An Introduction To Incidence Geometry

Author : Bart De Bruyn
Publisher : Birkhäuser
Page : 372 pages
File Size : 46,6 Mb
Release : 2016-11-09
Category : Mathematics
ISBN : 9783319438115

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An Introduction to Incidence Geometry by Bart De Bruyn Pdf

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.

Author : Johannes Ueberberg
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 52,6 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9783642209727

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Foundations of Incidence Geometry by Johannes Ueberberg Pdf

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.

Author : Francis Buekenhout
Publisher : North-Holland
Page : 1440 pages
File Size : 48,7 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015033341747

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Handbook of Incidence Geometry by Francis Buekenhout Pdf

Hardbound. This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively.More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.

Author : Rey Casse
Publisher : OUP Oxford
Page : 212 pages
File Size : 49,5 Mb
Release : 2006-08-03
Category : Mathematics
ISBN : 9780191538360

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Projective Geometry by Rey Casse Pdf

This lucid and accessible text provides an introductory guide to projective geometry, an area of mathematics concerned with the properties and invariants of geometric figures under projection. Including numerous worked examples and exercises throughout, the book covers axiomatic geometry, field planes and PG(r, F), coordinatising a projective plane, non-Desarguesian planes, conics and quadrics in PG(3, F). Assuming familiarity with linear algebra, elementary group theory, partial differentiation and finite fields, as well as some elementary coordinate geometry, this text is ideal for 3rd and 4th year mathematics undergraduates.

Author : Adam Sheffer
Publisher : Cambridge University Press
Page : 263 pages
File Size : 41,5 Mb
Release : 2022-03-24
Category : Mathematics
ISBN : 9781108832496

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Polynomial Methods and Incidence Theory by Adam Sheffer Pdf

A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.

Author : Larry Guth
Publisher : American Mathematical Soc.
Page : 273 pages
File Size : 48,7 Mb
Release : 2016-06-10
Category : Combinatorial analysis
ISBN : 9781470428907

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Polynomial Methods in Combinatorics by Larry Guth Pdf

This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.

Author : Harold Laird Dorwart
Publisher : Unknown
Page : 184 pages
File Size : 40,8 Mb
Release : 1966
Category : Mathematics
ISBN : UOM:39015017337414

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The Geometry of Incidence by Harold Laird Dorwart Pdf

Author : D. M.Y. Sommerville
Publisher : Courier Dover Publications
Page : 224 pages
File Size : 51,8 Mb
Release : 2020-03-18
Category : Mathematics
ISBN : 9780486842486

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Introduction to the Geometry of N Dimensions by D. M.Y. Sommerville Pdf

Classic exploration of topics of perennial interest to geometers: fundamental ideas of incidence, parallelism, perpendicularity, angles between linear spaces, polytopes. Examines analytical geometry from projective and analytic points of view. 1929 edition.

Author : Albrecht Beutelspacher,Ute Rosenbaum
Publisher : Cambridge University Press
Page : 272 pages
File Size : 43,5 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521483646

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Projective Geometry by Albrecht Beutelspacher,Ute Rosenbaum Pdf

Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.

Author : P. Garbacz,O. Kutz
Publisher : IOS Press
Page : 456 pages
File Size : 45,6 Mb
Release : 2014-09-05
Category : Computers
ISBN : 9781614994381

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Formal Ontology in Information Systems by P. Garbacz,O. Kutz Pdf

Formal Ontology in Information Systems (FOIS) is the flagship conference of the International Association for Ontology and its Applications (IAOA). Its interdisciplinary research focus lies at the intersection of philosophical ontology, linguistics, logic, cognitive science, and computer science, as well as in the applications of ontological analysis to conceptual modeling, knowledge engineering, knowledge management, information-systems development, library and information science, scientific research, and semantic technologies in general. As in previous years, FOIS 2014 was a nexus of interdisciplinary research and communication. The current proceedings is divided into four main sections, dealing with: foundations; processes, agency and dispositions; methods and tools; and applications. The last of these covers a broad spectrum of areas, including in particular biology and medicine, engineering, and economy. For the first time in its history, the conference hosted a special track: an ontology competition, the aim of which was to encourage authors to make their ontologies publicly available and to allow them to be evaluated according to a set of predetermined criteria. Papers discussing these ontologies can also be found in this volume. The book will be of interest to all those whose work involves the application of ontologies, and who are looking for a current overview of developments in formal ontology.

Author : F. Kárteszi
Publisher : Elsevier
Page : 281 pages
File Size : 50,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483278148

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Introduction to Finite Geometries by F. Kárteszi Pdf

North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geometrical configurations and nets, as well as pentagon theorem and the Desarguesian configuration, two pentagons inscribed into each other, and the concept of geometrical nets. The publication takes a look at combinatorial applications of finite geometries and combinatorics and finite geometries. Topics include generalizations of the Petersen graph, combinatorial extremal problem, and theorem of closure of the hyperbolic space. The book is a valuable source of data for readers interested in finite geometries.

Author : Jürgen Richter-Gebert
Publisher : Springer Science & Business Media
Page : 573 pages
File Size : 53,5 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9783642172861

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Perspectives on Projective Geometry by Jürgen Richter-Gebert Pdf

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Author : Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss
Publisher : Springer
Page : 333 pages
File Size : 47,7 Mb
Release : 2018-06-11
Category : Mathematics
ISBN : 9783319784342

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Discrete Geometry and Symmetry by Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss Pdf

This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.

Author : Yufei Zhao
Publisher : Cambridge University Press
Page : 335 pages
File Size : 53,5 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781009310949

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Graph Theory and Additive Combinatorics by Yufei Zhao Pdf

An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.

Author : Walter Prenowitz,Meyer Jordan
Publisher : Rowman & Littlefield
Page : 380 pages
File Size : 40,8 Mb
Release : 2012-10-04
Category : Mathematics
ISBN : 0912675489

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Basic Concepts of Geometry by Walter Prenowitz,Meyer Jordan Pdf

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