Mathematics and Its History: Edition 3

Springer Science & Business Media
2
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From the reviews of the second edition:

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community."

(European Mathematical Society)

"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."

(Denis Bonheure, Bulletin of the Belgian Society)

This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.

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About the author

John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books with Springer, including The Four Pillars of Geometry; Elements of Algebra; Numbers and Geometry; and many more.
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5.0
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Additional Information

Publisher
Springer Science & Business Media
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Published on
Jul 23, 2010
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Pages
662
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ISBN
9781441960535
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Best For
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Language
English
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Genres
Mathematics / Calculus
Mathematics / General
Mathematics / Geometry / General
Mathematics / History & Philosophy
Mathematics / Mathematical Analysis
Mathematics / Number Theory
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Content Protection
This content is DRM protected.
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NUMBERS AND GEOMETRY is a beautiful and relatively elementary account of a part of mathematics where three main fields--algebra, analysis and geometry--meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. The key is algebra, which brings arithmetic and geometry together, and allows them to flourish and branch out in new directions. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He believes that most of mathematics is about numbers, curves and functions, and the links between these concepts can be suggested by a thorough study of simple examples, such as the circle and the square. This book covers the main ideas of Euclid--geometry, arithmetic and the theory of real numbers, but with 2000 years of extra insights attached. NUMBERS AND GEOMETRY presupposes only high school algebra and therefore can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics because it is such an attractive and unusual treatment of fundamental topics. Also, it will serve admirably in courses aimed at giving students from other areas a view of some of the basic ideas in mathematics. There is a set of well-written exercises at the end of each section, so new ideas can be instantly tested and reinforced.
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 supra-national levels.

In order to understand the mechanisms of change and the impact of policies, the formulation, calibration and testing of models is required. Land-use change models help us to understand the complexities and interdependencies of the components that constitute spatial systems and can provide valuable insights into possible land-use configurations in the future. Models of land-use change incorporate a vast amount of knowledge from a wide range of disciplines. Geography contributes to the understanding of land-use change whilst demography and economics help explain underlying trends. Model building relies heavily on mathematics and (geographical) information systems, but also includes many elements from the softer sciences, such as management studies and environmental science. This book offers a cross-sectional overview of current research progress that allows the construction of successful land-use models. The contributions range from methodology and calibration to actual applications in studies of recent policy implementation and evaluation. The contributors originate from academic and applied research institutes around the world and thus offer an interesting mix of theory and practice in different case study contexts.

Several years have passed since John Stillwell and Henk Scholten published "Land Use Simulation for Europe" in 2001, and the subject has moved on since then. The current volume, "Modelling Land-use Change", is an indispensable guide for anyone interested in the state-of-the-art of land-use modelling, its background and its application. In summary, land-use change simulation modelling is a relatively new and dynamic field of study and this book provides a full overview of the topic, a wide range of applications (both geographically and thematically), a mix of theory and practice, a synthesis of recent research progress, and educational material for students and teachers.

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