This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem...

Winner of a CHOICE Outstanding Academic Title Award for 2011
This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject.

Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of...

Land use change is driven by a variety of forces, including spatial policies formulated at supra-national, national, regional and local levels. The main focus of this book is to contextualise, explain and illustrate a new methodology for simulating land use change in different parts of Europe. It considers some of the more important causal factors and identifies state-of-the-art approaches to modelling human and environmental systems, and for evaluating and visualising altenative scenarios. The last part of the volume presents material from two case studies, one from The Netherlands and one...

Encompassing a broad range of innovative studies on planning support science, this timely Handbook examines how the consequences of pressing societal challenges can be addressed using computer-based systems. Chapters explore the use of new streams of big and open data as well as data from traditional sources, offering significant critical insights into the field. Contributions from key scholars from around the world demonstrate how mature the field of planning support science has become in providing support for practitioners to confront diverse problems. The Handbook analyses a carefully...

Encompassing a broad range of innovative studies on planning support science, this timely Handbook examines how the consequences of pressing societal challenges can be addressed using computer-based systems. Chapters explore the use of new streams of big and open data as well as data from traditional sources, offering significant critical insights into the field. Contributions from key scholars from around the world demonstrate how mature the field of planning support science has become in providing support for practitioners to confront diverse problems. The Handbook analyses a carefully...