping and dopant profiles. Oxidation and photolithography. Metallization and packaging. Very large scale integration (VLSI), MOS (metal-oxide-semiconductor) and bipolar technologies. Photoemissive materials and devices. Light emitting diodes, photoconductivity and devices. Semi-conductor lasers.

MATH0001: Numbers
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 1
Assessment: EX100
Requisites:
Students must have A-level Mathematics, normally Grade B or better, or equivalent, in order to undertake this unit. Aims & learning objectives:
Aims: This course is designed to cater for first year students with widely different backgrounds in school and college mathematics. It will treat elementary matters of advanced arithmetic, such as summation formulae for progressions and will deal matters at a certain level of abstraction. This will include the principle of mathematical induction and some of its applications. Complex numbers will be introduced from first principles and developed to a level where special functions of a complex variable can be discussed at an elementary level. Objectives: Students will become proficient in the use of mathematical induction. Also they will have practice in real and complex arithmetic and be familiar with abstract ideas of primes, rationals, integers etc, and their algebraic properties. Calculations using classical circular and hyperbolic trigonometric functions and the complex roots of unity, and their uses, will also become familiar with practice.
Content:
Natural numbers, integers, rationals and reals. Highest common factor. Lowest common multiple. Prime numbers, statement of prime decomposition theorem, Euclid's Algorithm. Proofs by induction. Elementary formulae. Polynomials and their manipulation. Finite and infinite APs, GPs. Binomial polynomials for positive integer powers and binomial expansions for non-integer powers of a+b. Finite sums over multiple indices and changing the order of summation. Algebraic and geometric treatment of complex numbers, Argand diagrams, complex roots of unity. Trigonometric, log, exponential and hyperbolic functions of real and complex arguments. Gaussian integers. Trigonometric identities. Polynomial and transcendental equations.

MATH0002: Functions, differentiation & analytic geometry
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 1
Assessment: EX100
Requisites:
Students must have A-level Mathematics, normally Grade B or better, or equivalent, in order to undertake this unit. Aims & learning objectives:
Aims: To teach the basic notions of analytic geometry and the analysis of functions of a real variable at a level accessible to students with a good 'A' Level in Mathematics. At the end of the course the students should be ready to receive a first rigorous analysis course on these topics. Objectives: The students should be able to manipulate inequalities, classify conic sections, analyse and sketch functions defined by formulae, understand and formally manipulate the notions of limit, continuity and differentiability and compute derivatives and Taylor polynomials of functions.
Content:
Basic geometry of polygons, conic sections and other classical curves in the plane and their symmetry. Parametric representation of curves and surfaces. Review of differentiation: product, quotient, function-of-a-function rules and Leibniz rule. Maxima, minima, points of inflection, radius of curvature. Graphs as geometrical interpretation of functions. Monotone functions. Injectivity, surjectivity, bijectivity. Curve Sketching. Inequalities. Arithmetic manipulation and geometric representation of inequalities. Functions as formulae, natural domain, codomain, etc. Real valued functions and graphs. Introduction to MAPLE. Orders of magnitude. Taylor's Series and Taylor polynomials - the error term. Differentiation of Taylor series. Taylor Series for exp, log, sin etc. Orders of growth. Orthogonal and tangential curves.

MATH0003: Integration & differential equations
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 1
Assessment: EX100
Requisites:
Students must have A-level Mathematics, normally Grade B or better, or equivalent, in order to undertake this unit. Aims & learning objectives:
Aims: This module is designed to cover standard methods of differentiation and integration, and the methods of solving particular classes of differential equations, to guarantee a solid foundation for the applications of calculus to follow in later courses. Objective: The objective is to ensure familiarity with methods of differentiation and integration and their applications in problems involving differential equations. In particular, students will learn to recognise the classical functions whose derivatives and integrals must be committed to memory. In independent private study, students should be capable of identifying, and executing the detailed calculations specific to, particular classes of problems by the end of the course.
Content:
Review of basic formulae from trigonometry and algebra: polynomials, trigonometric and hyperbolic functions, exponentials and logs. Integration by substitution. Integration of rational functions by partial fractions. Integration of parameter dependent functions. Interchange of differentiation and integration for parameter dependent functions. Definite integrals as area and the fundamental theorem of calculus in practice. Particular definite integrals by ad hoc methods. Definite integrals by substitution and by parts. Volumes and surfaces of revolution. Definition of the order of a differential equation. Notion of linear independence of solutions. Statement of theorem on number of linear independent solutions. General Solutions. CF+PI. First order linear differential equations by integrating factors; general solution. Second order linear equations, characteristic equations; real and complex roots, general real solutions. Simple harmonic motion. Variation of constants for inhomogeneous equations. Reduction of order for higher order equations. Separable equations, homogeneous equations, exact equations. First and second order difference equations.

MATH0004: Sets & sequences
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 1
Assessment: EX100
Requisites: Pre MATH0115, Pre MATH0001
Aims & learning objectives:
Aims: To introduce the concepts of logic that underlie all mathematical reasoning and the notions of set theory that provide a rigorous foundation for mathematics. A real life example of all this machinery at work will be given in the form of an introduction to the analysis of sequences of real numbers. Objectives: By the end of this course, the students will be able to: understand and work with a formal definition; determine whether straight-forward definitions of particular mappings etc. are correct; determine whether straight-forward operations are, or are not, commutative; read and understand fairly complicated statements expressing, with the use of quantifiers, convergence properties of sequences.
Content:
Logic: Definitions and Axioms. Predicates and relations. The meaning of the logical operators Ù, Ú, ˜, ®, «, ", $. Logical equivalence and logical consequence. Direct and indirect methods of proof. Proof by contradiction. Counter-examples. Analysis of statements using Semantic Tableaux. Definitions of proof and deduction. Sets and Functions: Sets. Cardinality of finite sets. Countability and uncountability. Maxima and minima of finite sets, max (A) = - min (-A) etc. Unions, intersections, and/or statements and de Morgan's laws. Functions as rules, domain, co-domain, image. Injective (1-1), surjective (onto), bijective (1-1, onto) functions. Permutations as bijections. Functions and de Morgan's laws. Inverse functions and inverse images of sets. Relations and equivalence relations. Arithmetic mod p. Sequences: Definition and numerous examples. Convergent sequences and their manipulation. Arithmetic of limits.

MATH0005: Matrices & multivariate calculus
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 1
Assessment: EX100
Requisites: Pre MATH0002
Aims & learning objectives:
Aims: The course will provide students with an introduction to elementary matrix theory and an introduction to the calculus of functions from IRn ® IRm and to multivariate integrals. Objectives: At the end of the course the students will have a sound grasp of elementary matrix theory and multivariate calculus and will be proficient in performing such tasks as addition and multiplication of matrices, finding the determinant and inverse of a matrix, and finding the eigenvalues and associated eigenvectors of a matrix. The students will be familiar with calculation of partial derivatives, the chain rule and its applications and the definition of differentiability for vector valued functions and will be able to calculate the Jacobian matrix and determinant of such functions. The students will have a knowledge of the integration of real-valued functions from IR² ® IR and will be proficient in calculating multivariate integrals.
Content:
Lines and planes in two and three dimension. Linear dependence and independence. Simultaneous linear equations. Elementary row operations. Gaussian elimination. Gauss-Jordan form. Rank. Matrix transformations. Addition and multiplication. Inverse of a matrix. Determinants. Cramer's Rule. Similarity of matrices. Special matrices in geometry, orthogonal and symmetric matrices. Real and complex eigenvalues, eigenvectors. Relation between algebraic and geometric operators. Geometric effect of matrices and the geometric interpretation of determinants. Areas of triangles, volumes etc. Real valued functions on IR³. Partial derivatives and gradients; geometric interpretation. Maxima and Minima of functions of two variables. Saddle points. Discriminant. Change of coordinates. Chain rule. Vector valued functions and their derivatives. The Jacobian matrix and determinant, geometrical significance. Chain rule. Multivariate integrals. Change of order of integration. Change of variables formula.

MATH0006: Vectors & applications
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 1
Assessment: EX100
Requisites: Pre MATH0001, Pre MATH0002, Pre MATH0003
Aims & learning objectives:
Aims: To introduce the theory of three-dimensional vectors, their algebraic and geometrical properties and their use in mathematical modelling. To introduce Newtonian Mechanics by considering a selection of problems involving the dynamics of particles. Objectives: The student should be familiar with the laws of vector algebra and vector calculus and should be able to use them in the solution of 3D algebraic and geometrical problems. The student should also be able to use vectors to describe and model physical problems involving kinematics. The student should be able to apply Newton's second law of motion to derive governing equations of motion for problems of particle dynamics, and should also be able to analyse or solve such equations.
Content:
Vectors: Vector equations of lines and planes. Differentiation of vectors with respect to a scalar variable. Curvature. Cartesian, polar and spherical co-ordinates. Vector identities. Dot and cross product, vector and scalar triple product and determinants from geometric viewpoint. Basic concepts of mass, length and time, particles, force. Basic forces of nature: structure of matter, microscopic and macroscopic forces. Units and dimensions: dimensional analysis and scaling. Kinematics: the description of particle motion in terms of vectors, velocity and acceleration in polar coordinates, angular velocity, relative velocity. Newton's Laws: Kepler's laws, momentum, Newton's laws of motion, Newton's law of gravitation. Newtonian Mechanics of Particles: projectiles in a resisting medium, constrained particle motion; solution of the governing differential equations for a variety of problems. Central Forces: motion under a central force.

MATH0007: Analysis: Real numbers, real sequences & series
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0006, Pre MATH0004, Pre MATH0005
Aims & learning objectives:
Aims: To reinforce and extend the ideas and methodology (begun in the first year unit MATH0004) of the analysis of the elementary theory of sequences and series of real numbers and to extend these ideas to sequences of functions. Objectives: By the end of the module, students should be able to read and understand statements expressing, with the use of quantifiers, convergence properties of sequences and series. They should also be capable of investigating particular examples to which the theorems can be applied and of understanding, and constructing for themselves, rigorous proofs within this context.
Content:
Suprema and Infima, Maxima and Minima. The Completeness Axiom. Sequences. Limits of sequences in epsilon-N notation. Bounded sequences and monotone sequences. Cauchy sequences. Algebra-of-limits theorems. Subsequences. Limit Superior and Limit Inferior. Bolzano-Weierstrass Theorem. Sequences of partial sums of series. Convergence of series. Conditional and absolute convergence. Tests for convergence of series; ratio, comparison, alternating and nth root tests. Power series and radius of convergence. Functions, Limits and Continuity. Continuity in terms of convergence of sequences. Algebra of limits. Convergence of sequences of functions, point-wise and uniform. Interchanging limits.

MATH0008: Algebra 1
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0006, Pre MATH0004, Pre MATH0005
Aims & learning objectives:
Aims: To teach the definitions and basic theory of abstract linear algebra and, through exercises, to show its applicability. Objectives: Students should know, by heart, the main results in linear algebra and should be capable of independent detailed calculations with matrices which are involved in applications. Students should know how to execute the Gram-Schmidt process.
Content:
Real and complex vector spaces, subspaces, direct sums, linear independence, spanning sets, bases, dimension. The technical lemmas concerning linearly independent sequences. Dimension. Complementary subspaces. Projections. Linear transformations. Rank and nullity. The Dimension Theorem. Matrix representation, transition matrices, similar matrices. Examples. Inner products, induced norm, Cauchy-Schwarz inequality, triangle inequality, parallelogram law, orthogonality, Gram-Schmidt process.

MATH0009: Ordinary differential equations & control
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0001, Pre MATH0002, Pre MATH0003, Pre MATH0005
Aims & learning objectives:
Aims: This course will provide standard results and techniques for solving systems of linear autonoumous differential equations. Based on this material an accessible introduction to the ideas of mathematical control theory is given. The emphasis here will be on stability and stabilization by feedback. Foundations will be laid for more advanced studies in nonlinear differential equations and control theory. Phase plane techniques will be introduced. Objectives: At the end of the course, students will be conversant with the basic ideas in the theory of linear autonomous differential equations and, in particular, will be able to employ Laplace transform and matrix methods for their solution. Moreover, they will be familiar with a number of elementary concepts from control theory (such as stability, stabilization by feedback, controllability) and will be able to solve simple control problems. The student will be able to carry out simple phase plane analysis.
Content:
Systems of linear ODEs: Normal form; solution of homogeneous systems; fundamental matrices and matrix exponentials; repeated eigenvalues; complex eigenvalues; stability; solution of non-homogeneous systems by variation of parameters. Laplace transforms: Definition; statement of conditions for existence; properties including transforms of the first and higher derivatives, damping, delay; inversion by partial fractions; solution of ODEs; convolution theorem; solution of integral equations. Linear control systems: Systems: state-space; impulse response and delta functions; transfer function; frequency-response. Stability: exponential stability; input-output stability; Routh-Hurwitz criterion. Feedback: state and output feedback; servomechanisms. Introduction to controllability and observability: definitions, rank conditions (without full proof) and examples. Nonlinear ODEs: Phase plane techniques, stability of equilibria.

MATH0010: Vector calculus & partial differential equations
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0002, Pre MATH0003, Pre MATH0005, Pre MATH0006
Aims & learning objectives:
Aims: The first part of the course provides an introduction to vector calculus, an essential toolkit in most branches of applied mathematics. The second part introduces methods for the solution of linear partial differential equations. Objectives: At the end of this course students will be familiar with the fundamental results of vector calculus (Gauss' theorem, Stokes' theorem) and will be able to carry out line, surface and volume integrals in general curvilinear coordinates. They should be able to solve Laplace's equation, the wave equation and the diffusion equation in simple domains, using the techniques of separation of variables, Laplace transforms and, in the case of the wave equation, D'Alembert's solution.
Content:
Vector calculus: Work and energy; curves and surfaces in parametric form; line, surface and volume integrals. Grad, div and curl; divergence and Stokes' theorems; curvilinear coordinates; scalar potential. Fourier series: Formal introduction to Fourier series, statement of Fourier convergence theorem; Fourier cosine and sine series. Partial differential equations: classification of linear second order PDEs; Laplace's equation in 2-D, including solution by separation of variables in rectangular and circular domains; wave equation in one space dimension, including D'Alembert's solution; the diffusion equation in one space dimension, including solution by Laplace transform.

MATH0011: Analysis: Real-valued functions of a real variable
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0007
Aims & learning objectives:
Aims: To give a thorough grounding, through rigorous theory and exercises, in the method and theory of modern calculus. To define the definite integral of certain bounded functions, and to explain why some functions do not have integrals. Objectives: Students should be able to quote, verbatim, and prove, without recourse to notes, the main theorems in the syllabus. They should also be capable, on their own initiative, of applying the analytical methodology to problems in other disciplines, as they arise. They should have a thorough understanding of the abstract notion of an integral, and a facility in the manipulation of integrals.
Content:
Weierstrass's theorem on continuous functions attaining suprema and infima on compact interval. Intermediate Value Theorem. Functions and Derivatives. Algebra of derivatives. Leibniz Rule and compositions. Derivatives of inverse functions. Rolle's Theorem and Mean Value Theorem. Cauchy's Mean Value Theorem. L'Hôpital's Rule. Monotonic functions. Maxima/Minima. Uniform Convergence. Cauchy's Criterion for Uniform Convergence. Weierstrass M-test for series. Power series. Differentiation of power series. Reimann integration up to the Fundamental Theorem of Calculus for the integral of a Riemann-integrable derivative of a function. Integration of power series. Interchanging integrals and limits. Improper integrals.

MATH0012: Algebra 2
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0008
Aims & learning objectives:
Aims: In linear algebra the aim is to take the abstract theory to a new level, different from the elementary treatment in MATH0008. Groups will be introduced and the most basic consequences of the axioms derived. Objectives: Students should be capable of finding eigenvalues and minimum polynomials of matrices and of deciding the correct Jordan Normal Form. Students should know how to diagonalise matrices, while supplying supporting theoretical justification of the method. In group theory they should be able to write down the group axioms and the main theorems which are consequences of the axioms.
Content:
Linear Algebra: Properties of determinants. Eigenvalues and eigenvectors. Geometric and algebraic multiplicity. Diagonalisability. Characteristic polynomials. Cayley-Hamilton Theorem. Minimum polynomial and primary decomposition theorem. Statement of and motivation for the Jordan Canonical Form. Examples. Orthogonal and unitary transformations. Symmetric and Hermitian linear transformations and their diagonalisability. Quadratic forms. Norm of a linear transformation. Examples. Group Theory: Group axioms and examples. Deductions from the axioms (e.g. uniqueness of identity, cancellation). Subgroups. Cyclic groups and their properties. Homomorphisms, isomorphisms, automorphisms. Cosets and Lagrange's Theorem. Normal subgroups and Quotient groups. Fundamental Homomorphism Theorem.

MATH0013: Mathematical modelling & fluids
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 2
Assessment: EX75 CW25
Requisites: Pre MATH0009, Pre MATH0010
Aims & learning objectives:
Aims: To study, by example, how mathematical models are hypothesised, modified and elaborated. To study a classic example of mathematical modelling, that of fluid mechanics. Objectives: At the end of the course the student should be able to· construct an initial mathematical model for a real world process and assess this model critically· suggest alterations or elaborations of proposed model in light of discrepancies between model predictions and observed data or failures of the model to exhibit correct qualitative behaviour. The student will also be familiar with the equations of motion of an ideal inviscid fluid (Eulers equations, Bernoullis equation) and how to solve these in certain idealised flow situations.
Content:
Modelling and the scientific method: Objectives of mathematical modelling; the iterative nature of modelling; falsifiability and predictive accuracy; Occam's razor, paradigms and model components; self-consistency and structural stability. The three stages of modelling: (1) Model formulation, including the use of empirical information, (2) model fitting, and (3) model validation. Possible case studies and projects include: The dynamics of measles epidemics; population growth in the USA; prey-predator and competition models; modelling water pollution; assessment of heat loss prevention by double glazing; forest management. Fluids: Lagrangian and Eulerian specifications, material time derivative, acceleration, angular velocity. Mass conservation, incompressible flow, simple examples of potential flow.

MATH0014: Numerical analysis
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 2
Assessment: EX75 CW25
Requisites: Pre MATH0007, Pre MATH0008
Aims & learning objectives:
Aims: To teach elementary MATLAB programming. To teach those aspects of Numerical Analysis which are most relevant to a general mathematical training, and to lay the foundations for the more advanced courses in later years. Objectives: Students should have some facility with MATLAB programming. They should know simple methods for the approximation of functions and integrals, solution of initial and boundary value problems for ordinary differential equations and the solution of linear systems. They should also know basic methods for the analysis of the errors made by these methods, and be aware of some of the relevant practical issues involved in their implementation.
Content:
MATLAB Programming: handling matrices; M-files; graphics. Concepts of Convergence and Accuracy: Order of convergence, extrapolation and error estimation. Approximation of Functions: Polynomial Interpolation, error term. Quadrature and Numerical Differentiation: Newton-Cotes formulae. Gauss quadrature and numerical differentiation by method of undetermined coefficients. Composite formulae. Error terms. Numerical Solution of ODEs: Euler, Backward Euler, Trapezoidal and explicit Runge-Kutta methods. Stability. Consistency and convergence for one step methods. Error estimation and control. Shooting technique. Linear Algebraic Equations: Gaussian elimination, LU decomposition, pivoting, Matrix norms, conditioning, backward error analysis, iterative refinement. Direct methods for 2 point Boundary Value Problems.

MATH0015: Programming
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 1
Assessment: EX75 CW25
Requisites:
Aims & learning objectives:
Aims: To introduce functional programming while drawing out the similarities with abstract mathematics. To show that the mathematical thought process is a natural one for programming. To provide a gentle introduction to practical functional programming. Objectives: Students should be able to write simple functions, to understand the nature of types and to use data types appropriately. They should also appreciate the value and use of recursion.
Content:
Expressions, choice, scope and extent, functions, recursion, recursive datatypes, higher-order objects.

MATH0016: Information management 1
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 1
Assessment: EX50 CW50
Requisites: Ex MATH0126
Aims & learning objectives:
Aims: To introduce students to the use of a workstation, to word-processing, spreadsheets and relational data bases, and to the basic ideas of computing, and to the range of applications and misapplications of computers in science. To give students some experience of working in small groups. Objectives: Students should have a practical ability to use contemporary information management facilities. They should be able to write a good report, and they should have the confidence and the language to enable criticism of the use of computers in science.
Content:
Introduction: hardware, software, networking. Use of the workstation. Social issues. The relationship between computing and science. Computers as calculators, as simulating engines, and as new realities. Mathematical and computational models. The difficulty of validating or criticising computational models. Example of fluid flow, and the numerical wind tunnel. Experiment and decision making using computational models. Artificial intelligence, expert systems, neural nets, artificial evolution. The use and abuse of computers in science. Word processing, HTML, Scientific journalism and scientific reports. The goals of succinctness and clarity. Spreadsheets, organizing, exploring and presenting numerical data. Introduction to Statistics. Mean, standard deviation, histograms, the idea of probability density functions.

MATH0017: Principles of computer operation & architecture
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 1
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To introduce students to the structure, basic design, operation and programming of conventional, von Neumann computers at the machine level. Alternative approaches to machine design will also be examined so that some recent machine architectures can be introduced. In particular the course will develop to explore the relationships between what actually happens at the machine level and important ideas about, for example, aspects of high-level programming and data structures, that students encounter on parallel courses. Objectives: Familiarity with the von Neumann model, the nature and function of each of the main components and general principles of operation of the machines, including input and output transfers and basic numeric manipulations. Understanding of the characteristics of logic elements; the ability to manipulate/simplify Boolean functions; practical experience of simple combinatorial and sequential systems of logic gates; and a perception of the links between logic systems and elements of computer processors and store. Understanding of the role and function of an assembler and practical experience of reading and making simple changes to small, low-level programmes. Understanding of the test running and debugging of programmes.
Content:
Basic principles of computer operation: Brief historical introduction to computing machines. Binary basis of computer operation and binary numeration systems. Von Neumann computers and the structure, nature and relationship of their major elements. Principles of operation of digital computers; use of registers and the instruction cycle; simple addressing concepts; programming. Integers and floating point numbers. Input and output; basic principles and mechanisms of data transfer; programmed and data channel transfers; device status; interrupt programming; buffering; devices. Introduction to digital logic and low-level programming: Boolean algebra and behaviour of combinatorial and sequential logic circuits (supported by practical work). Logic circuits as building blocks for computer hardware. The nature and general characteristics of assemblers; a gentle introduction to simple assembler programmes to illustrate the major features and structures of low-level programmes. Running assembler programmes (supported by practical work).

MATH0018: Databases/performance analysis
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX75 CW25
Requisites: Pre MATH0023
Aims & learning objectives:
Aims: To present an introductory account of the theory and practice of databases. To convey an understanding of the wide variety of techniques available for assessing the performance of programs and of computer-based systems. Objectives: To demonstrate understanding of the basic structure of relational database systems and to be able to make elementary queries. Students should be able to use basic benchmark programs, and the standard profiling tools. They should be aware of the limitations of such techniques, and of the wide variety of possible approaches to measuring, assessing, comparing and planning the performance of computer-based systems.
Content:
Databases: Network and relational models. Completeness of relational models, Codd's classification of canonical forms: first, second, third, and fourth normal forms. Keys, join, query languages (SQL, Query-by-example). Object databases. Performance Analysis: Benchmarking, including standard benchmarks such as Whetstone, Dhrystone. Benchmarking suites; SPECMarks. Contrast performance and test suites. Determining where time goes; profiling, sampling, emulating. Use of memory. Effects of architecture. Comparison of hardware and software monitoring. Program Comparison, Pitfalls, Performance Engineering, Queueing Theory, Case Studies.

MATH0019: Foundations
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX75 CW25
Requisites: Pre MATH0004, Pre MATH0023
Aims & learning objectives:
Aims: To give the student an appreciation of the foundations of programming by considering functions as units of computation l-calculus and combinatory logic. To raise the issue of correctness and to develop a critical attitude toward computing in general and logic programming in particular. To illustrate how the various mathematical principles discussed in this Unit are translated in practical programming languages. Objectives: Students should be able to perform reductions in two reduction systems, and to prove elementary theorms in and about these calculi. To understand enough logic so that correct logic programming is possible. To be able to apply the theories of mathematical logic to the development of programming languages, to contrast pure rewriting with environment based interpretation operating over different domains (eg. values and types). To be able to read, understand and write programs in EuLisp.
Content:
String rewriting systems, Church-Rosser ideas, Zermelo Fraenkel set theory, types and sets, operations on types, examples in C and ML, functions as graphs, and functions as rules or processes; pure lambda calculus, reduction, Church Rosser again, ordered pairs, numerals in lambda calculus, Lisp; Scott domain theory; Logic, Logical validity, logical consequence, Conjunctive normal form, clausal form, semantic tableau methods, Prolog, resolution and unification.

MATH0020: Computability & decidability
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0004, Pre MATH0023
Aims & learning objectives:
Aims: To extend previous coverage of finite-state machines and Turing machines. To explore the limitations of Turing computability. Objectives: Students should appreciate the limitations of finite-state machines, and the availability of different possible standard formalisations of Turing machines. Students should understand what can and cannot be computed using Turing machines, and the rudiments of computational complexity theory.
Content:
Finite-State Machines: Revision of the basic properties of finite-state machines. Nondeterministic finite-state machines. What can and cannot be computed using finite-state machines. Turing Machines: Revision of Turing Machines. Connecting standard Turing Machines together. Introduction to Church's Thesis. Church's Thesis: Church's Thesis and the equivalence of different models of Turing machine. Church's Thesis (cont): Church's thesis and the equivalence of different models of computation - recursive functions, primitive and general recursion.Universal Turing Machines: Universal Turing Machines and limitations of Turing computability. Undecidability, the Halting Problem, reduction of one unsolvable problem to another. Computational Complexity: Philosophy of computational complexity, upper and lower time-bounded computations, complexity classes P and NP, NP-completeness.

MATH0021: Computer graphics
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX75 CW25
Requisites:
Aims & learning objectives:
Aims: To provide an introduction to the techniques of representing, rendering, and displaying computer graphics, with assessed coursework. Objectives: Students will be able to distinguish modelling from rendering. They will be able to describe the relevant components of Euclidean geometry and their relationships to matrix algebra formulations. Students will know the difference between solid and surface modelling and be able to describe typical computer representations of each. Rendering for raster displays will be explainable in detail, including lighting models and a variety visual effects and defects. Students will be expected to describe the sampling problem and solutions for static pictures.
Content:
Background: Basic mechanisms, concepts and techniques for creating and displaying line drawings. Output devices, input devices. Packages. Coordinate systems, Euclidean geometry and transformations. Modelling: Mesh models and their representation. Constructive solid geometry and its representation. Specialised models. Rendering: Raster images; illumination models; meshes and hidden surface removal; scan-line rendering. Constructive Solid Geometry; ray-casting; visual effects and defects. Ordering dither; resolution; aliasing; colour. Students should have the ability to program in order to undertake this unit.

MATH0022: Formal program development
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0023
Aims & learning objectives:
Aims: To convey to students the idea that programming can be presented as a systematic process of calculation with mathematically secure foundations. Objectives: Students should be able to develop modest programs systematically with a complete understanding of the mathematical foundations of the method advocated, and should understand the relationship between formal and informal methods for practical use.
Content:
Programs, specifications, code, refinement. Types, invariants and feasibility. Assignment and sequencing. Control structures: alternatives and iteration. Introduction to data refinement. Dijkstra's weakest precondition and language semantics in terms of it. Basic Theorems for the Alternative and Iterative Constructs and their relevance to program development. Use of the weakest precondition as a basis for the refinement calculus. Proving refinement laws from first principles; deriving one refinement law from another.

MATH0023: C Programming
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 1
Assessment: EX75 CW25
Requisites: Pre MATH0015, Pre MATH0126
Aims & learning objectives:
Aims: To ensure students appreciate the concept of an algorithm as an effective procedure. To introduce criteria by which algorithms may be chosen, and to demonstrate non-obvious algorithms. To provide practical skills at reading and writing programs in ISO Standard C. Objectives: Students should be able to determine the time and space complexity of short algorithms, and know 3 sorting algorithms and 2 searching algorithms. Students should be able to design, construct and test short programs in C, using standard libraries as appropriate. They should be able to read and comprehend the behaviour of programs written by others.
Content:
Algorithms: Introduction: Definition of an algorithm and characteristics of them. Basic Complexity: The efficiency of different algorithmic solutions. Best, average and worst case complexity in time and space. Fundamental Algorithms: Sorting. Searching. Space-time trade-offs. Graphs. Dijkstra's shortest path. C Programming: Introduction: C as a simplified programming language; ISO Standards. Basic Concepts: Functions, variables, weak typing. Statements and expressions. Data Structuring: Enumeration, struct and arrays. Pointers and construction of complex structures. The preprocessor: #include, #if and #define Programming: Input-output. Use of standard libraries. Multiple file programs. User interfaces. Professionalism: Coding standards, defensive programming, documentation, testing. Ethics.

MATH0024: Information management 2
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 1
Assessment: EX50 CW25 OT25
Requisites: Pre MATH0016, Pre MATH0126
Aims & learning objectives:
Aims: To introduce students to the use of a workstation, to wordprocessing, spreadsheets and relational databases, and to the basic ideas of computing, and to the range of applications and misapplications of computers in science. To give students some experience of working in small groups. Objectives: Students should have a practical ability to use contemporary information management facilities. They should be able to write a good report, and they should have the confidence and the language to enable criticism of the use of computers in science.
Content:
Normal and Poisson distributions. A simple introduction to confidence intervals and hypothesis testing. Elementary tools for dealing with non-normal data. An introduction to correlation. Computational experiments. Databases. Notations of set theory. Data types and structures. Hierarchical, network, and relational databases. Some natural operations on relations: union, projection, selection, Cartesian product, set difference. Design of relational databases. Access as an example of a database system. The integrated use of word processing, spreadsheets and relational databases.

MATH0025: Machine architectures, assemblers & low-level programming
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 1
Assessment: EX75 CW25
Requisites: Pre MATH0017
Aims & learning objectives:
Aims: To introduce students to the structure, basic design, operation and programming of conventional, von Neumann computers at the machine level. Alternative approaches to machine design will also be examined so that some recent machine architectures can be introduced. In particular the course will develop to explore the relationships between what actually happens at the machine level and important ideas about, for example, aspects of high-level programming and data structures, that students encounter on parallel courses. Objectives: Development of a critical awareness that what happens at machine level is strongly related to the forms and conventions developed at higher levels of programming. Reinforcement of structured programming by practical development of low-level programming skills that can be related to high-level practice. Awareness of the potential advantages and disadvantages of different architectures; appreciation of the importance of the synergistic relationship between hardware and system software, e.g. in operating systems. A launch point for more advanced architecture studies.
Content:
Low-level programming and structures: A more detailed examination of machine architecture and facilities, exemplified by the 68000 series. Further exploration of different modes of operand addressing; the implementation of program control mechanisms; and subroutines. The relationship between the low-level and aspects of high-level, structured programming such as decisions, loops and modules; nested and recursive routines and conventions for parameter transmission at high and low levels will be examined (supported by practical programming work which may continue throughout the semester). Aspects of modern computer architectures: Non von Neumann architectures and modern approaches to machine design, including , for example, RISC (vs. CISC) architectures. Topics in contemporary machine design, such as pipelining; parallel processing and multiprocessors. The interaction between hardware and software.

MATH0026: Projects & their management
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: CW100
Requisites:
Aims & learning objectives:
Aims: To gain experience of working with other people and, on a small-scale, some of the problems that arise in the commercial development of software. To appreciate the personal, corporate and public interest ethical problems arising from all aspects of computer systems. To distinguish between scientific and pseudo-scientific modes of presentation, and to encourage competence in the scientific mode. Objectives: To carry out the full cycle of the first phase of development of a software package, namely; requirements analysis, design, implementation, documentation and delivery. To know the main terms of the Data Protection Act and be able to explain its application in a variety of contexts. To be able to design a presentation for a given audience. To be able to assess a presentation critically.
Content:
Project Management: Software engineering techniques, Controlling software development, Project planning/ Management, Documentation, Design, Quality Assurance, Testing. Professional Issues: Ethical and legal matters in the context of information technology. Personal responsibilities: to employer, society, self. Professional responsibilities: codes of professional practice, Chartered Engineers. Legal responsibilities: Data Protection Act, Computer Misuse Act, Consumer Protection Act. Intellectual property rights. Whistle-blowing. Libel and slander. Confidentiality. Contracts. Presentation Skills: How to construct a good explanation. How to construct a good presentation. Sales and manipulative techniques, theatre, and scientific clarity. Active listening and reading. Some items in the charlatan's toolkit: jargon, pseudo-mathematics, ambiguity.

MATH0027: Object-oriented mechanisms
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX75 CW25
Requisites: Pre MATH0019
Aims & learning objectives:
Aims: To provide a grounding in the principles behind object oriented languages and how they are realised, in order to enable the student both to use any object oriented language and to use any language in an object oriented way. Objectives: To be able to classify a given object oriented language into the categories identified above, to describe the differences between those categories and to know the principles involved in implementing a language belonging to any one of those categories. Given a problem description, to be able to design suitable class hierarchies. To be able to read, understand and write programs in C++ and EuLisp.
Content:
Introduction: definition of inheritance and identification of the subclasses of the family of OO languages. Simple (single) inheritance. Extending arithmetic: Complex number arithmetic in C++ (overloading, message-passing) and EuLisp (generics). Sequence and iterators: For classical data structures (list, vector) in C++ and EuLisp. Polymorphism. Integration of user-defined sequence classes. Modelling OO mechanisms: Modelling message passing and class hierarchies. A method determination algorithm for generic functions. Advanced topics: Multiple inheritance and the superclass linearization problem. Meta-object protocols

MATH0028: Algorithms
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX75 CW25
Requisites: Pre MATH0020
Aims & learning objectives:
Aims: To present a detailed account of some fundamentally important and widely used algorithms. To induce an appreciation of the design and implementation of a selection of algorithms. Objectives: To lean the general principles of effective algorithms design and analysis on some famous examples, which are used as fundamental subroutines in major computational procedures. To be able to apply these principles in the development of algorithms and make an informed choice between basic subroutines and data structures.
Content:
Algorithms and complexity. Main principles of effective algorithms design: recursion, divide-and-conquer, dynamic programming. Sorting and order statistics. Strassen's algorithm for matrix multiplication and solving systems of linear equations. Arithmetic operations over integers and polynomials (including Karatsuba's algorithm), Fast Fourier Transform method. Greedy algorithms. Basic graph algorithms: minimum spanning trees, shortest paths, network flows. Number-theoretic algorithms: integer factorization, primality testing, the RSA public key cryptosystem.

MATH0029: Compilers
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX75 CW25
Requisites: Pre MATH0023, Pre MATH0020
Aims & learning objectives:
Aims: to give an introduction to the processes involved in compilation and the use of C-based compiler generation tools. Objectives: to know the phases of the compilation process and how to implement them. To be able to choose between different techniques and different representations, depending on the problem to be solved.
Content:
Formal grammars, lexical analysis using lex, parsing by recursive descent and by yacc, error handling in the parsing process, intermediate code representations, type checking, code generation using a code generator generator (burg).

MATH0030: History, heresy & heretics
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 2
Assessment: EX75 CW25
Requisites:
Aims & learning objectives:
Aims: To inform students of the rapid change in computing via an analysis of the history and development of the computing industry and subject. The course aims to do two things. First, to remove the almost mystical belief that computers can do anything. Secondly, to encourage students to question the appropriateness of computer systems as a solution to any given problem. Objectives: Describe the major trends and changes in hardware, programming languages and software; explain the evolution of the computing industry; extrapolate current trends in the industry, while realising the weakness of extrapolation. Students should be able to demonstrate reasoned arguments for and against the use of computer technology. They should be able to compare machine and human intelligence. They should understand the dangers of compulsive use of computers; and the hazards that a computer solution may introduce.
Content:
The pre-history (Pascal, Babbage, Turing etc.). 1940s and 1950s: the birth of an industry and a subject. Semiconductor technology and its evolution. 1960s and 1970s: the 'range' concept; IBM and the Seven Dwarfs; high-level languages; operating systems; the growth of on-line access. The rise of the mini-computer: workstations and Unix; growth of networking. 'Professionalism'. The PC Market; Intel and Microsoft. Where we are now. What computers do; what programmers do. Machines: engineering a computer system. Humans: language, understanding and reason. Human and machine problem solving: Eliza-like systems, artificial intelligence. Programming as a compulsion.

MATH0031: Statistics & probability 1
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 1
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To introduce some basic concepts in probability and statistics. Objectives: Ability to perform an exploratory analysis of a data set, apply the axioms and laws of probability, and compute quantities relating to discrete probability distributions
Content:
Descriptive statistics: Histograms, stem-and-leaf plots, box plots. Measures of location and dispersion. Scatter plots. Probability: Sample space, events as sets, unions and intersections. Axioms and laws of probability. Probability defined through symmetry, relative frequency and degree of belief. Conditional probability, independence. Bayes' Theorem. Combinations and permutations. Discrete random variables: Bernoulli and Binomial distributions. Mean and variance of a discrete random variable. Poisson distribution, Poisson approximation to the binomial distribution, introduction to the Poisson process. Geometric distribution. Hypergeometric distribution. Negative binomial distribution. Bivariate discrete distributions including marginal and conditional distributions. Expectation and variance of discrete random variables. General properties including expectation of a sum, variance of a sum of independent variables. Covariance. Probability generating function. Introduction to the random walk. Students must have A-level Mathematics, Grade B or better in order to undertake this unit.

MATH0032: Statistics & probability 2
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Level 1
Assessment: EX100
Requisites: Pre MATH0031
Aims & learning objectives:
Aims: To introduce further concepts in probability and statistics. Objectives: Ability to compute quantities relating to continuous probability distributions, fit certain types of statistical model to data, and be able to use the MINITAB package.
Content:
Continuous random variables: Density functions and cumulative distribution functions. Mean and variance of a continuous random variable. Uniform, exponential and normal distributions. Normal approximation to binomial and continuity correction. Fact that the sum of independent normals is normal. Distribution of a monotone transformation of a random variable. Fitting statistical models: Sampling distributions, particularly of sample mean. Standard error. Point and interval estimates. Properties of point estimators including bias and variance. Confidence intervals: for the mean of a normal distribution, for a proportion. Opinion polls. The t-distribution; confidence intervals for a normal mean with unknown variance. Regression and correlation: Scatter plot. Fitting a straight line by least squares. The linear regression model. Correlation.

MATH0033: Statistical inference 1
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0031, Pre MATH0032
Aims & learning objectives:
Aims: Introduce classical estimation and hypothesis-testing principles. Objectives: Ability to perform standard estimation procedures and tests on normal data. Ability to carry out goodness-of-fit tests, analyse contingency tables, and carry out non-parametric tests.
Content:
Point estimation: Maximum-likelihood estimation; further properties of estimators, including mean square error, efficiency and consistency; robust methods of estimation such as the median and trimmed mean. Interval estimation: Revision of confidence intervals. Hypothesis testing: Size and power of tests; one-sided and two-sided tests. Examples. Neyman-Pearson lemma. Distributions related to the normal: t, chi-square and F distributions. Inference for normal data: Tests and confidence intervals for normal means and variances, one-sample problems, paired and unpaired two-sample problems. Contingency tables and goodness-of-fit tests. Non-parametric methods: Sign test, signed rank test, Mann-Whitney U-test.

MATH0034: Probability & random processes
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0002, Pre MATH0032
Aims & learning objectives:
Aims: Knowledge and understanding of the statements of the three classical limit theorems of probability. Familiarity with the main results of discrete-time branching processes. Knowledge of the main properties of random walks on the integers. Knowledge of the various equivalent characterisations of the Poisson process. Objectives: Ability to perform computations concerning branching processes, random walks, and Poisson processes. Ability to use generating function techniques for effective calculations.
Content:
Revision of properties of expectation. Chebyshev's inequality. The Weak Law. Martingales. Statement of the Strong Law of Large Numbers. Random variables on the positive integers. Branching processes. Random walks expected first passage times. Poisson processes: inter-arrival times, the gamma distribution. Moment generating functions. Outline of the Central Limit Theorem.

MATH0035: Statistical inference 2
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Level 2
Assessment: EX75 CW25
Requisites: Pre MATH0033
Aims & learning objectives:
Aims: Introduce the principles of building and analysing linear models. Objectives: Ability to carry out analyses using linear Gaussian models, including regression and ANOVA. Understand the principles of statistical modelling.
Content:
One-way analysis of variance (ANOVA): One-way classification model, F-test, comparison of group means. Regression: Estimation of model parameters, tests and confidence intervals, prediction intervals, polynomial and multiple regression. Two-way ANOVA: Two-way classification model. Main effects and interaction, parameter estimation, F- and t-tests. Discussion of experimental design. Principles of modelling: Role of the statistical model. Critical appraisal of model selection methods. Use of residuals to check model assumptions: probability plots, identification and treatment of outliers. Multivariate distributions: Joint, marginal and conditional distributions; expectation and variance-covariance matrix of a random vector; statement of properties of the bivariate and multivariate normal distribution. The general linear model: Vector and matrix notation, examples of the design matrix for regression and ANOVA, least squares estimation, internally and externally Studentized residuals.

MATH0036: Stochastic processes
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Level 2
Assessment: EX100
Requisites: Pre MATH0034, Ex MATH0093
Aims & learning objectives:
Aims: To present a formal description of Markov chains and Markov processes, their qualitative properties and ergodic theory. To apply results in modelling real life phenomena, such as biological processes, queueing systems, renewal problems and machine repair problems. Objectives: On completing the course, students should be able to
* classify the states of a Markov chain, find hitting probabilities and ergodic distributions
* calculate waiting time distributions, transition probabilities and limiting behaviour of various Markov processes
Content:
Markov chains with discrete states in discrete time: Examples, including random walks. The Markov 'memorylessness' property, P-matrices, n-step transition probabilities, hitting probabilities, classification of states, symmetrizabilty, invariant distributions and ergodic theorems. Markov processes with discrete states in continuous time: Examples, including the Poisson process, birth and death processes, branching processes and various types of Markovian queues. Q-matrices, resolvents waiting time distributions, equilibrium distributions and ergodicity.

MATH0037: Galois theory
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0008, Pre MATH0012
Aims & learning objectives:
Aims This course develops the basic theory of rings and fields and expounds the fundamental theory of Galois on solvability of polynomials. Objectives At the end of the course, students will be conversant with the algebraic structures associated to rings and fields. Moreover, they will be able to state and prove the main theorems of Galois Theory as well as compute the Galois group of simple polynomials.
Content:
Rings, integral domains and fields. Field of quotients of an integral domain. Ideals and quotient rings. Rings of polynomials. Division algorithm and unique factorisation of polynomials over a field. Extension fields. Algebraic closure. Splitting fields. Normal field extensions. Galois groups. The Galois correspondence. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN EVEN YEAR.

MATH0038: Advanced group theory
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0008, Pre MATH0012
Aims & learning objectives:
Aims This course provides a solid introduction to modern group theory covering both the basic tools of the subject and more recent developments. Objectives At the end of the course, students should be able to state and prove the main theorems of classical group theory and know how to apply these. In addition, they will have some appreciation of the relations between group theory and other areas of mathematics.
Content:
Topics will be chosen from the following: Review of elementary group theory: homomorphisms, isomorphisms and Lagrange's theorem. Normalisers, centralisers and conjugacy classes. Group actions. p-groups and the Sylow theorems. Cayley graphs and geometric group theory. Free groups. Presentations of groups. Von Dyck's theorem. Tietze transformations. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR.

MATH0039: Differential geometry of curves & surfaces
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0007, Pre MATH0008, Pre MATH0011, Pre MATH0012
Aims & learning objectives:
Aims This will be a self-contained course which uses little more than elementary vector calculus to develop the local differential geometry of curves and surfaces in IR³. In this way, an accessible introduction is given to an area of mathematics which has been the subject of active research for over 200 years. Objectives At the end of the course, the students will be able to apply the methods of calculus with confidence to geometrical problems. They will be able to compute the curvatures of curves and surfaces and understand the geometric significance of these quantities.
Content:
Topics will be chosen from the following: Tangent spaces and tangent maps. Curvature and torsion of curves: Frenet-Serret formulae. The Euclidean group and congruences. Curvature and torsion determine a curve up to congruence. Global geometry of curves: isoperimetric inequality; four-vertex theorem. Local geometry of surfaces: parametrisations of surfaces; normals, shape operator, mean and Gauss curvature. Geodesics, integration and the local Gauss-Bonnet theorem.

MATH0041: Metric spaces
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0007, Pre MATH0011
Aims & learning objectives:
Aims This core course is intended to be an elementary and accessible introduction to the theory of metric spaces and the topology of IRn for students with both "pure" and "applied" interests. Objectives While the foundations will be laid for further studies in Analysis and Topology, topics useful in applied areas such as the Contraction Mapping Principle will also be covered. Students will know the fundamental results listed in the syllabus and have an instinct for their utility in analysis and numerical analysis.
Content:
Definition and examples of metric spaces. Convergence of sequences. Continuous maps and isometries. Sequential definition of continuity. Subspaces and product spaces. Complete metric spaces and the Contraction Mapping Principle. Sequential compactness, Bolzano-Weierstrass theorem and applications. Open and closed sets (with emphasis on IRn). Closure and interior of sets. Topological approach to continuity and compactness (with statement of Heine-Borel theorem). Connectedness and path-connectedness. Metric spaces of functions: C[0,1] is a complete metric space.

MATH0042: Measure theory & integration
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX100
Requisites: Pre MATH0008, Pre MATH0012, Pre MATH0041
Aims & learning objectives:
Aims The purpose of this course is to lay the basic technical foundations and establish the main principles which underpin the classical notions of area, volume and the related idea of an integral. Objectives The objective is to familiarise students with measure as a tool in analysis, functional analysis and probability theory. Students will be able to quote and apply the main inequalities in the subject, and to understand their significance in a wide range of contexts. Students will obtain a full understanding of the Lebesgue Integral.
Content:
Topics will be chosen from the following: Measurability for sets: algebras, s-algebras, p-systems, d-systems; Dynkin's Lemma; Borel s-algebras. Measure in the abstract: additive and s-additive set functions; monotone-convergence properties; Uniqueness Lemma; statement of Caratheodory's Theorem and discussion of the l-set concept used in its proof; full proof on handout. Lebesgue measure on IRn: existence; inner and outer regularity. Measurable functions. Sums, products, composition, lim sups, etc; The Monotone-Class Theorem. Probability. Sample space, events, random variables. Independence; rigorous statement of the Strong Law for coin tossing. Integration. Integral of a non-negative functions as sup of the integrals of simple non-negative functions dominated by it. Monotone-Convergence Theorem; 'Additivity'; Fatou's Lemma; integral of 'signed' function; definition of Lp and of Lp; linearity; Dominated-Convergence Theorem - with mention that it is not the `right' result. Product measures: definition; uniqueness; existence; Fubini's Theorem. Absolutely continuous measures: the idea; effect on integrals. Statement of the Radon-Nikodım Theorem. Inequalities: Jensen, Hölder, Minkowski. Completeness of Lp.

MATH0043: Real & abstract analysis
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX100
Requisites: Pre MATH0007, Pre MATH0008, Pre MATH0011, Pre MATH0012
Aims & learning objectives:
Aims To introduce and study abstract spaces and general ideas in analysis, to apply them to examples, and to lay the foundations for the year 4 blocks in functional analysis and Lebesgue integral. Objectives By the end of the block, students should be able to state and prove the principal theorems relating to uniform continuity and uniform convergence for real functions on metric spaces, compactness in spaces of continuous functions, and elementary Hilbert space theory, and to apply these notions and the theorems to simple examples.
Content:
Topics will be chosen from: Uniform continuity and uniform limits of continuous functions on [0,1]. Abstract Stone-Weierstrass Theorem. Uniform approximation of continuous functions. Polynomial and trigonometric polynomial approximation, separability of C[0,1]. Total Boundedness. Diagonalisation. Ascoli-Arzelà Theorem. Complete metric spaces. Baire Category Theorem. Nowhere differentiable function. Picard's theorem for c = f(c). Metric completion M of a metric space M. Real inner-product spaces. Hilbert spaces. Cauchy-Schwarz inequality, parallelogram identity. Examples: l², L²[0,1] := C[0,1]. Separability of L² . Orthogonality, Gram-Schmidt process. Bessel's inquality, Pythagoras' Theorem. Projections and subspaces. Orthogonal complements. Riesz Representation Theorem. Complete orthonormal sets in separable Hilbert spaces. Completeness of trigonometric polynomials in L² [0,1]. Fourier Series.

MATH0044: Mathematical methods 1
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0008, Pre MATH0009, Pre MATH0010, Pre MATH0012
Aims & learning objectives:
Aims: To furnish the student with a range of analytic techniques for the solution of ODEs and PDEs. Objectives: Students should be able to obtain the solution of certain ODEs and PDEs. They should also be aware of certain analytic properties associated with the solution e.g. uniqueness.
Content:
Sturm-Liouville theory: Reality of eigenvalues. Orthogonality of eigenfunctions. Expansion in eigenfunctions. Approximation in mean square. Statement of completeness. Fourier Transform: As a limit of Fourier series. Properties and applications to solution of differential equations. Frequency response of linear systems. Characteristic functions. Linear and quasi-linear first-order PDEs in two and three independent variables: Characteristics. Integral surfaces. Uniqueness (without proof). Linear and quasi-linear second-order PDEs in two independent variables: Cauchy-Koivalevskii theorem (without proof). Characteristic data. Lack of continuous dependence on initial data for Cauchy problem. Classification as elliptic, parabolic, and hyperbolic. Different standard forms. Constant and nonconstant coefficients. One-dimensional wave equation: d'Alembert's solution. Uniqueness theorem for corresponding Cauchy problem (with data on a spacelike curve).

MATH0045: Dynamical systems
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX100
Requisites: Pre MATH0007, Pre MATH0008, Pre MATH0009, Pre MATH0011, Pre MATH0012, Pre MATH0041, Pre MATH0062
Aims & learning objectives:
Aims: A treatment of the qualitative/geometric theory of dynamical systems to a level that will make accessible an area of mathematics (and allied disciplines) that is highly active and rapidly expanding. Objectives: Conversance with concepts, results and techniques fundamental to the study of qualitative behaviour of dynamical systems. An ability to investigate stability of equilibria and periodic orbits. A basic understanding and appreciation of bifurcation and chaotic behaviour
Content:
Topics will be chosen from the following: Stability of equilibria. Lyapunov functions. Invariance principle. Periodic orbits. Poincaré maps. Hyperbolic equilibria and orbits. Stable and unstable manifolds. Nonhyperbolic equilibria and orbits. Centre manifolds. Bifurcation from a simple eigenvalue. Introductory treatment of chaotic behaviour. Horseshoe maps. Symbolic dynamics.

MATH0046: Linear control theory
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0007, Pre MATH0008, Pre MATH0009, Pre MATH0011, Pre MATH0012
Aims & learning objectives:
Aims: The course is intended to provide an elementary and assessible introduction to the state-space theory of linear control systems. Main emphasis is on continuous-time autonomous systems, although discrete-time systems will receive some attention through sampling of continuous-time systems. Contact with classical (Laplace-transform based) control theory is made in the context of realization theory. Objectives: To instill basic concepts and results from control theory in a rigorous manner making use of elementary linear algebra and linear ordinary differential equations. Conversance with controllability, observability, stabilizabilty and realization theory in a linear, finite-dimensional context.
Content:
Topics will be chosen from the following: Controlled and observed dynamical systems: definitions and classifications. Controllability and observability: Gramians, rank conditions, Hautus criteria, controllable and unobservable subspaces. Input-output maps. Transfer functions and state-space realizations. State feedback: stabilizability and pole placement. Observers and output feedback: detectability, asymptotic state estimation, stabilization by dynamic feedback. Discrete-time systems: z-transform, deadbeat control and observation. Sampling of continuous-time systems: controllability and observability under sampling.

MATH0047: Mathematical biology 1
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX75 CW12
Requisites: Pre MATH0009, Pre MATH0013
Aims & learning objectives:
Aims: The purpose of this course is to introduce students to problems which arise in biology which can be tackled using applied mathematics. Emphasis will be laid upon deriving the equations describing the biological problem and at all times the interplay between the mathematics and the underlying biology will be brought to the fore. Objectives: Students should be able to derive a mathematical model of a given problem in biology using ODEs and give a qualitative account of the type of solution expected. They should be able to interpret the results in terms of the original biological problem.
Content:
Topics will be chosen from the following: Difference equations: Steady states and fixed points. Stability. Period doubling bifurcations. Chaos. Application to population growth. Systems of difference equations: Host-parasitoid systems. Systems of ODEs: Stability of solutions. Critical points. Phase plane analysis. Poincaré-Bendixson theorem. Bendixson and Dulac negative criteria. Conservative systems. Structural stability and instability. Lyapunov functions. Prey-predator models Epidemic models Travelling wave fronts: Waves of advance of an advantageous gene. Waves of excitation in nerves. Waves of advance of an epidemic.

MATH0048: Analytical & geometric theory of differential equations
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To give a unified presention of systems of ordinary differential equations that have a Hamiltonian or Lagrangian structure. Geomtrical and analytical insights will be used to prove qualitative properties of solutions. These ideas have generated many developments in modern pure mathematics, such as sympletic geometry and ergodic theory, besides being applicable to the equations of classical mechanics, and motivating much of modern physics. Objectives: Students will be able to state and prove general theorems for Lagrangian and Hamiltonian systems. Based on these theoretical results and key motivating examples they will identify general qualitative properties of solutions of these systems.
Content:
Lagrangian and Hamiltonian systems, phase space, phase flow, variational principles and Euler-Lagrange equations, Hamilton's Principle of least action, Legendre transform, Liouville's Theorem, Poincaré recurrence theorem, Noether's Theorem.

MATH0049: Linear elasticity
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To provide an introduction to the mathematical modelling of the behaviour of solid elastic materials. Objectives: Students should be able to derive the governing equations of the theory of linear elasticity and be able to solve simple problems.
Content:
Topics will be chosen from the following: Revision: Kinematics of deformation, stress analysis, global balance laws, boundary conditions. Constitutive law: Properties of real materials; constitutive law for linear isotropic elasticity, Lame moduli; field equations of linear elasticity; Young's modulus, Poisson's ratio. Some simple problems of elastostatics: Expansion of a spherical shell, bulk modulus; deformation of a block under gravity; elementary bending solution. Linear elastostatics: Strain energy function; uniqueness theorem; Betti's reciprocal theorem, mean value theorems; variational principles, application to composite materials; torsion of cylinders, Prandtl's stress function. Linear elastodynamics: Basic equations and general solutions; plane waves in unbounded media, simple reflection problems; surface waves.

MATH0050: Nonlinear equations & bifurcations
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX75 CW25
Requisites: Pre MATH0051, Pre MATH0041
Aims & learning objectives:
Aims: To extend the real analysis of implicitly defined functions into the numerical analysis of iterative methods for computing such functions and to teach an awareness of practical issues involved in applying such methods. Objectives: The students should be able to solve a variety of nonlinear equations in many variables and should be able to assess the performance of their solution methods using appropriate mathematical analysis.
Content:
Topics will be chosen from the following: Solution methods for nonlinear equations: Review of Newton's method for systems. Quasi-Newton Methods. Theoretical Tools: Local Convergence of Newton's Method. Implicit Function Theorem. Bifurcation from the trivial solution. Applications: Exothermic reaction and buckling problems. Continuous and discrete models. Analysis of parameter-dependent two-point boundary value problems using the shooting method. Practial use of the shooting method. The Lyapunov-Schmidt Reduction. Application to analysis of discretised boundary value problems. Computation of solution paths for systems of nonlinear algebraic equations. Pseudo-arclength continuation. Homotopy methods. Computation of turning points. Bordered systems and their solution. Exploitation of symmetry. Hopf bifurcation.

MATH0051: Numerical linear algebra
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX75 CW25
Requisites: Pre MATH0008, Pre MATH0010, Pre MATH0012, Pre MATH0014
Aims & learning objectives:
Aims: To teach an understanding of iterative methods for standard problems of linear algebra. Objectives: Students should know a range of modern iterative methods for solving linear systems and for solving the algebraic eigenvalue problem. They should be able to analyse their algorithms and should have an understanding of relevant practical issues.
Content:
Topics will be chosen from the following: The algebraic eigenvalue problem: Gerschgorin's theorems. The power method and its extensions. Backward Error Analysis (Bauer-Fike). The (Givens) QR factorization and the QR method for symmetric tridiagonal matrices. (Statement of convergence only). The Lanczos Procedure for reduction of a real symmetric matrix to tridiagonal form. Orthogonality properties of Lanczos iterates. Iterative Methods for Linear Systems: Convergence of stationary iteration methods. Special cases of symmetric positive definite and diagonally dominant matrices. Variational principles for linear systems with real symmetric matrices. The conjugate gradient method. Krylov subspaces. Convergence. Connection with the Lanczos method. Iterative Methods for Nonlinear Systems: Newton's Method. Convergence in 1D. Statement of algorithm for systems.

MATH0052: Algebra & combinatorics
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0008, Pre MATH0012
Aims & learning objectives:
Aims: This course provides an accessible introduction to various ideas in discrete mathematics based around the idea of counting arguments. As such, it will give an overview of the methods of modern algebra and their application for students who do not intend to become specialists in this area. Objectives: At the end of the course, students will be proficient in applying a variety of algebraic techniques to solve combinatorial problems arising in Mathematics and related disciplines.
Content:
Topics will be chosen from the following: Graphs, Trees and Forests. Philip Hall's marriage theorem. Möbius inversion and multiplicative functions in number theory. Finite fields and cyclotomic polynomials. Quadratic Reciprocity. Linear recurrences over finite fields and applications of quadratic reciprocity. Random functions and factoring methods.

MATH0053: Algebraic number theory
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0037
Aims & learning objectives:
Aims: This course will provide a solid introduction to Algebraic Number Theory, both as a subject in its own right and as a source of applications to Computer Science. Objectives: Students completing the course should understand algebraic numbers, how unique factorization fails, and how it can be restored by using "ideal numbers".
Content:
Topics will be chosen from the following: Quadratic reciprocity. Noetherian rings, Dedekind domains, algebraic number fields and rings of algebraic integers. Primes and irreducibles. Ramification of primes. Norms and traces. Integral bases. Class groups and the class number formula. Dirichlet's units theorem. Applications of Galois Theory. The method of Minkowski. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN EVEN YEAR.

MATH0054: Representation theory of finite groups
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0038
Aims & learning objectives:
Aims: The course explains some fundamental applications of linear algebra to the study of finite groups. In so doing, it will show by example how one area of mathematics can enhance and enrich the study of another. Objectives: At the end of the course, the students will be able to state and prove the main theorems of Maschke and Schur and be conversant with their many applications in representation theory and character theory. Moreover, they will be able to apply these results to problems in group theory.
Content:
Topics will be chosen from the following: Group algebras, their modules and associated representations. Maschke's theorem and complete reducibility. Irreducible representations and Schur's lemma. Decomposition of the regular representation. Character theory and orthogonality theorems. Burnside's pa qb theorem. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR.

MATH0055: Introduction to topology
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0041
Aims & learning objectives:
Aims: To provide an introduction to the ideas of point-set topology culminating with a sketch of the classification of compact surfaces. As such it provides a self-contained account of one of the triumphs of 20th century mathematics as well as providing the necessary background for Year 4 courses in Algebraic Topology and Functional Analysis. Objectives: To acquaint students with the important notion of a topology and to familiarise them with the basic theorems of analysis in their most general setting. Students will be able to distinguish between metric and topological space theory and to understand refinements, such as Hausdorff or compact spaces, and their applications.
Content:
Topics will be chosen from the following: Topologies and topological spaces. Subspaces. Bases and sub-bases: product spaces; compact-open topology. Continuous maps and homeomorphisms. Separation axioms. Connectedness. Compactness and its equivalent characterisations in a metric space. Axiom of Choice and Zorn's Lemma. Tychonoff's theorem. Quotient spaces. Compact surfaces and their representation as quotient spaces. Sketch of the classification of compact surfaces.

MATH0056: Complex analysis
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0007, Pre MATH0011
Aims & learning objectives:
Aims: The aim of this course is to cover the standard introductory material in the theory of functions of a complex variable and to cover complex function theory up to Cauchy's Residue Theorem and its applications. Objectives: Students should end up familiar with the theory of functions of a complex variable and be capable of calculating and justifying power series, Laurent series, contour integrals and applying them.
Content:
Topics will be chosen from the following: Functions of a complex variable. Continuity. Complex series and power series. Circle of convergence. The complex plane. Regions, paths, simple and closed paths. Path-connectedness. Analyticity and the Cauchy-Riemann equations. Harmonic functions. Cauchy's theorem. Cauchy's Integral Formulae and its application to power series. Isolated zeros. Differentiability of an analytic function. Liouville's Theorem. Zeros, poles and essential singularities. Laurent expansions. Cauchy's Residue Theorem and contour integration. Applications to real definite integrals.

MATH0057: Functional analysis
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX100
Requisites: Pre MATH0041, Pre MATH0043
Aims & learning objectives:
Aims: To introduce the theory of infinite-dimensional normed vector spaces, the linear mappings between them, and spectral theory. Objectives: By the end of the block, the students should be able to state and prove the principal theorems relating to Banach spaces, bounded linear operators, compact linear operators, and spectral theory of compact self-adjoint linear operators, and apply these notions and theorems to simple examples.
Content:
Topics will be chosen from the following: Normed vector spaces and their metric structure. Banach spaces. Young, Mikowski and Hölder inequalities. Examples - IRn, C[0,1], l, Hilbert spaces. Riesz Lemma and finite-dimensional subspaces. The space B(X,Y) of bounded linear operators is a Banach space when Y is complete. Dual spaces and second duals. Uniform Boundedness Theorem. Open Mapping Theorem. Closed Graph Theorem. Projections onto closed subspaces. Invertible operators form an open set. Power series expansion for (I-T)-1. Compact operators on Banach spaces. Spectrum of an operator - compactness of spectrum. Operators on Hilbert space and their adjoints. Spectral theory of self-adjoint compact operators. Zorn's Lemma. Hahn-Banach Theorem. Canonical embedding of X in X
*
* is isometric, reflexivity. Simple applications to weak topologies.

MATH0058: Martingale theory
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX100
Requisites: Pre MATH0041, Pre MATH0042, Pre MATH0031, Pre MATH0032
Aims & learning objectives:
Aims: To stimulate through theory and especially examples, an interest and appreciation of the power of this elegant method in analysis and probability. Applications of the theory are at the heart of this course. Objectives: By the end of the course, students should be familiar with the main results and techniques of discrete time martingale theory. They will have seen applications of martingales in proving some important results from classical probability theory, and they should be able to recognise and apply martingales in solving a variety of more elementary problems.
Content:
Topics will be chosen from the following: Review of fundamental concepts. Conditional expectation. Martingales, stopping times, Optional-Stopping Theorem. The Convergence Theorem. L²-bounded martingales, the random-signs problem. Angle-brackets process, Lévy's Borel-Cantelli Lemma. Uniform integrability. UI martingales, the "Downward" Theorem, the Strong Law, the Submartingale Inequality. Likelihood ratio, Kakutani's theorem.

MATH0059: Mathematical methods 2
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0044
Aims & learning objectives:
Aims: To introduce students to the applications of advanced analysis to the solution of PDEs. Objectives: Students should be able to obtain solutions to certain important PDEs using a variety of techniques e.g. Green's functions, separation of variables. They should also be familiar with important analytic properties of the solution.
Content:
Topics will be chosen from the following: Elliptic equations in two independent variables: Harmonic functions. Mean value property. Maximum principle (several proofs). Dirichlet and Neumann problems. Representation of solutions in terms of Green's functions. Continuous dependence of data for Dirichlet problem. Uniqueness. Parabolic equations in two independent variables: Representation theorems. Green's functions. Self-adjoint second-order operators: Eigenvalue problems (mainly by example). Separation of variables for inhomogeneous systems. Green's function methods in general: Method of images. Use of integral transforms. Conformal mapping. Calculus of variations: Maxima and minima. Lagrange multipliers. Extrema for integral functions. Euler's equation and its special first integrals. Integral and non-integral constraints.

MATH0060: Nonlinear systems & chaos
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX75 CW25
Requisites: Pre MATH0007, Pre MATH0008, Pre MATH0009, Pre MATH0010, Pre MATH0011, Pre MATH0012, Pre MATH0013, Pre MATH0014
Aims & learning objectives:
Aims: The course is intended to be an elementary and accessible introduction to dynamical systems. Main emphasis will be on discrete-time systems which permits the concepts and results to be presented in a rigorous manner, within the framework of the second year core material. Discrete-time systems will be followed by an introductory treatment of continuous-time systems and differential equations. Numerical approximation of differential equations will link with the earlier material on discrete-time systems. Objectives: An appreciation of the behaviour, and its potential complexity, of general dynamical systems through a study of discrete-time systems (which require relatively modest analytical prerequisites) and computer experimentation.
Content:
Topics will be chosen from the following: Discrete-time systems. Maps from IRn to IRn . Fixed points. Periodic orbits. a and w limit sets. Local bifurcations and stability. The logistic map and chaos. Global properties. Continuous-time systems. Periodic orbits and Poincaré maps. Numerical approximation of differential equations. Newton iteration as a dynamical system.

MATH0061: Nonlinear & optimal control theory
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX100
Requisites: Pre MATH0046, Pre MATH0062, Pre MATH0041
Aims & learning objectives:
Aims: Four concepts underpin control theory: controllability, observability, stabilizability and optimality. Of these, the first two essentially form the focus of the Year 3/4 course on linear control theory. In this course, the latter notions of stabilizability and optimality are developed. Together, the courses on linear control theory and nonlinear & optimal control provide a firm foundation for participating in theoretical and practical developments in an active and expanding discipline. Objectives: To present concepts and results pertaining to robustness, stabilization and optimization of (nonlinear) finite-dimensional control systems in a rigorous manner. Emphasis is placed on optimization, leading to conversance with both the Bellman-Hamilton-Jacobi approach and the maximum principle of Pontryagin, together with their application.
Content:
Topics will be chosen from the following: Controlled dynamical systems: nonlinear systems and linearization. Stability and robustness. Stabilization by feedback. Lyapunov-based design methods. Stability radii. Small-gain theorem. Optimal control. Value function. The Bellman-Hamilton-Jacobi equation. Verification theorem. Quadratic-cost control problem for linear systems. Riccati equations. The Pontryagin maximum principle and transversality conditions (a dynamic programming derivation of a restricted version and statement of the general result with applications). Proof of the maximum principle for the linear time-optimal control problem.

MATH0062: Ordinary differential equations
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX100
Requisites: Pre MATH0007, Pre MATH0011, Pre MATH0008, Pre MATH0013, Pre MATH0009, Pre MATH0041
Aims & learning objectives:
Aims: To provide an accessible but rigorous treatment of initial-value problems for nonlinear systems of ordinary differential equations. Foundations will be laid for advanced studies in dynamical systems and control. The material is also useful in mathematical biology and numerical analysis. Objectives: Conversance with existence theory for the initial-value problem, locally Lipschitz righthand sides and uniqueness, flow, continuous dependence on initial conditions and parameters, limit sets.
Content:
Topics will be chosen from the following: Motivating examples from diverse areas. Existence of solutions for the initial-value problem. Uniqueness. Maximal intervals of existence. Dependence on initial conditions and parameters. Flow. Global existence and dynamical systems. Limit sets and attractors.

MATH0063: Mathematical biology 2
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: The aim of the course is to introduce students to applications of partial differential equations to model problems arising in biology. The course will complement Mathematical Biology I where the emphasis was on ODEs and Difference Equations. Objectives: Students should be able to derive and interpret mathematical models of problems arising in biology using PDEs. They should be able to perform a linearised stability analysis of a reaction-diffusion system and determine criteria for diffusion-driven instability. They should be able to interpret the results in terms of the original biological problem.
Content:
Topics will be chosen from the following: Partial Differential Equation Models: Simple random walk derivation of the diffusion equation. Solutions of the diffusion equation. Density-dependent diffusion. Conservation equation. Reaction-diffusion equations. Chemotaxis. Examples for insect dispersal and cell aggregation. Spatial Pattern Formation: Turing mechanisms. Linear stability analysis. Conditions for diffusion-driven instability. Dispersion relation and Turing space. Scale and geometry effects. Mode selection and dispersion relation. Applications: Animal coat markings. "How the leopard got its spots". Butterfly wing patterns.

MATH0065: Viscous fluid mechanics
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To introduce the general theory of continuum mechanics and, through this, the study of viscous fluid flow. Objectives: Students should be able to explain the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, be able to formulate balance laws and be able to apply these to the solution of simple problems involving the flow of a viscous fluid.
Content:
Topics will be chosen from the following: Vectors: Linear transformation of vectors. Proper orthogonal transformations. Rotation of axes. Transformation of components under rotation. Cartesian Tensors: Transformations of components, symmetry and skew symmetry. Isotropic tensors. Kinematics: Transformation of line elements, deformation gradient, Green strain. Linear strain measure. Displacement, velocity, strain-rate. Stress: Cauchy stress; relation between traction vector and stress tensor. Global Balance Laws: Equations of motion, boundary conditions. Newtonian Fluids: The constitutive law, uniform flow, Poiseuille flow, flow between rotating cylinders.

MATH0066: Numerical solution of partial differential equations
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: EX75 CW25
Requisites: Pre MATH0010, Pre MATH0014
Aims & learning objectives:
Aims: To teach a broad understanding of discretisation methods for elliptic, hyperbolic and parabolic PDEs. Objectives: Students should be able to apply a range of standard methods for the most important PDEs arising in applications and should be able to perform an analysis of these methods applied to model problems.
Content:
Topics will be chosen from the following: Introduction: examples of physically relevant PDEs and their associated boundary conditions. Well-posed problems. Finite difference methods for parabolic and hyperbolic PDEs. Consistency, stability and convergence. Discrete maximum principles. Finite element method: variational formulation of Poisson's equation. Basis functions in one and two space dimensions. Assembly of the stiffness matrix. Best approximation property. Convergence properties.

MATH0067: Numerical solution of boundary-value problems
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX75 CW25
Requisites: Pre MATH0007, Pre MATH0011, Pre MATH0051
Aims & learning objectives:
Aims: To teach the basic notions behind the formulation and implementation of approximation techniques for elliptic PDEs based on variational principles. Objectives: An ability to implement and analyse the finite element method for a range of elliptic boundary value-problems.
Content:
Topics will be chosen from the following: Variational principles and weak forms of elliptic equations. Linear and quadratic finite element approximation on triangles and quadrilaterals. Stiffness matrix assembly. Isoparametric mapping. Quadrature. Preconditioned conjugate gradient method. Convergence theory for symmetric elliptic problems. Mixed boundary conditions. Connection with the finite difference method. Discrete maximum principles. Extensions to be chosen from: Monotone semilinear problems, Convection-diffusion problems, Obstacle problems. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN EVEN YEAR.

MATH0068: Finite difference methods for evolutionary problems
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: EX75 CW25
Requisites: Pre MATH0010, Pre MATH0014, Pre MATH0041
Aims & learning objectives:
Aims: To teach an understanding of linear stability theory and its application to ODEs and evolutionary PDEs. Objectives: The students should be able to analyse the stability and convergence of a range of numerical methods and assess the practical performance of these methods through computer experiments.
Content:
Topics will be chosen from the following: Solution of initial value problems for ODEs by Linear Multistep methods: local accuracy, order conditions; formulation as a one-step method; stability and convergence. Introduction to physically relevant PDEs. Well-posed problems. Truncation error; consistency, stability, convergence and the Lax Equivalence Theorem; techniques for finding the stability properties of particular numerical methods. Numerical methods for parabolic and hyperbolic PDEs. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR.

MATH0069: Programming language implementation techniques
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX75 CW25
Requisites: Pre MATH0029
Aims & learning objectives:
Aims: To acquire an appreciation of the suitability of different techniques for the analysis and representations for programming languages, followed by the various means to interpret them. Objectives: To be able to choose suitable techniques for lexing, parsing, type analysis, intermediate representation, transformation and interpretation given the properties of the language to be implemented.
Content:
Construction of lexical analysers, recursive descent parsing, construction of LR parser tables, type checking, polymorphic type synthesis, continuation passing style, combinators, lambda lifting, super-combinators, abstract interpretation, storage management, byte-code interpreters, code-threaded interpreters, partial evaluation, staging transformations.

MATH0070: Computer algebra
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX75 CW25
Requisites:
Students must have A-level Mathematics, normally Grade B or better, or equivalent, in order to undertake this unit. Aims & learning objectives:
Aims: To show how computer algebra can be used to solve some interesting mathematical problems Objectives: To understand the practical possibilities and limitations of symbolic computation, and to see how it is related to numerical computation.
Content:
Introduction to Reduce. Data representation questions. Normal and canonical forms. Polynomials, algebraic numbers, elementary numbers. Polynomial algebra: GCD and factorization algorithms, modular methods. LLL algorithm. Numerical and symbolic methods for solving systems of nonlinear equations: Newton, Wu's method, Gröbner bases. Introduction to integration.

MATH0072: Safety-critical computer systems
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To give an appreciation of the current state of safe systems development. To develop an understanding of risk in systems. To give a foundation in hazard analysis models and techniques. To show how safety principles may be built into all stages of the software development process. Objectives: At the end of this course a student should be able to demonstrate the following skills: An understanding of the nature of risk in developing computer-based systems. The ability to choose and apply appropriate hazard analysis models for simple safety-related problems. An understanding of how to approach the design of safety-critical software systems.
Content:
The nature of risk: computers and risk; how accidents happen; human error. System safety: historical approaches to system safety; basic concepts and terminology. Managing the development of safety-critical systems. Modelling human error and the accident process. Hazard analysis: basic principles; models and techniques. Safety principles in the software lifecycle: hazard analysis as part of requirements analysis; designing for safety; designing the human-machine interface; verification of safety in computer systems.

MATH0073: Advanced algorithms & complexity
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0028
Aims & learning objectives:
Aims: To present a detailed introduction to one of the central concepts of combinatorial algorithmics: NP-completeness; to extend this concept to real numbers computations; to study foundations of a more general problem of proving lower complexity bounds. Objectives: to be able to recognise NP-hard problems and prove the appropriate reductions. To cope with NP-complete problems. To know some fundamental methods of proving lower complexity bounds.
Content:
NP-completeness: Deterministic and Nondeterministic Turing Machines; class NP; versions of reducibility; NP-hard and NP-complete problems. Proof of NP-completeness of satisfiability problem for Boolean formulae. Other NP-complete problems: clique, vertex cover, travelling salesman, subgraph isomorphism, etc. Polynomial-time approximation algorithms for travelling salesman and some other NP-complete graph problems. Real Numbers Turing machines: Definitions; completeness of real roots existence problem for 4-degree polynomials. Lower complexity bounds: Straight-line programs and their complexities; complexity of matrix-vector multiplication; complexity of polynomial evaluation.

MATH0075: Advanced computer graphics
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX75 CW25
Requisites:
Aims & learning objectives:
Aims: The primary aims are to understand the ways of representing, rendering and displaying pictures of three-dimensional objects (in particular). In order to achieve this it will be necessary to understand the underlying mathematics and computer techniques. Objectives: Students will be able to distinguish modelling from rendering. They will be able to describe the relevant components of Euclidean and projective geometry and their relationships to matrix algebra formulations. Students will know the difference between solid- and surface-modelling and be able to describe typical computer representations of each. Rendering for raster displays will be explainable in detail, including lighting models and a variety of visual effects and defects. Students will be expected to describe the sampling problem and solutions for both static and moving pictures.
Content:
Euclidean and projective geometry transformations. Modelling: Mesh models and their representation. Constructive solid geometry and its representation. Specialised models. Rendering: Raster images; illumination models; meshes and hidden surface removal; scan-line rendering. CSG: ray-casting; visual effects and defects. Rendering for animation. Ordered dither; resolution; aliasing; colour.

MATH0076: Proposal writing
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: CW100
Requisites:
Aims & learning objectives:
Aims: To develop skills in writing and criticquing technical proposals. To develop abilities in requirements extraction. Objectives: To demonstrate skills in the above aims by examination of case-studies and the writing of the proposal for the project to be undertaken in the following semester.
Content:
Effective and ineffective written communication. When to use graphs, diagrams and pictures. Proposal structure. Styles of written English. Developing your own style. Interviewing. Selecting your project and preparing your proposal.

MATH0077: Formal software development
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To convey to students the idea that software development can be presented as a systematic process of calculation with mathematically secure foundations. Objectives: Students should be able to develop modest programs systematically with a complete understanding of the mathematical foundations of the method advocated, and should understand the relationship between formal and informal methods for practical use.
Content:
Software specification. Informal and formal development methods and their implications for the software life-cycle. Current status of formal development methods. Refinement methods and refinement calculi. Refinement Calculus: Programs, specifications, code, refinement. Types, invariants and feasibility. Assignment and sequencing. Control structures: alternatives and iteration. Introduction to data refinement. Foundations of the Refinement Calculus: Dijkstra's weakest precondition and language semantics in terms of it. Use of the weakest precondition as a basis for the refinement calculus. Proving refinement laws from first principles; deriving one refinement law from another.

MATH0078: Networking
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0025
Aims & learning objectives:
Aims: To understand the Internet, and associated background and theory, to a level sufficient for a competent domain manager. Objectives: Students should be able to explain the acronyms and concepts of the Internet and how they relate. Students should be able to state the steps required to connect a domain to the Internet, and be able to explain the issues involved to both technical and non-technical audiences. Students should be able to discuss the ethical issues involved, and have an "intelligent layman's" grasp of the legal issues and uncertainties. Students should be aware of the fundamental security issues, and should be able to advise on the configuration issues surrounding a firewall.
Content:
The ISO 7-layer model. The Internet: its history and evolution - predictions for the future. The TCP/IP stack: IP, ICMP, TCP, UDP, DNS, XDR, NFS and SMTP. Berkeley Introduction to packet layout: source routing etc. The CONS/CLNS debate: theory versus practice. Various link levels: SLIP, 802.5 and Ethernet, satellites, the "fat pipe", ATM. Performance issues: bandwidth, MSS and RTT; caching at various layers. Who 'owns' the Internet and who 'manages' it: RFCs, service providers, domain managers, IANA, UKERNA, commercial British activities. Routing protocols and default routers. HTML and electronic publishing. Legal and ethical issues: slander/libel, copyright, pornography, publishing versus carrying. Security and firewalls: Kerberos.

MATH0079: Computer speech processing
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To introduce the essential concepts and techniques of automatic speech processing and to use speech processing as an illustration of an area of active research and development in computer technology that is both novel and lies near the limits of present capability. Objectives: Students will be able to i) outline the essential processes of human speech production and read and write simple phonetic transcriptions, ii) to demonstrate an understanding of signal processing, iii) to describe, compare and contrast digital schemes for sampling, coding and analysing speech, iv) to comprehend the theoretical and practical issues in automatic speech processing and v) to explain, and assess major speech synthesis and recognition techniques.
Content:
Speech production: the articulatory system; acoustic-phonetics and prosody; phonetic transcription and co-articulation; phonemes, phones, phonology and allophones. Speech signals: their nature, characterisation and representation in different domains; theory of elementary signal processing. Speech coding and analysis: simple PCM; sampling and quantisation errors; other coding schemes for data compression and feature extraction. Speech synthesis: articulatory, formant and other types of synthesis; synthesis by rule and text-to-speech synthesis. Speech recognition: matching complex and variable patterns; segmentation of connected and continuous speech; speaker dependence; time variations and warping; statistically-oriented techniques for recognition and some current methods; recognition versus understanding. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN EVEN YEAR.

MATH0080: Computer vision
Semester 2
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0021
Aims & learning objectives:
Aims: To present a broad account of computer vision, with the emphasis on the image processing required for its low level stages. Objectives: To induce an appreciation of the processes involved in robotic vision and how this differs from human vision.
Content:
Image formation. Colour versus monochrome. Preprocessing of the image. Edge finding: elementary methods and their shortcomings; sophisticated methods such as those of Marr-Hildreth, Canny, and Prager. Optical flow. Hough transform. Global and local region segmentation techniques: histogram techniques, region growing. Representation of the results of low level processing. Some image interpretation methods employing probability arguments and fuzzy logic. Hardware. Practical problems based on an image processing package. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR.

MATH0081: Hardware architecture & compilation
Semester 1
Credits: 6
Contact:
Topic: Computing
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0029
Aims & learning objectives:
Aims: To demonstrate the impact that computer architecture is having on compiler design. To explore trends in hardware development, and examine techniques for efficient use of machine resources, Objectives: Students should be able to describe the philosophy of RISC and CISC architectures. They should know at least one technique for register allocation, and one technique for instruction scheduling. They should be able to write a simple code generator.
Content:
Description of several state-of-the-art chip designs. The implications for compilers of RISC architectures. Register allocation algorithms (colouring, DAGS, scheduling). Global data-flow analysis. Pipelines and instruction scheduling; delayed branches and loads. Multiple instruction issue. VLIW and the Bulldog compiler. Harvard architecture and Caches. Benchmarking.

MATH0082: Double module project
Semester 2
Credits: 12
Contact:
Topic: Computing
Level: Level 3
Assessment: CW100
Requisites: Pre MATH0076
Aims & learning objectives:
Aims: To satisfy as many of the objectives as possible as set out in the individual project proposal. Objectives: To produce the deliverables identified in the individual project proposal.
Content:
Defined in the individual project proposal.

MATH0084: Linear models
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0035, Pre MATH0002, Pre MATH0003, Pre MATH0005, Pre MATH0008
Aims & learning objectives:
Aims: To present the theory and application of normal linear models and generalised linear models, including estimation, hypothesis testing and confidence intervals. To describe methods of model choice and the use of residuals in diagnostic checking. Objectives: On completing the course, students should be able to (a) choose an appropriate generalised linear model for a given set of data; (b) fit this model using the GLIM program, select terms for inclusion in the model and assess the adequacy of a selected model; (c) make inferences on the basis of a fitted model and recognise the assumptions underlying these inferences and possible limitations to their accuracy.
Content:
Normal linear model: Vector and matrix representation, constraints on parameters, least squares estimation, distributions of parameter and variance estimates, t-tests and confidence intervals, the Analysis of Variance, F-tests for unbalanced designs. Model building: Criteria for use in model selection including Mallows Cp statistic, the PRESS criterion, Akaike's information criterion. Subset selection and stepwise regression methods with applications in polynomial regression and multiple regression. Effects of collinearity in regression variables. Implications of model choice on subsequent inferential statements. Uses of residuals: Probability plots, added variable plots, plotting residuals against fitted values to detect a mean-variance relationship, standardised residuals for outlier detection, masking. Generalised linear models: Exponential families, standard form, statement of asymptotic theory for i.i.d. samples, Fisher information. Linear predictors and link functions, statement of asymptotic theory for the generalised linear model, applications to z-tests and confidence intervals, c²-²tests and the analysis of deviance. Residuals from generalised linear models and their uses. Applications to bioassay, dose response relationships, logistic regression, contingency tables.

MATH0085: Time series
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0035
Aims & learning objectives:
Aims: To introduce a variety of statistical models for time series and cover the main methods for analysing these models. Objectives: At the end of the course, the student should be able to
* compute and interpret a correlogram and a sample spectrum
* derive the properties of ARIMA and state-space models
* choose an appropriate ARIMA model for a given set of data and fit the model using the MINITAB package
* compute forecasts for a variety of linear methods and models.
Content:
Introduction: Examples, simple descriptive techniques, trend, seasonality, the correlogram. Probability models for time series: Stationarity; moving average (MA), autoregressive (AR), ARMA and ARIMA models. Estimating the autocorrelation function and fitting ARIMA models. Forecasting: Exponential smoothing, Box-Jenkins method. Stationary processes in the frequency domain: The spectral density function, the periodogram, spectral analysis. Bivariate processes: Cross-correlation function, cross spectrum. Linear systems: Impulse response, step response and frequency response functions. State-space models: Dynamic linear models and the Kalman filter. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR.

MATH0086: Medical statistics
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0035, Pre MATH0003, Pre MATH0005
Aims & learning objectives:
Aims: To introduce students to the statistical needs of medical research and describe commonly used methods in the design and analysis of clinical trials. Objectives: On completing the course, students should be able to (a) recognise the statistically important features of a medical research problem and, where appropriate, suggest a suitable clinical trial design; (b)· analyse data collected from a comparative clinical trial, ncluding crossover and case-control studies, binary response data and survival data.
Content:
Drug development: Phases I to IV of drug development and testing. Ethical considerations. Design of clinical trials: Defining the patient population, the trial protocol, possible sources of bias, randomisation, blinding, use of placebo treatment, stratification, balancing prognostic variables across treatments by "minimisation". Formulation of clinical trials as hypothesis testing and decision problems. Sample size calculations, use of pilot studies, adaptive methods. Analysis of clinical trials: Patient withdrawals, "intent to treat" criterion for inclusion of patients in analysis, inclusion of stratification variables in the analysis. Interim analyses: Repeated significance tests, O'Brien and Fleming's stopping rule, sample size calculations. Statistical analysis following a group sequential trial, contrast between frequentist and Bayesian analyses. Crossover trials: Two treatment, two period design. Discussion of more complex designs. Case-control studies. Binary data: Comparison of treatments with binary outcomes, inclusion of prognostic variables in logit and probit models. Survival data: Life tables, censoring. Parametric models for censored survival data. Kaplan-Meier estimate, Greenwood's formula, the proportional hazards model, logrank test, Cox's proportional hazards regression model. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR.

MATH0087: Optimisation methods of operational research
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0002, Pre MATH0005
Aims & learning objectives:
Aims: To present methods of optimisation commonly used in OR, to explain their theoretical basis and give an appreciation of the variety of areas in which they are applicable. Objectives: On completing the course, students should be able to
* recognise practical problems where optimisation methods can be used effectively
* implement the simplex and dual simplex algorithms, Dantzig's method for the transportation problem and the Ford-Fulkerson algorithm
* explain the underlying theory of linear programming problems, including duality.
Content:
The Nature of OR: Brief introduction. Linear Programming: Basic solutions and the fundamental theorem. The simplex algorithm, two phase method for an initial solution. Interpretation of the optimal tableau. Duality. Sensitivity analysis and the dual simplex algorithm. Brief discussion of Karmarkar's method. Applications of LP. The transportation problem and its applications, solution by Dantzig's method. Network flow problems, the Ford-Fulkerson theorem. Non-linear Programming: Revision of classical Lagrangian methods. Kuhn-Tucker conditions, necessity and sufficiency. Illustration by application to quadratic programming.

MATH0088: Data collection
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0035
Aims & learning objectives:
Aims: To illustrate the principles of experimental design in randomised and factorial designs and a variety of sample survey methods. To present components of variance estimation in random effects models and discuss its application in industrial quality improvement. Objectives: On completing the course, students should be able to
* identify the features of a proposed study that affect the choice of experimental design
* choose a suitable, efficient design for a study and explain how the data collected under this design should ultimately be analysed
* design and analyse a components of variance experiment
* design and analyse a sample survey.
Content:
Principles of experimental design: Randomisation and the avoidance of bias. Advantages of orthogonal parameter estimates. Efficiency and optimal designs. Practical considerations. Observational studies: Confounding factors, reduction of bias by matching and regression modelling. The scope of inference from observational data. Randomised designs: Completely randomised and randomised block designs. Factorial designs: Complete factorial designs, confounding and fractional factorials, applications to modern quality improvement. Random effects: Split plot designs, statistical models and analyses. Sample surveys: Simple random sampling, stratified sampling, two-stage sampling, cluster sampling, quota sampling. Inference about the mean of a finite population. Randomised response methods for sensitive questions. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN EVEN YEAR.

MATH0089: Applied probability & finance
Semester 1
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0034
Aims & learning objectives:
Aims: To develop and apply the theory of probability and stochastic processes to examples from finance and economics. Objectives: At the end of the course, students should be able to
* formulate mathematically, and then solve, dynamic programming problems
* describe the Capital Asset Pricing Model and its conclusions
* price an option on a stock modelled by a single step of a random walk
* perform simple calculations involving properties of Brownian motion.
Content:
Dynamic programming: Markov decision processes, Bellman equation; examples including consumption/investment, bid acceptance, optimal stopping. Infinite horizon problems; discounted programming, the Howard Improvement Lemma, negative and positive programming, simple examples and counter-examples. Utility theory: Risk aversion, the Capital Asset Pricing Model. Option pricing for random walks: Arbitrage pricing theory, prices and discounted prices as Martingales, hedging. Brownian motion: Introduction to Brownian motion, definition and simple properties. Exponential Brownian motion as the model for a stock price, the Black-Scholes formula. THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN EVEN YEAR.

MATH0090: Multivariate analysis
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0035, Pre MATH0008
Aims & learning objectives:
Aims: To develop facility in the analysis and interpretation of multivariate data. Objectives: At the end of the course, students should be able to
*· use graphical methods to identify possible structure in high-dimensional data
*· select appropriately among a variety of techniques for dimensionality reduction
*· combine classical inferential methods with more recent computationally-intensive techniques to produce more in-depth analyses than were possible before the computer era.
Content:
Introduction: Graphical exploratory analysis of high-dimensional data. Revision of matrix techniques, eigenvalue and singular value decompositions. Principal components analysis: Derivation and interpretation, approximate reduction of dimensionality, scaling problems. Factor analysis. Multidimensional distributions: The multivariate normal distribution, its properties and estimation of parameters. One and two sample tests on means, the Wishart distribution, Hotelling's T-squared. The multivariate linear model. Canonical correlations and canonical variables: Discriminant analysis, classification problems and cluster analysis. Topics selected from: Metrics and similarity coefficients; multi-dimensional scaling; clustering algorithms; correspondence analysis, the biplot, Procrustes analysis and projection pursuit; Classification and Regression Trees.

MATH0091: Applied statistics
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: CW100
Requisites: Pre MATH0084
Aims & learning objectives:
Aims: To give students experience in tackling a variety of "real-life" statistical problems. Objectives: During the course, students should become proficient in
* formulating a problem and carrying out an exploratory data analysis
* tackling non-standard, "messy" data
* presenting the results of an analysis in a clear report.
Content:
Formulating statistical problems: Objectives, the importance of the initial examination of data, processing large-scale data sets. Analysis: Choosing an appropriate method of analysis, verification of assumptions. Presentation of results: Report writing, communication with non-statisticians. Using resources: The computer, the library. Project topics may include: Exploratory data analysis. Practical aspects of sample surveys. Fitting general and generalised linear models. The analysis of standard and non-standard data arising from theoretical work in other blocks.

MATH0092: Statistical inference
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0033
Aims & learning objectives:
Aims: To develop a formal basis for methods of statistical inference and decision making, including criteria for the comparison of procedures. To give an in depth description of Bayesian methods and the asymptotic theory of maximum likelihood methods. Objectives: On completing the course, students should be able to
* identify and compute admissible, minimax and Bayes decision rules
* calculate properties of estimates and hypothesis tests
* derive efficient estimates and tests for a broad range of problems, including applications to a variety of standard distributions.
Content:
Revision of standard distributions: Bernoulli, binomial, Poisson, exponential, gamma and normal, and their interrelationships. Sufficiency and Exponential families. Decision theory: Admissibility and minimax decision rules; Bayes risk and Bayes rules. Bayesian inference; prior and posterior distributions, conjugate priors. Point estimation: Bias and variance considerations, mean squared error. Cramer-Rao lower bound and efficiency. Unbiased minimum variance estimators and a direct appreciation of efficiency through some examples. Bias reduction. Asymptotic theory for maximum likelihood estimators. Hypothesis testing: Hypothesis testing, review of the Neyman-Pearson lemma and maximisation of power. Maximum likelihood ratio tests, asymptotic theory. Compound alternative hypotheses, uniformly most powerful tests, locally most powerful tests and score statistics. Compound null hypotheses, monotone likelihood ratio property, uniformly most powerful unbiased tests. Nuisance parameters, generalised likelihood ratio tests.

MATH0093: Stochastic processes
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites: Pre MATH0003, Pre MATH0005, Pre MATH0032, Ex MATH0036
Aims & learning objectives:
Aims: To present a formal description of Markov chains and Markov processes, their qualitative properties and ergodic theory. To apply results in modelling real life phenomena, such as biological processes and queueing systems, and in controlling such systems. Objectives: On completing the course, students should be able to
* classify the states of a Markov chain and find its ergodic distribution
* calculate generating functions, waiting time distributions and limiting behaviour of queues
* apply these results to solve OR type problems of process control.
Content:
Markov chains: Definitions and examples, n-step transition probabilities, equilibrium and stationary distributions, classification of states and ergodic theorems, multiplicative chains. Markov processes with discrete states in continuous time: Properties of the Poisson process, birth and death processes, immigration/emigration processes, equilibrium distributions. Queues: Kendall's classification system and examples, M/M/1 including time dependent solution, M/M/k and other Markov queues, the method of stages, machine interference, the queue M/G/l, priority systems.

MATH0094: Probability theory
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Undergraduate Masters
Assessment: EX100
Requisites: Pre MATH0034, Pre MATH0042
Aims & learning objectives:
Aims: To teach Probability (and Statistics) in a rigorous mathematical context. Objectives: On completing the course, students should be able to
* describe with precision distributional and sample path aspects of long-term behaviour
* deduce the consequences of this theory in the wide range of real-world problems to which it applies.
Content:
Foundations: First and second Borel-Cantelli lemmas, 0-1 law, Weak Law of Large Numbers, Strong Law of Large Numbers when X has finite fourth moment, Weierstrass's Theorem. Distributions: Characteristic functions and inversion formula. Weak convergence, Skorokhod representation. The Central Limit Theorem and analogues. Convergence of distributions on [0,1], [0,¥] and S¹. Weyl's Theorem. Ergodic theory: Measure preserving transformations, ergodicity. Riesz proof of the Ergodic Theorem. Applications to Markov chains, Strong Law of Large Numbers and continued fractions.

MATH0098: Mathematics 2A (service unit)
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 2
Assessment: EX100
Requisites: Pre PHYS0008
Aims & learning objectives:
To extend further the student's familiarity with relevant analytical and statistical techniques. On completion, the student should be able to: use statistical tests of significance; analyse experimental data using linear regression; solve simple and partial differential equations
Content:
Differential Equations: Formulation of equations of motion (Newton's second law, pendulum, mass-spring systems); free and forced linear oscillations (undamped motion, damped motion, resonance); Fourier series (periodic functions, Euler formulas, half-range expansions); wave and diffusion equations (separation of variables, use of Fourier series). Statistics: Elementary probability theory: conditioning, independence, distribution functions, hazard functions for failure times. Means, standard deviations. Sums of independent random variables. The Central Limit Theorem. Confidence intervals, t-distribution, regression. First thoughts on model validation. All topics will be illustrated via the use of a user-friendly computer package, full instructions for the use of which will be provided. A complete understanding of what the computer is doing in simple situations should equip the student to make judicious use of packages in more sophisticated contexts.

MATH0105: Industrial placement
Academic Year
Credits: 60
Contact:
Topic:
Level: Level 2
Assessment:
Requisites:


MATH0106: Study year abroad (BSc)
Academic Year
Credits: 60
Contact:
Topic:
Level: Level 2
Assessment:
Requisites:


MATH0107: Study year abroad (MMath)
Academic Year
Credits: 60
Contact:
Topic:
Level: Undergraduate Masters
Assessment:
Requisites:


MATH0115: Mathematical structures
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Level 1
Assessment: EX100
Requisites:
Students must have A-level Mathematics, normally Grade C or better, or equivalent, in order to undertake this unit. Aims & learning objectives:
Aims: To provide a thorough grounding in the elements of mathematics necessary for an understanding and analysis of computational concepts and processes and to lay the foundations for MATH0004. Objectives: To be able to perform accurately algorithms for combinatorial and arithmetical problems and to construct simple proofs.
Content:
Numbers: Natural numbers, integers, prime numbers, statement of prime decomposition theorem, complex numbers. Algebra: Permutations and combinations, proof by induction, Binomial Theorem. Graphs and Trees: Node/ edge representation of graphs, adjacency matrices, directed graphs, binary relations, decision trees, Huffman codes, graph alogrithms, Euler and Hamilton circuits. Matrix Algebra.

MATH0117: Project (MMath)
Semester 1
Credits: 6
Contact:
Topic: Mathematics
Level: Undergraduate Masters
Assessment: CW100
Requisites:
Aims & learning objectives:
Aims: To satisfy as many of the objectives as possible as set out in the individual project proposal. Objectives: To produce the deliverables identified in the individual project proposal.
Content:
Defined in the individual project proposal.

MATH0118: Management statistics
Semester 2
Credits: 5
Contact:
Topic:
Level: Level 3
Assessment: EX60 CW40
Requisites: Pre MATH0097
Aims & learning objectives:
This unit is designed primarily for DBA Final Year students who have taken the First and Second Year management statistics units but is also available for Final Year Statistics students from the School of Mathematical Sciences. Well qualified students from the IMML course would also be considered. It introduces three statistical topics which are particularly relevant to Management Science, namely quality control, forecasting and decision theory. Aims: To introduce some statistical topics which are particularly relevant to Management Science. Objectives: On completing the unit, students should be able to implement some quality control procedures, and some univariate forecasting procedures. They should also understand the ideas of decision theory.
Content:
Quality Control: Acceptance sampling, single and double schemes, SPRT applied to sequential scheme. Process control, Shewhart charts for mean and range, operating characteristics, ideas of cusum charts. Practical forecasting. Time plot. Trend-and-seasonal models. Exponential smoothing. Holt's linear trend model and Holt-Winters seasonal forecasting. Autoregressive models. Box-Jenkins ARIMA forecasting. Introduction to decision analysis for discrete events: Revision of Bayes' Theorem, admissability, Bayes' decisions, minimax. Decision trees, expected value of perfect information. Utility, subjective probability and its measurement.

MATH0125: Markov processes & applications
Semester 2
Credits: 6
Contact:
Topic: Statistics
Level: Level 3
Assessment: EX100
Requisites:
Aims & learning objectives:
Aims: To study further Markov processes in both discrete and continuous time. To apply results to random walks, networks of queues, communication networks, electrical networks, biological processes and elsewhere. Objectives: On completing the course, students should be able to:
* formulate an appropriate Markovian model for a given real life problem and apply suitable theoretical results to obtain a solution;
* calculate basic probabilities of a simple random walk using the excursion process;
* classify a birth process as explosive or non-explosive.
Content:
Topics from: Discrete-time chains; random walks, the Strong Markov Property, reflecting random walks as queueing models in one or more dimensions, electrical networks. Models of interference in communication networks, the ALOHA model. Branching processes. Continuous-time chains: Explosion. Open and closed migration processes, networks of queues, partial balance. The Wright-Fisher and Moran models, the coalescent. The Poisson process in time and space.

MATH0128: Project (BSc)
Semester 2
Credits: 6
Contact:
Topic: Mathematics
Level: Level 3
Assessment: CW100
Requisites:
Aims & learning objectives:
Aims: To satisfy as many of the objectives as possible as set out in the individual project proposal. Objectives: To produce the deliverables identified in the individual project proposal.
Content:
Defined in the individual project proposal.

MECH0137: Mathematics for Materials 2
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
To introduce basic mathematical techniques and show their use for different applications. To review and extend ideas of geometry, co-ordinate geometry, vectors and complex numbers. To introduce ordinary differential equations and methods for their solution.
Content:
Geometry and co-ordinate geometry: geometric proof, review of triangle, circle and polygon theorem; equations of lines, planes and simple curves in cartesian co-ordinates; polar, cylindrical and spherical co-ordinate systems; applications. Vectors: vector algebra, position vectors, scalar and vector products: triple products, geometric applications. Complex numbers: Argand diagram, manipulation of complex numbers; rexp (jq). Differential equations: variable separable; linear second order with constant coefficients; response of first and second order systems to step and sinusoidal input; simultaneous linear differential equations.

PHYS0002: Properties of matter
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX80 CW20
Requisites:
Students must have A-level Physics or Chemistry and A-level Mathematics to undertake this unit. Aims & learning objectives:
The aims of this unit are to gain insight into how the interplay between kinetic and potential energy at the atomic level governs the formation of different phases and to demonstrate how the macroscopic properties of materials can be derived from considerations of the microscopic properties at the atomic level. After taking this unit the student should be able to - use simple model potentials to describe molecules and solids - solve simple problems for ideal gases using kinetic theory - describe the energy changes in adiabatic and isothermal processes - derive thermodynamic relationships and analyse cycles - derive and use simple transport expressions in problems concerning viscosity, heat and electrical conduction.
Content:
Balance between kinetic and potential energy. The ideal gas - Kinetic Theory; Maxwell- Boltzmann distribution; Equipartition. The real gas - van der Waals model. The ideal solid - model potentials and equilibrium separations of molecules and Madelung crystals. Simple crystal structures, X-ray scattering and Bragg's law. First and second laws of thermodynamics, P-V-T surfaces, phase changes and critical points, thermodynamic temperature and heat capacity of gases. Derivation of mechanical (viscosity, elasticity, strength, defects) and transport properties (heat and electrical conduction) of gases and solids from considerations of atomic behaviour. Qualitative understanding of viscosity (Newtonian and non-Newtonian) in liquids based on cage models.

PHYS0004: Relativity & astrophysics
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX80 CW20
Requisites:
Students must have A-level Physics and Mathematics to undertake this unit. Aims & learning objectives:
The aims of this unit are to introduce the concepts and results of special relativity and to provide a broad introduction to astronomy and astrophysics. An additional aim is that the student's appreciation of important physical phenomena such as gravitation and blackbody radiation should be reinforced through their study in astrophysical contexts. After taking this unit, the student should be able to - write down the essential results and formulae of special relativity - describe the important special relativity experiments (real or thought) - solve simple kinematic and dynamical special relativity problems - give a qualitative account of how the sun and planets were formed - describe how stars of differing masses evolve - give a simple description of the expanding Universe and its large-scale structure - solve simple problems concerning orbital motion, blackbody radiation, cosmological redshift, stellar luminosity and magnitude.
Content:
Special Relativity: Galilean transformation. Speed of light - Michelson-Morley experiment; Einstein's postulates. Simultaneity; time dilation; space contraction; invariant intervals; rest frames; proper time; proper length. Lorentz transformation. Relativistic momentum, force, energy. Doppler effect. Astrophysical Techniques: Telescopes and detectors. Invisible astronomy : X-rays, gamma-rays, infrared and radio astronomy. Gravitation: Gravitational force and potential energy. Weight and mass. Circular orbits; Kepler's Laws; planetary motion. Escape velocity. Solar System: Earth-Moon system. Terrestrial planets; Jovian planets. Planetary atmospheres. Comets and meteoroids. Formation of the solar system. The interstellar medium and star birth. Stellar distances, magnitudes, luminosities; black-body radiation; stellar classification; Hertzsprung-Russell diagram. Stellar Evolution: Star death: white dwarfs, neutron stars. General Relativity: Gravity and geometry. The principle of equivalence. Deflection of light; curvature of space. Gravitational time dilation. Red shift. Black holes. Large scale structure of the Universe. Galaxies: Galactic structure; classification of galaxies. Formation and evolution of galaxies. Hubble's Law. The expanding universe. The hot Big Bang. Cosmic background radiation and ripples therein.

PHYS0024: Contemporary physics
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: ES100
Requisites:
Students should have taken an appropriate selection of Year 1 and Year 2 Physics units in order to undertake this unit. Aims & learning objectives:
The aim of this unit is to enable students to find out about some of the most exciting developments in contemporary Physics research. While taking this unit the student should be able to - demonstrate good time management skills in allocating appropriate amounts of time for the planning, research and writing of reports - carry out literature searching methods for academic journals and computer-based resources in order to research the topics studied - develop the ability to extract and assimilate relevant information from extensive sources of information - develop structured report writing skills - write a concise summary of each seminar, at a level understandable by a final year undergraduate unfamiliar with the subject of the seminar - write a detailed technical report on one of the seminar subjects of the student's choice, displaying an appropriate level of technical content, style and structure.
Content:
This unit will be based around 5 or 6 seminars from internal and external speakers who will introduce topics of current interest in Physics. Students will then choose one of these subjects on which to research and write a technical report. Topics are likely to include recent developments in: Astrophysics and Cosmology; Particle Physics; Medical Physics; Laser Physics; Semiconductor Physics; Superconductivity; Quantum Mechanical Simulation of Matter.

PHYS0029: Thermodynamics & statistical mechanics
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites: Pre PHYS0002, Pre PHYS0008
Aims & learning objectives:
The aims of this unit are to develop an appreciation of the concepts of classical thermodynamics and their application to physical processes and to introduce the concepts of statistical mechanics, showing how one builds from an elementary treatment based on ways of arranging objects to a discussion of Fermi-Dirac and Bose systems, simple phase transitions, and more advanced phenomena. After taking this unit, the student should be able to - define terms such as isobaric, isothermal, adiabatic, etc. and state and apply the 1st and 2nd Laws - calculate work done and heat interchanges as various paths are followed on a PV diagram - explain the operation of, and carry out calculations for, heat engines and refrigerators - write down the Clausius -Clapeyron equation and describe its applications - carry out simple calculations on various Virial equations of state - solve problems using Maxwell's relations in various contexts - define entropy, temperature, chemical potential in statistical terms - derive the Boltzmann, Planck, Fermi-Dirac and Bose-Einstein distribution functions and apply them to simple model systems - outline the mean-field approach to phase transitions in strongly interacting systems, and appreciate its limitations.
Content:
Classical thermodynamics; First and second laws of thermodynamics. Isothermal and adiabatic processes. Thermodynamic temperature scale, heat engines, refrigerators, the Carnot cycle, efficiency and entropy. Thermodynamic functions, Maxwell's relations and their applications. Specific heat equations, phase changes, latent heat equations and critical points. Statistical Mechanics; Basic postulates. Systems in thermal contact and thermal equilibrium. Statistical definitions of entropy, temperature and chemical potential. Boltzmann factor and partition function illustrated by harmonic oscillator and two-state system. Planck distribution: photons, radiation, phonons. Fermions and Bosons: Fermi-Dirac and Bose-Einstein distribution functions. Properties of Fermi systems: ground state of a Fermi gas, density of states; Fermi gas at non-zero temperature; electrons in solids, models of white dwarf and neutron stars. Properties of Bose systems: Bose-Einstein condensation, superfluidity and superconductivity. Applications of Statistical Mechanics to classical and quantum systems such as non-reacting and reacting mixtures of classical gases; equilibrium of two-phase assemblies; models of magnetic crystals, the Ising model; mean-field and other approaches to phase transitions in ferromagnets and binary alloys; elementary kinetic theory of transport processes; transport theory using the relaxation-time approximation: electrical conductivity, viscosity; propagation of heat and sound.

PHYS0030: Quantum mechanics
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites:
Students must have A-level Physics in order to undertake this unit and must have undertaken appropriate maths units provided by either the Departments of Physics or Mathematical Sciences. Aims & learning objectives:
The aims of this unit are to show how a mathematical model of considerable elegance may be constructed, from a few basic postulates, to describe the seemingly contradictory behaviour of the physical universe and to provide useful information on a wide range of physical problems. After taking this unit the student should be able to: - discuss the dual particle-wave nature of matter - explain the relation between wave functions, operators and experimental observables - justify the need for probability distributions to describe physical phenomena - set up the Schröödinger equation for simple model systems - derive eigenstates of energy, momentum and angular momentum - apply approximate methods to more complex systems.
Content:
Introduction: Breakdown of classical concepts. Old quantum theory. Quantum mechanical concepts and models: The "state" of a quantum mechanical system. Hilbert space. Observables and operators. Eigenvalues and eigenfunctions. Dirac bra and ket vectors. Basis functions and representations. Probability distributions and expectation values of observables. Schrodinger's equation: Operators for position, time, momentum and energy. Derivation of time-dependent Schrodinger equation. Correspondence to classical mechanics. Commutation relations and the Uncertainty Principle. Time evolution of states. Stationary states and the time-independent Schrodinger equation. Motion in one dimension: Free particles. Wave packets and momentum probability density. Time dependence of wave packets. Bound states in square wells. Parity. Reflection and transmission at a step. Tunnelling through a barrier. Linear harmonic oscillator. Motion in three dimensions: Stationary states of free particles. Central potentials; quantisation of angular momentum. The radial equation. Square well; ground state of the deuteron. Electrons in atoms; the hydrogen atom. Hydrogen-like atoms; the Periodic Table. Spin angular momentum: Pauli spin matrices. Identical particles. Symmetry relations for bosons and fermions. Pauli's exclusion principle. Approximate methods for stationary states: Time independent perturbation theory. The variational method. Scattering of particles; the Born approximation.

PHYS0031: Simulation techniques
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment: EX80 CW20
Requisites: Pre PHYS0020
Aims & learning objectives:
The aims of this unit are to identify some of the issues involved in constructing mathematical models of physical processes, and to introduce major techniques of computational science used to find approximate solutions to such models. After taking this unit the student should be able to - dedimensionalise an equation representing a physical system - discretise a differential equation using grid and basis set methods - outline the essential features of each of the simulation techniques introduced - give examples of the use of the techniques in contemporary science - use the simulation schemes to solve simple examples by hand - describe and compare algorithms used for key processes common to many computational schemes.
Content:
Construction of a mathematical model of a physical system; de-dimensionalisation, order of magnitude estimate of relative sizes of terms. Importance of boundary conditions. The need for computed solutions. Discretisation using grids or basis sets. Discretisation errors. The finite difference method; review of ODE solutions. Construction of difference equations from PDEs. Boundary conditions. Applications. The finite element method; Illustration of global, variational approach to solution of PDEs. Segmentation. Boundary conditions. Applications. Molecular Dynamics and Monte-Carlo Methods; examples of N-body problems, ensembles and averaging. The basic MD strategy. The basic MC strategy; random number generation and importance sampling. Applications in statistical mechanics. Simulated annealing. Computer experiments. Solving finite difference problems via random walks. Other major algorithms of computational science; the Fast Fourier Transform, matrix methods, including diagonalisation, optimisation methods, including non-linear least squares fitting.

UNIV0015: Information management 1A
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: PR60 CW30 OR10
Requisites:
Aims & learning objectives:
To enhance the skills of students in communicating their ideas, orally and in written form. On completion, the student should be able to: produce properly-structured reports and oral presentations; use spreadsheets and word processors to enhance the quality of their output; use the BIDS system in the library; access the WWW for academic purposes; have BASIC programming skills; make clear dimensioned drawings and sketches to convey visual concepts.
Content:
An introduction to the information technology tools available to materials scientists and engineers within the university and practical experience of using the appropriate ones. Use of Microcomputers: Self-taught introduction to computing in BASIC language using the School's microcomputers. Exercises in design and materials selection incorporated into some of the laboratory exercises. Solution of common materials science problems as they arise in the lecture courses. Engineering drawing: Principles of orthographic projections. Isometric sketching. Drawing conventions: BS308 and 7308. Titles, dimensions and scale. General assembly and detail drawings.

UNIV0038: Mathematics for Materials 1
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment: EX80 CW20
Requisites:
Aims & learning objectives:
To introduce basic mathematical techniques and show their use for different applications. To review common mathematical function, and their graphical representation. To develop differential and integral calculus.
Content:
Use of number: number and logarithms, change of base, log-lin graphs, binary numbers, estimation of results, sensitivity; mean, mode, standard deviation; introduction to normal distribution; error, uncertainty. Functions: standard functions, inverse functions, graphs, curve sketching, cartesian and log scales, polar co-ordinates; trigonmetric identities; roots of equations, factorisation of polynominals; partial fractions; binomial series; AP, GP, standard series; idea of linearity. Differentiation: derivative as a limit; tangents, normals, extrema; product, quotient and chain rules; higher derivatives; Taylor series; L'Hopital's rule; partial derivatives, chain, Taylor expansion. Integration area under a curve; standard integrals; substitution, by parts; surfaces and volumes of revolution.

XXXX0001: Any other units approved by the Director of Studies
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment:
Requisites:
This pseudo-unit indicates that you are allowed to choose other units from around the University subject to the normal constraints such as staff availability, timetabling restrictions, and minimum and maximum group sizes. You should make sure that you indicate your actual choice of units when requested to do so. Details of the University's Catalogue can be seen on the University's Home Page.

XXXX0001: Any other units approved by the Director of Studies
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 1
Assessment:
Requisites:
This pseudo-unit indicates that you are allowed to choose other units from around the University subject to the normal constraints such as staff availability, timetabling restrictions, and minimum and maximum group sizes. You should make sure that you indicate your actual choice of units when requested to do so. Details of the University's Catalogue can be seen on the University's Home Page.

XXXX0004: An approved list of units
Semester 1
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment:
Requisites:
This pseudo-unit indicates that you are allowed to choose other units from around the University subject to the normal constraints such as staff availability, timetabling restrictions, and minimum and maximum group sizes. You should make sure that you indicate your actual choice of units when requested to do so. Details of the University's Catalogue can be seen on the University's Home Page.

XXXX0004: An approved list of units
Semester 2
Credits: 6
Contact:
Topic:
Level: Level 3
Assessment:
Requisites:
This pseudo-unit indicates that you are allowed to choose other units from around the University subject to the normal constraints such as staff availability, timetabling restrictions, and minimum and maximum group sizes. You should make sure that you indicate your actual choice of units when requested to do so. Details of the University's Catalogue can be seen on the University's Home Page.