Geometric Introduction to Linear Algebra

Science & Math

Dan Pedoe

Mathematics

John Wiley&Sons, Inc.

"A lucid and masterly survey." — Mathematics GazetteProfessor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to help students enjoy geometry.Among the topics discussed: the use of vectors and their products in work on Desargues' and Pappus' theorem and the nine-point circle; circles and coaxal systems; the representation of circles by points in three dimensions; mappings of the Euclidean plane, similitudes, isometries, mappings of the inversive plane, and Moebius transformations; projective geometry of the plane, space, and n dimensions; the projective generation of conics and quadrics; Moebius tetrahedra; the tetrahedral complex; the twisted cubic curve; the cubic surface; oriented circles; and introduction to algebraic geometry.In addition, three appendices deal with Euclidean definitions, postulates, and propositions; the Grassmann-Pluecker coordinates of lines in S3, and the group of circular transformations. Among the outstanding features of this book are its many worked examples and over 500 exercises to test geometrical understanding.

Geometry: A Comprehensive Course (Dover Books on Mathematics)

Dover Publications

Methods of Algebraic Geometry, Volume 1, Book I: Algebraic Preliminaries. Book II: Projective Space

W.V.D. Hodge

CAMBRIDGE

In the third volume, the authors discuss algebraic varieties on a ground field without characteristic, and deal with more advanced geometrical methods, such as valuation theory.

Methods of Algebraic Geometry, Vol. 2 Book 3 / General Theory of Algebraic Varieties in Projective Space, Book 4, Quadrics and Grassmann Varieties

Cambridge Univ Pr

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Books by Dan Pedoe