A Background To Geometry
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A Background To Geometry
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Author : T. G. Room
language : en
Publisher: Cambridge University Press
Release Date : 2008-11-27
A Background To Geometry written by T. G. Room and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-27 with Mathematics categories.
The central theme of the book is the development of the idea of congruence, that relation between geometric figures which is basic to ordinary Euclidean geometry. The text is divided into four books corresponding to stages in the development of a geometrical system from simple axioms: 1. 'Geometry without numbers': the relations of order and sense. 2. 'Geometry and counting': properties of the systems obtained by repetitions of the operation of displacement. 3. 'Geometry and algebra': the consequences of adjoining new points to the system developed in Book 2. In particular the properties of an algebraic field are deduced from the geometric axioms. 4. 'Congruence': properties derived from the operation of reflexion. An early introduction of parallels makes possible the drawing of diagrams which resemble those of Euclid's geometry so that the reader may see the broad outline of a proof from observable properties of these diagrams. Particular geometrical systems are explored and some general topics investigated in detail in appendices following each section of the book.
A Background Natural Synthetic And Algebraic To Geometry
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Author : T. G. Room
language : en
Publisher: CUP Archive
Release Date : 1967
A Background Natural Synthetic And Algebraic To Geometry written by T. G. Room and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Congruences (Geometry) categories.
A Background Natural Synthetic And Algebraic To Geometry
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Author : Thomas Gerald Room
language : en
Publisher:
Release Date : 1967
A Background Natural Synthetic And Algebraic To Geometry written by Thomas Gerald Room and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Congruences (Geometry) categories.
A Background To Geometry
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Author : Thomas Gerald Room
language : en
Publisher:
Release Date : 1967
A Background To Geometry written by Thomas Gerald Room and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Congruences (Geometry) categories.
A Background To Geometry
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Author : Thomas G. Room
language : en
Publisher:
Release Date : 1967
A Background To Geometry written by Thomas G. Room and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Geometry categories.
A Background Natural Synthetic And Algebraic To Geometry By T G Room
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Author : T. G. Room
language : en
Publisher:
Release Date : 1967
A Background Natural Synthetic And Algebraic To Geometry By T G Room written by T. G. Room and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
An Introduction To Algebraic Geometry And Algebraic Groups
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Author : Meinolf Geck
language : en
Publisher: Clarendon Press
Release Date : 2013-03-14
An Introduction To Algebraic Geometry And Algebraic Groups written by Meinolf Geck and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.
Collineations And Conic Sections
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Author : Christopher Baltus
language : en
Publisher: Springer Nature
Release Date : 2020-09-01
Collineations And Conic Sections written by Christopher Baltus and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.
This volume combines an introduction to central collineations with an introduction to projective geometry, set in its historical context and aiming to provide the reader with a general history through the middle of the nineteenth century. Topics covered include but are not limited to: The Projective Plane and Central Collineations The Geometry of Euclid's Elements Conic Sections in Early Modern Europe Applications of Conics in History With rare exception, the only prior knowledge required is a background in high school geometry. As a proof-based treatment, this monograph will be of interest to those who enjoy logical thinking, and could also be used in a geometry course that emphasizes projective geometry.
Geometry From Isometries To Special Relativity
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Author : Nam-Hoon Lee
language : en
Publisher: Springer Nature
Release Date : 2020-04-28
Geometry From Isometries To Special Relativity written by Nam-Hoon Lee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Mathematics categories.
This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.
Notes On Geometry And Arithmetic
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Author : Daniel Coray
language : en
Publisher: Springer Nature
Release Date : 2020-07-06
Notes On Geometry And Arithmetic written by Daniel Coray and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-06 with Mathematics categories.
This English translation of Daniel Coray’s original French textbook Notes de géométrie et d’arithmétique introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical geometry, setting aside all but the most essential ideas from algebraic geometry and commutative algebra. Readers are invited to discover rational points on varieties through an appealing ‘hands on’ approach that offers a pathway toward active research in arithmetic geometry. Along the way, the reader encounters the state of the art on solving certain classes of polynomial equations with beautiful geometric realizations, and travels a unique ascent towards variations on the Hasse Principle. Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert’s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.