Many people think there is only one right way to teach geometry. For two millennia, the right way was Euclid s way, and it is still good in many respects. But in the 1950s the cry Down with triangles was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new right way, or was the right way something else again, perhaps transformation groups? In this book, I wish to show that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Euclid-style...
Many people think there is only one right way to teach geometry. For two millennia, the right way was Euclid s way, and it is still good in many respe...
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...
This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it ...
Geometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I welcome the opportunity to make a fresh start. Classical geometry is no longer an adequate basis for mathematics or physics-both of which are becoming increasingly geometric-and geometry can no longer be divorced from algebra, topology, and analysis. Students need a geometry of greater scope, and the fact that there is no room for geometry in the curriculum un- til the third or fourth year at least allows us to assume some mathematical background....
Geometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I we...
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept...
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsber...
Only applications-driven book dealing with commerically-sponsored spatial analysis research. * Focuses on business and public sector planning case studies, offering readers a snapshot of the use of spatial analysis across a broad range of areas. * Internationally-renowned editors and contributors present a broad variety of global applications, and demonstrate GIS components and spatial methodologies in practice.
Only applications-driven book dealing with commerically-sponsored spatial analysis research. * Focuses on business and public sector planning ca...
The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir "Sur la Theorie des Nombres Entiers Algebriques" first appeared in installments in the Bulletin des sciences mathematiques in 1877. This book is a translation of that work by John Stillwell, who adds a detailed introduction giving historical background and who outlines the mathematical obstructions that Dedekind was striving to overcome. Dedekind's memoir offers a candid account of the development of an elegant theory and...
The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number...
The use of land changes over time as both natural and man-made environments are influenced by the pressures associated with the processes of development. The demand for land for new residential housing has been a huge challenge for governments striving to protect greenfield sites across Europe in recent years, whilst regeneration has been a common response to the decline of manufacturing in the old industrial heartlands. The variety of forces that drive change in the use of land are extensive and complex, including spatial planning policies designed at local, regional, national and...
The use of land changes over time as both natural and man-made environments are influenced by the pressures associated with the processes of develo...
This book demonstrates the state of the art in the use of information systems and modelling methods in different spatial/geographical planning contexts. It provides a review of developments in the 1990s and detailed insights into the current application of geographical information technology in urban, physical, environmental and socio-economic planning. Important advances in the use of the Internet for access to data and to GIS for planning are also considered. Perspectives are provided by a wide range of contributors from academia, planning practice and the business world.
This book demonstrates the state of the art in the use of information systems and modelling methods in different spatial/geographical planning context...
Many parts of the world are experiencing rapid demographic restructuring, resulting in an ageing population with increasingly significant work and care pressures on cohorts less able or willing to provide support. This book examines some of the important trends that have underpinned reductions in fertility, including delayed child-bearing and increased childlessness. It demonstrates how relationships between partners have resulted in new living arrangements with changing attitudes from marriage to co-habitation as the social norm, and it considers the health and well-being for particular...
Many parts of the world are experiencing rapid demographic restructuring, resulting in an ageing population with increasingly significant work and ...
Inequality is one of the major problems of the contemporary world. Significant geographical disparities exist within nations of the developed world, as well as between these countries and those referred to as the 'South' in the Bruntland Report. Issues of equity and deprivation must be addressed in view of sustainable development. However, before policymakers can remove the obstacles to a fairer world, it is essential to understand the nature of inequality, both in terms of its spatial and socio-demographic characteristics.
This second volume in the series contains population studies...
Inequality is one of the major problems of the contemporary world. Significant geographical disparities exist within nations of the developed world...
