Aims and Objectives: |
The main purposes of this module are to enable students to develop their practical and creative skills in a specific genre, and also their critical skills in exploring the aims and processes involved in their work and that of notable practitioners. They will also gain critical insights into the work of other contemporary writers and the processes of literary production. The module will assist the student in:
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Learning Outcomes: |
By the end of this module the student will be able to: demonstrate a practical and critical knowledge of one of the following genres in terms of subject, appropriate research, synthesis of materials, language, genre, form, narrative, character, and description, and of representative examples by published writers, namely: poetry, fiction, stage-writing and screen-writing. |
Teaching Methods: |
There is no syllabus. A series of one-to-one discussions are held between supervisor and student. These tend to be three or four 1-hour meetings per term. In case of larger number students taking one genre this may take place in small groups. You are encouraged to set up peer-review workshops with friends and fellow-students taking this course. A useful starting point for the module is David Morley's The Cambridge Introduction to Creative Writing (CUP, 2007). Formal meetings with supervisors will stop at the end of Term 2. |
Assessment: |
A Portfolio of creative writing and a critical, reflective essay on the aims and processes involved. The portfolio will be one of the following, however, please see this LINK about word counts and possible penalties for over/under word count:
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Search results: 826
The module is divided into four units, each focusing on one of the genres. Each unit is assessed, and the assessments are spread out across the academic year. There is also a fifth and final assessment: a portfolio that allows students to mix genres and showcase their strengths and interests.
Personal Writing Project
Prescribed reasing
Martial Epigrams 10 (esp. 10.1-12).
Lowrie, M. (2009). Writing, Performance, and Authority in Augustan Rome. (Oxford: Oxford University Press): 1–23 (chapter “Introduction; arma virumque cano”).
The module will serve both as an introduction to contemporary theatre and as a first investigation of the relationship between literary texts and the conditions of performance. Major plays of the period will be studied in their own right but also as examples of trends and developments in the period. Design, theatrical architecture, performance styles, organisations and repertoires will be studied, with special attention to assumptions concerning the social role of the drama. Where possible, texts will be related to specific productions. Writers studied will normally include: John Osborne, Arnold Wesker, Samuel Beckett, Harold Pinter, Edward Bond, Caryl Churchill, Brian Friel.
It wasn't until director Dominic Cooke arrived at Warwick University in 1985 that he began to understand theatre's capacity to be both a political and a moral force. Fittingly enough, it was the Royal Court that seized his attention:
"We did this brilliant course, which was basically all about the Court – about the shift from T. S. Eliot's The Cocktail Party to Look Back in Anger, right through Wesker, Bond, all those writers. Plays that really engaged, which were asking questions."'
Dominic Cooke, Artistic Director of the Royal Court Theatre (Guardia
Drama is the most public literary form - at many points in history the most immediately engaged in social change. Dublin's Abbey Theatre, Cape Town's Space Theatre, and New York's Cherry Lane Theatre are among the many sites that have played a major part in defining national identities at times of crisis and have been platforms for protest.
This module looks at major English-language plays written since the beginning of the twentieth century. We shall examine theatre in Ireland, South Africa, and the USA to investigate some of the ways writers have dramatised political, racial, class, and gender issues and have tried to foster a sense of community and intervene in history. Developments in theatrical form will be studied as vehicles for ideas. The work of designers, directors, and actors will be considered alongside the texts. At the heart of the module is the shifting relationship between theatre and social change.
SYLLABUS
TERM 1
Ireland
Week 1: Introduction. Types, Stereotypes, Myths and Two Histories of Ireland. Dion Boucicault, The Colleen Bawn (1860); W. B. Yeats and Lady Gregory, Cathleen ni Houlihan (1902)
Week 2: Sean O'Casey, The Shadow of a Gunman (1923) and The Plough and the Stars (1926)
Week 3: Frank McGuinness, Observe the Sons of Ulster Marching Towards the Somme (1986) and Sebastian Barry, The Steward of Christendom (1995)
Week 4: Anne Devlin, Ourselves Alone (1985) and Marina Carr, By the Bog of Cats (1998)
Week 5: David Ireland, Cyprus Avenue (2016)
Week 6: Reading week
South Africa
Week 7: Athol Fugard, John Kani, and Winston Ntshona, Sizwe Bansi is Dead (1972); The Island (1973)
Week 8: Athol Fugard, Statements After an Arrest (1972); 'Master Harold'... and the Boys (1982)
Week 9: Mbongeni Ngema, Sarafina! (1985), Janet Suzman, The Free State: A South African response to Chekov's The Cherry Orchard (2000)
Week 10: Mongiwekhaya, I See You (2016)
TERM 2
USA
Week 1: Eugene O'Neill, The Hairy Ape (1922) and All God's Chillun Got Wings (1924)
Week 2: Arthur Miller, The Death of a Salesman (1949) and Lorraine Hansberry, A Raisin in the Sun (1959)
Week 3: Tennessee Williams, A Streetcar Named Desire (1947)
Week 4: Arthur Miller, The Crucible (1953)
Week 5: James Baldwin, Blues for Mister Charlie (1964); Amiri Baraka, Dutchman (1964)
Week 6: Reading week
Week 7: Ntozake Shange, for colored girls... (1976); August Wilson, Ma Rainey's Black Bottom (1982)
Week 8: Tony Kushner, Angels in America: Millennium Approaches(1991) and Tarell Alvin McCraney, The Brothers Size (2015)
Week 9: Anne Washburn, Mr. Burns (2012); Lynn Nottage, Sweat(2015)
Week 10: Branden Jacobs-Jenkins, An Octoroon (2014); Lin-Manuel Miranda, Hamilton (2015)
PRIMARY TEXTS
It is essential for all students to bring copies of the week's readings (book, hardcopy printout, or laptop/e-reader) to seminar. Find more information here.
ASSESSMENT
TBA: watch this space over the summer
FILMS/VIDEOS
Recommended films/videos for context:
Term 1
- The Plough and the Stars (dir. John Ford, 1936)
- Michael Collins (dir. Neil Jordan, 1996)
- The Wind That Shakes the Barley (dir. Ken Loach, 2006)
- Bloody Sunday (dir. Paul Greengrass, 2002)
- Hunger (dir. Steve McQueen, 2008)
- The Biko Inquest (dir. Graham Evans, Albert Finney, 1984)
- Cry Freedom (dir. Richard Attenborough, 1987)
- Sarafina! (dir. Darrell Roodt, 1992)
- Mandela: Long Walk to Freedom (dir. Justin Chadwick, 2013)
Term 2
- Citizen Kane (dir. Orson Welles, 1941)
- The Crucible (dir. Nicholas Hytner, 1996)
- On the Waterfront (dir. Elia Kazan, 1954)
- A Streetcar Named Desire (dir. Elia Kazan, 1951)
- A Raisin in the Sun (dir. Daniel Petrie, 1961)
- In the Heat of the Night (dir. Norman Jewison, 1967)
- Dutchman (dir. Anthony Harvey, 1966)
- Do the Right Thing (dir. Spike Lee, 1989)
- Philadelphia (dir. Jonathan Demme, 1993)
- Cradle Will Rock (dir. Tim Robbins, 1999)
- Selma (dir. Ava DuVernay, 2014)
- Moonlight (dir. Barry Jenkins, 2016)
- Fences (dir. Denzel Washington, 2016)
Photograph: The National Theatre's An Octoroon (2018), Richard Davenport, The Other Richard/The Guardian
Example first-class essays
What Next?: A Future Beyond Postmodernity in Washburn's Post-Capitalist Realist America
2020/21 Proposed teaching timeslots available - *subject to change*
| DAY/TIME | |
| TUE - 2:00 - 3:45 | |
| TUE - 4:15 - 6:00 | |
This is a core module for English and Theatre Studies second-year students and open only to them.
Module Tutor: Dr. Emma Williams
Please see Announcements page for news relating to the module
This is an introduction to Special Educational Needs and Disability field. The aim of this module is to expose you to the theory, policy and practice in the field and help you to understand the implications of policy for classroom practice and also the influences of the wider social context on child development and learning.
The module is taught online and face to face, through a combination of asynchronous and synchronous teaching, and face to face seminars each week. Students are expected to prepare the assigned activities and actively participate in the online and face to face seminars. Information and supporting documents / research papers / videos for the activities are presented in the Lecture webpages. Please come prepared to contribute to the group discussion.
The module aims to inform students in their choice of engineering discipline and on what it means to be an Engineer. Students may have already made their decision on a discipline (or strongly decide to pursue general Engineering); therefore, this module will allow them to be sure they made the right decision. The module provides the students with essential tools for studies in engineering, such as communication skills, professionalism and ethics and prepares them for internships and future employment. Furthermore, the module informs engineering students about the UK-SPEC (UK-Standard for Professional Engineering Competence) which is the cornerstone of degree accreditation, continuing professional development (CPD), and eventual professional registration. Overall the aim of this module is to induct engineers into their degree, and show them that everything they are learning can be considered to support their development.
Here is last year's introductory lecture to give you an idea of the course content.
Aims
This module provides an introduction to biomedical engineering, its main outcomes (i.e. medical devices) and to clinical engineering as a profession. The module will give an overview of medical technologies for screening, diagnosis, treatment and rehabilitation and an appreciation for the role of Engineers in medicine and biology across the world and in different contexts (i.e. research, innovation, development, manufacturing, NHS, agencies, ONGs).
Principal learning outcomes
By the end of the module you will be able to:
- Identify the large array of biomedical engineering fields.
- Explain the basic tenets of fundamental technologies in biomedical engineering (i.e. engineering in biology and medicine) including medical devices for screening, diagnosis, treatment, rehabilitation and end of life.
- Analyze trends in technological innovations in the main medical specializations (e.g. cardiovascular, neurology, geriatric, pediatric, ophthalmology) and in the main medical setting (e.g. biological labs, medical wards, imaging units, surgical theaters, outpatient unit, chronic patient home etc.)
- Understand Biomedical Engineering as a profession and ethical considerations.
- Critically assess the appropriateness of innovative health care technologies by reading a health technology assessment report
This module will be assessed as following:
- 30% via a homework assignment (i.e., a 3000-words max assay one one particular healthcare technology), and
- 70% via a 2 hours final examination (i.e., summer 2019)
This module will provide engineers with an opportunity to develop their understanding of fuels and combustion technologies. The first part of the course will discuss the fundamentals of fuels; and provide context into the necessity for sustainable development of conventional fuel use and options for alternative fuels and technologies to augment and replace these. The main content of the module will focus on the principles of combustion, covering both theories and basic calculation methods for combustion equations, different flame types and emission index. The module also aims to facilitate understanding of practical combustion systems and their applications including the introduction of renewable fuels in some practical applications.
| ZN47 PLCM Timetable | ||||||||||||||||||||||||||||||||||||||||||||||||
| 8-9am | 9-10am | 10-11am | 11am-12pm | 12-1pm | 1-2pm | 2-3pm | 3-4pm | 4-5pm | 5-6pm | 6-7pm | 7-8pm | |||||||||||||||||||||||||||||||||||||
| Monday 15th July 2019 | Introduction to PLCM Angela Clarke |
break | The Market Perspective (LCM
1) Russell Collins Astra Zeneca |
lunch | IMCC briefing and IMCC (1) |
break | Technology Mgt and TRM Angela Clarke |
break | IMCC (2) |
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| Tuesday 16th July 2019 | QFD Angela Clarke |
break | IMCC (3) |
lunch | Launch & Growth (LCM 2)
Andrea Sting Syngenta |
break | Growth & Maturity
(LCM 3) Paul Evans PZ Cussons |
break | IMCC
(4) |
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| Wednesday 17th July 2019 | PLCM at Xerox Ton van Esch |
break | IMCC (5) |
lunch | reflection time | Innovative practice in Product Development Steve May Russell |
break | Interim
review and IMCC (6) |
PMA briefing | |||||||||||||||||||||||||||||||||||||||
| Thursday 18th July 2019 | Bravo for a Mature Product (LCM4) Bruce Reid, Syngenta |
break | Human Factors in PLC Ray Charlton |
lunch | Human Factors in PLC Ray Charlton |
break | IMCC (7)
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IMCC prep for present'n AC | break | IMCC (8) Presentations & Feedback |
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| Friday 19th July 2019 | Expert Panel BR/JO'L/AF/TvE |
break | Integration & Business Benefit Angela Clarke |
Module review & PMA briefing | 12 midday finish | |||||||||||||||||||||||||||||||||||||||||||
The course is in general on the introduction and application of a specific numerical analysis method, namely finite element method (FEM), soil behaviour and practical simulation of tunnel and other geo-structures simulations using FEM.
This module is an introduction to the syntax of the English Language using a linear system of brackets, subscript and superscript annotation (no trees!).
This course covers an introduction to food allergens and allergic reactions.
The module is intended to be an approachable
introduction to the scope of economics. It deliberately takes an applied
approach so as to demonstrate how the economist’s toolkit can be used to
analyse real-world issues, including those of relevance to the world of
business.
Why and how are areas divided into different disciplines?
How does this help/ hinder us when considering the Sustainable Development Goals?
Ahead of the seminar, please complete the following two tasks:
-Read Chapter 2, 'The Rise of the Modern Disciplines and Interdisciplinarity', from Introduction to interdisciplinary studies by Allen F. Repko, Rick Szostak, and Michele Phillips Buchberger.
The uncompromising modernity of Kafka’s writing has fascinated generations of readers across the world. His fiction has added the word Kafkaesque to the English dictionary for the experience of an obscure and dislocating modernity. A vast body of criticism concerns the question of how to read a body of writing that upsets many of the reader’s conventional expectations about meaning-making. In this module we will analyse how Kafka employs realist, symbolist and allegorical frames of reference in order to challenge the very notion of stable meaning. You will study a selection of Kafka’s short stories with reference to the following themes: narrative perspective; authority, law and justice; gender roles; performance art and Kafka’s animals. The module is optional for students on all degrees and runs over one term.
Course Outline and Weekly Schedule
Week 1: Introduction: Auf der Galerie
Week 2: NO CLASS! Preparation for: Patriarchal Power and the Power of the Unconscious in Das Urteil [See 'Student Preparation']
Week 3: Patriarchal Power and the Power of the Unconscious in Das Urteil (continued)
Week 4: NO CLASS! Social Power and Collective Memory in Beim Bau der chinesischen Mauer and “Eine kaiserliche Botschaft”
Week 5 a): Performance Art or Art as Sham? Ein Hungerkünstler
Week 5 b): Lecture, Wednesday 31 October, 2018, 5-7pm: When Anti-World Literature Turns into World Literature: Kafka’s Archives of Resistance
Week 6: READING WEEK
Week 7: Kafka's Animals: Kafka‘s Kleine Fabel in Comparison with Aesop’s Der Löwe und die Maus
Week 8: Kafka's Animals: The Ape and his Audience in Ein Bericht für eine Akademie
Week 9: Kafka's Animals: Narrative Perspective and Gender in Josefine, die Sängerin oder das Volk der Mäuse
Week 10 a): Make-up lesson for week 4, Monday 3rd December [room: TBA]: Social Power and Collective Memory in Beim Bau der chinesischen Mauer and “Eine kaiserliche Botschaft”
Week 10 b) Course Summary: “Vor dem Gesetz” and Franz Kafka's Engagement with Modernity
Module Outline
This module has been designed to introduce students to the critical evaluation of visual and documentary evidence through a discussion of works of art that have been revealed or are polemically considered to be fakes. Taking a thematic approach, the module will consider cases from the medieval to the contemporary across different media. The following questions will be addressed: What is authenticity? When did the notion of forgery emerge? What is the difference between copy, replica, and forgery? Is restoration a sort of forgery? Is there a science to reveal forgeries? What is the relationship between fake and mass culture? Two important 20th-century films will provide further points for study. The module will be team-taught and will also introduce students to the range and presentation methods of the members of the department.
Syllabus
Introduction: Restoration or Replication?
Reproduction, Revival, Forgery
Technical Analysis: An Anti-Forgery?
Archives of Forgeries
The Forger as Artist?
The Architectural Simulacrum
Appropriation, Authorship, Copyright
The Real/Fake Debate
Forgery and Connoisseurship
Assessment:
Essay (1500 words; 100%; to be submitted by the end of the term)
Bibliography
Walter Benjamin, The Work of Art in the Age of Mechanical Reproduction (London: Penguin, 2008).
Lynn Catterson, Finding, Fixing, Faking, Making: Supplying Sculpture in ‘400 Florence (Todi: Ediart, 2014).
Leah R. Clark, “Transient Possessions: Circulation, Replication, and Transmission of Gems and Jewels in Quattrocento Italy,” in Journal of Early Modern History 15 (2011):185–221.
Bruce Cole and Ulrich Middledorf: “Masaccio, Lippi, or Hugford?,” in Burlington Magazine 113 (1971):500–507.
Thomas Da Costa Kaufmann, “Antiquarianism, the History of Objects, and the History of Art before Winckelmann,” in Journal of the History of Ideas 62 (2001):523–41.
Jonathon Keats, Forged: Why Fakes Are the Great Art of Our Age (Oxford: Oxford University Press, 2013).
Joris Kila and Marc Balcells, eds., Cultural Property Crime (Leiden and Boston: Brill, 2014).
Thierry Lenain, Art Forgery: The History of a Modern Obsession (London: Reaktion Books, 2011).
Tomas Loch, “The Changing Meaning of Copies: Citations and Use of Plaster Casts in Art from the Renaissance to the Beginning of the 20th Century,” in Copia e invención (Valladolid: Museo Nacional de Escultura, 2013):107–39.
Ken Perenyi, Caveat Emptor: The Secret Life of an American Art Forger (New York: Pegasus, 2012).
David A. Scott, Art: Authenticity, Restoration, Forgery (Los Angeles: Cotsen Institute of Archeology Press, 2016).
Walter Stephens, “When Noah Ruled the Etruscans: Annius of Viterbo and his Forged Antiquities,” in MLN 119 (2004):201–23.
Module Outline
Mannerism defines a key historical period in European arts, bridging the Renaissance and Baroque periods, which is characterised by a shift towards an increasingly more artful, idiosyncratic approach to artistic invention and practice. The term itself, however, is controversial, as it was forged by modern critics on the basis of the Italian sixteenth-century expression maniera (‘manner’, ‘style’). The broad aim of this module is to bring to the fore a number of critical issues raised by the many-sided notion of Mannerism, provide an in-depth examination of a large body of artists and artworks (drawings, paintings, sculptures and architecture) associated with it. The module is based on student-centred seminars, and structured in such a way that students will be invited to reflect on how their understanding of the concept of Mannerism changes throughout. It focuses on how theorists and artists developed new ways of conceiving of artistic practice, by placing unprecedented emphasis on the individual’s inventiveness and talent, and taking the ideal of beauty well beyond the rules of classical art that had prevailed in the High Renaissance. The analysis of theoretical principles elaborated by Italian treatise writers such as Vasari and Lomazzo is combined with an extensive survey of artistic practices and stylistic features that spread from Italy across Europe in the sixteenth century.
Sample Syllabus
Vasari's art theory
Mannerism in the modern scholarship
Models to imitate: Michelangelo and Raphael
The study of the human figure
Drawing and draughtsmanship
Between Florence and Rome: the early Italian Mannerists (Rosso Fiorentino, Pontormo, Parmigianino, Bronzino, Salviati)
Mannerism in sculpture: Cellini to Giambologna
Mannerism in architecture
The School of Fontainebleau
Dutch Mannerists
The School of Prague
Art and Nature: the Mannerist garden
The question of the sacred images
The Later Mannerists
Module Format
This module consists of both lectures and seminars. Seminars are student-centred; you should be prepared to contribute to the discussion in order to reap the benefits. Seminars may vary in format, and will entail a variety of in-class group activities including occasional group presentations.
Module Aims
By the end of the module you should be able to understand and compare/contrast:
- Demonstrate critical understanding of how Mannerism impacted on the development of Western art and how it has been discussed in modern scholarship.
- Learn how to deal critically with periodisation, stylistic categories and complex theoretical concepts.
- Demonstrate a grasp of the main lines of Mannerism-related artworks and the notion of Mannerism in contemporary art theory
- Demonstrate detailed knowledge of the works studied and their contexts
- Deploy these ideas critically in relation to other forms of art
Moreover, you should be able to:
- Make use of primary sources to contextualise the material;
- Improve your analytical skills and incorporate visual analysis in your work;
- Frame artists and artworks in their historical contexts and situate them in a broader art historical discourse;
- Deal with theoretical issues and historiographical concepts related to the Renaissance.
Workload
2 x 2-hour lecture/seminar per week
1 x Field trip
You should carry our a minimum of 7 hours preparatory reading and independent research per week
Assessment
3,500 word Portfolio including both documentary evidence and reflective writing (50%)
Slide test Assignment (20%)
1,500 word Essay (30%)
Introductory Reading
Essential
Giorgio Vasari, Lives of the Painters, Sculptors and Architects (ed. 1568), translated by Conaway, J., and Bondanella, P. (Oxford, 1991), ‘Preface’ to Part 3. [http://webcat.warwick.ac.uk/record=b2952624~S1]
Robert Williams, ‘Italian Renaissance Art and the Systemacity of Representation’, in Elkins, J, and Williams, R., Renaissance Theory (New York: Routledge, 2008), pp. 159-184 [http://webcat.warwick.ac.uk/record=b2344574~S1]
Michael Levey, High Renaissance (Harmondsworth: Penguin, 1975), esp. Ch. 1, pp. 15-63.
Walter Friedlaender, Mannerism and Anti-mannerism in Italian Painting (New York: Columbia University Press, 1990).
John Shearman, Mannerism (Harmondsworth: Penguin, 1967).
Philip Sohm, Style in the Theory of Early Modern Italy (New York: Cambridge University Press, 2001), pp. 86-114Chapter 4, 'Giorgio Vasari: Aestheticizing and Historicizing Style'.
Robert Williams, Art, Theory, and Culture in Sixteenth-Century Italy: From Techne to Metatechne (Cambridge, MA: Cambridge University Press, 1997), pp. 29-72 (ch. 1, ‘Vasari's Concept of Disegno’), and pp. 73-122 (Ch. 2, ‘Style, Decorum and the Viewer’s Experience’)
Further
The concept of Mannerism in modern scholarship
Anthony Blunt, Artistic Theory in Italy, 1450–1600 (Oxford: Oxford University Press, 1962).
Arnold Hauser, Mannerism: The Crisis of the Renaissance and the Origin of Modern Art (London: Routledge and Kegan Paul, 1965).
Enrst H. Gombrich, ‘Mannerism: The Historiographic Background’, in Norm and Form: Studies in the Art of the Renaissance (London and New York: Phaidon, 1966), pp. 99-106.
Hessel Miedema, ‘On Mannerism and Maniera’, Simiolus: Netherlands Quarterly for the History of Art, Vol. 10 (1978–1979), No. 1, pp. 19-45.
Jeroen Stumpel, ‘Speaking of Manner’, Word and Image, Vol. 4 (1988), No. 1, pp. 246-264.
Introduction to more specific themes
Sydney J. Freedberg, Painting of the High Renaissance in Rome and Florence (New York: Hacker Art Books, 1985).
Linda Murray, The High Renaissance and Mannerism: Italy, the North, and Spain, 1500–1600 (London: Thames and Hudson, 1977).
Wolfgang Lotz, Architecture in Italy, 1500-1600 (New Haven: Yale University Press, 1995).
Marcia B. Hall, After Raphael: Painting in Central Italy in the Sixteenth Century (New York: Cambridge University Press, 1999)
Bastien Eclercy (ed.), Maniera: Pontormo, Bronzino and Medici Florence, exh. cat. (Munich, London, New York : Prestel, 2016).
Michael Cole, Cellini and the Principles of Sculpture (New York: Cambridge University Press, 2002).
David Franklin, Painting in Renaissance Florence, 1500–1550 (New Haven: Yale University Press, 2001).
Henri Zerner, Renaissance Art in France: The Invention of Classicism (Paris: Flammarion, 2004).
Thomas Da Costa Kaufmann, The School of Prague: Painting at the Court of Rudolf II (Chicago: Chicago University Press, 1988).
This 30 CATS first-year option module is an introduction to the modern social and political history of sub-Saharan Africa. The course takes a chronological approach, covering three broad periods: the nineteenth-century precolonial period, colonial rule, and the postcolonial period. Starting with a discussion of the idea of ‘Africa’, students will familiarise themselves with the changing nature of African trade and commerce after the ending of the slave trade; with the character and development of political authority in the nineteenth century; with the establishment of colonial rule through treaty and conquest; with the effects of colonialism on colonised African societies; with the growth of anti-colonial sentiments and the emergence of nationalisms; and with the impact of decolonization and the formation of postcolonial states. The final lectures and seminars will explore the nature of postcolonial African states, and include discussion of episodes of violence and of ‘development’ in Africa.
Weekly lectures will provide a chronological framework. Seminars elaborate the themes from the lectures, but concentrate on regional case studies and debates within the historiography.
This 30 CATS first-year option module is an introduction to the modern social and political history of sub-Saharan Africa. The course takes a chronological approach, covering three broad periods: the nineteenth-century precolonial period, colonial rule, and the postcolonial period. Starting with a discussion of the idea of ‘Africa’, students will familiarise themselves with the changing nature of African trade and commerce after the ending of the slave trade; with the character and development of political authority in the nineteenth century; with the establishment of colonial rule through treaty and conquest; with the effects of colonialism on colonised African societies; with the growth of anti-colonial sentiments and the emergence of nationalisms; and with the impact of decolonization and the formation of postcolonial states. The final lectures and seminars will explore the nature of postcolonial African states, and include discussion of episodes of violence and of ‘development’ in Africa.
Weekly lectures will provide a chronological framework. Seminars elaborate the themes from the lectures, but concentrate on regional case studies and debates within the historiography
This 30 CATS first-year option module is an introduction to the modern social and political history of sub-Saharan Africa. The course takes a chronological approach, covering three broad periods: the nineteenth-century precolonial, colonial, and postcolonial eras. Starting with a discussion of the idea of ‘Africa’, students will familiarise themselves with the changing nature of African trade and commerce after the ending of the slave trade; with the character and development of political authority in the nineteenth century; with the establishment of colonial rule through treaty and conquest; with the effects of colonialism on colonised African societies; with the growth of anti-colonial sentiments and the emergence of nationalisms; and with the impact of decolonization and the formation of postcolonial states. The final lectures and seminars will explore the nature of postcolonial African states, and include discussion of issues such as the Rwandan genocide and ‘development’ in Africa.
Weekly lectures will provide a chronological framework. Seminars elaborate the themes from the lectures, but concentrate on regional case studies and debates within the historiography.
Societies are identified, at least in part, by whom they choose to marginalise. This first-year 30 CAT undergraduate module offers students an introduction to early modern history and the opportunity to explore why and how some individuals and groups were marginalised and persecuted because of differences in their beliefs, gender, ethnicity and behaviour. The early modern period was a time of great social, economic, and religious uncertainty. Conflicts and social tensions created by developments in Europe led to the emergence of new types of deviant and radical groups and new measures to control their behaviour. The module will be structured around a series of case studies of groups and individuals identified as 'deviants' in order to test established hypotheses about exclusion, prejudice and scapegoating.
Though this module focuses on early modern Europe, many of the groups we discuss will be set firmly within the context of wider global developments and economic transformations. Students will also be encouraged to reflect on their own ideas about deviant behaviour. The assessment for this module will encourage examining different deviant groups through a comparative framework.
While Historiography I
introduced students to key methodological and theoretical approaches in
history writing from the Enlightenment to roughly the 1990s,
Historiography II explores such themes from the 1990s to the present.
However, unlike Historiography I, the 9 lectures/seminars do not proceed
chronologically. Instead, each week focuses on a different important
theme/theory/methodology which is currently hotly debated among academic
historians. Each lecture is therefore presented by a member of staff
specialised in the week’s theme. While each lecture will start off with a
brief introduction into the historiography of the subject, the bulk of
it will concentrate on the individual lecturer’s methodological and
theoretical approach. Historiography II aims to offer students a clear
idea of what is currently exciting and important in Anglo-American
academic history writing. It will develop students’ abilities in study,
research, and oral and written communication, through a programme of
seminars, lectures and essay work. Students are encouraged to link their
studies in Historiography II with their other second- and third-year
modules. Historiographical knowledge will help students to choose a
dissertation topic and supervisor in year 3.
This course explores the relationship between cinema, mobility and the city through the close analysis of contemporary films from Argentina, Brazil, Mexico and Uruguay. In encouraging students to think geographically about film, we will consider how cinematic locations – urban, rural and mobile – enable filmmakers to address broader social and cultural issues, such as migration, neo-colonialism, transnationalism and social inequality.
How is this course taught?
The course is taught through a combination of weekly lectures and seminars. The lectures will serve to contextualise the individual films, while the seminars will include close textual analysis. Students will be required to watch each of the seven films before lectures/seminars, as well as carry out background readings on both the films and their geographical contexts. References to the background readings will be available for each week on Moodle.
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Week 1 |
Introduction to the module How to analyse a film
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Week 2 |
Amores perros (Alejandro González Iñárritu, 2000) |
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Week 3 |
Y Tu Mamá También (Alfonso Cuarón, 2001) |
|
Week 4 |
Central do Brasil (Walter Salles, 1998) |
|
Week 5 |
Whisky (Pablo Stoll and Juan Pablo Rebella, 2004) |
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Week 6 |
Reading Week |
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Week 7 |
Elefante blanco (Pablo Trapero, 2012) |
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Week 8 |
La antena (Esteban Sapir, 2007) |
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Week 9 |
La mujer sin cabeza (Lucrecia Martel, 2008) |
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Week 10 |
Essay writing and revision |
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This course provides a detailed introduction to Spanish film from the 1950s until the present day. It explores the ways in which Spanish cinema has frequently explored, constructed and problematized Spanish nationhood across a diverse range of cinematic movements and genres. In studying the works of key directors such as Pedro Almodóvar, Alex de la Iglesia and Julio Medem, the course considers how Spanish film has responded to key moments, crises and contradictions in Spanish history. The course will consider the practices of both Spanish art cinema and popular cinema alike, and closely examine these trends within their sociohistorical, political and industrial contexts.
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Week 1 |
Introduction to module Introduction to Spanish film |
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Week 2 |
¡Bienvenido Mr Marshall!(Luis García Berlanga, 1953)*
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Week 3 |
El espíritu de la colmena (Víctor Erice, 1973)
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Week 4 |
Mujeres al borde de un ataque de nervios (Pedro Almodóvar, 1988)
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Week 5 |
Vacas (Julio Medem, 1992) Practice commentary in class |
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Week 6 |
Reading Week |
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Week 7 |
Los lunes al sol (Fernando de León, 2002)
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Week 8 |
Volver (Pedro Almodóvar, 2006)
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Week 9 |
Balada triste de trompeta (Alex de la Iglesia, 2010)
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Week 10 |
Revision and essay writing |
Module page for the 2020 - 2021 academic year.
This interdisciplinary postgraduate module offers an in-depth introduction to Design Thinking as research and practice and focuses on its uses in the field of "social change".
Design Thinking for Social Impact is an effective way to gain insights into pressing human problems and build the skills required to develop innovative and sustainable solutions.
Syllabus
Week 1 – Introduction: Genealogies of the Interface
Week 2 – The Interface as Socio-Technical Assemblage
Week 3 – What is a User?
Week 4 – [Graphics] – The Operational Image
Week 5 – [Workflow] – Governance of Actions
Week 6 – [Processing] – Time and Cognition
Week 7 – [Analytics] – Trace Data, Optimization and Social Media Platforms
Week 8 – [Storage] – From Web Archives to Digital Folklore
Week 9 – Conclusion: The Mediation of Behaviour
For further information please contact cim@warwick.ac.uk or go to https://warwick.ac.uk/fac/cross_fac/cim/apply-to-study/cross-disciplinary-postgraduate-modules/im923-user-interface/
This module serves as an interdisciplinary introduction to contemporary machine learning research and applications, specifically focusing on the techniques of deep learning which use convolutional and/or recurrent neural network structures to both recognize and generate content from image, text, signals, sound, speech, and other forms of predominantly unstructured data. Using a combination of theoretical/conceptual/historical analysis and practical programming projects in the R programming language, the module will teach both the basic application of these techniques while also conveying the historical origins and ethical implications of such applications.
For further information please contact cim@warwick.ac.uk or go to https://warwick.ac.uk/fac/cross_fac/cim/apply-to-study/cross-disciplinary-postgraduate-modules/im931-interdisciplinary-approaches-to-machine-learning/
This module serves as an interdisciplinary introduction to contemporary machine learning research and applications, specifically focusing on the techniques of deep learning which use convolutional and/or recurrent neural network structures to both recognize and generate content from image, text, signals, sound, speech, and other forms of predominantly unstructured data. Using a combination of theoretical/conceptual/historical analysis and practical programming projects in the R programming language, the module will teach both the basic application of these techniques while also conveying the historical origins and ethical implications of such applications.
For further information please contact cim@warwick.ac.uk or go to https://warwick.ac.uk/fac/cross_fac/cim/apply-to-study/cross-disciplinary-postgraduate-modules/im931-interdisciplinary-approaches-to-machine-learning/
This module introduces students to the fundamental techniques, concepts and contemporary discussions across the broad field of data science. With data and data related artefacts becoming ubiquitous in all aspects of social life, data science gains access to new sources of data, is taken up across an expanding range of research fields and disciplines, and increasingly engages with societal challenges. The module provides an advanced introduction to the theoretical and scientific frameworks of data science, and to the fundamental techniques for working with data using appropriate procedures, algorithms and visualisation. Students learn how to critically approach data and data-driven artefacts, and engage with and critically reflect on contemporary discussions around the practice of data science, its compatibility with different analytics frameworks and disciplinary, and its relation to on-going digital transformations of society. As well as lectures discussing the theoretical, scientific and ethical frameworks of data science, the module features coding labs and workshops that expose students to the practice of working effectively with data, algorithms, and analytical techniques, as well as providing a platform for reflective and critical discussions on data science practices, resulting data artefacts and how they can be interpreted, actioned and influence society.
This course space will be used to focus on the Moodle activity tools for collaboration, communication and interactivity. We will explore how these tools can support and promote asynchronous active learning. Come along for ideas, inspiration and also share examples of how Moodle is working for you.
This course gives some basic knowledge about what a SEM is, it's operating principles and capacities. After going through the content of the course, you need to pass the test before participating any hands-on training sessions.
This course is the RSE training course on the Introduction to the Linux Desktop
Welcome
Welcome to the International Economic Law Core Module. You will find relevant information about the module here. Please see below for details on how the module will be organised and what expectations are for preparation and other work for the module.
The Module Introduction and Information Handout containing all relevant information about the module and a schedule of classes and assessments can be found below.
The Reading List for the module can be found here and materials available electronically via TalisAspire.
This course offers an advanced introduction to international trade law, with particular emphasis on the legal framework of the World Trade Organization (WTO). With 166 Members, the rules of the WTO govern around 98 per cent of global trade. Yet the rules-based multilateral trading system has come under increasing strain in recent years, marked by tariff wars, rising protectionism, and a deepening institutional crisis.
Against this backdrop, the course examines the laws, principles, and jurisprudence of the WTO, situating them within contemporary geopolitical and economic developments. It also critically engages with the enduring tensions between trade liberalisation and the need to preserve domestic regulatory space for legitimate public policy objectives, including public health, environmental protection, and national security.
We will explore the origins and evolution of the WTO, its institutional structure, and the core agreements governing trade in goods, dispute settlement, intellectual property rights, trade remedies, health-related measures, and technical standards. Through close textual analysis of key provisions of the WTO Covered Agreements, complemented by critical engagement with jurisprudence from the WTO Dispute Settlement Body and in-class exercises based on hypothetical dispute scenarios, the course will equip students with a foundational understanding of the core principles of international trade law.
The course also addresses the contemporary challenges facing the multilateral trading system, including trade wars, the resurgence of protectionism, emerging trade issues, and ongoing institutional reform debates. By integrating doctrinal analysis with case law, policy discussions, and real-world controversies, the course is intended to provide students with the analytical tools needed to critically assess the role of international trade law in global governance.
This is a course on the law and policy of international trade. The course will build on the short introduction to the WTO in the IEL core module and explore the treaty-based WTO international economic law system, its principal agreements and institutions, its core doctrines, and the current proposals for reform.
The WTO is regarded as one of the most successful international organisations governing activities between states because it has a highly effective dispute settlement system. The course will explore whether the WTO remains relevant in an increasingly globalised world where economic disputes typically cover national, transnational and international law as well as a multiplicity of economic actors, like states and multinational corporations. It will evaluate the effectiveness of the WTO rules against the background of the rise of the mega-regional agreements- the Transatlantic Trade and Investment Partnership (TTIP) and the Trans-Pacific Partnership Agreement (TPPA). It will consider how demands for trade justice affect how we interpret the WTO rules and what reforms of WTO rules may be necessary to achieve that goal.
This module provides an overview of the main contemporary issues in international development law and human rights. It provides an introduction to topics that all students are expected to have an understanding of and thus provides the background for all modules and the dissertation. Students who read and understand the module materials are more likely to achieve higher grades. Group work is an important part of the module as experience shows that participatory study is a successful pedagogical method.
Module Aims
- To provide students with knowledge and understanding of and the inter-relationships between the main legal theories relating to international development, gender, governance, globalization and human rights
- To provide students with a range of practical legal and academic skills used by lawyers and development practitioners.
- To facilitate the development of an understanding of the relationship between theory and practice.
- To develop a critical ability to read theoretical materials, distil and synthesize such materials, and incorporate insights into written legal and academic documents.
- To develop oral and advocacy skills appropriate to legal and developmental practice.
• This module is COMPULSORY.
• Sessions will also take place in LIB 2 on Wednesdays between 2pm – 4pm.
B. Introduction to the Module
The aim of the module is to provide students with the knowledge, skills and confidence required to develop critical reading, writing and research skills in preparation for undertaking independent research and writing up academic work. This module brings together experts from the Law School, Library and Student Careers and Skills. The module is taught in Terms 1, 2 & 3.
C. Principal Module Aims
The Legal Research and Writing Skills module is a core component of the taught LLM programme. It is designed primarily to prepare students for the research and writing requirements associated with their assessments including essays and examinations, and the dissertation element of the LLM.
D. Outline of Topics
· Mastering Your Masters
· Developing and Applying Critical Reading Skills
· Developing Research and Writing Skills
· Choosing a Dissertation Topic
· Conducting a Literature Survey
· Good Academic Practice
· Choosing Your Dissertation Topic
· Dissertation Planning
· Project Planning and Management
· Specialist Dissertation Research
· Building, Structuring and Articulating Arguments
· Working with Feedback
· Peer Learning
E. Assessment
This module is linked to your assessed essays, examinations and the LLM Dissertation module. It is aimed at supporting the completion of your assessments and the 10,000 words dissertation due at the end of the academic year.
F. Materials
Useful materials online through the module website. You will also find presentations and other supplementary materials and links to useful resources on the module website.
G. Timetable
* Session topics may change
Term 1
Weeks 1 & 2: No class
Week 3: Introduction to Postgraduate Legal Study
-- introducing academic expectations for postgraduate study in law including the nature of knowledge production, participation in academic debates, and the importance of disciplinary literacy.
Week 4: Conducting a Literature Survey
-- led by Jackie Hanes, Research and Academic Support Librarian; focusing on planning a literature search and finding academic and legal information for essays and assignments; introducing specialist library and legal research resources for students on the different LLM pathways.
Week 5: Moving from ‘Consumer’ to ‘Producer’ of Knowledge
-- introducing some of the skills necessary to support your journey from a ‘consumer’ of knowledge to a ‘producer’ of knowledge; exploring some essential skills that will help you make the most out of your LLM and teach you how to embed them in your study and research.
Week 6: no class (reading week).
Week 7: academic citation
-- led by Jackie Hanes, Research and Academic Support Librarian; focusing on the use of OSCOLA in legal academic writings.
Week 8: Writing: A Matter of Presenting Research
-- introducing legal wirting style; providing tips for good legal writing.
Week 9: Good Academic Practice
-- introducing the Law Schoo's policy on academi integrity and AI's use in this regard; distingusihing between good academic practice and bad academic practice; helping to enhance academic prowess by learning how to avoid charges of plagiarism including the importance of paraphrasing, referencing, and attribution.
Week 10: Q&A and Feedback.
Languages and Cultures Beyond Boundaries
This module aims to critique and interrogate the concept of national languages and cultures by focusing on the cross-cultural aspects of a number of key texts from medieval travel writing, to contemporary film. It seeks to challenge assumptions about the relationship between national borders and linguistic/cultural identity by exploring the cross-fertilization of European languages and cultural ideas across both European and global boundaries. It will thus invite students to reflect on contemporary ideas about intercultural identity in the light of textual expressions on this theme across time and across European cultures. It examines how ideas of self and other are constructed through representation and introduces students to some theoretical concepts related to culture and identity.
You will develop a understanding of a number of key texts from a range of cultures and reflect on the cross-cultural influences inherent in their making and reception. You will critically reflect on representations of self and other in the core texts, and explore notions of culture, identity and languages using appropriate theoretical concepts.
As well as developing research and presentation skills, you will develop the ability to analyse written and visual forms of cultural expression, both in the modern language(s) you study, and in English.
Topics and texts will include travel writing (The Travels of Marco Polo; writings of George Borrow); Italian opera and eighteenth-century European culture (Casanova's memoirs and Mozart's and Da Ponte's Don Giovanni); France and the Orient (Lettres persanes), Introduction to French film (Jean de Florette and L'auberge espagnole); Spain between East and West (Tales from the Alhambra, Carmen); the Enlightenment in Germany (Nathan the Wise; Measuring the World); Transnational Identities in the 21st century (Clash of Civilizations over an Elevator in Piazza Vittorio)
This module provides an introduction to some of the major European political thinkers through a close engagement with their most celebrated works. We will read Niccolò Machiavelli's The Prince, Jean-Jacques Rousseau's The Social Contract, Edmund Burke, Reflections on the Revolution in France, and Karl Marx and Friedrich Engels' The Communist Manifesto. Some of these texts, it would be no exaggeration to say, have changed the world; all are considered classic works of political theory, and continue to shape our understanding of politics and society. Many of these writers' key concepts remain fundamental terms in our political vocabulary, and are consistently appealed to and evoked across the political spectrum.
We will situate each thinker and text in their specific historical context, thereby covering some of the key political sequences in modern European history, but also de-contextualise them so as to discuss and appreciate their continued relevance to and importance for European politics today in time of systemic crisis and popular revolt. Our approach to the material will therefore be filtered through a set of three key themes: power, collective self-determination and the people.
Notes of the course: https://moodle.warwick.ac.uk/pluginfile.php/946222/course/summary/LectureNotesMA125.pdf
Notes of last week of the course: https://moodle.warwick.ac.uk/pluginfile.php/946222/course/summary/LectureOnStereographicProjection.pdf
Problem sheet 1: this is suggested at the end of week 2/week 3. This is not compulsory but strongly recommended to train yourself and check if the basic concepts are clear. https://moodle.warwick.ac.uk/pluginfile.php/946222/course/summary/Problem%20Sheet%201.pdf
Content: How do you reconstruct a curve given its slope at every point? Can you predict the trajectory of a tennis ball? The basic theory of ordinary differential equations (ODEs) as covered in this module is the cornerstone of all applied mathematics. Indeed, modern applied mathematics essentially began when Newton developed the calculus in order to solve (and to state precisely) the differential equations that followed from his laws of motion.
However, this theory is not only of interest to the applied mathematician: indeed, it is an integral part of any rigorous mathematical training, and is developed here in a systematic way. Just as a `pure' subject like group theory can be part of the daily armoury of the `applied' mathematician , so ideas from the theory of ODEs prove invaluable in various branches of pure mathematics, such as geometry and topology.
In this module we will cover relatively simple examples, first order equations, linear second order equations and coupled first order linear systems with constant coefficients, for most of which we can find an explicit solution. However, even when we can write the solution down it is important to understand what the solution means, i.e. its `qualitative' properties. This approach is invaluable for equations for which we cannot find an explicit solution.
We also show how the techniques we learned for second order differential equations have natural analogues that can be used to solve difference equations.
The course looks at solutions to differential equations in the cases where we are concerned with one- and two-dimensional systems, where the increase in complexity will be followed during the lectures. At the end of the module, in preparation for more advanced modules in this subject, we will discuss why in three-dimensions we see new phenomena, and have a first glimpse of chaotic solutions.
Aims: To introduce simple differential and difference equations and methods for their solution, to illustrate the importance of a qualitative understanding of these solutions and to understand the techniques of phase-plane analysis.
Objectives: You should be able to solve various simple differential equations (first order, linear second order and coupled systems of first order equations) and to interpret their qualitative behaviour; and to do the same for simple difference equations.
Books:
The primary text will be:
J. C. Robinson An Introduction to Ordinary Differential Equations, Cambridge University Press 2003.
Additional references are:
W. Boyce and R. Di Prima, Elementary Differential Equations and Boundary Value Problems, Wiley 1997.
C. H. Edwards and D. E. Penney, Differential Equations and Boundary Value Problems, Prentice Hall 2000.
K. R. Nagle, E. Saff, and D. A. Snider, Fundamentals of Differential Equations and Boundary Value Problems, Addison Wesley 1999.
Content: How do you reconstruct a curve given its slope at every point? Can you predict the trajectory of a tennis ball? The basic theory of ordinary differential equations (ODEs) as covered in this module is the cornerstone of all applied mathematics. Indeed, modern applied mathematics essentially began when Newton developed the calculus in order to solve (and to state precisely) the differential equations that followed from his laws of motion.
However, this theory is not only of interest to the applied mathematician: indeed, it is an integral part of any rigorous mathematical training, and is developed here in a systematic way. Just as a `pure' subject like group theory can be part of the daily armoury of the `applied' mathematician , so ideas from the theory of ODEs prove invaluable in various branches of pure mathematics, such as geometry and topology.
In this module we will cover relatively simple examples, first order equations
,
linear second order equations
and coupled first order linear systems with constant coefficients, for most of which we can find an explicit solution. However, even when we can write the solution down it is important to understand what the solution means, i.e. its `qualitative' properties. This approach is invaluable for equations for which we cannot find an explicit solution.
We also show how the techniques we learned for second order differential equations have natural analogues that can be used to solve difference equations.
The course looks at solutions to differential equations in the cases where we are concerned with one- and two-dimensional systems, where the increase in complexity will be followed during the lectures. At the end of the module, in preparation for more advanced modules in this subject, we will discuss why in three-dimensions we see new phenomena, and have a first glimpse of chaotic solutions.
Aims: To introduce simple differential and difference equations and methods for their solution, to illustrate the importance of a qualitative understanding of these solutions and to understand the techniques of phase-plane analysis.
Objectives: You should be able to solve various simple differential equations (first order, linear second order and coupled systems of first order equations) and to interpret their qualitative behaviour; and to do the same for simple difference equations.
Books:
The primary text will be:
J. C. Robinson An Introduction to Ordinary Differential Equations, Cambridge University Press 2003.
Additional references are:
W. Boyce and R. Di Prima, Elementary Differential Equations and Boundary Value Problems, Wiley 1997.
C. H. Edwards and D. E. Penney, Differential Equations and Boundary Value Problems, Prentice Hall 2000.
K. R. Nagle, E. Saff, and D. A. Snider, Fundamentals of Differential Equations and Boundary Value Problems, Addison Wesley 1999.
Content: How do you reconstruct a curve given its slope at every point? Can you predict the trajectory of a tennis ball? The basic theory of ordinary differential equations (ODEs) as covered in this module is the cornerstone of all applied mathematics. Indeed, modern applied mathematics essentially began when Newton developed the calculus in order to solve (and to state precisely) the differential equations that followed from his laws of motion.
However, this theory is not only of interest to the applied mathematician: indeed, it is an integral part of any rigorous mathematical training, and is developed here in a systematic way. Just as a `pure' subject like group theory can be part of the daily armoury of the `applied' mathematician , so ideas from the theory of ODEs prove invaluable in various branches of pure mathematics, such as geometry and topology.
In this module we will cover relatively simple examples, first order equations, linear second order equations and coupled first order linear systems with constant coefficients, for most of which we can find an explicit solution. However, even when we can write the solution down it is important to understand what the solution means, i.e. its `qualitative' properties. This approach is invaluable for equations for which we cannot find an explicit solution.
We also show how the techniques we learned for second order differential equations have natural analogues that can be used to solve difference equations.
The course looks at solutions to differential equations in the cases where we are concerned with one- and two-dimensional systems, where the increase in complexity will be followed during the lectures. At the end of the module, in preparation for more advanced modules in this subject, we will discuss why in three-dimensions we see new phenomena, and have a first glimpse of chaotic solutions.
Aims: To introduce simple differential and difference equations and methods for their solution, to illustrate the importance of a qualitative understanding of these solutions and to understand the techniques of phase-plane analysis.
Objectives: You should be able to solve various simple differential equations (first order, linear second order and coupled systems of first order equations) and to interpret their qualitative behaviour; and to do the same for simple difference equations.
Books:
The primary text will be:
J. C. Robinson An Introduction to Ordinary Differential Equations, Cambridge University Press 2003.
Additional references are:
W. Boyce and R. Di Prima, Elementary Differential Equations and Boundary Value Problems, Wiley 1997.
C. H. Edwards and D. E. Penney, Differential Equations and Boundary Value Problems, Prentice Hall 2000.
K. R. Nagle, E. Saff, and D. A. Snider, Fundamentals of Differential Equations and Boundary Value Problems, Addison Wesley 1999.
Lecturer: Christian Boehning
Term(s): Term 1
Status for Mathematics students: List A for Mathematics
Commitment: 30 lectures plus weekly worksheets
Assessment: The weekly worksheets carry 15% assessed credit; the remaining 85% credit by 2-hour examination.
Prerequisites: None, but an understanding of MA125 Introduction to Geometry will be helpful.
Leads To: Third and fourth year courses in Algebra and Geometry, including: MA3D9 Geometry of Curves and Surfaces, MA3E1 Groups and Representations, MA4A5 Algebraic Geometry, MA4E0 Lie Groups, MA473 Reflection Groups, MA4H4 Geometric Group Theory, MA448 Hyperbolic Geometry and others
Content: Geometry is the attempt to understand and describe the world around us and all that is in it; it is the central activity in many branches of mathematics and physics, and offers a whole range of views on the nature and meaning of the universe.
Klein's Erlangen program describes geometry as the study of properties invariant under a group of transformations. Affine and projective geometries consider properties such as collinearity of points, and the typical group is the full matrix group. Metric geometries, such as Euclidean geometry and hyperbolic geometry (the non-Euclidean geometry of Gauss, Lobachevsky and Bolyai) include the property of distance between two points, and the typical group is the group of rigid motions (isometries or congruences) of 3-space. The study of the group of motions throws light on the chosen model of the world.
Aims: To introduce students to various interesting geometries via explicit examples; to emphasize the importance of the algebraic concept of group in the geometric framework; to illustrate the historical development of a mathematical subject by the discussion of parallelism.
Objectives: Students at the end of the module should be able to give a full analysis of Euclidean geometry; discuss the geometry of the sphere and the hyperbolic plane; compare the different geometries in terms of their metric properties, trigonometry and parallels; concentrate on the abstract properties of lines and their incidence relation, leading to the idea of affine and projective geometry.
Books:
M Reid and B Szendröi, Geometry and Topology, CUP, 2005 (some Chapters will be available from the General office).
E G Rees, Notes on Geometry, Springer
HSM Coxeter, Introduction to Geometry, John Wiley & Sons
The focus of combinatorial optimisation is on finding the "optimal" object (i.e. an object that maximises or minimises a particular function) from a finite set of mathematical objects. Problems of this type arise frequently in real world settings and throughout pure and applied mathematics, operations research and theoretical computer science. Typically, it is impractical to apply an exhaustive search as the number of possible solutions grows rapidly with the "size" of the input to the problem. The aim of combinatorial optimisation is to find more clever methods (i.e. algorithms) for exploring the solution space.
This module provides an introduction to combinatorial optimisation. Our main focus is on several fundamental problems arising in graph theory and linear programming and algorithms developed to solve them. These include problems related to shortest paths, minimum weight spanning trees, linear programming, matchings, network flows, cliques, colourings, dynamic programming, multicommodity flows and matroids. We will also discuss "intractible" (e.g. NP-hard) problems.
Many fundamental problems in the applied sciences reduce to understanding solutions of ordinary differential equations (ODEs). Examples include the laws of Newtonian mechanics, predator-prey models in Biology, and non-linear oscillations in electrical circuits, to name only a few. These equations are often too complicated to solve exactly, so one tries to understand qualitative features of solutions.
When do solutions of ODEs exist and when are they unique? What is the long time behaviour of solutions and can they "blow-up" in finite time? These questions are answered by the Picard Theorem on existence and uniqueness of solutions of ODEs, and its consequences.
The main part of the course will focus on phase space methods. This is a beautiful geometrical approach which often enables one to understand the qualitative behaviour of solutions even when we cannot solve the equations exactly. We will develop techniques to answer important questions about the stability/attraction properties (or instabilities) of given solutions, often fixed points.
We will eventually apply these powerful methods to particular examples of practical importance, including the Lotka-Volterra model for the competition between two species, Hamiltonian systems, and the Lorenz equations, and give an informal introduction to some more advanced topics (e.g. bifurcation theory, Lyapunov exponents).
MA266 Multilinear Algebra
Lecturer: Christian Böhning
Term(s): Term 2
Status for Mathematics students: Core for MMath G103, Optional Core for BSc G100
Commitment: 30 one-hour lectures plus assignments
Assessment: 85% by 2-hour examination, 15% coursework
Formal registration prerequisites: None
Assumed knowledge: Knowledge of vector spaces and matrices from MA150 Algebra 2 or MA149 Linear Algebraor MA148 Vectors and Matrices. In particular, understanding change of basis matrices, eigenvalues and eigenvectors, elementary row and column operations and diagonalisation of matrices
Useful background: Group theory from MA151 Algebra 1 or MA267 Groups and Rings especially abelian groups
Synergies: The following modules go well with this module:
Leads to: The following modules have this module listed as assumed knowledge or useful background:
- MA3E1 Groups and Representations
- MA3H6 Algebraic Topology
- MA3J9 Historical Challenges in Mathematics
- MA3G6 Commutative Algebra
- MA3A6 Algebraic Number Theory
- MA377 Rings and Modules
- MA3F1 Introduction to Topology
- MA3K4 Introduction to Group Theory
- MA398 Matrix Analysis and Algorithms
- MA4C0 Differential Geometry
- MA453 Lie Algebras
- MA4H4 Geometric Group Theory
- MA4H0 Applied Dynamical Systems
- MA473 Reflection Groups
Aims: By the end of the module students should be familiar with the Jordan canonical form and some of its applications; have working knowledge of bilinear, quadratic and Hermitian forms and related theory; command the basic concepts of multilinear algebra in vector spaces and be comfortable to use arguments involving duals.
Content: This is a second linear algebra module. Its contents can be divided into three major groups.
The first main topic is the Jordan canonical form and related results. Abstractly, this solves the classification problem for pairs (V, T) where V is a finite dimensional vector space over the complex numbers (or any other algebraically closed field) and T a linear self-map of V, up to the equivalence relation induced by bijective linear self-maps of V; more concretely, we classify n by n complex matrices A up to conjugation by invertible matrices P, i.e., the operation A -> P^{-1}AP.
Secondly, we treat bilinear, sesquilinear and quadratic forms on finite dimensional (real and complex) vector spaces. These structures are ubiquitous and fundamental in mathematics and many parts of the sciences. For example, the standard scalar product in R^n is an example. In passing we mention that the description of amplitudes, probabilities and expectation values in quantum theory places such structures at the very heart of how nature works at the smallest levels. We will cover orthonormal basis, Gram-Schmidt process, diagonalisation, singular value decomposition, hermitian forms and normal matrices, among other things.
The third part is concerned with a thorough discussion of the very useful concept of duality (dual vector spaces, dual linear maps, dual bases etc.) and its applications, and after that tensor, exterior and symmetric algebras and their basic properties.
Objectives:
Books:
P M Cohn, Algebra, Vol. 1, Wiley, 1982
I N Herstein, Topics in Algebra, Wiley, 1975
Jorg Liesen and Volker Mehrmann, Linear Algebra, Springer, 2015
Peter Petersen, Linear Algebra, Springer, 2012
F. Gantmacher, The Theory of Matrices, American Mathematical Society, 2001
Peter Lax, Linear Algebra and Its Applications, 2nd Edition, Wiley, 2007
This is the third module in the series Analysis 1, 2, 3 that covers rigorous Analysis. It covers convergence of functions and its applications to Integration, an introduction to multivariable calculus and Complex Analysis.
Status for Mathematics students: List B for third years. If numbers permit second and fourth years may take this module as an unusual option, but confirmation will only be given at the start of Term 2.
Commitment: 10 two hour and10 one hour seminars (including some assessed problem solving)
Assessment: 10% from weekley seminars, 40% from assignment, 50% two hour exam in June
Prerequisites: None
Introduction
This module gives you the opportunity to engage in mathematical problem solving and to develop problem solving skills through reflecting on a set of heuristics. You will work both individually and in groups on mathematical problems, drawing out the strategies you use and comparing them with other approaches.
General aims
This module will enable you to develop your problem solving skills; use explicit strategies for beginning, working on and reflecting on mathematical problems; draw together mathematical and reasoning techniques to explore open ended problems; use and develop schema of heuristics for problem solving.
This module provides an underpinning for subsequent mathematical modules. It should provide you with the confidence to tackle unfamiliar problems, think through solutions and present rigorous and convincing arguments for your conjectures. While only small amounts of mathematical content will be used in this course which will extend directly into other courses, the skills developed should have wide ranging applicability.
Intended Outcomes
Learning objectives
The intended outcomes are that by the end of the module you should be able to:
- Use an explicit problem solving scheme to control your approach to mathematical problems
- Explain the role played by different phases of problem solving
- Critically evaluate your own problem solving practice
Organisation
The module runs in term 2, weeks 1-10
Thursday 14:00-15:00 OC0.04 (new teaching and learning building)
Friday 15:00-17:00 OC0.04
Most weeks the Thursday slot will be used for the weekly (assessed) problem session, but this will not be the case every week. You are expected to attend all three timetabled hours.
Assessment Details
- A flat 10% given for ‘serious attempts’ at problems during the course. Each week, you will be assigned a problem for the seminar. At then end of the seminar, you should present a ‘rubric’ of your work on that problem so far. If you submit at least 7 rubrics, deemed to be ‘serious attempts’, you will get 10%.
- One problem-solving assignment (40%) (deemed to be the equivalent of 2000 words) due by noon on Monday 20th March 2017 by electronic upload (pdf).
- A 2 hour examination in Summer Term 2017 (50%).
Topology is the study of properties of spaces that are invariant under continuous deformations. An often cited example is that a cup is topologically equivalent to a torus, but not to a sphere. In general, topology is the rigorous development of ideas related to concepts such “nearness”, “neighbourhood”, and “convergence”.
This module covers topological spaces and their properties, homotopy, the fundamental group, Galois correspondence, universal covers, free products, and CV complexes.
The course will follow largely the first chapter of
- Allen Hatcher. Algebraic Topology. Cambridge University Press.
An electronic version of the book is freely available on the author’s web page, and a printed version should be available in the library or the campus bookshop.
The important and pervasive role played by pdes in both pure and applied mathematics is described in MA250 Introduction to Partial Differential Equations. In this module I will introduce methods for solving (or at least establishing the existence of a solution!) various types of pdes. Unlike odes, the domain on which a pde is to be solved plays an important role. In the second year course MA250, most pdes were solved on domains with symmetry (eg round disk or square) by using special methods (like separation of variables) which are not applicable on general domains. You will see in this module the essential role that much of the analysis you have been taught in the first two years plays in the general theory of pdes. You will also see how advanced topics in analysis, such as MA3G7 Functional Analysis I, grew out of an abstract formulation of pdes. Topics in this module include:
Method of characteristics for first order PDEs.
Fundamental solution of Laplace equation, Green's function.
Harmonic functions and their properties, including compactness and regularity.
Comparison and maximum principles.
The Gaussian heat kernel, diffusion equations.
Basics of wave equation (time permitting).
The course will start by introducing the concept of a manifold (without recourse to an embedding into an ambient space). In the words of Hermann Weyl (Space, Time, Matter, paragraph 11):
“The characteristic of an n-dimensional manifold is that each of the elements composing it (in our examples, single points, conditions of a gas, colours, tones) may be specified by the giving of n quantities, the “co-ordinates,” which are continuous functions within the manifold. This does not mean that the whole manifold with all its elements must be represented in a single and reversible manner by value systems of n co-ordinates (e.g. this is impossible in the case of the sphere, for which n = 2); it signifies only that if P is an arbitrary element of the manifold, then in every case a certain domain surrounding the point P must be representable singly and reversibly by the value system of n co-ordinates.”
Thus the points on the surface of a sphere form a manifold. The possible configurations of a double pendulum (one pendulum hung off the pendulum bob of another) is a manifold that is nothing but the surface of a two-torus: the surface of a donut (a triple pendulum would give a three-torus etc.) The possible positions of a rigid body in three-space form a six-dimensional manifold. Colour qualities form a two-dimensional manifold (cf. Maxwell’s colour triangle).
It becomes clear that manifolds are ubiquitous in mathematics and other sciences: in mechanics they occur as phase-spaces; in relativity as space-time; in economics as indifference surfaces; whenever dynamical processes are studied, they occur as “state-spaces” (in hydrodynamics, population genetics etc.)
Moreover, in the theory of complex functions, the problem of extending one function to its largest domain of definition naturally leads to the idea of a Riemann surface, a special kind of manifold.
Although it seems so natural from a modern vantage point, it took some time and quite a bit of work (by Gauss, Riemann, Poincare, Weyl, Whitney, …) till mathematicians arrived at the concept of a manifold as we use it today. It is indispensable in most areas of geometry and topology as well as neighbouring fields making use of geometric methods (ordinary and partial differential equations, modular and automorphic forms, Arakelov theory, geometric group theory…)
Some buzz words suggesting topics which we plan to cover include:
-The notion of a manifold (in different setups), examples of constructions of manifolds (submanifolds, quotients, surgery)
-The tangent space, vector fields, flows/1-parameter groups of diffeomorphisms
-Tangent bundle and vector bundles
-Tensor and exterior algebras, differential forms
-Integration on manifolds, Stokes’ theorem
-de Rham cohomology, examples of their computation (spheres, tori, real projective spaces...)
-Degree theory, applications: argument principle, linking numbers, indices of singularities of vector fields
We will also discuss a lot of concrete and interesting examples of manifolds in the lectures and work sheets, such as for example: tori, n-holed tori, spheres, the Moebius strip, the (real and complex) projective plane, higher-dimensional projective spaces, blow-ups, Hopf manifolds…
The nature of the material makes it inevitable that considerable time must be devoted to establishing the foundations of the theory and defining as well as clarifying key concepts and geometric notions. However, to make the content more vivid and interesting, we will also seek to include some attractive and non-obvious theorems, which at the same time are not too hard to prove and natural applications of the techniques introduced, such as, for instance, Ehresmann's theorem on differentiable fibrations, or that a sphere cannot be diffeomorphic to a product of (positive-dimensional) manifolds.
This Module is mathematically closely related to, but formally completely independent of MA3D9 Geometry of Curves and Surfaces.
Books:
Frank W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer (1983) (esp. Chapters 1, 2, 4)
M. Berger, B. Gostiaux, Differential Geometry: Manifolds, Curves, and Surfaces, Springer (1988) (esp. Chapters 2-6)
Spivak, A Comprehensive Introduction to Differential Geometry, vol. 1, Publish or Perish, Inc. (2005) (esp. Chapters 1-8)
John Lee, Introduction to smooth manifolds, Springer (2012)
Loring W. Tu, An Introduction to Manifolds, Springer (2011)
(some other more specialised, but potentially interesting books can be found among the references at the end of the lecture notes)Lecturer: Dr. David Wood
Term(s): Term 2
Status for Mathematics students: List A
Commitment: 30 Lectures
Assessment: 100% exam
Prerequisites: MA133 Differential Equations, MA249 Algebra II, MA259 Multivariable Calculus. MA254 Theory of ODEs would be useful, but is not essential.
Leads to:
Content: This module investigates how solutions to systems of ODEs (in particular) change as parameters are smoothly varied resulting in smooth changes to steady states (bifurcations), sudden changes (catastrophes) and how inherent symmetry in the system can also be exploited. The module will be application driven with suitable reference to the historical significance of the material in relation to the Mathematics Institute (chiefly through the work of Christopher Zeeman and later Ian Stewart). It will be most suitable for third year BSc. students with an interest in modelling and applications of mathematics to the real world relying only on core modules from previous years as prerequisites and concentrating more on the application of theories rather than rigorous proof.
Indicative content (precise details and order still being finalised):
1. Typical one-parameter bifurcations: transcritical, saddle-node, pitchfork bifurcations, Bogdanov-Takens, Hopf bifurcations leading to periodic solutions. Structural stability.
2. Motivating examples from catastrophe and equivariant bifurcation theories, for example Zeeman Catastrophe Machine, ship dynamics, deformations of an elastic cube, D_4-invariant functional.
3. Germs, equivalence of germs, unfoldings. The cusp catastrophe, examples including Spruce-Budworm, speciation, stock market, caustics. Thom’s 7 Elementary Catastrophes (largely through exposition rather than proof). Some discussion on the historical controversies.
4. Steady-State Bifurcations in symmetric systems, equivariance, Equivariant Branching Lemma, linear stability and applications including coupled cell networks and speciation.
5. Time Periocicity and Spatio-Temporal Symmetry: Animal gaits, characterization of possible spatio-temporal symmetries, rings of cells, coupled cell networks, H/K Theorem, Equivariant Hopf Theorem.
Further topics from (if time and interest):
Euclidean Equivariant systems (example of liquid crystals), bifurcation from group orbits (Taylor Couette), heteroclinic cycles, symmetric chaos, Reaction-Diffusion equations, networks of cells (groupoid formalism).
Aims: Understand how steady states can be dramatically affected by smoothly changing one or more parameters, how these ideas can be applied to real world applications and appreciate this work in the historical context of the department.
Objectives:
Books:
There is no one text book for this module, but the following may be useful references:
• Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Guckenheimer/Holmes 1983
• Catastrophe Theory and its Applications, Poston and Stewart, 1978
• The Symmetry Perspective, Golubitsky and Stewart, 2002
• Singularities and Groups in Bifurcation Theory Vol 2, Golubitsky/Stewart/Schaeffer 1988
• Pattern Formation, an introduction to methods, Hoyle 2006.
Lecturer: Christian Böhning
Term(s): Term 2
Status for Mathematics students: List C
Commitment: 30 lectures plus assignments
Assessment: Assignments (15%), 3 hour written exam (85%).
Prerequisites:
A background in algebra (especially MA249 Algebra II) is essential. The module develops more specialised material in commutative algebra and in geometry from first principles, but MA3G6 Commutative Algebra will be useful. More than technical prerequisites, the main requirement is the sophistication to work simultaneously with ideas from several areas of mathematics, and to think algebraically and geometrically. Some familiarity with projective geometry (e.g. from MA243 Geometry) is helpful, though not essential.
Leads To:
A first module in algebraic geometry is a basic requirement for study in geometry, number theory or many branches of algebra or mathematical physics at the MSc or PhD level. Many MA469 projects are on offer involving ideas from algebraic geometry.
Content:
Algebraic geometry studies solution sets of polynomial equations by geometric methods. This type of equations is ubiquitous in mathematics and much more versatile and flexible than one might as first expect (for example, every compact smooth manifold is diffeomorphic to the zero set of a certain number of real polynomials in R^N). On the other hand, polynomials show remarkable rigidity properties in other situations and can be defined over any ring, and this leads to important arithmetic ramifications of algebraic geometry.
Methodically, two contrasting cross-fertilizing aspects have pervaded the subject: one providing formidable abstract machinery and striving for maximum generality, the other experimental and computational, focusing on illuminating examples and forming the concrete geometric backbone of the first aspect, often uncovering fascinating phenomena overlooked from the bird's eye view of the abstract approach.
In the lectures, we will introduce the category of (quasi-projective) varieties, morphisms and rational maps between them, and then proceed to a study of some of the most basic geometric attributes of varieties: dimension, tangent spaces, regular and singular points, degree. Moreover, we will present many concrete examples, e.g., rational normal curves, Grassmannians, flag and Schubert varieties, surfaces in projective three-space and their lines, Veronese and Segre varieties etc.
Books:
- Atiyah M.& Macdonald I. G., Introduction to commutative algebra, Addison-Wesley, Reading MA (1969)
- Harris, J., Algebraic Geometry, A First Course, Graduate Texts in Mathematics 133, Springer-Verlag (1992)
- Mumford, D., Algebraic Geometry I: Complex Projective Varieties, Classics in Mathematics, reprint of the 1st ed. (1976); Springer-Verlag (1995)
- Reid, M., Undergraduate Algebraic Geometry, London Math. Soc. Student Texts 12, Cambridge University Press (2010)
- Shafarevich, I.R., Basic Algebraic Geometry 1, second edition, Springer-Verlag (1994)
- Zariski, O. & Samuel, P., Commutative algebra, Vol. II, Van Nos- trand, New York (1960)
• Relational family: hypergraphs, simplicial complexes and hierachical hypergraphs.Overview
In this lecture will learn how to start the modelling process by thinking about the model's static structure, which then in a dynamic model gives rise to the choice of variables. Finally, with the dive into mathematical learning theories, the students will understand that a mathematical model is never finished, but needs recursive learning steps to improve its parametrisation and even structure.
A very important aspect of the lecture is the smooth transition from static to dynamic stochastic models with the help of rule-based system descriptions which have evolved from the modelling of chemical reactions.Weekly Overview
Week 1: Mathematical Modelling, Past, Present and Future
• What is Mathematical Modelling?
• Why Complex Systems?..
• Philosophy of Science, Empirical Data and Prediction.
• About this course.
Part I Structural Modelling
Week 2: Relational Structures
• Graph characteristics, examples from real world complex systems (social science, infrastructure, economy, biology, internet).
• Introduction to algebraic and computational graph theory.
Week 3: Transformations of Relational Models
• Connections between graphs, hypergraphs, simplicial complexes and hierachical hypergraphs.
• Applications of hierachical hypergraphs.
• Stochastic processes of changing relational model topologies.
Part II Dynamic Modelling
Week 4: Stochastic Processes
• Basic concepts, Poisson Process.
• Opinion formation: relations and correlations.
• Master eqation type-rule based stochastic collision processes.
Week 5: Applications of type-rule based stochastic collision processes
• Chemical reactions and Biochemistry.
• Covid-19 Epidemiology.
• Economics and Sociology, Agent-based modelling.
Week 6: Dynamical Systems (single compartment)
• Basic concepts, examples.
• Relation between type-rule-based stochastic collision processes in single compartments and ODE
• Applications, connections between dynamical systems and structural modelling (from Part I), the interaction graph, feedback loops.
• Time scales: evolutionary outlook.
Week 7: Spatial processes and Partial Differential Equations:
• Type-rule-based multi-compartment models.
• Reaction-Diffusion Equations.
• Applications.
Part III Data Analysis and Machine Learning
Week 8: Statistics and Mathematical Modelling
• Statistical Models and Data.
• Classification.
• Parametrisation.
Week 9: Machine Learning and Mathematical Modelling:
• Mathematical Learning Theory.
• Bayesian Networks.
• Bayesian Model Selection.
Week 10: Neural Networks and Deep Learning:
• Basic concepts.
• Neural Networks and Machine Learning.
• Discussion and outlook.
https://www.mathematical-modelling.science/index.php/lectures/warwick-2020-2021
This module, MA4J7 (cohomology and Poincaré duality), has the prerequisites MA3F1 (introduction to topology) and MA3H6 (algebraic topology).
Cohomology is a dual theory to homology; it continues our development of algebraic tools for the study of topological spaces. Cohomology is a richer, more algebraic, theory than homology is because it has a naturally defined ring structure coming from the cup product. It is also a key tool in the modern proof of Poincaré duality for manifolds.
The material covered in this module is essentially required for advanced study in the fields of topology, differential geometry, algebraic geometry, algebraic number theory, and others.
The module MA4K0 Introduction to Uncertainty Quantification sits at the meeting point of mathematics, statistics, and many applications. We draw on techniques from functional analysis, numerical analysis, probability theory, Bayesian statistics, and computational mathematics to answer questions such as
- How do we represent random or uncertain quantities?
- How can we propagate uncertainty forwards through systems of interest in the real world to make predictions?
- How can we propagate uncertainty backwards through systems of interest in the real world to learn about them, e.g. initial conditions or governing parameters?
Overview
There is much active mathematical research into aeroacoustics (the study of sound in aircraft engines). This field is closely followed, and often contributed to (sometimes helpfully) by engineers in both academia and industry (e.g. Airbus, Boeing, NASA, etc). The aim of this course is to give an overview of the mathematical techniques needed to understand the current research problems, and read current papers in the area. This could lead on to several possible PhD projects, including in asymptotics, numerical analysis, and stability theory.
Aims
The application of wave theory to problems involving the generation, propagation and scattering of acoustic and other waves is of considerable relevance in many practical situations. These include, for example, underwater sound propagation, aircraft noise, remote sensing, the effect of noise in built-up areas, and a variety of medical diagnostic applications. This course would aim to provide the basic theory of wave generation, propagation and scattering, and an overview of the mathematical methods and approximations used to tackle these problems, with emphasis on applications to aeroacoustics. The ultimate aim is for students to understand the underlying mathematical tools of acoustics sufficiently to read current research publications on acoustics, and to be able to apply these techniques to current research questions within mathematics, engineering and industry.
Learning Outcomes
- Reproduce standard models and arguments for sound generation and propagation.
- Apply mathematical techniques to model sound generation and propagation in simple systems.
- Understand and apply Wiener-Hopf factorisation in the scalar case.
Approximate Syllabus
- Some general acoustic theory.
- Sound generation by turbulence and moving bodies (including the Lighthill and Ffowcs Williams Hawkings acoustic analogies).
- Scattering (including the scalar Wiener-Hopf technique applied to the Sommerfeld problem of scattering by a sharp edge)
- Long-distance sound propagation including nonlinear and viscous effects.
- Wave-guides.
- High frequencies and Ray Tracing.
Reading List
- D.G. Crighton, A.P. Dowling, J.E. Ffowcs Williams, et al, "Modern Methods in Analyticial Acoustics", Springer 1992.
- M. Howe, "Acoustics & Aerodynamic Sound", Cambridge 2015 (available online through Warwick Library).
- S.W. Rienstra & A. Hirschberg, "An Introduction to Acoustics", (available online).
Topological Data Analysis (TDA) is an approach to data analysis based on techniques from algebraic topology. Topology is the study of properties of sets that are invariant under continuous deformations; it is concerned with concepts such as ``nearness'', ``neighbourhood'', and ``convergence''. Nowadays, topological ideas are an indispensable part of many fields of mathematics, ranging from number theory to partial differential equations. Algebraic topology, in particular, aims to understand topological properties of spaces through algebraic invariants. The premise of topological data analysis is that data there is an underlying topological structure to data. Familiar examples include clustering, where the aim is to subdivide data into different clusters, or ``connected components'', and connectivity in networks. In this module we introduce persistent homology, a powerful method for studying the topology of data. We discuss the theoretical foundations, as well as computational and algorithmic aspects and various applications. While the course is mainly theoretical in nature, you are encouraged to experiment using a range of available software and applications. The lecture material will be available as video recording and slides, and exercises will be published semi-regularly.
Intended Learning Outcomes
Upon completion of this module you should be able to:
- understand how topological information can be extracted from discrete data;
- use persistent homology to compute persistence diagrams and barcodes;
- explain the different parts of the persistent homology pipeline and the computational challenges involved;
- evaluate the stability and robustness of persistent homology computations;
- summarize different approaches to the topology of data and discuss applications
Literature
- Steve Oudot. Persistence Theory: From Quiver Representations to Data Analysis. AMS 2015
- Herbert Edelsbrunner and John Harer. Computational Topology, An Introduction. AMS 2010
- Nina Otter, Mason A Porter, Ulrike Tillmann, Peter Grindrod & Heather A Harrington. A roadmap for the computation of persistent homology. 2017
More specialised sources and papers will be made available in time.
Material to be covered:
Reminder of measure theory
modes of convergence
law of large numbers
central limit theorem (via characteristic functions, Lindeberg principle, Stein's method)
stable laws
large deviations
martingales
References:
S.R.S. Varadhan, Probability Theory (Courant lecture notes), online notes
L. Breiman, Probability theory
F. den Hollander, Large Deviations
N. Zygouras, Discrete stochastic analysis
Notes on Large Deviations
The purpose of this module is to provide rigorous training in probability theory for students who plan to specialise in this area or expect probability to feature as an essential tool in their subsequent research. It will also be accessible to students who never got into probability theory beyond core-module level taught in the first year and who are eager to get acquainted with basic probability theory, in particular, the aim is to appeal to but not limited to students working in analysis, dynamical systems, combinatorics & discrete mathematics, and statistical mechanics. To include these two different groups of students and to accommodate their needs and various background the module will cover in the first two weeks a steep learning curve into basic probability theory (see part I below). Secondly, the written assessment, 50 % essay with 16 pages, can be chosen either from a list of basic probability theory (standard textbooks in probability and graduate lecture notes on probability theory) or from a list of high-level hot research topics including original research papers and reviews and lecture notes (see below). List of possible essay topics see attached pdf - file.
- Measures, Carathéodory's construction, integration and convergence theorems.
- Riesz representation theorem, weak* convergence and Prokhorov's theorem.
- Hardy-Littlewood maximal inequality and Rademacher’s theorem.
The second part provides an introduction to geometric measure theory. Time permitting, we will cover some of the following topics:
- Hausdorff distance.
- Hausdorff measure, rectifiable and purely unrectifiable sets.
- Sard's theorem.
- The Besicovitch projection theorem.
Overview
There is much active mathematical research into aeroacoustics (the study of sound in aircraft engines). This field is closely followed, and often contributed to (sometimes helpfully) by engineers in both academia and industry (e.g. Airbus, Boeing, NASA, etc). The aim of this course is to give an overview of the mathematical techniques needed to understand the current research problems, and read current papers in the area. This could lead on to several possible PhD projects, including in asymptotics, numerical analysis, and stability theory.
Aims
The application of wave theory to problems involving the generation, propagation and scattering of acoustic and other waves is of considerable relevance in many practical situations. These include, for example, underwater sound propagation, aircraft noise, remote sensing, the effect of noise in built-up areas, and a variety of medical diagnostic applications. This course would aim to provide the basic theory of wave generation, propagation and scattering, and an overview of the mathematical methods and approximations used to tackle these problems, with emphasis on applications to aeroacoustics. The ultimate aim is for students to understand the underlying mathematical tools of acoustics sufficiently to read current research publications on acoustics, and to be able to apply these techniques to current research questions within mathematics, engineering and industry.
Learning Outcomes
- Reproduce standard models and arguments for sound generation and propagation.
- Apply mathematical techniques to model sound generation and propagation in simple systems.
- Understand and apply Wiener-Hopf factorisation in the scalar case.
Approximate Syllabus
- Some general acoustic theory.
- Sound generation by turbulence and moving bodies (including the Lighthill and Ffowcs Williams Hawkings acoustic analogies).
- Scattering (including the scalar Wiener-Hopf technique applied to the Sommerfeld problem of scattering by a sharp edge)
- Long-distance sound propagation including nonlinear and viscous effects.
- Wave-guides.
- High frequencies and Ray Tracing.
Reading List
- D.G. Crighton, A.P. Dowling, J.E. Ffowcs Williams, et al, "Modern Methods in Analyticial Acoustics", Springer 1992.
- M. Howe, "Acoustics & Aerodynamic Sound", Cambridge 2015 (available online through Warwick Library).
- S.W. Rienstra & A. Hirschberg, "An Introduction to Acoustics", (available online).
Throughout this module, we hope to show you that many of the challenges health care systems face are fundamentally economic. With this in mind, this module aims to offer an informative introduction to economic concepts and tools, with a view to understanding how these concepts can be used to answer various questions in health care.
Over the 5 days of the module, we will be looking at various issues, topics and questions that modern health care systems (such as our NHS) are called to answer, including the extent of government intervention in health care provision, contemporary ways of financing health care, methods for estimating the inputs and outputs of health care programmes, and, importantly, optimal ways of allocating our limited resources to existing and new interventions and technologies.We look forward to welcoming you to our module in early March.
Many of the challenges health care systems face are fundamentally economic. Introduction to Health Economics (MD990) aims to provide a
solid foundation of economic concepts and tools with a view to understanding how these can be used to answer various questions. Such questions may relate to appropriate ways of financing health care systems, methods for measuring public preference of health care outcomes, or, importantly, optimal ways of allocating our limited resources to existing and new interventions and technologies.
Introduction to Health Economics (for non-economists)
Dear All,
Welcome to Qualitative Research Methods in Health.
This module aims to provide you with a) a critical perspective on the contribution of qualitative research methods to understanding and improving health and b) an introduction to qualitative research methods and their application in health related research.
Aims
Develop knowledge and understanding of qualitative methods as used in health related research and develop your skills in the use of these methods. Gain the capability to use these research methods appropriately for undertaking research and evaluation both as part of postgraduate study and in your working environment.
Learning Outcomes
By the end of the module you should be able to:
Demonstrate a critical understanding of the origins and usage of qualitative research methods in relation to health.
Demonstrate how to develop a research question and use appropriate qualitative and methods to answer it.
Demonstrate an understanding of the range of research methods and when and how they should be used.
Demonstrate a critical understanding of the use of qualitative methods in relation to other widely used research methods in health care.
Here and in the module guide, you will find the pre-course preparation task. We strongly encourage you to undertake the preparatory work, especially if you are new to qualitative research methods.
We look forward to meeting you.
Frances Griffiths and Bronwyn Harris
Module Co-leads
The first 5-6 weeks of this module introduce students to Kant’s Critique of Judgement, the foundational text of modern aesthetics for both the analytic and the continental traditions. It aims to give students a good overview of this difficult text, and to help them engage critically with both key ideas in the text, and some of the debates in recent scholarship and aesthetic theory to which it has given rise. It will cover aspects of the Introduction, particularly the idea of reflective judgement, the Analytic of the Beautiful, the Deduction of Aesthetic Judgements, the Analytic of the Sublime, as well as Kant’s generally overlooked remarks on fine art and genius. Key questions to be considered include: are judgements of taste subjective or objective, and in what sense?; what is the relation between the sublime and morality for Kant; how are work of art possible? We will also consider the extent to which Kant’s analysis of aesthetic judgement can be applied to works of art, and ways in which this might be problematic. The remaining 3-4 weeks of the course focus on Martin Heidegger’s antipathy to aesthetics as a philosophical understanding of art. Our focus will be the ‘Origin of the Work of Art’ informed by Heidegger’s critique of modern subjectivism in ‘The Age of the World Picture’ and contrast between art and technology as ‘modes of disclosure’ in ‘The Question Concerning Technology.’ Questions to be considered include: why is Heidegger hostile to the very idea of aesthetics as a philosophical understanding of art? What is the ontological function of works of art according to Heidegger, and is this credible? What is the relation of art to truth on the one hand and technology on the other?
This course is a first introduction to philosophy of mathematics, via one of our most fascinating and perplexing concepts: the infinite. We encounter the concept of infinity in myriad ways. In Zeno’s paradoxes of time, space, and motion, the idea of infinite division is used to argue in favour of a radical monism. The ancient atomists Leucippus and Democritus claimed that the universe consisted of an infinity of atoms moving in an infinite void, and contemporary cosmology still considers the issue of whether the universe is infinite to be an open question.
But what does it mean for something to be infinite? It is mathematics that offers us the precise definitions that let us begin to answer this question, and thus in mathematics that many of the most important questions concerning the infinite arise. Do the infinite structures that we talk about in mathematics really exist? If so, how can we have knowledge of them? Is it even coherent to talk about the truly infinite, or does it fall victim to paradox? This course will investigate these and other questions by engaging with the ideas of philosophers and mathematicians from across history, with a focus on the reception of Georg Cantor’s theory of sets, and the crisis in the foundations of mathematics that it precipitated.
Welcome to the Gender and Development Moodle page!
The module is taught through one lecture and one seminar each week. The lectures provide an introduction and overview of the topic under discussion and the seminars explore the main issues in more detail.
Please be aware that there is NO seminars in both week 1 and week 2, but you will need to complete a group exercise before week 3 (detailed instructions regarding the exercise, please see announcement).
**Seminar classes begin in Week 3** of the autumn term and finish in Week 20, which is the last week of the spring term in the following year. The exceptions are Weeks 6 and 16, which are PAIS Reading Weeks.
The main teaching part of the course is scheduled to finish in Week 20 to allow you to complete essays over the Easter break. When we reconvene in the summer term, we will be holding revision classes.
in office room E1.15
LECTURE 1. INTRODUCTION TO EU POLICY MAKING
Why study EU policy-making? How has the EU developed, and how has its development been theorized? What are the main characterisations of the EU as a system? What are the different perspectives on the EU’s legitimacy and the existence or not of a ‘democratic deficit’?
Reading
Basic text on the EU
Kenealy, D. et al (2022) The European Union: how does it work? Oxford, chs 1-3, 5
Theoretical reflections on the EU
Marks, G., Hooghe, L., & Blank, K. (1996). European integration from the 1980s: State‐centric v. multi‐level governance. JCMS: Journal of Common Market Studies, 34(3), 341-378
Laffan, B., O’Donnell, R. and Smith, M. (1999) Experimental Union: Rethinking Integration, Routledge, chapter 1
Fabbrini, S. & Puetter, U. (2016). Integration without supranationalisation: studying the lead roles of the European Council and the Council in post-Lisbon EU politics, Journal of European Integration, 38(5), 481–495, https://doi.org/10.1080/07036337.2016.1178254
The EU and the world
Bradford, A. (2012)The Brussels Effect, https://scholarship.law.columbia.edu/faculty_scholarship/271/
The EU, democracy and legitimacy
Kenealy, D. et al (2022) The European Union: how does it work? Oxford, ch 6
Kassim, H. (2007) ‘The Institutions of the European Union’ in C. Hay & A. Menon (eds), European Politics,Oxford University Press, pp. 168-99 [old, but has useful overview of diagnoses of the ‘democratic deficit’]
Scharpf, F.W. (1999) Governing in Europe: Effective and Democratic? Oxford UP [for reference to ‘output legitimacy’].
SEMINAR: INTRODUCTION
Please come to class having watched this short video, , and having read the two items below.
Questions:
1. What remaining hurdles does Ursula von der Leyen face before her College is elected?
2. Can we expect more of the same from a second von der Leyen Presidency?
Essential reading:
Fabian Bohnenberger’s EU post-election timeline, https://fabianbohnenberger.com/2024/07/31/eu-post-election-timeline-update/
Ursula von der Leyen (2024) Political Guidelines 2024-29, https://commission.europa.eu/document/e6cd4328-673c-4e7a-8683-f63ffb2cf648_en
Introduction: what is this module about?
Democracy is a crucial ideal – ‘rule by the people’ - and set of political practices, such as voting in free and fair elections and public debate and deliberation. It is also a deeply contested ideal and a practice. In several countries it is not unusual to find proponents of very different policy or ideological positions each using the rhetoric of democracy in favour of their position and against their opponents.
The ambiguities at the heart of democracy – what is it exactly, how should it be practiced? – are viewed by some as a weakness: maybe, in the end, it is an idea empty of real meaning? However, this very ambiguity may reflect something positive and offer opportunities. Perhaps democracy is flexible: it can be thought of and done differently in different places and contexts. Could democracy be a matter of design for different purposes and contexts; creative and experimental uses of a range of institutions enacting distinct sets of ideals?
The module explores democratic design. Looking at a range of democratic principles (equality, freedom, etc.) and institutions (from the familiar such as parliaments to the new and innovative, such as the Brazil-inspired participatory budgeting process), it interrogates the notions of democracy and design. It considers new approaches to democratic change in the face of varied challenges to democratic organisation and effectiveness.
Democratic Design is an experimental module in which ideas will be debated and tested without preordained conclusions.
Welcome to the Moodle page for PO383, 'The Politics of Religion'.
The module is taught through one lecture and one seminar each week. Lectures are all online and pre-recorded. The lecture links are available below, and will go live every Friday at midnight. The lectures will provide an introduction and overview of the weekly topics, and the seminars shall explore the core issues in more detail.
PX920: Homogenisation of Non-linear Heterogeneous Solids
Short description
The module aims to provide students with understanding and practical aspects of homogenisation methods for predicting overall macroscopic response of heterogeneous solids through lectures and workshop activities.
Learning objectives:
- Understand the concept of the effective behaviour of heterogeneous materials
- Understand the concept of homogenisation
- Implement homogenisation process into finite-element solution
- Apply homogenisation to analyse simple heterogeneous solids
Syllabus:
- Effective behaviour of heterogeneous solids (week 1): introduction; implementation of bounds into a finite-element procedure
- Mathematical asymptotic homogenisation (weeks 2-3): theory
- Asymptotic homogenisation (week 4): computer implementation
- Mini-Project (week 5)
Illustrative Bibliography:
J. Fish: Practical multiscaling, Wiley (available from the Library).
S. Torquato: Random heterogeneous materials, Springer (available from the Library).
In this module, we will explore how new technologies, including Artificial Intelligence (AI)-based technologies, are shaping the governance of mobility. AI-based technologies are increasingly integrated into various aspects of our lives, including public decision-making systems. Some countries have even started incorporating them into their immigration systems, using them to predict future migration and displacement, process visa applications, and conduct various forms of profiling and risk assessments for decision-making purposes. With large-scale interoperable information systems, it has become possible to deduce individual characteristics, screen them through different systems to obtain more information about an individual, and ultimately make decisions based on comparisons with others.
This module aims to provide students with an introduction to the latest developments in this field and explore the conditions in which these technologies have been integrated into immigration and asylum decision-making systems, as well as humanitarian actions. Through a variety of case studies, mainly from Europe and North America, we will examine how these new technologies are reshaping the definition of territorial state borders and methods of identifying and governing individuals. Additionally, we will explore how humanitarian actors have employed new technologies in countries in Africa and the Middle East and how migrants themselves navigate, adapt, and resist their use.
By the end of this module, you should be able to:
• Have the knowledge and understanding of how and to what extent the operation of territorial borders is changing in the digital age.
• Have the knowledge and ability to critically analyse the ethical, political and social implications of the implementation of new technologies in border management, immigration, and asylum application processing, as well as humanitarian actions.
• Have the knowledge and ability to analyse the ways in which migrants navigate, adopt or challenge the use of a variety of new technologies.
• Be able to describe and critically participate in political and intellectual discussions on the use of new technologies in areas related to migration, asylum and humanitarian actions.
• Develop skills in accessing and evaluating relevant literature for seminar discussion, presentations, conducting independent study, research, and essay writing.
Provisional Outline of Course
Week 1: Introduction: Indigenous feminisms, post/colonial feminisms and the intersections of political struggles
Week 2: Feminism, post/coloniality and the question of sovereignty (Assam)
Week 3: Feminism, terror and security (Afghanistan, Iraq, Syria, Sudan)
Week 4: Feminism, socialism and authoritarianism (China)
Week 5: Feminist engagements with the politics of religion, secularism and border controlWeek 6: Reading Week
Week 7: Feminist movements in a settler colonial context: political prisoners and decolonial methods (Palestine)
Week 8: Feminism, reproduction and land rights in settler colonial states (Australia, US, Canada)
Week 9: Feminism and Revolution (Algeria)
Week 10: Summary workshop/ Time for assessment discussion
Illustrative Bibliography
R. Icaza (2017) 'Decolonial Feminism and Global Politics: Border Thinking and Vulnerability as a Knowing Otherwise' in M. Woons & S. Weier (eds.) Critical Epistemologies of Global Politics, E-International Relations Publishing.
Kaul, N. & Zia, A.(2018) ‘Knowing in our Own Ways: Women and Kashmir’, Special Issue EPW/RWS
Osuri, G.(2018) ‘Sovereignty, vulnerability, and a gendered resistance in Indian-occupied Kashmir’, Third World Thematics: A TWQ Journal, 3(2) 228-43.
Das, N. K. (2019) 'Indigenous Feminism and Women Resistance: Customary Law, Codification Issue and Legal Pluralism in North East India', Journal of Cultural and Social Anthropology, 1(2), pp. 19-27.Menon, Nivedita. 2012. "Victims or Agents?" in Seeing like a Feminist. pp. 173-212.
Radha Kumar (1999) 'From Chipko to Sati: The Contemporary Indian Women's Movement'. in N. Menon (ed.), Gender and Politics in India. OUP, pp.342-369.
Fong, M. (2016) One Child: The story of China’s most radical experiment, Houghton, Mifflin, Harcourt.
Lydia H. Liu, Rebecca E. Karl and Dorothy Ko (eds.) (2013) The Birth of Chinese Feminism: Essential Texts in Transnational Theory, Columbia University Press.
Hershatter, G. (2018) Women and China’s Revolutions, Rowman & Littlefield.
Maha El Said, Lena Meari and Nicola Pratt (eds.) (2015) Rethinking Gender in Revolutions and Resistance: Lessons from the Arab World, London: Zed.
Nadje Al-Ali & Nicola Pratt (2009) What Kind of Liberation? Women and the Occupation of Iraq, Berkeley: University of California Press.
Seedat, F.(ed.) (2017) ‘Special Issue: Women, Religion and Security’, Agenda, 30(3).
M.E.M.Kolawole (1997) Womanism and African Consciousness, Africa World Press Inc.
B. Badri & A. M. Tripp (eds.) (2017) Women’s Activism in Africa, London: Zed.
B. Fredericks (1997) ‘Reempowering Ourselves: Australian Aboriginal Women’, Signs. Journal of Women in Culture and Society, 35(3).
Green, J. (ed.) (2017) Making Space for Indigenous Feminism(2ndedition), Fernwood Publishing.
R. Aída Hernández Castillo (2010) ‘The Emergence of Indigenous Feminism in Latin America’, Signs, 35(3).
This module is intended as a 12CATS introduction to mathematical
statistics to enable non-Statistics second-year students to study
sufficient material to make it possible to deal and benefit from the
final years modules in statistics offered by the Statistics Department.
Now that we are half-way through the module, I'd like to see how things are going so far with respect to the first three chapters, i.e. statistical models, transformations and approximation theorems. Based on the results of the feedback, I will provide you with additional videos/materials/resources on the topics that are causing more troubles, ensuring that you are on top of everything.
You can self-enrol to get access to the Moodle resources if you are struggling to complete module registration.
Your self-enrolment will expire 7 days after enrolment to flag that your module registration is not complete and you will not be entered for assessments.
If you are still struggling to complete module registration you can self-enrol again.
This module explores the cultural history of madness through a variety of artistic forms. The module seeks to explore the relationship between psychiatric and artistic accounts of 'mad' experience. Through a close examination of texts, films, plays, and art, students will examine philosophical and political questions about the mind, the self, and experience. This module, therefore, aims to introduce students to the area of madness and representation. The module will primarily explore twentieth and twenty first century examples of theatre, film, and literature that seek to represent mental ill health. Students will explore a range of theoretical, philosophical, historical, sociological and medical texts that attempt to understand alternative experiences. Students will place these theoretical works in dynamic dialogue with performance practice that is concerned to explore madness through aesthetic practice. We will ask not only what is 'madness', but how and why one might choose to represent it. This module aims to offer students a rigorous introduction to the relationship between representation, pathology, and ethics.
This module explores the relationship between identity and performance through a variety of artistic forms. The module will examine a range of practices from biographical drama to live art to stand up comedy in order to interrogate questions of selfhood, otherness, and identity. The module synthesises critical discourse with practical experimentation in order to better understand how and why we represent ourselves and others. Moreover, we will question what it means to have a 'self' to represent. We will examine questions of truth, authenticty, alterity, ethics, and antitheatricality. The module will begin by exploring key examples from different modes of performance (both practically and theoretically) and then, in the Spring Term, move towards developing devising skills and creating small group and solo practice-based projects. Throughout the course of the module we will not only investigate how and why people have sough to represent 'true' lives but consider the role of performance within the our everyday identities. The module, thus, aims to offer an engaging and challenging introduction to the politics of identity and performance.
Introduction
Logistics is concerned with the design and administration of processes to plan movement and geographical positioning of raw materials, work-in-progress and finished inventories at the lowest cost.
In this module you will analyse how logistics adds value to the overall supply chain, and where inventory can be strategically positioned to achieve sales.
You will examine how factors such as order management, inventory, transportation, warehousing and capacity need to be effectively and efficiently managed in order to support procurement, manufacturing and the customer supply chain requirements.