As taught in 2006-2007 and 2007-2008.

Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions.

This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include:

– norm topology and topological isomorphism;
– boundedness of operators;
– compactness and finite dimensionality;
– extension of functionals;
– weak*-compactness;
– sequence spaces and duality;
– basic properties of Banach algebras.

Suitable for: Undergraduate students Level Four

Dr Joel F. Feinstein
School of Mathematical Sciences

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras.

Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.

The aim of this module is to provide students with an overview of current work and debates on the subject of Sustainability. Sustainability is a complex term that can mean different things to different people depending upon their cultural and subject backgrounds, and the context within which they live and work.

Dr Sarah Speigh, University of Nottingham

This is a module framework. It can be viewed online or downloaded as a zip file.

Last taught in Spring Semester 2006

A compilation of fourteen lectures in PDF format on the subject of quantum field theory. This module is suitable for 3rd or 4th year undergraduate and postgraduate level learners.

Suitable for year 3/4 undergraduate and postgraduate study.

Dr Kirill Krasnov, School of Mathematical Sciences

Dr Kirill Krasnov is a Lecturer at the University of Nottingham. After studying physics in Kiev, Ukraine, he carried out research for his doctorate at Pennsylvania State University, USA and then held post-doctoral positions at University of California, Santa Barbara and Max Planck Institute for Gravitational Physics, Germany. His main research interest is in the field of quantum gravity. Dr Krasnov is a holder of an EPSRC Advanced Fellowship.

In June 2009 the Operator Algebras and Applications International Summer School was held in Lisbon. Dr Joel Feinstein taught one of the four courses available on Regularity conditions for Banach function algebras. He delivered four 90 minute lectures on and this learning object contains the slides, handouts, annotated slides and audio podcasts from each session.

Banach function algebras are complete normed algebras of bounded, continuous, complex-valued functions defined on topological spaces.

This module is intended to give you a broad understanding of issues related to environmental sustainability in the context of engineering. The environmental problems facing our world are becoming more apparent day by day, and the term “sustainability” is used more frequently in the media. This module will explore the concept of sustainability and discuss some of the issues surrounding the subject.

Each chapter will begin with an overview of the content, and will then introduce key factors and the current world systems in place for the subject matter such as energy, materials, food, water and shelter. The social and economic factors of sustainability in an engineering context will also be covered. The problems associated with these systems will then be highlighted, specifically their environmental or social impacts and what part of the systems that could be considered unsustainable. Alternatives will then be introduced and outlined including what options there are and what are the challenges involved in implementing them.

School of Engineering, University of Nottingham

The aim of this module is to introduce students to the concept of ‘sustainability’ as perceived from within the Arts and Humanities, in particular within the disciplines of archaeology, classics, history (including art history and landscape history), music, philosophy and theology. The module will review a number of topical issues – such as climate change, food security, water and waste management, landscape, environment and biodiversity – through the lens of the Arts and Humanities to consider how our disciplines can contribute to current debates and offer new routes to sustainable futures.

It is expected that the module will foster and develop students’ knowledge of issues in sustainability and, by placing evidence in its wider context, encourage students to think critically about possible solutions. Importantly, this module will render students ‘educated consumers’, aware that their daily decisions have an impact and that their choices can be equally influential. Above all it is about giving students the confidence, as individuals, to bring about social change for the future

Dr Naomi Sykes, University of Nottingham

My research focuses on human-animal-landscape relationships and how they inform on the structure, ideology and practice of past societies. My approach is to integrate animal bone data with other categories of material culture, and with wider archaeological, historical, scientific and anthropological discussions. As such, my research has wide geographical and temporal applicability.

There is growing recognition across business that the reductionist ‘mind set’ founded on unlimited economic growth impervious to the social and environmental impacts of commercial activities will not resolve the converging environmental, social and economic crises now faced by the global community. Ever greater numbers of Boards and CEOs are grappling with a notion of sustainability and attempting to define precisely what it means for their business.

The primary aim of this unit is to capture this transition and define what businesses are doing to adopt a more sustainable approach. Looking at a number of case studies, the unit will attempt to demonstrate how individual businesses are attempting to align their activities to address global sustainability challenges such as climate change and carbon reduction, energy and water scarcity and poverty reduction.

This module considers sustainability with respect to water, food, agriculture, forestry and energy. For each of these elements of sustainability, the module illustrates why their sustainable management is important, given that we are living within finite environmental limits. A novel aspect of the module is that in most sessions you update your own personal blog (or offline document), which can be used to provide a record of your opinions on sustainability, details on your awareness of sustainability, and specific examples of sustainability. The module is assessed by means of producing and presenting a poster at an internal “Sustainability Conference”.

Dr Simon Gosling, University of Nottingham.

My main interests are in understanding the impacts of climate change on natural and human systems, and bridging the boundary between physical science and impact and policy-related areas.

Much of my current research investigates the potential impact of climate change on global- and catchment-scale hydrology and water resources. I am interested in understanding how average conditions and extremes (floods and droughts) might be affected by climate change. I apply a variety of climate and hydrological numerical models to achieve this. I also have strong interests in modelling the relationship between climate and human health; specifically, on the association between extreme temperature events (heat waves and cold snaps) and temperature-related mortality.