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The Foundations of Geometry was first published in 1897, and is based on Russell's Cambridge dissertation as well as lectures given during a journey through the USA. This is the first reprint, complete with a new introduction by John Slater. It provides both an insight into the foundations of Russell's philosophical thinking and an introduction to the philosophy of mathematics and logic. As such it will be an invaluable resource not only for students of philosophy, but also for those interested...

This text for advanced undergraduates emphasizes the logical connections of the subject. The derivations of formulas from the axioms do not make use of models of the hyperbolic plane until the axioms are shown to be categorical; the differential geometry of surfaces is developed far enough to establish its connections to the hyperbolic plane; and the axioms and proofs use the properties of the real number system to avoid the tedium of a completely synthetic approach. The development includes pro...

This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer - even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. 'Hilbert and Cohn-Vossen' is full of interesting facts,...

This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two appendices contain more advanc...

The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner. The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop-Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmuller spaces and mapping class g...

The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audie...

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in t...

Als Felix Klein den Plan faBte, die wichtigsten seiner autogra- phierten Vorlesungen im Druck erscheinen zu lassen, gedachte er, mit der Nichteuklidischen Geometrie zu beginnen und den alten Text zu- vor mit Hille eines jiingeren Geometers, des Herro Dr. Rosemann, in der Anlage und den Einzelheiten einer griindlichen Neubearbeitung zu unterziehen. Diese Arbeit erwies sich als langwieriger wie urspriing- lich geschatzt. Klein selbst konnte ihren AbschluB nicht mehr erleben. Zwar hatte er in tagli...

This graduate level text covers an exciting and active area of research at the crossroads of several different fields in Mathematics and Physics. In Mathematics it involves Differential Geometry, Complex Algebraic Geometry, Symplectic Geometry, and in Physics String Theory and Mirror Symmetry. Drawing extensively on the author's previous work, the text explains the advanced mathematics involved simply and clearly to both mathematicians and physicists. Starting with the basic geometry of connec...