Combinatorics of Finite Geometries is an introductory text on the combinatorial theory of finite geometry. 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. 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. Later, it addresses polar spaces, partial geometries, and generalized quadrangles. 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. Extensive exercises at the end of each chapter insure the usefulness of this book for senior undergraduate and beginning graduate students.
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"The whole book is warmly recommended to undergraduate students." Tamás Szõnyi, Mathematical Reviews
Book 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. 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. Extensive exercises at the end of each chapter insure the usefulness of this book for senior undergraduate and beginning graduate students.
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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.
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Inside This Book
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First Sentence:
The understanding throughout this book is that we work with a set P whose elements are called points, and set L of certain subsets of P, whose elements are called lines. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine perspectivity, polar space arising, extended real plane, diagonal axiom, partial geometry, proper subquadrangle, central collineation, partial geometries, generalized quadrangles, blocking set, restricted linear spaces, maximal linear subspace, polar spaces, finite linear space, projective hyperplane, collineation groups, distinct collinear points, affine plane, finite projective spaces, finite projective planes, dual grid, line regularity, point regularity, regular pair, parallel class Key Phrases - Capitalized Phrases (CAPs): (learn more)
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The understanding throughout this book is that we work with a set P whose elements are called points, and set L of certain subsets of P, whose elements are called lines. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine perspectivity, polar space arising, extended real plane, diagonal axiom, partial geometry, proper subquadrangle, central collineation, partial geometries, generalized quadrangles, blocking set, restricted linear spaces, maximal linear subspace, polar spaces, finite linear space, projective hyperplane, collineation groups, distinct collinear points, affine plane, finite projective spaces, finite projective planes, dual grid, line regularity, point regularity, regular pair, parallel class Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Desargues New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 30
books:
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15
books
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- An Outline of Projective Geometry by Lynn E. Garner in Back Matter
- Combinatorial Theory (Wiley Classics Library) by Marshall Hall in Back Matter
- Projective geometry, by Oswald Veblen and John Wesley Young. (Michigan Historical Reprint) by Oswald Veblen in Back Matter
- Geometric Algebra (Wiley Classics Library) by E. Artin in Back Matter
- Foundations of Projective Geometry by Robin Hartshorne in Back Matter
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- The Theory of Finite Linear Spaces: Combinatorics of Points and Lines (Cambridge Studies Advancd Math) by Lynn Margaret Batten on page 20, page 165, and page 187
- Quasi-symmetric Designs (London Mathematical Society Lecture Note Series) by Mohan S. Shrikhande in Front Matter, and Back Matter
- Projective Geometry: From Foundations to Applications by Albrecht Beutelspacher in Back Matter
- Designs and their Codes (Cambridge Tracts in Mathematics) by E. F. Assmus in Back Matter
- Combinatorics of Symmetric Designs (New Mathematical Monographs) by Yury J. Ionin in Back Matter
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