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Finite Projective Planes And Related Topics
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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.
Book Synopsis Finite Projective Planes and Related Topics by : Patrick Scott Fleming
Download or read book Finite Projective Planes and Related Topics written by Patrick Scott Fleming and published by ProQuest. This book was released on 2006 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unitals in Projective Planes by : Susan Barwick
Download or read book Unitals in Projective Planes written by Susan Barwick and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a monograph on unitals embedded in ?nite projective planes. Unitals are an interesting structure found in square order projective planes, and numerous research articles constructing and discussing these structures have appeared in print. More importantly, there still are many open pr- lems, and this remains a fruitful area for Ph.D. dissertations. Unitals play an important role in ?nite geometry as well as in related areas of mathematics. For example, unitals play a parallel role to Baer s- planes when considering extreme values for the size of a blocking set in a square order projective plane (see Section 2.3). Moreover, unitals meet the upper bound for the number of absolute points of any polarity in a square order projective plane (see Section 1.5). From an applications point of view, the linear codes arising from unitals have excellent technical properties (see 2 Section 6.4). The automorphism group of the classical unitalH =H(2,q ) is 2-transitive on the points ofH, and so unitals are of interest in group theory. In the ?eld of algebraic geometry over ?nite ?elds,H is a maximal curve that contains the largest number of F -rational points with respect to its genus, 2 q as established by the Hasse-Weil bound.
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.
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.
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.
Book Synopsis Handbook of the Tutte Polynomial and Related Topics by : Joanna A. Ellis-Monaghan
Download or read book Handbook of the Tutte Polynomial and Related Topics written by Joanna A. Ellis-Monaghan and published by CRC Press. This book was released on 2022-07-06 with total page 805 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials. Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial’s many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial. Features Written in an accessible style for non-experts, yet extensive enough for experts Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations
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:
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)
Book Synopsis Prime Numbers and the Riemann Hypothesis by : Barry Mazur
Download or read book Prime Numbers and the Riemann Hypothesis written by Barry Mazur and published by Cambridge University Press. This book was released on 2016-04-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Book Synopsis Handbook of Finite Translation Planes by : Norman Johnson
Download or read book Handbook of Finite Translation Planes written by Norman Johnson and published by CRC Press. This book was released on 2007-02-15 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems. From the methods of Andre to coordi
Book Synopsis Projective Geometry by : T. Ewan Faulkner
Download or read book Projective Geometry written by T. Ewan Faulkner and published by Courier Corporation. This book was released on 2013-02-20 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960 edition.
Book Synopsis Finite Generalized Quadrangles by : Stanley E. Payne
Download or read book Finite Generalized Quadrangles written by Stanley E. Payne and published by European Mathematical Society. This book was released on 2009 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized quadrangles (GQ) were formally introduced by J. Tits in 1959 to describe geometric properties of simple groups of Lie type of rank 2. The first edition of Finite Generalized Quadrangles (FGQ) quickly became the standard reference for finite GQ. The second edition is essentially a reprint of the first edition. It is a careful rendering into LaTeX of the original, along with an appendix that brings to the attention of the reader those major new results pertaining to GQ, especially in those areas where the authors of this work have made a contribution. The first edition has been out of print for many years. The new edition makes available again this classical reference in the rapidly increasing field of finite geometries.
Download or read book Projective Geometry written by Rey Casse and published by OUP Oxford. This book was released on 2006-08-03 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Handbook of Algebraic Topology by : I.M. James
Download or read book Handbook of Algebraic Topology written by I.M. James and published by Elsevier. This book was released on 1995-07-18 with total page 1336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.
Book Synopsis Discrete Mathematics with Proof by : Eric Gossett
Download or read book Discrete Mathematics with Proof written by Eric Gossett and published by John Wiley & Sons. This book was released on 2009-06-22 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.
Book Synopsis Finite Geometries by : Peter Dembowski
Download or read book Finite Geometries written by Peter Dembowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.