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.

Mathematical modeling is becoming increasingly versatile and multi-disciplinary. This text demonstrates the broadness of this field as the authors consider the principles of model construction and use common approaches to build models from a range of subject areas. The book reflects the interests and experiences of the authors, but it explores mathematical modeling across a wide range of applications, from mechanics to social science. A general approach is adopted, where ideas and examples are favored over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers, and students across a wide range of disciplines..

"Its range is far broader than the majority of methods texts, being concerned with both human and physical geography... Given the seriousness with which Key Methods in Geography approaches all aspects of research, it will continue to find wide favour among undergraduate geographers." - Times Higher Education Textbook Guide "All geographers, whatever their interest, need to do research. This book will help them get started in the best possible way, with thoughtful advice on everything from project design, through choice of methods, to data analysis and presentation. The editors have assembled an impressive array of authors, all experts in their chosen field." - Tim Burt, University of Durham "Excellent book. Valuable teaching aid. Well written and covers a wide range of methods thoroughly." - Sue Rodway-Dyer, Exeter University "This is an excellent book and deals with a number of topics (which I teach) outside of the tutorial module where it is a recommended text for geographers. A very useful textbook throughout a 3 year Geography programme." - Ian Harris, Bangor University Key Methods in Geography is an introduction to the principal methodological issues involved in the collection, analysis and presentation of geographical information. It is unique in the reference literature for providing an overview of qualitative and quantitative methods for human and physical geography. An accessible primer, it will be used by students as a reference throughout their degree, on all issues from research design to presentation. This second edition has been fully revised and updated and includes new chapters on internet mediated research, diaries as a research method, making observations and measurements in the field, and the analysis of natural systems. Organized into four sections: Getting Started in Geographical Research; Generating and Working with Data in Human Geography; Generating and Working with Data in Physical Geography; Representing and Interpreting Geographical Data; each chapter comprises: A short definition A summary of the principal arguments A substantive 5,000-word discussion Use of real-life examples Annotated notes for further reading. The teaching of research methods is integral to all geography courses: Key Methods in Geography, 2nd Edition explains all of the key methods with which geography undergraduates must be conversant.

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.

This comprehensive textbook offers a conceptual and practicalintroduction to research methodology, data collection, andtechniques used in both human and physical geography. Explores a full range of contemporary geographic techniques,including statistics, mathematical analysis, GIS, and remotesensing Unique in both content and organization, it brings together ateam of internationally recognized specialists to create a balancedapproach between physical geography, human geography, and researchtechniques Includes a series of foundational chapters offering multipleperspectives on the central questions in research methods Examines the conceptual frameworks and practical issues behinddata acquisition and analysis, and how to interpret results Includes explanations of key terminology and exercisesthroughout

First published in 1989. It seems such a long time ago, another age—yet it is a mere twenty-odd years since the original Models in Geography was published. It is an even shorter time since the first tentative steps were taken towards an alternative formulation of what might constitute a geographical perspective within the social sciences. What came to be called the political-economy perspective has progressed with remarkable speed and energy to generate its own framework of conceptualization and analysis, its own questions and debates. The papers in these two volumes are witness to the richness and range of the work which has developed over this relatively short period within the political economy approach. Moreover, from being a debate within an institutionally defined ‘discipline of geography’, to introducing into that discipline ideas and discussions from the wider fields of philosophy and social science and the humanities more generally, it has now flowered into a consistent part of enquiries that span the entire realm of social studies.

Based on the authors' combined teaching and research experience over many years, this is an integrated and unified account of systems on all scales from planetary to molecular.

First published in 1989. The publication of Models in geography presaged a sea change in the practice of Anglo-American geography. For a new set of models, this book provides a summary of their nature, spirit and purpose based upon a political-economy perspective. The book is split into two volumes, each consisting of four parts. This makes the title suitable for students and geographers with an interest in models of the city, civil society and social theory.

"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.

The International Encyclopedia of Human Geography provides an authoritative and comprehensive source of information on the discipline of human geography and its constituent, and related, subject areas. The encyclopedia includes over 1,000 detailed entries on philosophy and theory, key concepts, methods and practices, biographies of notable geographers, and geographical thought and praxis in different parts of the world. This groundbreaking project covers every field of human geography and the discipline’s relationships to other disciplines, and is global in scope, involving an international set of contributors. Given its broad, inclusive scope and unique online accessibility, it is anticipated that the International Encyclopedia of Human Geography will become the major reference work for the discipline over the coming decades. The Encyclopedia will be available in both limited edition print and online via ScienceDirect – featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy. For more information, pricing options and availability visit http://info.sciencedirect.com/content/books/ref_works/coming/ Available online on ScienceDirect and in limited edition print format Broad, interdisciplinary coverage across human geography: Philosophy, Methods, People, Social/Cultural, Political, Economic, Development, Health, Cartography, Urban, Historical, Regional Comprehensive and unique - the first of its kind in human geography