Existence Of Finite Projective Planes

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Projective Geometry

Author : Albrecht Beutelspacher
Publisher : Cambridge University Press
ISBN 13 : 9780521483643
Total Pages : 272 pages
Book Rating : 4.4/5 (836 download)

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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.

Finite Geometry and Character Theory

Author : Alexander Pott
Publisher : Springer
ISBN 13 : 3540491821
Total Pages : 185 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Finite Geometry and Character Theory by : Alexander Pott

Download or read book Finite Geometry and Character Theory written by Alexander Pott and published by Springer. This book was released on 2006-11-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Difference sets are of central interest in finite geometry and design theory. One of the main techniques to investigate abelian difference sets is a discrete version of the classical Fourier transform (i.e., character theory) in connection with algebraic number theory. This approach is described using only basic knowledge of algebra and algebraic number theory. It contains not only most of our present knowledge about abelian difference sets, but also gives applications of character theory to projective planes with quasiregular collineation groups. Therefore, the book is of interest both to geometers and mathematicians working on difference sets. Moreover, the Fourier transform is important in more applied branches of discrete mathematics such as coding theory and shift register sequences.

Transversals in Linear Uniform Hypergraphs

Author : Michael A. Henning
Publisher : Springer Nature
ISBN 13 : 3030465594
Total Pages : 231 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Transversals in Linear Uniform Hypergraphs by : Michael A. Henning

Download or read book Transversals in Linear Uniform Hypergraphs written by Michael A. Henning and published by Springer Nature. This book was released on 2020-07-28 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives the state-of-the-art on transversals in linear uniform hypergraphs. The notion of transversal is fundamental to hypergraph theory and has been studied extensively. Very few articles have discussed bounds on the transversal number for linear hypergraphs, even though these bounds are integral components in many applications. This book is one of the first to give strong non-trivial bounds on the transversal number for linear hypergraphs. The discussion may lead to further study of those problems which have not been solved completely, and may also inspire the readers to raise new questions and research directions. The book is written with two readerships in mind. The first is the graduate student who may wish to work on open problems in the area or is interested in exploring the field of transversals in hypergraphs. This exposition will go far to familiarize the student with the subject, the research techniques, and the major accomplishments in the field. The photographs included allow the reader to associate faces with several researchers who made important discoveries and contributions to the subject. The second audience is the established researcher in hypergraph theory who will benefit from having easy access to known results and latest developments in the field of transversals in linear hypergraphs.

Projective and Polar Spaces

Author : Peter Jephson Cameron
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Projective and Polar Spaces by : Peter Jephson Cameron

Download or read book Projective and Polar Spaces written by Peter Jephson Cameron and published by . This book was released on 1992 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorics with Emphasis on the Theory of Graphs

Author : J. E. Graver
Publisher : Springer Science & Business Media
ISBN 13 : 1461299144
Total Pages : 363 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Combinatorics with Emphasis on the Theory of Graphs by : J. E. Graver

Download or read book Combinatorics with Emphasis on the Theory of Graphs written by J. E. Graver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and graph theory have mushroomed in recent years. Many overlapping or equivalent results have been produced. Some of these are special cases of unformulated or unrecognized general theorems. The body of knowledge has now reached a stage where approaches toward unification are overdue. To paraphrase Professor Gian-Carlo Rota (Toronto, 1967), "Combinatorics needs fewer theorems and more theory. " In this book we are doing two things at the same time: A. We are presenting a unified treatment of much of combinatorics and graph theory. We have constructed a concise algebraically based, but otherwise self-contained theory, which at one time embraces the basic theorems that one normally wishes to prove while giving a common terminology and framework for the develop ment of further more specialized results. B. We are writing a textbook whereby a student of mathematics or a mathematician with another specialty can learn combinatorics and graph theory. We want this learning to be done in a much more unified way than has generally been possible from the existing literature. Our most difficult problem in the course of writing this book has been to keep A and B in balance. On the one hand, this book would be useless as a textbook if certain intuitively appealing, classical combinatorial results were either overlooked or were treated only at a level of abstraction rendering them beyond all recognition.

Compact Projective Planes

Author : Helmut Salzmann
Publisher : Walter de Gruyter
ISBN 13 : 3110876833
Total Pages : 705 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Compact Projective Planes by : Helmut Salzmann

Download or read book Compact Projective Planes written by Helmut Salzmann and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

An Introduction to Finite Projective Planes

Author : Abraham Adrian Albert
Publisher : Courier Corporation
ISBN 13 : 0486789942
Total Pages : 116 pages
Book Rating : 4.4/5 (867 download)

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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.

Projective Geometries Over Finite Fields

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)

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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.

Algebraic Curves and Riemann Surfaces

Author : Rick Miranda
Publisher : American Mathematical Soc.
ISBN 13 : 0821802682
Total Pages : 414 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Curves and Riemann Surfaces by : Rick Miranda

Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda and published by American Mathematical Soc.. This book was released on 1995 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.

From Great Discoveries in Number Theory to Applications

Author : Michal Křížek
Publisher : Springer Nature
ISBN 13 : 3030838994
Total Pages : 342 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis From Great Discoveries in Number Theory to Applications by : Michal Křížek

Download or read book From Great Discoveries in Number Theory to Applications written by Michal Křížek and published by Springer Nature. This book was released on 2021-09-21 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.

Combinatorial Theory

Author : Marshall Hall
Publisher : John Wiley & Sons
ISBN 13 : 1118031113
Total Pages : 462 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Combinatorial Theory by : Marshall Hall

Download or read book Combinatorial Theory written by Marshall Hall and published by John Wiley & Sons. This book was released on 2011-08-15 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.

Introduction to Enumerative and Analytic Combinatorics

Author : Miklos Bona
Publisher : CRC Press
ISBN 13 : 1482249103
Total Pages : 555 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Introduction to Enumerative and Analytic Combinatorics by : Miklos Bona

Download or read book Introduction to Enumerative and Analytic Combinatorics written by Miklos Bona and published by CRC Press. This book was released on 2015-09-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumerat

Introduction to Abstract Algebra, Third Edition

Author : T.A. Whitelaw
Publisher : Routledge
ISBN 13 : 1351437305
Total Pages : 256 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Introduction to Abstract Algebra, Third Edition by : T.A. Whitelaw

Download or read book Introduction to Abstract Algebra, Third Edition written by T.A. Whitelaw and published by Routledge. This book was released on 2020-04-14 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra.

The Theory of Finite Linear Spaces

Author : Lynn Margaret Batten
Publisher : Cambridge University Press
ISBN 13 : 0521333172
Total Pages : 228 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis The Theory of Finite Linear Spaces by : Lynn Margaret Batten

Download or read book The Theory of Finite Linear Spaces written by Lynn Margaret Batten and published by Cambridge University Press. This book was released on 1993-11-26 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive text to cover finite linear spaces. It contains all the important results that have been published up to the present day and is designed to be used not only as a resource for researchers in this and related areas but also as a graduate level text. A combinatorial approach is used for the greater part of the book but in the final chapter recent advances in group theory relating to finite linear spaces are presented. At the end of each chapter there are exercises and a section of research problems.

Quasi-symmetric Designs

Author : Mohan S. Shrikhande
Publisher : Cambridge University Press
ISBN 13 : 0521414075
Total Pages : 245 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Quasi-symmetric Designs by : Mohan S. Shrikhande

Download or read book Quasi-symmetric Designs written by Mohan S. Shrikhande and published by Cambridge University Press. This book was released on 1991-11-29 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design theory is a branch of combinatorics with applications in number theory, coding theory and geometry. In this book the authors discuss the generalization of results and applications to quasi-symmetric designs. The coverage is comprehensive and will be useful for researchers and graduate students. An attractive feature is the discussion of unsolved problems.

Geometry of Lie Groups

Author : B. Rosenfeld
Publisher : Springer Science & Business Media
ISBN 13 : 9780792343905
Total Pages : 424 pages
Book Rating : 4.3/5 (439 download)

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Book Synopsis Geometry of Lie Groups by : B. Rosenfeld

Download or read book Geometry of Lie Groups written by B. Rosenfeld and published by Springer Science & Business Media. This book was released on 1997-02-28 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.

Applied Combinatorics, Third Edition

Author : Fred S. Roberts
Publisher : CRC Press
ISBN 13 : 1040120296
Total Pages : 757 pages
Book Rating : 4.0/5 (41 download)

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Book Synopsis Applied Combinatorics, Third Edition by : Fred S. Roberts

Download or read book Applied Combinatorics, Third Edition written by Fred S. Roberts and published by CRC Press. This book was released on 2024-06-03 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition of this popular text presents the tools of combinatorics for a first undergraduate course. After introducing fundamental counting rules, tools of graph theory and relations, the focus is on three basic problems of combinatorics: counting, existence, and optimization problems.