Geo-mathematical modelling: models from complexity science Sir Alan Wilson, Centre for Advanced Spatial Analysis, University College London Mathematical and computer models for a complexity science tool kit Geographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals and organisations to countries. Our understanding, often partial, of these entities, and in many cases this understanding is represented in theories and associated mathematical models. In this book, the main examples are models that represent elements of the global system covering such topics as trade, migration, security and development aid together with examples at finer scales. This provides an effective toolkit that can not only be applied to global systems, but more widely in the modelling of complex systems. All complex systems involve nonlinearities involving path dependence and the possibility of phase changes and this makes the mathematical aspects particularly interesting. It is through these mechanisms that new structures can be seen to ‘emerge’, and hence the current notion of ‘emergent behaviour’. The range of models demonstrated include account-based models and biproportional fitting, structural dynamics, space-time statistical analysis, real-time response models, Lotka-Volterra models representing ‘war’, agent-based models, epidemiology and reaction-diffusion approaches, game theory, network models and finally, integrated models. Geo-mathematical modelling: Presents mathematical models with spatial dimensions. Provides representations of path dependence and phase changes. Illustrates complexity science using models of trade, migration, security and development aid. Demonstrates how generic models from the complexity science tool kit can each be applied in a variety of situations This book is for practitioners and researchers in applied mathematics, geography, economics, and interdisciplinary fields such as regional science and complexity science. It can also be used as the basis of a modelling course for postgraduate students.

A world model: economies, trade, migration, security and development aid. This bookprovides the analytical capability to understand and explore the dynamics of globalisation. It is anchored in economic input-output models of over 200 countries and their relationships through trade, migration, security and development aid. The tools of complexity science are brought to bear and mathematical and computer models are developed both for the elements and for an integrated whole. Models are developed at a variety of scales ranging from the global and international trade through a European model of inter-sub-regional migration to piracy in the Gulf and the London riots of 2011. The models embrace the changing technology of international shipping, the impacts of migration on economic development along with changing patterns of military expenditure and development aid. A unique contribution is the level of spatial disaggregation which presents each of 200+ countries and their mutual interdependencies – along with some finer scale analyses of cities and regions. This is the first global model which offers this depth of detail with fully work-out models, these provide tools for policy making at national, European and global scales. Global dynamics: Presents in depth models of global dynamics. Provides a world economic model of 200+ countries and their interactions through trade, migration, security and development aid. Provides pointers to the deployment of analytical capability through modelling in policy development. Features a variety of models that constitute a formidable toolkit for analysis and policy development. Offers a demonstration of the practicalities of complexity science concepts. This book is for practitioners and policy analysts as well as those interested in mathematical model building and complexity science as well as advanced undergraduate and postgraduate level students.

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.

"The book covers some of the (traditionally) most obtuse and difficult-to-grasp philosophical ideas that have influenced geographers/geography. The fact that these are presented in an inclusive and accessible manner is a key strength. Many students have commented that the chapters they have read have encouraged them to read more in this field, which is fantastic from a lecturer′s perspective." - Richard White, Sheffield Hallam University A new edition of the classic Approaches text for students, organised in three sections, which overviews and explains the history and philosophy of Human Geographies in all its applications by those who practise it: Section One – Philosophies: Positivist Geography / Humanism / Feminist Geographies / Marxisms / Structuration Theory / Human Animal / Realism / Postmodern Geographies/ Poststructuralist Theories / Actor-Network Theory, / Postcolonialism / Geohumanities / Technologies Section Two – People: Institutions and Cultures / Places and Contexts / Memories and Desires / Understanding Place / Personal and Political / Becoming a Geographer / Movement and Encounter / Spaces and Flows / Places as Thoughts Section Three – Practices: Mapping and Geovisualization / Quantification, Evidence, and Positivism / Geographic Information Systems / Humanism / Activism / Feminist Geographies / Poststructuralist Theories / Psychoanalysis / Environmental Inquiry / Contested Geographies and Culture Wars Fully updated throughout and with eight brand new chapters - this is the core text for modules on history, theory, and practice in Human Geography.

Approaches to Human Geography is the essential student primer on theory and practice in Human Geography. It is a systematic review of the key ideas and debates informing post-war geography, explaining how those ideas work in practice. Avoiding jargon - while attentive to the rigor and complexity of the ideas that underlie geographic knowledge – the text is written for students who have not met philosophical or theoretical approaches before. This is a beginning guide to geographic research and practice.

"Practical, accessible, careful and interesting, this...revised volume brings the subject up-to-date and explains, in bite sized chunks, the ′how′s′ and ′why′s′ of modern day geographical study...[It] brings together physical and human approaches again in a new synthesis." —Danny Dorling, Professor of Geography, University of Oxford Key Methods in Geography is the perfect introductory companion, providing an overview of qualitative and quantitative methods for human and physical geography. This Third Edition Features: 12 new chapters representing emerging themes including online, virtual and digital geographical methods Real-life case study examples Summaries and exercises for each chapter Free online access to full text of Progress in Human Geography and Progress in Physical Geography Progress Reports The teaching of research methods is integral to all geography courses: Key Methods in Geography, Third Edition explains all of the key methods with which geography undergraduates must be conversant.

Model-based Geostatistics for Global Public Health: Methods and Applications provides an introductory account of model-based geostatistics, its implementation in open-source software and its application in public health research. In the public health problems that are the focus of this book, the authors describe and explain the pattern of spatial variation in a health outcome or exposure measurement of interest. Model-based geostatistics uses explicit probability models and established principles of statistical inference to address questions of this kind. Features: Presents state-of-the-art methods in model-based geostatistics. Discusses the application these methods some of the most challenging global public health problems including disease mapping, exposure mapping and environmental epidemiology. Describes exploratory methods for analysing geostatistical data, including: diagnostic checking of residuals standard linear and generalized linear models; variogram analysis; Gaussian process models and geostatistical design issues. Includes a range of more complex geostatistical problems where research is ongoing. All of the results in the book are reproducible using publicly available R code and data-sets, as well as a dedicated R package. This book has been written to be accessible not only to statisticians but also to students and researchers in the public health sciences. The Authors Peter Diggle is Distinguished University Professor of Statistics in the Faculty of Health and Medicine, Lancaster University. He also holds honorary positions at the Johns Hopkins University School of Public Health, Columbia University International Research Institute for Climate and Society, and Yale University School of Public Health. His research involves the development of statistical methods for analyzing spatial and longitudinal data and their applications in the biomedical and health sciences. Dr Emanuele Giorgi is a Lecturer in Biostatistics and member of the CHICAS research group at Lancaster University, where he formerly obtained a PhD in Statistics and Epidemiology in 2015. His research interests involve the development of novel geostatistical methods for disease mapping, with a special focus on malaria and other tropical diseases. In 2018, Dr Giorgi was awarded the Royal Statistical Society Research Prize "for outstanding published contribution at the interface of statistics and epidemiology." He is also the lead developer of PrevMap, an R package where all the methodology found in this book has been implemented.