Description: 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 the only comprehensive treatise on this area of mathematics. This new edition is a complete reworking, containing extensive revisions. Part I gives a survey of finite fields and an outline of the fundamental properties of projective spaces and their automorphisms. Part II covers, in an arbitrary dimension, the properties of subspaces, of partitions into both subspaces and subgeometires, and of quadrics and Hermitian varieties, as well as polarities. Part III is a detailed acount of the line and plane. This volume is an invaluable resource for researchers in finite geometry, combinatorics, and coding theory.
Review Quotes: "Seven years ago, James Hirschfeld completed his ambitious project of giving a self-contained and comprehensive account of projective spaces over finite fields. The three volumes comprising this work . . . are Projective geometries over finite fields (1979), Finite projective spaces of three dimensions (1986) and General Galois geometries (1991). . . . Dr Hirschfeld has now written a second edition of the first volume of the trilogy. This is, in fact, a complete reworking, taking account of many new results proved since 1979. . . . As before, the volume is concisely but clearly written . . . The author is not planning second editions of the successor volumes, and so 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. The publishers are currently offering the three-volume set at just over half-price. Snap it up!"--Bulletin of the London Mathematical Society