This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective spaces over three dimensions (1985), which is devoted to three dimensions, and General Galois geometries (1991), on a general dimension, it provides a comprehensive treatise of this area of mathematics. The area is interesting in itself, but is important for its applications to coding theory and statistics, and its use of group theory, algebraic geometry, and number theory. This edition is a complete reworking of the first edition. The chapters bear almost the same titles as the first edition, but every chapter has been changed. The most significant changes are to Chapters 2, 10, 12, 13, which respectively describe generalities, the geometry of arcs in ovals, the geometry of arcs of higher degree, and blocking sets. The book is divided into three parts. The first part comprises two chapters, the first of which is a survey of finite fields; the second outlines the fundamental properties of projective spaces and their automorphisms, as well as properties of algebraic varieties and curves, in particular, that are used in the rest of the book and the accompanying two volumes. Parts II and III are entirely self-contained; all proofs of results are given. The second part comprises Chapters 3 to 5. They cover, in an arbitrary dimension, the properties of subspaces such as their number and characterization, of partitions into both subspaces and subgeometries, and of quadrics and Hermitian varieties, as well as polarities. Part III is a detailed account of the line and the plane. In the plane, fundamental properties are first revisited without much resort to the generalities of Parts I and II. Then, the structure of arcs and their relation to curves is described; this includes arcs both of degree two and higher degrees. There are further chapters on blocking sets and on small planes, which means

*"synopsis" may belong to another edition of this title.*

*The first edition of this work appeared in 1979, and was immediately recognized as an outstanding contribution to the field of finite geometry; the present volume is a complete revision of the earlier work...The book can serve as the text for a basic course...or as a detailed reference work for all topics in spaces of dimension two...The work is an indispensable aid to all workers in finite geometry, from beginning students to advanced researchers.* (*Short Book Reviews*)*...A complete reworking [of the first edition]. As before, the volume is concisely but clearly written, and contains a wealth of interesting material...the new trilogy, comprising the 1998, 1986 and 1991 volumes, looks set to be the standard reference work on projective spaces over finite fields for many years to come.* (*Bulletin of the London Mathematical Society*)

'Snap it up !' Bulletin London mathematical Society

Dr J. W. P. Hirschfeld, School of Mathematical Sciences, University of Sussex, Brighton, BN1 9QH. Tel.: +44 1273 678080; fax: +44 1273 678097

*"About this title" may belong to another edition of this title.*

Published by
OUP Oxford
(2016)

ISBN 10: 0198502958
ISBN 13: 9780198502951

New
Paperback
Quantity Available: 1

Seller:

Rating

**Book Description **OUP Oxford, 2016. Paperback. Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Seller Inventory # ria9780198502951_lsuk

Published by
Clarendon Press
(1998)

ISBN 10: 0198502958
ISBN 13: 9780198502951

New
Quantity Available: > 20

Seller:

Rating

**Book Description **Clarendon Press, 1998. HRD. Condition: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Seller Inventory # IP-9780198502951

Published by
Clarendon Press
(1998)

ISBN 10: 0198502958
ISBN 13: 9780198502951

New
Quantity Available: > 20

Seller:

Rating

**Book Description **Clarendon Press, 1998. HRD. Condition: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # IP-9780198502951

Published by
Oxford University Press, United Kingdom
(1998)

ISBN 10: 0198502958
ISBN 13: 9780198502951

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **Oxford University Press, United Kingdom, 1998. Hardback. Condition: New. 2nd Revised edition. Language: English . Brand New Book ***** Print on Demand *****.This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective spaces over three dimensions (1985), which is devoted to three dimensions, and General Galois geometries (1991), on a general dimension, it provides a comprehensive treatise of this area of mathematics. The area is interesting in itself, but is important for its applications to coding theory and statistics, and its use of group theory, algebraic geometry, and number theory. This edition is a complete reworking of the first edition. The chapters bear almost the same titles as the first edition, but every chapter has been changed. The most significant changes are to Chapters 2, 10, 12, 13, which respectively describe generalities, the geometry of arcs in ovals, the geometry of arcs of higher degree, and blocking sets. The book is divided into three parts. The first part comprises two chapters, the first of which is a survey of finite fields; the second outlines the fundamental properties of projective spaces and their automorphisms, as well as properties of algebraic varieties and curves, in particular, that are used in the rest of the book and the accompanying two volumes. Parts II and III are entirely self-contained; all proofs of results are given. The second part comprises Chapters 3 to 5. They cover, in an arbitrary dimension, the properties of subspaces such as their number and characterization, of partitions into both subspaces and subgeometries, and of quadrics and Hermitian varieties, as well as polarities. Part III is a detailed account of the line and the plane. In the plane, fundamental properties are first revisited without much resort to the generalities of Parts I and II. Then, the structure of arcs and their relation to curves is described; this includes arcs both of degree two and higher degrees. There are further chapters on blocking sets and on small planes, which means of orders up to thirteen. A comprehensive bibliography of more than 3000 items is provided. At the end of each chapter is a section, Notes and References, which attributes proofs, includes further comments, and lists every relevant reference from the bibliography. Seller Inventory # APC9780198502951

Published by
Oxford University Press, United Kingdom
(1998)

ISBN 10: 0198502958
ISBN 13: 9780198502951

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **Oxford University Press, United Kingdom, 1998. Hardback. Condition: New. 2nd Revised edition. Language: English . Brand New Book ***** Print on Demand *****. This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective spaces over three dimensions (1985), which is devoted to three dimensions, and General Galois geometries (1991), on a general dimension, it provides a comprehensive treatise of this area of mathematics. The area is interesting in itself, but is important for its applications to coding theory and statistics, and its use of group theory, algebraic geometry, and number theory. This edition is a complete reworking of the first edition. The chapters bear almost the same titles as the first edition, but every chapter has been changed. The most significant changes are to Chapters 2, 10, 12, 13, which respectively describe generalities, the geometry of arcs in ovals, the geometry of arcs of higher degree, and blocking sets. The book is divided into three parts. The first part comprises two chapters, the first of which is a survey of finite fields; the second outlines the fundamental properties of projective spaces and their automorphisms, as well as properties of algebraic varieties and curves, in particular, that are used in the rest of the book and the accompanying two volumes. Parts II and III are entirely self-contained; all proofs of results are given. The second part comprises Chapters 3 to 5. They cover, in an arbitrary dimension, the properties of subspaces such as their number and characterization, of partitions into both subspaces and subgeometries, and of quadrics and Hermitian varieties, as well as polarities. Part III is a detailed account of the line and the plane. In the plane, fundamental properties are first revisited without much resort to the generalities of Parts I and II. Then, the structure of arcs and their relation to curves is described; this includes arcs both of degree two and higher degrees. There are further chapters on blocking sets and on small planes, which means of orders up to thirteen. A comprehensive bibliography of more than 3000 items is provided. At the end of each chapter is a section, Notes and References, which attributes proofs, includes further comments, and lists every relevant reference from the bibliography. Seller Inventory # APC9780198502951

Published by
Clarendon Press

ISBN 10: 0198502958
ISBN 13: 9780198502951

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Clarendon Press. Condition: New. Hardcover. Worldwide shipping. FREE fast shipping inside USA (express 2-3 day delivery also available). Tracking service included. Ships from United States of America. Seller Inventory # 0198502958

Published by
Clarendon Press
(2017)

ISBN 10: 0198502958
ISBN 13: 9780198502951

New
Hardcover
Quantity Available: 2

Seller:

Rating

**Book Description **Clarendon Press, 2017. Hardcover. Condition: New. Never used! This item is printed on demand. Seller Inventory # P110198502958

Published by
Clarendon Press

ISBN 10: 0198502958
ISBN 13: 9780198502951

New
Hardcover
Quantity Available: > 20

Seller:

Rating

**Book Description **Clarendon Press. Hardcover. Condition: New. 0198502958 Special order direct from the distributor. Seller Inventory # ING9780198502951