Combinatorics of Finite Geometries
|Rating||:||4.91 (877 Votes)|
|Number of Pages||:||208 Pages|
"The whole book is warmly recommended to undergraduate students." Tamás Szõnyi, Mathematical Reviews
Combinatorics of Finite Geometries This is my favorite finite geometry text. The treatment is a mixture of basic and complex and is hence suitable for a wise variety of readers, probably best for undergraduate/beginning graduate courses, but works well for self-study. I am excited about the generalized quadrangles sections.
This book 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. Extensive exercises at the end of each chapter insure the usefulness of this book for senior undergraduate and beginning graduate students.. The revised 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. Assuming only a basic knowledge of set theory and analysis, it provides a thorough review of the topic and leads the student to results at the frontiers of research. Later, it addresses polar spaces, partial geometries, and generalized quadrangles. Combinatorics of Finite Geometries is an introductory text on the combinatorial theory of finite geometry