Finite Fields Projective Geometries And Related Topics

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Finite Fields Projective Geometries And Related Topics

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Author : Rita Vincenti
language : en
Publisher:
Release Date : 2021

Finite Fields Projective Geometries And Related Topics written by Rita Vincenti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.

General Galois Geometries

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Author : James William Peter Hirschfeld
language : en
Publisher: Oxford University Press, USA
Release Date : 1991

General Galois Geometries written by James William Peter Hirschfeld and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

Projective spaces over a finite field, otherwise known as Galois geometries, find wide application in coding theory, algebraic geometry, design theory, graph theory, and group theory as well as being beautiful objects of study in their own right. This volume is the culmination of a three volume treatise on this subject. With its companion volumes (Projective Geometries Over Finite Fields and Finite Projective Spaces of Three Dimensions) this work will provide a major reference to the subject. It is essentially self-contained and will be an invaluable companion for research workers and post-graduate students working on these topics. The authors study three main themes: the study of algebraic varieties over finite fields, the combinatorics of Galois geometries, and the identification of various incidence structures associated with them. In particular, much attention is devoted to hermitian varieties, to Grassmannian varieties, and to polar spaces. The topics covered find application across a wide-range of topics in pure mathematics. The book will be useful to research workers and postgraduate students in combinatorics and geometry, and some computer scientists.

An Introduction To Finite Projective Planes

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Author : Abraham Adrian Albert
language : en
Publisher: Courier Dover Publications
Release Date : 2014-12-16

An Introduction To Finite Projective Planes written by Abraham Adrian Albert 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 2014-12-16 with Mathematics categories.

Geared toward both beginning and advanced undergraduate and graduate students, this self-contained treatment offers an elementary approach to finite projective planes. Following a review of the basics of projective geometry, the text examines finite planes, field planes, and coordinates in an arbitrary plane. Additional topics include central collineations and the little Desargues' property, the fundamental theorem, and examples of finite non-Desarguesian planes. Virtually no knowledge or sophistication on the part of the student is assumed, and every algebraic system that arises is defined and discussed as necessary. Many exercises appear throughout the book, offering significant tools for understanding the subject as well as developing the mathematical methods needed for its study. References and a helpful appendix on the Bruck-Ryser theorem conclude the text.

Projective Geometries Over Finite Fields

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Author : James William Peter Hirschfeld
language : en
Publisher: Oxford University Press, USA
Release Date : 1979

Projective Geometries Over Finite Fields written by James William Peter Hirschfeld and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with History categories.

Current Research Topics In Galois Geometry

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Author : Leo Storme
language : en
Publisher: Nova Science Publishers
Release Date : 2014-05

Current Research Topics In Galois Geometry written by Leo Storme and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05 with categories.

Galois geometry is the theory that deals with substructures living in projective spaces over finite fields, also called Galois fields. This collected work presents current research topics in Galois geometry, and their applications. Presented topics include classical objects, blocking sets and caps in projective spaces, substructures in finite classical polar spaces, the polynomial method in Galois geometry, finite semifields, links between Galois geometry and coding theory, as well as links between Galois geometry and cryptography.

Current Research Topics On Galois Geometry

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Author : Leo Storme
language : en
Publisher: Nova Science Publishers
Release Date : 2014-05-14

Current Research Topics On Galois Geometry written by Leo Storme and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Galois theory categories.

Galois geometry is the theory that deals with substructures living in projective spaces over finite fields, also called Galois fields. This collected work presents current research topics in Galois geometry, and their applications. Presented topics include classical objects, blocking sets and caps in projective spaces, substructures in finite classical polar spaces, the polynomial method in Galois geometry, finite semifields, links between Galois geometry and coding theory, as well as links between Galois geometry and cryptography. (Imprint: Nova)

Introduction To Finite Geometries

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Author : F. Kárteszi
language : en
Publisher: Elsevier
Release Date : 2014-05-12

Introduction To Finite Geometries written by F. Kárteszi and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.

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.

Finite Fields Theory Applications And Algorithms

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Author : Gary L. Mullen
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Finite Fields Theory Applications And Algorithms written by Gary L. Mullen 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 1994 with Mathematics categories.

Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.

Finite Fields And Their Applications

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Author : James A. Davis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-26

Finite Fields And Their Applications written by James A. Davis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-26 with Mathematics categories.

The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.

Projective Geometry And Algebraic Structures

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Author : R. J. Mihalek
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Projective Geometry And Algebraic Structures written by R. J. Mihalek and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Projective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers. The book first elaborates on euclidean, projective, and affine planes, including axioms for a projective plane, algebraic incidence bases, and self-dual axioms. The text then ponders on affine and projective planes, theorems of Desargues and Pappus, and coordination. Topics include algebraic systems and incidence bases, coordinatization theorem, finite projective planes, coordinates, deletion subgeometries, imbedding theorem, and isomorphism. The publication examines projectivities, harmonic quadruples, real projective plane, and projective spaces. Discussions focus on subspaces and dimension, intervals and complements, dual spaces, axioms for a projective space, ordered fields, completeness and the real numbers, real projective plane, and harmonic quadruples. The manuscript is a dependable reference for students and researchers interested in projective planes, system of real numbers, isomorphism, and subspaces and dimensions.