Psychology Unit Catalogue
ECOI0001: Principles of microeconomics
Semester 1
Credits: 6
Contact:
Topic: Economics
Level: Level 1
Assessment: EX100
Requisites: Ex ECOI0006
Aims & learning objectives:
This course is designed for non-specialist economists and will provide an introduction to micro economic analysis with a minimum of technical apparatus. The emphasis will be on policy application and evaluation with particular reference to the UK.
Content:
Scarcity and choice; resource allocation; distribution and fairness; the market economy; the cases for and against government intervention; policy issues - protecting the environment, privatisation and regulation of industry.
ECOI0002: Principles of macroeconomics
Semester 2
Credits: 6
Contact:
Topic: Economics
Level: Level 1
Assessment: EX100
Requisites: Ex ECOI0007
Aims & learning objectives:
This course is designed for non-specialist economists and will provide an introduction to macro economic analysis with a minimum of technical apparatus. The emphasis will be on policy application and evaluation with particular reference to the UK.
Content:
The aggregate economy: measuring output; economic growth; inflation; unemployment; the balance of payments ; the UK and the European economy.
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.
ECOI0022: Developing societies 1
Semester 1
Credits: 6
Contact:
Topic: Sociology
Level: Level 2
Assessment: EX50 ES50
Requisites: Co ECOI0023
Aims & learning objectives:
To provide an understanding of the major ways in which processes of development and change have been analysed in the social sciences as the basis for critiquing and evaluating policy initiatives towards growth and poverty alleviation in the developing world. Although available to all social science disciplines, it presents a primarily sociological perspective on poor country development issues. Lectures will touch on economics and politics, but not in a way that demands specialist knowledge. Non-sociologists can be reassured that sociological terms will be explained in context.
Content:
An introduction to ways of thinking in sociology and anthropology as they apply to an understanding of social change. A critique of the major paradigms of modernisation and dependency. Reference to the need to acknowledge agency explanations in the context of globalisation. A review of concepts of poverty, given the significance of poverty alleviation in most peoples development agendas. An analysis of peasant production and exchange systems, and the role of women within such systems, drawing on illustrations from South Asia, Sub-Saharan Africa and Latin America. An examination of rural values, beliefs and ideologies, especially in relation to wider sets of institutions and markets. Significance of technological developments in agriculture on social structures and opportunities for commercial activity and labour markets.
ECOI0023: Developing societies 2
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 2
Assessment: EX50 ES50
Requisites: Co ECOI0022
Aims & learning objectives:
To provide an understanding of the major ways in which processes of development and change have been analysed in the social sciences as the basis for critiquing and evaluating policy initiatives towards growth and poverty alleviation in the developing world. Although available to all social science disciplines, it presents a primarily sociological perspective on poor country development issues. Lectures will touch on economics and politics, but not in a way that demands specialist knowledge. Non-sociologists can be reassured that sociological terms will be explained in context.
Content:
Following from Developing Societies I, the course opens with a discussion of urbanisation in the developing world, analysing growth trends and regional patterns, and reviewing ethnographical studies on livelihood strategies among the urban poor. This leads into a broader examination of the various forms of social and political action through which inequality and poverty is challenged (revolution, protest movements and social mobilisation in pursuit of development objectives). State-society relations are considered in the context of managing scarcity (involving concepts of labelling, targeting and controlling access). Ethical issues, especially in relation to the rights of minority cultures and local use of natural resources, lead into broader questions about environmental sustainability, managing the commons and common property management as institutional alternatives to state regulation on the one hand, and privatisation on the other. Such questions entail a discussion about participation and social development as practice, drawing upon the original theoretical notions of agency and actor-oriented analysis as a conclusion to the course.
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.
ESML0030: German written & spoken language 1A
Semester 1
Credits: 6
Contact:
Topic: German
Level: Level 1
Assessment: CW100
Requisites:
Aims & learning objectives:
The unit pursues a dual aim. (1) To refresh and consolidate students knowledge and understanding of grammatical structures; to enable them to apply the acquired skills to the production of coherent and fluent written composition; to introduce them to a variety of German texts dealing with appropriate contemporary issues. (2) To improve students communicative and listening skills (oral/aural) and to expand their vocabulary so that they are able to express themselves clearly in everyday as well as in academic contexts as appropriate; to enable students to formulate their own ideas and to interact effectively in German and to adjust flexibly to various situations by using a suitable register.
Content:
(1) In respect of i. the consolidation of German language structures: this unit focuses on the various classes of words, their declension and their function within the phrase/ sentence; ii. written communication: a variety of linguistic skills are developed by means of translation into and from German and essay writing in German (2) Spoken language classes may consist of free discussions with the entire group, interactive exercises (e.g. role play, small-group discussions, one-to-one exchange of ideas). Austrian and German video material and newspaper articles form the basis for discussion and assessment, whilst improving awareness of contemporary life in the German-speaking world.
ESML0031: German written & spoken language 1B
Semester 2
Credits: 6
Contact:
Topic: German
Level: Level 1
Assessment: CW100
Requisites: Pre ESML0030
Aims & learning objectives:
The unit builds on ESML0030, pursuing the same dual aim. (1) To refresh and consolidate students knowledge and understanding of grammatical structures; enable them to apply the acquired skills to the production of coherent and fluent written composition; to introduce them to a variety of German texts dealing with appropriate contemporary issues. (2) To improve students communicative and listening skills (oral/aural) and to expand their vocabulary so that they are able to express themselves clearly in everyday as well as in academic contexts as appropriate; to enable students to formulate their own ideas and to interact effectively in German and to adjust flexibly to various situations by using a suitable register.
Content:
(1) In respect of i. the consolidation of German language structures: this unit focuses on complex grammar points and German syntax; ii. written communication: a variety of linguistic skills are developed by means of translation into and from German and essay writing in German. (2) Spoken language classes may consist of free discussions with the entire group, interactive exercises (e.g. role play, small-group discussions, one-to-one exchange of ideas). Austrian and German video material and newspaper articles form the basis for discussion and assessment, whilst improving awareness of contemporary life in the German-speaking world.
ESML0036: German written & spoken language 2A
Semester 1
Credits: 6
Contact:
Topic: German
Level: Level 2
Assessment: CW100
Requisites: Pre ESML0031, Co ESML0037
Aims & learning objectives:
To build on knowledge (grammatical accuracy and range of vocabulary) and writing skills acquired in Year 1. Having successfully completed this unit, students should be able, at the appropriate level, to: translate texts (German to English); summarize English texts into German and write short essays expressing a personal opinion on a given topic.
Content:
German to English translation, English to German summarisation, German essay-writing in response to text-based questions.
ESML0037: German written & spoken language 2B
Semester 2
Credits: 6
Contact:
Topic: German
Level: Level 2
Assessment: EX54 CW20 OR26
Requisites: Co ESML0036
Aims & learning objectives:
To build on knowledge (grammatical accuracy and range of vocabulary) and writing skills acquired in Year 2 semester 1. Having successfully completed this unit, students should be able, at the appropriate level, to: translate texts (German to English) with an increased awareness of nuance of meaning; summarize English texts (as wide-ranging in topic and style as time and circumstances permit) into German and write short essays with good grammatical awareness and fluency of style, and to translate a dictated English text into German.
Content:
German to English translation, English to German summarisation, German essay-writing in response to text-based questions; extempore German-to-English translation.
ESML0048: German written & spoken language 4A
Semester 1
Credits: 6
Contact:
Topic: German
Level: Level 3
Assessment: CW100
Requisites: Pre ESML0037, Co ESML0049
Aims & learning objectives:
To refine students' ability to translate competently from German into English in a variety of contemporary registers. To develop their summarisation skills so that they are able to produce a précis in sophisticated German of a complex English text on a subject of broad contemporary interest. To enable students to write coherent, well-argued and grammatically correct essays in German in response to issues raised in complex German texts. To enhance students' knowledge of the spoken language acquired during their year abroad so that they are able to converse fluently on contemporary issues and deliver sophisticated oral presentations on topics of their choice.
Content:
Written language: (a) Translation from German into English is the focus of one of the two weekly hours. The main emphasis in this semester will be placed on dealing with texts written in more colloquial registers. (b) The second weekly hour is devoted to the production of German in summarisation and essay-writing exercises. In this semester particular attention will be devoted to developing essay-writing skills.
Spoken language: The emphasis is on project work carried out both on a group and an individual basis, with the chosen topics of an appropriately complex and controversial nature.
ESML0049: German written & spoken language 4B
Semester 2
Credits: 6
Contact:
Topic: German
Level: Level 3
Assessment: EX38 CW17 OR27 OT18
Requisites: Co ESML0048
Aims & learning objectives:
To refine students' ability to translate competently from German into English in a variety of contemporary registers. To develop their summarisation skills so that they are able to produce a précis in sophisticated German of a complex English text on a subject of broad contemporary interest. To enable students to write coherent, well-argued and grammatically correct essays in German in response to issues raised in complex German texts. To enhance students' knowledge of the spoken language acquired during their year abroad so that they are able to converse fluently on contemporary issues and deliver sophisticated oral presentations on topics of their choice.
Content:
Written language: (a) Translation from German into English is the focus of one of the two weekly hours. The main emphasis in this semester will be placed on translating texts written in more formal registers. (b) The second weekly hour is devoted to the production of German in summarisation and essay-writing exercises. In this semester particular attention will be paid to developing summarisation skills.
Spoken language: As before, project work will be carried out both on a group and an individual basis. Additional emphasis will now be placed on developing students' presentational skills in preparation for their oral examination.
ESML0081: Russian written & spoken language 1A
Semester 1
Credits: 6
Contact:
Topic: Russian
Level: Level 1
Assessment: CW100
Requisites:
Aims & learning objectives:
To consolidate knowledge of basic grammar, broaden vocabulary and improve aural comprehension. To develop fluency in spoken Russian at the level of everyday conversation.
Content:
Prose and essay composition; translation into English; grammar revision; conversation.
Students must be qualified in Russian to approximately A-level standard.
ESML0084: Russian written & spoken language 1B
Semester 2
Credits: 6
Contact:
Topic: Russian
Level: Level 1
Assessment: CW100
Requisites: Pre ESML0081
Aims & learning objectives:
To further consolidate knowledge of basic grammar, broaden vocabulary and improve aural comprehension. To further develop fluency in spoken Russian at the level of everyday conversation.
Content:
Prose and essay composition; translation into English; grammar revision; conversation.
ESML0089: Russian written & spoken language 2A
Semester 1
Credits: 6
Contact:
Topic: Russian
Level: Level 2
Assessment: CW100
Requisites: Pre ESML0084, Pre ESML0085
Students must have taken either ESML0084, or ESML0085.
Aims & learning objectives:
To deepen knowledge of Russian grammar, expand lexis and develop translation skills in several registers. To give students practice in expressing themselves in writing. To improve aural comprehension and to begin to develop fluency in spoken Russian at the level of everyday conversation.
Content:
Written Language: systematic review of Russian grammar with exercises and drills drawn from a variety of sources; translations into Russian and English with discussion of grammatical points, lexis etc. Essay writing in Russian with discussion of stylistic points and vocabulary. Spoken Language: small group conversation on a range of themes; role-playing; task-based use of audio-visual material. To assist vocabulary acquisition, work in written and spoken language will be organised around themes of geography & peoples and culture & recreation.
ESML0092: Russian written & spoken language 2B
Semester 2
Credits: 6
Contact:
Topic: Russian
Level: Level 2
Assessment: EX54 CW20 OR26
Requisites: Pre ESML0089
Aims & learning objectives:
To deepen knowledge of Russian grammar, expand lexis and develop translation skills in several registers. To give students practice in expressing themselves in writing. To improve aural comprehension to the point at which the gist of a TV news item can be understood and to develop fluency in spoken Russian at the level of everyday conversation.
Content:
Written Language: systematic review of Russian grammar with exercises and drills drawn from a variety of sources; translations into Russian and English with discussion of grammatical points, lexis etc. Essay writing in Russian with discussion of stylistic points and vocabulary. Spoken Language: small group conversation on a range of themes; role-playing; task-based use of audio-visual material. To assist vocabulary acquisition, work in written and spoken language will be organised around themes of social issues, history and politics.
ESML0095: Russian written & spoken language 4A
Semester 1
Credits: 6
Contact:
Topic: Russian
Level: Level 3
Assessment: CW100
Requisites: Pre ESML0092, Co ESML0096
Aims & learning objectives:
To consolidate knowledge of Russian grammar, further expand lexis and further develop translation skills. To enable students to translate modern literary Russian and non-technical academic and journalistic Russian, into English. To enable students to translate selected English passages into Russian, and to express ideas and arguments in writing. To improve fluency in spoken Russian.
Content:
Written Language: translation into and from Russian and discussion of grammatical points, lexis etc. Conversation and audio-visual classes. Spoken Language: discussion of selected topics on a range of themes (ecology, social issues, feminism etc).
ESML0096: Russian written & spoken language 4B
Semester 2
Credits: 6
Contact:
Topic: Russian
Level: Level 3
Assessment: EX56 CW17 OR27
Requisites: Co ESML0095
Aims & learning objectives:
To consolidate knowledge of Russian grammar, further expand lexis and further develop translation skills. To enable students to translate modern literary Russian and non-technical academic and journalistic Russian, into English with minimal use of a dictionary. To enable students to translate selected English passages into idiomatic Russian, and to express complex ideas and arguments in writing. To develop fluency in spoken Russian.
Content:
Written Language: translation into and from Russian and discussion of grammatical points, lexis etc. Conversation and audio-visual classes. Spoken Language: discussion of selected topics on a range of themes (culture, politics in Russia etc).
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
HASS0002: British politics
Semester 1
Credits: 6
Contact:
Topic: Politics
Level: Level 1
Assessment: EX100
Requisites:
Aims & learning objectives:
To provide a grounding in the study of the British political system, including wider aspects of Britain's relations with the EU.
Content:
The lectures will focus on a wide range of specific topics central to beginning to study politics (parties, institutions, etc.). Lectures will include: conservatism; social democracy; voting behaviour; the media; electoral systems; parliament; executive; pressure groups; Britain and the European Union.
HASS0003: European politics
Semester 2
Credits: 6
Contact:
Topic: Politics
Level: Level 1
Assessment: EX50 ES50
Requisites:
Aims & learning objectives:
This course is more thematic than the British Politics course (SOCS0102), as it focuses on the relative strengths of the twin forces of diversity, including a revived nationalism and integration within Europe.
Content:
The lectures will primarily adopt a 'political culture' approach to national systems and to the question of whether a wider European culture is emerging; lectures will include: the political culture approach; how to explain the relative success of the Greens in Germany?; the politics of race and immigration in France; explaining political violence - the case of Northern Ireland; the decline of extremism in Italy; Poland, Russia and where does Europe end?; theories of European integration and nationalism; towards a European political culture?
HASS0006: Core skills for social scientists: information technology methods
Semester 1
Credits: 3
Contact:
Topic: Â鶹´«Ã½ Methods
Level: Level 1
Assessment: PR50 CW50
Requisites: Co SOCP0059, Co SOCP0060
Aims & learning objectives:
To introduce students to basic computing skills needed to support methods modules in Years 1 and 2.
Content:
Through practical experience students will acquire basic skills in word-processing, spreadsheets, simple databases, file management, use of networked PCs and accessing remote sources (WWWeb); competence will be assessed through practicals and through successful use of skills in later methods modules.
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 .
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-Nikodým 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, ³¦²-²tests 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.
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.
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.
PSYC0001: Psychology 1
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 1
Assessment: ES100
Requisites:
Aims & learning objectives:
The aim of this course is to introduce students to basic concepts and current themes and debates within psychology.
Content:
Lectures will be broadly based on the question - 'WHO AM I'? In order to answer this question, we will consider: drives; hormones and the mind/body question; our animal history and the influence of genetics; learning and socialisation; personality; society and the individual; intelligence and creativity; family relationships; social groups and social interaction attitudes; values, cultural beliefs, gender and social identity; normality and deviance; language and communication. These lectures will provide the student with a grounding in the major domains within psychology, thereby preparing them for a critical understanding of the discipline as a whole.
PSYC0002: Psychology 2
Semester 2
Credits: 6
Contact:
Topic: Psychology
Level: Level 1
Assessment: EX100
Requisites: Pre PSYC0001
Aims & learning objectives:
Psychology II builds upon psychology I both conceptually and in terms of course content. This course will focus more heavily, however, on issues in biological psychology, although prior contact with the biological sciences will not be required. The purpose of this course is to provide the student with a more critical understanding of the nature of psychology as a discipline and its relation to neighbouring sciences (i.e., biology & psychiatry).
Content:
Lecture topics in this course will include; aggression and violence; altruism and helping; social skills; stress and emotions; fear, anxiety, depression, guilt and happiness; thinking and reasoning; social perceptions; prejudice and attribution; competition and co-operation; the autonomic nervous system; brain specialisation; the eye and brain.
PSYC0003: Psychology laboratory 1
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 1
Assessment: PR100
Requisites:
Aims & learning objectives:
The laboratory practical classes provide part of the training the student requires to develop skills in the methods of scientific enquiry.
Content:
The class will examine basic concepts used in experimental psychology. We will then work through the design of 4 experiments which students will carry out on their own. These experiments will address a range of issues such as social psychology, learning, eyewitness testimony, cognition, gender stereotyping and personality.
PSYC0004: Psychology laboratory 2
Semester 2
Credits: 6
Contact:
Topic: Psychology
Level: Level 1
Assessment: PR100
Requisites:
Aims & learning objectives:
This course continues the development of skills the methods of scientific enquiry.
Content:
As well as gathering data for three taught experiments, students will be required to design and carry out an experiment of their own, employing many of the scientific research techniques examined on the course. This independent research project provides experience of work in teams.
PSYC0005: Psychology research project 1
Semester 1
Credits: 3
Contact:
Topic: Psychology
Level: Level 2
Assessment: CW100
Requisites: Co PSYC0006
Aims & learning objectives:
To provide the opportunity for students to develop their understanding of research methods and the analysis of data through participation in a project.
Content:
Students will design and carry out a research project over two semesters. At the end of semester 1, they will be assessed on the research proposal. During the second semester they will conduct and analyse the project, present their findings to the class, and write up the project for assessment.
PSYC0006: Psychology research project 2
Semester 2
Credits: 3
Contact:
Topic: Psychology
Level: Level 2
Assessment: CW100
Requisites: Co PSYC0005
Aims & learning objectives:
To provide the opportunity for students to develop their understanding of research methods and the analysis of data through participation in a project.
Content:
Students will design and carry out a research project over two semesters. At the end of semester 1, they will be assessed on the research proposal. During the second semester they will conduct and analyse the project, present their findings to the class, and write up the project for assessment.
PSYC0007: Developmental psychology
Semester 2
Credits: 6
Contact:
Topic: Psychology
Level: Level 2
Assessment: EX50 ES50
Requisites: Pre PSYC0001, Pre PSYC0002
Aims & learning objectives:
To equip the student with the basic principles of Developmental Psychology, including theory, methodology and critiques. The student will have the groundwork for being able to apply an understanding of human development to other fields such as social work, educational
psychology or sociology of the family.
Content:
This course concentrates on the progression from infancy to adulthood, but also includes a life-span perspective. How does the 'well-equipped stranger' infant become a competent adult ? The course takes account of major theoretical perspectives in human development, while paying particular attention to cognitive and cultural approaches that reflect recent theoretical developments. Cognitive, moral, social, linguistic and emotional development are addressed. The concepts of 'stage', 'normal life crisis' and life transitions are highlighted.
PSYC0008: Cognitive psychology
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 2
Assessment: EX50 ES50
Requisites: Pre PSYC0001, Pre PSYC0002
Aims & learning objectives:
To equip the student with the basic principles of Cognitive Psychology, including theory, methodology and critiques. The student will be able to undertake more advanced courses relating to Cognitive Psychology, for example on Artificial Intelligence. The student will also be able to appreciate the relationship of Cognitive Psychology to other fields of social and cognitive science.
*
Content:
How do we process information
* How do we organise information
* How do we store, and retrieve, information
* How do we solve problems
We will consider three main approaches to research in this field; experimental methods: model-building based on case studies, and learning from brain damage.
PSYC0009: Social psychology
Semester 2
Credits: 6
Contact:
Topic: Psychology
Level: Level 2
Assessment: EX50 ES50
Requisites: Pre PSYC0001, Pre PSYC0002
Aims & learning objectives:
To equip students with an understanding of social interaction and social processes in dyads, group and communities.
Content:
This course focuses on the individual in interaction with others, in dyads, small groups and large groups. It examines the reciprocal relationship between the individual and their community, the röle of the individual as a group member, decision-making processes in small and large groups, inter-group relations and crowd behaviour. We will also examine how our impressions of others are formed and what it is that distinguishes human sciences from all others.
PSYC0010: Clinical psychology
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 2
Assessment: EX50 ES50
Requisites: Pre PSYC0001, Pre PSYC0002
Aims & learning objectives:
To introduce the work of clinical psychologists in the main areas of Adult Mental Health, Learning Disabilities and work with older adults. At the end of the course students should be able to set this work within the context of organisational change within the NHS and to contrast a psychological approach with other approaches, such as those of psychiatry. Students will also have more extensive knowledge of a specific psychotherapeutic technique.
Content:
The basis of psychiatric diagnosis; introduction to counselling and psychotherapy; depression; loss and bereavement; anxiety; schizophrenia; learning disabilities; older adults; eating disorders; the context of work and evaluating interventions.
PSYC0011: Psychology dissertation 1
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: OR100
Requisites:
Aims & learning objectives:
To plan, execute and report a piece of original empirical research in psychology.
Content:
PSYC0012: Psychology dissertation 2
Semester 2
Credits: 12
Contact:
Topic: Psychology
Level: Level 3
Assessment: DS100
Requisites: Co PSYC0011
Aims & learning objectives:
To plan, execute and report a piece of original empirical research in psychology.
Content:
PSYC0013: Models of counselling & psychotherapy
Semester 2
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: EX50 ES50
Requisites:
Aims & learning objectives:
To introduce the main models of counselling and psychotherapy used in clinical practice. At the end of the course students should be able to set this work within the context of the main issues and dilemmas involved in working psychotherapeutically and to be familiar with some of the clinical problems that people present to a therapist. Students will also be able to formulate a clinical case.
Content:
The context within which psychotherapists and counsellors work; the main models of psychotherapy (i.e., psychodynamic, behavioural, cognitive, systemic, humanistic and group); evaluating interventions (outcome and process research); a postmodernist approach to counselling and psychotherapy.
PSYC0014: History of psychology
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: EX50 ES50
Requisites: Pre PSYC0001, Pre PSYC0002
Aims & learning objectives:
To equip the student with an understanding of the History of Psychology, including the development of theory and methodology and critiques. The student will also be able to appreciate the relationship of Psychology to the development of other fields of social and cognitive science, and to the social and historical context.
Content:
This course considers the development of ideas over time, and what function a historical perspective plays in how we think about a field. It contextualises some key ideas in psychology, showing what their roots were, and how they waxed and waned, and why. By paying attention to specific people's intellectual lives, we see how the development
of ideas is embedded in context and culture.
Students must have undertaken 2 units from Cognitive (SOCS0089), Clinical (SOCS0091), Developmental (SOCS0088) and Social Psychology (SOCS0090) as well as the other necessary pre-requisites (SOCS0082 & SOCS0083).
PSYC0015: Economic & political psychology
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: EX50 ES50
Requisites: Pre PSYC0009
Aims & learning objectives:
The theoretical basis of this course will be on the psychological organisation of social, political, economic and ethical beliefs, and their development and aetiology. The implicit models of psychological processes that underpin expert and common-sense conceptions of rationality and ethics. The problematic nature of links between beliefs and action. The tensions between 'discourse' and 'ideology' models of explanation.
Content:
Topics include: psychological models of ideology in the organisation of beliefs; mainstream and emergent political-social beliefs (feminism, Green politics); lay beliefs, e.g., about unemployment, poverty, ethics; concepts of fairness and equity; moral development; elite beliefs - what constitutes 'legitimation'? Political propaganda and rhetoric. Social movements, social change and intergroup relations.
Students must have undertaken one other unit from Cognitive (SOCS0089), Developmental (SOCS0088) and Clinical Psychology (SOCS0091), as well as the necessary pre-requisite (SOCS0090).
PSYC0016: Health psychology
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: EX50 ES50
Requisites: Pre PSYC0008, Pre PSYC0009
Aims & learning objectives:
To introduce students to concepts, theory, methods and applications of health psychology. Students will be introduced to health psychology theory and methods using the concepts of social psychology and psychobiology. They will be expected to know about the range of methods appropriate to the measuring process and evaluating outcomes in health psychology. A major theme in the course questions what it means to be healthy or well and to have a good quality of life in relation to health care and investigates how this can be assessed. They will be in a position to appreciate some of the key interventions designed by health psychologists for use in clinical and non-clinical settings with patients suffering from the major chronic disease groups, e.g., cardiovascular, cancer and chronic pain conditions. The reporting of symptoms and the management of acute illness in GP consultations forms a central part of the course. Attention will be paid to the range of settings in which health care is delivered and the impact of hospitalisation and institutionalisation. The seminars provide a range of topics connected with preventing disease e.g., AIDS and on health promotion and education. Students will be expected to be able to set the psychology of health within a broad multidisciplinary context in the health and social sciences. They will be encouraged to understand not only how health care is appraised by patients/clients, but also the reciprocal role of giving care on the part of health care workers. They should be able to appraise the dynamics of organising psychological care within the health care system.
PSYC0017: Controversies in cognition
Semester 2
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: EX50 ES50
Requisites: Pre PSYC0007, Pre PSYC0008
Aims & learning objectives:
To equip the student with an understanding of current issues and controversies in psychology
Content:
The course will address key issues in contemporary psychology relating to cognition, language and models of mind. These will include: problems of consciousness and the interface of neuroscience, cognitive science and philosophy; connectionist theory and its implications; the rise of evolutionary psychology; debates about culture and human development.
PSYC0018: Mind & social being
Semester 2
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: EX50 CW50
Requisites: Pre PSYC0008, Pre PSYC0009, Pre PSYC0014
Aims & learning objectives:
Students should have a conceptual understanding of the social construction of knowledge. They should be able to analytically apply this understanding to the central issues of psychological research: consciousness, identity, physical and emotional being.
PSYC0019: Artificial intelligence 1: Minds, machines & persons
Semester 1
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: ES80 OT20
Requisites: Pre PSYC0025, Pre PSYC0008
Students must have taken one of the above pre-requisites in order to take this unit.
Aims & learning objectives:
This course introduces some recent research in the field of computer-based modelling and simulation of human activities which require the intelligent use of knowledge, otherwise known as Artificial Intelligence. We will approach machine intelligence through two complementary questions: could human intelligence be simulated, equalled or even exceeded by machines? Can the machine-metaphor still help us understand human cognitive and social processes?
Content:
Machine-metaphors for human thinking and reasoning now compete with evolutionary biology and neurology for influence in both psychological and sociological approaches to human behaviour. The course will provide historical background, will introduce some of the main approaches and research projects in the field, and will set out two main areas of debate: criticisms made by AI researchers about rival approaches, and arguments of philosophers, sociologists and psychologists about the attempt to simulate intelligence. Students will become familiar with key authors and texts, and will learn to evaluate claims about computer programs relating to:
* their power, intelligence or other capabilities
* their influence upon psychological and social theory
* their continuing role in psychological and social research
* their influence on our notions of expertise, intelligence, creativity and humanity.
PSYC0020: Artificial intelligence 2: Microsimulation
Semester 2
Credits: 6
Contact:
Topic: Psychology
Level: Level 3
Assessment: ES80 CW20
Requisites: Pre PSYC0019
Aims & learning objectives:
This unit allows students to develop their understanding of issues introduced in Artificial Intelligence 1 [PSYC0019] through a more detailed study of recent theoretical developments and of the development and applications of some AI programs. Students will be required to examine the literature relating to two influential developments in AI. No programming or modeling experience is required for this course
Content:
This course explores the application of biological models in AI as well as the more traditional approaches. Students will be expected to understand the applications of computer simulation in the social sciences (especially cognitive psychology), the methods of two major research projects, and the implications of computer simulation for social and psychological theory. Students may also undertake practical projects in the form of experiments with computer models and simulation programs, which can be written up as a project report.
PSYC0021: Â鶹´«Ã½ design & measurement
Semester 1
Credits: 3
Contact:
Topic: Â鶹´«Ã½ Methods
Level: Level 2
Assessment: EX100
Requisites: Co SOCP0061
Aims & learning objectives:
To equip the student with an appreciation of measurement and quantitative research methods.
Content:
The course will introduce the student to a range of measurement methods used within psychological research, for example questionnaires and surveys. Students will develop their own competencies as well as the ability to evaluate the relative merits and applicability of different approaches.
PSYC0022: Quantitative methods 3
Semester 2
Credits: 3
Contact:
Topic: Â鶹´«Ã½ Methods
Level: Level 2
Assessment: CW100
Requisites: Pre PSYC0021, Pre SOCP0061
Aims & learning objectives:
To equip the student with skills and an appreciation of more advanced quantitative research methods and their applications.
Content:
The course will build on the statistical methods introduced in Quantitative Methods 2 and extend their application. More advanced methods will be introduced and applied to existing datasets.
PSYC0023: Qualitative research methods in psychology
Semester 1
Credits: 3
Contact:
Topic: Â鶹´«Ã½ Methods
Level: Level 2
Assessment: CW100
Requisites:
Aims & learning objectives:
To equip the student with an appreciation of qualitative research methods and their applications
Content:
The course will introduce the student to a range of qualitative methods used within psychological research, including interviewing, observation, analysis of discourse and text. Students will develop competence through practical exercises.
PSYC0026: Public knowledge 3a: history, philosophy & sociology of science
Semester 1
Credits: 6
Contact:
Topic: Sociology
Level: Level 3
Assessment: ES75 CW25
Requisites: Pre PSYC0008, Pre PSYC0025, Co PSYC0027
Students must have taken one of the above pre-requisites in order to take this unit.
Aims & learning objectives:
The course aims to enable students to develop an informed and critical view of the nature of all aspects of scientific activity and the problems arising from the differences between scientific and other approaches to problems.
Content:
Scientific, Expert and Lay Knowledge; Science and Public Understanding; Public Acceptance of Science and Technology; Science and Public Policy; Science and other Modes of Knowledge. The course is seminar based with considerable directed reading. All students will read and discuss a number of key authors in the seminars, will be expected to evaluate a number of television programs about science, and will undertake a research project.
PSYC0027: Public knowledge 3b: history, philosophy & sociology of science
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 3
Assessment: EX25 ES50 CW25
Requisites: Co PSYC0026
Aims & learning objectives:
The course aims to enable students to develop an informed and critical view of the nature of all aspects of scientific activity and the problems arising from the differences between scientific and other approaches to problems.
Content:
Scientific, Expert and Lay Knowledge; Science and Public Understanding; Public Acceptance of Science and Technology; Science and Public Policy; Science and other Modes of Knowledge. The course is seminar based with considerable directed reading. All students will read and discuss a number of key authors in the seminars, will be expected to evaluate a number of television programs about science, and will undertake a research project.
PSYC0028: Placement
Academic Year
Credits: 60
Contact:
Topic: Psychology
Level: Level 2
Assessment:
Requisites:
SOCP0001: Introduction to social policy & the welfare state 1
Semester 1
Credits: 6
Contact:
Topic: Social Policy
Level: Level 1
Assessment: EX50 ES50
Requisites: Co SOCP0002
Aims & learning objectives:
To provide an introduction to social policy as a field of study. To examine the nature and extent of poverty and inequality in Britain today, as a means of developing an understanding of social policy as a field of study.
Content:
Introduction to Social Policy; Concepts and Definitions of Poverty; Social Exclusion; Evidence on the Incidence of Poverty and Inequality; Demographic Factors and their relationship to Poverty; Poverty, Gender and 'Race'; Poverty and Policy.
SOCP0002: Introduction to social policy & the welfare state 2
Semester 2
Credits: 6
Contact:
Topic: Social Policy
Level: Level 1
Assessment: EX50 ES50
Requisites: Co SOCP0001
Aims & learning objectives:
To further develop an understanding of social policy as a field of study. To examine the historical evolution of social policy and the welfare state in Britain. To introduce and examine the concept of the 'mixed economy of welfare'. To review and analyse recent developments in the major social service areas.
Content:
Services and sectors in Social Policy; 1834 Poor Law; the 1842 'Sanitary Report'; The Liberal Reforms and the Introduction of Pensions; Beveridge and the impact of the 2nd World war; the Post-War Welfare State; Thatcherism and Social Policy; Educational Reform; Housing; Community Care
SOCP0003: 'Race' & racism
Semester 2
Credits: 6
Contact:
Topic: Social Policy
Level: Level 1
Assessment: EX50 ES50
Requisites:
Aims & learning objectives:
To develop an understanding of issues of 'race' and ethnicity. To examine the dimensions of discrimination and disadvantage in Britain. To analyse key policy areas to highlight the prevalence and effects of racism. To evaluate attempts to eradicate racism, discrimination and disadvantage.
Content:
Concepts of 'Race' and Ethnicity; Racial Inequality in Britain; Racism; Colonialism; Racial Harassment; Immigration; Race Relations Law; Multi-Culturalism, Anti-Racism and Education; Urban Unrest; 'Race', Racism and Policing; 'Race' and Citizenship.
SOCP0004: Family, gender & social policy
Semester 1
Credits: 6
Contact:
Topic: Social Policy
Level: Level 1
Assessment: EX50 ES50
Requisites:
Aims & learning objectives:
To examine changing patterns of family and working life, the causes of these, and their implications for gender roles and for social policy, in the UK and elsewhere.
Content:
Definitions of the family; The politics of the family; The regulation of sexual behaviour, marriage & divorce; Lone parenthood; Feminist theory and the family; Childhood and children's rights; Support for families; Concepts of Family policy; The relationship between family policy and other areas of policy.
SOCP0005: The social policy process
Semester 2
Credits: 6
Contact:
Topic: Social Policy
Level: Level 2
Assessment: EX50 ES50
Requisites: Ex HASS0004
Aims & learning objectives:
This unit introduces students to key concepts for analysing the policy-making process. By the end of the unit students should have a basic understanding of problems and issues in the making and implementation of social policy in Britain. This course has a common lecture programme with the Politics and Policy course, however each course has a separate seminar programme.
Content:
Each lecture covers one conceptual topic, including: Introduction to Policy Analysis; Theories of the State; Power; Models of Decision-making and Policy Formulation; Implementation; Street-Level Decision-Making; Organisational Constraints; Interest Groups and Policy Communities. The seminars apply these to topical issues in social policy.
SOCP0006: Social values & social policy
Semester 1
Credits: 6
Contact:
Topic: Social Policy
Level: Level 2
Assessment: EX50 ES50
Requisites:
Aims & learning objectives:
This unit introduces students to a range of values and principles used to justify the role of the state in social policy. By the end of the module students should be familiar with the broad range of principles and should be able to apply some of them to current debates.
Content:
Each lectures will cover one core principle, including: Need, Freedom, Equality, Justice, Citizenship, Community. The seminars will apply each to one issue or problem in contemporary social policy; for example, training schemes and equality of opportunity; citizenship and rights to a basic income.
SOCP0011: Health policies & politics
Semester 2
Credits: 6
Contact:
Topic: Social Policy
Level: Level 3
Assessment: EX50 ES50
Requisites: Pre SOCP0005, Pre SOCP0006
Aims & learning objectives:
This course aims to develop an understanding of how health policy integrates with wider social policy issues, as well as a detailed understanding of the content and dynamism of health policy processes. As a result , students should
* understand the impact of different welfare models on health care systems in Europe and America
* understand the political forces behind health care reform in the British NHS
* understand the pressures exerted on health care systems and the range of responses that have arisen
* be able to compare and contrast the strengths of the different approaches and their uses in different settings
Content:
1. Health, health care and health policy
2. Comparing health systems: the UK
3. Comparing health systems: the USA and Europe
4. Pressures on health care systems (1) Demographic and economic changes
5. Pressures on health care systems (2) Science and technology
6. Politics of reform: 50 years of the NHS
7. Rationing and priority setting
8. Medicine and the media: the effect on policy
9. Paying for care and the mixed economy
10. Evaluating health care and health policy
11. Informing health policy: the politics of data gathering
12. The New Public Health
SOCP0043: Sociology of industrial societies 1: classical theories
Semester 1
Credits: 6
Contact:
Topic: Sociology
Level: Level 1
Assessment: ES100
Requisites: Co SOCP0044
Aims & learning objectives:
To understand the basic sociological questions, theories and evidence of industrial society
Content:
To answer the following questions: 1) How and why is industrial society distinctive? 2) Does industrial society have a logic of social differentiation, based on conflict , control, or social order? Differences in work, authority and decision making, kinship and gender, culture and community. The theories of Marx, Durkheim and Weber.
SOCP0044: Sociology of industrial societies 2: social change & social control
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 1
Assessment: EX50 ES50
Requisites: Co SOCP0043
Aims & learning objectives:
To understand the changing nature of industrial societies, modern and post-modern theories and evidence of social stratification, organisation and control
Content:
To answer the following questions: 1) Do industrial societies display common trends, even superseding industrialism? 2) What are the main modes of social regulation and social control in changing societies? Theories and evidence of post-industrialism, convergence, managerialism, ethnic and gender forms of social stratification in relation to social control and citizenship.
SOCP0047: Sociology of work & industry
Semester 1
Credits: 6
Contact:
Topic: Sociology
Level: Level 2
Assessment: EX50 ES50
Requisites: Pre SOCP0044
Aims & learning objectives:
This course examines sociological approaches to the changing forms of work and work organisations. Key issues include rationalisation and bureaucratisation; the introduction and impact of new technologies; managerial and worker strategies in the control of work; conflict and accommodation at the workplace; corporate structure - ownership, control and managerialism, implications for theories of class and gender relationships. The course investigates these issues in three broad contexts: the period of early industrialisation, the development of mass production and 'Fordism' and the growth and consolidation of modern industrial structures.
SOCP0048: Understanding industrial behaviour
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 2
Assessment: EX50 ES50
Requisites: Pre SOCP0044
Aims & learning objectives:
The aim of the course is to give students a Sociological understanding of industrial
behaviour, showing the competing paradigms and theories that describe industrial relationships, institutions and social structures.
Content:
The course takes students through the main debates in management and work organisation theory, looking at Taylorism and Fordism. The Hawthorne Studies and the early Human Relations School. This is followed by an analysis of the Socio-Technical School and its prescriptions. Contingency Theory and Labour Process Theory bring the debates up to the 1990s. During the course a number of case study examples are used to illustrate the key points of the differing schools.
SOCP0049: The sociology of crime & deviance
Semester 1
Credits: 6
Contact:
Topic: Sociology
Level: Level 2
Assessment: EX50 CW50
Requisites: Pre SOCP0044
Aims & learning objectives:
Introduction to the main sociological theories of crime and deviance. The course also provides invaluable preparation for the Sociology of Criminal Justice Policy and the necessary undergraduate training for all those who intend to do postgraduate work in the areas of crime and/or social control.
Content:
Divided into two parts the lectures and seminars cover, in the first part, the history of the sociology of crime from the late 19th century to the present day; in the second, they deal with THREE major crime-related sociological issues: class and crime, racism and crime; and gender and crime.
SOCP0050: Sociology of criminal justice policy
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 2
Assessment: EX50 ES50
Requisites: Pre SOCP0049
Aims & learning objectives:
Current research and policy issues in the criminal justice and penal systems. It will examine trends in criminal policy; the politics of policing and police accountability; the development of penal sanctions and the related issues of alternatives to custodial measures; the efficacy and equity, or lack of them, of the legal processes of the criminal courts; the role of new technologies; the management of prisons including the issues of privatisation and other issues concerning the social context of penal policy.
SOCP0051: Social structure & languages of class
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 2
Assessment: EX50 ES50
Requisites:
Aims & learning objectives:
The aims of this unit are to demonstrate differences in structural theories of industrial and capitalist societies, and to develop an understanding of the ways in which classical sociological theory has been developed and changed to explain social stratification and inequality.
Content:
Parsons' AGIL framework, and the Functionalist Theory of Stratification. Althusser and 'structuralist' Marxism, contributions from the Frankfurt School. Empirical issues and evidence from the sociology of class and stratification.
SOCP0052: Theoretical issues in sociology
Semester 1
Credits: 6
Contact:
Topic: Sociology
Level: Level 3
Assessment: EX50 ES50
Requisites: Pre SOCP0062
Aims & learning objectives:
This module examines key debates in contemporary social theory and their relationship to classical sociology. These will include such issues as: the debate over human agency versus social structure; power and knowledge; language and social interaction; modernity and postmodernity; industrialism and postindustrialism and globalisation.
SOCP0054: Power & commitment in organisations
Semester 1
Credits: 6
Contact:
Topic: Sociology
Level: Level 3
Assessment: EX50 ES50
Requisites: Pre SOCP0044, Pre SOCP0048
Aims & learning objectives:
The aim of the course is to explore the themes of ideology, power and legitimacy in the context of organisations. To look at different methodological and empirical attempts to study these issues in enterprise and organisational contexts. By the end of the course the student will have familiarity with a number of ways of qualitatively apprehending the operation and construction of legitimate forms of management.
Content:
The course begins with the theoretical problem of conceptualising power. Students are introduced to the Marxist and Weberian approaches and to Lukes' philosophical attempt to distinguish three different dimensions. The course then looks at specific themes starting with Decision-making in enterprises and boardroom activity. Other themes are Collective bargaining, the creation of rules and industrial legality. Worker participation and consultation. Managerial strategies to gain commitment, the growth of corporate cultures, Japanisation and Human Resource Management practices.
SOCP0055: Comparative industrial relations
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 3
Assessment: EX50 ES40 CW10
Requisites: Pre SOCP0043, Pre SOCP0044
Aims & learning objectives:
This course examines the changing role of trade unions in industrial societies - their relationship to the state and political parties, the significance of ideology and different national traditions; the economic and social causes and consequences of industrial conflict. Comparative cross-national studies will focus on the post-war period, conflict and maturation approaches and union responses to economic, social and political adversity.
SOCP0056: Environmental policy & the countryside
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 3
Assessment: EX50 ES50
Requisites:
Aims & learning objectives:
To develop a clear understanding of the politics of the policy process as it applies to the countryside and the environment
Content:
Concern for the environment has become a radical and innovative element in European politics. By focusing on developments between the passage of the 1981 Wildlife and Countryside Act and the publication of the 1995 Rural White Paper the Unit explains the factors which have transformed the agenda of rural policy making. Corporatist politics and competitive pluralist politics are contrasted and special attention is given to the changing balance of private and public rights and responsibilities in the countryside.
SOCP0059: Core skills for social scientists: social research methods
Semester 1
Credits: 3
Contact:
Topic: Â鶹´«Ã½ Methods
Level: Level 1
Assessment: EX50 ES50
Requisites: Co HASS0006, Co SOCP0060
Aims & learning objectives:
To introduce students to classical, influential examples of investigations and research in various social sciences, and to introduce the main methods as well as philosophical and methodological issues raised by each.
Content:
Classical and influential case studies in political, sociological and psychological research; different types of methods; classification, quantification and meaning; controversial studies and their implications.
SOCP0060: Core skills for social scientists: quantitative methods 1
Semester 2
Credits: 6
Contact:
Topic: Â鶹´«Ã½ Methods
Level: Level 1
Assessment: EX50 PR50
Requisites: Co HASS0006, Co SOCP0059
Aims & learning objectives:
To introduce students to the main assumptions, concepts and methods of descriptive and inferential statistics, and to establish basic competence sufficient for investigative, exploratory data analysis using a spreadsheet and/or dedicated statistical software.
Content:
Description, Classification, Quantification; Descriptive Statistics; accessing and exploring a data set; Inferential Statistics; Causation and Correlation; types of statistical test; learning to select appropriate tests; designing an investigative project. The emphasis is on practical competence.
SOCP0061: Quantitative methods 2
Semester 1
Credits: 3
Contact:
Topic: Â鶹´«Ã½ Methods
Level: Level 2
Assessment: EX50 PR50
Requisites: Pre SOCP0060, Co PSYC0021
Aims & learning objectives:
To develop an understanding of the application and use of a range of quantitative techniques together with complementary/supporting research methods, and to establish competence in conducting specialised tests, sufficient data analysis using dedicated statistical software. Specific methods and tests will vary according to the degree specialism being followed.
Content:
Specific research methods and quantitative techniques, specified according the degree specialism being followed.
SOCP0069: Social science methodology & social theory
Semester 2
Credits: 6
Contact:
Topic: Sociology
Level: Level 2
Assessment: EX50 ES50
Requisites:
Aims & learning objectives:
The aims of this unit are to demonstrate the significance of different theories of scientific methodology for the social sciences and the distinctive contribution of the interpretivist perspective to sociological and related social sciences. Students should learn the problematic relevance of natural science models for social science and the substantive and methodological claims and value of interpretivist social theory.
Content:
Positivist models of scientific method and the interpretivist tradition in sociology: Popper, Kuhn, Winch and Weber. 'Actor-based' approaches: Goffman and ethnomethodology.
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.