[PDF] Introduction To Finite Geometries eBook

Author : F. Kárteszi
Publisher : Elsevier
Page : 281 pages
File Size : 18,38 MB
Release : 2014-05-12
Category : Mathematics
ISBN : 148327814X

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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 : Ferenc Kárteszi
Publisher :
Page : 0 pages
File Size : 44,21 MB
Release : 1976
Category : Combinatorial geometry
ISBN : 9780720428322

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This book contains material elaborated during courses held at the Eötvös Loránd University of Budapest since 1948, under the title 'projective geometry' wherein the notation of finite projective planes in connection with the classical projective geometry was mentioned. The share of finite geometries increased over time. The book is somewhat experimental--as the lectures were--thus the presentation of these lectures in the form of an introductory textbook of a didactical character. -- Author's preface.

Author : Abraham Adrian Albert
Publisher : Courier Corporation
Page : 116 pages
File Size : 42,7 MB
Release : 2015-02-18
Category : Mathematics
ISBN : 0486789942

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Text for both beginning and advanced undergraduate and graduate students covers finite planes, field planes, coordinates in an arbitrary plane, central collineations and the little Desargues' property, the fundamental theorem, and non-Desarguesian planes. 1968 edition.

Author : Steven T. Dougherty
Publisher : Springer Nature
Page : 374 pages
File Size : 18,59 MB
Release : 2020-10-30
Category : Mathematics
ISBN : 3030563952

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This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.

Author : Rudolf Lidl
Publisher : Cambridge University Press
Page : 784 pages
File Size : 10,36 MB
Release : 1997
Category : Mathematics
ISBN : 9780521392310

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This book is devoted entirely to the theory of finite fields.

Author : Albrecht Beutelspacher
Publisher : Cambridge University Press
Page : 272 pages
File Size : 32,93 MB
Release : 1998-01-29
Category : Mathematics
ISBN : 9780521483643

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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 : Simeon Ball
Publisher : Cambridge University Press
Page : 299 pages
File Size : 32,69 MB
Release : 2015-07-02
Category : Mathematics
ISBN : 1107107997

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A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.

Author : Peter Dembowski
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 16,98 MB
Release : 1997
Category : Mathematics
ISBN : 9783540617860

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Peter Dembowski was born in Berlin on April 1, 1928. After studying mathematics at the University of Frankfurt of Main, he pursued his graduate studies at Brown Unviersity and the University of Illinois, mainly with R. Baer. Dembowski returned to Frankfurt in 1956. Shortly before his premature death in January 1971, he had been appointed to a chair at the University of Tuebingen. Dembowski taught at the universities of Frankfurt and Tuebingen and - as visiting Professor - in London (Queen Mary College), Rome, and Madison, WI. Dembowski's chief research interest lay in the connections between finite geometries and group theory. His book "Finite Geometries" brought together essentially all that was known at that time about finite geometrical structures, including key results of the author, in a unified and structured perspective. This book became a standard reference as soon as it appeared in 1968. It influenced the expansion of combinatorial geometric research, and left its trace also in neighbouring areas.

Author : Judith N. Cederberg
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 12,12 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475738315

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A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3 - 4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. Each chapter includes a list of suggested sources for applications and/or related topics.