Mathematics : Geometry

Rigorous descriptions and analyses of the main algorithms for different variations of the Geometric Spanner Network Problem. more...

Price: $73.00

This volume presents a comprehensive introduction into rigorous geometrical dynamics of complex systems of various natures. "Complex systems", in this book, are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a unified geometrical approach to dynamics of complex systems of various kinds: engineering, physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these Multi-Input Multi-Output (MIMO) systems have something in common: the underlying physics. Using sophisticated machinery composed of differential geometry, topology and path integrals, this book proposes a unified approach to complex dynamics - of predictive power much greater than the currently popular "soft-science" approach to complex systems. The main objective of this book is to show that high-dimensional nonlinear systems in "real life" can be modeled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. The book has two chapters and an appendix. The first chapter develops the geometrical machinery in both an intuitive and rigorous manner. The second chapter applies this geometrical machinery to a number of examples of complex systems, including mechanical, physical, control, biomechanical, robotic, neurodynamical and psycho-social-economical systems. The appendix gives all the necessary background for comprehensive reading of this book. more...

Price: $239.00

Covering the many aspects of geometry, this volume of the History of Mathematics series presents a compelling look at mathematical theories alongside historical occurrences. The engaging and informative text, complemented by photographs and illustrations, introduces students to the fascinating story of how geometry has developed. Biographical information on key figures, a look at different applications of geometry over time, and the groundbreaking discoveries related to geometry are comprehensively covered. more...

Price: $40.00

Based on a seminar for graduates held at the Feza Gürsey Institute, there are articles by some key researchers. One attractive feature is the inclusion of the algebro-geometric material as well as the twistor space methods, which form a bridge between the pure mathematics and the more physical approaches. more...

Price: $48.00

Geometry, literally, measuring the earth, aims to describe the world around us. It is central to many branches of mathematics and physics, and offers a whole range of views on the universe. This is an introduction to the ideas of geometry and includes generous helpings of simple explanations and examples. more...

Price: $38.00