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Introduction To Finite Geometries
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Book Synopsis Introduction to Finite Geometries by : F. Kárteszi
Download or read book Introduction to Finite Geometries written by F. Kárteszi and published by Elsevier. This book was released on 2014-05-12 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Finite Geometries by : Ferenc Kárteszi
Download or read book Introduction to Finite Geometries written by Ferenc Kárteszi and published by . This book was released on 1976 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Combinatorics and Finite Geometry by : Steven T. Dougherty
Download or read book Combinatorics and Finite Geometry written by Steven T. Dougherty and published by Springer Nature. This book was released on 2020-10-30 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Fields written by Rudolf Lidl and published by Cambridge University Press. This book was released on 1997 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted entirely to the theory of finite fields.
Book Synopsis Projective Geometry by : Albrecht Beutelspacher
Download or read book Projective Geometry written by Albrecht Beutelspacher and published by Cambridge University Press. This book was released on 1998-01-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :James William Peter Hirschfeld Publisher :Oxford University Press on Demand ISBN 13 :9780198502951 Total Pages :555 pages Book Rating :4.5/5 (29 download)
Book Synopsis Projective Geometries Over Finite Fields by : James William Peter Hirschfeld
Download or read book Projective Geometries Over Finite Fields written by James William Peter Hirschfeld and published by Oxford University Press on Demand. This book was released on 1998 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: I. Introduction 1. Finite fields 2. Projective spaces and algebraic varieties II. Elementary general properties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities III. The line and the plane 6. The line 7. First properties of the plane 8. Ovals 9. Arithmetic of arcs of degree two 10. Arcs in ovals 11. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes Appendix Notation References.
Book Synopsis Finite Geometry and Combinatorics by : Albrecht Beutelspacher
Download or read book Finite Geometry and Combinatorics written by Albrecht Beutelspacher and published by Cambridge University Press. This book was released on 1993 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Included here are articles from many of the leading practitioners in the field, including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results, and the growing use of computer algebra packages in this area is also demonstrated.
Book Synopsis A Course in Modern Geometries by : Judith N. Cederberg
Download or read book A Course in Modern Geometries written by Judith N. Cederberg and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Incidence Geometry by : Bart De Bruyn
Download or read book An Introduction to Incidence Geometry written by Bart De Bruyn and published by Birkhäuser. This book was released on 2016-11-09 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Geometry and Combinatorial Applications by : Simeon Ball
Download or read book Finite Geometry and Combinatorial Applications written by Simeon Ball and published by Cambridge University Press. This book was released on 2015-07-02 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.
Book Synopsis General Galois Geometries by : James Hirschfeld
Download or read book General Galois Geometries written by James Hirschfeld and published by Springer. This book was released on 2016-02-03 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.
Book Synopsis An Introduction to Finite Projective Planes by : Abraham Adrian Albert
Download or read book An Introduction to Finite Projective Planes written by Abraham Adrian Albert and published by Courier Corporation. This book was released on 2015-02-18 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Algebraic Geometry and Algebraic Groups by : Meinolf Geck
Download or read book An Introduction to Algebraic Geometry and Algebraic Groups written by Meinolf Geck and published by Oxford University Press. This book was released on 2013-03-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Download or read book Finite Geometries written by Gyorgy Kiss and published by CRC Press. This book was released on 2019-07-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works. The authors examine how finite geometries’ applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments. Features: Includes exercise sets for possible use in a graduate course Discusses applications to graph theory and extremal combinatorics Covers coding theory and cryptography Translated and revised text from the Hungarian published version
Book Synopsis Projective Geometry by : H.S.M. Coxeter
Download or read book Projective Geometry written by H.S.M. Coxeter and published by Springer Science & Business Media. This book was released on 2003-10-09 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.
Book Synopsis A Modern View of Geometry by : Leonard M. Blumenthal
Download or read book A Modern View of Geometry written by Leonard M. Blumenthal and published by Courier Dover Publications. This book was released on 2017-04-19 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elegant exposition of postulation geometry of planes offers rigorous, lucid treatment of coordination of affine and projective planes, set theory, propositional calculus, affine planes with Desargues and Pappus properties, more. 1961 edition.
Book Synopsis Algebraic Curves over a Finite Field by : J. W. P. Hirschfeld
Download or read book Algebraic Curves over a Finite Field written by J. W. P. Hirschfeld and published by Princeton University Press. This book was released on 2013-03-25 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
