Author: James William Peter Hirschfeld Publisher: Oxford University Press on Demand ISBN: 9780198502951 Category : Law Languages : en Pages : 555
Book Description
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.
Author: Peter Dembowski Publisher: Springer Science & Business Media ISBN: 9783540617860 Category : Mathematics Languages : en Pages : 414
Book Description
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: Steven T. Dougherty Publisher: Springer Nature ISBN: 3030563952 Category : Mathematics Languages : en Pages : 374
Book Description
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: Aart Blokhuis Publisher: Springer Science & Business Media ISBN: 1461302838 Category : Computers Languages : en Pages : 366
Book Description
When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: • combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; • geometric and algebraic coding theory; • finite groups and incidence geometries, as in polar spaces, gener alized polygons and diagram geometries; • algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory.
Author: James Hirschfeld Publisher: Springer ISBN: 1447167902 Category : Mathematics Languages : en Pages : 422
Book Description
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.
Author: Peter Dembowski Publisher: Springer Science & Business Media ISBN: 3642620124 Category : Mathematics Languages : en Pages : 394
Book Description
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: Alekseĭ Bronislavovich Sosinskiĭ Publisher: American Mathematical Soc. ISBN: 082187571X Category : Mathematics Languages : en Pages : 322
Book Description
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms ``toy geometries'', the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking this knowledge may refer to a compendium in Chapter 0. Per the author's predilection, the book contains very little regarding the axiomatic approach to geometry (save for a single chapter on the history of non-Euclidean geometry), but two Appendices provide a detailed treatment of Euclid's and Hilbert's axiomatics. Perhaps the most important aspect of this course is the problems, which appear at the end of each chapter and are supplemented with answers at the conclusion of the text. By analyzing and solving these problems, the reader will become capable of thinking and working geometrically, much more so than by simply learning the theory. Ultimately, the author makes the distinction between concrete mathematical objects called ``geometries'' and the singular ``geometry'', which he understands as a way of thinking about mathematics. Although the book does not address branches of mathematics and mathematical physics such as Riemannian and Kahler manifolds or, say, differentiable manifolds and conformal field theories, the ideology of category language and transformation groups on which the book is based prepares the reader for the study of, and eventually, research in these important and rapidly developing areas of contemporary mathematics.
Author: N.S. Narasimha Sastry Publisher: Springer Science & Business Media ISBN: 1461407095 Category : Mathematics Languages : en Pages : 348
Book Description
This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.
Author: Catherine Anne Baker Publisher: CRC Press ISBN: 1000146685 Category : Mathematics Languages : en Pages : 399
Book Description
This book is a compilation of the papers presented at the conference in Winnipeg on the subject of finite geometry in 1984. It covers different fields in finite geometry: classical finite geometry, the geometry of finite planes, geometric structures and the theory of translation planes.
Author: James William Peter Hirschfeld
Author: Peter Dembowski
Author: Steven T. Dougherty
Author: Aart Blokhuis
Author: James Hirschfeld
Author: Lynn Margaret Batten
Author: Peter Dembowski
Author: Alekseĭ Bronislavovich Sosinskiĭ
Author: N.S. Narasimha Sastry
Author: Catherine Anne Baker