Geometry: A Comprehensive Course (eBook)

Dan Pedoe (Autor)

eBook Download: EPUB

2013
464 Seiten
Dover Publications (Verlag)
978-0-486-13173-3 (ISBN)

Infos

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

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"e;A lucid and masterly survey."e; — 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.

Produkt-Details

• Erscheint lt. Verlag: 2.4.2013
• Reihe/Serie: Dover Books on Mathematics
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 170 x 170 mm
• Gewicht: 635 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: abstract algebra • advanced concepts • advanced study • Algebraic Geometry • Analytic • arithmetic • Axiomatic • books on abstract algebras • books on advanced concepts • books on advanced studies • books on algebraic geometries • books on arithmetics • books on brannan • books on calculus • books on combinatorics • books on coxeters • books on education majors • books on euclidean geometries • books on euclids • books on fundamentals • books on geometry classes • books on graphs • books on graph theories • books on liberal arts • books on linear algebras • books on mappings • books on math majors • books on math textbooks • books on mendelson • books on moebius • books on odd times • books on partitions • books on poincare • books on projective geometries • books on proofs • books on pure mathematics • books on self-studies • books on spaces • books on theorems • books on theory classes • books on topologies • books on transformations • books on upper halves • books on wylie • brannan • Calculus • cited • combinatorial • combinatorics • Coxeter • Definitions • education majors • Euclid • Euclidean Geometry • Exercises • fundamentals • generating • geometry class • Graphs • graph theory • introductory • Liberal Arts • linear algebra • Mappings • mathematical background • math major • math textbook • Mendelson • metric • Moebius • non-euclidean • odd times • one-semester • Partitions • pleasant memories • Poincare • primitive roots • Projective Geometry • proofs • Pure Mathematics • Quadratic • Revisited • Self-study • Spaces • terseness • Theorems • theory class • Topological • Topology • transformations • upper half • wait awhile • waiting awhile • wylie
• ISBN-10: 0-486-13173-4 / 0486131734
• ISBN-13: 978-0-486-13173-3 / 9780486131733