Combinatorics of Finite Geometries
Editorial Reviews
Book Description
This textbook is intended as an introduction to the combinatorial theory of finite geometry for undergraduate students of mathematics. Although only a basic knowledge of set theory and analysis is assumed, the student is soon led Op results at the frontiers of research. Professor Batten begins with a discussion of near-linear spaces before proceeding to treat linear, projective and affine spaces. This half of the book in itself would be suitable for use as a text for a course in synthethic geometry. The remainder of the book is devoted to the relatively new areas of polar spaces, generalized quadrangles and partial geometries. These subjects are currently the focus of much research in combinatorial geometry.
Card catalog description
This book is an introductory text on the combinatorial theory of finite geometry. It assumes only a basic knowledge of set theory and analysis, but soon leads the student to results at the frontiers of research. It begins with an elementary combinatorial approach to finite geometries based on finite sets of points and lines, and moves into the classical work on affine and projective planes. This is followed by chapters dealing with polar spaces, partial geometries, and generalized quadrangles. The second edition contains an entirely new chapter on blocking sets in linear spaces, which highlights some of the most important applications of blocking sets - from the initial game-theoretic setting to their very recent use in cryptography. Extensive exercises at the end of each chapter ensure the usefulness of this book for senior undergraduate and beginning graduate students.
--This text refers to the
Paperback
edition.
Combinatorics of finite geometries,L. M. Batten,Cambridge University Press,0521318572,Finite geometries,General,Geometry - General,Mathematics,Science/Mathematics,Geometry,Mathematics / Probability
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