Synopses & Reviews
This classic work (first published in 1947), in three volumes, provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasized throughout. This first volume is divided into two parts. The first is devoted to pure algebra: the basic notions, the theory of matrices over a non-commutative ground field and a study of algebraic equations. The second part is in n dimensions. It concludes with a purely algebraic account of collineations and correlations.
Review
'This treatise ... is notable for its clarity of treatment and for the rigour of its demonstrations, and will repay careful study even in those parts which deal with matters generally considered familiar.' Nature
Review
'The book is well set out, and is a pleasure to work through.' Times Literary Supplement
Review
'Motivations are given. Examples of significant and useful varieties are numerous. All the algebra needed is given, and, what is more, these books tell how to translate geometry into algebra, and conversely.' Bulletin of the American Mathematical Society
Synopsis
This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties, but throughout the emphasis is on geometrical meaning. The other two volumes of Hodge and Pedoe's classic work are also available, and together these books give an insight into algebraic geometry that is unique and unsurpassed.
Synopsis
The authors have confined themselves to fundamental concepts and geometric methods, and do not provide detailed developments of geometrical properties, although geometrical meaning has been emphasized throughout in this classic 3-volume work originally published in 1947.
Table of Contents
Book I. Algebraic Preliminaries: 1. Rings and fields; 2. Linear algebra, matrices, determinants; 3. Algebraic dependence; 4. Algebraic equations; Book II. Projective Space: 5. Projective space: algebraic definition; 6. Projective space: synthetic definition; 7. Grassmann coordinates; 8. Collineations; 9. Correlations.