Описание: The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments.This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.
Описание: Suitable for junior, senior, and first-year graduate courses. This work interweaves historical material with a rigorous ruler - and protractor axiomatic development of the Euclidean and hyperbolic planes. It also includes topics such as axiom systems for three and four dimensional absolute geometry, and Pieri`s system based on rigid motions.
Описание: Can Socrates be serious in his claims that human excellence is constituted by one virtue, that vice is merely the result of ignorance, and that the correct response to crime is therefore not punishment but education? Or are these assertions mere rhetorical ploys by a notoriously complex thinker? This book deals with these questions.
Описание: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Автор: Ratcliffe Название: Foundations of Hyperbolic Manifolds ISBN: 0387331972 ISBN-13(EAN): 9780387331973 Издательство: Springer Рейтинг: Цена: 6347 р. Наличие на складе: Поставка под заказ.
Описание: This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. This book has been heavily class-tested and each chapter contains exercises and a section of historical remarks.
Описание: This book presents a fresh and original exposition of the foundations of classical electrodynamics in the tradition of the so-called metric-free approach. The text provides an axiomatic treatment of the subject, along with a careful discussion of the relevant mathematics, particularly the calculus of exterior differential forms and the tools of computer algebra. However, strong emphasis is placed not only on mathematical definitions of physical notions, but also on the actual physical measurement procedures and their operational interpretation. Requiring some knowledge of elementary electrodynamics, linear algebra, and basic vector analysis, this systematic work interweaves both mathematics and physics, and will be appropriate for graduate students and researchers in physics, mathematics, and electrical engineering.
Автор: Ueberberg Название: Foundations of Incidence Geometry ISBN: 3642209718 ISBN-13(EAN): 9783642209710 Издательство: Springer Рейтинг: Цена: 9234 р. Наличие на складе: Поставка под заказ.
Описание: Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces.Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout.The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.
Автор: Russell Название: An Essay on the Foundations of Geometry ISBN: 1107679451 ISBN-13(EAN): 9781107679450 Издательство: Cambridge Academ Рейтинг: Цена: 5203 р. Наличие на складе: Поставка под заказ.
Описание: Originally published in 1897, this book was based on the dissertation Russell presented for the Fellowship Examination of Trinity College, Cambridge, together with a series of lectures given in the USA around the same time. It provides an account of geometrical concepts in relation to logic, psychology and mathematics, shedding light on the development of Russell's philosophical perspective. This is a highly readable text that will be of value to anyone with an interest in geometry, philosophy and Russell's early thought.
Описание: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Описание: Contains sets of notes for lectures on the foundations of geometry held by Hilbert in the period, 1891-1902. The lectures document the emergence of a fresh approach to foundational study (the `axiomatic method`), which concentrates on assessing the logical weight of central propositions by exploiting the method of independence proofs by modelling.
Описание: This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems. The insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology.
Автор: Tu, Loring W. Название: Differential Geometry ISBN: 3319550829 ISBN-13(EAN): 9783319550824 Издательство: Springer Рейтинг: Цена: 7391 р. Наличие на складе: Невозможна поставка.
Описание: Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein`s general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory.
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