Differential equations occupy a central role in mathematics because they allow us to describe a wide variety of real-world systems. Their study and applications range from pure and applied mathematics to physics, engineering , biology and finance, among others. The module begins with ordinary differential equations (ODEs) discussing how to solved first and second order homogeneous and inhomogeneous ODEs. We study boundary value problems and develop Sturm-Liouville theory. We then look at how one can express a general periodic function in terms of Fourier series of sine and cosine functions. Next, we introduce some of the basic concepts of partial differential equations (PDEs). The three important classes of second order PDE appropriate for modelling different sorts of phenomena are introduced and the appropriate boundary conditions for each of these are considered. The technique of separation of variables is used to reduce the problem to that of solving the sort of ordinary differential equations seen at the start of the module and writing the general solution using Fourier series and Sturm-Liouville theory. Throughout the module there will be a strong emphasis on problem solving and examples. The last part of the module is an introduction to integral transforms with emphasis on Laplace transforms. We show how Laplace transforms may be used to solve ordinary and partial differential equations.
Partial Differential Equations (PDEs) are the mathematical language of change in space and time. They are used to describe a wide variety of real-world systems. Examples of their applications include describing how waves travel, how heat spreads, weather forecasting, how the fundamental laws of Nature work, the pricing of financial derivatives such as stock options, and many others. The module begins with a review of ordinary differential equations (ODEs), discussing first- and second-order methods, boundary value problems, and eigenvalue problems. We then introduce Sturm-Liouville theory and Fourier Series, seeing that it is possible to express a general periodic function as a sum of sine and cosine functions. Next, we introduce some of the basic concepts of PDEs. The three important classes of second order PDE appropriate for modelling different sorts of phenomena are introduced, and the appropriate boundary conditions for each of these are considered. The technique of separation of variables is used to reduce a PDE to a set of ODEs of the kind reviewed at the start of the module, and to derive the general solution using Fourier Series and Sturm-Liouville theory. Throughout the module there will be a strong emphasis on problem solving and examples. The last part of the module is an introduction to integral transforms, comprising Laplace Transforms and Fourier Transforms. We show how Laplace transforms are a very powerful technique to solve ODEs and PDEs, and how Fourier Transforms are very useful to solve PDEs.
Relativistic wave equations with their predictions of anti-particles and fermion spin will be explored. The fundamental role of gauge symmetries in current theories of force will lead to the study of the standard model of particle physics, including the spontaneous electroweak symmetry breaking via the Higgs mechanism. Finally theories of particle physics beyond the standard model will be briefly investigated concentrating on their motivations and testable consequences.
This unit entirely consists of a research-level project Upon successful completion of the project the student will have completed the final year of their Physics with Particle Physics Year Abroad MPhys degree. The supervisor(s) at RAL and CERN will have directed completion of a significant research ideally of publishable quality.
Equal opportunity In line with the University’s Equal Opportunities Policy, individuals are treated on their relevant merits and abilities and are given equal opportunities within the module, School and University. The aim of the policy is to ensure that no prospective student or current student should receive any less favourable treatment on any grounds which are not relevant to academic ability and attainment. Every effort is made to ensure that disabled students are aware of and assisted in making use of the support provided by the University; to ensure access to lectures, classes, learning materials; and to ensure that where necessary appropriate variations to normal examining arrangements are made.
This course introduces key theories and models in the study of political behaviour and political psychology and seeks to encourage students to develop a critical appreciation of how people develop their political beliefs and preferences, and how this affects their engagement in politics. The course is also designed to provide a practical and applied introduction to the study of political behaviour, applying theories to everyday political life and making use of the wealth of empirical data available on public opinion and political psychology. It deals with questions such as how people form their political beliefs and their attachments to political parties, how they evaluate political candidates and leaders, and why people do or don’t get involved in different forms of politics, be it voting, protest or civic action.
Students will recognise and demonstrate an understanding of collaborative and community conservation issues within the context of the WHO's One Health philosophy. Based on case studies of ongoing conservation work at Marwell Wildlife, this module highlights the interconnectedness of people, animals and ecosystem health, placing emphasis on the crucial nature of a partnership based approach for real world conservation. The module includes a 10 day field trip to one of Marwell Wildlife's conservation and research sites in Kenya, with vital emphasis placed upon collaborative conservation in a real-world field setting, including Marwell’s Kenya-based partners and community-led initiatives. A combination of theoretical and practical field sessions will allow students to develop expertise in a variety of techniques and technical skills required for ecological surveying and monitoring of wildlife. Through facilitated discussion, drawing on colleagues' and classmates' knowledge and ideas and through facilitated discussions with community leaders and partners, students will plan and undertake a mini-survey and compare, contrast and critically evaluate success and limitations of data gained on the field course. Emphasis is placed upon how these approaches are crucial for informing conservation decision-making, and stakeholder engagement relating to wildlife.
The 1960s are remembered in Britain as a time of dramatic change: political reforms, economic growth, social shifts and cultural freedoms. Sex, drugs, rock and roll; tie-dye, mini skirts and the Beatles. But the 1960s weren’t swinging for everyone. Some people welcomed these changes, but some people resented them: and for some people, life didn’t get better at all. Although many people experienced the decade as one of comfortable prosperity, this masked a decline in the competitiveness of the British economy against its European rivals. Strikes were increasingly common as workers tried to fight for better conditions, and the ‘rediscovery’ of poverty led to panic about inequality, with rising levels of homelessness and unemployment. The end of the British empire led to anxiety about Britain’s place in the world, and increasing levels of immigration led to a rise in racist politics that bitterly divided communities. Women enjoyed more freedoms than before, but still felt ignored and oppressed by male-dominated politics and society. In Northern Ireland, the divided sectarian politics erupted into the Troubles by the end of the decade. And British young people might have enjoyed listening to the Rolling Stones in their university halls; but they were also anxious about the Vietnam War, the Cold War, and their future in a turbulent and uncertain world. This module will explore the complex contradictions that made up Britain in the 1960s.
Late Antiquity can be narrated as a period of powerful emperors, domineering bishops, and barbarian warlords. In this module we will be looking, instead, at the lives and agency of women during the same period. We look at women’s legal and social status and at how they exercised power, whether in their own right or indirectly as mothers, wives or sisters of powerful men. We investigate how women are portrayed in the sources, from the “good empress” Eusebia to Theodora, the actress turned empress. We discuss how and to what extent Christianity changed the lives of women and think about the effect of war on women. Our case studies will include women from a wide range of social spheres, from a Gaulish girl of humble status who eloped with her boyfriend to Justa Grata Honoria, sister of the emperor Valentinian III, who proposed to Attila the Hun in a bid to escape the control of her brother.
In this module we will examine some of the emerging and innovative practices that are occurring in schools, colleges, and Higher Education. We will explore some of the new digital technologies such as Artificial Intelligence, their impact and how they can be used in teaching. We will also focus on advances in pedagogy such as adopting online approaches to learning or assessment and explore how they are applicable to your own practice.
England and Wales now imprisons a greater proportion of its population than any other country in Western Europe, the population in custody having doubled in 12 years. Yet the prison population continues to grow. The criminal justice system more generally, including probation and policing, have been subject to dramatic change over recent decades that have raised fundamental questions including the appropriate role of the state and the private sector in criminal justice, the role of public opinion as a driver of criminal justice policy and the underlying policy factors that have led to the present situation. The importance of this policy area is illustrated by the high-profile 'crises' and 'scandals' that regularly erupt in the media, including issues relating to prisoner votes, the release of indeterminately-sentenced prisoners, and the failings of private companies to deliver criminal justice services. This module seeks to cast a spotlight on this troublesome area of law and public policy. It draws upon literature from law, criminology, history, political science and some comparative material to ask where our contemporary penal policy comes from and to speculate on possible futures.
Penology is the study of punishment, in prison and in the community. Students are encouraged to think critically about the multiple purposes and debatable effectiveness of our contemporary modes of punishment, and to understand why this 'end product' of the criminal justice system has become, in recent decades, such a politically contested issue. Questions which CRIM3001 poses include: What is it society hopes to achieve when it punishes offenders? If the answer seems obvious, why do some theorists argue punishment has 'hidden functions' and why do approaches to punishment vary between countries? Why does, for example, the United States continue to use the death penalty, while Canada, Australia, and New Zealand have pioneered an approach known as restorative justice? Is either method more successful, in deterring or rehabilitating offenders, than our reliance on prison and probation? What is it like to go to, and spend years living in, prison? Is a term of imprisonment, or should it be, primarily a painful or positive experience? Do some categories of prisoners - women, for example, or sexual offenders - experience prison differently, and if so, does it matter? How does one successfully resettle in the community after a lengthy custodial sentence?
The module is designed to introduce the main elements of individual and organisational behaviour and human resource (HR) practices in organisations, and therefore focuses on people management. In particular, the module provides a context for you to appreciate the complexities of managing people and organisations in the 21st century. The content of this module is focused on the challenges of managing individuals, teams, groups and organisations, by examining a variety of issues inherent in modern organisations and, importantly, the skills that managers require to deal with them. The module also calls for significant reflection on your own skills and career development, since a critical part of the MBA programme is to learn to manage yourself and other people in a work-based environment. During the module you will receive assessments of your personality type and team interaction style.
Historians have become interested in ‘ordinary people’ in recent years. Why? This module explores this question through looking at case-studies of women’s, men’s and children’s histories in nineteenth- and twentieth-century Britain, and at varieties of ‘ordinary sources’. We examine how a focus on ‘the ordinary’ maps onto, and complicates, other historically-shifting identities – race, ethnicity, class, gender, age, ability, region, and religious faith – and the implications. Claire Langhamer has asked, ‘Who do we mean when we refer to ordinary people and who did the people we study mean?’, and we will also consider this key question through tracing the roots of the historiographical turn to ‘the ordinary’, drawing on the wide-ranging expertise in the histories of modern Britain we have at Southampton.
The module will cover basic topics in perceptual psychology. We will discuss how the visual brain uses information from the two eyes in combination with learnt heuristics and other information sources to construct a perceptual representation of the world. We will discuss basic anatomy and physiology associated with perception, as well as introduce topics such as motion perception, colour perception, the perception of depth and size. In addition, we cover higher-level visual cognition, including attention, object recognition. We will also cover auditory perception, including pitch perception and source localisation. We will frame perception in the context of psychology in general, highlighting the role of perception in aspects of cognitive, social, clinical and health psychology. The module will be taught by lectures including classroom demonstrations whenever possible. The module is core for BSc Psychology students, and can be taken as an optional module for non-Psychology students as part of the Curriculum Innovation Project.
This module introduces music performance skills. You undertake individual tuition in your chosen performance specialism* (8 hours of lessons) along with a variety of workshops exploring topics from across the performance spectrum. With the help of your teachers, you will learn to self-critique and analyse your own performance(s) with an emphasis on self-reflection. *You elect the performance specialism you wish to be assessed; alongside instruments and singing, you can be assessed in electronic performance too. If you wish, you may wish to take two performance specialisms– e.g. flute and vocals – your individual tuition will be split equally across each specialism.
This module allows you to develop your music performance skills to a new level. A combination of individual tuition in your chosen performance specialism* (12 hours of lessons) and a variety of workshop and public performance opportunities provide you with the chance to study new repertoire, improve your technical skills and add to your performance experience. Interacting with concerts and events also gives you the opportunity to see professional musicians in performance. *You elect the performance specialism you wish to be assessed; alongside instruments and singing, you can be assessed in electronic performance too. If you wish, you may wish to take two performance specialisms– e.g. flute and vocals – your individual tuition will be split equally across each specialism.
This module introduces the student to the use of reflective practice in professional development, enhancing their experience of performance teaching and providing them with a foundation for future learning and progress. Students attend practically-oriented seminars, discuss teaching techniques and methods observed in workshops, practise teaching demonstration lessons.
The Personal and Professional (PPD1) module runs throughout year 1 and is the first of three related modules with PPD 2 and 3 running through year 2 and Final year respectively. The personal and professional development highlighted in these modules is based upon the General Medical Council (GMC) Get to know Good medical practice, 2024. https://www.gmc-uk.org/professional-standards/good-medical-practice-2024/get-to-know-good-medical-practice-2024. This includes ethical guidance and standards of practice to help students recognise health professionals' central responsibility of patient care and to demonstrate an understanding of all elements of the behaviours expected of doctors in the NHS. PPD1 requires students to consider, learn and demonstrate self-organisation, and effective and timely communication with their peers, healthcare colleagues, patients, families and all staff. The module has an additional focus on assisting students to adapt their learning approach and study skills to maximise engagement and learning from the teaching resources on the medical programme.
