Introduction To Geometry
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Introduction To Geometry
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Author : Richard Rusczyk
language : en
Publisher: Aops Incorporated
Release Date : 2006-01-01
Introduction To Geometry written by Richard Rusczyk and has been published by Aops Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Juvenile Nonfiction categories.
Introduction To Projective Geometry
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Author : C. R. Wylie
language : en
Publisher: Courier Corporation
Release Date : 2008-12-09
Introduction To Projective Geometry written by C. R. Wylie and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Mathematics categories.
This lucid introductory text offers both analytic and axiomatic approaches to plane projective geometry. Strong reinforcement for its teachings include detailed examples and numerous theorems, proofs, and exercises, plus answers to all odd-numbered problems. In addition to its value to students, this volume provides an excellent reference for professionals. 1970 edition.
College Geometry
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Author : Nathan Altshiller-Court
language : en
Publisher: Dover Publications
Release Date : 2013-12-30
College Geometry written by Nathan Altshiller-Court and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-30 with categories.
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
Introduction To Tropical Geometry
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Author : Diane Maclagan
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-13
Introduction To Tropical Geometry written by Diane Maclagan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-13 with Mathematics categories.
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina
Geometry Illuminated
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Author : Matthew Harvey
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-09-25
Geometry Illuminated written by Matthew Harvey and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-25 with Mathematics categories.
Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.
Introduction To Algebraic Geometry
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Author : Steven Dale Cutkosky
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-06-01
Introduction To Algebraic Geometry written by Steven Dale Cutkosky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-01 with Mathematics categories.
This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
An Introduction To The Geometry Of N Dimensions
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Author : Duncan M'Laren Young Sommerville
language : en
Publisher:
Release Date : 1929
An Introduction To The Geometry Of N Dimensions written by Duncan M'Laren Young Sommerville and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1929 with Hyperspace categories.
Elementary Euclidean Geometry
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Author : C. G. Gibson
language : en
Publisher: Cambridge University Press
Release Date : 2003
Elementary Euclidean Geometry written by C. G. Gibson 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 2003 with Mathematics categories.
This book, first published in 2004, is an example based and self contained introduction to Euclidean geometry with numerous examples and exercises.
An Introduction To Incidence Geometry
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Author : Bart De Bruyn
language : en
Publisher: Birkhäuser
Release Date : 2016-11-09
An Introduction To Incidence Geometry written by Bart De Bruyn and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-09 with Mathematics categories.
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.
Introduction To Algebraic Geometry
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Author : Serge Lang
language : en
Publisher: Courier Dover Publications
Release Date : 2019-03-20
Introduction To Algebraic Geometry written by Serge Lang and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Mathematics categories.
Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.